Date: 2019-12-25 20:17:11 CET, cola version: 1.3.2
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All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 21168 rows and 54 columns.
#> Top rows are extracted by 'SD, CV, MAD, ATC' methods.
#> Subgroups are detected by 'hclust, kmeans, skmeans, pam, mclust, NMF' method.
#> Number of partitions are tried for k = 2, 3, 4, 5, 6.
#> Performed in total 30000 partitions by row resampling.
#>
#> Following methods can be applied to this 'ConsensusPartitionList' object:
#> [1] "cola_report" "collect_classes" "collect_plots" "collect_stats"
#> [5] "colnames" "functional_enrichment" "get_anno_col" "get_anno"
#> [9] "get_classes" "get_matrix" "get_membership" "get_stats"
#> [13] "is_best_k" "is_stable_k" "ncol" "nrow"
#> [17] "rownames" "show" "suggest_best_k" "test_to_known_factors"
#> [21] "top_rows_heatmap" "top_rows_overlap"
#>
#> You can get result for a single method by, e.g. object["SD", "hclust"] or object["SD:hclust"]
#> or a subset of methods by object[c("SD", "CV")], c("hclust", "kmeans")]
The call of run_all_consensus_partition_methods() was:
#> run_all_consensus_partition_methods(data = mat, mc.cores = 4, anno = anno)
Dimension of the input matrix:
mat = get_matrix(res_list)
dim(mat)
#> [1] 21168 54
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| SD:hclust | 2 | 1.000 | 0.980 | 0.989 | ** | |
| CV:pam | 2 | 1.000 | 0.962 | 0.984 | ** | |
| MAD:mclust | 3 | 1.000 | 0.973 | 0.988 | ** | |
| ATC:hclust | 2 | 1.000 | 0.978 | 0.987 | ** | |
| ATC:kmeans | 2 | 1.000 | 0.997 | 0.994 | ** | |
| ATC:skmeans | 2 | 1.000 | 0.974 | 0.991 | ** | |
| ATC:pam | 2 | 1.000 | 0.999 | 0.999 | ** | |
| ATC:mclust | 2 | 1.000 | 0.977 | 0.989 | ** | |
| CV:hclust | 4 | 0.991 | 0.927 | 0.973 | ** | |
| SD:mclust | 3 | 0.978 | 0.929 | 0.963 | ** | 2 |
| MAD:hclust | 4 | 0.972 | 0.916 | 0.969 | ** | 2,3 |
| ATC:NMF | 3 | 0.968 | 0.961 | 0.976 | ** | 2 |
| CV:mclust | 3 | 0.957 | 0.947 | 0.971 | ** | |
| MAD:pam | 5 | 0.944 | 0.891 | 0.957 | * | 2 |
| SD:NMF | 3 | 0.944 | 0.924 | 0.967 | * | 2 |
| SD:skmeans | 2 | 0.925 | 0.947 | 0.977 | * | |
| MAD:kmeans | 5 | 0.919 | 0.950 | 0.929 | * | |
| CV:NMF | 2 | 0.887 | 0.937 | 0.972 | ||
| MAD:skmeans | 3 | 0.887 | 0.892 | 0.952 | ||
| MAD:NMF | 2 | 0.885 | 0.920 | 0.967 | ||
| CV:kmeans | 3 | 0.869 | 0.937 | 0.946 | ||
| SD:kmeans | 3 | 0.859 | 0.961 | 0.968 | ||
| SD:pam | 3 | 0.806 | 0.916 | 0.943 | ||
| CV:skmeans | 2 | 0.742 | 0.923 | 0.963 |
**: 1-PAC > 0.95, *: 1-PAC > 0.9
Cumulative distribution function curves of consensus matrix for all methods.
collect_plots(res_list, fun = plot_ecdf)
Consensus heatmaps for all methods. (What is a consensus heatmap?)
collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = consensus_heatmap, mc.cores = 4)
Membership heatmaps for all methods. (What is a membership heatmap?)
collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = membership_heatmap, mc.cores = 4)
Signature heatmaps for all methods. (What is a signature heatmap?)
Note in following heatmaps, rows are scaled.
collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 3, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 4, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 5, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 6, fun = get_signatures, mc.cores = 4)
The statistics used for measuring the stability of consensus partitioning. (How are they defined?)
get_stats(res_list, k = 2)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 2 0.960 0.951 0.978 0.408 0.609 0.609
#> CV:NMF 2 0.887 0.937 0.972 0.421 0.591 0.591
#> MAD:NMF 2 0.885 0.920 0.967 0.434 0.575 0.575
#> ATC:NMF 2 1.000 1.000 1.000 0.373 0.628 0.628
#> SD:skmeans 2 0.925 0.947 0.977 0.451 0.547 0.547
#> CV:skmeans 2 0.742 0.923 0.963 0.471 0.525 0.525
#> MAD:skmeans 2 0.811 0.888 0.954 0.470 0.535 0.535
#> ATC:skmeans 2 1.000 0.974 0.991 0.433 0.560 0.560
#> SD:mclust 2 1.000 0.978 0.990 0.470 0.535 0.535
#> CV:mclust 2 0.826 0.930 0.967 0.438 0.547 0.547
#> MAD:mclust 2 0.827 0.971 0.983 0.442 0.547 0.547
#> ATC:mclust 2 1.000 0.977 0.989 0.479 0.516 0.516
#> SD:kmeans 2 0.543 0.953 0.940 0.345 0.628 0.628
#> CV:kmeans 2 0.547 0.958 0.937 0.337 0.628 0.628
#> MAD:kmeans 2 0.547 0.964 0.946 0.341 0.628 0.628
#> ATC:kmeans 2 1.000 0.997 0.994 0.371 0.628 0.628
#> SD:pam 2 0.581 0.936 0.910 0.316 0.669 0.669
#> CV:pam 2 1.000 0.962 0.984 0.323 0.669 0.669
#> MAD:pam 2 1.000 0.963 0.987 0.338 0.669 0.669
#> ATC:pam 2 1.000 0.999 0.999 0.372 0.628 0.628
#> SD:hclust 2 1.000 0.980 0.989 0.375 0.628 0.628
#> CV:hclust 2 0.866 0.921 0.958 0.368 0.628 0.628
#> MAD:hclust 2 0.926 0.955 0.978 0.378 0.609 0.609
#> ATC:hclust 2 1.000 0.978 0.987 0.366 0.628 0.628
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.944 0.924 0.967 0.398 0.821 0.706
#> CV:NMF 3 0.896 0.891 0.949 0.394 0.781 0.642
#> MAD:NMF 3 0.854 0.895 0.949 0.379 0.758 0.606
#> ATC:NMF 3 0.968 0.961 0.976 0.260 0.893 0.831
#> SD:skmeans 3 0.851 0.884 0.949 0.488 0.704 0.494
#> CV:skmeans 3 0.672 0.814 0.905 0.424 0.709 0.490
#> MAD:skmeans 3 0.887 0.892 0.952 0.437 0.720 0.509
#> ATC:skmeans 3 0.658 0.808 0.836 0.381 0.781 0.615
#> SD:mclust 3 0.978 0.929 0.963 0.106 0.937 0.883
#> CV:mclust 3 0.957 0.947 0.971 0.163 0.955 0.917
#> MAD:mclust 3 1.000 0.973 0.988 0.128 0.955 0.917
#> ATC:mclust 3 0.792 0.911 0.922 0.223 0.893 0.796
#> SD:kmeans 3 0.859 0.961 0.968 0.448 0.874 0.800
#> CV:kmeans 3 0.869 0.937 0.946 0.487 0.874 0.800
#> MAD:kmeans 3 0.709 0.885 0.920 0.559 0.874 0.800
#> ATC:kmeans 3 0.633 0.788 0.857 0.413 0.874 0.800
#> SD:pam 3 0.806 0.916 0.943 0.532 0.867 0.802
#> CV:pam 3 0.566 0.839 0.885 0.560 0.867 0.802
#> MAD:pam 3 0.671 0.826 0.874 0.549 0.834 0.754
#> ATC:pam 3 0.573 0.634 0.847 0.378 0.945 0.913
#> SD:hclust 3 0.854 0.961 0.960 0.276 0.874 0.800
#> CV:hclust 3 0.870 0.914 0.968 0.352 0.874 0.800
#> MAD:hclust 3 0.964 0.944 0.980 0.333 0.878 0.799
#> ATC:hclust 3 0.908 0.920 0.951 0.116 0.971 0.953
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.726 0.842 0.902 0.1439 0.969 0.927
#> CV:NMF 4 0.642 0.804 0.885 0.1323 0.944 0.866
#> MAD:NMF 4 0.620 0.732 0.846 0.1499 0.941 0.860
#> ATC:NMF 4 0.710 0.839 0.903 0.2901 0.823 0.681
#> SD:skmeans 4 0.877 0.903 0.949 0.1116 0.879 0.655
#> CV:skmeans 4 0.624 0.733 0.841 0.1212 0.878 0.652
#> MAD:skmeans 4 0.759 0.820 0.900 0.1102 0.882 0.660
#> ATC:skmeans 4 0.624 0.762 0.863 0.1387 0.924 0.791
#> SD:mclust 4 0.862 0.925 0.935 0.1002 0.983 0.963
#> CV:mclust 4 0.643 0.805 0.844 0.1934 0.979 0.958
#> MAD:mclust 4 0.685 0.671 0.808 0.2373 0.899 0.801
#> ATC:mclust 4 0.806 0.925 0.937 0.0454 0.976 0.942
#> SD:kmeans 4 0.746 0.878 0.719 0.2691 0.774 0.550
#> CV:kmeans 4 0.723 0.702 0.699 0.2784 0.767 0.538
#> MAD:kmeans 4 0.723 0.908 0.830 0.2410 0.774 0.549
#> ATC:kmeans 4 0.615 0.747 0.814 0.1741 0.830 0.662
#> SD:pam 4 0.867 0.907 0.955 0.4619 0.751 0.535
#> CV:pam 4 0.590 0.741 0.863 0.3689 0.727 0.504
#> MAD:pam 4 0.820 0.831 0.933 0.3548 0.741 0.513
#> ATC:pam 4 0.582 0.635 0.798 0.1291 0.876 0.793
#> SD:hclust 4 0.944 0.913 0.971 0.1018 0.979 0.958
#> CV:hclust 4 0.991 0.927 0.973 0.0937 0.948 0.896
#> MAD:hclust 4 0.972 0.916 0.969 0.0681 0.969 0.935
#> ATC:hclust 4 1.000 0.966 0.986 0.0308 0.992 0.986
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.696 0.765 0.832 0.1242 0.819 0.555
#> CV:NMF 5 0.591 0.560 0.772 0.1073 0.888 0.713
#> MAD:NMF 5 0.705 0.693 0.826 0.1055 0.814 0.525
#> ATC:NMF 5 0.668 0.736 0.865 0.0548 0.994 0.984
#> SD:skmeans 5 0.723 0.668 0.823 0.0624 0.977 0.912
#> CV:skmeans 5 0.605 0.547 0.741 0.0616 0.966 0.870
#> MAD:skmeans 5 0.664 0.602 0.788 0.0638 0.991 0.964
#> ATC:skmeans 5 0.613 0.630 0.821 0.0770 0.896 0.700
#> SD:mclust 5 0.642 0.692 0.823 0.2399 0.777 0.521
#> CV:mclust 5 0.619 0.620 0.841 0.1768 0.783 0.550
#> MAD:mclust 5 0.796 0.746 0.871 0.1138 0.800 0.542
#> ATC:mclust 5 0.725 0.859 0.873 0.1410 0.878 0.694
#> SD:kmeans 5 0.709 0.947 0.902 0.1606 0.959 0.855
#> CV:kmeans 5 0.671 0.894 0.877 0.1461 0.882 0.628
#> MAD:kmeans 5 0.919 0.950 0.929 0.1328 0.960 0.857
#> ATC:kmeans 5 0.638 0.731 0.814 0.1362 0.932 0.801
#> SD:pam 5 0.845 0.894 0.957 0.0564 0.965 0.879
#> CV:pam 5 0.623 0.726 0.857 0.0656 0.917 0.736
#> MAD:pam 5 0.944 0.891 0.957 0.0429 0.941 0.806
#> ATC:pam 5 0.539 0.605 0.774 0.1822 0.742 0.497
#> SD:hclust 5 0.727 0.914 0.916 0.0829 0.992 0.983
#> CV:hclust 5 0.803 0.844 0.907 0.0797 0.994 0.988
#> MAD:hclust 5 0.696 0.809 0.889 0.1076 0.991 0.980
#> ATC:hclust 5 0.656 0.835 0.890 0.3216 0.874 0.787
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.875 0.795 0.901 0.0767 0.938 0.755
#> CV:NMF 6 0.747 0.762 0.860 0.0902 0.826 0.482
#> MAD:NMF 6 0.849 0.747 0.874 0.0553 0.924 0.708
#> ATC:NMF 6 0.568 0.662 0.790 0.0862 0.956 0.891
#> SD:skmeans 6 0.705 0.520 0.724 0.0457 0.977 0.907
#> CV:skmeans 6 0.640 0.427 0.677 0.0400 0.967 0.856
#> MAD:skmeans 6 0.664 0.528 0.715 0.0409 0.948 0.793
#> ATC:skmeans 6 0.631 0.586 0.764 0.0550 0.977 0.922
#> SD:mclust 6 0.615 0.553 0.749 0.0953 0.818 0.437
#> CV:mclust 6 0.637 0.446 0.731 0.0952 0.892 0.647
#> MAD:mclust 6 0.696 0.667 0.778 0.1241 0.931 0.765
#> ATC:mclust 6 0.675 0.838 0.872 0.0759 0.992 0.970
#> SD:kmeans 6 0.788 0.738 0.768 0.0781 0.951 0.797
#> CV:kmeans 6 0.760 0.736 0.849 0.0687 0.988 0.951
#> MAD:kmeans 6 0.805 0.862 0.872 0.0552 1.000 1.000
#> ATC:kmeans 6 0.705 0.730 0.837 0.0783 0.886 0.644
#> SD:pam 6 0.811 0.822 0.912 0.0294 0.974 0.900
#> CV:pam 6 0.669 0.727 0.881 0.0296 0.983 0.934
#> MAD:pam 6 0.853 0.841 0.911 0.0324 0.983 0.936
#> ATC:pam 6 0.721 0.732 0.885 0.1035 0.869 0.587
#> SD:hclust 6 0.708 0.785 0.811 0.1162 1.000 1.000
#> CV:hclust 6 0.589 0.733 0.815 0.0989 0.971 0.935
#> MAD:hclust 6 0.676 0.699 0.753 0.1601 0.776 0.521
#> ATC:hclust 6 0.695 0.844 0.886 0.0682 0.971 0.937
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) cell.type(p) k
#> SD:NMF 54 2.33e-06 1.17e-03 2
#> CV:NMF 53 9.92e-06 2.43e-03 2
#> MAD:NMF 53 2.77e-05 3.04e-03 2
#> ATC:NMF 54 5.97e-07 6.72e-04 2
#> SD:skmeans 53 6.87e-05 9.70e-03 2
#> CV:skmeans 54 5.02e-04 2.14e-02 2
#> MAD:skmeans 51 2.44e-04 1.83e-02 2
#> ATC:skmeans 53 2.77e-05 3.04e-03 2
#> SD:mclust 54 1.14e-05 4.79e-05 2
#> CV:mclust 53 6.04e-06 2.65e-05 2
#> MAD:mclust 54 4.59e-06 2.04e-05 2
#> ATC:mclust 54 5.52e-05 2.06e-04 2
#> SD:kmeans 54 5.97e-07 6.72e-04 2
#> CV:kmeans 54 5.97e-07 6.72e-04 2
#> MAD:kmeans 54 5.97e-07 6.72e-04 2
#> ATC:kmeans 54 5.97e-07 6.72e-04 2
#> SD:pam 53 2.67e-08 1.83e-04 2
#> CV:pam 53 2.95e-09 6.95e-05 2
#> MAD:pam 53 2.67e-08 1.83e-04 2
#> ATC:pam 54 5.97e-07 6.72e-04 2
#> SD:hclust 54 5.97e-07 6.72e-04 2
#> CV:hclust 52 1.08e-06 8.91e-04 2
#> MAD:hclust 53 8.04e-07 7.74e-04 2
#> ATC:hclust 54 5.97e-07 6.72e-04 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) cell.type(p) k
#> SD:NMF 53 4.58e-07 6.93e-09 3
#> CV:NMF 52 2.66e-06 1.99e-08 3
#> MAD:NMF 52 2.78e-06 1.35e-07 3
#> ATC:NMF 54 1.50e-07 3.78e-04 3
#> SD:skmeans 51 4.51e-06 3.34e-04 3
#> CV:skmeans 50 6.18e-06 6.36e-04 3
#> MAD:skmeans 51 1.53e-05 5.42e-04 3
#> ATC:skmeans 50 5.25e-05 1.11e-05 3
#> SD:mclust 51 3.42e-09 3.82e-11 3
#> CV:mclust 54 2.57e-07 8.46e-14 3
#> MAD:mclust 54 2.57e-07 8.46e-14 3
#> ATC:mclust 53 1.21e-07 6.60e-08 3
#> SD:kmeans 53 3.58e-07 1.61e-13 3
#> CV:kmeans 54 2.57e-07 8.46e-14 3
#> MAD:kmeans 54 2.57e-07 8.46e-14 3
#> ATC:kmeans 53 3.58e-07 1.61e-13 3
#> SD:pam 52 1.22e-09 2.39e-14 3
#> CV:pam 53 7.99e-10 1.20e-14 3
#> MAD:pam 53 8.86e-09 3.34e-14 3
#> ATC:pam 42 4.32e-06 3.71e-10 3
#> SD:hclust 54 2.57e-07 8.46e-14 3
#> CV:hclust 52 4.99e-07 3.05e-13 3
#> MAD:hclust 53 3.58e-07 1.61e-13 3
#> ATC:hclust 53 1.26e-06 4.07e-04 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) cell.type(p) k
#> SD:NMF 52 9.58e-08 3.47e-09 4
#> CV:NMF 52 1.25e-08 3.47e-09 4
#> MAD:NMF 49 3.02e-07 9.05e-08 4
#> ATC:NMF 51 1.17e-06 1.72e-09 4
#> SD:skmeans 53 7.85e-06 1.27e-08 4
#> CV:skmeans 47 4.68e-05 2.11e-07 4
#> MAD:skmeans 50 1.91e-05 5.19e-08 4
#> ATC:skmeans 49 8.04e-06 3.00e-05 4
#> SD:mclust 54 3.60e-08 3.28e-14 4
#> CV:mclust 52 4.64e-10 2.91e-14 4
#> MAD:mclust 41 5.82e-07 6.34e-10 4
#> ATC:mclust 53 5.55e-07 2.20e-13 4
#> SD:kmeans 53 1.61e-06 2.73e-12 4
#> CV:kmeans 48 8.02e-06 6.07e-11 4
#> MAD:kmeans 53 1.61e-06 2.73e-12 4
#> ATC:kmeans 51 3.06e-06 9.46e-12 4
#> SD:pam 52 6.37e-09 4.29e-13 4
#> CV:pam 48 3.28e-08 6.15e-12 4
#> MAD:pam 48 2.88e-07 1.52e-11 4
#> ATC:pam 51 8.01e-07 3.06e-12 4
#> SD:hclust 51 7.26e-10 5.96e-14 4
#> CV:hclust 51 7.28e-08 2.59e-13 4
#> MAD:hclust 49 6.39e-09 5.84e-14 4
#> ATC:hclust 54 1.73e-07 1.60e-05 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) cell.type(p) k
#> SD:NMF 50 7.15e-07 8.69e-09 5
#> CV:NMF 37 2.51e-06 2.20e-06 5
#> MAD:NMF 45 3.77e-06 1.19e-07 5
#> ATC:NMF 48 1.19e-05 2.48e-07 5
#> SD:skmeans 45 8.51e-05 5.35e-07 5
#> CV:skmeans 31 2.28e-03 3.45e-05 5
#> MAD:skmeans 40 1.24e-04 3.51e-06 5
#> ATC:skmeans 42 1.88e-04 7.59e-07 5
#> SD:mclust 44 4.64e-06 3.30e-10 5
#> CV:mclust 39 7.13e-07 7.13e-10 5
#> MAD:mclust 47 1.93e-07 1.29e-10 5
#> ATC:mclust 53 2.03e-06 2.70e-12 5
#> SD:kmeans 54 1.42e-07 4.23e-13 5
#> CV:kmeans 54 1.42e-07 4.23e-13 5
#> MAD:kmeans 54 1.42e-07 4.23e-13 5
#> ATC:kmeans 46 9.79e-05 2.02e-08 5
#> SD:pam 53 1.75e-08 2.70e-12 5
#> CV:pam 47 1.93e-07 1.29e-10 5
#> MAD:pam 50 5.83e-08 1.88e-11 5
#> ATC:pam 34 2.91e-04 7.90e-06 5
#> SD:hclust 53 1.30e-09 1.88e-13 5
#> CV:hclust 49 1.78e-09 2.49e-13 5
#> MAD:hclust 48 5.21e-10 2.84e-14 5
#> ATC:hclust 51 1.07e-06 5.14e-14 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) cell.type(p) k
#> SD:NMF 48 7.29e-08 3.70e-10 6
#> CV:NMF 47 7.14e-07 1.63e-08 6
#> MAD:NMF 49 2.61e-07 2.78e-08 6
#> ATC:NMF 43 5.46e-07 5.54e-08 6
#> SD:skmeans 30 2.20e-04 4.12e-05 6
#> CV:skmeans 22 7.25e-03 2.15e-03 6
#> MAD:skmeans 27 2.09e-04 7.73e-05 6
#> ATC:skmeans 39 1.83e-04 4.32e-08 6
#> SD:mclust 27 2.37e-03 2.02e-05 6
#> CV:mclust 27 1.05e-04 9.31e-06 6
#> MAD:mclust 42 1.42e-06 3.16e-09 6
#> ATC:mclust 52 6.75e-06 4.64e-11 6
#> SD:kmeans 45 1.12e-05 1.37e-09 6
#> CV:kmeans 49 8.68e-07 1.20e-11 6
#> MAD:kmeans 54 1.42e-07 4.23e-13 6
#> ATC:kmeans 48 1.55e-04 5.11e-08 6
#> SD:pam 49 3.46e-08 1.37e-16 6
#> CV:pam 46 8.86e-07 2.22e-13 6
#> MAD:pam 51 8.68e-08 1.09e-13 6
#> ATC:pam 46 3.94e-06 2.25e-11 6
#> SD:hclust 53 1.30e-09 1.88e-13 6
#> CV:hclust 48 2.78e-09 5.08e-13 6
#> MAD:hclust 45 1.07e-08 4.31e-12 6
#> ATC:hclust 52 1.72e-07 2.44e-14 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 21168 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.980 0.989 0.3753 0.628 0.628
#> 3 3 0.854 0.961 0.960 0.2763 0.874 0.800
#> 4 4 0.944 0.913 0.971 0.1018 0.979 0.958
#> 5 5 0.727 0.914 0.916 0.0829 0.992 0.983
#> 6 6 0.708 0.785 0.811 0.1162 1.000 1.000
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
#> GSM49613 1 0.0376 0.987 0.996 0.004
#> GSM49604 2 0.1414 0.982 0.020 0.980
#> GSM49605 2 0.0376 0.986 0.004 0.996
#> GSM49606 2 0.0376 0.986 0.004 0.996
#> GSM49607 2 0.0376 0.986 0.004 0.996
#> GSM49608 2 0.0376 0.986 0.004 0.996
#> GSM49609 2 0.0376 0.986 0.004 0.996
#> GSM49610 2 0.0376 0.986 0.004 0.996
#> GSM49611 2 0.0376 0.986 0.004 0.996
#> GSM49612 2 0.0376 0.986 0.004 0.996
#> GSM49614 1 0.0376 0.987 0.996 0.004
#> GSM49615 1 0.0376 0.987 0.996 0.004
#> GSM49616 1 0.0376 0.987 0.996 0.004
#> GSM49617 1 0.0376 0.987 0.996 0.004
#> GSM49564 1 0.0000 0.990 1.000 0.000
#> GSM49565 1 0.0000 0.990 1.000 0.000
#> GSM49566 1 0.0000 0.990 1.000 0.000
#> GSM49567 1 0.0000 0.990 1.000 0.000
#> GSM49568 1 0.0000 0.990 1.000 0.000
#> GSM49569 1 0.0000 0.990 1.000 0.000
#> GSM49570 2 0.2603 0.969 0.044 0.956
#> GSM49571 1 0.7219 0.750 0.800 0.200
#> GSM49572 1 0.0000 0.990 1.000 0.000
#> GSM49573 2 0.2603 0.969 0.044 0.956
#> GSM49574 1 0.0000 0.990 1.000 0.000
#> GSM49575 1 0.0000 0.990 1.000 0.000
#> GSM49576 1 0.0000 0.990 1.000 0.000
#> GSM49577 1 0.0000 0.990 1.000 0.000
#> GSM49578 1 0.0000 0.990 1.000 0.000
#> GSM49579 1 0.0000 0.990 1.000 0.000
#> GSM49580 1 0.0000 0.990 1.000 0.000
#> GSM49581 1 0.0000 0.990 1.000 0.000
#> GSM49582 1 0.0000 0.990 1.000 0.000
#> GSM49583 2 0.1843 0.978 0.028 0.972
#> GSM49584 1 0.0000 0.990 1.000 0.000
#> GSM49585 1 0.0000 0.990 1.000 0.000
#> GSM49586 1 0.6148 0.819 0.848 0.152
#> GSM49587 1 0.0000 0.990 1.000 0.000
#> GSM49588 1 0.0000 0.990 1.000 0.000
#> GSM49589 1 0.0000 0.990 1.000 0.000
#> GSM49590 1 0.0000 0.990 1.000 0.000
#> GSM49591 1 0.0000 0.990 1.000 0.000
#> GSM49592 1 0.0000 0.990 1.000 0.000
#> GSM49593 1 0.0000 0.990 1.000 0.000
#> GSM49594 1 0.0000 0.990 1.000 0.000
#> GSM49595 1 0.0000 0.990 1.000 0.000
#> GSM49596 1 0.0000 0.990 1.000 0.000
#> GSM49597 2 0.2603 0.969 0.044 0.956
#> GSM49598 1 0.0000 0.990 1.000 0.000
#> GSM49599 1 0.0000 0.990 1.000 0.000
#> GSM49600 1 0.0000 0.990 1.000 0.000
#> GSM49601 1 0.0000 0.990 1.000 0.000
#> GSM49602 1 0.0000 0.990 1.000 0.000
#> GSM49603 1 0.0000 0.990 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM49613 3 0.4702 1.000 0.212 0.000 0.788
#> GSM49604 2 0.3141 0.914 0.020 0.912 0.068
#> GSM49605 2 0.0000 0.946 0.000 1.000 0.000
#> GSM49606 2 0.0000 0.946 0.000 1.000 0.000
#> GSM49607 2 0.0000 0.946 0.000 1.000 0.000
#> GSM49608 2 0.0000 0.946 0.000 1.000 0.000
#> GSM49609 2 0.0000 0.946 0.000 1.000 0.000
#> GSM49610 2 0.0000 0.946 0.000 1.000 0.000
#> GSM49611 2 0.0000 0.946 0.000 1.000 0.000
#> GSM49612 2 0.0000 0.946 0.000 1.000 0.000
#> GSM49614 3 0.4702 1.000 0.212 0.000 0.788
#> GSM49615 3 0.4702 1.000 0.212 0.000 0.788
#> GSM49616 3 0.4702 1.000 0.212 0.000 0.788
#> GSM49617 3 0.4702 1.000 0.212 0.000 0.788
#> GSM49564 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49565 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49566 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49567 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49568 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49569 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49570 2 0.6247 0.807 0.044 0.744 0.212
#> GSM49571 1 0.5514 0.683 0.800 0.156 0.044
#> GSM49572 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49573 2 0.6247 0.807 0.044 0.744 0.212
#> GSM49574 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49575 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49576 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49577 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49578 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49579 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49580 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49581 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49582 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49583 2 0.2681 0.921 0.028 0.932 0.040
#> GSM49584 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49585 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49586 1 0.4676 0.770 0.848 0.112 0.040
#> GSM49587 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49588 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49589 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49590 1 0.0237 0.982 0.996 0.000 0.004
#> GSM49591 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49592 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49593 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49594 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49595 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49596 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49597 2 0.3267 0.904 0.044 0.912 0.044
#> GSM49598 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49599 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49600 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49601 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49602 1 0.0000 0.986 1.000 0.000 0.000
#> GSM49603 1 0.0000 0.986 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM49613 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM49604 2 0.4454 0.451 0.000 0.692 0.000 0.308
#> GSM49605 2 0.0000 0.903 0.000 1.000 0.000 0.000
#> GSM49606 2 0.0000 0.903 0.000 1.000 0.000 0.000
#> GSM49607 2 0.0000 0.903 0.000 1.000 0.000 0.000
#> GSM49608 2 0.0000 0.903 0.000 1.000 0.000 0.000
#> GSM49609 2 0.0000 0.903 0.000 1.000 0.000 0.000
#> GSM49610 2 0.0000 0.903 0.000 1.000 0.000 0.000
#> GSM49611 2 0.0000 0.903 0.000 1.000 0.000 0.000
#> GSM49612 2 0.0000 0.903 0.000 1.000 0.000 0.000
#> GSM49614 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM49615 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM49616 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM49617 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM49564 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49565 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49566 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49567 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49568 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49569 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49570 4 0.0000 0.684 0.000 0.000 0.000 1.000
#> GSM49571 1 0.3764 0.733 0.784 0.000 0.000 0.216
#> GSM49572 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49573 4 0.0000 0.684 0.000 0.000 0.000 1.000
#> GSM49574 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49575 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49576 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49577 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49578 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49579 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49580 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49581 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49582 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49583 2 0.4761 0.226 0.000 0.628 0.000 0.372
#> GSM49584 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49585 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49586 1 0.3123 0.818 0.844 0.000 0.000 0.156
#> GSM49587 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49588 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49589 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49590 1 0.0524 0.978 0.988 0.000 0.004 0.008
#> GSM49591 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49592 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49593 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49594 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49595 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49596 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49597 4 0.5000 -0.139 0.000 0.496 0.000 0.504
#> GSM49598 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49599 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49600 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49601 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49602 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49603 1 0.0000 0.989 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM49613 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM49604 2 0.4983 0.475 0.000 0.664 0.000 0.272 0.064
#> GSM49605 2 0.0000 0.952 0.000 1.000 0.000 0.000 0.000
#> GSM49606 2 0.0000 0.952 0.000 1.000 0.000 0.000 0.000
#> GSM49607 2 0.0000 0.952 0.000 1.000 0.000 0.000 0.000
#> GSM49608 2 0.0000 0.952 0.000 1.000 0.000 0.000 0.000
#> GSM49609 2 0.0000 0.952 0.000 1.000 0.000 0.000 0.000
#> GSM49610 2 0.0000 0.952 0.000 1.000 0.000 0.000 0.000
#> GSM49611 2 0.0000 0.952 0.000 1.000 0.000 0.000 0.000
#> GSM49612 2 0.0000 0.952 0.000 1.000 0.000 0.000 0.000
#> GSM49614 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM49615 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM49616 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM49617 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM49564 1 0.1908 0.916 0.908 0.000 0.000 0.000 0.092
#> GSM49565 1 0.1608 0.925 0.928 0.000 0.000 0.000 0.072
#> GSM49566 1 0.1908 0.916 0.908 0.000 0.000 0.000 0.092
#> GSM49567 1 0.1410 0.927 0.940 0.000 0.000 0.000 0.060
#> GSM49568 1 0.1478 0.919 0.936 0.000 0.000 0.000 0.064
#> GSM49569 1 0.1608 0.923 0.928 0.000 0.000 0.000 0.072
#> GSM49570 4 0.0162 0.994 0.000 0.000 0.000 0.996 0.004
#> GSM49571 1 0.4234 0.746 0.760 0.000 0.000 0.184 0.056
#> GSM49572 1 0.1410 0.920 0.940 0.000 0.000 0.000 0.060
#> GSM49573 4 0.0000 0.994 0.000 0.000 0.000 1.000 0.000
#> GSM49574 1 0.1851 0.909 0.912 0.000 0.000 0.000 0.088
#> GSM49575 1 0.1851 0.909 0.912 0.000 0.000 0.000 0.088
#> GSM49576 1 0.1732 0.920 0.920 0.000 0.000 0.000 0.080
#> GSM49577 1 0.1608 0.926 0.928 0.000 0.000 0.000 0.072
#> GSM49578 1 0.1851 0.909 0.912 0.000 0.000 0.000 0.088
#> GSM49579 1 0.1851 0.921 0.912 0.000 0.000 0.000 0.088
#> GSM49580 1 0.1043 0.924 0.960 0.000 0.000 0.000 0.040
#> GSM49581 1 0.1410 0.919 0.940 0.000 0.000 0.000 0.060
#> GSM49582 1 0.1851 0.909 0.912 0.000 0.000 0.000 0.088
#> GSM49583 5 0.4849 0.744 0.000 0.140 0.000 0.136 0.724
#> GSM49584 1 0.1043 0.924 0.960 0.000 0.000 0.000 0.040
#> GSM49585 1 0.1544 0.918 0.932 0.000 0.000 0.000 0.068
#> GSM49586 1 0.3814 0.804 0.808 0.000 0.000 0.124 0.068
#> GSM49587 1 0.1732 0.913 0.920 0.000 0.000 0.000 0.080
#> GSM49588 1 0.1544 0.927 0.932 0.000 0.000 0.000 0.068
#> GSM49589 1 0.1908 0.916 0.908 0.000 0.000 0.000 0.092
#> GSM49590 1 0.2233 0.909 0.892 0.000 0.004 0.000 0.104
#> GSM49591 1 0.1732 0.913 0.920 0.000 0.000 0.000 0.080
#> GSM49592 1 0.1851 0.909 0.912 0.000 0.000 0.000 0.088
#> GSM49593 1 0.1732 0.920 0.920 0.000 0.000 0.000 0.080
#> GSM49594 1 0.1608 0.923 0.928 0.000 0.000 0.000 0.072
#> GSM49595 1 0.1608 0.923 0.928 0.000 0.000 0.000 0.072
#> GSM49596 1 0.1732 0.920 0.920 0.000 0.000 0.000 0.080
#> GSM49597 5 0.3318 0.727 0.000 0.008 0.000 0.192 0.800
#> GSM49598 1 0.1732 0.920 0.920 0.000 0.000 0.000 0.080
#> GSM49599 1 0.1043 0.925 0.960 0.000 0.000 0.000 0.040
#> GSM49600 1 0.0963 0.927 0.964 0.000 0.000 0.000 0.036
#> GSM49601 1 0.1792 0.919 0.916 0.000 0.000 0.000 0.084
#> GSM49602 1 0.1792 0.919 0.916 0.000 0.000 0.000 0.084
#> GSM49603 1 0.1792 0.919 0.916 0.000 0.000 0.000 0.084
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM49613 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 NA
#> GSM49604 2 0.5993 0.290 0.000 0.608 0 0.148 0.068 NA
#> GSM49605 2 0.3428 0.757 0.000 0.696 0 0.000 0.000 NA
#> GSM49606 2 0.3428 0.757 0.000 0.696 0 0.000 0.000 NA
#> GSM49607 2 0.3428 0.757 0.000 0.696 0 0.000 0.000 NA
#> GSM49608 2 0.3428 0.757 0.000 0.696 0 0.000 0.000 NA
#> GSM49609 2 0.0000 0.776 0.000 1.000 0 0.000 0.000 NA
#> GSM49610 2 0.0000 0.776 0.000 1.000 0 0.000 0.000 NA
#> GSM49611 2 0.0000 0.776 0.000 1.000 0 0.000 0.000 NA
#> GSM49612 2 0.0000 0.776 0.000 1.000 0 0.000 0.000 NA
#> GSM49614 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 NA
#> GSM49615 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 NA
#> GSM49616 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 NA
#> GSM49617 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 NA
#> GSM49564 1 0.3823 0.710 0.564 0.000 0 0.000 0.000 NA
#> GSM49565 1 0.1327 0.806 0.936 0.000 0 0.000 0.000 NA
#> GSM49566 1 0.3817 0.713 0.568 0.000 0 0.000 0.000 NA
#> GSM49567 1 0.1267 0.808 0.940 0.000 0 0.000 0.000 NA
#> GSM49568 1 0.0713 0.798 0.972 0.000 0 0.000 0.000 NA
#> GSM49569 1 0.3592 0.761 0.656 0.000 0 0.000 0.000 NA
#> GSM49570 4 0.0713 0.969 0.000 0.000 0 0.972 0.028 NA
#> GSM49571 1 0.4862 0.570 0.720 0.000 0 0.060 0.064 NA
#> GSM49572 1 0.0632 0.799 0.976 0.000 0 0.000 0.000 NA
#> GSM49573 4 0.0000 0.969 0.000 0.000 0 1.000 0.000 NA
#> GSM49574 1 0.0547 0.787 0.980 0.000 0 0.000 0.000 NA
#> GSM49575 1 0.1501 0.752 0.924 0.000 0 0.000 0.000 NA
#> GSM49576 1 0.3659 0.753 0.636 0.000 0 0.000 0.000 NA
#> GSM49577 1 0.2219 0.805 0.864 0.000 0 0.000 0.000 NA
#> GSM49578 1 0.0547 0.787 0.980 0.000 0 0.000 0.000 NA
#> GSM49579 1 0.3647 0.754 0.640 0.000 0 0.000 0.000 NA
#> GSM49580 1 0.1007 0.806 0.956 0.000 0 0.000 0.000 NA
#> GSM49581 1 0.0713 0.803 0.972 0.000 0 0.000 0.000 NA
#> GSM49582 1 0.0547 0.787 0.980 0.000 0 0.000 0.000 NA
#> GSM49583 5 0.3073 0.820 0.000 0.080 0 0.000 0.840 NA
#> GSM49584 1 0.0865 0.804 0.964 0.000 0 0.000 0.000 NA
#> GSM49585 1 0.0937 0.804 0.960 0.000 0 0.000 0.000 NA
#> GSM49586 1 0.4205 0.630 0.744 0.000 0 0.012 0.060 NA
#> GSM49587 1 0.0363 0.791 0.988 0.000 0 0.000 0.000 NA
#> GSM49588 1 0.1556 0.809 0.920 0.000 0 0.000 0.000 NA
#> GSM49589 1 0.3817 0.713 0.568 0.000 0 0.000 0.000 NA
#> GSM49590 1 0.4067 0.698 0.548 0.000 0 0.000 0.008 NA
#> GSM49591 1 0.0458 0.793 0.984 0.000 0 0.000 0.000 NA
#> GSM49592 1 0.0547 0.787 0.980 0.000 0 0.000 0.000 NA
#> GSM49593 1 0.3659 0.753 0.636 0.000 0 0.000 0.000 NA
#> GSM49594 1 0.3684 0.750 0.628 0.000 0 0.000 0.000 NA
#> GSM49595 1 0.3684 0.750 0.628 0.000 0 0.000 0.000 NA
#> GSM49596 1 0.3659 0.753 0.636 0.000 0 0.000 0.000 NA
#> GSM49597 5 0.0000 0.817 0.000 0.000 0 0.000 1.000 NA
#> GSM49598 1 0.3244 0.782 0.732 0.000 0 0.000 0.000 NA
#> GSM49599 1 0.0865 0.806 0.964 0.000 0 0.000 0.000 NA
#> GSM49600 1 0.2135 0.806 0.872 0.000 0 0.000 0.000 NA
#> GSM49601 1 0.3797 0.721 0.580 0.000 0 0.000 0.000 NA
#> GSM49602 1 0.3797 0.721 0.580 0.000 0 0.000 0.000 NA
#> GSM49603 1 0.3797 0.721 0.580 0.000 0 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) cell.type(p) k
#> SD:hclust 54 5.97e-07 6.72e-04 2
#> SD:hclust 54 2.57e-07 8.46e-14 3
#> SD:hclust 51 7.26e-10 5.96e-14 4
#> SD:hclust 53 1.30e-09 1.88e-13 5
#> SD:hclust 53 1.30e-09 1.88e-13 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21168 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.543 0.953 0.940 0.3452 0.628 0.628
#> 3 3 0.859 0.961 0.968 0.4485 0.874 0.800
#> 4 4 0.746 0.878 0.719 0.2691 0.774 0.550
#> 5 5 0.709 0.947 0.902 0.1606 0.959 0.855
#> 6 6 0.788 0.738 0.768 0.0781 0.951 0.797
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM49613 1 0.644 0.810 0.836 0.164
#> GSM49604 2 0.644 1.000 0.164 0.836
#> GSM49605 2 0.644 1.000 0.164 0.836
#> GSM49606 2 0.644 1.000 0.164 0.836
#> GSM49607 2 0.644 1.000 0.164 0.836
#> GSM49608 2 0.644 1.000 0.164 0.836
#> GSM49609 2 0.644 1.000 0.164 0.836
#> GSM49610 2 0.644 1.000 0.164 0.836
#> GSM49611 2 0.644 1.000 0.164 0.836
#> GSM49612 2 0.644 1.000 0.164 0.836
#> GSM49614 1 0.644 0.810 0.836 0.164
#> GSM49615 1 0.644 0.810 0.836 0.164
#> GSM49616 1 0.644 0.810 0.836 0.164
#> GSM49617 1 0.644 0.810 0.836 0.164
#> GSM49564 1 0.000 0.967 1.000 0.000
#> GSM49565 1 0.000 0.967 1.000 0.000
#> GSM49566 1 0.000 0.967 1.000 0.000
#> GSM49567 1 0.000 0.967 1.000 0.000
#> GSM49568 1 0.000 0.967 1.000 0.000
#> GSM49569 1 0.000 0.967 1.000 0.000
#> GSM49570 2 0.644 1.000 0.164 0.836
#> GSM49571 1 0.833 0.538 0.736 0.264
#> GSM49572 1 0.000 0.967 1.000 0.000
#> GSM49573 2 0.644 1.000 0.164 0.836
#> GSM49574 1 0.000 0.967 1.000 0.000
#> GSM49575 1 0.000 0.967 1.000 0.000
#> GSM49576 1 0.000 0.967 1.000 0.000
#> GSM49577 1 0.000 0.967 1.000 0.000
#> GSM49578 1 0.000 0.967 1.000 0.000
#> GSM49579 1 0.000 0.967 1.000 0.000
#> GSM49580 1 0.000 0.967 1.000 0.000
#> GSM49581 1 0.000 0.967 1.000 0.000
#> GSM49582 1 0.000 0.967 1.000 0.000
#> GSM49583 2 0.644 1.000 0.164 0.836
#> GSM49584 1 0.000 0.967 1.000 0.000
#> GSM49585 1 0.000 0.967 1.000 0.000
#> GSM49586 1 0.000 0.967 1.000 0.000
#> GSM49587 1 0.000 0.967 1.000 0.000
#> GSM49588 1 0.000 0.967 1.000 0.000
#> GSM49589 1 0.000 0.967 1.000 0.000
#> GSM49590 1 0.000 0.967 1.000 0.000
#> GSM49591 1 0.000 0.967 1.000 0.000
#> GSM49592 1 0.000 0.967 1.000 0.000
#> GSM49593 1 0.000 0.967 1.000 0.000
#> GSM49594 1 0.000 0.967 1.000 0.000
#> GSM49595 1 0.000 0.967 1.000 0.000
#> GSM49596 1 0.000 0.967 1.000 0.000
#> GSM49597 2 0.644 1.000 0.164 0.836
#> GSM49598 1 0.000 0.967 1.000 0.000
#> GSM49599 1 0.000 0.967 1.000 0.000
#> GSM49600 1 0.000 0.967 1.000 0.000
#> GSM49601 1 0.000 0.967 1.000 0.000
#> GSM49602 1 0.000 0.967 1.000 0.000
#> GSM49603 1 0.000 0.967 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM49613 3 0.2959 1.000 0.100 0.000 0.900
#> GSM49604 2 0.2796 0.936 0.000 0.908 0.092
#> GSM49605 2 0.0424 0.970 0.000 0.992 0.008
#> GSM49606 2 0.0424 0.970 0.000 0.992 0.008
#> GSM49607 2 0.0424 0.970 0.000 0.992 0.008
#> GSM49608 2 0.0424 0.970 0.000 0.992 0.008
#> GSM49609 2 0.0000 0.970 0.000 1.000 0.000
#> GSM49610 2 0.0000 0.970 0.000 1.000 0.000
#> GSM49611 2 0.0000 0.970 0.000 1.000 0.000
#> GSM49612 2 0.0000 0.970 0.000 1.000 0.000
#> GSM49614 3 0.2959 1.000 0.100 0.000 0.900
#> GSM49615 3 0.2959 1.000 0.100 0.000 0.900
#> GSM49616 3 0.2959 1.000 0.100 0.000 0.900
#> GSM49617 3 0.2959 1.000 0.100 0.000 0.900
#> GSM49564 1 0.1289 0.968 0.968 0.000 0.032
#> GSM49565 1 0.0000 0.973 1.000 0.000 0.000
#> GSM49566 1 0.1031 0.969 0.976 0.000 0.024
#> GSM49567 1 0.0237 0.974 0.996 0.000 0.004
#> GSM49568 1 0.0237 0.974 0.996 0.000 0.004
#> GSM49569 1 0.1163 0.968 0.972 0.000 0.028
#> GSM49570 2 0.2796 0.936 0.000 0.908 0.092
#> GSM49571 1 0.7848 0.429 0.640 0.264 0.096
#> GSM49572 1 0.0237 0.974 0.996 0.000 0.004
#> GSM49573 2 0.2796 0.936 0.000 0.908 0.092
#> GSM49574 1 0.0237 0.974 0.996 0.000 0.004
#> GSM49575 1 0.0237 0.974 0.996 0.000 0.004
#> GSM49576 1 0.1163 0.968 0.972 0.000 0.028
#> GSM49577 1 0.0000 0.973 1.000 0.000 0.000
#> GSM49578 1 0.0237 0.974 0.996 0.000 0.004
#> GSM49579 1 0.0747 0.971 0.984 0.000 0.016
#> GSM49580 1 0.0237 0.974 0.996 0.000 0.004
#> GSM49581 1 0.0237 0.974 0.996 0.000 0.004
#> GSM49582 1 0.0237 0.974 0.996 0.000 0.004
#> GSM49583 2 0.0424 0.970 0.000 0.992 0.008
#> GSM49584 1 0.0237 0.974 0.996 0.000 0.004
#> GSM49585 1 0.0237 0.974 0.996 0.000 0.004
#> GSM49586 1 0.1163 0.968 0.972 0.000 0.028
#> GSM49587 1 0.0237 0.974 0.996 0.000 0.004
#> GSM49588 1 0.0237 0.974 0.996 0.000 0.004
#> GSM49589 1 0.1163 0.968 0.972 0.000 0.028
#> GSM49590 1 0.1163 0.968 0.972 0.000 0.028
#> GSM49591 1 0.0237 0.974 0.996 0.000 0.004
#> GSM49592 1 0.0237 0.974 0.996 0.000 0.004
#> GSM49593 1 0.1163 0.968 0.972 0.000 0.028
#> GSM49594 1 0.1163 0.968 0.972 0.000 0.028
#> GSM49595 1 0.1163 0.968 0.972 0.000 0.028
#> GSM49596 1 0.0000 0.973 1.000 0.000 0.000
#> GSM49597 2 0.2959 0.936 0.000 0.900 0.100
#> GSM49598 1 0.1163 0.968 0.972 0.000 0.028
#> GSM49599 1 0.0237 0.974 0.996 0.000 0.004
#> GSM49600 1 0.0237 0.974 0.996 0.000 0.004
#> GSM49601 1 0.1163 0.968 0.972 0.000 0.028
#> GSM49602 1 0.1163 0.968 0.972 0.000 0.028
#> GSM49603 1 0.1163 0.968 0.972 0.000 0.028
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM49613 3 0.1706 0.994 0.016 0.000 0.948 0.036
#> GSM49604 2 0.5503 0.611 0.468 0.516 0.016 0.000
#> GSM49605 2 0.0188 0.837 0.000 0.996 0.004 0.000
#> GSM49606 2 0.0000 0.837 0.000 1.000 0.000 0.000
#> GSM49607 2 0.0188 0.837 0.000 0.996 0.004 0.000
#> GSM49608 2 0.0188 0.837 0.000 0.996 0.004 0.000
#> GSM49609 2 0.1042 0.836 0.008 0.972 0.020 0.000
#> GSM49610 2 0.1042 0.836 0.008 0.972 0.020 0.000
#> GSM49611 2 0.1042 0.836 0.008 0.972 0.020 0.000
#> GSM49612 2 0.1042 0.836 0.008 0.972 0.020 0.000
#> GSM49614 3 0.1452 0.995 0.008 0.000 0.956 0.036
#> GSM49615 3 0.1706 0.994 0.016 0.000 0.948 0.036
#> GSM49616 3 0.1305 0.995 0.004 0.000 0.960 0.036
#> GSM49617 3 0.1452 0.995 0.008 0.000 0.956 0.036
#> GSM49564 4 0.0469 0.973 0.012 0.000 0.000 0.988
#> GSM49565 1 0.4998 0.896 0.512 0.000 0.000 0.488
#> GSM49566 4 0.0336 0.980 0.008 0.000 0.000 0.992
#> GSM49567 1 0.4996 0.901 0.516 0.000 0.000 0.484
#> GSM49568 1 0.4999 0.912 0.508 0.000 0.000 0.492
#> GSM49569 4 0.0000 0.984 0.000 0.000 0.000 1.000
#> GSM49570 2 0.5914 0.603 0.468 0.504 0.016 0.012
#> GSM49571 1 0.7928 -0.440 0.468 0.184 0.016 0.332
#> GSM49572 1 0.4996 0.901 0.516 0.000 0.000 0.484
#> GSM49573 2 0.5914 0.603 0.468 0.504 0.016 0.012
#> GSM49574 1 0.4999 0.912 0.508 0.000 0.000 0.492
#> GSM49575 1 0.4999 0.912 0.508 0.000 0.000 0.492
#> GSM49576 4 0.0336 0.980 0.008 0.000 0.000 0.992
#> GSM49577 4 0.1716 0.887 0.064 0.000 0.000 0.936
#> GSM49578 1 0.4999 0.912 0.508 0.000 0.000 0.492
#> GSM49579 4 0.0707 0.970 0.020 0.000 0.000 0.980
#> GSM49580 1 0.4999 0.912 0.508 0.000 0.000 0.492
#> GSM49581 1 0.4999 0.912 0.508 0.000 0.000 0.492
#> GSM49582 1 0.4999 0.912 0.508 0.000 0.000 0.492
#> GSM49583 2 0.0188 0.837 0.000 0.996 0.004 0.000
#> GSM49584 1 0.4999 0.912 0.508 0.000 0.000 0.492
#> GSM49585 1 0.4999 0.912 0.508 0.000 0.000 0.492
#> GSM49586 4 0.0000 0.984 0.000 0.000 0.000 1.000
#> GSM49587 1 0.4999 0.912 0.508 0.000 0.000 0.492
#> GSM49588 1 0.4999 0.912 0.508 0.000 0.000 0.492
#> GSM49589 4 0.0000 0.984 0.000 0.000 0.000 1.000
#> GSM49590 4 0.0336 0.980 0.008 0.000 0.000 0.992
#> GSM49591 1 0.4999 0.912 0.508 0.000 0.000 0.492
#> GSM49592 1 0.4999 0.912 0.508 0.000 0.000 0.492
#> GSM49593 4 0.0000 0.984 0.000 0.000 0.000 1.000
#> GSM49594 4 0.0336 0.980 0.008 0.000 0.000 0.992
#> GSM49595 4 0.0336 0.980 0.008 0.000 0.000 0.992
#> GSM49596 4 0.0592 0.963 0.016 0.000 0.000 0.984
#> GSM49597 2 0.5995 0.608 0.448 0.520 0.020 0.012
#> GSM49598 4 0.0000 0.984 0.000 0.000 0.000 1.000
#> GSM49599 1 0.4999 0.912 0.508 0.000 0.000 0.492
#> GSM49600 1 0.5000 0.905 0.504 0.000 0.000 0.496
#> GSM49601 4 0.0000 0.984 0.000 0.000 0.000 1.000
#> GSM49602 4 0.0000 0.984 0.000 0.000 0.000 1.000
#> GSM49603 4 0.0000 0.984 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
#> GSM49613 3 0.0579 0.990 0.008 0.000 0.984 0.008 0.000
#> GSM49604 4 0.2966 0.917 0.000 0.184 0.000 0.816 0.000
#> GSM49605 2 0.0963 0.942 0.036 0.964 0.000 0.000 0.000
#> GSM49606 2 0.0000 0.945 0.000 1.000 0.000 0.000 0.000
#> GSM49607 2 0.1121 0.938 0.044 0.956 0.000 0.000 0.000
#> GSM49608 2 0.0963 0.942 0.036 0.964 0.000 0.000 0.000
#> GSM49609 2 0.1628 0.939 0.056 0.936 0.000 0.008 0.000
#> GSM49610 2 0.1628 0.939 0.056 0.936 0.000 0.008 0.000
#> GSM49611 2 0.1628 0.939 0.056 0.936 0.000 0.008 0.000
#> GSM49612 2 0.1628 0.939 0.056 0.936 0.000 0.008 0.000
#> GSM49614 3 0.0162 0.992 0.000 0.000 0.996 0.004 0.000
#> GSM49615 3 0.0579 0.990 0.008 0.000 0.984 0.008 0.000
#> GSM49616 3 0.0000 0.993 0.000 0.000 1.000 0.000 0.000
#> GSM49617 3 0.0162 0.992 0.000 0.000 0.996 0.004 0.000
#> GSM49564 5 0.1549 0.952 0.016 0.000 0.000 0.040 0.944
#> GSM49565 1 0.4291 0.942 0.772 0.000 0.000 0.092 0.136
#> GSM49566 5 0.1740 0.939 0.012 0.000 0.000 0.056 0.932
#> GSM49567 1 0.3551 0.942 0.820 0.000 0.000 0.044 0.136
#> GSM49568 1 0.2753 0.959 0.856 0.000 0.000 0.008 0.136
#> GSM49569 5 0.0807 0.962 0.012 0.000 0.000 0.012 0.976
#> GSM49570 4 0.3355 0.916 0.012 0.184 0.000 0.804 0.000
#> GSM49571 4 0.3047 0.771 0.004 0.044 0.000 0.868 0.084
#> GSM49572 1 0.4238 0.944 0.776 0.000 0.000 0.088 0.136
#> GSM49573 4 0.2966 0.917 0.000 0.184 0.000 0.816 0.000
#> GSM49574 1 0.3966 0.957 0.796 0.000 0.000 0.072 0.132
#> GSM49575 1 0.2818 0.957 0.856 0.000 0.000 0.012 0.132
#> GSM49576 5 0.0290 0.962 0.008 0.000 0.000 0.000 0.992
#> GSM49577 5 0.2922 0.877 0.056 0.000 0.000 0.072 0.872
#> GSM49578 1 0.2864 0.960 0.852 0.000 0.000 0.012 0.136
#> GSM49579 5 0.1195 0.953 0.012 0.000 0.000 0.028 0.960
#> GSM49580 1 0.3151 0.951 0.836 0.000 0.000 0.020 0.144
#> GSM49581 1 0.2864 0.958 0.852 0.000 0.000 0.012 0.136
#> GSM49582 1 0.2753 0.959 0.856 0.000 0.000 0.008 0.136
#> GSM49583 2 0.1197 0.936 0.048 0.952 0.000 0.000 0.000
#> GSM49584 1 0.2753 0.959 0.856 0.000 0.000 0.008 0.136
#> GSM49585 1 0.3932 0.956 0.796 0.000 0.000 0.064 0.140
#> GSM49586 5 0.1701 0.951 0.016 0.000 0.000 0.048 0.936
#> GSM49587 1 0.3825 0.958 0.804 0.000 0.000 0.060 0.136
#> GSM49588 1 0.3932 0.956 0.796 0.000 0.000 0.064 0.140
#> GSM49589 5 0.1430 0.960 0.004 0.000 0.000 0.052 0.944
#> GSM49590 5 0.0162 0.963 0.004 0.000 0.000 0.000 0.996
#> GSM49591 1 0.3906 0.956 0.800 0.000 0.000 0.068 0.132
#> GSM49592 1 0.3950 0.958 0.796 0.000 0.000 0.068 0.136
#> GSM49593 5 0.0404 0.963 0.012 0.000 0.000 0.000 0.988
#> GSM49594 5 0.1357 0.955 0.004 0.000 0.000 0.048 0.948
#> GSM49595 5 0.1357 0.955 0.004 0.000 0.000 0.048 0.948
#> GSM49596 5 0.0807 0.962 0.012 0.000 0.000 0.012 0.976
#> GSM49597 4 0.4617 0.856 0.060 0.224 0.000 0.716 0.000
#> GSM49598 5 0.0404 0.963 0.012 0.000 0.000 0.000 0.988
#> GSM49599 1 0.3506 0.958 0.824 0.000 0.000 0.044 0.132
#> GSM49600 1 0.3359 0.939 0.816 0.000 0.000 0.020 0.164
#> GSM49601 5 0.1522 0.958 0.012 0.000 0.000 0.044 0.944
#> GSM49602 5 0.1364 0.960 0.012 0.000 0.000 0.036 0.952
#> GSM49603 5 0.1364 0.960 0.012 0.000 0.000 0.036 0.952
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM49613 3 0.0881 0.9819 0.000 0.000 0.972 0.012 0.008 0.008
#> GSM49604 4 0.2146 0.8904 0.000 0.116 0.000 0.880 0.000 0.004
#> GSM49605 2 0.2703 0.8800 0.000 0.824 0.000 0.004 0.000 0.172
#> GSM49606 2 0.2135 0.8866 0.000 0.872 0.000 0.000 0.000 0.128
#> GSM49607 2 0.3215 0.8451 0.000 0.756 0.000 0.004 0.000 0.240
#> GSM49608 2 0.2703 0.8800 0.000 0.824 0.000 0.004 0.000 0.172
#> GSM49609 2 0.0260 0.8785 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM49610 2 0.0260 0.8785 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM49611 2 0.0260 0.8785 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM49612 2 0.0260 0.8785 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM49614 3 0.0806 0.9790 0.000 0.000 0.972 0.000 0.008 0.020
#> GSM49615 3 0.0881 0.9819 0.000 0.000 0.972 0.012 0.008 0.008
#> GSM49616 3 0.0146 0.9846 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM49617 3 0.0520 0.9831 0.000 0.000 0.984 0.000 0.008 0.008
#> GSM49564 5 0.4596 0.3718 0.024 0.000 0.000 0.016 0.612 0.348
#> GSM49565 1 0.2687 0.8092 0.872 0.000 0.000 0.024 0.092 0.012
#> GSM49566 5 0.4626 0.3224 0.024 0.000 0.000 0.028 0.652 0.296
#> GSM49567 1 0.4872 0.7804 0.596 0.000 0.000 0.064 0.336 0.004
#> GSM49568 1 0.3456 0.8415 0.788 0.000 0.000 0.040 0.172 0.000
#> GSM49569 5 0.4326 0.5007 0.024 0.000 0.000 0.000 0.572 0.404
#> GSM49570 4 0.3165 0.8846 0.000 0.116 0.000 0.836 0.008 0.040
#> GSM49571 4 0.3456 0.7741 0.004 0.028 0.000 0.800 0.004 0.164
#> GSM49572 1 0.2384 0.8247 0.884 0.000 0.000 0.032 0.084 0.000
#> GSM49573 4 0.2003 0.8907 0.000 0.116 0.000 0.884 0.000 0.000
#> GSM49574 1 0.1313 0.8395 0.952 0.000 0.000 0.016 0.028 0.004
#> GSM49575 1 0.5104 0.8021 0.648 0.000 0.000 0.048 0.260 0.044
#> GSM49576 5 0.4554 0.4796 0.024 0.000 0.000 0.008 0.568 0.400
#> GSM49577 5 0.5611 0.0486 0.144 0.000 0.000 0.032 0.624 0.200
#> GSM49578 1 0.3102 0.8445 0.816 0.000 0.000 0.028 0.156 0.000
#> GSM49579 5 0.4707 0.3582 0.032 0.000 0.000 0.012 0.588 0.368
#> GSM49580 1 0.4368 0.7846 0.656 0.000 0.000 0.048 0.296 0.000
#> GSM49581 1 0.3766 0.8299 0.748 0.000 0.000 0.040 0.212 0.000
#> GSM49582 1 0.3283 0.8424 0.804 0.000 0.000 0.036 0.160 0.000
#> GSM49583 2 0.3519 0.8346 0.000 0.744 0.004 0.004 0.004 0.244
#> GSM49584 1 0.3588 0.8403 0.776 0.000 0.000 0.044 0.180 0.000
#> GSM49585 1 0.1829 0.8326 0.928 0.000 0.000 0.008 0.028 0.036
#> GSM49586 6 0.4035 0.6024 0.020 0.000 0.000 0.004 0.296 0.680
#> GSM49587 1 0.0653 0.8430 0.980 0.000 0.000 0.012 0.004 0.004
#> GSM49588 1 0.1405 0.8357 0.948 0.000 0.000 0.004 0.024 0.024
#> GSM49589 6 0.4784 0.4397 0.028 0.000 0.000 0.012 0.464 0.496
#> GSM49590 5 0.4561 0.4741 0.024 0.000 0.000 0.008 0.564 0.404
#> GSM49591 1 0.1173 0.8383 0.960 0.000 0.000 0.008 0.016 0.016
#> GSM49592 1 0.0870 0.8404 0.972 0.000 0.000 0.012 0.004 0.012
#> GSM49593 5 0.4381 0.4709 0.024 0.000 0.000 0.000 0.536 0.440
#> GSM49594 6 0.4513 0.6186 0.028 0.000 0.000 0.004 0.396 0.572
#> GSM49595 6 0.4513 0.6186 0.028 0.000 0.000 0.004 0.396 0.572
#> GSM49596 5 0.4434 0.5004 0.028 0.000 0.000 0.000 0.544 0.428
#> GSM49597 4 0.5293 0.7557 0.000 0.124 0.004 0.644 0.012 0.216
#> GSM49598 5 0.4381 0.4634 0.024 0.000 0.000 0.000 0.536 0.440
#> GSM49599 1 0.3943 0.8233 0.756 0.000 0.000 0.056 0.184 0.004
#> GSM49600 1 0.4594 0.7285 0.600 0.000 0.000 0.032 0.360 0.008
#> GSM49601 6 0.4251 0.6717 0.028 0.000 0.000 0.000 0.348 0.624
#> GSM49602 6 0.4379 0.5910 0.028 0.000 0.000 0.000 0.396 0.576
#> GSM49603 6 0.4379 0.5910 0.028 0.000 0.000 0.000 0.396 0.576
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) cell.type(p) k
#> SD:kmeans 54 5.97e-07 6.72e-04 2
#> SD:kmeans 53 3.58e-07 1.61e-13 3
#> SD:kmeans 53 1.61e-06 2.73e-12 4
#> SD:kmeans 54 1.42e-07 4.23e-13 5
#> SD:kmeans 45 1.12e-05 1.37e-09 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21168 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.925 0.947 0.977 0.4506 0.547 0.547
#> 3 3 0.851 0.884 0.949 0.4884 0.704 0.494
#> 4 4 0.877 0.903 0.949 0.1116 0.879 0.655
#> 5 5 0.723 0.668 0.823 0.0624 0.977 0.912
#> 6 6 0.705 0.520 0.724 0.0457 0.977 0.907
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
#> GSM49613 1 0.0672 0.978 0.992 0.008
#> GSM49604 2 0.0000 0.957 0.000 1.000
#> GSM49605 2 0.0000 0.957 0.000 1.000
#> GSM49606 2 0.0000 0.957 0.000 1.000
#> GSM49607 2 0.0000 0.957 0.000 1.000
#> GSM49608 2 0.0000 0.957 0.000 1.000
#> GSM49609 2 0.0000 0.957 0.000 1.000
#> GSM49610 2 0.0000 0.957 0.000 1.000
#> GSM49611 2 0.0000 0.957 0.000 1.000
#> GSM49612 2 0.0000 0.957 0.000 1.000
#> GSM49614 2 0.7950 0.687 0.240 0.760
#> GSM49615 1 0.0672 0.978 0.992 0.008
#> GSM49616 1 0.0672 0.978 0.992 0.008
#> GSM49617 1 0.4690 0.885 0.900 0.100
#> GSM49564 1 0.0000 0.984 1.000 0.000
#> GSM49565 1 0.0000 0.984 1.000 0.000
#> GSM49566 1 0.0000 0.984 1.000 0.000
#> GSM49567 1 0.0000 0.984 1.000 0.000
#> GSM49568 1 0.0000 0.984 1.000 0.000
#> GSM49569 1 0.0000 0.984 1.000 0.000
#> GSM49570 2 0.0000 0.957 0.000 1.000
#> GSM49571 2 0.0000 0.957 0.000 1.000
#> GSM49572 1 0.0000 0.984 1.000 0.000
#> GSM49573 2 0.0000 0.957 0.000 1.000
#> GSM49574 1 0.0000 0.984 1.000 0.000
#> GSM49575 1 0.5842 0.832 0.860 0.140
#> GSM49576 1 0.0000 0.984 1.000 0.000
#> GSM49577 2 0.9608 0.402 0.384 0.616
#> GSM49578 1 0.0000 0.984 1.000 0.000
#> GSM49579 1 0.0000 0.984 1.000 0.000
#> GSM49580 1 0.0000 0.984 1.000 0.000
#> GSM49581 1 0.0000 0.984 1.000 0.000
#> GSM49582 1 0.0000 0.984 1.000 0.000
#> GSM49583 2 0.0000 0.957 0.000 1.000
#> GSM49584 1 0.0000 0.984 1.000 0.000
#> GSM49585 1 0.0000 0.984 1.000 0.000
#> GSM49586 2 0.2043 0.935 0.032 0.968
#> GSM49587 1 0.0000 0.984 1.000 0.000
#> GSM49588 1 0.0000 0.984 1.000 0.000
#> GSM49589 1 0.0000 0.984 1.000 0.000
#> GSM49590 1 0.0376 0.981 0.996 0.004
#> GSM49591 1 0.0000 0.984 1.000 0.000
#> GSM49592 1 0.0000 0.984 1.000 0.000
#> GSM49593 1 0.0000 0.984 1.000 0.000
#> GSM49594 2 0.3431 0.908 0.064 0.936
#> GSM49595 1 0.7528 0.715 0.784 0.216
#> GSM49596 1 0.0000 0.984 1.000 0.000
#> GSM49597 2 0.0000 0.957 0.000 1.000
#> GSM49598 1 0.0000 0.984 1.000 0.000
#> GSM49599 1 0.2948 0.937 0.948 0.052
#> GSM49600 1 0.0000 0.984 1.000 0.000
#> GSM49601 1 0.0000 0.984 1.000 0.000
#> GSM49602 1 0.0000 0.984 1.000 0.000
#> GSM49603 1 0.0000 0.984 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM49613 3 0.0000 0.9223 0.000 0.000 1.000
#> GSM49604 2 0.0000 0.9677 0.000 1.000 0.000
#> GSM49605 2 0.0000 0.9677 0.000 1.000 0.000
#> GSM49606 2 0.0000 0.9677 0.000 1.000 0.000
#> GSM49607 2 0.0000 0.9677 0.000 1.000 0.000
#> GSM49608 2 0.0000 0.9677 0.000 1.000 0.000
#> GSM49609 2 0.0000 0.9677 0.000 1.000 0.000
#> GSM49610 2 0.0000 0.9677 0.000 1.000 0.000
#> GSM49611 2 0.0000 0.9677 0.000 1.000 0.000
#> GSM49612 2 0.0000 0.9677 0.000 1.000 0.000
#> GSM49614 3 0.0000 0.9223 0.000 0.000 1.000
#> GSM49615 3 0.0000 0.9223 0.000 0.000 1.000
#> GSM49616 3 0.0000 0.9223 0.000 0.000 1.000
#> GSM49617 3 0.0000 0.9223 0.000 0.000 1.000
#> GSM49564 3 0.0000 0.9223 0.000 0.000 1.000
#> GSM49565 1 0.0000 0.9494 1.000 0.000 0.000
#> GSM49566 3 0.2261 0.9053 0.068 0.000 0.932
#> GSM49567 1 0.0000 0.9494 1.000 0.000 0.000
#> GSM49568 1 0.0000 0.9494 1.000 0.000 0.000
#> GSM49569 3 0.1163 0.9211 0.028 0.000 0.972
#> GSM49570 2 0.0000 0.9677 0.000 1.000 0.000
#> GSM49571 2 0.0000 0.9677 0.000 1.000 0.000
#> GSM49572 1 0.0000 0.9494 1.000 0.000 0.000
#> GSM49573 2 0.0000 0.9677 0.000 1.000 0.000
#> GSM49574 1 0.0000 0.9494 1.000 0.000 0.000
#> GSM49575 1 0.0237 0.9465 0.996 0.004 0.000
#> GSM49576 3 0.0424 0.9226 0.008 0.000 0.992
#> GSM49577 1 0.5036 0.7578 0.808 0.172 0.020
#> GSM49578 1 0.0000 0.9494 1.000 0.000 0.000
#> GSM49579 3 0.5216 0.6796 0.260 0.000 0.740
#> GSM49580 1 0.0592 0.9408 0.988 0.000 0.012
#> GSM49581 1 0.0000 0.9494 1.000 0.000 0.000
#> GSM49582 1 0.0000 0.9494 1.000 0.000 0.000
#> GSM49583 2 0.0000 0.9677 0.000 1.000 0.000
#> GSM49584 1 0.0000 0.9494 1.000 0.000 0.000
#> GSM49585 1 0.0000 0.9494 1.000 0.000 0.000
#> GSM49586 2 0.7169 0.2069 0.028 0.568 0.404
#> GSM49587 1 0.0000 0.9494 1.000 0.000 0.000
#> GSM49588 1 0.0237 0.9468 0.996 0.000 0.004
#> GSM49589 3 0.0000 0.9223 0.000 0.000 1.000
#> GSM49590 3 0.0000 0.9223 0.000 0.000 1.000
#> GSM49591 1 0.0000 0.9494 1.000 0.000 0.000
#> GSM49592 1 0.0000 0.9494 1.000 0.000 0.000
#> GSM49593 3 0.1860 0.9155 0.052 0.000 0.948
#> GSM49594 3 0.7868 0.2156 0.056 0.420 0.524
#> GSM49595 3 0.5435 0.8216 0.144 0.048 0.808
#> GSM49596 1 0.6274 0.0846 0.544 0.000 0.456
#> GSM49597 2 0.0000 0.9677 0.000 1.000 0.000
#> GSM49598 3 0.3038 0.8835 0.104 0.000 0.896
#> GSM49599 1 0.0237 0.9465 0.996 0.004 0.000
#> GSM49600 1 0.4842 0.6864 0.776 0.000 0.224
#> GSM49601 3 0.3340 0.8710 0.120 0.000 0.880
#> GSM49602 3 0.1753 0.9172 0.048 0.000 0.952
#> GSM49603 3 0.1753 0.9172 0.048 0.000 0.952
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM49613 3 0.0000 0.8998 0.000 0.000 1.000 0.000
#> GSM49604 2 0.0000 0.9965 0.000 1.000 0.000 0.000
#> GSM49605 2 0.0000 0.9965 0.000 1.000 0.000 0.000
#> GSM49606 2 0.0000 0.9965 0.000 1.000 0.000 0.000
#> GSM49607 2 0.0000 0.9965 0.000 1.000 0.000 0.000
#> GSM49608 2 0.0000 0.9965 0.000 1.000 0.000 0.000
#> GSM49609 2 0.0000 0.9965 0.000 1.000 0.000 0.000
#> GSM49610 2 0.0000 0.9965 0.000 1.000 0.000 0.000
#> GSM49611 2 0.0000 0.9965 0.000 1.000 0.000 0.000
#> GSM49612 2 0.0000 0.9965 0.000 1.000 0.000 0.000
#> GSM49614 3 0.0000 0.8998 0.000 0.000 1.000 0.000
#> GSM49615 3 0.0000 0.8998 0.000 0.000 1.000 0.000
#> GSM49616 3 0.0000 0.8998 0.000 0.000 1.000 0.000
#> GSM49617 3 0.0000 0.8998 0.000 0.000 1.000 0.000
#> GSM49564 3 0.0672 0.8921 0.008 0.000 0.984 0.008
#> GSM49565 1 0.1022 0.9565 0.968 0.000 0.000 0.032
#> GSM49566 4 0.5462 0.7237 0.112 0.000 0.152 0.736
#> GSM49567 1 0.0376 0.9611 0.992 0.000 0.004 0.004
#> GSM49568 1 0.0336 0.9619 0.992 0.000 0.000 0.008
#> GSM49569 4 0.3999 0.8136 0.036 0.000 0.140 0.824
#> GSM49570 2 0.0336 0.9898 0.000 0.992 0.008 0.000
#> GSM49571 2 0.1118 0.9625 0.000 0.964 0.000 0.036
#> GSM49572 1 0.0336 0.9608 0.992 0.000 0.000 0.008
#> GSM49573 2 0.0000 0.9965 0.000 1.000 0.000 0.000
#> GSM49574 1 0.0707 0.9610 0.980 0.000 0.000 0.020
#> GSM49575 1 0.1004 0.9590 0.972 0.004 0.000 0.024
#> GSM49576 4 0.3208 0.8179 0.004 0.000 0.148 0.848
#> GSM49577 4 0.6772 0.5762 0.228 0.116 0.016 0.640
#> GSM49578 1 0.0000 0.9609 1.000 0.000 0.000 0.000
#> GSM49579 4 0.3088 0.8648 0.052 0.000 0.060 0.888
#> GSM49580 1 0.1256 0.9516 0.964 0.000 0.028 0.008
#> GSM49581 1 0.0817 0.9599 0.976 0.000 0.000 0.024
#> GSM49582 1 0.0000 0.9609 1.000 0.000 0.000 0.000
#> GSM49583 2 0.0000 0.9965 0.000 1.000 0.000 0.000
#> GSM49584 1 0.0376 0.9613 0.992 0.000 0.004 0.004
#> GSM49585 1 0.2589 0.8885 0.884 0.000 0.000 0.116
#> GSM49586 4 0.0524 0.8945 0.000 0.008 0.004 0.988
#> GSM49587 1 0.0000 0.9609 1.000 0.000 0.000 0.000
#> GSM49588 1 0.2868 0.8613 0.864 0.000 0.000 0.136
#> GSM49589 3 0.3300 0.7847 0.008 0.000 0.848 0.144
#> GSM49590 3 0.4994 -0.0178 0.000 0.000 0.520 0.480
#> GSM49591 1 0.1211 0.9488 0.960 0.000 0.000 0.040
#> GSM49592 1 0.0336 0.9617 0.992 0.000 0.000 0.008
#> GSM49593 4 0.1151 0.8931 0.008 0.000 0.024 0.968
#> GSM49594 4 0.0524 0.8944 0.004 0.008 0.000 0.988
#> GSM49595 4 0.0188 0.8954 0.004 0.000 0.000 0.996
#> GSM49596 4 0.3658 0.7994 0.144 0.000 0.020 0.836
#> GSM49597 2 0.0000 0.9965 0.000 1.000 0.000 0.000
#> GSM49598 4 0.0657 0.8953 0.012 0.000 0.004 0.984
#> GSM49599 1 0.2039 0.9443 0.940 0.016 0.008 0.036
#> GSM49600 1 0.4236 0.8274 0.824 0.000 0.088 0.088
#> GSM49601 4 0.0469 0.8953 0.012 0.000 0.000 0.988
#> GSM49602 4 0.0376 0.8957 0.004 0.000 0.004 0.992
#> GSM49603 4 0.0524 0.8955 0.004 0.000 0.008 0.988
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM49613 3 0.0000 0.9234 0.000 0.000 1.000 0.000 0.000
#> GSM49604 2 0.3424 0.7691 0.000 0.760 0.000 0.240 0.000
#> GSM49605 2 0.0000 0.8801 0.000 1.000 0.000 0.000 0.000
#> GSM49606 2 0.0000 0.8801 0.000 1.000 0.000 0.000 0.000
#> GSM49607 2 0.0000 0.8801 0.000 1.000 0.000 0.000 0.000
#> GSM49608 2 0.0162 0.8794 0.000 0.996 0.000 0.004 0.000
#> GSM49609 2 0.0000 0.8801 0.000 1.000 0.000 0.000 0.000
#> GSM49610 2 0.0000 0.8801 0.000 1.000 0.000 0.000 0.000
#> GSM49611 2 0.0000 0.8801 0.000 1.000 0.000 0.000 0.000
#> GSM49612 2 0.0000 0.8801 0.000 1.000 0.000 0.000 0.000
#> GSM49614 3 0.0000 0.9234 0.000 0.000 1.000 0.000 0.000
#> GSM49615 3 0.0000 0.9234 0.000 0.000 1.000 0.000 0.000
#> GSM49616 3 0.0000 0.9234 0.000 0.000 1.000 0.000 0.000
#> GSM49617 3 0.0000 0.9234 0.000 0.000 1.000 0.000 0.000
#> GSM49564 3 0.2728 0.8450 0.004 0.000 0.888 0.040 0.068
#> GSM49565 1 0.3863 0.7413 0.772 0.000 0.000 0.200 0.028
#> GSM49566 5 0.6417 0.1840 0.072 0.000 0.088 0.220 0.620
#> GSM49567 1 0.4138 0.6939 0.708 0.000 0.000 0.276 0.016
#> GSM49568 1 0.2938 0.7754 0.876 0.000 0.008 0.084 0.032
#> GSM49569 5 0.5278 0.4212 0.048 0.000 0.068 0.156 0.728
#> GSM49570 2 0.4570 0.6721 0.000 0.632 0.020 0.348 0.000
#> GSM49571 2 0.5148 0.5321 0.000 0.528 0.000 0.432 0.040
#> GSM49572 1 0.2890 0.7741 0.836 0.000 0.000 0.160 0.004
#> GSM49573 2 0.4060 0.6773 0.000 0.640 0.000 0.360 0.000
#> GSM49574 1 0.2971 0.7742 0.836 0.000 0.000 0.156 0.008
#> GSM49575 1 0.4682 0.5576 0.620 0.000 0.000 0.356 0.024
#> GSM49576 5 0.4433 0.5162 0.004 0.000 0.076 0.156 0.764
#> GSM49577 4 0.7840 0.0000 0.164 0.084 0.004 0.388 0.360
#> GSM49578 1 0.0404 0.7854 0.988 0.000 0.000 0.012 0.000
#> GSM49579 5 0.5526 0.3047 0.072 0.000 0.028 0.224 0.676
#> GSM49580 1 0.4501 0.6747 0.740 0.000 0.012 0.212 0.036
#> GSM49581 1 0.3449 0.7492 0.812 0.000 0.000 0.164 0.024
#> GSM49582 1 0.1043 0.7816 0.960 0.000 0.000 0.040 0.000
#> GSM49583 2 0.0510 0.8761 0.000 0.984 0.000 0.016 0.000
#> GSM49584 1 0.1571 0.7831 0.936 0.000 0.004 0.060 0.000
#> GSM49585 1 0.5372 0.6430 0.676 0.000 0.008 0.216 0.100
#> GSM49586 5 0.4276 0.1894 0.000 0.004 0.000 0.380 0.616
#> GSM49587 1 0.2179 0.7835 0.896 0.000 0.000 0.100 0.004
#> GSM49588 1 0.4989 0.6530 0.708 0.000 0.000 0.168 0.124
#> GSM49589 3 0.5397 0.5726 0.016 0.000 0.684 0.088 0.212
#> GSM49590 5 0.4968 0.0773 0.000 0.000 0.456 0.028 0.516
#> GSM49591 1 0.3639 0.7507 0.792 0.000 0.000 0.184 0.024
#> GSM49592 1 0.1952 0.7799 0.912 0.000 0.000 0.084 0.004
#> GSM49593 5 0.1851 0.5926 0.000 0.000 0.000 0.088 0.912
#> GSM49594 5 0.4497 0.4784 0.008 0.044 0.004 0.188 0.756
#> GSM49595 5 0.2690 0.5690 0.000 0.000 0.000 0.156 0.844
#> GSM49596 5 0.4855 0.3220 0.112 0.000 0.000 0.168 0.720
#> GSM49597 2 0.2690 0.8190 0.000 0.844 0.000 0.156 0.000
#> GSM49598 5 0.2237 0.5976 0.008 0.000 0.004 0.084 0.904
#> GSM49599 1 0.4630 0.6913 0.672 0.000 0.008 0.300 0.020
#> GSM49600 1 0.7153 0.1950 0.524 0.000 0.056 0.240 0.180
#> GSM49601 5 0.2338 0.5884 0.004 0.000 0.000 0.112 0.884
#> GSM49602 5 0.0963 0.6163 0.000 0.000 0.000 0.036 0.964
#> GSM49603 5 0.0880 0.6165 0.000 0.000 0.000 0.032 0.968
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM49613 3 0.0000 0.8831 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM49604 2 0.3727 -0.4777 0.000 0.612 0.000 0.388 0.000 0.000
#> GSM49605 2 0.0000 0.8557 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM49606 2 0.0291 0.8565 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM49607 2 0.0260 0.8524 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM49608 2 0.0260 0.8524 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM49609 2 0.0508 0.8535 0.000 0.984 0.000 0.012 0.000 0.004
#> GSM49610 2 0.0291 0.8565 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM49611 2 0.0508 0.8535 0.000 0.984 0.000 0.012 0.000 0.004
#> GSM49612 2 0.0508 0.8535 0.000 0.984 0.000 0.012 0.000 0.004
#> GSM49614 3 0.0000 0.8831 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM49615 3 0.0000 0.8831 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM49616 3 0.0000 0.8831 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM49617 3 0.0000 0.8831 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM49564 3 0.4199 0.7071 0.004 0.000 0.780 0.036 0.128 0.052
#> GSM49565 1 0.4538 0.4815 0.536 0.000 0.000 0.020 0.008 0.436
#> GSM49566 5 0.7506 -0.0271 0.080 0.000 0.060 0.148 0.480 0.232
#> GSM49567 1 0.5001 0.4402 0.596 0.000 0.000 0.096 0.000 0.308
#> GSM49568 1 0.3141 0.6133 0.852 0.000 0.000 0.040 0.024 0.084
#> GSM49569 5 0.6579 0.2721 0.036 0.000 0.092 0.112 0.604 0.156
#> GSM49570 4 0.3989 0.8373 0.000 0.468 0.004 0.528 0.000 0.000
#> GSM49571 4 0.4479 0.7837 0.000 0.356 0.000 0.608 0.032 0.004
#> GSM49572 1 0.4416 0.5361 0.600 0.000 0.000 0.020 0.008 0.372
#> GSM49573 4 0.3838 0.8615 0.000 0.448 0.000 0.552 0.000 0.000
#> GSM49574 1 0.3897 0.6043 0.696 0.000 0.000 0.024 0.000 0.280
#> GSM49575 1 0.6066 0.3613 0.500 0.000 0.000 0.260 0.012 0.228
#> GSM49576 5 0.5882 0.3439 0.004 0.000 0.100 0.104 0.644 0.148
#> GSM49577 6 0.7626 0.0000 0.092 0.040 0.004 0.172 0.228 0.464
#> GSM49578 1 0.1398 0.6345 0.940 0.000 0.000 0.008 0.000 0.052
#> GSM49579 5 0.6263 -0.0650 0.028 0.000 0.012 0.116 0.484 0.360
#> GSM49580 1 0.6369 0.3784 0.592 0.000 0.020 0.092 0.080 0.216
#> GSM49581 1 0.5211 0.5016 0.680 0.000 0.000 0.076 0.056 0.188
#> GSM49582 1 0.1196 0.6297 0.952 0.000 0.000 0.008 0.000 0.040
#> GSM49583 2 0.1007 0.8113 0.000 0.956 0.000 0.044 0.000 0.000
#> GSM49584 1 0.2701 0.6088 0.864 0.000 0.004 0.028 0.000 0.104
#> GSM49585 1 0.6137 0.4545 0.492 0.000 0.008 0.056 0.068 0.376
#> GSM49586 5 0.4720 0.2046 0.000 0.000 0.000 0.388 0.560 0.052
#> GSM49587 1 0.3349 0.6091 0.748 0.000 0.000 0.008 0.000 0.244
#> GSM49588 1 0.5749 0.4935 0.532 0.000 0.000 0.044 0.072 0.352
#> GSM49589 3 0.6328 0.3875 0.008 0.000 0.556 0.080 0.268 0.088
#> GSM49590 5 0.6149 0.1184 0.000 0.000 0.368 0.088 0.484 0.060
#> GSM49591 1 0.4385 0.5786 0.636 0.000 0.000 0.032 0.004 0.328
#> GSM49592 1 0.3384 0.6077 0.760 0.000 0.000 0.008 0.004 0.228
#> GSM49593 5 0.4011 0.4529 0.008 0.000 0.016 0.080 0.796 0.100
#> GSM49594 5 0.6091 0.2650 0.008 0.036 0.000 0.164 0.588 0.204
#> GSM49595 5 0.4923 0.3515 0.004 0.000 0.000 0.144 0.668 0.184
#> GSM49596 5 0.6703 0.1347 0.136 0.000 0.012 0.108 0.560 0.184
#> GSM49597 2 0.3555 0.0886 0.000 0.712 0.000 0.280 0.000 0.008
#> GSM49598 5 0.4319 0.4353 0.020 0.000 0.004 0.104 0.768 0.104
#> GSM49599 1 0.6250 0.3527 0.432 0.004 0.000 0.188 0.012 0.364
#> GSM49600 1 0.8156 -0.0327 0.384 0.000 0.072 0.116 0.180 0.248
#> GSM49601 5 0.3566 0.4659 0.016 0.000 0.000 0.080 0.820 0.084
#> GSM49602 5 0.1434 0.5063 0.000 0.000 0.000 0.048 0.940 0.012
#> GSM49603 5 0.1549 0.5066 0.000 0.000 0.000 0.044 0.936 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) cell.type(p) k
#> SD:skmeans 53 6.87e-05 9.70e-03 2
#> SD:skmeans 51 4.51e-06 3.34e-04 3
#> SD:skmeans 53 7.85e-06 1.27e-08 4
#> SD:skmeans 45 8.51e-05 5.35e-07 5
#> SD:skmeans 30 2.20e-04 4.12e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "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 21168 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.581 0.936 0.910 0.3156 0.669 0.669
#> 3 3 0.806 0.916 0.943 0.5316 0.867 0.802
#> 4 4 0.867 0.907 0.955 0.4619 0.751 0.535
#> 5 5 0.845 0.894 0.957 0.0564 0.965 0.879
#> 6 6 0.811 0.822 0.912 0.0294 0.974 0.900
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM49613 1 0.5408 0.848 0.876 0.124
#> GSM49604 2 0.5408 0.970 0.124 0.876
#> GSM49605 2 0.5408 0.970 0.124 0.876
#> GSM49606 2 0.5408 0.970 0.124 0.876
#> GSM49607 2 0.5408 0.970 0.124 0.876
#> GSM49608 2 0.5408 0.970 0.124 0.876
#> GSM49609 2 0.5408 0.970 0.124 0.876
#> GSM49610 2 0.5408 0.970 0.124 0.876
#> GSM49611 2 0.5408 0.970 0.124 0.876
#> GSM49612 2 0.5408 0.970 0.124 0.876
#> GSM49614 1 0.5946 0.850 0.856 0.144
#> GSM49615 1 0.5408 0.848 0.876 0.124
#> GSM49616 1 0.5842 0.850 0.860 0.140
#> GSM49617 1 0.5946 0.850 0.856 0.144
#> GSM49564 1 0.0000 0.964 1.000 0.000
#> GSM49565 1 0.0000 0.964 1.000 0.000
#> GSM49566 1 0.0000 0.964 1.000 0.000
#> GSM49567 1 0.0000 0.964 1.000 0.000
#> GSM49568 1 0.0000 0.964 1.000 0.000
#> GSM49569 1 0.0938 0.962 0.988 0.012
#> GSM49570 1 0.9129 0.406 0.672 0.328
#> GSM49571 1 0.1414 0.961 0.980 0.020
#> GSM49572 1 0.0000 0.964 1.000 0.000
#> GSM49573 1 0.1414 0.961 0.980 0.020
#> GSM49574 1 0.0000 0.964 1.000 0.000
#> GSM49575 1 0.0000 0.964 1.000 0.000
#> GSM49576 1 0.1414 0.961 0.980 0.020
#> GSM49577 1 0.1414 0.961 0.980 0.020
#> GSM49578 1 0.0000 0.964 1.000 0.000
#> GSM49579 1 0.1414 0.961 0.980 0.020
#> GSM49580 1 0.0000 0.964 1.000 0.000
#> GSM49581 1 0.0000 0.964 1.000 0.000
#> GSM49582 1 0.0000 0.964 1.000 0.000
#> GSM49583 2 0.5408 0.970 0.124 0.876
#> GSM49584 1 0.0000 0.964 1.000 0.000
#> GSM49585 1 0.0000 0.964 1.000 0.000
#> GSM49586 1 0.1414 0.961 0.980 0.020
#> GSM49587 1 0.0000 0.964 1.000 0.000
#> GSM49588 1 0.0000 0.964 1.000 0.000
#> GSM49589 1 0.1414 0.961 0.980 0.020
#> GSM49590 1 0.1414 0.961 0.980 0.020
#> GSM49591 1 0.0000 0.964 1.000 0.000
#> GSM49592 1 0.0000 0.964 1.000 0.000
#> GSM49593 1 0.1414 0.961 0.980 0.020
#> GSM49594 1 0.1414 0.961 0.980 0.020
#> GSM49595 1 0.1414 0.961 0.980 0.020
#> GSM49596 1 0.0000 0.964 1.000 0.000
#> GSM49597 2 0.9552 0.573 0.376 0.624
#> GSM49598 1 0.1414 0.961 0.980 0.020
#> GSM49599 1 0.0376 0.964 0.996 0.004
#> GSM49600 1 0.0000 0.964 1.000 0.000
#> GSM49601 1 0.1414 0.961 0.980 0.020
#> GSM49602 1 0.1414 0.961 0.980 0.020
#> GSM49603 1 0.1414 0.961 0.980 0.020
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM49613 3 0.0000 1.000 0.000 0.000 1.000
#> GSM49604 2 0.0000 0.942 0.000 1.000 0.000
#> GSM49605 2 0.0000 0.942 0.000 1.000 0.000
#> GSM49606 2 0.0000 0.942 0.000 1.000 0.000
#> GSM49607 2 0.0000 0.942 0.000 1.000 0.000
#> GSM49608 2 0.0000 0.942 0.000 1.000 0.000
#> GSM49609 2 0.0000 0.942 0.000 1.000 0.000
#> GSM49610 2 0.0000 0.942 0.000 1.000 0.000
#> GSM49611 2 0.0000 0.942 0.000 1.000 0.000
#> GSM49612 2 0.0000 0.942 0.000 1.000 0.000
#> GSM49614 3 0.0000 1.000 0.000 0.000 1.000
#> GSM49615 3 0.0000 1.000 0.000 0.000 1.000
#> GSM49616 3 0.0000 1.000 0.000 0.000 1.000
#> GSM49617 3 0.0000 1.000 0.000 0.000 1.000
#> GSM49564 1 0.2711 0.928 0.912 0.000 0.088
#> GSM49565 1 0.0237 0.925 0.996 0.004 0.000
#> GSM49566 1 0.2945 0.928 0.908 0.004 0.088
#> GSM49567 1 0.0000 0.926 1.000 0.000 0.000
#> GSM49568 1 0.0000 0.926 1.000 0.000 0.000
#> GSM49569 1 0.3587 0.927 0.892 0.020 0.088
#> GSM49570 1 0.8470 0.422 0.552 0.344 0.104
#> GSM49571 1 0.4092 0.925 0.876 0.036 0.088
#> GSM49572 1 0.0000 0.926 1.000 0.000 0.000
#> GSM49573 1 0.3973 0.926 0.880 0.032 0.088
#> GSM49574 1 0.0000 0.926 1.000 0.000 0.000
#> GSM49575 1 0.0000 0.926 1.000 0.000 0.000
#> GSM49576 1 0.4092 0.925 0.876 0.036 0.088
#> GSM49577 1 0.2806 0.929 0.928 0.032 0.040
#> GSM49578 1 0.0000 0.926 1.000 0.000 0.000
#> GSM49579 1 0.4092 0.925 0.876 0.036 0.088
#> GSM49580 1 0.0000 0.926 1.000 0.000 0.000
#> GSM49581 1 0.0000 0.926 1.000 0.000 0.000
#> GSM49582 1 0.0000 0.926 1.000 0.000 0.000
#> GSM49583 2 0.0000 0.942 0.000 1.000 0.000
#> GSM49584 1 0.0000 0.926 1.000 0.000 0.000
#> GSM49585 1 0.0237 0.926 0.996 0.000 0.004
#> GSM49586 1 0.4092 0.925 0.876 0.036 0.088
#> GSM49587 1 0.0000 0.926 1.000 0.000 0.000
#> GSM49588 1 0.2625 0.928 0.916 0.000 0.084
#> GSM49589 1 0.4092 0.925 0.876 0.036 0.088
#> GSM49590 1 0.4092 0.925 0.876 0.036 0.088
#> GSM49591 1 0.0000 0.926 1.000 0.000 0.000
#> GSM49592 1 0.0000 0.926 1.000 0.000 0.000
#> GSM49593 1 0.3973 0.926 0.880 0.032 0.088
#> GSM49594 1 0.4092 0.925 0.876 0.036 0.088
#> GSM49595 1 0.4092 0.925 0.876 0.036 0.088
#> GSM49596 1 0.3129 0.928 0.904 0.008 0.088
#> GSM49597 2 0.6255 0.385 0.320 0.668 0.012
#> GSM49598 1 0.3973 0.926 0.880 0.032 0.088
#> GSM49599 1 0.0237 0.926 0.996 0.004 0.000
#> GSM49600 1 0.0237 0.926 0.996 0.000 0.004
#> GSM49601 1 0.4092 0.925 0.876 0.036 0.088
#> GSM49602 1 0.4092 0.925 0.876 0.036 0.088
#> GSM49603 1 0.4092 0.925 0.876 0.036 0.088
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM49613 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM49604 2 0.0000 0.947 0.000 1.000 0 0.000
#> GSM49605 2 0.0000 0.947 0.000 1.000 0 0.000
#> GSM49606 2 0.0000 0.947 0.000 1.000 0 0.000
#> GSM49607 2 0.0000 0.947 0.000 1.000 0 0.000
#> GSM49608 2 0.0000 0.947 0.000 1.000 0 0.000
#> GSM49609 2 0.0000 0.947 0.000 1.000 0 0.000
#> GSM49610 2 0.0000 0.947 0.000 1.000 0 0.000
#> GSM49611 2 0.0000 0.947 0.000 1.000 0 0.000
#> GSM49612 2 0.0000 0.947 0.000 1.000 0 0.000
#> GSM49614 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM49615 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM49616 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM49617 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM49564 4 0.0000 0.937 0.000 0.000 0 1.000
#> GSM49565 1 0.1474 0.932 0.948 0.000 0 0.052
#> GSM49566 4 0.0336 0.935 0.008 0.000 0 0.992
#> GSM49567 1 0.0592 0.947 0.984 0.000 0 0.016
#> GSM49568 1 0.0921 0.945 0.972 0.000 0 0.028
#> GSM49569 4 0.0000 0.937 0.000 0.000 0 1.000
#> GSM49570 4 0.2142 0.902 0.056 0.016 0 0.928
#> GSM49571 4 0.2011 0.892 0.080 0.000 0 0.920
#> GSM49572 1 0.0592 0.947 0.984 0.000 0 0.016
#> GSM49573 4 0.2921 0.856 0.140 0.000 0 0.860
#> GSM49574 1 0.0817 0.945 0.976 0.000 0 0.024
#> GSM49575 1 0.1940 0.907 0.924 0.000 0 0.076
#> GSM49576 4 0.2281 0.877 0.096 0.000 0 0.904
#> GSM49577 4 0.4888 0.272 0.412 0.000 0 0.588
#> GSM49578 1 0.0592 0.947 0.984 0.000 0 0.016
#> GSM49579 4 0.2530 0.863 0.112 0.000 0 0.888
#> GSM49580 1 0.0921 0.945 0.972 0.000 0 0.028
#> GSM49581 1 0.0592 0.947 0.984 0.000 0 0.016
#> GSM49582 1 0.0592 0.947 0.984 0.000 0 0.016
#> GSM49583 2 0.0000 0.947 0.000 1.000 0 0.000
#> GSM49584 1 0.0592 0.947 0.984 0.000 0 0.016
#> GSM49585 1 0.2530 0.883 0.888 0.000 0 0.112
#> GSM49586 4 0.0000 0.937 0.000 0.000 0 1.000
#> GSM49587 1 0.0817 0.946 0.976 0.000 0 0.024
#> GSM49588 4 0.3311 0.800 0.172 0.000 0 0.828
#> GSM49589 4 0.0000 0.937 0.000 0.000 0 1.000
#> GSM49590 4 0.0000 0.937 0.000 0.000 0 1.000
#> GSM49591 1 0.1302 0.939 0.956 0.000 0 0.044
#> GSM49592 1 0.1118 0.943 0.964 0.000 0 0.036
#> GSM49593 4 0.0000 0.937 0.000 0.000 0 1.000
#> GSM49594 4 0.0000 0.937 0.000 0.000 0 1.000
#> GSM49595 4 0.0000 0.937 0.000 0.000 0 1.000
#> GSM49596 4 0.0336 0.935 0.008 0.000 0 0.992
#> GSM49597 2 0.5298 0.370 0.016 0.612 0 0.372
#> GSM49598 4 0.0469 0.932 0.012 0.000 0 0.988
#> GSM49599 1 0.3486 0.786 0.812 0.000 0 0.188
#> GSM49600 1 0.3975 0.721 0.760 0.000 0 0.240
#> GSM49601 4 0.0000 0.937 0.000 0.000 0 1.000
#> GSM49602 4 0.0000 0.937 0.000 0.000 0 1.000
#> GSM49603 4 0.0000 0.937 0.000 0.000 0 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM49613 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM49604 2 0.3913 0.530 0.000 0.676 0 0.324 0.000
#> GSM49605 2 0.0000 0.962 0.000 1.000 0 0.000 0.000
#> GSM49606 2 0.0000 0.962 0.000 1.000 0 0.000 0.000
#> GSM49607 2 0.0000 0.962 0.000 1.000 0 0.000 0.000
#> GSM49608 2 0.0162 0.959 0.000 0.996 0 0.004 0.000
#> GSM49609 2 0.0000 0.962 0.000 1.000 0 0.000 0.000
#> GSM49610 2 0.0000 0.962 0.000 1.000 0 0.000 0.000
#> GSM49611 2 0.0000 0.962 0.000 1.000 0 0.000 0.000
#> GSM49612 2 0.0000 0.962 0.000 1.000 0 0.000 0.000
#> GSM49614 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM49615 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM49616 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM49617 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM49564 5 0.0000 0.919 0.000 0.000 0 0.000 1.000
#> GSM49565 1 0.0000 0.948 1.000 0.000 0 0.000 0.000
#> GSM49566 5 0.0703 0.905 0.024 0.000 0 0.000 0.976
#> GSM49567 1 0.0000 0.948 1.000 0.000 0 0.000 0.000
#> GSM49568 1 0.0000 0.948 1.000 0.000 0 0.000 0.000
#> GSM49569 5 0.0000 0.919 0.000 0.000 0 0.000 1.000
#> GSM49570 4 0.0000 0.852 0.000 0.000 0 1.000 0.000
#> GSM49571 5 0.3659 0.679 0.012 0.000 0 0.220 0.768
#> GSM49572 1 0.0000 0.948 1.000 0.000 0 0.000 0.000
#> GSM49573 4 0.0000 0.852 0.000 0.000 0 1.000 0.000
#> GSM49574 1 0.0162 0.947 0.996 0.000 0 0.000 0.004
#> GSM49575 1 0.1341 0.907 0.944 0.000 0 0.000 0.056
#> GSM49576 5 0.2074 0.836 0.104 0.000 0 0.000 0.896
#> GSM49577 5 0.4227 0.256 0.420 0.000 0 0.000 0.580
#> GSM49578 1 0.0000 0.948 1.000 0.000 0 0.000 0.000
#> GSM49579 5 0.2230 0.823 0.116 0.000 0 0.000 0.884
#> GSM49580 1 0.0404 0.943 0.988 0.000 0 0.000 0.012
#> GSM49581 1 0.0000 0.948 1.000 0.000 0 0.000 0.000
#> GSM49582 1 0.0000 0.948 1.000 0.000 0 0.000 0.000
#> GSM49583 2 0.0000 0.962 0.000 1.000 0 0.000 0.000
#> GSM49584 1 0.0000 0.948 1.000 0.000 0 0.000 0.000
#> GSM49585 1 0.2329 0.842 0.876 0.000 0 0.000 0.124
#> GSM49586 5 0.1341 0.881 0.000 0.000 0 0.056 0.944
#> GSM49587 1 0.0000 0.948 1.000 0.000 0 0.000 0.000
#> GSM49588 5 0.2852 0.755 0.172 0.000 0 0.000 0.828
#> GSM49589 5 0.0000 0.919 0.000 0.000 0 0.000 1.000
#> GSM49590 5 0.0000 0.919 0.000 0.000 0 0.000 1.000
#> GSM49591 1 0.1544 0.900 0.932 0.000 0 0.000 0.068
#> GSM49592 1 0.0609 0.938 0.980 0.000 0 0.000 0.020
#> GSM49593 5 0.0000 0.919 0.000 0.000 0 0.000 1.000
#> GSM49594 5 0.0000 0.919 0.000 0.000 0 0.000 1.000
#> GSM49595 5 0.0000 0.919 0.000 0.000 0 0.000 1.000
#> GSM49596 5 0.0290 0.915 0.008 0.000 0 0.000 0.992
#> GSM49597 4 0.4075 0.703 0.000 0.060 0 0.780 0.160
#> GSM49598 5 0.0000 0.919 0.000 0.000 0 0.000 1.000
#> GSM49599 1 0.2516 0.821 0.860 0.000 0 0.000 0.140
#> GSM49600 1 0.3210 0.721 0.788 0.000 0 0.000 0.212
#> GSM49601 5 0.0000 0.919 0.000 0.000 0 0.000 1.000
#> GSM49602 5 0.0000 0.919 0.000 0.000 0 0.000 1.000
#> GSM49603 5 0.0000 0.919 0.000 0.000 0 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM49613 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49604 4 0.3998 0.429 0.000 0.340 0 0.644 0.000 0.016
#> GSM49605 6 0.2697 0.739 0.000 0.188 0 0.000 0.000 0.812
#> GSM49606 2 0.3851 -0.285 0.000 0.540 0 0.000 0.000 0.460
#> GSM49607 6 0.2631 0.739 0.000 0.180 0 0.000 0.000 0.820
#> GSM49608 6 0.2762 0.734 0.000 0.196 0 0.000 0.000 0.804
#> GSM49609 2 0.0000 0.836 0.000 1.000 0 0.000 0.000 0.000
#> GSM49610 2 0.0000 0.836 0.000 1.000 0 0.000 0.000 0.000
#> GSM49611 2 0.0000 0.836 0.000 1.000 0 0.000 0.000 0.000
#> GSM49612 2 0.0000 0.836 0.000 1.000 0 0.000 0.000 0.000
#> GSM49614 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49615 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49616 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49617 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49564 5 0.0000 0.909 0.000 0.000 0 0.000 1.000 0.000
#> GSM49565 1 0.1007 0.932 0.956 0.000 0 0.000 0.000 0.044
#> GSM49566 5 0.0632 0.899 0.024 0.000 0 0.000 0.976 0.000
#> GSM49567 1 0.0713 0.936 0.972 0.000 0 0.000 0.000 0.028
#> GSM49568 1 0.0547 0.937 0.980 0.000 0 0.000 0.000 0.020
#> GSM49569 5 0.0000 0.909 0.000 0.000 0 0.000 1.000 0.000
#> GSM49570 4 0.0146 0.780 0.000 0.000 0 0.996 0.000 0.004
#> GSM49571 5 0.3780 0.719 0.016 0.000 0 0.204 0.760 0.020
#> GSM49572 1 0.0547 0.938 0.980 0.000 0 0.000 0.000 0.020
#> GSM49573 4 0.0000 0.781 0.000 0.000 0 1.000 0.000 0.000
#> GSM49574 1 0.0632 0.937 0.976 0.000 0 0.000 0.000 0.024
#> GSM49575 1 0.1765 0.903 0.924 0.000 0 0.000 0.052 0.024
#> GSM49576 5 0.2537 0.832 0.096 0.000 0 0.000 0.872 0.032
#> GSM49577 5 0.5303 0.385 0.332 0.000 0 0.000 0.548 0.120
#> GSM49578 1 0.0547 0.937 0.980 0.000 0 0.000 0.000 0.020
#> GSM49579 5 0.3041 0.788 0.128 0.000 0 0.000 0.832 0.040
#> GSM49580 1 0.1124 0.933 0.956 0.000 0 0.000 0.008 0.036
#> GSM49581 1 0.0632 0.936 0.976 0.000 0 0.000 0.000 0.024
#> GSM49582 1 0.0547 0.937 0.980 0.000 0 0.000 0.000 0.020
#> GSM49583 6 0.3854 0.175 0.000 0.464 0 0.000 0.000 0.536
#> GSM49584 1 0.0458 0.937 0.984 0.000 0 0.000 0.000 0.016
#> GSM49585 1 0.2999 0.830 0.836 0.000 0 0.000 0.124 0.040
#> GSM49586 5 0.1151 0.894 0.000 0.000 0 0.032 0.956 0.012
#> GSM49587 1 0.0865 0.933 0.964 0.000 0 0.000 0.000 0.036
#> GSM49588 5 0.3455 0.726 0.180 0.000 0 0.000 0.784 0.036
#> GSM49589 5 0.0000 0.909 0.000 0.000 0 0.000 1.000 0.000
#> GSM49590 5 0.0000 0.909 0.000 0.000 0 0.000 1.000 0.000
#> GSM49591 1 0.2294 0.886 0.892 0.000 0 0.000 0.072 0.036
#> GSM49592 1 0.1564 0.929 0.936 0.000 0 0.000 0.024 0.040
#> GSM49593 5 0.0000 0.909 0.000 0.000 0 0.000 1.000 0.000
#> GSM49594 5 0.1910 0.856 0.000 0.000 0 0.000 0.892 0.108
#> GSM49595 5 0.1910 0.856 0.000 0.000 0 0.000 0.892 0.108
#> GSM49596 5 0.0260 0.907 0.008 0.000 0 0.000 0.992 0.000
#> GSM49597 6 0.4151 0.387 0.000 0.000 0 0.264 0.044 0.692
#> GSM49598 5 0.0000 0.909 0.000 0.000 0 0.000 1.000 0.000
#> GSM49599 1 0.2199 0.878 0.892 0.000 0 0.000 0.088 0.020
#> GSM49600 1 0.2981 0.793 0.820 0.000 0 0.000 0.160 0.020
#> GSM49601 5 0.0146 0.908 0.000 0.000 0 0.000 0.996 0.004
#> GSM49602 5 0.0000 0.909 0.000 0.000 0 0.000 1.000 0.000
#> GSM49603 5 0.0000 0.909 0.000 0.000 0 0.000 1.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> SD:pam 53 2.67e-08 1.83e-04 2
#> SD:pam 52 1.22e-09 2.39e-14 3
#> SD:pam 52 6.37e-09 4.29e-13 4
#> SD:pam 53 1.75e-08 2.70e-12 5
#> SD:pam 49 3.46e-08 1.37e-16 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "mclust"]
# you can also extract it by
# res = res_list["SD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.978 0.990 0.4700 0.535 0.535
#> 3 3 0.978 0.929 0.963 0.1056 0.937 0.883
#> 4 4 0.862 0.925 0.935 0.1002 0.983 0.963
#> 5 5 0.642 0.692 0.823 0.2399 0.777 0.521
#> 6 6 0.615 0.553 0.749 0.0953 0.818 0.437
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
#> GSM49613 2 0.0376 0.996 0.004 0.996
#> GSM49604 2 0.0000 0.998 0.000 1.000
#> GSM49605 2 0.0000 0.998 0.000 1.000
#> GSM49606 2 0.0000 0.998 0.000 1.000
#> GSM49607 2 0.0000 0.998 0.000 1.000
#> GSM49608 2 0.0000 0.998 0.000 1.000
#> GSM49609 2 0.0000 0.998 0.000 1.000
#> GSM49610 2 0.0000 0.998 0.000 1.000
#> GSM49611 2 0.0000 0.998 0.000 1.000
#> GSM49612 2 0.0000 0.998 0.000 1.000
#> GSM49614 2 0.0376 0.996 0.004 0.996
#> GSM49615 2 0.0376 0.996 0.004 0.996
#> GSM49616 2 0.0376 0.996 0.004 0.996
#> GSM49617 2 0.0376 0.996 0.004 0.996
#> GSM49564 1 0.0376 0.981 0.996 0.004
#> GSM49565 1 0.0000 0.985 1.000 0.000
#> GSM49566 1 0.0000 0.985 1.000 0.000
#> GSM49567 1 0.0000 0.985 1.000 0.000
#> GSM49568 1 0.0000 0.985 1.000 0.000
#> GSM49569 1 0.0000 0.985 1.000 0.000
#> GSM49570 2 0.0000 0.998 0.000 1.000
#> GSM49571 2 0.0938 0.988 0.012 0.988
#> GSM49572 1 0.0000 0.985 1.000 0.000
#> GSM49573 2 0.0000 0.998 0.000 1.000
#> GSM49574 1 0.0000 0.985 1.000 0.000
#> GSM49575 1 0.8081 0.677 0.752 0.248
#> GSM49576 1 0.0000 0.985 1.000 0.000
#> GSM49577 1 0.0000 0.985 1.000 0.000
#> GSM49578 1 0.0000 0.985 1.000 0.000
#> GSM49579 1 0.0000 0.985 1.000 0.000
#> GSM49580 1 0.0000 0.985 1.000 0.000
#> GSM49581 1 0.0000 0.985 1.000 0.000
#> GSM49582 1 0.0000 0.985 1.000 0.000
#> GSM49583 2 0.0000 0.998 0.000 1.000
#> GSM49584 1 0.0000 0.985 1.000 0.000
#> GSM49585 1 0.0000 0.985 1.000 0.000
#> GSM49586 1 0.0000 0.985 1.000 0.000
#> GSM49587 1 0.0000 0.985 1.000 0.000
#> GSM49588 1 0.0000 0.985 1.000 0.000
#> GSM49589 1 0.0000 0.985 1.000 0.000
#> GSM49590 1 0.8144 0.670 0.748 0.252
#> GSM49591 1 0.0000 0.985 1.000 0.000
#> GSM49592 1 0.0000 0.985 1.000 0.000
#> GSM49593 1 0.0000 0.985 1.000 0.000
#> GSM49594 1 0.0000 0.985 1.000 0.000
#> GSM49595 1 0.0000 0.985 1.000 0.000
#> GSM49596 1 0.0000 0.985 1.000 0.000
#> GSM49597 2 0.0000 0.998 0.000 1.000
#> GSM49598 1 0.0000 0.985 1.000 0.000
#> GSM49599 1 0.0000 0.985 1.000 0.000
#> GSM49600 1 0.0000 0.985 1.000 0.000
#> GSM49601 1 0.0000 0.985 1.000 0.000
#> GSM49602 1 0.0000 0.985 1.000 0.000
#> GSM49603 1 0.0000 0.985 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM49613 3 0.0000 0.755 0.000 0.000 1.000
#> GSM49604 3 0.6225 0.471 0.000 0.432 0.568
#> GSM49605 2 0.0000 1.000 0.000 1.000 0.000
#> GSM49606 2 0.0000 1.000 0.000 1.000 0.000
#> GSM49607 2 0.0000 1.000 0.000 1.000 0.000
#> GSM49608 2 0.0000 1.000 0.000 1.000 0.000
#> GSM49609 2 0.0000 1.000 0.000 1.000 0.000
#> GSM49610 2 0.0000 1.000 0.000 1.000 0.000
#> GSM49611 2 0.0000 1.000 0.000 1.000 0.000
#> GSM49612 2 0.0000 1.000 0.000 1.000 0.000
#> GSM49614 3 0.0000 0.755 0.000 0.000 1.000
#> GSM49615 3 0.0000 0.755 0.000 0.000 1.000
#> GSM49616 3 0.0000 0.755 0.000 0.000 1.000
#> GSM49617 3 0.0000 0.755 0.000 0.000 1.000
#> GSM49564 1 0.0237 0.994 0.996 0.000 0.004
#> GSM49565 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49566 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49567 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49568 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49569 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49570 3 0.5560 0.631 0.000 0.300 0.700
#> GSM49571 3 0.8645 0.420 0.300 0.132 0.568
#> GSM49572 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49573 3 0.5882 0.588 0.000 0.348 0.652
#> GSM49574 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49575 1 0.2066 0.933 0.940 0.000 0.060
#> GSM49576 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49577 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49578 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49579 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49580 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49581 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49582 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49583 2 0.0000 1.000 0.000 1.000 0.000
#> GSM49584 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49585 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49586 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49587 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49588 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49589 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49590 1 0.0747 0.982 0.984 0.000 0.016
#> GSM49591 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49592 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49593 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49594 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49595 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49596 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49597 3 0.6225 0.471 0.000 0.432 0.568
#> GSM49598 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49599 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49600 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49601 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49602 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49603 1 0.0000 0.997 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM49613 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM49604 4 0.4988 0.756 0.000 0.236 0.036 0.728
#> GSM49605 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM49606 2 0.0188 0.995 0.000 0.996 0.000 0.004
#> GSM49607 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM49608 2 0.0469 0.987 0.000 0.988 0.000 0.012
#> GSM49609 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM49610 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM49611 2 0.0188 0.995 0.000 0.996 0.000 0.004
#> GSM49612 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM49614 3 0.0188 0.995 0.000 0.000 0.996 0.004
#> GSM49615 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM49616 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM49617 3 0.0188 0.995 0.000 0.000 0.996 0.004
#> GSM49564 1 0.5151 0.799 0.760 0.000 0.100 0.140
#> GSM49565 1 0.1398 0.943 0.956 0.000 0.004 0.040
#> GSM49566 1 0.2266 0.929 0.912 0.000 0.004 0.084
#> GSM49567 1 0.1059 0.936 0.972 0.012 0.000 0.016
#> GSM49568 1 0.0336 0.941 0.992 0.000 0.000 0.008
#> GSM49569 1 0.2412 0.927 0.908 0.000 0.008 0.084
#> GSM49570 4 0.4093 0.824 0.000 0.096 0.072 0.832
#> GSM49571 4 0.6809 0.560 0.208 0.084 0.044 0.664
#> GSM49572 1 0.0592 0.940 0.984 0.000 0.000 0.016
#> GSM49573 4 0.3919 0.832 0.000 0.104 0.056 0.840
#> GSM49574 1 0.0592 0.940 0.984 0.000 0.000 0.016
#> GSM49575 1 0.1471 0.933 0.960 0.012 0.004 0.024
#> GSM49576 1 0.5151 0.799 0.760 0.000 0.100 0.140
#> GSM49577 1 0.1635 0.941 0.948 0.008 0.000 0.044
#> GSM49578 1 0.0524 0.942 0.988 0.000 0.004 0.008
#> GSM49579 1 0.2125 0.932 0.920 0.000 0.004 0.076
#> GSM49580 1 0.1004 0.941 0.972 0.000 0.004 0.024
#> GSM49581 1 0.0469 0.941 0.988 0.000 0.000 0.012
#> GSM49582 1 0.0844 0.941 0.980 0.004 0.004 0.012
#> GSM49583 2 0.0188 0.995 0.000 0.996 0.000 0.004
#> GSM49584 1 0.1004 0.941 0.972 0.000 0.004 0.024
#> GSM49585 1 0.0592 0.940 0.984 0.000 0.000 0.016
#> GSM49586 1 0.2222 0.935 0.924 0.016 0.000 0.060
#> GSM49587 1 0.0469 0.941 0.988 0.000 0.000 0.012
#> GSM49588 1 0.0469 0.944 0.988 0.000 0.000 0.012
#> GSM49589 1 0.5199 0.795 0.756 0.000 0.100 0.144
#> GSM49590 1 0.5280 0.780 0.752 0.000 0.124 0.124
#> GSM49591 1 0.0657 0.941 0.984 0.000 0.004 0.012
#> GSM49592 1 0.0524 0.942 0.988 0.000 0.004 0.008
#> GSM49593 1 0.2011 0.933 0.920 0.000 0.000 0.080
#> GSM49594 1 0.1970 0.937 0.932 0.008 0.000 0.060
#> GSM49595 1 0.1970 0.937 0.932 0.008 0.000 0.060
#> GSM49596 1 0.1940 0.933 0.924 0.000 0.000 0.076
#> GSM49597 4 0.4153 0.832 0.000 0.132 0.048 0.820
#> GSM49598 1 0.1743 0.937 0.940 0.000 0.004 0.056
#> GSM49599 1 0.1174 0.934 0.968 0.012 0.000 0.020
#> GSM49600 1 0.1004 0.941 0.972 0.000 0.004 0.024
#> GSM49601 1 0.1792 0.937 0.932 0.000 0.000 0.068
#> GSM49602 1 0.2266 0.929 0.912 0.000 0.004 0.084
#> GSM49603 1 0.2266 0.929 0.912 0.000 0.004 0.084
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM49613 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM49604 4 0.0794 0.963 0.000 0.028 0 0.972 0.000
#> GSM49605 2 0.0000 0.969 0.000 1.000 0 0.000 0.000
#> GSM49606 2 0.0000 0.969 0.000 1.000 0 0.000 0.000
#> GSM49607 2 0.0000 0.969 0.000 1.000 0 0.000 0.000
#> GSM49608 2 0.1671 0.914 0.000 0.924 0 0.076 0.000
#> GSM49609 2 0.0000 0.969 0.000 1.000 0 0.000 0.000
#> GSM49610 2 0.0000 0.969 0.000 1.000 0 0.000 0.000
#> GSM49611 2 0.0000 0.969 0.000 1.000 0 0.000 0.000
#> GSM49612 2 0.0000 0.969 0.000 1.000 0 0.000 0.000
#> GSM49614 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM49615 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM49616 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM49617 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM49564 5 0.0000 0.652 0.000 0.000 0 0.000 1.000
#> GSM49565 1 0.3561 0.633 0.740 0.000 0 0.000 0.260
#> GSM49566 5 0.1908 0.708 0.092 0.000 0 0.000 0.908
#> GSM49567 1 0.2471 0.656 0.864 0.000 0 0.000 0.136
#> GSM49568 5 0.4114 0.569 0.376 0.000 0 0.000 0.624
#> GSM49569 5 0.1908 0.708 0.092 0.000 0 0.000 0.908
#> GSM49570 4 0.0000 0.980 0.000 0.000 0 1.000 0.000
#> GSM49571 1 0.3730 0.156 0.712 0.000 0 0.288 0.000
#> GSM49572 1 0.3336 0.657 0.772 0.000 0 0.000 0.228
#> GSM49573 4 0.0703 0.969 0.024 0.000 0 0.976 0.000
#> GSM49574 1 0.3395 0.653 0.764 0.000 0 0.000 0.236
#> GSM49575 1 0.0162 0.580 0.996 0.000 0 0.000 0.004
#> GSM49576 5 0.0000 0.652 0.000 0.000 0 0.000 1.000
#> GSM49577 1 0.3074 0.664 0.804 0.000 0 0.000 0.196
#> GSM49578 5 0.3932 0.613 0.328 0.000 0 0.000 0.672
#> GSM49579 5 0.1965 0.707 0.096 0.000 0 0.000 0.904
#> GSM49580 5 0.4210 0.518 0.412 0.000 0 0.000 0.588
#> GSM49581 1 0.3752 0.473 0.708 0.000 0 0.000 0.292
#> GSM49582 5 0.4294 0.396 0.468 0.000 0 0.000 0.532
#> GSM49583 2 0.2852 0.804 0.000 0.828 0 0.172 0.000
#> GSM49584 5 0.3999 0.606 0.344 0.000 0 0.000 0.656
#> GSM49585 1 0.4201 0.320 0.592 0.000 0 0.000 0.408
#> GSM49586 1 0.2966 0.670 0.816 0.000 0 0.000 0.184
#> GSM49587 5 0.4273 0.264 0.448 0.000 0 0.000 0.552
#> GSM49588 1 0.4305 -0.183 0.512 0.000 0 0.000 0.488
#> GSM49589 5 0.0000 0.652 0.000 0.000 0 0.000 1.000
#> GSM49590 5 0.0000 0.652 0.000 0.000 0 0.000 1.000
#> GSM49591 5 0.3895 0.620 0.320 0.000 0 0.000 0.680
#> GSM49592 5 0.3913 0.618 0.324 0.000 0 0.000 0.676
#> GSM49593 1 0.4307 0.362 0.504 0.000 0 0.000 0.496
#> GSM49594 1 0.4262 0.493 0.560 0.000 0 0.000 0.440
#> GSM49595 1 0.4268 0.488 0.556 0.000 0 0.000 0.444
#> GSM49596 5 0.2329 0.698 0.124 0.000 0 0.000 0.876
#> GSM49597 4 0.0000 0.980 0.000 0.000 0 1.000 0.000
#> GSM49598 5 0.3480 0.661 0.248 0.000 0 0.000 0.752
#> GSM49599 1 0.1544 0.627 0.932 0.000 0 0.000 0.068
#> GSM49600 5 0.4101 0.577 0.372 0.000 0 0.000 0.628
#> GSM49601 1 0.4249 0.466 0.568 0.000 0 0.000 0.432
#> GSM49602 5 0.1908 0.708 0.092 0.000 0 0.000 0.908
#> GSM49603 5 0.1908 0.708 0.092 0.000 0 0.000 0.908
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM49613 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49604 4 0.1682 0.9269 0.000 0.052 0 0.928 0.000 0.020
#> GSM49605 2 0.0000 0.9352 0.000 1.000 0 0.000 0.000 0.000
#> GSM49606 2 0.0937 0.9369 0.000 0.960 0 0.000 0.000 0.040
#> GSM49607 2 0.0000 0.9352 0.000 1.000 0 0.000 0.000 0.000
#> GSM49608 2 0.1471 0.8957 0.000 0.932 0 0.064 0.000 0.004
#> GSM49609 2 0.0937 0.9369 0.000 0.960 0 0.000 0.000 0.040
#> GSM49610 2 0.0000 0.9352 0.000 1.000 0 0.000 0.000 0.000
#> GSM49611 2 0.0937 0.9369 0.000 0.960 0 0.000 0.000 0.040
#> GSM49612 2 0.0937 0.9369 0.000 0.960 0 0.000 0.000 0.040
#> GSM49614 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49615 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49616 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49617 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49564 5 0.0858 0.5757 0.004 0.000 0 0.000 0.968 0.028
#> GSM49565 1 0.4587 0.4444 0.688 0.000 0 0.000 0.204 0.108
#> GSM49566 5 0.3266 0.4724 0.272 0.000 0 0.000 0.728 0.000
#> GSM49567 6 0.3867 0.3735 0.488 0.000 0 0.000 0.000 0.512
#> GSM49568 1 0.4147 0.4082 0.716 0.000 0 0.000 0.224 0.060
#> GSM49569 5 0.2912 0.5169 0.216 0.000 0 0.000 0.784 0.000
#> GSM49570 4 0.0000 0.9599 0.000 0.000 0 1.000 0.000 0.000
#> GSM49571 6 0.3841 0.0693 0.028 0.000 0 0.256 0.000 0.716
#> GSM49572 1 0.3522 0.3853 0.800 0.000 0 0.000 0.072 0.128
#> GSM49573 4 0.1075 0.9390 0.000 0.000 0 0.952 0.000 0.048
#> GSM49574 1 0.3501 0.4248 0.804 0.000 0 0.000 0.080 0.116
#> GSM49575 6 0.2703 0.4893 0.172 0.000 0 0.004 0.000 0.824
#> GSM49576 5 0.0909 0.5885 0.020 0.000 0 0.000 0.968 0.012
#> GSM49577 1 0.3956 0.2958 0.704 0.000 0 0.000 0.032 0.264
#> GSM49578 1 0.4282 0.4853 0.720 0.000 0 0.000 0.192 0.088
#> GSM49579 5 0.3838 0.1750 0.448 0.000 0 0.000 0.552 0.000
#> GSM49580 1 0.5551 0.2173 0.556 0.000 0 0.000 0.220 0.224
#> GSM49581 6 0.4408 0.1792 0.488 0.000 0 0.000 0.024 0.488
#> GSM49582 1 0.5963 0.0541 0.476 0.000 0 0.004 0.216 0.304
#> GSM49583 2 0.3371 0.5871 0.000 0.708 0 0.292 0.000 0.000
#> GSM49584 1 0.5607 0.2260 0.544 0.000 0 0.000 0.240 0.216
#> GSM49585 1 0.2398 0.5309 0.876 0.000 0 0.000 0.104 0.020
#> GSM49586 6 0.4523 0.1581 0.452 0.000 0 0.000 0.032 0.516
#> GSM49587 1 0.2706 0.5452 0.852 0.000 0 0.000 0.124 0.024
#> GSM49588 1 0.1910 0.5458 0.892 0.000 0 0.000 0.108 0.000
#> GSM49589 5 0.0622 0.5855 0.008 0.000 0 0.000 0.980 0.012
#> GSM49590 5 0.0622 0.5855 0.008 0.000 0 0.000 0.980 0.012
#> GSM49591 1 0.3645 0.4728 0.740 0.000 0 0.000 0.236 0.024
#> GSM49592 1 0.3894 0.5052 0.760 0.000 0 0.000 0.168 0.072
#> GSM49593 1 0.3534 0.3372 0.716 0.000 0 0.000 0.276 0.008
#> GSM49594 1 0.4910 0.3643 0.640 0.000 0 0.000 0.116 0.244
#> GSM49595 1 0.5027 0.4086 0.640 0.000 0 0.000 0.200 0.160
#> GSM49596 1 0.3482 0.2938 0.684 0.000 0 0.000 0.316 0.000
#> GSM49597 4 0.0000 0.9599 0.000 0.000 0 1.000 0.000 0.000
#> GSM49598 5 0.5723 -0.0491 0.408 0.000 0 0.000 0.428 0.164
#> GSM49599 6 0.3789 0.4641 0.416 0.000 0 0.000 0.000 0.584
#> GSM49600 1 0.5747 0.2207 0.500 0.000 0 0.000 0.300 0.200
#> GSM49601 1 0.4804 0.3432 0.656 0.000 0 0.000 0.112 0.232
#> GSM49602 5 0.3860 0.1379 0.472 0.000 0 0.000 0.528 0.000
#> GSM49603 5 0.3838 0.1859 0.448 0.000 0 0.000 0.552 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) cell.type(p) k
#> SD:mclust 54 1.14e-05 4.79e-05 2
#> SD:mclust 51 3.42e-09 3.82e-11 3
#> SD:mclust 54 3.60e-08 3.28e-14 4
#> SD:mclust 44 4.64e-06 3.30e-10 5
#> SD:mclust 27 2.37e-03 2.02e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "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 21168 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.960 0.951 0.978 0.4081 0.609 0.609
#> 3 3 0.944 0.924 0.967 0.3976 0.821 0.706
#> 4 4 0.726 0.842 0.902 0.1439 0.969 0.927
#> 5 5 0.696 0.765 0.832 0.1242 0.819 0.555
#> 6 6 0.875 0.795 0.901 0.0767 0.938 0.755
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
#> GSM49613 1 0.0000 0.971 1.000 0.000
#> GSM49604 2 0.0000 0.993 0.000 1.000
#> GSM49605 2 0.0000 0.993 0.000 1.000
#> GSM49606 2 0.0000 0.993 0.000 1.000
#> GSM49607 2 0.0000 0.993 0.000 1.000
#> GSM49608 2 0.0000 0.993 0.000 1.000
#> GSM49609 2 0.0000 0.993 0.000 1.000
#> GSM49610 2 0.0000 0.993 0.000 1.000
#> GSM49611 2 0.0000 0.993 0.000 1.000
#> GSM49612 2 0.0000 0.993 0.000 1.000
#> GSM49614 1 0.0000 0.971 1.000 0.000
#> GSM49615 1 0.0000 0.971 1.000 0.000
#> GSM49616 1 0.0000 0.971 1.000 0.000
#> GSM49617 1 0.0000 0.971 1.000 0.000
#> GSM49564 1 0.0000 0.971 1.000 0.000
#> GSM49565 1 0.6623 0.797 0.828 0.172
#> GSM49566 1 0.0000 0.971 1.000 0.000
#> GSM49567 1 0.0000 0.971 1.000 0.000
#> GSM49568 1 0.0000 0.971 1.000 0.000
#> GSM49569 1 0.0000 0.971 1.000 0.000
#> GSM49570 2 0.0938 0.984 0.012 0.988
#> GSM49571 2 0.3584 0.923 0.068 0.932
#> GSM49572 1 0.0000 0.971 1.000 0.000
#> GSM49573 2 0.0000 0.993 0.000 1.000
#> GSM49574 1 0.1414 0.956 0.980 0.020
#> GSM49575 1 0.0000 0.971 1.000 0.000
#> GSM49576 1 0.0000 0.971 1.000 0.000
#> GSM49577 1 0.6801 0.787 0.820 0.180
#> GSM49578 1 0.0000 0.971 1.000 0.000
#> GSM49579 1 0.0000 0.971 1.000 0.000
#> GSM49580 1 0.0000 0.971 1.000 0.000
#> GSM49581 1 0.0000 0.971 1.000 0.000
#> GSM49582 1 0.0000 0.971 1.000 0.000
#> GSM49583 2 0.0000 0.993 0.000 1.000
#> GSM49584 1 0.0000 0.971 1.000 0.000
#> GSM49585 1 0.0000 0.971 1.000 0.000
#> GSM49586 1 0.9209 0.526 0.664 0.336
#> GSM49587 1 0.0000 0.971 1.000 0.000
#> GSM49588 1 0.0000 0.971 1.000 0.000
#> GSM49589 1 0.0000 0.971 1.000 0.000
#> GSM49590 1 0.0000 0.971 1.000 0.000
#> GSM49591 1 0.0000 0.971 1.000 0.000
#> GSM49592 1 0.0000 0.971 1.000 0.000
#> GSM49593 1 0.0000 0.971 1.000 0.000
#> GSM49594 1 0.9323 0.502 0.652 0.348
#> GSM49595 1 0.2948 0.928 0.948 0.052
#> GSM49596 1 0.0000 0.971 1.000 0.000
#> GSM49597 2 0.0000 0.993 0.000 1.000
#> GSM49598 1 0.0000 0.971 1.000 0.000
#> GSM49599 1 0.0000 0.971 1.000 0.000
#> GSM49600 1 0.0000 0.971 1.000 0.000
#> GSM49601 1 0.0000 0.971 1.000 0.000
#> GSM49602 1 0.0000 0.971 1.000 0.000
#> GSM49603 1 0.0000 0.971 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM49613 3 0.0424 0.957 0.008 0.000 0.992
#> GSM49604 2 0.0000 0.930 0.000 1.000 0.000
#> GSM49605 2 0.0237 0.931 0.000 0.996 0.004
#> GSM49606 2 0.0237 0.931 0.000 0.996 0.004
#> GSM49607 2 0.0237 0.931 0.000 0.996 0.004
#> GSM49608 2 0.0424 0.929 0.000 0.992 0.008
#> GSM49609 2 0.0000 0.930 0.000 1.000 0.000
#> GSM49610 2 0.0424 0.929 0.000 0.992 0.008
#> GSM49611 2 0.0000 0.930 0.000 1.000 0.000
#> GSM49612 2 0.0000 0.930 0.000 1.000 0.000
#> GSM49614 3 0.0424 0.952 0.000 0.008 0.992
#> GSM49615 3 0.0237 0.957 0.004 0.000 0.996
#> GSM49616 3 0.0237 0.957 0.004 0.000 0.996
#> GSM49617 3 0.0424 0.952 0.000 0.008 0.992
#> GSM49564 3 0.0592 0.955 0.012 0.000 0.988
#> GSM49565 1 0.0661 0.968 0.988 0.008 0.004
#> GSM49566 1 0.1411 0.956 0.964 0.000 0.036
#> GSM49567 1 0.0661 0.968 0.988 0.008 0.004
#> GSM49568 1 0.0237 0.971 0.996 0.000 0.004
#> GSM49569 1 0.1964 0.939 0.944 0.000 0.056
#> GSM49570 2 0.1031 0.918 0.000 0.976 0.024
#> GSM49571 2 0.6520 0.031 0.488 0.508 0.004
#> GSM49572 1 0.0661 0.968 0.988 0.008 0.004
#> GSM49573 2 0.3293 0.825 0.088 0.900 0.012
#> GSM49574 1 0.0661 0.968 0.988 0.008 0.004
#> GSM49575 1 0.0661 0.968 0.988 0.008 0.004
#> GSM49576 1 0.4931 0.710 0.768 0.000 0.232
#> GSM49577 1 0.0983 0.964 0.980 0.016 0.004
#> GSM49578 1 0.0000 0.971 1.000 0.000 0.000
#> GSM49579 1 0.0237 0.971 0.996 0.000 0.004
#> GSM49580 1 0.0747 0.967 0.984 0.000 0.016
#> GSM49581 1 0.0000 0.971 1.000 0.000 0.000
#> GSM49582 1 0.0237 0.971 0.996 0.000 0.004
#> GSM49583 2 0.0000 0.930 0.000 1.000 0.000
#> GSM49584 1 0.1031 0.963 0.976 0.000 0.024
#> GSM49585 1 0.0000 0.971 1.000 0.000 0.000
#> GSM49586 1 0.4351 0.799 0.828 0.168 0.004
#> GSM49587 1 0.0000 0.971 1.000 0.000 0.000
#> GSM49588 1 0.0237 0.971 0.996 0.000 0.004
#> GSM49589 3 0.3941 0.794 0.156 0.000 0.844
#> GSM49590 3 0.1643 0.931 0.044 0.000 0.956
#> GSM49591 1 0.0237 0.970 0.996 0.000 0.004
#> GSM49592 1 0.0000 0.971 1.000 0.000 0.000
#> GSM49593 1 0.1163 0.961 0.972 0.000 0.028
#> GSM49594 1 0.3112 0.888 0.900 0.096 0.004
#> GSM49595 1 0.0661 0.968 0.988 0.008 0.004
#> GSM49596 1 0.0237 0.971 0.996 0.000 0.004
#> GSM49597 2 0.0424 0.929 0.000 0.992 0.008
#> GSM49598 1 0.0892 0.965 0.980 0.000 0.020
#> GSM49599 1 0.0661 0.968 0.988 0.008 0.004
#> GSM49600 1 0.1411 0.956 0.964 0.000 0.036
#> GSM49601 1 0.0237 0.971 0.996 0.000 0.004
#> GSM49602 1 0.0424 0.970 0.992 0.000 0.008
#> GSM49603 1 0.1163 0.961 0.972 0.000 0.028
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM49613 3 0.0188 0.9368 0.000 0.000 0.996 0.004
#> GSM49604 4 0.4040 0.7346 0.000 0.248 0.000 0.752
#> GSM49605 2 0.0336 0.9903 0.000 0.992 0.000 0.008
#> GSM49606 2 0.0000 0.9899 0.000 1.000 0.000 0.000
#> GSM49607 2 0.0592 0.9862 0.000 0.984 0.000 0.016
#> GSM49608 2 0.0336 0.9903 0.000 0.992 0.000 0.008
#> GSM49609 2 0.0000 0.9899 0.000 1.000 0.000 0.000
#> GSM49610 2 0.0469 0.9889 0.000 0.988 0.000 0.012
#> GSM49611 2 0.0000 0.9899 0.000 1.000 0.000 0.000
#> GSM49612 2 0.0000 0.9899 0.000 1.000 0.000 0.000
#> GSM49614 3 0.2216 0.8726 0.000 0.000 0.908 0.092
#> GSM49615 3 0.0000 0.9368 0.000 0.000 1.000 0.000
#> GSM49616 3 0.0817 0.9307 0.000 0.000 0.976 0.024
#> GSM49617 3 0.1557 0.9104 0.000 0.000 0.944 0.056
#> GSM49564 3 0.0469 0.9345 0.000 0.000 0.988 0.012
#> GSM49565 1 0.1059 0.8733 0.972 0.012 0.000 0.016
#> GSM49566 1 0.4227 0.8211 0.820 0.000 0.120 0.060
#> GSM49567 1 0.1792 0.8564 0.932 0.000 0.000 0.068
#> GSM49568 1 0.1305 0.8688 0.960 0.000 0.004 0.036
#> GSM49569 1 0.4046 0.8247 0.828 0.000 0.124 0.048
#> GSM49570 4 0.2329 0.8319 0.000 0.072 0.012 0.916
#> GSM49571 4 0.3427 0.7594 0.112 0.028 0.000 0.860
#> GSM49572 1 0.0336 0.8724 0.992 0.000 0.000 0.008
#> GSM49573 4 0.2036 0.8239 0.032 0.032 0.000 0.936
#> GSM49574 1 0.0817 0.8720 0.976 0.000 0.000 0.024
#> GSM49575 1 0.5000 0.0449 0.504 0.000 0.000 0.496
#> GSM49576 1 0.5721 0.6428 0.660 0.000 0.284 0.056
#> GSM49577 1 0.1209 0.8714 0.964 0.004 0.000 0.032
#> GSM49578 1 0.1118 0.8671 0.964 0.000 0.000 0.036
#> GSM49579 1 0.3885 0.8394 0.844 0.000 0.064 0.092
#> GSM49580 1 0.1978 0.8584 0.928 0.000 0.004 0.068
#> GSM49581 1 0.2345 0.8365 0.900 0.000 0.000 0.100
#> GSM49582 1 0.1637 0.8599 0.940 0.000 0.000 0.060
#> GSM49583 2 0.0921 0.9754 0.000 0.972 0.000 0.028
#> GSM49584 1 0.1706 0.8723 0.948 0.000 0.016 0.036
#> GSM49585 1 0.0376 0.8730 0.992 0.000 0.004 0.004
#> GSM49586 1 0.5769 0.4221 0.588 0.036 0.000 0.376
#> GSM49587 1 0.1059 0.8737 0.972 0.000 0.012 0.016
#> GSM49588 1 0.1724 0.8708 0.948 0.000 0.032 0.020
#> GSM49589 3 0.1975 0.8860 0.048 0.000 0.936 0.016
#> GSM49590 3 0.2500 0.8736 0.040 0.000 0.916 0.044
#> GSM49591 1 0.0707 0.8711 0.980 0.000 0.000 0.020
#> GSM49592 1 0.0921 0.8692 0.972 0.000 0.000 0.028
#> GSM49593 1 0.3840 0.8337 0.844 0.000 0.104 0.052
#> GSM49594 1 0.5180 0.7195 0.740 0.196 0.000 0.064
#> GSM49595 1 0.4155 0.8279 0.840 0.084 0.008 0.068
#> GSM49596 1 0.2411 0.8624 0.920 0.000 0.040 0.040
#> GSM49597 4 0.4198 0.7387 0.004 0.224 0.004 0.768
#> GSM49598 1 0.2589 0.8578 0.884 0.000 0.000 0.116
#> GSM49599 1 0.4605 0.5165 0.664 0.000 0.000 0.336
#> GSM49600 1 0.1733 0.8744 0.948 0.000 0.028 0.024
#> GSM49601 1 0.4147 0.8330 0.840 0.008 0.088 0.064
#> GSM49602 1 0.4469 0.8192 0.808 0.000 0.080 0.112
#> GSM49603 1 0.4786 0.8057 0.788 0.000 0.104 0.108
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM49613 3 0.0290 0.9396 0.000 0.000 0.992 0.008 0.000
#> GSM49604 4 0.2388 0.8205 0.000 0.072 0.000 0.900 0.028
#> GSM49605 2 0.0162 0.9308 0.000 0.996 0.000 0.000 0.004
#> GSM49606 2 0.0000 0.9309 0.000 1.000 0.000 0.000 0.000
#> GSM49607 2 0.2563 0.8749 0.000 0.872 0.000 0.008 0.120
#> GSM49608 2 0.1704 0.9071 0.000 0.928 0.000 0.004 0.068
#> GSM49609 2 0.1270 0.9116 0.000 0.948 0.000 0.000 0.052
#> GSM49610 2 0.0324 0.9309 0.000 0.992 0.000 0.004 0.004
#> GSM49611 2 0.1043 0.9198 0.000 0.960 0.000 0.000 0.040
#> GSM49612 2 0.0609 0.9279 0.000 0.980 0.000 0.000 0.020
#> GSM49614 3 0.1211 0.9169 0.000 0.000 0.960 0.016 0.024
#> GSM49615 3 0.0162 0.9399 0.000 0.000 0.996 0.004 0.000
#> GSM49616 3 0.0162 0.9407 0.000 0.000 0.996 0.004 0.000
#> GSM49617 3 0.0162 0.9407 0.000 0.000 0.996 0.004 0.000
#> GSM49564 3 0.0000 0.9408 0.000 0.000 1.000 0.000 0.000
#> GSM49565 1 0.0609 0.8901 0.980 0.000 0.000 0.000 0.020
#> GSM49566 5 0.4821 0.5300 0.464 0.000 0.020 0.000 0.516
#> GSM49567 1 0.1270 0.8664 0.948 0.000 0.000 0.000 0.052
#> GSM49568 1 0.0404 0.8914 0.988 0.000 0.000 0.000 0.012
#> GSM49569 5 0.5201 0.6526 0.424 0.000 0.044 0.000 0.532
#> GSM49570 4 0.2233 0.8199 0.000 0.000 0.004 0.892 0.104
#> GSM49571 4 0.2228 0.8187 0.012 0.000 0.004 0.908 0.076
#> GSM49572 1 0.0880 0.8834 0.968 0.000 0.000 0.000 0.032
#> GSM49573 4 0.0579 0.8352 0.008 0.000 0.000 0.984 0.008
#> GSM49574 1 0.0000 0.8926 1.000 0.000 0.000 0.000 0.000
#> GSM49575 1 0.3513 0.6744 0.800 0.000 0.000 0.180 0.020
#> GSM49576 5 0.6008 0.7103 0.292 0.000 0.148 0.000 0.560
#> GSM49577 1 0.4387 0.1916 0.640 0.012 0.000 0.000 0.348
#> GSM49578 1 0.0162 0.8919 0.996 0.000 0.000 0.000 0.004
#> GSM49579 5 0.4420 0.6107 0.448 0.000 0.004 0.000 0.548
#> GSM49580 1 0.0898 0.8899 0.972 0.000 0.000 0.008 0.020
#> GSM49581 1 0.0510 0.8915 0.984 0.000 0.000 0.000 0.016
#> GSM49582 1 0.0290 0.8909 0.992 0.000 0.000 0.000 0.008
#> GSM49583 2 0.4240 0.7400 0.004 0.732 0.000 0.024 0.240
#> GSM49584 1 0.0854 0.8906 0.976 0.000 0.008 0.004 0.012
#> GSM49585 1 0.2408 0.8154 0.892 0.000 0.004 0.008 0.096
#> GSM49586 5 0.4826 -0.2298 0.020 0.000 0.000 0.472 0.508
#> GSM49587 1 0.0000 0.8926 1.000 0.000 0.000 0.000 0.000
#> GSM49588 1 0.1557 0.8614 0.940 0.000 0.008 0.000 0.052
#> GSM49589 3 0.3430 0.6764 0.004 0.000 0.776 0.000 0.220
#> GSM49590 5 0.4425 0.0439 0.004 0.000 0.452 0.000 0.544
#> GSM49591 1 0.0609 0.8902 0.980 0.000 0.000 0.000 0.020
#> GSM49592 1 0.0671 0.8898 0.980 0.000 0.000 0.004 0.016
#> GSM49593 5 0.4551 0.7213 0.368 0.000 0.016 0.000 0.616
#> GSM49594 5 0.4930 0.7314 0.244 0.072 0.000 0.000 0.684
#> GSM49595 5 0.4437 0.7453 0.316 0.020 0.000 0.000 0.664
#> GSM49596 1 0.4251 -0.0983 0.624 0.000 0.004 0.000 0.372
#> GSM49597 4 0.5906 0.5331 0.000 0.104 0.000 0.492 0.404
#> GSM49598 5 0.4675 0.7021 0.380 0.000 0.000 0.020 0.600
#> GSM49599 1 0.2570 0.8268 0.888 0.000 0.000 0.084 0.028
#> GSM49600 1 0.1569 0.8676 0.944 0.000 0.008 0.004 0.044
#> GSM49601 5 0.5079 0.7247 0.232 0.028 0.040 0.000 0.700
#> GSM49602 5 0.4309 0.7487 0.308 0.000 0.016 0.000 0.676
#> GSM49603 5 0.5059 0.7329 0.224 0.000 0.052 0.020 0.704
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM49613 3 0.0405 0.9036 0.000 0.000 0.988 0.000 0.008 0.004
#> GSM49604 4 0.3313 0.6178 0.000 0.124 0.000 0.816 0.000 0.060
#> GSM49605 2 0.1663 0.8511 0.000 0.912 0.000 0.000 0.000 0.088
#> GSM49606 2 0.0937 0.8730 0.000 0.960 0.000 0.000 0.000 0.040
#> GSM49607 2 0.2941 0.6638 0.000 0.780 0.000 0.000 0.000 0.220
#> GSM49608 2 0.2355 0.8211 0.000 0.876 0.008 0.000 0.004 0.112
#> GSM49609 2 0.1806 0.8418 0.000 0.928 0.000 0.020 0.008 0.044
#> GSM49610 2 0.0146 0.8777 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM49611 2 0.1196 0.8604 0.000 0.952 0.000 0.008 0.000 0.040
#> GSM49612 2 0.0837 0.8725 0.000 0.972 0.000 0.004 0.004 0.020
#> GSM49614 3 0.1152 0.8721 0.000 0.000 0.952 0.004 0.000 0.044
#> GSM49615 3 0.0260 0.9046 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM49616 3 0.0260 0.9046 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM49617 3 0.0405 0.9006 0.000 0.000 0.988 0.000 0.004 0.008
#> GSM49564 3 0.0603 0.8999 0.000 0.000 0.980 0.000 0.016 0.004
#> GSM49565 1 0.0806 0.9572 0.972 0.000 0.000 0.000 0.008 0.020
#> GSM49566 5 0.3718 0.7389 0.084 0.000 0.000 0.000 0.784 0.132
#> GSM49567 1 0.0603 0.9604 0.980 0.000 0.000 0.004 0.000 0.016
#> GSM49568 1 0.0000 0.9628 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM49569 5 0.1737 0.8552 0.040 0.000 0.008 0.000 0.932 0.020
#> GSM49570 4 0.3979 0.4592 0.000 0.000 0.004 0.540 0.000 0.456
#> GSM49571 4 0.0551 0.6608 0.004 0.004 0.000 0.984 0.008 0.000
#> GSM49572 1 0.0363 0.9623 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM49573 4 0.3221 0.6493 0.004 0.000 0.004 0.772 0.000 0.220
#> GSM49574 1 0.0291 0.9629 0.992 0.000 0.004 0.000 0.000 0.004
#> GSM49575 1 0.2632 0.8254 0.832 0.000 0.000 0.164 0.000 0.004
#> GSM49576 5 0.0972 0.8590 0.008 0.000 0.000 0.000 0.964 0.028
#> GSM49577 5 0.6465 0.0963 0.336 0.024 0.000 0.000 0.412 0.228
#> GSM49578 1 0.0000 0.9628 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM49579 5 0.2106 0.8380 0.032 0.000 0.000 0.000 0.904 0.064
#> GSM49580 1 0.0653 0.9616 0.980 0.000 0.000 0.004 0.004 0.012
#> GSM49581 1 0.0000 0.9628 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM49582 1 0.0146 0.9628 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM49583 6 0.3999 -0.1785 0.000 0.496 0.000 0.000 0.004 0.500
#> GSM49584 1 0.0405 0.9628 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM49585 1 0.3282 0.8592 0.844 0.000 0.004 0.096 0.020 0.036
#> GSM49586 4 0.4561 0.4160 0.000 0.016 0.004 0.676 0.272 0.032
#> GSM49587 1 0.0260 0.9630 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM49588 1 0.2051 0.9332 0.924 0.000 0.012 0.020 0.032 0.012
#> GSM49589 3 0.3728 0.4526 0.000 0.000 0.652 0.004 0.344 0.000
#> GSM49590 5 0.1334 0.8522 0.000 0.000 0.032 0.000 0.948 0.020
#> GSM49591 1 0.1116 0.9510 0.960 0.000 0.000 0.028 0.004 0.008
#> GSM49592 1 0.1478 0.9444 0.944 0.000 0.004 0.032 0.000 0.020
#> GSM49593 5 0.0870 0.8599 0.012 0.000 0.012 0.004 0.972 0.000
#> GSM49594 5 0.0692 0.8574 0.000 0.004 0.000 0.000 0.976 0.020
#> GSM49595 5 0.0665 0.8603 0.008 0.000 0.000 0.008 0.980 0.004
#> GSM49596 5 0.3565 0.5888 0.276 0.000 0.000 0.004 0.716 0.004
#> GSM49597 6 0.3089 0.1219 0.000 0.040 0.000 0.024 0.080 0.856
#> GSM49598 5 0.1440 0.8568 0.032 0.000 0.004 0.012 0.948 0.004
#> GSM49599 1 0.0692 0.9590 0.976 0.000 0.000 0.020 0.000 0.004
#> GSM49600 1 0.1621 0.9287 0.936 0.000 0.008 0.004 0.048 0.004
#> GSM49601 5 0.4324 0.7217 0.008 0.020 0.036 0.088 0.800 0.048
#> GSM49602 5 0.0436 0.8590 0.004 0.000 0.000 0.004 0.988 0.004
#> GSM49603 5 0.1129 0.8543 0.004 0.000 0.012 0.012 0.964 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) cell.type(p) k
#> SD:NMF 54 2.33e-06 1.17e-03 2
#> SD:NMF 53 4.58e-07 6.93e-09 3
#> SD:NMF 52 9.58e-08 3.47e-09 4
#> SD:NMF 50 7.15e-07 8.69e-09 5
#> SD:NMF 48 7.29e-08 3.70e-10 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21168 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.866 0.921 0.958 0.3676 0.628 0.628
#> 3 3 0.870 0.914 0.968 0.3520 0.874 0.800
#> 4 4 0.991 0.927 0.973 0.0937 0.948 0.896
#> 5 5 0.803 0.844 0.907 0.0797 0.994 0.988
#> 6 6 0.589 0.733 0.815 0.0989 0.971 0.935
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM49613 1 0.2778 0.929 0.952 0.048
#> GSM49604 2 0.6048 0.891 0.148 0.852
#> GSM49605 2 0.2778 0.950 0.048 0.952
#> GSM49606 2 0.2778 0.950 0.048 0.952
#> GSM49607 2 0.2778 0.950 0.048 0.952
#> GSM49608 2 0.2778 0.950 0.048 0.952
#> GSM49609 2 0.2778 0.950 0.048 0.952
#> GSM49610 2 0.2778 0.950 0.048 0.952
#> GSM49611 2 0.2778 0.950 0.048 0.952
#> GSM49612 2 0.2778 0.950 0.048 0.952
#> GSM49614 1 0.2778 0.929 0.952 0.048
#> GSM49615 1 0.2778 0.929 0.952 0.048
#> GSM49616 1 0.2778 0.929 0.952 0.048
#> GSM49617 1 0.2778 0.929 0.952 0.048
#> GSM49564 1 0.0000 0.968 1.000 0.000
#> GSM49565 1 0.0000 0.968 1.000 0.000
#> GSM49566 1 0.0000 0.968 1.000 0.000
#> GSM49567 1 0.0000 0.968 1.000 0.000
#> GSM49568 1 0.0000 0.968 1.000 0.000
#> GSM49569 1 0.0000 0.968 1.000 0.000
#> GSM49570 2 0.7674 0.807 0.224 0.776
#> GSM49571 1 0.9996 -0.129 0.512 0.488
#> GSM49572 1 0.0000 0.968 1.000 0.000
#> GSM49573 2 0.7674 0.807 0.224 0.776
#> GSM49574 1 0.0000 0.968 1.000 0.000
#> GSM49575 1 0.0000 0.968 1.000 0.000
#> GSM49576 1 0.0000 0.968 1.000 0.000
#> GSM49577 1 0.0000 0.968 1.000 0.000
#> GSM49578 1 0.0000 0.968 1.000 0.000
#> GSM49579 1 0.0000 0.968 1.000 0.000
#> GSM49580 1 0.0000 0.968 1.000 0.000
#> GSM49581 1 0.0000 0.968 1.000 0.000
#> GSM49582 1 0.0000 0.968 1.000 0.000
#> GSM49583 2 0.2778 0.950 0.048 0.952
#> GSM49584 1 0.0000 0.968 1.000 0.000
#> GSM49585 1 0.0000 0.968 1.000 0.000
#> GSM49586 1 0.9460 0.331 0.636 0.364
#> GSM49587 1 0.0000 0.968 1.000 0.000
#> GSM49588 1 0.0000 0.968 1.000 0.000
#> GSM49589 1 0.0000 0.968 1.000 0.000
#> GSM49590 1 0.0000 0.968 1.000 0.000
#> GSM49591 1 0.0000 0.968 1.000 0.000
#> GSM49592 1 0.0000 0.968 1.000 0.000
#> GSM49593 1 0.0000 0.968 1.000 0.000
#> GSM49594 1 0.0938 0.958 0.988 0.012
#> GSM49595 1 0.0938 0.958 0.988 0.012
#> GSM49596 1 0.0000 0.968 1.000 0.000
#> GSM49597 2 0.5842 0.897 0.140 0.860
#> GSM49598 1 0.0000 0.968 1.000 0.000
#> GSM49599 1 0.0000 0.968 1.000 0.000
#> GSM49600 1 0.0000 0.968 1.000 0.000
#> GSM49601 1 0.0000 0.968 1.000 0.000
#> GSM49602 1 0.0000 0.968 1.000 0.000
#> GSM49603 1 0.0000 0.968 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM49613 3 0.0747 1.0000 0.016 0.000 0.984
#> GSM49604 2 0.4128 0.7969 0.132 0.856 0.012
#> GSM49605 2 0.0000 0.8962 0.000 1.000 0.000
#> GSM49606 2 0.0000 0.8962 0.000 1.000 0.000
#> GSM49607 2 0.0000 0.8962 0.000 1.000 0.000
#> GSM49608 2 0.0000 0.8962 0.000 1.000 0.000
#> GSM49609 2 0.0000 0.8962 0.000 1.000 0.000
#> GSM49610 2 0.0000 0.8962 0.000 1.000 0.000
#> GSM49611 2 0.0000 0.8962 0.000 1.000 0.000
#> GSM49612 2 0.0000 0.8962 0.000 1.000 0.000
#> GSM49614 3 0.0747 1.0000 0.016 0.000 0.984
#> GSM49615 3 0.0747 1.0000 0.016 0.000 0.984
#> GSM49616 3 0.0747 1.0000 0.016 0.000 0.984
#> GSM49617 3 0.0747 1.0000 0.016 0.000 0.984
#> GSM49564 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49565 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49566 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49567 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49568 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49569 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49570 2 0.5551 0.6844 0.224 0.760 0.016
#> GSM49571 1 0.6819 -0.0567 0.512 0.476 0.012
#> GSM49572 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49573 2 0.5551 0.6844 0.224 0.760 0.016
#> GSM49574 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49575 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49576 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49577 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49578 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49579 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49580 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49581 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49582 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49583 2 0.0661 0.8915 0.008 0.988 0.004
#> GSM49584 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49585 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49586 1 0.6318 0.3689 0.636 0.356 0.008
#> GSM49587 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49588 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49589 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49590 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49591 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49592 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49593 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49594 1 0.0661 0.9613 0.988 0.008 0.004
#> GSM49595 1 0.0661 0.9613 0.988 0.008 0.004
#> GSM49596 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49597 2 0.4261 0.7889 0.140 0.848 0.012
#> GSM49598 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49599 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49600 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49601 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49602 1 0.0000 0.9721 1.000 0.000 0.000
#> GSM49603 1 0.0000 0.9721 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM49613 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM49604 4 0.4331 0.505 0.000 0.288 0 0.712
#> GSM49605 2 0.0000 0.996 0.000 1.000 0 0.000
#> GSM49606 2 0.0000 0.996 0.000 1.000 0 0.000
#> GSM49607 2 0.0000 0.996 0.000 1.000 0 0.000
#> GSM49608 2 0.0000 0.996 0.000 1.000 0 0.000
#> GSM49609 2 0.0000 0.996 0.000 1.000 0 0.000
#> GSM49610 2 0.0000 0.996 0.000 1.000 0 0.000
#> GSM49611 2 0.0000 0.996 0.000 1.000 0 0.000
#> GSM49612 2 0.0000 0.996 0.000 1.000 0 0.000
#> GSM49614 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM49615 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM49616 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM49617 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM49564 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49565 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49566 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49567 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49568 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49569 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49570 4 0.0000 0.615 0.000 0.000 0 1.000
#> GSM49571 4 0.5172 0.286 0.404 0.008 0 0.588
#> GSM49572 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49573 4 0.0000 0.615 0.000 0.000 0 1.000
#> GSM49574 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49575 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49576 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49577 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49578 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49579 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49580 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49581 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49582 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49583 2 0.0921 0.969 0.000 0.972 0 0.028
#> GSM49584 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49585 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49586 1 0.5212 0.128 0.572 0.008 0 0.420
#> GSM49587 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49588 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49589 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49590 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49591 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49592 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49593 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49594 1 0.0469 0.973 0.988 0.000 0 0.012
#> GSM49595 1 0.0469 0.973 0.988 0.000 0 0.012
#> GSM49596 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49597 4 0.4277 0.493 0.000 0.280 0 0.720
#> GSM49598 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49599 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49600 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49601 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49602 1 0.0000 0.985 1.000 0.000 0 0.000
#> GSM49603 1 0.0000 0.985 1.000 0.000 0 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM49613 3 0.000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM49604 4 0.507 0.33668 0.000 0.168 0 0.700 0.132
#> GSM49605 2 0.141 0.94902 0.000 0.940 0 0.000 0.060
#> GSM49606 2 0.141 0.94902 0.000 0.940 0 0.000 0.060
#> GSM49607 2 0.141 0.94902 0.000 0.940 0 0.000 0.060
#> GSM49608 2 0.154 0.94367 0.000 0.932 0 0.000 0.068
#> GSM49609 2 0.000 0.95107 0.000 1.000 0 0.000 0.000
#> GSM49610 2 0.000 0.95107 0.000 1.000 0 0.000 0.000
#> GSM49611 2 0.000 0.95107 0.000 1.000 0 0.000 0.000
#> GSM49612 2 0.000 0.95107 0.000 1.000 0 0.000 0.000
#> GSM49614 3 0.000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM49615 3 0.000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM49616 3 0.000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM49617 3 0.000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM49564 1 0.185 0.90568 0.912 0.000 0 0.000 0.088
#> GSM49565 1 0.167 0.90920 0.924 0.000 0 0.000 0.076
#> GSM49566 1 0.185 0.90568 0.912 0.000 0 0.000 0.088
#> GSM49567 1 0.127 0.91936 0.948 0.000 0 0.000 0.052
#> GSM49568 1 0.161 0.91104 0.928 0.000 0 0.000 0.072
#> GSM49569 1 0.179 0.90737 0.916 0.000 0 0.000 0.084
#> GSM49570 4 0.120 0.54599 0.000 0.000 0 0.952 0.048
#> GSM49571 4 0.578 0.21822 0.332 0.008 0 0.576 0.084
#> GSM49572 1 0.112 0.91927 0.956 0.000 0 0.000 0.044
#> GSM49573 4 0.029 0.55074 0.000 0.000 0 0.992 0.008
#> GSM49574 1 0.173 0.90523 0.920 0.000 0 0.000 0.080
#> GSM49575 1 0.173 0.90523 0.920 0.000 0 0.000 0.080
#> GSM49576 1 0.185 0.90568 0.912 0.000 0 0.000 0.088
#> GSM49577 1 0.173 0.90841 0.920 0.000 0 0.000 0.080
#> GSM49578 1 0.173 0.90523 0.920 0.000 0 0.000 0.080
#> GSM49579 1 0.134 0.91803 0.944 0.000 0 0.000 0.056
#> GSM49580 1 0.120 0.91856 0.952 0.000 0 0.000 0.048
#> GSM49581 1 0.112 0.91895 0.956 0.000 0 0.000 0.044
#> GSM49582 1 0.173 0.90523 0.920 0.000 0 0.000 0.080
#> GSM49583 5 0.367 0.00000 0.000 0.236 0 0.008 0.756
#> GSM49584 1 0.127 0.92126 0.948 0.000 0 0.000 0.052
#> GSM49585 1 0.127 0.92141 0.948 0.000 0 0.000 0.052
#> GSM49586 1 0.596 -0.00109 0.500 0.008 0 0.408 0.084
#> GSM49587 1 0.134 0.91575 0.944 0.000 0 0.000 0.056
#> GSM49588 1 0.134 0.92102 0.944 0.000 0 0.000 0.056
#> GSM49589 1 0.134 0.91672 0.944 0.000 0 0.000 0.056
#> GSM49590 1 0.185 0.90568 0.912 0.000 0 0.000 0.088
#> GSM49591 1 0.167 0.90723 0.924 0.000 0 0.000 0.076
#> GSM49592 1 0.173 0.90523 0.920 0.000 0 0.000 0.080
#> GSM49593 1 0.179 0.90708 0.916 0.000 0 0.000 0.084
#> GSM49594 1 0.179 0.90290 0.916 0.000 0 0.000 0.084
#> GSM49595 1 0.179 0.90290 0.916 0.000 0 0.000 0.084
#> GSM49596 1 0.179 0.90708 0.916 0.000 0 0.000 0.084
#> GSM49597 4 0.402 0.32792 0.000 0.000 0 0.652 0.348
#> GSM49598 1 0.173 0.90898 0.920 0.000 0 0.000 0.080
#> GSM49599 1 0.161 0.91401 0.928 0.000 0 0.000 0.072
#> GSM49600 1 0.112 0.91895 0.956 0.000 0 0.000 0.044
#> GSM49601 1 0.120 0.92210 0.952 0.000 0 0.000 0.048
#> GSM49602 1 0.154 0.91280 0.932 0.000 0 0.000 0.068
#> GSM49603 1 0.154 0.91280 0.932 0.000 0 0.000 0.068
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM49613 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49604 5 0.5590 -0.421 0.000 0.184 0 0.196 0.604 0.016
#> GSM49605 2 0.0146 0.830 0.000 0.996 0 0.000 0.004 0.000
#> GSM49606 2 0.0000 0.831 0.000 1.000 0 0.000 0.000 0.000
#> GSM49607 2 0.0146 0.830 0.000 0.996 0 0.000 0.004 0.000
#> GSM49608 2 0.0363 0.824 0.000 0.988 0 0.000 0.012 0.000
#> GSM49609 2 0.3394 0.841 0.000 0.776 0 0.000 0.200 0.024
#> GSM49610 2 0.3394 0.841 0.000 0.776 0 0.000 0.200 0.024
#> GSM49611 2 0.3394 0.841 0.000 0.776 0 0.000 0.200 0.024
#> GSM49612 2 0.3394 0.841 0.000 0.776 0 0.000 0.200 0.024
#> GSM49614 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49615 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49616 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49617 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49564 1 0.3309 0.700 0.720 0.000 0 0.000 0.000 0.280
#> GSM49565 1 0.2473 0.790 0.856 0.000 0 0.000 0.008 0.136
#> GSM49566 1 0.3221 0.710 0.736 0.000 0 0.000 0.000 0.264
#> GSM49567 1 0.1858 0.805 0.904 0.000 0 0.000 0.004 0.092
#> GSM49568 1 0.2362 0.777 0.860 0.000 0 0.000 0.004 0.136
#> GSM49569 1 0.3023 0.749 0.768 0.000 0 0.000 0.000 0.232
#> GSM49570 4 0.1141 0.564 0.000 0.000 0 0.948 0.052 0.000
#> GSM49571 5 0.6362 0.377 0.236 0.000 0 0.084 0.552 0.128
#> GSM49572 1 0.1910 0.791 0.892 0.000 0 0.000 0.000 0.108
#> GSM49573 4 0.4109 0.419 0.000 0.000 0 0.576 0.412 0.012
#> GSM49574 1 0.2595 0.762 0.836 0.000 0 0.000 0.004 0.160
#> GSM49575 1 0.2980 0.731 0.800 0.000 0 0.000 0.008 0.192
#> GSM49576 1 0.3023 0.739 0.768 0.000 0 0.000 0.000 0.232
#> GSM49577 1 0.2664 0.751 0.816 0.000 0 0.000 0.000 0.184
#> GSM49578 1 0.2558 0.764 0.840 0.000 0 0.000 0.004 0.156
#> GSM49579 1 0.2762 0.780 0.804 0.000 0 0.000 0.000 0.196
#> GSM49580 1 0.0790 0.809 0.968 0.000 0 0.000 0.000 0.032
#> GSM49581 1 0.0790 0.809 0.968 0.000 0 0.000 0.000 0.032
#> GSM49582 1 0.2558 0.764 0.840 0.000 0 0.000 0.004 0.156
#> GSM49583 6 0.6515 0.000 0.000 0.220 0 0.052 0.224 0.504
#> GSM49584 1 0.1556 0.806 0.920 0.000 0 0.000 0.000 0.080
#> GSM49585 1 0.2664 0.804 0.848 0.000 0 0.000 0.016 0.136
#> GSM49586 5 0.6115 0.386 0.376 0.000 0 0.020 0.448 0.156
#> GSM49587 1 0.2178 0.782 0.868 0.000 0 0.000 0.000 0.132
#> GSM49588 1 0.2513 0.807 0.852 0.000 0 0.000 0.008 0.140
#> GSM49589 1 0.2932 0.781 0.820 0.000 0 0.000 0.016 0.164
#> GSM49590 1 0.3050 0.739 0.764 0.000 0 0.000 0.000 0.236
#> GSM49591 1 0.2558 0.765 0.840 0.000 0 0.000 0.004 0.156
#> GSM49592 1 0.2768 0.763 0.832 0.000 0 0.000 0.012 0.156
#> GSM49593 1 0.2854 0.758 0.792 0.000 0 0.000 0.000 0.208
#> GSM49594 1 0.3445 0.778 0.796 0.000 0 0.000 0.048 0.156
#> GSM49595 1 0.3445 0.778 0.796 0.000 0 0.000 0.048 0.156
#> GSM49596 1 0.2854 0.758 0.792 0.000 0 0.000 0.000 0.208
#> GSM49597 4 0.4447 0.335 0.000 0.020 0 0.744 0.092 0.144
#> GSM49598 1 0.2003 0.794 0.884 0.000 0 0.000 0.000 0.116
#> GSM49599 1 0.2632 0.755 0.832 0.000 0 0.000 0.004 0.164
#> GSM49600 1 0.1610 0.805 0.916 0.000 0 0.000 0.000 0.084
#> GSM49601 1 0.2536 0.806 0.864 0.000 0 0.000 0.020 0.116
#> GSM49602 1 0.3133 0.757 0.780 0.000 0 0.000 0.008 0.212
#> GSM49603 1 0.3133 0.757 0.780 0.000 0 0.000 0.008 0.212
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) cell.type(p) k
#> CV:hclust 52 1.08e-06 8.91e-04 2
#> CV:hclust 52 4.99e-07 3.05e-13 3
#> CV:hclust 51 7.28e-08 2.59e-13 4
#> CV:hclust 49 1.78e-09 2.49e-13 5
#> CV:hclust 48 2.78e-09 5.08e-13 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21168 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.547 0.958 0.937 0.3373 0.628 0.628
#> 3 3 0.869 0.937 0.946 0.4867 0.874 0.800
#> 4 4 0.723 0.702 0.699 0.2784 0.767 0.538
#> 5 5 0.671 0.894 0.877 0.1461 0.882 0.628
#> 6 6 0.760 0.736 0.849 0.0687 0.988 0.951
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM49613 1 0.689 0.785 0.816 0.184
#> GSM49604 2 0.689 0.999 0.184 0.816
#> GSM49605 2 0.689 0.999 0.184 0.816
#> GSM49606 2 0.689 0.999 0.184 0.816
#> GSM49607 2 0.689 0.999 0.184 0.816
#> GSM49608 2 0.689 0.999 0.184 0.816
#> GSM49609 2 0.689 0.999 0.184 0.816
#> GSM49610 2 0.689 0.999 0.184 0.816
#> GSM49611 2 0.689 0.999 0.184 0.816
#> GSM49612 2 0.689 0.999 0.184 0.816
#> GSM49614 1 0.689 0.785 0.816 0.184
#> GSM49615 1 0.689 0.785 0.816 0.184
#> GSM49616 1 0.689 0.785 0.816 0.184
#> GSM49617 1 0.689 0.785 0.816 0.184
#> GSM49564 1 0.000 0.969 1.000 0.000
#> GSM49565 1 0.000 0.969 1.000 0.000
#> GSM49566 1 0.000 0.969 1.000 0.000
#> GSM49567 1 0.000 0.969 1.000 0.000
#> GSM49568 1 0.000 0.969 1.000 0.000
#> GSM49569 1 0.000 0.969 1.000 0.000
#> GSM49570 2 0.697 0.996 0.188 0.812
#> GSM49571 1 0.373 0.885 0.928 0.072
#> GSM49572 1 0.000 0.969 1.000 0.000
#> GSM49573 2 0.697 0.996 0.188 0.812
#> GSM49574 1 0.000 0.969 1.000 0.000
#> GSM49575 1 0.000 0.969 1.000 0.000
#> GSM49576 1 0.000 0.969 1.000 0.000
#> GSM49577 1 0.000 0.969 1.000 0.000
#> GSM49578 1 0.000 0.969 1.000 0.000
#> GSM49579 1 0.000 0.969 1.000 0.000
#> GSM49580 1 0.000 0.969 1.000 0.000
#> GSM49581 1 0.000 0.969 1.000 0.000
#> GSM49582 1 0.000 0.969 1.000 0.000
#> GSM49583 2 0.689 0.999 0.184 0.816
#> GSM49584 1 0.000 0.969 1.000 0.000
#> GSM49585 1 0.000 0.969 1.000 0.000
#> GSM49586 1 0.000 0.969 1.000 0.000
#> GSM49587 1 0.000 0.969 1.000 0.000
#> GSM49588 1 0.000 0.969 1.000 0.000
#> GSM49589 1 0.000 0.969 1.000 0.000
#> GSM49590 1 0.000 0.969 1.000 0.000
#> GSM49591 1 0.000 0.969 1.000 0.000
#> GSM49592 1 0.000 0.969 1.000 0.000
#> GSM49593 1 0.000 0.969 1.000 0.000
#> GSM49594 1 0.000 0.969 1.000 0.000
#> GSM49595 1 0.000 0.969 1.000 0.000
#> GSM49596 1 0.000 0.969 1.000 0.000
#> GSM49597 2 0.697 0.996 0.188 0.812
#> GSM49598 1 0.000 0.969 1.000 0.000
#> GSM49599 1 0.000 0.969 1.000 0.000
#> GSM49600 1 0.000 0.969 1.000 0.000
#> GSM49601 1 0.000 0.969 1.000 0.000
#> GSM49602 1 0.000 0.969 1.000 0.000
#> GSM49603 1 0.000 0.969 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM49613 3 0.4178 0.960 0.172 0.000 0.828
#> GSM49604 2 0.3686 0.896 0.000 0.860 0.140
#> GSM49605 2 0.0000 0.949 0.000 1.000 0.000
#> GSM49606 2 0.0424 0.949 0.000 0.992 0.008
#> GSM49607 2 0.0000 0.949 0.000 1.000 0.000
#> GSM49608 2 0.0000 0.949 0.000 1.000 0.000
#> GSM49609 2 0.0892 0.947 0.000 0.980 0.020
#> GSM49610 2 0.0892 0.947 0.000 0.980 0.020
#> GSM49611 2 0.0892 0.947 0.000 0.980 0.020
#> GSM49612 2 0.0892 0.947 0.000 0.980 0.020
#> GSM49614 3 0.2356 0.829 0.072 0.000 0.928
#> GSM49615 3 0.4178 0.960 0.172 0.000 0.828
#> GSM49616 3 0.4178 0.960 0.172 0.000 0.828
#> GSM49617 3 0.4178 0.960 0.172 0.000 0.828
#> GSM49564 1 0.2448 0.941 0.924 0.000 0.076
#> GSM49565 1 0.0000 0.951 1.000 0.000 0.000
#> GSM49566 1 0.2537 0.941 0.920 0.000 0.080
#> GSM49567 1 0.0000 0.951 1.000 0.000 0.000
#> GSM49568 1 0.0000 0.951 1.000 0.000 0.000
#> GSM49569 1 0.2537 0.941 0.920 0.000 0.080
#> GSM49570 2 0.3879 0.890 0.000 0.848 0.152
#> GSM49571 1 0.6004 0.691 0.780 0.064 0.156
#> GSM49572 1 0.0000 0.951 1.000 0.000 0.000
#> GSM49573 2 0.4047 0.890 0.004 0.848 0.148
#> GSM49574 1 0.0000 0.951 1.000 0.000 0.000
#> GSM49575 1 0.0000 0.951 1.000 0.000 0.000
#> GSM49576 1 0.2537 0.941 0.920 0.000 0.080
#> GSM49577 1 0.0237 0.950 0.996 0.000 0.004
#> GSM49578 1 0.0000 0.951 1.000 0.000 0.000
#> GSM49579 1 0.2356 0.944 0.928 0.000 0.072
#> GSM49580 1 0.0892 0.949 0.980 0.000 0.020
#> GSM49581 1 0.0000 0.951 1.000 0.000 0.000
#> GSM49582 1 0.0000 0.951 1.000 0.000 0.000
#> GSM49583 2 0.0237 0.949 0.000 0.996 0.004
#> GSM49584 1 0.0424 0.950 0.992 0.000 0.008
#> GSM49585 1 0.0000 0.951 1.000 0.000 0.000
#> GSM49586 1 0.2066 0.947 0.940 0.000 0.060
#> GSM49587 1 0.0000 0.951 1.000 0.000 0.000
#> GSM49588 1 0.0000 0.951 1.000 0.000 0.000
#> GSM49589 1 0.2537 0.941 0.920 0.000 0.080
#> GSM49590 1 0.2537 0.941 0.920 0.000 0.080
#> GSM49591 1 0.0000 0.951 1.000 0.000 0.000
#> GSM49592 1 0.0000 0.951 1.000 0.000 0.000
#> GSM49593 1 0.2537 0.941 0.920 0.000 0.080
#> GSM49594 1 0.2066 0.947 0.940 0.000 0.060
#> GSM49595 1 0.2066 0.947 0.940 0.000 0.060
#> GSM49596 1 0.2165 0.947 0.936 0.000 0.064
#> GSM49597 2 0.3879 0.890 0.000 0.848 0.152
#> GSM49598 1 0.2537 0.941 0.920 0.000 0.080
#> GSM49599 1 0.0000 0.951 1.000 0.000 0.000
#> GSM49600 1 0.2066 0.947 0.940 0.000 0.060
#> GSM49601 1 0.2066 0.947 0.940 0.000 0.060
#> GSM49602 1 0.2537 0.941 0.920 0.000 0.080
#> GSM49603 1 0.2537 0.941 0.920 0.000 0.080
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM49613 3 0.6482 0.82756 0.072 0.000 0.504 0.424
#> GSM49604 2 0.4989 0.62057 0.000 0.528 0.472 0.000
#> GSM49605 2 0.1004 0.83496 0.000 0.972 0.024 0.004
#> GSM49606 2 0.0188 0.83190 0.000 0.996 0.000 0.004
#> GSM49607 2 0.1004 0.83496 0.000 0.972 0.024 0.004
#> GSM49608 2 0.1004 0.83496 0.000 0.972 0.024 0.004
#> GSM49609 2 0.1284 0.83224 0.000 0.964 0.024 0.012
#> GSM49610 2 0.1284 0.83224 0.000 0.964 0.024 0.012
#> GSM49611 2 0.1284 0.83224 0.000 0.964 0.024 0.012
#> GSM49612 2 0.1284 0.83224 0.000 0.964 0.024 0.012
#> GSM49614 3 0.6222 0.81273 0.056 0.000 0.532 0.412
#> GSM49615 3 0.6482 0.82756 0.072 0.000 0.504 0.424
#> GSM49616 3 0.6465 0.82787 0.072 0.000 0.516 0.412
#> GSM49617 3 0.6465 0.82787 0.072 0.000 0.516 0.412
#> GSM49564 1 0.1118 0.76959 0.964 0.000 0.000 0.036
#> GSM49565 4 0.4972 0.97379 0.456 0.000 0.000 0.544
#> GSM49566 1 0.1118 0.77671 0.964 0.000 0.000 0.036
#> GSM49567 4 0.4977 0.97049 0.460 0.000 0.000 0.540
#> GSM49568 4 0.4985 0.97758 0.468 0.000 0.000 0.532
#> GSM49569 1 0.0000 0.79412 1.000 0.000 0.000 0.000
#> GSM49570 2 0.5163 0.61283 0.004 0.516 0.480 0.000
#> GSM49571 3 0.7953 -0.00382 0.400 0.080 0.456 0.064
#> GSM49572 4 0.4981 0.97212 0.464 0.000 0.000 0.536
#> GSM49573 2 0.5163 0.61283 0.004 0.516 0.480 0.000
#> GSM49574 4 0.4972 0.97379 0.456 0.000 0.000 0.544
#> GSM49575 4 0.4967 0.96878 0.452 0.000 0.000 0.548
#> GSM49576 1 0.0000 0.79412 1.000 0.000 0.000 0.000
#> GSM49577 1 0.4898 -0.58078 0.584 0.000 0.000 0.416
#> GSM49578 4 0.4985 0.97758 0.468 0.000 0.000 0.532
#> GSM49579 1 0.0469 0.78928 0.988 0.000 0.000 0.012
#> GSM49580 1 0.4999 -0.90033 0.508 0.000 0.000 0.492
#> GSM49581 4 0.4985 0.97758 0.468 0.000 0.000 0.532
#> GSM49582 4 0.4985 0.97758 0.468 0.000 0.000 0.532
#> GSM49583 2 0.1004 0.83496 0.000 0.972 0.024 0.004
#> GSM49584 4 0.5000 0.91434 0.496 0.000 0.000 0.504
#> GSM49585 1 0.4830 -0.52943 0.608 0.000 0.000 0.392
#> GSM49586 1 0.1635 0.76843 0.948 0.000 0.008 0.044
#> GSM49587 4 0.4985 0.97758 0.468 0.000 0.000 0.532
#> GSM49588 1 0.4948 -0.74172 0.560 0.000 0.000 0.440
#> GSM49589 1 0.0524 0.79074 0.988 0.000 0.004 0.008
#> GSM49590 1 0.0188 0.79305 0.996 0.000 0.004 0.000
#> GSM49591 4 0.4985 0.95614 0.468 0.000 0.000 0.532
#> GSM49592 4 0.4977 0.97410 0.460 0.000 0.000 0.540
#> GSM49593 1 0.0000 0.79412 1.000 0.000 0.000 0.000
#> GSM49594 1 0.1661 0.76739 0.944 0.000 0.004 0.052
#> GSM49595 1 0.1661 0.76739 0.944 0.000 0.004 0.052
#> GSM49596 1 0.0592 0.78776 0.984 0.000 0.000 0.016
#> GSM49597 2 0.5308 0.61636 0.004 0.540 0.452 0.004
#> GSM49598 1 0.0000 0.79412 1.000 0.000 0.000 0.000
#> GSM49599 4 0.4972 0.97167 0.456 0.000 0.000 0.544
#> GSM49600 1 0.3444 0.42887 0.816 0.000 0.000 0.184
#> GSM49601 1 0.0592 0.79106 0.984 0.000 0.000 0.016
#> GSM49602 1 0.0376 0.79298 0.992 0.000 0.004 0.004
#> GSM49603 1 0.0376 0.79298 0.992 0.000 0.004 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM49613 3 0.0324 0.997 0.004 0.000 0.992 0.000 0.004
#> GSM49604 4 0.2648 0.897 0.000 0.152 0.000 0.848 0.000
#> GSM49605 2 0.1668 0.914 0.028 0.940 0.000 0.032 0.000
#> GSM49606 2 0.0510 0.920 0.000 0.984 0.000 0.016 0.000
#> GSM49607 2 0.1915 0.909 0.040 0.928 0.000 0.032 0.000
#> GSM49608 2 0.1668 0.914 0.028 0.940 0.000 0.032 0.000
#> GSM49609 2 0.2074 0.913 0.060 0.920 0.004 0.016 0.000
#> GSM49610 2 0.2074 0.913 0.060 0.920 0.004 0.016 0.000
#> GSM49611 2 0.2074 0.913 0.060 0.920 0.004 0.016 0.000
#> GSM49612 2 0.2074 0.913 0.060 0.920 0.004 0.016 0.000
#> GSM49614 3 0.0451 0.993 0.008 0.000 0.988 0.000 0.004
#> GSM49615 3 0.0324 0.997 0.004 0.000 0.992 0.000 0.004
#> GSM49616 3 0.0162 0.997 0.000 0.000 0.996 0.000 0.004
#> GSM49617 3 0.0162 0.997 0.000 0.000 0.996 0.000 0.004
#> GSM49564 5 0.2291 0.895 0.036 0.000 0.000 0.056 0.908
#> GSM49565 1 0.3695 0.908 0.800 0.000 0.000 0.036 0.164
#> GSM49566 5 0.2300 0.881 0.024 0.000 0.000 0.072 0.904
#> GSM49567 1 0.3922 0.901 0.780 0.000 0.000 0.040 0.180
#> GSM49568 1 0.3381 0.917 0.808 0.000 0.000 0.016 0.176
#> GSM49569 5 0.0451 0.927 0.008 0.000 0.000 0.004 0.988
#> GSM49570 4 0.2877 0.898 0.004 0.144 0.004 0.848 0.000
#> GSM49571 4 0.3817 0.691 0.056 0.012 0.000 0.824 0.108
#> GSM49572 1 0.3883 0.903 0.780 0.000 0.000 0.036 0.184
#> GSM49573 4 0.2719 0.898 0.004 0.144 0.000 0.852 0.000
#> GSM49574 1 0.3183 0.913 0.828 0.000 0.000 0.016 0.156
#> GSM49575 1 0.2920 0.903 0.852 0.000 0.000 0.016 0.132
#> GSM49576 5 0.0693 0.922 0.012 0.000 0.000 0.008 0.980
#> GSM49577 1 0.5533 0.609 0.580 0.000 0.000 0.084 0.336
#> GSM49578 1 0.3171 0.917 0.816 0.000 0.000 0.008 0.176
#> GSM49579 5 0.0807 0.920 0.012 0.000 0.000 0.012 0.976
#> GSM49580 1 0.3940 0.888 0.756 0.000 0.000 0.024 0.220
#> GSM49581 1 0.3419 0.915 0.804 0.000 0.000 0.016 0.180
#> GSM49582 1 0.3132 0.917 0.820 0.000 0.000 0.008 0.172
#> GSM49583 2 0.2580 0.881 0.044 0.892 0.000 0.064 0.000
#> GSM49584 1 0.3745 0.905 0.780 0.000 0.000 0.024 0.196
#> GSM49585 1 0.5063 0.711 0.632 0.000 0.000 0.056 0.312
#> GSM49586 5 0.2992 0.891 0.068 0.000 0.000 0.064 0.868
#> GSM49587 1 0.3132 0.918 0.820 0.000 0.000 0.008 0.172
#> GSM49588 1 0.4452 0.800 0.696 0.000 0.000 0.032 0.272
#> GSM49589 5 0.1915 0.921 0.032 0.000 0.000 0.040 0.928
#> GSM49590 5 0.0290 0.926 0.000 0.000 0.000 0.008 0.992
#> GSM49591 1 0.3734 0.904 0.796 0.000 0.000 0.036 0.168
#> GSM49592 1 0.3695 0.910 0.800 0.000 0.000 0.036 0.164
#> GSM49593 5 0.0671 0.926 0.016 0.000 0.000 0.004 0.980
#> GSM49594 5 0.2580 0.899 0.044 0.000 0.000 0.064 0.892
#> GSM49595 5 0.2580 0.899 0.044 0.000 0.000 0.064 0.892
#> GSM49596 5 0.0671 0.926 0.016 0.000 0.000 0.004 0.980
#> GSM49597 4 0.4150 0.851 0.044 0.180 0.004 0.772 0.000
#> GSM49598 5 0.0609 0.926 0.020 0.000 0.000 0.000 0.980
#> GSM49599 1 0.3276 0.893 0.836 0.000 0.000 0.032 0.132
#> GSM49600 5 0.4065 0.504 0.264 0.000 0.000 0.016 0.720
#> GSM49601 5 0.2370 0.908 0.040 0.000 0.000 0.056 0.904
#> GSM49602 5 0.1579 0.924 0.032 0.000 0.000 0.024 0.944
#> GSM49603 5 0.1579 0.924 0.032 0.000 0.000 0.024 0.944
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM49613 3 0.0862 0.976 0.008 0.000 0.972 0.004 0.000 0.016
#> GSM49604 4 0.2011 0.887 0.004 0.064 0.000 0.912 0.000 0.020
#> GSM49605 2 0.3374 0.864 0.000 0.772 0.000 0.020 0.000 0.208
#> GSM49606 2 0.2703 0.871 0.000 0.824 0.000 0.004 0.000 0.172
#> GSM49607 2 0.3711 0.840 0.000 0.720 0.000 0.020 0.000 0.260
#> GSM49608 2 0.3374 0.864 0.000 0.772 0.000 0.020 0.000 0.208
#> GSM49609 2 0.0146 0.861 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM49610 2 0.0146 0.861 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM49611 2 0.0146 0.861 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM49612 2 0.0146 0.861 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM49614 3 0.1500 0.949 0.012 0.000 0.936 0.000 0.000 0.052
#> GSM49615 3 0.0862 0.976 0.008 0.000 0.972 0.004 0.000 0.016
#> GSM49616 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM49617 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM49564 5 0.4148 0.643 0.048 0.000 0.000 0.016 0.748 0.188
#> GSM49565 1 0.3892 0.604 0.752 0.000 0.000 0.000 0.060 0.188
#> GSM49566 5 0.4086 0.538 0.028 0.000 0.000 0.008 0.708 0.256
#> GSM49567 1 0.4400 0.410 0.684 0.000 0.000 0.000 0.068 0.248
#> GSM49568 1 0.2231 0.713 0.900 0.000 0.000 0.004 0.068 0.028
#> GSM49569 5 0.0291 0.844 0.004 0.000 0.000 0.000 0.992 0.004
#> GSM49570 4 0.1194 0.896 0.004 0.032 0.000 0.956 0.000 0.008
#> GSM49571 4 0.3839 0.750 0.012 0.004 0.000 0.776 0.032 0.176
#> GSM49572 1 0.4394 0.548 0.716 0.000 0.000 0.008 0.068 0.208
#> GSM49573 4 0.0790 0.896 0.000 0.032 0.000 0.968 0.000 0.000
#> GSM49574 1 0.3521 0.685 0.812 0.000 0.000 0.008 0.060 0.120
#> GSM49575 1 0.3771 0.542 0.764 0.000 0.000 0.000 0.056 0.180
#> GSM49576 5 0.0405 0.842 0.008 0.000 0.000 0.000 0.988 0.004
#> GSM49577 6 0.6057 0.000 0.360 0.000 0.000 0.004 0.216 0.420
#> GSM49578 1 0.1787 0.718 0.920 0.000 0.000 0.004 0.068 0.008
#> GSM49579 5 0.1218 0.838 0.012 0.000 0.000 0.004 0.956 0.028
#> GSM49580 1 0.4100 0.574 0.760 0.000 0.000 0.004 0.112 0.124
#> GSM49581 1 0.3047 0.689 0.848 0.000 0.000 0.004 0.084 0.064
#> GSM49582 1 0.1787 0.718 0.920 0.000 0.000 0.004 0.068 0.008
#> GSM49583 2 0.4711 0.800 0.020 0.676 0.000 0.052 0.000 0.252
#> GSM49584 1 0.3565 0.644 0.808 0.000 0.000 0.004 0.096 0.092
#> GSM49585 1 0.5510 0.262 0.604 0.000 0.000 0.012 0.220 0.164
#> GSM49586 5 0.4181 0.675 0.028 0.000 0.000 0.012 0.704 0.256
#> GSM49587 1 0.2361 0.718 0.896 0.000 0.000 0.008 0.064 0.032
#> GSM49588 1 0.4733 0.513 0.704 0.000 0.000 0.012 0.172 0.112
#> GSM49589 5 0.2784 0.819 0.012 0.000 0.000 0.008 0.848 0.132
#> GSM49590 5 0.0520 0.844 0.008 0.000 0.000 0.000 0.984 0.008
#> GSM49591 1 0.3844 0.671 0.796 0.000 0.000 0.016 0.076 0.112
#> GSM49592 1 0.2962 0.697 0.848 0.000 0.000 0.000 0.068 0.084
#> GSM49593 5 0.0405 0.845 0.008 0.000 0.000 0.000 0.988 0.004
#> GSM49594 5 0.3486 0.756 0.024 0.000 0.000 0.008 0.788 0.180
#> GSM49595 5 0.3486 0.756 0.024 0.000 0.000 0.008 0.788 0.180
#> GSM49596 5 0.0405 0.845 0.008 0.000 0.000 0.000 0.988 0.004
#> GSM49597 4 0.3629 0.828 0.024 0.032 0.000 0.804 0.000 0.140
#> GSM49598 5 0.0291 0.844 0.004 0.000 0.000 0.000 0.992 0.004
#> GSM49599 1 0.4739 0.322 0.636 0.000 0.000 0.008 0.056 0.300
#> GSM49600 5 0.4663 0.346 0.244 0.000 0.000 0.004 0.672 0.080
#> GSM49601 5 0.3000 0.791 0.016 0.000 0.000 0.004 0.824 0.156
#> GSM49602 5 0.1644 0.837 0.004 0.000 0.000 0.000 0.920 0.076
#> GSM49603 5 0.1644 0.837 0.004 0.000 0.000 0.000 0.920 0.076
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> CV:kmeans 54 5.97e-07 6.72e-04 2
#> CV:kmeans 54 2.57e-07 8.46e-14 3
#> CV:kmeans 48 8.02e-06 6.07e-11 4
#> CV:kmeans 54 1.42e-07 4.23e-13 5
#> CV:kmeans 49 8.68e-07 1.20e-11 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 21168 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.742 0.923 0.963 0.4712 0.525 0.525
#> 3 3 0.672 0.814 0.905 0.4244 0.709 0.490
#> 4 4 0.624 0.733 0.841 0.1212 0.878 0.652
#> 5 5 0.605 0.547 0.741 0.0616 0.966 0.870
#> 6 6 0.640 0.427 0.677 0.0400 0.967 0.856
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM49613 1 0.0000 0.973 1.000 0.000
#> GSM49604 2 0.0000 0.935 0.000 1.000
#> GSM49605 2 0.0000 0.935 0.000 1.000
#> GSM49606 2 0.0000 0.935 0.000 1.000
#> GSM49607 2 0.0000 0.935 0.000 1.000
#> GSM49608 2 0.0000 0.935 0.000 1.000
#> GSM49609 2 0.0000 0.935 0.000 1.000
#> GSM49610 2 0.0000 0.935 0.000 1.000
#> GSM49611 2 0.0000 0.935 0.000 1.000
#> GSM49612 2 0.0000 0.935 0.000 1.000
#> GSM49614 2 0.7950 0.712 0.240 0.760
#> GSM49615 1 0.0000 0.973 1.000 0.000
#> GSM49616 1 0.0672 0.967 0.992 0.008
#> GSM49617 1 0.6623 0.785 0.828 0.172
#> GSM49564 1 0.0000 0.973 1.000 0.000
#> GSM49565 1 0.6801 0.782 0.820 0.180
#> GSM49566 1 0.0000 0.973 1.000 0.000
#> GSM49567 1 0.5408 0.851 0.876 0.124
#> GSM49568 1 0.0000 0.973 1.000 0.000
#> GSM49569 1 0.0000 0.973 1.000 0.000
#> GSM49570 2 0.0000 0.935 0.000 1.000
#> GSM49571 2 0.0000 0.935 0.000 1.000
#> GSM49572 1 0.0376 0.970 0.996 0.004
#> GSM49573 2 0.0000 0.935 0.000 1.000
#> GSM49574 1 0.5408 0.855 0.876 0.124
#> GSM49575 2 0.9087 0.567 0.324 0.676
#> GSM49576 1 0.0000 0.973 1.000 0.000
#> GSM49577 2 0.2603 0.910 0.044 0.956
#> GSM49578 1 0.0000 0.973 1.000 0.000
#> GSM49579 1 0.0000 0.973 1.000 0.000
#> GSM49580 1 0.0000 0.973 1.000 0.000
#> GSM49581 1 0.0000 0.973 1.000 0.000
#> GSM49582 1 0.0000 0.973 1.000 0.000
#> GSM49583 2 0.0000 0.935 0.000 1.000
#> GSM49584 1 0.0000 0.973 1.000 0.000
#> GSM49585 1 0.0000 0.973 1.000 0.000
#> GSM49586 2 0.6531 0.805 0.168 0.832
#> GSM49587 1 0.0000 0.973 1.000 0.000
#> GSM49588 1 0.0000 0.973 1.000 0.000
#> GSM49589 1 0.0000 0.973 1.000 0.000
#> GSM49590 1 0.0000 0.973 1.000 0.000
#> GSM49591 1 0.0000 0.973 1.000 0.000
#> GSM49592 1 0.0000 0.973 1.000 0.000
#> GSM49593 1 0.0000 0.973 1.000 0.000
#> GSM49594 2 0.6623 0.800 0.172 0.828
#> GSM49595 1 0.7219 0.749 0.800 0.200
#> GSM49596 1 0.0000 0.973 1.000 0.000
#> GSM49597 2 0.0000 0.935 0.000 1.000
#> GSM49598 1 0.0000 0.973 1.000 0.000
#> GSM49599 2 0.8016 0.712 0.244 0.756
#> GSM49600 1 0.0000 0.973 1.000 0.000
#> GSM49601 1 0.0000 0.973 1.000 0.000
#> GSM49602 1 0.0000 0.973 1.000 0.000
#> GSM49603 1 0.0000 0.973 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM49613 3 0.0000 0.8538 0.000 0.000 1.000
#> GSM49604 2 0.0000 0.9344 0.000 1.000 0.000
#> GSM49605 2 0.0000 0.9344 0.000 1.000 0.000
#> GSM49606 2 0.0000 0.9344 0.000 1.000 0.000
#> GSM49607 2 0.0000 0.9344 0.000 1.000 0.000
#> GSM49608 2 0.0000 0.9344 0.000 1.000 0.000
#> GSM49609 2 0.0000 0.9344 0.000 1.000 0.000
#> GSM49610 2 0.0000 0.9344 0.000 1.000 0.000
#> GSM49611 2 0.0000 0.9344 0.000 1.000 0.000
#> GSM49612 2 0.0000 0.9344 0.000 1.000 0.000
#> GSM49614 3 0.3752 0.7469 0.000 0.144 0.856
#> GSM49615 3 0.0000 0.8538 0.000 0.000 1.000
#> GSM49616 3 0.0000 0.8538 0.000 0.000 1.000
#> GSM49617 3 0.0000 0.8538 0.000 0.000 1.000
#> GSM49564 3 0.1163 0.8548 0.028 0.000 0.972
#> GSM49565 1 0.0000 0.9071 1.000 0.000 0.000
#> GSM49566 3 0.3192 0.8293 0.112 0.000 0.888
#> GSM49567 1 0.1781 0.8967 0.960 0.020 0.020
#> GSM49568 1 0.0747 0.9062 0.984 0.000 0.016
#> GSM49569 3 0.2066 0.8568 0.060 0.000 0.940
#> GSM49570 2 0.0000 0.9344 0.000 1.000 0.000
#> GSM49571 2 0.0237 0.9312 0.000 0.996 0.004
#> GSM49572 1 0.0829 0.9070 0.984 0.004 0.012
#> GSM49573 2 0.0000 0.9344 0.000 1.000 0.000
#> GSM49574 1 0.0237 0.9071 0.996 0.004 0.000
#> GSM49575 1 0.2537 0.8628 0.920 0.080 0.000
#> GSM49576 3 0.0892 0.8575 0.020 0.000 0.980
#> GSM49577 1 0.7801 0.1903 0.520 0.428 0.052
#> GSM49578 1 0.0424 0.9069 0.992 0.000 0.008
#> GSM49579 3 0.5431 0.7041 0.284 0.000 0.716
#> GSM49580 1 0.4121 0.7557 0.832 0.000 0.168
#> GSM49581 1 0.0747 0.9057 0.984 0.000 0.016
#> GSM49582 1 0.0000 0.9071 1.000 0.000 0.000
#> GSM49583 2 0.0000 0.9344 0.000 1.000 0.000
#> GSM49584 1 0.1964 0.8860 0.944 0.000 0.056
#> GSM49585 1 0.3340 0.8200 0.880 0.000 0.120
#> GSM49586 2 0.8637 0.3282 0.128 0.564 0.308
#> GSM49587 1 0.0424 0.9072 0.992 0.000 0.008
#> GSM49588 1 0.2625 0.8552 0.916 0.000 0.084
#> GSM49589 3 0.0592 0.8567 0.012 0.000 0.988
#> GSM49590 3 0.0237 0.8541 0.004 0.000 0.996
#> GSM49591 1 0.0000 0.9071 1.000 0.000 0.000
#> GSM49592 1 0.0000 0.9071 1.000 0.000 0.000
#> GSM49593 3 0.4291 0.8101 0.180 0.000 0.820
#> GSM49594 2 0.9679 0.0545 0.232 0.448 0.320
#> GSM49595 3 0.8597 0.4184 0.380 0.104 0.516
#> GSM49596 3 0.6126 0.5304 0.400 0.000 0.600
#> GSM49597 2 0.0000 0.9344 0.000 1.000 0.000
#> GSM49598 3 0.5058 0.7581 0.244 0.000 0.756
#> GSM49599 1 0.6487 0.6110 0.700 0.268 0.032
#> GSM49600 3 0.6026 0.5464 0.376 0.000 0.624
#> GSM49601 3 0.4605 0.7929 0.204 0.000 0.796
#> GSM49602 3 0.3116 0.8450 0.108 0.000 0.892
#> GSM49603 3 0.2959 0.8471 0.100 0.000 0.900
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM49613 3 0.0000 0.8727 0.000 0.000 1.000 0.000
#> GSM49604 2 0.0188 0.9798 0.000 0.996 0.000 0.004
#> GSM49605 2 0.0000 0.9816 0.000 1.000 0.000 0.000
#> GSM49606 2 0.0000 0.9816 0.000 1.000 0.000 0.000
#> GSM49607 2 0.0000 0.9816 0.000 1.000 0.000 0.000
#> GSM49608 2 0.0000 0.9816 0.000 1.000 0.000 0.000
#> GSM49609 2 0.0000 0.9816 0.000 1.000 0.000 0.000
#> GSM49610 2 0.0000 0.9816 0.000 1.000 0.000 0.000
#> GSM49611 2 0.0000 0.9816 0.000 1.000 0.000 0.000
#> GSM49612 2 0.0000 0.9816 0.000 1.000 0.000 0.000
#> GSM49614 3 0.0779 0.8576 0.000 0.016 0.980 0.004
#> GSM49615 3 0.0000 0.8727 0.000 0.000 1.000 0.000
#> GSM49616 3 0.0000 0.8727 0.000 0.000 1.000 0.000
#> GSM49617 3 0.0000 0.8727 0.000 0.000 1.000 0.000
#> GSM49564 3 0.2797 0.8161 0.032 0.000 0.900 0.068
#> GSM49565 1 0.2760 0.7687 0.872 0.000 0.000 0.128
#> GSM49566 4 0.7843 0.1801 0.172 0.012 0.404 0.412
#> GSM49567 1 0.3093 0.7688 0.884 0.004 0.020 0.092
#> GSM49568 1 0.2973 0.7742 0.884 0.000 0.020 0.096
#> GSM49569 4 0.6079 0.4554 0.052 0.000 0.380 0.568
#> GSM49570 2 0.0804 0.9718 0.000 0.980 0.008 0.012
#> GSM49571 2 0.4588 0.7567 0.012 0.788 0.024 0.176
#> GSM49572 1 0.2053 0.7732 0.924 0.000 0.004 0.072
#> GSM49573 2 0.0469 0.9759 0.000 0.988 0.000 0.012
#> GSM49574 1 0.3052 0.7641 0.860 0.004 0.000 0.136
#> GSM49575 1 0.5460 0.6998 0.736 0.040 0.020 0.204
#> GSM49576 4 0.5510 0.2124 0.016 0.000 0.480 0.504
#> GSM49577 1 0.8789 0.1388 0.388 0.264 0.044 0.304
#> GSM49578 1 0.0469 0.7680 0.988 0.000 0.000 0.012
#> GSM49579 4 0.6363 0.6360 0.172 0.000 0.172 0.656
#> GSM49580 1 0.6159 0.5823 0.672 0.000 0.196 0.132
#> GSM49581 1 0.3052 0.7580 0.860 0.000 0.004 0.136
#> GSM49582 1 0.0592 0.7683 0.984 0.000 0.000 0.016
#> GSM49583 2 0.0000 0.9816 0.000 1.000 0.000 0.000
#> GSM49584 1 0.3697 0.7377 0.852 0.000 0.100 0.048
#> GSM49585 1 0.6613 0.4287 0.560 0.000 0.096 0.344
#> GSM49586 4 0.4191 0.7100 0.024 0.068 0.060 0.848
#> GSM49587 1 0.1807 0.7739 0.940 0.000 0.008 0.052
#> GSM49588 1 0.5512 0.5761 0.660 0.000 0.040 0.300
#> GSM49589 3 0.3945 0.6515 0.004 0.000 0.780 0.216
#> GSM49590 3 0.4679 0.2652 0.000 0.000 0.648 0.352
#> GSM49591 1 0.4008 0.7004 0.756 0.000 0.000 0.244
#> GSM49592 1 0.2011 0.7727 0.920 0.000 0.000 0.080
#> GSM49593 4 0.4332 0.7482 0.072 0.000 0.112 0.816
#> GSM49594 4 0.4604 0.6869 0.040 0.100 0.036 0.824
#> GSM49595 4 0.2335 0.7363 0.060 0.000 0.020 0.920
#> GSM49596 4 0.5218 0.6664 0.200 0.000 0.064 0.736
#> GSM49597 2 0.0376 0.9779 0.000 0.992 0.004 0.004
#> GSM49598 4 0.4953 0.7412 0.104 0.000 0.120 0.776
#> GSM49599 1 0.8024 0.5161 0.584 0.168 0.076 0.172
#> GSM49600 1 0.7543 -0.0729 0.420 0.000 0.188 0.392
#> GSM49601 4 0.3474 0.7477 0.064 0.000 0.068 0.868
#> GSM49602 4 0.3392 0.7426 0.020 0.000 0.124 0.856
#> GSM49603 4 0.3577 0.7318 0.012 0.000 0.156 0.832
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM49613 3 0.0000 0.8018 0.000 0.000 1.000 0.000 0.000
#> GSM49604 2 0.2338 0.8640 0.000 0.884 0.000 0.112 0.004
#> GSM49605 2 0.0000 0.9060 0.000 1.000 0.000 0.000 0.000
#> GSM49606 2 0.0324 0.9058 0.000 0.992 0.000 0.004 0.004
#> GSM49607 2 0.0324 0.9057 0.000 0.992 0.000 0.004 0.004
#> GSM49608 2 0.0451 0.9057 0.000 0.988 0.000 0.008 0.004
#> GSM49609 2 0.0451 0.9051 0.000 0.988 0.000 0.008 0.004
#> GSM49610 2 0.0162 0.9061 0.000 0.996 0.000 0.004 0.000
#> GSM49611 2 0.0451 0.9051 0.000 0.988 0.000 0.008 0.004
#> GSM49612 2 0.0451 0.9051 0.000 0.988 0.000 0.008 0.004
#> GSM49614 3 0.0865 0.7859 0.000 0.004 0.972 0.024 0.000
#> GSM49615 3 0.0000 0.8018 0.000 0.000 1.000 0.000 0.000
#> GSM49616 3 0.0000 0.8018 0.000 0.000 1.000 0.000 0.000
#> GSM49617 3 0.0290 0.7992 0.000 0.000 0.992 0.008 0.000
#> GSM49564 3 0.5042 0.6370 0.064 0.000 0.760 0.080 0.096
#> GSM49565 1 0.5137 0.4888 0.676 0.004 0.000 0.244 0.076
#> GSM49566 5 0.8367 -0.0223 0.140 0.000 0.252 0.304 0.304
#> GSM49567 1 0.5661 0.3501 0.596 0.004 0.012 0.332 0.056
#> GSM49568 1 0.4512 0.5500 0.776 0.000 0.016 0.132 0.076
#> GSM49569 5 0.7155 0.3736 0.056 0.000 0.272 0.160 0.512
#> GSM49570 2 0.4032 0.7867 0.000 0.772 0.032 0.192 0.004
#> GSM49571 2 0.6663 0.4143 0.016 0.548 0.012 0.296 0.128
#> GSM49572 1 0.5112 0.4655 0.664 0.000 0.004 0.268 0.064
#> GSM49573 2 0.3643 0.7880 0.000 0.776 0.004 0.212 0.008
#> GSM49574 1 0.4901 0.5267 0.716 0.000 0.000 0.168 0.116
#> GSM49575 1 0.6431 0.1991 0.560 0.044 0.012 0.332 0.052
#> GSM49576 5 0.7072 0.2892 0.028 0.000 0.340 0.184 0.448
#> GSM49577 4 0.8692 0.2237 0.228 0.192 0.020 0.392 0.168
#> GSM49578 1 0.1469 0.5858 0.948 0.000 0.000 0.036 0.016
#> GSM49579 5 0.6861 0.2706 0.092 0.000 0.064 0.332 0.512
#> GSM49580 1 0.7308 0.1693 0.508 0.000 0.104 0.280 0.108
#> GSM49581 1 0.5371 0.4470 0.684 0.000 0.012 0.208 0.096
#> GSM49582 1 0.1787 0.5812 0.936 0.000 0.004 0.044 0.016
#> GSM49583 2 0.1121 0.8960 0.000 0.956 0.000 0.044 0.000
#> GSM49584 1 0.5515 0.4703 0.680 0.000 0.056 0.224 0.040
#> GSM49585 1 0.7669 0.0972 0.424 0.000 0.064 0.228 0.284
#> GSM49586 5 0.5717 0.4029 0.024 0.060 0.004 0.272 0.640
#> GSM49587 1 0.3764 0.5814 0.800 0.000 0.000 0.156 0.044
#> GSM49588 1 0.6540 0.3464 0.544 0.000 0.012 0.220 0.224
#> GSM49589 3 0.5948 0.3138 0.012 0.000 0.572 0.092 0.324
#> GSM49590 3 0.6144 0.0235 0.024 0.000 0.512 0.072 0.392
#> GSM49591 1 0.5367 0.4830 0.668 0.000 0.000 0.184 0.148
#> GSM49592 1 0.3471 0.5697 0.836 0.000 0.000 0.092 0.072
#> GSM49593 5 0.5478 0.5587 0.080 0.000 0.084 0.108 0.728
#> GSM49594 5 0.6645 0.4144 0.036 0.100 0.036 0.188 0.640
#> GSM49595 5 0.4009 0.5440 0.036 0.004 0.008 0.152 0.800
#> GSM49596 5 0.6546 0.4582 0.172 0.000 0.052 0.164 0.612
#> GSM49597 2 0.2773 0.8580 0.000 0.868 0.020 0.112 0.000
#> GSM49598 5 0.6077 0.5266 0.084 0.000 0.072 0.180 0.664
#> GSM49599 4 0.8030 0.0478 0.336 0.100 0.048 0.444 0.072
#> GSM49600 4 0.8551 0.0211 0.272 0.000 0.192 0.280 0.256
#> GSM49601 5 0.4393 0.5395 0.088 0.000 0.020 0.100 0.792
#> GSM49602 5 0.2772 0.5893 0.028 0.000 0.044 0.032 0.896
#> GSM49603 5 0.4180 0.5852 0.040 0.000 0.080 0.064 0.816
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM49613 3 0.0260 0.7747 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM49604 2 0.2994 0.5798 0.000 0.788 0.000 0.208 0.000 0.004
#> GSM49605 2 0.0508 0.8005 0.000 0.984 0.000 0.012 0.000 0.004
#> GSM49606 2 0.0458 0.8003 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM49607 2 0.0363 0.7997 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM49608 2 0.0547 0.8010 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM49609 2 0.1082 0.7881 0.000 0.956 0.000 0.040 0.000 0.004
#> GSM49610 2 0.0935 0.7980 0.000 0.964 0.000 0.032 0.000 0.004
#> GSM49611 2 0.0935 0.7917 0.000 0.964 0.000 0.032 0.000 0.004
#> GSM49612 2 0.0935 0.7923 0.000 0.964 0.000 0.032 0.000 0.004
#> GSM49614 3 0.0547 0.7674 0.000 0.000 0.980 0.020 0.000 0.000
#> GSM49615 3 0.0146 0.7752 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM49616 3 0.0291 0.7754 0.000 0.000 0.992 0.004 0.004 0.000
#> GSM49617 3 0.0146 0.7741 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM49564 3 0.6215 0.5106 0.072 0.000 0.656 0.068 0.112 0.092
#> GSM49565 1 0.5698 0.4263 0.580 0.012 0.000 0.060 0.036 0.312
#> GSM49566 5 0.8700 -0.0496 0.124 0.004 0.144 0.152 0.324 0.252
#> GSM49567 1 0.6369 0.2344 0.448 0.004 0.012 0.116 0.024 0.396
#> GSM49568 1 0.4857 0.4941 0.732 0.000 0.016 0.052 0.040 0.160
#> GSM49569 5 0.7201 0.3343 0.036 0.000 0.148 0.124 0.532 0.160
#> GSM49570 2 0.4640 0.0933 0.000 0.604 0.044 0.348 0.000 0.004
#> GSM49571 4 0.6470 0.0000 0.012 0.368 0.016 0.480 0.100 0.024
#> GSM49572 1 0.5511 0.4279 0.568 0.000 0.008 0.068 0.020 0.336
#> GSM49573 2 0.3727 0.0709 0.000 0.612 0.000 0.388 0.000 0.000
#> GSM49574 1 0.5453 0.4662 0.604 0.004 0.000 0.056 0.040 0.296
#> GSM49575 1 0.7182 0.2487 0.500 0.024 0.012 0.192 0.048 0.224
#> GSM49576 5 0.7716 0.1957 0.020 0.000 0.272 0.196 0.384 0.128
#> GSM49577 6 0.8779 0.1463 0.164 0.164 0.012 0.224 0.096 0.340
#> GSM49578 1 0.2458 0.5419 0.892 0.000 0.000 0.024 0.016 0.068
#> GSM49579 6 0.7993 -0.1528 0.060 0.004 0.072 0.196 0.328 0.340
#> GSM49580 1 0.7375 0.2025 0.464 0.000 0.064 0.072 0.108 0.292
#> GSM49581 1 0.6399 0.3035 0.544 0.000 0.000 0.084 0.128 0.244
#> GSM49582 1 0.2136 0.5440 0.908 0.000 0.000 0.016 0.012 0.064
#> GSM49583 2 0.1788 0.7621 0.000 0.916 0.004 0.076 0.000 0.004
#> GSM49584 1 0.5805 0.4234 0.620 0.000 0.044 0.040 0.040 0.256
#> GSM49585 6 0.7892 -0.0767 0.308 0.000 0.036 0.108 0.204 0.344
#> GSM49586 5 0.6054 0.3045 0.008 0.052 0.004 0.308 0.560 0.068
#> GSM49587 1 0.3999 0.5188 0.744 0.000 0.000 0.020 0.024 0.212
#> GSM49588 1 0.6938 0.2306 0.496 0.000 0.020 0.056 0.184 0.244
#> GSM49589 3 0.6931 0.1916 0.020 0.000 0.492 0.096 0.292 0.100
#> GSM49590 3 0.6674 0.0203 0.004 0.000 0.452 0.112 0.352 0.080
#> GSM49591 1 0.5912 0.3658 0.556 0.000 0.000 0.060 0.080 0.304
#> GSM49592 1 0.4686 0.4825 0.712 0.000 0.000 0.020 0.084 0.184
#> GSM49593 5 0.4405 0.4981 0.020 0.000 0.032 0.080 0.784 0.084
#> GSM49594 5 0.7585 0.1994 0.028 0.084 0.008 0.220 0.460 0.200
#> GSM49595 5 0.5928 0.3706 0.032 0.000 0.004 0.200 0.596 0.168
#> GSM49596 5 0.6709 0.3273 0.128 0.000 0.020 0.104 0.572 0.176
#> GSM49597 2 0.3678 0.5335 0.000 0.752 0.024 0.220 0.000 0.004
#> GSM49598 5 0.5221 0.4497 0.036 0.000 0.012 0.140 0.704 0.108
#> GSM49599 6 0.8635 0.0997 0.188 0.104 0.024 0.300 0.068 0.316
#> GSM49600 6 0.8547 0.0469 0.240 0.000 0.092 0.128 0.256 0.284
#> GSM49601 5 0.5029 0.4340 0.060 0.000 0.008 0.084 0.728 0.120
#> GSM49602 5 0.2816 0.5112 0.004 0.000 0.012 0.064 0.876 0.044
#> GSM49603 5 0.2911 0.5160 0.012 0.000 0.032 0.048 0.880 0.028
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> CV:skmeans 54 5.02e-04 2.14e-02 2
#> CV:skmeans 50 6.18e-06 6.36e-04 3
#> CV:skmeans 47 4.68e-05 2.11e-07 4
#> CV:skmeans 31 2.28e-03 3.45e-05 5
#> CV:skmeans 22 7.25e-03 2.15e-03 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21168 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.962 0.984 0.3228 0.669 0.669
#> 3 3 0.566 0.839 0.885 0.5597 0.867 0.802
#> 4 4 0.590 0.741 0.863 0.3689 0.727 0.504
#> 5 5 0.623 0.726 0.857 0.0656 0.917 0.736
#> 6 6 0.669 0.727 0.881 0.0296 0.983 0.934
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
#> GSM49613 1 0.0376 0.990 0.996 0.004
#> GSM49604 2 0.4022 0.892 0.080 0.920
#> GSM49605 2 0.0376 0.943 0.004 0.996
#> GSM49606 2 0.0376 0.943 0.004 0.996
#> GSM49607 2 0.0376 0.943 0.004 0.996
#> GSM49608 2 0.0376 0.943 0.004 0.996
#> GSM49609 2 0.0376 0.943 0.004 0.996
#> GSM49610 2 0.0376 0.943 0.004 0.996
#> GSM49611 2 0.0376 0.943 0.004 0.996
#> GSM49612 2 0.0376 0.943 0.004 0.996
#> GSM49614 1 0.0376 0.990 0.996 0.004
#> GSM49615 1 0.0376 0.990 0.996 0.004
#> GSM49616 1 0.0376 0.990 0.996 0.004
#> GSM49617 1 0.0376 0.990 0.996 0.004
#> GSM49564 1 0.0000 0.993 1.000 0.000
#> GSM49565 1 0.0000 0.993 1.000 0.000
#> GSM49566 1 0.0000 0.993 1.000 0.000
#> GSM49567 1 0.0000 0.993 1.000 0.000
#> GSM49568 1 0.0000 0.993 1.000 0.000
#> GSM49569 1 0.0000 0.993 1.000 0.000
#> GSM49570 1 0.7950 0.655 0.760 0.240
#> GSM49571 1 0.0000 0.993 1.000 0.000
#> GSM49572 1 0.0000 0.993 1.000 0.000
#> GSM49573 1 0.0376 0.990 0.996 0.004
#> GSM49574 1 0.0000 0.993 1.000 0.000
#> GSM49575 1 0.0000 0.993 1.000 0.000
#> GSM49576 1 0.0000 0.993 1.000 0.000
#> GSM49577 1 0.0000 0.993 1.000 0.000
#> GSM49578 1 0.0000 0.993 1.000 0.000
#> GSM49579 1 0.0000 0.993 1.000 0.000
#> GSM49580 1 0.0000 0.993 1.000 0.000
#> GSM49581 1 0.0000 0.993 1.000 0.000
#> GSM49582 1 0.0000 0.993 1.000 0.000
#> GSM49583 2 0.3431 0.906 0.064 0.936
#> GSM49584 1 0.0000 0.993 1.000 0.000
#> GSM49585 1 0.0000 0.993 1.000 0.000
#> GSM49586 1 0.0000 0.993 1.000 0.000
#> GSM49587 1 0.0000 0.993 1.000 0.000
#> GSM49588 1 0.0000 0.993 1.000 0.000
#> GSM49589 1 0.0000 0.993 1.000 0.000
#> GSM49590 1 0.0000 0.993 1.000 0.000
#> GSM49591 1 0.0000 0.993 1.000 0.000
#> GSM49592 1 0.0000 0.993 1.000 0.000
#> GSM49593 1 0.0000 0.993 1.000 0.000
#> GSM49594 1 0.0000 0.993 1.000 0.000
#> GSM49595 1 0.0000 0.993 1.000 0.000
#> GSM49596 1 0.0000 0.993 1.000 0.000
#> GSM49597 2 0.9850 0.274 0.428 0.572
#> GSM49598 1 0.0000 0.993 1.000 0.000
#> GSM49599 1 0.0000 0.993 1.000 0.000
#> GSM49600 1 0.0000 0.993 1.000 0.000
#> GSM49601 1 0.0000 0.993 1.000 0.000
#> GSM49602 1 0.0000 0.993 1.000 0.000
#> GSM49603 1 0.0000 0.993 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM49613 3 0.1411 0.896194 0.036 0.000 0.964
#> GSM49604 2 0.3856 0.780821 0.072 0.888 0.040
#> GSM49605 2 0.0000 0.893978 0.000 1.000 0.000
#> GSM49606 2 0.0000 0.893978 0.000 1.000 0.000
#> GSM49607 2 0.0000 0.893978 0.000 1.000 0.000
#> GSM49608 2 0.0000 0.893978 0.000 1.000 0.000
#> GSM49609 2 0.0000 0.893978 0.000 1.000 0.000
#> GSM49610 2 0.0000 0.893978 0.000 1.000 0.000
#> GSM49611 2 0.0000 0.893978 0.000 1.000 0.000
#> GSM49612 2 0.0000 0.893978 0.000 1.000 0.000
#> GSM49614 3 0.2066 0.893608 0.060 0.000 0.940
#> GSM49615 3 0.3752 0.863300 0.144 0.000 0.856
#> GSM49616 3 0.2066 0.906452 0.060 0.000 0.940
#> GSM49617 3 0.3686 0.876580 0.140 0.000 0.860
#> GSM49564 1 0.5098 0.862066 0.752 0.000 0.248
#> GSM49565 1 0.1163 0.824817 0.972 0.000 0.028
#> GSM49566 1 0.4931 0.865190 0.768 0.000 0.232
#> GSM49567 1 0.0892 0.821073 0.980 0.000 0.020
#> GSM49568 1 0.0892 0.821073 0.980 0.000 0.020
#> GSM49569 1 0.5138 0.860823 0.748 0.000 0.252
#> GSM49570 1 0.8894 0.599574 0.572 0.192 0.236
#> GSM49571 1 0.4605 0.869388 0.796 0.000 0.204
#> GSM49572 1 0.0747 0.824010 0.984 0.000 0.016
#> GSM49573 1 0.5247 0.864704 0.768 0.008 0.224
#> GSM49574 1 0.2066 0.842190 0.940 0.000 0.060
#> GSM49575 1 0.2625 0.847582 0.916 0.000 0.084
#> GSM49576 1 0.4178 0.871476 0.828 0.000 0.172
#> GSM49577 1 0.4002 0.851071 0.840 0.000 0.160
#> GSM49578 1 0.1289 0.823868 0.968 0.000 0.032
#> GSM49579 1 0.2959 0.860369 0.900 0.000 0.100
#> GSM49580 1 0.3412 0.868587 0.876 0.000 0.124
#> GSM49581 1 0.1964 0.843192 0.944 0.000 0.056
#> GSM49582 1 0.0892 0.821073 0.980 0.000 0.020
#> GSM49583 2 0.2773 0.835098 0.048 0.928 0.024
#> GSM49584 1 0.2356 0.848616 0.928 0.000 0.072
#> GSM49585 1 0.3340 0.857137 0.880 0.000 0.120
#> GSM49586 1 0.5138 0.860823 0.748 0.000 0.252
#> GSM49587 1 0.0892 0.821073 0.980 0.000 0.020
#> GSM49588 1 0.2959 0.855113 0.900 0.000 0.100
#> GSM49589 1 0.5138 0.860823 0.748 0.000 0.252
#> GSM49590 1 0.5098 0.861701 0.752 0.000 0.248
#> GSM49591 1 0.0592 0.826582 0.988 0.000 0.012
#> GSM49592 1 0.1289 0.824092 0.968 0.000 0.032
#> GSM49593 1 0.5138 0.860823 0.748 0.000 0.252
#> GSM49594 1 0.4887 0.868772 0.772 0.000 0.228
#> GSM49595 1 0.5138 0.860823 0.748 0.000 0.252
#> GSM49596 1 0.4974 0.866270 0.764 0.000 0.236
#> GSM49597 2 0.9335 -0.000253 0.324 0.492 0.184
#> GSM49598 1 0.4654 0.869575 0.792 0.000 0.208
#> GSM49599 1 0.4062 0.871813 0.836 0.000 0.164
#> GSM49600 1 0.4842 0.866578 0.776 0.000 0.224
#> GSM49601 1 0.4654 0.866620 0.792 0.000 0.208
#> GSM49602 1 0.5138 0.860823 0.748 0.000 0.252
#> GSM49603 1 0.5138 0.860823 0.748 0.000 0.252
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM49613 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM49604 2 0.3009 0.8667 0.052 0.892 0 0.056
#> GSM49605 2 0.0188 0.9713 0.000 0.996 0 0.004
#> GSM49606 2 0.0000 0.9742 0.000 1.000 0 0.000
#> GSM49607 2 0.0000 0.9742 0.000 1.000 0 0.000
#> GSM49608 2 0.0000 0.9742 0.000 1.000 0 0.000
#> GSM49609 2 0.0000 0.9742 0.000 1.000 0 0.000
#> GSM49610 2 0.0000 0.9742 0.000 1.000 0 0.000
#> GSM49611 2 0.0000 0.9742 0.000 1.000 0 0.000
#> GSM49612 2 0.0000 0.9742 0.000 1.000 0 0.000
#> GSM49614 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM49615 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM49616 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM49617 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM49564 4 0.2530 0.8290 0.112 0.000 0 0.888
#> GSM49565 1 0.1389 0.7477 0.952 0.000 0 0.048
#> GSM49566 4 0.3311 0.8045 0.172 0.000 0 0.828
#> GSM49567 1 0.0000 0.7439 1.000 0.000 0 0.000
#> GSM49568 1 0.0336 0.7464 0.992 0.000 0 0.008
#> GSM49569 4 0.1716 0.8343 0.064 0.000 0 0.936
#> GSM49570 4 0.3266 0.7585 0.084 0.040 0 0.876
#> GSM49571 1 0.4998 0.2196 0.512 0.000 0 0.488
#> GSM49572 1 0.0469 0.7478 0.988 0.000 0 0.012
#> GSM49573 4 0.3123 0.7498 0.156 0.000 0 0.844
#> GSM49574 1 0.4999 -0.2018 0.508 0.000 0 0.492
#> GSM49575 1 0.4543 0.4099 0.676 0.000 0 0.324
#> GSM49576 4 0.4454 0.6231 0.308 0.000 0 0.692
#> GSM49577 4 0.4431 0.6233 0.304 0.000 0 0.696
#> GSM49578 1 0.1302 0.7431 0.956 0.000 0 0.044
#> GSM49579 1 0.4040 0.6252 0.752 0.000 0 0.248
#> GSM49580 1 0.4989 -0.0525 0.528 0.000 0 0.472
#> GSM49581 1 0.3942 0.5580 0.764 0.000 0 0.236
#> GSM49582 1 0.0000 0.7439 1.000 0.000 0 0.000
#> GSM49583 2 0.2282 0.9093 0.024 0.924 0 0.052
#> GSM49584 1 0.2408 0.7240 0.896 0.000 0 0.104
#> GSM49585 1 0.4356 0.5931 0.708 0.000 0 0.292
#> GSM49586 4 0.1716 0.8343 0.064 0.000 0 0.936
#> GSM49587 1 0.0188 0.7453 0.996 0.000 0 0.004
#> GSM49588 1 0.3649 0.6628 0.796 0.000 0 0.204
#> GSM49589 4 0.2868 0.8066 0.136 0.000 0 0.864
#> GSM49590 4 0.2530 0.8299 0.112 0.000 0 0.888
#> GSM49591 1 0.1637 0.7485 0.940 0.000 0 0.060
#> GSM49592 1 0.2281 0.7238 0.904 0.000 0 0.096
#> GSM49593 4 0.1716 0.8343 0.064 0.000 0 0.936
#> GSM49594 4 0.2530 0.8268 0.112 0.000 0 0.888
#> GSM49595 4 0.1867 0.8358 0.072 0.000 0 0.928
#> GSM49596 4 0.3486 0.7445 0.188 0.000 0 0.812
#> GSM49597 4 0.4319 0.5899 0.012 0.228 0 0.760
#> GSM49598 4 0.4746 0.3866 0.368 0.000 0 0.632
#> GSM49599 4 0.4454 0.6352 0.308 0.000 0 0.692
#> GSM49600 4 0.3837 0.7667 0.224 0.000 0 0.776
#> GSM49601 1 0.4996 0.2248 0.516 0.000 0 0.484
#> GSM49602 4 0.1716 0.8343 0.064 0.000 0 0.936
#> GSM49603 4 0.1792 0.8343 0.068 0.000 0 0.932
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM49613 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM49604 2 0.3942 0.850 0.020 0.748 0 0.232 0.000
#> GSM49605 2 0.0290 0.884 0.000 0.992 0 0.008 0.000
#> GSM49606 2 0.0290 0.887 0.000 0.992 0 0.008 0.000
#> GSM49607 2 0.0162 0.885 0.000 0.996 0 0.004 0.000
#> GSM49608 2 0.0290 0.884 0.000 0.992 0 0.008 0.000
#> GSM49609 2 0.3210 0.881 0.000 0.788 0 0.212 0.000
#> GSM49610 2 0.3210 0.881 0.000 0.788 0 0.212 0.000
#> GSM49611 2 0.3210 0.881 0.000 0.788 0 0.212 0.000
#> GSM49612 2 0.3210 0.881 0.000 0.788 0 0.212 0.000
#> GSM49614 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM49615 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM49616 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM49617 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM49564 5 0.0880 0.736 0.032 0.000 0 0.000 0.968
#> GSM49565 1 0.1043 0.779 0.960 0.000 0 0.000 0.040
#> GSM49566 5 0.3305 0.634 0.224 0.000 0 0.000 0.776
#> GSM49567 1 0.0000 0.775 1.000 0.000 0 0.000 0.000
#> GSM49568 1 0.0162 0.776 0.996 0.000 0 0.000 0.004
#> GSM49569 5 0.0000 0.736 0.000 0.000 0 0.000 1.000
#> GSM49570 4 0.3760 0.921 0.028 0.000 0 0.784 0.188
#> GSM49571 5 0.3966 0.392 0.336 0.000 0 0.000 0.664
#> GSM49572 1 0.0404 0.779 0.988 0.000 0 0.000 0.012
#> GSM49573 4 0.3885 0.913 0.040 0.000 0 0.784 0.176
#> GSM49574 1 0.4138 0.271 0.616 0.000 0 0.000 0.384
#> GSM49575 1 0.3684 0.534 0.720 0.000 0 0.000 0.280
#> GSM49576 5 0.4045 0.446 0.356 0.000 0 0.000 0.644
#> GSM49577 5 0.3857 0.522 0.312 0.000 0 0.000 0.688
#> GSM49578 1 0.1608 0.757 0.928 0.000 0 0.000 0.072
#> GSM49579 1 0.3366 0.641 0.768 0.000 0 0.000 0.232
#> GSM49580 1 0.4219 0.227 0.584 0.000 0 0.000 0.416
#> GSM49581 1 0.3074 0.658 0.804 0.000 0 0.000 0.196
#> GSM49582 1 0.0000 0.775 1.000 0.000 0 0.000 0.000
#> GSM49583 2 0.1121 0.866 0.000 0.956 0 0.044 0.000
#> GSM49584 1 0.2020 0.755 0.900 0.000 0 0.000 0.100
#> GSM49585 1 0.4182 0.348 0.600 0.000 0 0.000 0.400
#> GSM49586 5 0.0000 0.736 0.000 0.000 0 0.000 1.000
#> GSM49587 1 0.0000 0.775 1.000 0.000 0 0.000 0.000
#> GSM49588 1 0.3109 0.672 0.800 0.000 0 0.000 0.200
#> GSM49589 5 0.1270 0.735 0.052 0.000 0 0.000 0.948
#> GSM49590 5 0.2471 0.692 0.136 0.000 0 0.000 0.864
#> GSM49591 1 0.1410 0.781 0.940 0.000 0 0.000 0.060
#> GSM49592 1 0.3003 0.658 0.812 0.000 0 0.000 0.188
#> GSM49593 5 0.0000 0.736 0.000 0.000 0 0.000 1.000
#> GSM49594 5 0.1671 0.725 0.076 0.000 0 0.000 0.924
#> GSM49595 5 0.0290 0.738 0.008 0.000 0 0.000 0.992
#> GSM49596 5 0.1792 0.721 0.084 0.000 0 0.000 0.916
#> GSM49597 4 0.4194 0.853 0.004 0.012 0 0.708 0.276
#> GSM49598 5 0.3707 0.579 0.284 0.000 0 0.000 0.716
#> GSM49599 5 0.4219 0.266 0.416 0.000 0 0.000 0.584
#> GSM49600 5 0.3837 0.539 0.308 0.000 0 0.000 0.692
#> GSM49601 5 0.3983 0.380 0.340 0.000 0 0.000 0.660
#> GSM49602 5 0.0000 0.736 0.000 0.000 0 0.000 1.000
#> GSM49603 5 0.0000 0.736 0.000 0.000 0 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM49613 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49604 2 0.1536 0.858 0.016 0.940 0 0.004 0.000 0.040
#> GSM49605 6 0.0260 0.953 0.000 0.008 0 0.000 0.000 0.992
#> GSM49606 2 0.3817 0.209 0.000 0.568 0 0.000 0.000 0.432
#> GSM49607 6 0.0260 0.953 0.000 0.008 0 0.000 0.000 0.992
#> GSM49608 6 0.0713 0.947 0.000 0.028 0 0.000 0.000 0.972
#> GSM49609 2 0.0000 0.890 0.000 1.000 0 0.000 0.000 0.000
#> GSM49610 2 0.0000 0.890 0.000 1.000 0 0.000 0.000 0.000
#> GSM49611 2 0.0000 0.890 0.000 1.000 0 0.000 0.000 0.000
#> GSM49612 2 0.0000 0.890 0.000 1.000 0 0.000 0.000 0.000
#> GSM49614 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49615 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49616 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49617 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49564 5 0.0713 0.785 0.028 0.000 0 0.000 0.972 0.000
#> GSM49565 1 0.0547 0.794 0.980 0.000 0 0.000 0.020 0.000
#> GSM49566 5 0.3189 0.633 0.236 0.000 0 0.000 0.760 0.004
#> GSM49567 1 0.0146 0.792 0.996 0.000 0 0.000 0.000 0.004
#> GSM49568 1 0.0146 0.793 0.996 0.000 0 0.000 0.004 0.000
#> GSM49569 5 0.0000 0.786 0.000 0.000 0 0.000 1.000 0.000
#> GSM49570 4 0.0000 0.834 0.000 0.000 0 1.000 0.000 0.000
#> GSM49571 5 0.3446 0.452 0.308 0.000 0 0.000 0.692 0.000
#> GSM49572 1 0.0603 0.795 0.980 0.000 0 0.000 0.016 0.004
#> GSM49573 4 0.0000 0.834 0.000 0.000 0 1.000 0.000 0.000
#> GSM49574 1 0.3620 0.358 0.648 0.000 0 0.000 0.352 0.000
#> GSM49575 1 0.3221 0.567 0.736 0.000 0 0.000 0.264 0.000
#> GSM49576 5 0.3782 0.428 0.360 0.000 0 0.000 0.636 0.004
#> GSM49577 5 0.3636 0.514 0.320 0.000 0 0.000 0.676 0.004
#> GSM49578 1 0.1556 0.765 0.920 0.000 0 0.000 0.080 0.000
#> GSM49579 1 0.3081 0.662 0.776 0.000 0 0.000 0.220 0.004
#> GSM49580 1 0.3756 0.293 0.600 0.000 0 0.000 0.400 0.000
#> GSM49581 1 0.2597 0.689 0.824 0.000 0 0.000 0.176 0.000
#> GSM49582 1 0.0000 0.791 1.000 0.000 0 0.000 0.000 0.000
#> GSM49583 6 0.1663 0.889 0.000 0.088 0 0.000 0.000 0.912
#> GSM49584 1 0.1814 0.766 0.900 0.000 0 0.000 0.100 0.000
#> GSM49585 1 0.3774 0.334 0.592 0.000 0 0.000 0.408 0.000
#> GSM49586 5 0.0000 0.786 0.000 0.000 0 0.000 1.000 0.000
#> GSM49587 1 0.0000 0.791 1.000 0.000 0 0.000 0.000 0.000
#> GSM49588 1 0.2730 0.690 0.808 0.000 0 0.000 0.192 0.000
#> GSM49589 5 0.1141 0.780 0.052 0.000 0 0.000 0.948 0.000
#> GSM49590 5 0.2482 0.717 0.148 0.000 0 0.000 0.848 0.004
#> GSM49591 1 0.1267 0.791 0.940 0.000 0 0.000 0.060 0.000
#> GSM49592 1 0.2823 0.643 0.796 0.000 0 0.000 0.204 0.000
#> GSM49593 5 0.0000 0.786 0.000 0.000 0 0.000 1.000 0.000
#> GSM49594 5 0.1610 0.761 0.084 0.000 0 0.000 0.916 0.000
#> GSM49595 5 0.0260 0.787 0.008 0.000 0 0.000 0.992 0.000
#> GSM49596 5 0.1327 0.772 0.064 0.000 0 0.000 0.936 0.000
#> GSM49597 4 0.4423 0.573 0.000 0.000 0 0.668 0.060 0.272
#> GSM49598 5 0.3290 0.631 0.252 0.000 0 0.000 0.744 0.004
#> GSM49599 5 0.3971 0.167 0.448 0.000 0 0.000 0.548 0.004
#> GSM49600 5 0.3565 0.542 0.304 0.000 0 0.000 0.692 0.004
#> GSM49601 5 0.3482 0.431 0.316 0.000 0 0.000 0.684 0.000
#> GSM49602 5 0.0000 0.786 0.000 0.000 0 0.000 1.000 0.000
#> GSM49603 5 0.0000 0.786 0.000 0.000 0 0.000 1.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> CV:pam 53 2.95e-09 6.95e-05 2
#> CV:pam 53 7.99e-10 1.20e-14 3
#> CV:pam 48 3.28e-08 6.15e-12 4
#> CV:pam 47 1.93e-07 1.29e-10 5
#> CV:pam 46 8.86e-07 2.22e-13 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21168 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.826 0.930 0.967 0.4376 0.547 0.547
#> 3 3 0.957 0.947 0.971 0.1634 0.955 0.917
#> 4 4 0.643 0.805 0.844 0.1934 0.979 0.958
#> 5 5 0.619 0.620 0.841 0.1768 0.783 0.550
#> 6 6 0.637 0.446 0.731 0.0952 0.892 0.647
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM49613 2 0.8327 0.719 0.264 0.736
#> GSM49604 2 0.0000 0.918 0.000 1.000
#> GSM49605 2 0.0000 0.918 0.000 1.000
#> GSM49606 2 0.0000 0.918 0.000 1.000
#> GSM49607 2 0.0000 0.918 0.000 1.000
#> GSM49608 2 0.0000 0.918 0.000 1.000
#> GSM49609 2 0.0000 0.918 0.000 1.000
#> GSM49610 2 0.0000 0.918 0.000 1.000
#> GSM49611 2 0.0000 0.918 0.000 1.000
#> GSM49612 2 0.0000 0.918 0.000 1.000
#> GSM49614 2 0.8267 0.724 0.260 0.740
#> GSM49615 2 0.8327 0.719 0.264 0.736
#> GSM49616 2 0.8327 0.719 0.264 0.736
#> GSM49617 2 0.8327 0.719 0.264 0.736
#> GSM49564 1 0.0000 0.986 1.000 0.000
#> GSM49565 1 0.0000 0.986 1.000 0.000
#> GSM49566 1 0.0000 0.986 1.000 0.000
#> GSM49567 1 0.0000 0.986 1.000 0.000
#> GSM49568 1 0.0000 0.986 1.000 0.000
#> GSM49569 1 0.0000 0.986 1.000 0.000
#> GSM49570 2 0.0000 0.918 0.000 1.000
#> GSM49571 1 0.9686 0.243 0.604 0.396
#> GSM49572 1 0.0000 0.986 1.000 0.000
#> GSM49573 2 0.0672 0.913 0.008 0.992
#> GSM49574 1 0.0000 0.986 1.000 0.000
#> GSM49575 1 0.0000 0.986 1.000 0.000
#> GSM49576 1 0.0000 0.986 1.000 0.000
#> GSM49577 1 0.0000 0.986 1.000 0.000
#> GSM49578 1 0.0000 0.986 1.000 0.000
#> GSM49579 1 0.0000 0.986 1.000 0.000
#> GSM49580 1 0.0000 0.986 1.000 0.000
#> GSM49581 1 0.0000 0.986 1.000 0.000
#> GSM49582 1 0.0000 0.986 1.000 0.000
#> GSM49583 2 0.0000 0.918 0.000 1.000
#> GSM49584 1 0.0000 0.986 1.000 0.000
#> GSM49585 1 0.0000 0.986 1.000 0.000
#> GSM49586 1 0.0000 0.986 1.000 0.000
#> GSM49587 1 0.0000 0.986 1.000 0.000
#> GSM49588 1 0.0000 0.986 1.000 0.000
#> GSM49589 1 0.0000 0.986 1.000 0.000
#> GSM49590 1 0.0376 0.982 0.996 0.004
#> GSM49591 1 0.0000 0.986 1.000 0.000
#> GSM49592 1 0.0000 0.986 1.000 0.000
#> GSM49593 1 0.0000 0.986 1.000 0.000
#> GSM49594 1 0.0000 0.986 1.000 0.000
#> GSM49595 1 0.0000 0.986 1.000 0.000
#> GSM49596 1 0.0000 0.986 1.000 0.000
#> GSM49597 2 0.0000 0.918 0.000 1.000
#> GSM49598 1 0.0000 0.986 1.000 0.000
#> GSM49599 1 0.2423 0.943 0.960 0.040
#> GSM49600 1 0.0000 0.986 1.000 0.000
#> GSM49601 1 0.0000 0.986 1.000 0.000
#> GSM49602 1 0.0000 0.986 1.000 0.000
#> GSM49603 1 0.0000 0.986 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM49613 3 0.0000 1.000 0.000 0.000 1.000
#> GSM49604 2 0.4974 0.754 0.000 0.764 0.236
#> GSM49605 2 0.0000 0.899 0.000 1.000 0.000
#> GSM49606 2 0.0000 0.899 0.000 1.000 0.000
#> GSM49607 2 0.0000 0.899 0.000 1.000 0.000
#> GSM49608 2 0.0000 0.899 0.000 1.000 0.000
#> GSM49609 2 0.0000 0.899 0.000 1.000 0.000
#> GSM49610 2 0.0000 0.899 0.000 1.000 0.000
#> GSM49611 2 0.0000 0.899 0.000 1.000 0.000
#> GSM49612 2 0.0000 0.899 0.000 1.000 0.000
#> GSM49614 3 0.0000 1.000 0.000 0.000 1.000
#> GSM49615 3 0.0000 1.000 0.000 0.000 1.000
#> GSM49616 3 0.0000 1.000 0.000 0.000 1.000
#> GSM49617 3 0.0000 1.000 0.000 0.000 1.000
#> GSM49564 1 0.1529 0.962 0.960 0.000 0.040
#> GSM49565 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49566 1 0.0892 0.976 0.980 0.000 0.020
#> GSM49567 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49568 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49569 1 0.1289 0.968 0.968 0.000 0.032
#> GSM49570 2 0.5650 0.663 0.000 0.688 0.312
#> GSM49571 1 0.4452 0.752 0.808 0.000 0.192
#> GSM49572 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49573 2 0.5831 0.695 0.008 0.708 0.284
#> GSM49574 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49575 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49576 1 0.1411 0.965 0.964 0.000 0.036
#> GSM49577 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49578 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49579 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49580 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49581 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49582 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49583 2 0.1753 0.880 0.000 0.952 0.048
#> GSM49584 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49585 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49586 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49587 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49588 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49589 1 0.1411 0.965 0.964 0.000 0.036
#> GSM49590 1 0.1411 0.965 0.964 0.000 0.036
#> GSM49591 1 0.0424 0.984 0.992 0.000 0.008
#> GSM49592 1 0.0592 0.982 0.988 0.000 0.012
#> GSM49593 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49594 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49595 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49596 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49597 2 0.5016 0.751 0.000 0.760 0.240
#> GSM49598 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49599 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49600 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49601 1 0.0000 0.988 1.000 0.000 0.000
#> GSM49602 1 0.0237 0.986 0.996 0.000 0.004
#> GSM49603 1 0.0424 0.984 0.992 0.000 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM49613 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM49604 2 0.4941 -0.526 0.000 0.564 0.000 0.436
#> GSM49605 2 0.0336 0.849 0.000 0.992 0.000 0.008
#> GSM49606 2 0.0000 0.855 0.000 1.000 0.000 0.000
#> GSM49607 2 0.0000 0.855 0.000 1.000 0.000 0.000
#> GSM49608 2 0.2408 0.732 0.000 0.896 0.000 0.104
#> GSM49609 2 0.0000 0.855 0.000 1.000 0.000 0.000
#> GSM49610 2 0.0000 0.855 0.000 1.000 0.000 0.000
#> GSM49611 2 0.0000 0.855 0.000 1.000 0.000 0.000
#> GSM49612 2 0.0000 0.855 0.000 1.000 0.000 0.000
#> GSM49614 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM49615 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM49616 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM49617 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM49564 1 0.1114 0.834 0.972 0.008 0.004 0.016
#> GSM49565 1 0.4804 0.750 0.616 0.000 0.000 0.384
#> GSM49566 1 0.0779 0.844 0.980 0.000 0.004 0.016
#> GSM49567 1 0.4948 0.718 0.560 0.000 0.000 0.440
#> GSM49568 1 0.3219 0.834 0.836 0.000 0.000 0.164
#> GSM49569 1 0.0657 0.837 0.984 0.000 0.004 0.012
#> GSM49570 4 0.6532 0.934 0.000 0.368 0.084 0.548
#> GSM49571 1 0.5233 0.725 0.580 0.004 0.004 0.412
#> GSM49572 1 0.4877 0.737 0.592 0.000 0.000 0.408
#> GSM49573 4 0.5775 0.885 0.000 0.408 0.032 0.560
#> GSM49574 1 0.4830 0.746 0.608 0.000 0.000 0.392
#> GSM49575 1 0.4948 0.718 0.560 0.000 0.000 0.440
#> GSM49576 1 0.0657 0.837 0.984 0.000 0.004 0.012
#> GSM49577 1 0.4877 0.737 0.592 0.000 0.000 0.408
#> GSM49578 1 0.3649 0.828 0.796 0.000 0.000 0.204
#> GSM49579 1 0.0000 0.842 1.000 0.000 0.000 0.000
#> GSM49580 1 0.2868 0.841 0.864 0.000 0.000 0.136
#> GSM49581 1 0.4713 0.767 0.640 0.000 0.000 0.360
#> GSM49582 1 0.4193 0.805 0.732 0.000 0.000 0.268
#> GSM49583 2 0.3908 0.486 0.000 0.784 0.004 0.212
#> GSM49584 1 0.1637 0.843 0.940 0.000 0.000 0.060
#> GSM49585 1 0.0188 0.842 0.996 0.000 0.000 0.004
#> GSM49586 1 0.4643 0.765 0.656 0.000 0.000 0.344
#> GSM49587 1 0.3726 0.826 0.788 0.000 0.000 0.212
#> GSM49588 1 0.0000 0.842 1.000 0.000 0.000 0.000
#> GSM49589 1 0.0992 0.834 0.976 0.008 0.004 0.012
#> GSM49590 1 0.0992 0.834 0.976 0.008 0.004 0.012
#> GSM49591 1 0.3444 0.834 0.816 0.000 0.000 0.184
#> GSM49592 1 0.2921 0.840 0.860 0.000 0.000 0.140
#> GSM49593 1 0.0469 0.838 0.988 0.000 0.000 0.012
#> GSM49594 1 0.4164 0.793 0.736 0.000 0.000 0.264
#> GSM49595 1 0.3764 0.806 0.784 0.000 0.000 0.216
#> GSM49596 1 0.0336 0.840 0.992 0.000 0.000 0.008
#> GSM49597 4 0.6443 0.940 0.000 0.376 0.076 0.548
#> GSM49598 1 0.1118 0.836 0.964 0.000 0.000 0.036
#> GSM49599 1 0.4941 0.721 0.564 0.000 0.000 0.436
#> GSM49600 1 0.1474 0.839 0.948 0.000 0.000 0.052
#> GSM49601 1 0.0921 0.841 0.972 0.000 0.000 0.028
#> GSM49602 1 0.0469 0.838 0.988 0.000 0.000 0.012
#> GSM49603 1 0.0657 0.837 0.984 0.000 0.004 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM49613 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000
#> GSM49604 4 0.4300 -0.1186 0.000 0.476 0 0.524 0.000
#> GSM49605 2 0.0609 0.8638 0.000 0.980 0 0.020 0.000
#> GSM49606 2 0.0000 0.8758 0.000 1.000 0 0.000 0.000
#> GSM49607 2 0.0000 0.8758 0.000 1.000 0 0.000 0.000
#> GSM49608 2 0.3796 0.4865 0.000 0.700 0 0.300 0.000
#> GSM49609 2 0.0000 0.8758 0.000 1.000 0 0.000 0.000
#> GSM49610 2 0.0162 0.8738 0.000 0.996 0 0.004 0.000
#> GSM49611 2 0.0000 0.8758 0.000 1.000 0 0.000 0.000
#> GSM49612 2 0.0000 0.8758 0.000 1.000 0 0.000 0.000
#> GSM49614 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000
#> GSM49615 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000
#> GSM49616 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000
#> GSM49617 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000
#> GSM49564 5 0.1197 0.7197 0.048 0.000 0 0.000 0.952
#> GSM49565 1 0.4171 0.5468 0.604 0.000 0 0.000 0.396
#> GSM49566 5 0.0451 0.7438 0.008 0.000 0 0.004 0.988
#> GSM49567 1 0.2377 0.6150 0.872 0.000 0 0.000 0.128
#> GSM49568 5 0.4074 0.2555 0.364 0.000 0 0.000 0.636
#> GSM49569 5 0.0000 0.7430 0.000 0.000 0 0.000 1.000
#> GSM49570 4 0.0162 0.8068 0.000 0.004 0 0.996 0.000
#> GSM49571 1 0.1285 0.5644 0.956 0.004 0 0.004 0.036
#> GSM49572 1 0.4161 0.5419 0.608 0.000 0 0.000 0.392
#> GSM49573 4 0.0162 0.8068 0.000 0.004 0 0.996 0.000
#> GSM49574 1 0.4150 0.5505 0.612 0.000 0 0.000 0.388
#> GSM49575 1 0.0162 0.5625 0.996 0.000 0 0.000 0.004
#> GSM49576 5 0.0162 0.7419 0.004 0.000 0 0.000 0.996
#> GSM49577 1 0.3876 0.5984 0.684 0.000 0 0.000 0.316
#> GSM49578 5 0.3949 0.3087 0.332 0.000 0 0.000 0.668
#> GSM49579 5 0.0671 0.7433 0.016 0.000 0 0.004 0.980
#> GSM49580 5 0.4390 0.2594 0.428 0.000 0 0.004 0.568
#> GSM49581 1 0.3857 0.3543 0.688 0.000 0 0.000 0.312
#> GSM49582 1 0.4256 0.1042 0.564 0.000 0 0.000 0.436
#> GSM49583 2 0.4304 -0.0609 0.000 0.516 0 0.484 0.000
#> GSM49584 5 0.3336 0.5652 0.228 0.000 0 0.000 0.772
#> GSM49585 5 0.2389 0.6774 0.116 0.000 0 0.004 0.880
#> GSM49586 1 0.3814 0.5841 0.720 0.000 0 0.004 0.276
#> GSM49587 5 0.4114 0.2097 0.376 0.000 0 0.000 0.624
#> GSM49588 5 0.1671 0.7214 0.076 0.000 0 0.000 0.924
#> GSM49589 5 0.0162 0.7419 0.004 0.000 0 0.000 0.996
#> GSM49590 5 0.0162 0.7419 0.004 0.000 0 0.000 0.996
#> GSM49591 5 0.3857 0.3427 0.312 0.000 0 0.000 0.688
#> GSM49592 5 0.3876 0.3423 0.316 0.000 0 0.000 0.684
#> GSM49593 5 0.1864 0.7186 0.068 0.004 0 0.004 0.924
#> GSM49594 1 0.4594 0.4146 0.508 0.004 0 0.004 0.484
#> GSM49595 1 0.4452 0.3944 0.500 0.000 0 0.004 0.496
#> GSM49596 5 0.1544 0.7280 0.068 0.000 0 0.000 0.932
#> GSM49597 4 0.0290 0.8053 0.000 0.008 0 0.992 0.000
#> GSM49598 5 0.3906 0.4371 0.292 0.000 0 0.004 0.704
#> GSM49599 1 0.0162 0.5625 0.996 0.000 0 0.000 0.004
#> GSM49600 5 0.4135 0.3868 0.340 0.000 0 0.004 0.656
#> GSM49601 5 0.3569 0.6411 0.152 0.028 0 0.004 0.816
#> GSM49602 5 0.0162 0.7436 0.004 0.000 0 0.000 0.996
#> GSM49603 5 0.0000 0.7430 0.000 0.000 0 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM49613 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49604 2 0.3966 0.2089 0.000 0.552 0 0.444 0.000 0.004
#> GSM49605 2 0.0260 0.7597 0.000 0.992 0 0.008 0.000 0.000
#> GSM49606 2 0.1663 0.7548 0.000 0.912 0 0.000 0.000 0.088
#> GSM49607 2 0.0000 0.7608 0.000 1.000 0 0.000 0.000 0.000
#> GSM49608 2 0.2730 0.6346 0.000 0.808 0 0.192 0.000 0.000
#> GSM49609 2 0.3151 0.7096 0.000 0.748 0 0.000 0.000 0.252
#> GSM49610 2 0.0146 0.7607 0.000 0.996 0 0.004 0.000 0.000
#> GSM49611 2 0.3151 0.7096 0.000 0.748 0 0.000 0.000 0.252
#> GSM49612 2 0.3151 0.7096 0.000 0.748 0 0.000 0.000 0.252
#> GSM49614 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49615 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49616 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49617 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49564 5 0.3151 0.5133 0.000 0.000 0 0.000 0.748 0.252
#> GSM49565 1 0.4863 -0.2357 0.528 0.000 0 0.000 0.060 0.412
#> GSM49566 5 0.2790 0.5782 0.024 0.000 0 0.000 0.844 0.132
#> GSM49567 1 0.2854 0.2837 0.792 0.000 0 0.000 0.000 0.208
#> GSM49568 5 0.6023 -0.2227 0.320 0.000 0 0.000 0.420 0.260
#> GSM49569 5 0.1895 0.5846 0.016 0.000 0 0.000 0.912 0.072
#> GSM49570 4 0.0000 0.9911 0.000 0.000 0 1.000 0.000 0.000
#> GSM49571 1 0.2190 0.3487 0.900 0.000 0 0.000 0.040 0.060
#> GSM49572 1 0.4409 -0.0920 0.588 0.000 0 0.000 0.032 0.380
#> GSM49573 4 0.0000 0.9911 0.000 0.000 0 1.000 0.000 0.000
#> GSM49574 1 0.5029 -0.2675 0.524 0.000 0 0.000 0.076 0.400
#> GSM49575 1 0.0000 0.3949 1.000 0.000 0 0.000 0.000 0.000
#> GSM49576 5 0.3050 0.5184 0.000 0.000 0 0.000 0.764 0.236
#> GSM49577 1 0.3984 -0.0663 0.596 0.000 0 0.000 0.008 0.396
#> GSM49578 1 0.5795 -0.0553 0.476 0.000 0 0.000 0.328 0.196
#> GSM49579 5 0.2949 0.5606 0.028 0.000 0 0.000 0.832 0.140
#> GSM49580 1 0.4283 0.0298 0.592 0.000 0 0.000 0.384 0.024
#> GSM49581 1 0.2106 0.3920 0.904 0.000 0 0.000 0.064 0.032
#> GSM49582 1 0.4252 0.2587 0.652 0.000 0 0.000 0.312 0.036
#> GSM49583 2 0.3979 0.1818 0.000 0.540 0 0.456 0.000 0.004
#> GSM49584 5 0.3619 0.4761 0.232 0.000 0 0.000 0.744 0.024
#> GSM49585 5 0.4253 0.4042 0.044 0.000 0 0.000 0.672 0.284
#> GSM49586 1 0.4986 -0.1773 0.600 0.000 0 0.000 0.096 0.304
#> GSM49587 1 0.5922 -0.3274 0.432 0.000 0 0.000 0.216 0.352
#> GSM49588 5 0.4153 0.3386 0.024 0.000 0 0.000 0.636 0.340
#> GSM49589 5 0.3126 0.5144 0.000 0.000 0 0.000 0.752 0.248
#> GSM49590 5 0.3126 0.5144 0.000 0.000 0 0.000 0.752 0.248
#> GSM49591 1 0.5956 -0.1864 0.420 0.000 0 0.000 0.356 0.224
#> GSM49592 5 0.6015 -0.4213 0.376 0.000 0 0.000 0.384 0.240
#> GSM49593 5 0.4301 0.2344 0.024 0.000 0 0.000 0.584 0.392
#> GSM49594 6 0.5879 0.9452 0.344 0.000 0 0.000 0.208 0.448
#> GSM49595 6 0.5932 0.9463 0.336 0.000 0 0.000 0.224 0.440
#> GSM49596 5 0.4028 0.3932 0.024 0.000 0 0.000 0.668 0.308
#> GSM49597 4 0.0603 0.9819 0.000 0.016 0 0.980 0.000 0.004
#> GSM49598 5 0.3778 0.4626 0.288 0.000 0 0.000 0.696 0.016
#> GSM49599 1 0.0000 0.3949 1.000 0.000 0 0.000 0.000 0.000
#> GSM49600 5 0.3738 0.4777 0.280 0.000 0 0.000 0.704 0.016
#> GSM49601 5 0.4573 0.2451 0.044 0.000 0 0.000 0.584 0.372
#> GSM49602 5 0.2709 0.5669 0.020 0.000 0 0.000 0.848 0.132
#> GSM49603 5 0.1092 0.5933 0.020 0.000 0 0.000 0.960 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) cell.type(p) k
#> CV:mclust 53 6.04e-06 2.65e-05 2
#> CV:mclust 54 2.57e-07 8.46e-14 3
#> CV:mclust 52 4.64e-10 2.91e-14 4
#> CV:mclust 39 7.13e-07 7.13e-10 5
#> CV:mclust 27 1.05e-04 9.31e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21168 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.887 0.937 0.972 0.4214 0.591 0.591
#> 3 3 0.896 0.891 0.949 0.3945 0.781 0.642
#> 4 4 0.642 0.804 0.885 0.1323 0.944 0.866
#> 5 5 0.591 0.560 0.772 0.1073 0.888 0.713
#> 6 6 0.747 0.762 0.860 0.0902 0.826 0.482
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM49613 1 0.0000 0.967 1.000 0.000
#> GSM49604 2 0.0000 0.975 0.000 1.000
#> GSM49605 2 0.0000 0.975 0.000 1.000
#> GSM49606 2 0.0000 0.975 0.000 1.000
#> GSM49607 2 0.0000 0.975 0.000 1.000
#> GSM49608 2 0.0000 0.975 0.000 1.000
#> GSM49609 2 0.0000 0.975 0.000 1.000
#> GSM49610 2 0.0000 0.975 0.000 1.000
#> GSM49611 2 0.0000 0.975 0.000 1.000
#> GSM49612 2 0.0000 0.975 0.000 1.000
#> GSM49614 1 0.9323 0.473 0.652 0.348
#> GSM49615 1 0.0000 0.967 1.000 0.000
#> GSM49616 1 0.0000 0.967 1.000 0.000
#> GSM49617 1 0.0000 0.967 1.000 0.000
#> GSM49564 1 0.0000 0.967 1.000 0.000
#> GSM49565 1 0.5294 0.861 0.880 0.120
#> GSM49566 1 0.0000 0.967 1.000 0.000
#> GSM49567 1 0.1184 0.957 0.984 0.016
#> GSM49568 1 0.0000 0.967 1.000 0.000
#> GSM49569 1 0.0000 0.967 1.000 0.000
#> GSM49570 2 0.0000 0.975 0.000 1.000
#> GSM49571 2 0.1633 0.954 0.024 0.976
#> GSM49572 1 0.0000 0.967 1.000 0.000
#> GSM49573 2 0.0000 0.975 0.000 1.000
#> GSM49574 1 0.2948 0.927 0.948 0.052
#> GSM49575 1 0.1843 0.947 0.972 0.028
#> GSM49576 1 0.0000 0.967 1.000 0.000
#> GSM49577 2 0.8813 0.544 0.300 0.700
#> GSM49578 1 0.0000 0.967 1.000 0.000
#> GSM49579 1 0.0000 0.967 1.000 0.000
#> GSM49580 1 0.0000 0.967 1.000 0.000
#> GSM49581 1 0.0000 0.967 1.000 0.000
#> GSM49582 1 0.0000 0.967 1.000 0.000
#> GSM49583 2 0.0000 0.975 0.000 1.000
#> GSM49584 1 0.0000 0.967 1.000 0.000
#> GSM49585 1 0.0000 0.967 1.000 0.000
#> GSM49586 1 0.7453 0.744 0.788 0.212
#> GSM49587 1 0.0000 0.967 1.000 0.000
#> GSM49588 1 0.0000 0.967 1.000 0.000
#> GSM49589 1 0.0000 0.967 1.000 0.000
#> GSM49590 1 0.0000 0.967 1.000 0.000
#> GSM49591 1 0.0000 0.967 1.000 0.000
#> GSM49592 1 0.0000 0.967 1.000 0.000
#> GSM49593 1 0.0000 0.967 1.000 0.000
#> GSM49594 1 0.7602 0.737 0.780 0.220
#> GSM49595 1 0.0376 0.965 0.996 0.004
#> GSM49596 1 0.0000 0.967 1.000 0.000
#> GSM49597 2 0.0000 0.975 0.000 1.000
#> GSM49598 1 0.0000 0.967 1.000 0.000
#> GSM49599 1 0.7139 0.760 0.804 0.196
#> GSM49600 1 0.0000 0.967 1.000 0.000
#> GSM49601 1 0.0000 0.967 1.000 0.000
#> GSM49602 1 0.0000 0.967 1.000 0.000
#> GSM49603 1 0.0000 0.967 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM49613 3 0.1031 0.854 0.024 0.000 0.976
#> GSM49604 2 0.0237 0.969 0.000 0.996 0.004
#> GSM49605 2 0.0592 0.969 0.000 0.988 0.012
#> GSM49606 2 0.0000 0.968 0.000 1.000 0.000
#> GSM49607 2 0.0592 0.969 0.000 0.988 0.012
#> GSM49608 2 0.0747 0.967 0.000 0.984 0.016
#> GSM49609 2 0.0592 0.962 0.000 0.988 0.012
#> GSM49610 2 0.0592 0.969 0.000 0.988 0.012
#> GSM49611 2 0.0592 0.962 0.000 0.988 0.012
#> GSM49612 2 0.0424 0.965 0.000 0.992 0.008
#> GSM49614 3 0.0892 0.837 0.000 0.020 0.980
#> GSM49615 3 0.1031 0.854 0.024 0.000 0.976
#> GSM49616 3 0.0661 0.846 0.004 0.008 0.988
#> GSM49617 3 0.0592 0.843 0.000 0.012 0.988
#> GSM49564 3 0.1643 0.851 0.044 0.000 0.956
#> GSM49565 1 0.1620 0.935 0.964 0.024 0.012
#> GSM49566 1 0.2711 0.883 0.912 0.000 0.088
#> GSM49567 1 0.1482 0.937 0.968 0.020 0.012
#> GSM49568 1 0.0000 0.946 1.000 0.000 0.000
#> GSM49569 1 0.2796 0.879 0.908 0.000 0.092
#> GSM49570 2 0.4291 0.799 0.000 0.820 0.180
#> GSM49571 2 0.3031 0.872 0.076 0.912 0.012
#> GSM49572 1 0.1015 0.942 0.980 0.012 0.008
#> GSM49573 2 0.0592 0.969 0.000 0.988 0.012
#> GSM49574 1 0.1482 0.937 0.968 0.020 0.012
#> GSM49575 1 0.1482 0.937 0.968 0.020 0.012
#> GSM49576 3 0.6307 0.131 0.488 0.000 0.512
#> GSM49577 1 0.6647 0.360 0.592 0.396 0.012
#> GSM49578 1 0.0000 0.946 1.000 0.000 0.000
#> GSM49579 1 0.0237 0.946 0.996 0.000 0.004
#> GSM49580 1 0.1753 0.923 0.952 0.000 0.048
#> GSM49581 1 0.0000 0.946 1.000 0.000 0.000
#> GSM49582 1 0.0000 0.946 1.000 0.000 0.000
#> GSM49583 2 0.0237 0.969 0.000 0.996 0.004
#> GSM49584 1 0.1289 0.934 0.968 0.000 0.032
#> GSM49585 1 0.0000 0.946 1.000 0.000 0.000
#> GSM49586 1 0.2749 0.905 0.924 0.064 0.012
#> GSM49587 1 0.0237 0.946 0.996 0.004 0.000
#> GSM49588 1 0.0000 0.946 1.000 0.000 0.000
#> GSM49589 3 0.5254 0.672 0.264 0.000 0.736
#> GSM49590 3 0.2959 0.823 0.100 0.000 0.900
#> GSM49591 1 0.1015 0.942 0.980 0.012 0.008
#> GSM49592 1 0.0475 0.945 0.992 0.004 0.004
#> GSM49593 1 0.0747 0.941 0.984 0.000 0.016
#> GSM49594 1 0.2749 0.904 0.924 0.064 0.012
#> GSM49595 1 0.1182 0.940 0.976 0.012 0.012
#> GSM49596 1 0.0000 0.946 1.000 0.000 0.000
#> GSM49597 2 0.0592 0.969 0.000 0.988 0.012
#> GSM49598 1 0.1163 0.936 0.972 0.000 0.028
#> GSM49599 1 0.5378 0.675 0.756 0.236 0.008
#> GSM49600 1 0.1643 0.925 0.956 0.000 0.044
#> GSM49601 1 0.0000 0.946 1.000 0.000 0.000
#> GSM49602 1 0.0237 0.946 0.996 0.000 0.004
#> GSM49603 1 0.1289 0.934 0.968 0.000 0.032
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM49613 3 0.0469 0.868 0.012 0.000 0.988 0.000
#> GSM49604 4 0.4624 0.474 0.000 0.340 0.000 0.660
#> GSM49605 2 0.0921 0.909 0.000 0.972 0.000 0.028
#> GSM49606 2 0.0469 0.908 0.000 0.988 0.000 0.012
#> GSM49607 2 0.2401 0.883 0.000 0.904 0.004 0.092
#> GSM49608 2 0.2197 0.892 0.000 0.916 0.004 0.080
#> GSM49609 2 0.0469 0.899 0.000 0.988 0.000 0.012
#> GSM49610 2 0.2125 0.897 0.000 0.920 0.004 0.076
#> GSM49611 2 0.0336 0.903 0.000 0.992 0.000 0.008
#> GSM49612 2 0.0188 0.905 0.000 0.996 0.000 0.004
#> GSM49614 3 0.2944 0.753 0.000 0.004 0.868 0.128
#> GSM49615 3 0.0188 0.867 0.004 0.000 0.996 0.000
#> GSM49616 3 0.0336 0.862 0.000 0.000 0.992 0.008
#> GSM49617 3 0.1004 0.850 0.000 0.004 0.972 0.024
#> GSM49564 3 0.0779 0.868 0.016 0.000 0.980 0.004
#> GSM49565 1 0.1629 0.879 0.952 0.024 0.000 0.024
#> GSM49566 1 0.3737 0.826 0.840 0.004 0.136 0.020
#> GSM49567 1 0.3123 0.803 0.844 0.000 0.000 0.156
#> GSM49568 1 0.0657 0.882 0.984 0.000 0.004 0.012
#> GSM49569 1 0.4323 0.773 0.788 0.000 0.184 0.028
#> GSM49570 4 0.2775 0.748 0.000 0.084 0.020 0.896
#> GSM49571 4 0.4711 0.686 0.064 0.152 0.000 0.784
#> GSM49572 1 0.1474 0.873 0.948 0.000 0.000 0.052
#> GSM49573 4 0.2310 0.751 0.004 0.068 0.008 0.920
#> GSM49574 1 0.1042 0.880 0.972 0.008 0.000 0.020
#> GSM49575 1 0.3873 0.733 0.772 0.000 0.000 0.228
#> GSM49576 3 0.5440 0.263 0.384 0.000 0.596 0.020
#> GSM49577 1 0.4800 0.708 0.760 0.044 0.000 0.196
#> GSM49578 1 0.0779 0.882 0.980 0.000 0.004 0.016
#> GSM49579 1 0.1510 0.881 0.956 0.000 0.016 0.028
#> GSM49580 1 0.3972 0.752 0.788 0.000 0.008 0.204
#> GSM49581 1 0.2345 0.849 0.900 0.000 0.000 0.100
#> GSM49582 1 0.0895 0.881 0.976 0.000 0.004 0.020
#> GSM49583 2 0.4761 0.505 0.000 0.664 0.004 0.332
#> GSM49584 1 0.0672 0.883 0.984 0.000 0.008 0.008
#> GSM49585 1 0.1975 0.882 0.936 0.000 0.016 0.048
#> GSM49586 1 0.6449 0.610 0.644 0.152 0.000 0.204
#> GSM49587 1 0.0592 0.881 0.984 0.000 0.000 0.016
#> GSM49588 1 0.1520 0.882 0.956 0.000 0.020 0.024
#> GSM49589 3 0.2500 0.838 0.040 0.000 0.916 0.044
#> GSM49590 3 0.2300 0.840 0.048 0.000 0.924 0.028
#> GSM49591 1 0.1022 0.884 0.968 0.000 0.000 0.032
#> GSM49592 1 0.1443 0.885 0.960 0.008 0.004 0.028
#> GSM49593 1 0.3697 0.839 0.852 0.000 0.100 0.048
#> GSM49594 1 0.5792 0.598 0.648 0.296 0.000 0.056
#> GSM49595 1 0.4261 0.817 0.820 0.112 0.000 0.068
#> GSM49596 1 0.1706 0.880 0.948 0.000 0.016 0.036
#> GSM49597 4 0.3725 0.701 0.000 0.180 0.008 0.812
#> GSM49598 1 0.1743 0.882 0.940 0.000 0.004 0.056
#> GSM49599 4 0.4331 0.534 0.288 0.000 0.000 0.712
#> GSM49600 1 0.0657 0.883 0.984 0.000 0.004 0.012
#> GSM49601 1 0.6375 0.754 0.728 0.088 0.096 0.088
#> GSM49602 1 0.3691 0.847 0.856 0.000 0.076 0.068
#> GSM49603 1 0.4764 0.802 0.788 0.000 0.124 0.088
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM49613 3 0.0000 0.877078 0.000 0.000 1.000 0.000 0.000
#> GSM49604 4 0.5849 0.595904 0.000 0.100 0.000 0.508 0.392
#> GSM49605 2 0.0955 0.899861 0.000 0.968 0.000 0.028 0.004
#> GSM49606 2 0.0324 0.904032 0.000 0.992 0.000 0.004 0.004
#> GSM49607 2 0.3895 0.683424 0.004 0.728 0.000 0.264 0.004
#> GSM49608 2 0.2929 0.815322 0.000 0.840 0.000 0.152 0.008
#> GSM49609 2 0.1671 0.868660 0.000 0.924 0.000 0.000 0.076
#> GSM49610 2 0.0671 0.903760 0.000 0.980 0.000 0.016 0.004
#> GSM49611 2 0.1270 0.887584 0.000 0.948 0.000 0.000 0.052
#> GSM49612 2 0.0609 0.901172 0.000 0.980 0.000 0.000 0.020
#> GSM49614 3 0.2522 0.801520 0.000 0.000 0.880 0.108 0.012
#> GSM49615 3 0.0000 0.877078 0.000 0.000 1.000 0.000 0.000
#> GSM49616 3 0.0324 0.874830 0.000 0.000 0.992 0.004 0.004
#> GSM49617 3 0.1168 0.859329 0.000 0.000 0.960 0.032 0.008
#> GSM49564 3 0.0451 0.874853 0.004 0.000 0.988 0.000 0.008
#> GSM49565 1 0.1485 0.691143 0.948 0.000 0.000 0.032 0.020
#> GSM49566 1 0.6565 0.440232 0.604 0.004 0.048 0.112 0.232
#> GSM49567 1 0.3238 0.627958 0.836 0.000 0.000 0.136 0.028
#> GSM49568 1 0.0609 0.698868 0.980 0.000 0.000 0.000 0.020
#> GSM49569 1 0.6089 0.300142 0.568 0.000 0.124 0.008 0.300
#> GSM49570 4 0.4317 0.634045 0.000 0.004 0.008 0.668 0.320
#> GSM49571 5 0.5322 -0.571697 0.012 0.036 0.000 0.372 0.580
#> GSM49572 1 0.2712 0.658872 0.880 0.000 0.000 0.088 0.032
#> GSM49573 4 0.4516 0.597391 0.000 0.004 0.004 0.576 0.416
#> GSM49574 1 0.0898 0.695984 0.972 0.000 0.000 0.008 0.020
#> GSM49575 1 0.4138 0.544783 0.780 0.000 0.000 0.072 0.148
#> GSM49576 1 0.7011 0.001922 0.452 0.000 0.248 0.016 0.284
#> GSM49577 1 0.6107 0.339626 0.584 0.032 0.000 0.308 0.076
#> GSM49578 1 0.0794 0.694908 0.972 0.000 0.000 0.000 0.028
#> GSM49579 1 0.4423 0.493957 0.684 0.000 0.008 0.012 0.296
#> GSM49580 1 0.3474 0.657423 0.836 0.000 0.004 0.116 0.044
#> GSM49581 1 0.1582 0.700584 0.944 0.000 0.000 0.028 0.028
#> GSM49582 1 0.1082 0.696372 0.964 0.000 0.000 0.008 0.028
#> GSM49583 4 0.4710 -0.000644 0.012 0.364 0.000 0.616 0.008
#> GSM49584 1 0.0671 0.698882 0.980 0.000 0.004 0.000 0.016
#> GSM49585 1 0.4065 0.508606 0.720 0.000 0.016 0.000 0.264
#> GSM49586 5 0.2790 0.053419 0.028 0.020 0.000 0.060 0.892
#> GSM49587 1 0.0324 0.698436 0.992 0.000 0.000 0.004 0.004
#> GSM49588 1 0.2520 0.678579 0.888 0.000 0.012 0.004 0.096
#> GSM49589 3 0.3769 0.709476 0.028 0.000 0.796 0.004 0.172
#> GSM49590 3 0.4723 0.521515 0.032 0.000 0.688 0.008 0.272
#> GSM49591 1 0.2280 0.669924 0.880 0.000 0.000 0.000 0.120
#> GSM49592 1 0.2329 0.662398 0.876 0.000 0.000 0.000 0.124
#> GSM49593 1 0.5582 0.258429 0.544 0.000 0.056 0.008 0.392
#> GSM49594 5 0.6060 0.096517 0.384 0.124 0.000 0.000 0.492
#> GSM49595 1 0.5193 0.041232 0.484 0.032 0.004 0.000 0.480
#> GSM49596 1 0.4280 0.491236 0.676 0.000 0.004 0.008 0.312
#> GSM49597 4 0.2228 0.539361 0.004 0.092 0.000 0.900 0.004
#> GSM49598 1 0.4876 0.255916 0.544 0.000 0.012 0.008 0.436
#> GSM49599 4 0.5476 0.488003 0.160 0.000 0.000 0.656 0.184
#> GSM49600 1 0.2463 0.679671 0.888 0.000 0.004 0.008 0.100
#> GSM49601 5 0.6970 0.296744 0.324 0.056 0.116 0.000 0.504
#> GSM49602 1 0.5236 0.095379 0.492 0.000 0.044 0.000 0.464
#> GSM49603 5 0.5965 0.253056 0.328 0.000 0.128 0.000 0.544
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM49613 3 0.0363 0.919 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM49604 4 0.2420 0.727 0.008 0.044 0.000 0.904 0.016 0.028
#> GSM49605 2 0.2531 0.773 0.000 0.856 0.000 0.000 0.012 0.132
#> GSM49606 2 0.1531 0.802 0.000 0.928 0.000 0.004 0.000 0.068
#> GSM49607 2 0.3989 0.253 0.000 0.528 0.000 0.000 0.004 0.468
#> GSM49608 2 0.3835 0.571 0.000 0.668 0.000 0.000 0.012 0.320
#> GSM49609 2 0.2103 0.759 0.000 0.912 0.000 0.020 0.012 0.056
#> GSM49610 2 0.1477 0.807 0.000 0.940 0.000 0.008 0.004 0.048
#> GSM49611 2 0.1585 0.779 0.000 0.940 0.000 0.012 0.012 0.036
#> GSM49612 2 0.0436 0.802 0.000 0.988 0.000 0.004 0.004 0.004
#> GSM49614 3 0.1969 0.868 0.000 0.004 0.920 0.020 0.004 0.052
#> GSM49615 3 0.0260 0.920 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM49616 3 0.0146 0.920 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM49617 3 0.0146 0.917 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM49564 3 0.0964 0.914 0.000 0.000 0.968 0.012 0.016 0.004
#> GSM49565 1 0.2382 0.877 0.896 0.008 0.000 0.004 0.020 0.072
#> GSM49566 5 0.5315 0.500 0.124 0.004 0.004 0.000 0.612 0.256
#> GSM49567 1 0.3161 0.831 0.828 0.000 0.000 0.008 0.028 0.136
#> GSM49568 1 0.0837 0.893 0.972 0.004 0.000 0.004 0.020 0.000
#> GSM49569 5 0.2867 0.851 0.064 0.000 0.040 0.000 0.872 0.024
#> GSM49570 4 0.2454 0.690 0.000 0.000 0.000 0.840 0.000 0.160
#> GSM49571 4 0.2570 0.718 0.012 0.012 0.000 0.896 0.032 0.048
#> GSM49572 1 0.2911 0.854 0.856 0.000 0.000 0.008 0.036 0.100
#> GSM49573 4 0.1787 0.730 0.008 0.000 0.000 0.920 0.004 0.068
#> GSM49574 1 0.1198 0.891 0.960 0.004 0.000 0.004 0.012 0.020
#> GSM49575 1 0.2380 0.847 0.892 0.000 0.000 0.068 0.004 0.036
#> GSM49576 5 0.2467 0.842 0.020 0.000 0.036 0.000 0.896 0.048
#> GSM49577 6 0.6248 0.434 0.136 0.044 0.000 0.008 0.252 0.560
#> GSM49578 1 0.0912 0.891 0.972 0.004 0.000 0.004 0.012 0.008
#> GSM49579 5 0.3159 0.814 0.068 0.000 0.000 0.000 0.832 0.100
#> GSM49580 1 0.4441 0.765 0.768 0.000 0.000 0.068 0.080 0.084
#> GSM49581 1 0.1908 0.888 0.924 0.000 0.000 0.012 0.044 0.020
#> GSM49582 1 0.0622 0.892 0.980 0.000 0.000 0.000 0.012 0.008
#> GSM49583 6 0.3850 0.459 0.004 0.196 0.000 0.024 0.012 0.764
#> GSM49584 1 0.1391 0.890 0.944 0.000 0.000 0.000 0.040 0.016
#> GSM49585 1 0.3834 0.786 0.812 0.008 0.000 0.032 0.108 0.040
#> GSM49586 4 0.5678 0.443 0.012 0.032 0.000 0.612 0.264 0.080
#> GSM49587 1 0.1148 0.892 0.960 0.000 0.000 0.004 0.020 0.016
#> GSM49588 1 0.2056 0.874 0.904 0.000 0.000 0.004 0.080 0.012
#> GSM49589 3 0.3198 0.604 0.000 0.000 0.740 0.000 0.260 0.000
#> GSM49590 5 0.2358 0.802 0.000 0.000 0.108 0.000 0.876 0.016
#> GSM49591 1 0.2007 0.878 0.916 0.000 0.000 0.004 0.044 0.036
#> GSM49592 1 0.1465 0.884 0.948 0.004 0.000 0.004 0.020 0.024
#> GSM49593 5 0.2006 0.855 0.080 0.000 0.016 0.000 0.904 0.000
#> GSM49594 5 0.1592 0.838 0.012 0.016 0.000 0.004 0.944 0.024
#> GSM49595 5 0.1526 0.853 0.036 0.004 0.000 0.008 0.944 0.008
#> GSM49596 5 0.2915 0.759 0.184 0.000 0.000 0.000 0.808 0.008
#> GSM49597 6 0.4323 0.509 0.000 0.044 0.000 0.148 0.048 0.760
#> GSM49598 5 0.2062 0.850 0.088 0.000 0.000 0.008 0.900 0.004
#> GSM49599 4 0.5302 0.442 0.172 0.000 0.000 0.616 0.004 0.208
#> GSM49600 1 0.4343 0.338 0.592 0.000 0.000 0.004 0.384 0.020
#> GSM49601 5 0.6460 0.578 0.056 0.088 0.056 0.044 0.668 0.088
#> GSM49602 5 0.1452 0.857 0.032 0.000 0.008 0.004 0.948 0.008
#> GSM49603 5 0.2368 0.843 0.028 0.000 0.036 0.020 0.908 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) cell.type(p) k
#> CV:NMF 53 9.92e-06 2.43e-03 2
#> CV:NMF 52 2.66e-06 1.99e-08 3
#> CV:NMF 52 1.25e-08 3.47e-09 4
#> CV:NMF 37 2.51e-06 2.20e-06 5
#> CV:NMF 47 7.14e-07 1.63e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21168 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.926 0.955 0.978 0.3780 0.609 0.609
#> 3 3 0.964 0.944 0.980 0.3329 0.878 0.799
#> 4 4 0.972 0.916 0.969 0.0681 0.969 0.935
#> 5 5 0.696 0.809 0.889 0.1076 0.991 0.980
#> 6 6 0.676 0.699 0.753 0.1601 0.776 0.521
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM49613 1 0.0672 0.987 0.992 0.008
#> GSM49604 2 0.3584 0.909 0.068 0.932
#> GSM49605 2 0.0672 0.937 0.008 0.992
#> GSM49606 2 0.0672 0.937 0.008 0.992
#> GSM49607 2 0.0672 0.937 0.008 0.992
#> GSM49608 2 0.0672 0.937 0.008 0.992
#> GSM49609 2 0.0672 0.937 0.008 0.992
#> GSM49610 2 0.0672 0.937 0.008 0.992
#> GSM49611 2 0.0672 0.937 0.008 0.992
#> GSM49612 2 0.0672 0.937 0.008 0.992
#> GSM49614 1 0.0672 0.987 0.992 0.008
#> GSM49615 1 0.0672 0.987 0.992 0.008
#> GSM49616 1 0.0672 0.987 0.992 0.008
#> GSM49617 1 0.0672 0.987 0.992 0.008
#> GSM49564 1 0.0000 0.993 1.000 0.000
#> GSM49565 1 0.0000 0.993 1.000 0.000
#> GSM49566 1 0.0000 0.993 1.000 0.000
#> GSM49567 1 0.0000 0.993 1.000 0.000
#> GSM49568 1 0.0000 0.993 1.000 0.000
#> GSM49569 1 0.0000 0.993 1.000 0.000
#> GSM49570 2 0.5408 0.864 0.124 0.876
#> GSM49571 2 0.9983 0.152 0.476 0.524
#> GSM49572 1 0.0000 0.993 1.000 0.000
#> GSM49573 2 0.5408 0.864 0.124 0.876
#> GSM49574 1 0.0000 0.993 1.000 0.000
#> GSM49575 1 0.3114 0.934 0.944 0.056
#> GSM49576 1 0.0000 0.993 1.000 0.000
#> GSM49577 1 0.0000 0.993 1.000 0.000
#> GSM49578 1 0.0000 0.993 1.000 0.000
#> GSM49579 1 0.0000 0.993 1.000 0.000
#> GSM49580 1 0.0000 0.993 1.000 0.000
#> GSM49581 1 0.0000 0.993 1.000 0.000
#> GSM49582 1 0.0000 0.993 1.000 0.000
#> GSM49583 2 0.0672 0.937 0.008 0.992
#> GSM49584 1 0.0000 0.993 1.000 0.000
#> GSM49585 1 0.0000 0.993 1.000 0.000
#> GSM49586 1 0.6343 0.793 0.840 0.160
#> GSM49587 1 0.0000 0.993 1.000 0.000
#> GSM49588 1 0.0000 0.993 1.000 0.000
#> GSM49589 1 0.0000 0.993 1.000 0.000
#> GSM49590 1 0.0000 0.993 1.000 0.000
#> GSM49591 1 0.0000 0.993 1.000 0.000
#> GSM49592 1 0.0000 0.993 1.000 0.000
#> GSM49593 1 0.0000 0.993 1.000 0.000
#> GSM49594 1 0.0000 0.993 1.000 0.000
#> GSM49595 1 0.0000 0.993 1.000 0.000
#> GSM49596 1 0.0000 0.993 1.000 0.000
#> GSM49597 2 0.2778 0.921 0.048 0.952
#> GSM49598 1 0.0000 0.993 1.000 0.000
#> GSM49599 1 0.0000 0.993 1.000 0.000
#> GSM49600 1 0.0000 0.993 1.000 0.000
#> GSM49601 1 0.0000 0.993 1.000 0.000
#> GSM49602 1 0.0000 0.993 1.000 0.000
#> GSM49603 1 0.0000 0.993 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM49613 3 0.0000 1.000 0.000 0.000 1.000
#> GSM49604 2 0.2165 0.853 0.064 0.936 0.000
#> GSM49605 2 0.0000 0.896 0.000 1.000 0.000
#> GSM49606 2 0.0000 0.896 0.000 1.000 0.000
#> GSM49607 2 0.0000 0.896 0.000 1.000 0.000
#> GSM49608 2 0.0000 0.896 0.000 1.000 0.000
#> GSM49609 2 0.0000 0.896 0.000 1.000 0.000
#> GSM49610 2 0.0000 0.896 0.000 1.000 0.000
#> GSM49611 2 0.0000 0.896 0.000 1.000 0.000
#> GSM49612 2 0.0000 0.896 0.000 1.000 0.000
#> GSM49614 3 0.0000 1.000 0.000 0.000 1.000
#> GSM49615 3 0.0000 1.000 0.000 0.000 1.000
#> GSM49616 3 0.0000 1.000 0.000 0.000 1.000
#> GSM49617 3 0.0000 1.000 0.000 0.000 1.000
#> GSM49564 1 0.0424 0.986 0.992 0.000 0.008
#> GSM49565 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49566 1 0.0237 0.989 0.996 0.000 0.004
#> GSM49567 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49568 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49569 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49570 2 0.3412 0.790 0.124 0.876 0.000
#> GSM49571 2 0.6299 0.138 0.476 0.524 0.000
#> GSM49572 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49573 2 0.3412 0.790 0.124 0.876 0.000
#> GSM49574 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49575 1 0.1964 0.934 0.944 0.056 0.000
#> GSM49576 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49577 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49578 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49579 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49580 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49581 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49582 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49583 2 0.0000 0.896 0.000 1.000 0.000
#> GSM49584 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49585 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49586 1 0.4002 0.795 0.840 0.160 0.000
#> GSM49587 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49588 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49589 1 0.0237 0.989 0.996 0.000 0.004
#> GSM49590 1 0.0592 0.983 0.988 0.000 0.012
#> GSM49591 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49592 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49593 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49594 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49595 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49596 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49597 2 0.1529 0.873 0.040 0.960 0.000
#> GSM49598 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49599 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49600 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49601 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49602 1 0.0000 0.992 1.000 0.000 0.000
#> GSM49603 1 0.0000 0.992 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM49613 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM49604 4 0.4996 0.0198 0.000 0.484 0.000 0.516
#> GSM49605 2 0.0000 0.9910 0.000 1.000 0.000 0.000
#> GSM49606 2 0.0000 0.9910 0.000 1.000 0.000 0.000
#> GSM49607 2 0.0000 0.9910 0.000 1.000 0.000 0.000
#> GSM49608 2 0.0000 0.9910 0.000 1.000 0.000 0.000
#> GSM49609 2 0.0000 0.9910 0.000 1.000 0.000 0.000
#> GSM49610 2 0.0000 0.9910 0.000 1.000 0.000 0.000
#> GSM49611 2 0.0000 0.9910 0.000 1.000 0.000 0.000
#> GSM49612 2 0.0000 0.9910 0.000 1.000 0.000 0.000
#> GSM49614 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM49615 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM49616 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM49617 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM49564 1 0.0336 0.9845 0.992 0.000 0.008 0.000
#> GSM49565 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49566 1 0.0188 0.9880 0.996 0.000 0.004 0.000
#> GSM49567 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49568 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49569 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49570 4 0.0000 0.4791 0.000 0.000 0.000 1.000
#> GSM49571 4 0.5193 0.2269 0.412 0.008 0.000 0.580
#> GSM49572 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49573 4 0.0000 0.4791 0.000 0.000 0.000 1.000
#> GSM49574 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49575 1 0.1637 0.9276 0.940 0.000 0.000 0.060
#> GSM49576 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49577 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49578 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49579 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49580 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49581 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49582 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49583 2 0.1557 0.9236 0.000 0.944 0.000 0.056
#> GSM49584 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49585 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49586 1 0.3444 0.7553 0.816 0.000 0.000 0.184
#> GSM49587 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49588 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49589 1 0.0188 0.9880 0.996 0.000 0.004 0.000
#> GSM49590 1 0.0469 0.9806 0.988 0.000 0.012 0.000
#> GSM49591 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49592 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49593 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49594 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49595 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49596 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49597 4 0.4981 0.0447 0.000 0.464 0.000 0.536
#> GSM49598 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49599 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49600 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49601 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49602 1 0.0000 0.9912 1.000 0.000 0.000 0.000
#> GSM49603 1 0.0000 0.9912 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM49613 3 0.0000 1.00000 0.000 0.000 1.000 0.000 0.000
#> GSM49604 4 0.4656 -0.19963 0.000 0.480 0.000 0.508 0.012
#> GSM49605 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM49606 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM49607 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM49608 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM49609 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM49610 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM49611 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM49612 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM49614 3 0.0000 1.00000 0.000 0.000 1.000 0.000 0.000
#> GSM49615 3 0.0000 1.00000 0.000 0.000 1.000 0.000 0.000
#> GSM49616 3 0.0000 1.00000 0.000 0.000 1.000 0.000 0.000
#> GSM49617 3 0.0000 1.00000 0.000 0.000 1.000 0.000 0.000
#> GSM49564 1 0.3242 0.85539 0.784 0.000 0.000 0.000 0.216
#> GSM49565 1 0.1197 0.88917 0.952 0.000 0.000 0.000 0.048
#> GSM49566 1 0.3210 0.86120 0.788 0.000 0.000 0.000 0.212
#> GSM49567 1 0.0703 0.88483 0.976 0.000 0.000 0.000 0.024
#> GSM49568 1 0.0609 0.88369 0.980 0.000 0.000 0.000 0.020
#> GSM49569 1 0.3039 0.86527 0.808 0.000 0.000 0.000 0.192
#> GSM49570 4 0.3274 -0.00937 0.000 0.000 0.000 0.780 0.220
#> GSM49571 4 0.4621 0.11500 0.412 0.008 0.000 0.576 0.004
#> GSM49572 1 0.0609 0.88369 0.980 0.000 0.000 0.000 0.020
#> GSM49573 4 0.0000 0.11999 0.000 0.000 0.000 1.000 0.000
#> GSM49574 1 0.0609 0.88369 0.980 0.000 0.000 0.000 0.020
#> GSM49575 1 0.2012 0.84484 0.920 0.000 0.000 0.060 0.020
#> GSM49576 1 0.3143 0.86047 0.796 0.000 0.000 0.000 0.204
#> GSM49577 1 0.1908 0.88938 0.908 0.000 0.000 0.000 0.092
#> GSM49578 1 0.0609 0.88369 0.980 0.000 0.000 0.000 0.020
#> GSM49579 1 0.3003 0.86877 0.812 0.000 0.000 0.000 0.188
#> GSM49580 1 0.0963 0.88934 0.964 0.000 0.000 0.000 0.036
#> GSM49581 1 0.0880 0.88875 0.968 0.000 0.000 0.000 0.032
#> GSM49582 1 0.0609 0.88369 0.980 0.000 0.000 0.000 0.020
#> GSM49583 5 0.5077 0.16664 0.000 0.428 0.000 0.036 0.536
#> GSM49584 1 0.0963 0.88934 0.964 0.000 0.000 0.000 0.036
#> GSM49585 1 0.0963 0.88935 0.964 0.000 0.000 0.000 0.036
#> GSM49586 1 0.4948 0.66806 0.708 0.000 0.000 0.184 0.108
#> GSM49587 1 0.0609 0.88369 0.980 0.000 0.000 0.000 0.020
#> GSM49588 1 0.0880 0.88656 0.968 0.000 0.000 0.000 0.032
#> GSM49589 1 0.3074 0.86574 0.804 0.000 0.000 0.000 0.196
#> GSM49590 1 0.3607 0.83299 0.752 0.000 0.004 0.000 0.244
#> GSM49591 1 0.0609 0.88369 0.980 0.000 0.000 0.000 0.020
#> GSM49592 1 0.0609 0.88369 0.980 0.000 0.000 0.000 0.020
#> GSM49593 1 0.3074 0.86337 0.804 0.000 0.000 0.000 0.196
#> GSM49594 1 0.2424 0.88202 0.868 0.000 0.000 0.000 0.132
#> GSM49595 1 0.2424 0.88202 0.868 0.000 0.000 0.000 0.132
#> GSM49596 1 0.3074 0.86337 0.804 0.000 0.000 0.000 0.196
#> GSM49597 5 0.3876 0.10995 0.000 0.000 0.000 0.316 0.684
#> GSM49598 1 0.3177 0.85862 0.792 0.000 0.000 0.000 0.208
#> GSM49599 1 0.0609 0.88369 0.980 0.000 0.000 0.000 0.020
#> GSM49600 1 0.0963 0.88913 0.964 0.000 0.000 0.000 0.036
#> GSM49601 1 0.3109 0.86114 0.800 0.000 0.000 0.000 0.200
#> GSM49602 1 0.3177 0.85660 0.792 0.000 0.000 0.000 0.208
#> GSM49603 1 0.3177 0.85660 0.792 0.000 0.000 0.000 0.208
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM49613 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49604 2 0.7091 0.00351 0.000 0.468 0 0.212 0.160 0.160
#> GSM49605 2 0.0146 0.91528 0.000 0.996 0 0.000 0.004 0.000
#> GSM49606 2 0.0000 0.91645 0.000 1.000 0 0.000 0.000 0.000
#> GSM49607 2 0.0146 0.91528 0.000 0.996 0 0.000 0.004 0.000
#> GSM49608 2 0.0146 0.91528 0.000 0.996 0 0.000 0.004 0.000
#> GSM49609 2 0.0000 0.91645 0.000 1.000 0 0.000 0.000 0.000
#> GSM49610 2 0.0000 0.91645 0.000 1.000 0 0.000 0.000 0.000
#> GSM49611 2 0.0000 0.91645 0.000 1.000 0 0.000 0.000 0.000
#> GSM49612 2 0.0000 0.91645 0.000 1.000 0 0.000 0.000 0.000
#> GSM49614 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49615 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49616 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49617 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49564 5 0.3769 0.90483 0.356 0.000 0 0.000 0.640 0.004
#> GSM49565 1 0.1610 0.74313 0.916 0.000 0 0.000 0.084 0.000
#> GSM49566 5 0.3795 0.90155 0.364 0.000 0 0.000 0.632 0.004
#> GSM49567 1 0.1663 0.74150 0.912 0.000 0 0.000 0.088 0.000
#> GSM49568 1 0.0146 0.78225 0.996 0.000 0 0.000 0.004 0.000
#> GSM49569 5 0.3819 0.91562 0.372 0.000 0 0.000 0.624 0.004
#> GSM49570 4 0.1204 0.28759 0.000 0.000 0 0.944 0.000 0.056
#> GSM49571 1 0.7490 -0.21496 0.384 0.000 0 0.212 0.192 0.212
#> GSM49572 1 0.0291 0.78130 0.992 0.000 0 0.000 0.004 0.004
#> GSM49573 4 0.5406 0.45295 0.000 0.000 0 0.568 0.160 0.272
#> GSM49574 1 0.0405 0.78115 0.988 0.000 0 0.000 0.008 0.004
#> GSM49575 1 0.2136 0.72110 0.904 0.000 0 0.000 0.048 0.048
#> GSM49576 5 0.3728 0.90821 0.344 0.000 0 0.000 0.652 0.004
#> GSM49577 1 0.3133 0.53229 0.780 0.000 0 0.000 0.212 0.008
#> GSM49578 1 0.0000 0.78149 1.000 0.000 0 0.000 0.000 0.000
#> GSM49579 5 0.3672 0.91044 0.368 0.000 0 0.000 0.632 0.000
#> GSM49580 1 0.1714 0.74142 0.908 0.000 0 0.000 0.092 0.000
#> GSM49581 1 0.1714 0.74611 0.908 0.000 0 0.000 0.092 0.000
#> GSM49582 1 0.0000 0.78149 1.000 0.000 0 0.000 0.000 0.000
#> GSM49583 6 0.3351 0.32655 0.000 0.288 0 0.000 0.000 0.712
#> GSM49584 1 0.1387 0.75830 0.932 0.000 0 0.000 0.068 0.000
#> GSM49585 1 0.2482 0.65367 0.848 0.000 0 0.000 0.148 0.004
#> GSM49586 1 0.5119 0.00167 0.496 0.000 0 0.008 0.436 0.060
#> GSM49587 1 0.0146 0.78134 0.996 0.000 0 0.000 0.000 0.004
#> GSM49588 1 0.1285 0.76662 0.944 0.000 0 0.000 0.052 0.004
#> GSM49589 5 0.3841 0.90115 0.380 0.000 0 0.000 0.616 0.004
#> GSM49590 5 0.3584 0.87900 0.308 0.000 0 0.000 0.688 0.004
#> GSM49591 1 0.0692 0.77984 0.976 0.000 0 0.000 0.020 0.004
#> GSM49592 1 0.0260 0.78167 0.992 0.000 0 0.000 0.008 0.000
#> GSM49593 5 0.3819 0.91499 0.372 0.000 0 0.000 0.624 0.004
#> GSM49594 1 0.3998 -0.66706 0.504 0.000 0 0.000 0.492 0.004
#> GSM49595 1 0.3998 -0.66706 0.504 0.000 0 0.000 0.492 0.004
#> GSM49596 5 0.3923 0.87315 0.416 0.000 0 0.000 0.580 0.004
#> GSM49597 6 0.3864 0.06634 0.000 0.000 0 0.480 0.000 0.520
#> GSM49598 5 0.3782 0.86011 0.412 0.000 0 0.000 0.588 0.000
#> GSM49599 1 0.0260 0.78144 0.992 0.000 0 0.000 0.008 0.000
#> GSM49600 1 0.1714 0.74191 0.908 0.000 0 0.000 0.092 0.000
#> GSM49601 5 0.3852 0.90662 0.384 0.000 0 0.000 0.612 0.004
#> GSM49602 5 0.3862 0.89262 0.388 0.000 0 0.000 0.608 0.004
#> GSM49603 5 0.3862 0.89262 0.388 0.000 0 0.000 0.608 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) cell.type(p) k
#> MAD:hclust 53 8.04e-07 7.74e-04 2
#> MAD:hclust 53 3.58e-07 1.61e-13 3
#> MAD:hclust 49 6.39e-09 5.84e-14 4
#> MAD:hclust 48 5.21e-10 2.84e-14 5
#> MAD:hclust 45 1.07e-08 4.31e-12 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21168 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.547 0.964 0.946 0.3414 0.628 0.628
#> 3 3 0.709 0.885 0.920 0.5585 0.874 0.800
#> 4 4 0.723 0.908 0.830 0.2410 0.774 0.549
#> 5 5 0.919 0.950 0.929 0.1328 0.960 0.857
#> 6 6 0.805 0.862 0.872 0.0552 1.000 1.000
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM49613 1 0.6247 0.826 0.844 0.156
#> GSM49604 2 0.6247 0.992 0.156 0.844
#> GSM49605 2 0.6247 0.992 0.156 0.844
#> GSM49606 2 0.6247 0.992 0.156 0.844
#> GSM49607 2 0.6247 0.992 0.156 0.844
#> GSM49608 2 0.6247 0.992 0.156 0.844
#> GSM49609 2 0.6247 0.992 0.156 0.844
#> GSM49610 2 0.6247 0.992 0.156 0.844
#> GSM49611 2 0.6247 0.992 0.156 0.844
#> GSM49612 2 0.6247 0.992 0.156 0.844
#> GSM49614 1 0.6247 0.826 0.844 0.156
#> GSM49615 1 0.6247 0.826 0.844 0.156
#> GSM49616 1 0.6247 0.826 0.844 0.156
#> GSM49617 1 0.6247 0.826 0.844 0.156
#> GSM49564 1 0.0376 0.973 0.996 0.004
#> GSM49565 1 0.0000 0.976 1.000 0.000
#> GSM49566 1 0.0000 0.976 1.000 0.000
#> GSM49567 1 0.0000 0.976 1.000 0.000
#> GSM49568 1 0.0000 0.976 1.000 0.000
#> GSM49569 1 0.0000 0.976 1.000 0.000
#> GSM49570 2 0.6531 0.978 0.168 0.832
#> GSM49571 1 0.1414 0.956 0.980 0.020
#> GSM49572 1 0.0000 0.976 1.000 0.000
#> GSM49573 2 0.7139 0.954 0.196 0.804
#> GSM49574 1 0.0000 0.976 1.000 0.000
#> GSM49575 1 0.0000 0.976 1.000 0.000
#> GSM49576 1 0.0376 0.973 0.996 0.004
#> GSM49577 1 0.0000 0.976 1.000 0.000
#> GSM49578 1 0.0000 0.976 1.000 0.000
#> GSM49579 1 0.0000 0.976 1.000 0.000
#> GSM49580 1 0.0000 0.976 1.000 0.000
#> GSM49581 1 0.0000 0.976 1.000 0.000
#> GSM49582 1 0.0000 0.976 1.000 0.000
#> GSM49583 2 0.6247 0.992 0.156 0.844
#> GSM49584 1 0.0000 0.976 1.000 0.000
#> GSM49585 1 0.0000 0.976 1.000 0.000
#> GSM49586 1 0.0000 0.976 1.000 0.000
#> GSM49587 1 0.0000 0.976 1.000 0.000
#> GSM49588 1 0.0000 0.976 1.000 0.000
#> GSM49589 1 0.0376 0.973 0.996 0.004
#> GSM49590 1 0.0672 0.970 0.992 0.008
#> GSM49591 1 0.0000 0.976 1.000 0.000
#> GSM49592 1 0.0000 0.976 1.000 0.000
#> GSM49593 1 0.0000 0.976 1.000 0.000
#> GSM49594 1 0.0000 0.976 1.000 0.000
#> GSM49595 1 0.0000 0.976 1.000 0.000
#> GSM49596 1 0.0000 0.976 1.000 0.000
#> GSM49597 2 0.6531 0.978 0.168 0.832
#> GSM49598 1 0.0000 0.976 1.000 0.000
#> GSM49599 1 0.0000 0.976 1.000 0.000
#> GSM49600 1 0.0000 0.976 1.000 0.000
#> GSM49601 1 0.0000 0.976 1.000 0.000
#> GSM49602 1 0.0000 0.976 1.000 0.000
#> GSM49603 1 0.0000 0.976 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM49613 3 0.2356 0.985 0.072 0.000 0.928
#> GSM49604 2 0.1643 0.938 0.000 0.956 0.044
#> GSM49605 2 0.0747 0.956 0.000 0.984 0.016
#> GSM49606 2 0.0747 0.956 0.000 0.984 0.016
#> GSM49607 2 0.0747 0.956 0.000 0.984 0.016
#> GSM49608 2 0.0747 0.956 0.000 0.984 0.016
#> GSM49609 2 0.0000 0.955 0.000 1.000 0.000
#> GSM49610 2 0.0000 0.955 0.000 1.000 0.000
#> GSM49611 2 0.0000 0.955 0.000 1.000 0.000
#> GSM49612 2 0.0000 0.955 0.000 1.000 0.000
#> GSM49614 3 0.1411 0.940 0.036 0.000 0.964
#> GSM49615 3 0.2356 0.985 0.072 0.000 0.928
#> GSM49616 3 0.2356 0.985 0.072 0.000 0.928
#> GSM49617 3 0.2356 0.985 0.072 0.000 0.928
#> GSM49564 1 0.4654 0.828 0.792 0.000 0.208
#> GSM49565 1 0.0237 0.885 0.996 0.000 0.004
#> GSM49566 1 0.4504 0.836 0.804 0.000 0.196
#> GSM49567 1 0.0000 0.885 1.000 0.000 0.000
#> GSM49568 1 0.0000 0.885 1.000 0.000 0.000
#> GSM49569 1 0.4750 0.826 0.784 0.000 0.216
#> GSM49570 2 0.3619 0.876 0.000 0.864 0.136
#> GSM49571 1 0.5677 0.800 0.792 0.048 0.160
#> GSM49572 1 0.0000 0.885 1.000 0.000 0.000
#> GSM49573 2 0.4665 0.810 0.100 0.852 0.048
#> GSM49574 1 0.0000 0.885 1.000 0.000 0.000
#> GSM49575 1 0.0237 0.883 0.996 0.000 0.004
#> GSM49576 1 0.4750 0.826 0.784 0.000 0.216
#> GSM49577 1 0.0592 0.882 0.988 0.000 0.012
#> GSM49578 1 0.0000 0.885 1.000 0.000 0.000
#> GSM49579 1 0.4121 0.846 0.832 0.000 0.168
#> GSM49580 1 0.0237 0.884 0.996 0.000 0.004
#> GSM49581 1 0.0000 0.885 1.000 0.000 0.000
#> GSM49582 1 0.0000 0.885 1.000 0.000 0.000
#> GSM49583 2 0.0747 0.956 0.000 0.984 0.016
#> GSM49584 1 0.0000 0.885 1.000 0.000 0.000
#> GSM49585 1 0.0000 0.885 1.000 0.000 0.000
#> GSM49586 1 0.4702 0.830 0.788 0.000 0.212
#> GSM49587 1 0.0000 0.885 1.000 0.000 0.000
#> GSM49588 1 0.0000 0.885 1.000 0.000 0.000
#> GSM49589 1 0.4750 0.826 0.784 0.000 0.216
#> GSM49590 1 0.5560 0.720 0.700 0.000 0.300
#> GSM49591 1 0.0000 0.885 1.000 0.000 0.000
#> GSM49592 1 0.0000 0.885 1.000 0.000 0.000
#> GSM49593 1 0.4750 0.826 0.784 0.000 0.216
#> GSM49594 1 0.4702 0.830 0.788 0.000 0.212
#> GSM49595 1 0.4702 0.830 0.788 0.000 0.212
#> GSM49596 1 0.0424 0.884 0.992 0.000 0.008
#> GSM49597 2 0.3879 0.876 0.000 0.848 0.152
#> GSM49598 1 0.4750 0.826 0.784 0.000 0.216
#> GSM49599 1 0.0237 0.883 0.996 0.000 0.004
#> GSM49600 1 0.0592 0.883 0.988 0.000 0.012
#> GSM49601 1 0.4654 0.830 0.792 0.000 0.208
#> GSM49602 1 0.4750 0.826 0.784 0.000 0.216
#> GSM49603 1 0.4750 0.826 0.784 0.000 0.216
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM49613 3 0.2334 0.993 0.004 0.000 0.908 0.088
#> GSM49604 2 0.5916 0.702 0.000 0.656 0.072 0.272
#> GSM49605 2 0.0000 0.862 0.000 1.000 0.000 0.000
#> GSM49606 2 0.0000 0.862 0.000 1.000 0.000 0.000
#> GSM49607 2 0.0000 0.862 0.000 1.000 0.000 0.000
#> GSM49608 2 0.0000 0.862 0.000 1.000 0.000 0.000
#> GSM49609 2 0.0804 0.862 0.000 0.980 0.008 0.012
#> GSM49610 2 0.0804 0.862 0.000 0.980 0.008 0.012
#> GSM49611 2 0.0804 0.862 0.000 0.980 0.008 0.012
#> GSM49612 2 0.0804 0.862 0.000 0.980 0.008 0.012
#> GSM49614 3 0.1978 0.988 0.004 0.000 0.928 0.068
#> GSM49615 3 0.2334 0.993 0.004 0.000 0.908 0.088
#> GSM49616 3 0.2125 0.994 0.004 0.000 0.920 0.076
#> GSM49617 3 0.2125 0.994 0.004 0.000 0.920 0.076
#> GSM49564 4 0.4624 0.931 0.340 0.000 0.000 0.660
#> GSM49565 1 0.0469 0.983 0.988 0.000 0.000 0.012
#> GSM49566 4 0.4624 0.936 0.340 0.000 0.000 0.660
#> GSM49567 1 0.0469 0.980 0.988 0.000 0.000 0.012
#> GSM49568 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49569 4 0.4661 0.940 0.348 0.000 0.000 0.652
#> GSM49570 2 0.6454 0.625 0.000 0.544 0.076 0.380
#> GSM49571 4 0.4726 0.401 0.108 0.012 0.072 0.808
#> GSM49572 1 0.0469 0.980 0.988 0.000 0.000 0.012
#> GSM49573 2 0.7456 0.594 0.036 0.508 0.080 0.376
#> GSM49574 1 0.0188 0.988 0.996 0.000 0.000 0.004
#> GSM49575 1 0.0188 0.988 0.996 0.000 0.000 0.004
#> GSM49576 4 0.4605 0.936 0.336 0.000 0.000 0.664
#> GSM49577 4 0.4925 0.814 0.428 0.000 0.000 0.572
#> GSM49578 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49579 4 0.4679 0.930 0.352 0.000 0.000 0.648
#> GSM49580 1 0.0188 0.986 0.996 0.000 0.000 0.004
#> GSM49581 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49582 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49583 2 0.0000 0.862 0.000 1.000 0.000 0.000
#> GSM49584 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49585 1 0.0336 0.986 0.992 0.000 0.000 0.008
#> GSM49586 4 0.4837 0.938 0.348 0.000 0.004 0.648
#> GSM49587 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49588 1 0.0188 0.986 0.996 0.000 0.000 0.004
#> GSM49589 4 0.4643 0.940 0.344 0.000 0.000 0.656
#> GSM49590 4 0.4605 0.936 0.336 0.000 0.000 0.664
#> GSM49591 1 0.0188 0.988 0.996 0.000 0.000 0.004
#> GSM49592 1 0.0188 0.988 0.996 0.000 0.000 0.004
#> GSM49593 4 0.4661 0.940 0.348 0.000 0.000 0.652
#> GSM49594 4 0.4643 0.939 0.344 0.000 0.000 0.656
#> GSM49595 4 0.4643 0.939 0.344 0.000 0.000 0.656
#> GSM49596 4 0.4967 0.792 0.452 0.000 0.000 0.548
#> GSM49597 2 0.6362 0.627 0.000 0.560 0.072 0.368
#> GSM49598 4 0.4661 0.940 0.348 0.000 0.000 0.652
#> GSM49599 1 0.0336 0.986 0.992 0.000 0.000 0.008
#> GSM49600 1 0.1557 0.910 0.944 0.000 0.000 0.056
#> GSM49601 4 0.4661 0.939 0.348 0.000 0.000 0.652
#> GSM49602 4 0.4661 0.940 0.348 0.000 0.000 0.652
#> GSM49603 4 0.4661 0.940 0.348 0.000 0.000 0.652
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM49613 3 0.0510 0.996 0.000 0.000 0.984 0.000 0.016
#> GSM49604 4 0.3878 0.823 0.000 0.236 0.000 0.748 0.016
#> GSM49605 2 0.0324 0.979 0.000 0.992 0.004 0.000 0.004
#> GSM49606 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> GSM49607 2 0.0324 0.979 0.000 0.992 0.004 0.000 0.004
#> GSM49608 2 0.0324 0.979 0.000 0.992 0.004 0.000 0.004
#> GSM49609 2 0.0960 0.978 0.000 0.972 0.004 0.008 0.016
#> GSM49610 2 0.0960 0.978 0.000 0.972 0.004 0.008 0.016
#> GSM49611 2 0.0960 0.978 0.000 0.972 0.004 0.008 0.016
#> GSM49612 2 0.0960 0.978 0.000 0.972 0.004 0.008 0.016
#> GSM49614 3 0.0703 0.991 0.000 0.000 0.976 0.000 0.024
#> GSM49615 3 0.0510 0.996 0.000 0.000 0.984 0.000 0.016
#> GSM49616 3 0.0404 0.996 0.000 0.000 0.988 0.000 0.012
#> GSM49617 3 0.0404 0.996 0.000 0.000 0.988 0.000 0.012
#> GSM49564 5 0.2300 0.954 0.072 0.000 0.000 0.024 0.904
#> GSM49565 1 0.1892 0.946 0.916 0.000 0.000 0.080 0.004
#> GSM49566 5 0.3459 0.929 0.072 0.000 0.004 0.080 0.844
#> GSM49567 1 0.1443 0.953 0.948 0.000 0.004 0.044 0.004
#> GSM49568 1 0.0324 0.970 0.992 0.000 0.000 0.004 0.004
#> GSM49569 5 0.2228 0.958 0.076 0.000 0.004 0.012 0.908
#> GSM49570 4 0.2773 0.880 0.000 0.164 0.000 0.836 0.000
#> GSM49571 4 0.3318 0.646 0.008 0.000 0.000 0.800 0.192
#> GSM49572 1 0.1357 0.961 0.948 0.000 0.000 0.048 0.004
#> GSM49573 4 0.3183 0.879 0.000 0.156 0.000 0.828 0.016
#> GSM49574 1 0.0880 0.968 0.968 0.000 0.000 0.032 0.000
#> GSM49575 1 0.0912 0.965 0.972 0.000 0.000 0.016 0.012
#> GSM49576 5 0.2300 0.957 0.072 0.000 0.000 0.024 0.904
#> GSM49577 5 0.3859 0.897 0.096 0.000 0.004 0.084 0.816
#> GSM49578 1 0.0162 0.970 0.996 0.000 0.000 0.000 0.004
#> GSM49579 5 0.3012 0.948 0.072 0.000 0.004 0.052 0.872
#> GSM49580 1 0.1153 0.963 0.964 0.000 0.004 0.024 0.008
#> GSM49581 1 0.0833 0.967 0.976 0.000 0.004 0.016 0.004
#> GSM49582 1 0.0162 0.970 0.996 0.000 0.000 0.000 0.004
#> GSM49583 2 0.0968 0.966 0.000 0.972 0.004 0.012 0.012
#> GSM49584 1 0.0451 0.969 0.988 0.000 0.000 0.008 0.004
#> GSM49585 1 0.1697 0.952 0.932 0.000 0.000 0.060 0.008
#> GSM49586 5 0.2376 0.934 0.052 0.000 0.000 0.044 0.904
#> GSM49587 1 0.0865 0.969 0.972 0.000 0.000 0.024 0.004
#> GSM49588 1 0.1331 0.964 0.952 0.000 0.000 0.040 0.008
#> GSM49589 5 0.2853 0.958 0.072 0.000 0.000 0.052 0.876
#> GSM49590 5 0.2006 0.960 0.072 0.000 0.000 0.012 0.916
#> GSM49591 1 0.0963 0.966 0.964 0.000 0.000 0.036 0.000
#> GSM49592 1 0.0955 0.968 0.968 0.000 0.000 0.028 0.004
#> GSM49593 5 0.1956 0.959 0.076 0.000 0.000 0.008 0.916
#> GSM49594 5 0.3119 0.952 0.072 0.000 0.000 0.068 0.860
#> GSM49595 5 0.3119 0.952 0.072 0.000 0.000 0.068 0.860
#> GSM49596 5 0.2407 0.951 0.088 0.000 0.004 0.012 0.896
#> GSM49597 4 0.3399 0.874 0.000 0.172 0.004 0.812 0.012
#> GSM49598 5 0.2069 0.960 0.076 0.000 0.000 0.012 0.912
#> GSM49599 1 0.0671 0.969 0.980 0.000 0.004 0.016 0.000
#> GSM49600 1 0.2304 0.909 0.908 0.000 0.004 0.020 0.068
#> GSM49601 5 0.2843 0.954 0.076 0.000 0.000 0.048 0.876
#> GSM49602 5 0.2770 0.955 0.076 0.000 0.000 0.044 0.880
#> GSM49603 5 0.2694 0.955 0.076 0.000 0.000 0.040 0.884
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM49613 3 0.1285 0.965 0.000 0.000 0.944 0.000 0.004 NA
#> GSM49604 4 0.2699 0.806 0.000 0.124 0.000 0.856 0.008 NA
#> GSM49605 2 0.1806 0.904 0.000 0.908 0.000 0.000 0.004 NA
#> GSM49606 2 0.0291 0.916 0.000 0.992 0.000 0.000 0.004 NA
#> GSM49607 2 0.1958 0.900 0.000 0.896 0.000 0.000 0.004 NA
#> GSM49608 2 0.1918 0.904 0.000 0.904 0.000 0.000 0.008 NA
#> GSM49609 2 0.1493 0.914 0.000 0.936 0.000 0.004 0.004 NA
#> GSM49610 2 0.1493 0.914 0.000 0.936 0.000 0.004 0.004 NA
#> GSM49611 2 0.1493 0.914 0.000 0.936 0.000 0.004 0.004 NA
#> GSM49612 2 0.1493 0.914 0.000 0.936 0.000 0.004 0.004 NA
#> GSM49614 3 0.0717 0.966 0.000 0.000 0.976 0.000 0.008 NA
#> GSM49615 3 0.1285 0.965 0.000 0.000 0.944 0.000 0.004 NA
#> GSM49616 3 0.0000 0.973 0.000 0.000 1.000 0.000 0.000 NA
#> GSM49617 3 0.0000 0.973 0.000 0.000 1.000 0.000 0.000 NA
#> GSM49564 5 0.2964 0.837 0.040 0.000 0.000 0.004 0.848 NA
#> GSM49565 1 0.3668 0.769 0.668 0.000 0.000 0.000 0.004 NA
#> GSM49566 5 0.3770 0.785 0.032 0.000 0.000 0.004 0.752 NA
#> GSM49567 1 0.2980 0.808 0.800 0.000 0.000 0.000 0.008 NA
#> GSM49568 1 0.0000 0.880 1.000 0.000 0.000 0.000 0.000 NA
#> GSM49569 5 0.1723 0.877 0.036 0.000 0.000 0.000 0.928 NA
#> GSM49570 4 0.1745 0.842 0.000 0.020 0.000 0.924 0.000 NA
#> GSM49571 4 0.3974 0.707 0.004 0.000 0.000 0.752 0.056 NA
#> GSM49572 1 0.3534 0.811 0.716 0.000 0.000 0.000 0.008 NA
#> GSM49573 4 0.0806 0.844 0.000 0.020 0.000 0.972 0.000 NA
#> GSM49574 1 0.2632 0.867 0.832 0.000 0.000 0.004 0.000 NA
#> GSM49575 1 0.1732 0.878 0.920 0.000 0.000 0.004 0.004 NA
#> GSM49576 5 0.1921 0.875 0.032 0.000 0.000 0.000 0.916 NA
#> GSM49577 5 0.4475 0.572 0.032 0.000 0.000 0.000 0.556 NA
#> GSM49578 1 0.0000 0.880 1.000 0.000 0.000 0.000 0.000 NA
#> GSM49579 5 0.3062 0.841 0.032 0.000 0.000 0.000 0.824 NA
#> GSM49580 1 0.1913 0.856 0.908 0.000 0.000 0.000 0.012 NA
#> GSM49581 1 0.1141 0.871 0.948 0.000 0.000 0.000 0.000 NA
#> GSM49582 1 0.0000 0.880 1.000 0.000 0.000 0.000 0.000 NA
#> GSM49583 2 0.2562 0.851 0.000 0.828 0.000 0.000 0.000 NA
#> GSM49584 1 0.0937 0.873 0.960 0.000 0.000 0.000 0.000 NA
#> GSM49585 1 0.3454 0.822 0.760 0.000 0.000 0.012 0.004 NA
#> GSM49586 5 0.3821 0.820 0.024 0.000 0.000 0.020 0.768 NA
#> GSM49587 1 0.2234 0.873 0.872 0.000 0.000 0.004 0.000 NA
#> GSM49588 1 0.2810 0.863 0.832 0.000 0.000 0.008 0.004 NA
#> GSM49589 5 0.3275 0.874 0.032 0.000 0.000 0.008 0.820 NA
#> GSM49590 5 0.1498 0.879 0.032 0.000 0.000 0.000 0.940 NA
#> GSM49591 1 0.2778 0.861 0.824 0.000 0.000 0.008 0.000 NA
#> GSM49592 1 0.2302 0.873 0.872 0.000 0.000 0.008 0.000 NA
#> GSM49593 5 0.1644 0.881 0.040 0.000 0.000 0.000 0.932 NA
#> GSM49594 5 0.3947 0.841 0.036 0.000 0.000 0.008 0.744 NA
#> GSM49595 5 0.3918 0.844 0.036 0.000 0.000 0.008 0.748 NA
#> GSM49596 5 0.1713 0.878 0.044 0.000 0.000 0.000 0.928 NA
#> GSM49597 4 0.3699 0.777 0.000 0.036 0.000 0.752 0.000 NA
#> GSM49598 5 0.2078 0.881 0.040 0.000 0.000 0.004 0.912 NA
#> GSM49599 1 0.2595 0.872 0.836 0.000 0.000 0.004 0.000 NA
#> GSM49600 1 0.3552 0.761 0.800 0.000 0.000 0.000 0.116 NA
#> GSM49601 5 0.3433 0.859 0.040 0.000 0.000 0.012 0.816 NA
#> GSM49602 5 0.2833 0.873 0.040 0.000 0.000 0.008 0.864 NA
#> GSM49603 5 0.2833 0.873 0.040 0.000 0.000 0.008 0.864 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) cell.type(p) k
#> MAD:kmeans 54 5.97e-07 6.72e-04 2
#> MAD:kmeans 54 2.57e-07 8.46e-14 3
#> MAD:kmeans 53 1.61e-06 2.73e-12 4
#> MAD:kmeans 54 1.42e-07 4.23e-13 5
#> MAD:kmeans 54 1.42e-07 4.23e-13 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21168 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.811 0.888 0.954 0.4698 0.535 0.535
#> 3 3 0.887 0.892 0.952 0.4374 0.720 0.509
#> 4 4 0.759 0.820 0.900 0.1102 0.882 0.660
#> 5 5 0.664 0.602 0.788 0.0638 0.991 0.964
#> 6 6 0.664 0.528 0.715 0.0409 0.948 0.793
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM49613 1 0.0376 0.950 0.996 0.004
#> GSM49604 2 0.0000 0.941 0.000 1.000
#> GSM49605 2 0.0000 0.941 0.000 1.000
#> GSM49606 2 0.0000 0.941 0.000 1.000
#> GSM49607 2 0.0000 0.941 0.000 1.000
#> GSM49608 2 0.0000 0.941 0.000 1.000
#> GSM49609 2 0.0000 0.941 0.000 1.000
#> GSM49610 2 0.0000 0.941 0.000 1.000
#> GSM49611 2 0.0000 0.941 0.000 1.000
#> GSM49612 2 0.0000 0.941 0.000 1.000
#> GSM49614 2 0.8267 0.643 0.260 0.740
#> GSM49615 1 0.0376 0.950 0.996 0.004
#> GSM49616 1 0.4022 0.881 0.920 0.080
#> GSM49617 2 0.9963 0.151 0.464 0.536
#> GSM49564 1 0.0000 0.952 1.000 0.000
#> GSM49565 1 0.9460 0.440 0.636 0.364
#> GSM49566 1 0.0000 0.952 1.000 0.000
#> GSM49567 1 0.0938 0.945 0.988 0.012
#> GSM49568 1 0.0000 0.952 1.000 0.000
#> GSM49569 1 0.0000 0.952 1.000 0.000
#> GSM49570 2 0.0000 0.941 0.000 1.000
#> GSM49571 2 0.0000 0.941 0.000 1.000
#> GSM49572 1 0.0672 0.948 0.992 0.008
#> GSM49573 2 0.0000 0.941 0.000 1.000
#> GSM49574 1 0.6712 0.772 0.824 0.176
#> GSM49575 1 0.9129 0.521 0.672 0.328
#> GSM49576 1 0.0000 0.952 1.000 0.000
#> GSM49577 2 0.2948 0.906 0.052 0.948
#> GSM49578 1 0.0000 0.952 1.000 0.000
#> GSM49579 1 0.0000 0.952 1.000 0.000
#> GSM49580 1 0.0000 0.952 1.000 0.000
#> GSM49581 1 0.0000 0.952 1.000 0.000
#> GSM49582 1 0.0000 0.952 1.000 0.000
#> GSM49583 2 0.0000 0.941 0.000 1.000
#> GSM49584 1 0.0000 0.952 1.000 0.000
#> GSM49585 1 0.0000 0.952 1.000 0.000
#> GSM49586 2 0.5629 0.828 0.132 0.868
#> GSM49587 1 0.0000 0.952 1.000 0.000
#> GSM49588 1 0.0000 0.952 1.000 0.000
#> GSM49589 1 0.0376 0.950 0.996 0.004
#> GSM49590 1 0.0376 0.950 0.996 0.004
#> GSM49591 1 0.0000 0.952 1.000 0.000
#> GSM49592 1 0.0000 0.952 1.000 0.000
#> GSM49593 1 0.0000 0.952 1.000 0.000
#> GSM49594 2 0.4298 0.875 0.088 0.912
#> GSM49595 1 0.9775 0.303 0.588 0.412
#> GSM49596 1 0.0000 0.952 1.000 0.000
#> GSM49597 2 0.0000 0.941 0.000 1.000
#> GSM49598 1 0.0000 0.952 1.000 0.000
#> GSM49599 1 0.4815 0.862 0.896 0.104
#> GSM49600 1 0.0000 0.952 1.000 0.000
#> GSM49601 1 0.0000 0.952 1.000 0.000
#> GSM49602 1 0.0000 0.952 1.000 0.000
#> GSM49603 1 0.0000 0.952 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM49613 3 0.0000 0.940 0.000 0.000 1.000
#> GSM49604 2 0.0000 0.945 0.000 1.000 0.000
#> GSM49605 2 0.0000 0.945 0.000 1.000 0.000
#> GSM49606 2 0.0000 0.945 0.000 1.000 0.000
#> GSM49607 2 0.0000 0.945 0.000 1.000 0.000
#> GSM49608 2 0.0000 0.945 0.000 1.000 0.000
#> GSM49609 2 0.0000 0.945 0.000 1.000 0.000
#> GSM49610 2 0.0000 0.945 0.000 1.000 0.000
#> GSM49611 2 0.0000 0.945 0.000 1.000 0.000
#> GSM49612 2 0.0000 0.945 0.000 1.000 0.000
#> GSM49614 3 0.2796 0.872 0.000 0.092 0.908
#> GSM49615 3 0.0000 0.940 0.000 0.000 1.000
#> GSM49616 3 0.0000 0.940 0.000 0.000 1.000
#> GSM49617 3 0.0000 0.940 0.000 0.000 1.000
#> GSM49564 3 0.0000 0.940 0.000 0.000 1.000
#> GSM49565 1 0.0237 0.957 0.996 0.004 0.000
#> GSM49566 3 0.2448 0.897 0.076 0.000 0.924
#> GSM49567 1 0.0237 0.958 0.996 0.000 0.004
#> GSM49568 1 0.0424 0.957 0.992 0.000 0.008
#> GSM49569 3 0.0592 0.938 0.012 0.000 0.988
#> GSM49570 2 0.0000 0.945 0.000 1.000 0.000
#> GSM49571 2 0.0661 0.937 0.008 0.988 0.004
#> GSM49572 1 0.0237 0.958 0.996 0.000 0.004
#> GSM49573 2 0.0000 0.945 0.000 1.000 0.000
#> GSM49574 1 0.0000 0.959 1.000 0.000 0.000
#> GSM49575 1 0.0475 0.957 0.992 0.004 0.004
#> GSM49576 3 0.0237 0.939 0.004 0.000 0.996
#> GSM49577 2 0.7337 0.506 0.300 0.644 0.056
#> GSM49578 1 0.0000 0.959 1.000 0.000 0.000
#> GSM49579 3 0.4121 0.797 0.168 0.000 0.832
#> GSM49580 1 0.1031 0.947 0.976 0.000 0.024
#> GSM49581 1 0.0000 0.959 1.000 0.000 0.000
#> GSM49582 1 0.0000 0.959 1.000 0.000 0.000
#> GSM49583 2 0.0000 0.945 0.000 1.000 0.000
#> GSM49584 1 0.0237 0.958 0.996 0.000 0.004
#> GSM49585 1 0.1031 0.947 0.976 0.000 0.024
#> GSM49586 3 0.6769 0.324 0.016 0.392 0.592
#> GSM49587 1 0.0000 0.959 1.000 0.000 0.000
#> GSM49588 1 0.1163 0.943 0.972 0.000 0.028
#> GSM49589 3 0.0000 0.940 0.000 0.000 1.000
#> GSM49590 3 0.0000 0.940 0.000 0.000 1.000
#> GSM49591 1 0.0000 0.959 1.000 0.000 0.000
#> GSM49592 1 0.0000 0.959 1.000 0.000 0.000
#> GSM49593 3 0.0892 0.937 0.020 0.000 0.980
#> GSM49594 2 0.7192 0.203 0.028 0.560 0.412
#> GSM49595 3 0.5060 0.833 0.064 0.100 0.836
#> GSM49596 1 0.5859 0.476 0.656 0.000 0.344
#> GSM49597 2 0.0000 0.945 0.000 1.000 0.000
#> GSM49598 3 0.1964 0.919 0.056 0.000 0.944
#> GSM49599 1 0.0424 0.955 0.992 0.008 0.000
#> GSM49600 1 0.5138 0.677 0.748 0.000 0.252
#> GSM49601 3 0.1643 0.925 0.044 0.000 0.956
#> GSM49602 3 0.0592 0.938 0.012 0.000 0.988
#> GSM49603 3 0.0424 0.939 0.008 0.000 0.992
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM49613 3 0.0188 0.892 0.000 0.000 0.996 0.004
#> GSM49604 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM49605 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM49606 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM49607 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM49608 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM49609 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM49610 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM49611 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM49612 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM49614 3 0.0707 0.875 0.000 0.020 0.980 0.000
#> GSM49615 3 0.0188 0.892 0.000 0.000 0.996 0.004
#> GSM49616 3 0.0188 0.892 0.000 0.000 0.996 0.004
#> GSM49617 3 0.0000 0.891 0.000 0.000 1.000 0.000
#> GSM49564 3 0.2053 0.852 0.004 0.000 0.924 0.072
#> GSM49565 1 0.2960 0.887 0.892 0.020 0.004 0.084
#> GSM49566 4 0.6762 0.374 0.104 0.000 0.360 0.536
#> GSM49567 1 0.0817 0.916 0.976 0.000 0.000 0.024
#> GSM49568 1 0.2131 0.908 0.932 0.000 0.032 0.036
#> GSM49569 4 0.5508 0.627 0.056 0.000 0.252 0.692
#> GSM49570 2 0.2081 0.902 0.000 0.916 0.084 0.000
#> GSM49571 2 0.5496 0.646 0.016 0.724 0.040 0.220
#> GSM49572 1 0.0336 0.915 0.992 0.000 0.000 0.008
#> GSM49573 2 0.0188 0.967 0.000 0.996 0.004 0.000
#> GSM49574 1 0.0817 0.916 0.976 0.000 0.000 0.024
#> GSM49575 1 0.2465 0.906 0.924 0.012 0.020 0.044
#> GSM49576 4 0.4830 0.394 0.000 0.000 0.392 0.608
#> GSM49577 4 0.8104 0.414 0.176 0.276 0.036 0.512
#> GSM49578 1 0.0000 0.913 1.000 0.000 0.000 0.000
#> GSM49579 4 0.4938 0.701 0.080 0.000 0.148 0.772
#> GSM49580 1 0.2522 0.885 0.908 0.000 0.076 0.016
#> GSM49581 1 0.1302 0.914 0.956 0.000 0.000 0.044
#> GSM49582 1 0.0188 0.914 0.996 0.000 0.000 0.004
#> GSM49583 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM49584 1 0.0779 0.914 0.980 0.000 0.016 0.004
#> GSM49585 1 0.5102 0.739 0.732 0.000 0.048 0.220
#> GSM49586 4 0.1520 0.779 0.000 0.024 0.020 0.956
#> GSM49587 1 0.0895 0.917 0.976 0.000 0.004 0.020
#> GSM49588 1 0.4434 0.738 0.756 0.000 0.016 0.228
#> GSM49589 3 0.2760 0.806 0.000 0.000 0.872 0.128
#> GSM49590 3 0.4843 0.205 0.000 0.000 0.604 0.396
#> GSM49591 1 0.2408 0.888 0.896 0.000 0.000 0.104
#> GSM49592 1 0.0817 0.916 0.976 0.000 0.000 0.024
#> GSM49593 4 0.2546 0.775 0.008 0.000 0.092 0.900
#> GSM49594 4 0.3432 0.717 0.008 0.120 0.012 0.860
#> GSM49595 4 0.0524 0.779 0.000 0.004 0.008 0.988
#> GSM49596 4 0.5972 0.529 0.292 0.000 0.068 0.640
#> GSM49597 2 0.1302 0.937 0.000 0.956 0.044 0.000
#> GSM49598 4 0.2319 0.783 0.036 0.000 0.040 0.924
#> GSM49599 1 0.2895 0.895 0.908 0.032 0.016 0.044
#> GSM49600 1 0.6457 0.555 0.644 0.000 0.200 0.156
#> GSM49601 4 0.1022 0.781 0.000 0.000 0.032 0.968
#> GSM49602 4 0.1474 0.782 0.000 0.000 0.052 0.948
#> GSM49603 4 0.1867 0.780 0.000 0.000 0.072 0.928
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM49613 3 0.0000 0.8353 0.000 0.000 1.000 0.000 0.000
#> GSM49604 2 0.1410 0.8593 0.000 0.940 0.000 0.060 0.000
#> GSM49605 2 0.0000 0.8843 0.000 1.000 0.000 0.000 0.000
#> GSM49606 2 0.0000 0.8843 0.000 1.000 0.000 0.000 0.000
#> GSM49607 2 0.0000 0.8843 0.000 1.000 0.000 0.000 0.000
#> GSM49608 2 0.0162 0.8839 0.000 0.996 0.000 0.004 0.000
#> GSM49609 2 0.0290 0.8836 0.000 0.992 0.000 0.008 0.000
#> GSM49610 2 0.0000 0.8843 0.000 1.000 0.000 0.000 0.000
#> GSM49611 2 0.0290 0.8836 0.000 0.992 0.000 0.008 0.000
#> GSM49612 2 0.0290 0.8836 0.000 0.992 0.000 0.008 0.000
#> GSM49614 3 0.0162 0.8323 0.000 0.000 0.996 0.004 0.000
#> GSM49615 3 0.0000 0.8353 0.000 0.000 1.000 0.000 0.000
#> GSM49616 3 0.0000 0.8353 0.000 0.000 1.000 0.000 0.000
#> GSM49617 3 0.0000 0.8353 0.000 0.000 1.000 0.000 0.000
#> GSM49564 3 0.4743 0.6695 0.040 0.000 0.772 0.064 0.124
#> GSM49565 1 0.5371 0.5588 0.596 0.020 0.000 0.352 0.032
#> GSM49566 5 0.8138 -0.0539 0.128 0.000 0.192 0.304 0.376
#> GSM49567 1 0.4622 0.6260 0.696 0.000 0.008 0.268 0.028
#> GSM49568 1 0.3543 0.7125 0.828 0.000 0.012 0.136 0.024
#> GSM49569 5 0.6180 0.3964 0.040 0.000 0.168 0.148 0.644
#> GSM49570 2 0.5136 0.6242 0.000 0.692 0.128 0.180 0.000
#> GSM49571 2 0.7504 -0.0119 0.044 0.452 0.008 0.316 0.180
#> GSM49572 1 0.4161 0.6598 0.704 0.000 0.000 0.280 0.016
#> GSM49573 2 0.4251 0.6889 0.004 0.740 0.020 0.232 0.004
#> GSM49574 1 0.3527 0.7046 0.792 0.000 0.000 0.192 0.016
#> GSM49575 1 0.5217 0.5895 0.648 0.004 0.008 0.296 0.044
#> GSM49576 5 0.6127 0.2385 0.000 0.000 0.316 0.152 0.532
#> GSM49577 4 0.8766 0.0000 0.112 0.180 0.040 0.372 0.296
#> GSM49578 1 0.0880 0.7217 0.968 0.000 0.000 0.032 0.000
#> GSM49579 5 0.6858 0.1018 0.088 0.000 0.064 0.348 0.500
#> GSM49580 1 0.5322 0.6188 0.716 0.000 0.040 0.176 0.068
#> GSM49581 1 0.4088 0.6723 0.776 0.000 0.000 0.168 0.056
#> GSM49582 1 0.0880 0.7206 0.968 0.000 0.000 0.032 0.000
#> GSM49583 2 0.0510 0.8810 0.000 0.984 0.000 0.016 0.000
#> GSM49584 1 0.2777 0.7164 0.864 0.000 0.016 0.120 0.000
#> GSM49585 1 0.6674 0.4832 0.544 0.000 0.032 0.284 0.140
#> GSM49586 5 0.4225 0.4951 0.012 0.008 0.016 0.196 0.768
#> GSM49587 1 0.2930 0.7158 0.832 0.000 0.000 0.164 0.004
#> GSM49588 1 0.6311 0.4981 0.568 0.000 0.012 0.264 0.156
#> GSM49589 3 0.4432 0.6758 0.008 0.000 0.772 0.076 0.144
#> GSM49590 3 0.5452 -0.0585 0.000 0.000 0.492 0.060 0.448
#> GSM49591 1 0.4221 0.6661 0.732 0.000 0.000 0.236 0.032
#> GSM49592 1 0.2411 0.7181 0.884 0.000 0.000 0.108 0.008
#> GSM49593 5 0.2151 0.5934 0.016 0.000 0.020 0.040 0.924
#> GSM49594 5 0.5781 0.3122 0.004 0.116 0.012 0.212 0.656
#> GSM49595 5 0.3740 0.5266 0.008 0.016 0.004 0.168 0.804
#> GSM49596 5 0.6960 0.1454 0.244 0.000 0.040 0.184 0.532
#> GSM49597 2 0.3112 0.8014 0.000 0.856 0.044 0.100 0.000
#> GSM49598 5 0.3736 0.5674 0.052 0.000 0.020 0.092 0.836
#> GSM49599 1 0.6045 0.4863 0.552 0.020 0.012 0.368 0.048
#> GSM49600 1 0.7744 0.1860 0.460 0.000 0.092 0.236 0.212
#> GSM49601 5 0.2635 0.5846 0.016 0.000 0.008 0.088 0.888
#> GSM49602 5 0.1701 0.5964 0.000 0.000 0.016 0.048 0.936
#> GSM49603 5 0.1560 0.6000 0.004 0.000 0.028 0.020 0.948
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM49613 3 0.0000 0.8749 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM49604 2 0.3073 0.5463 0.000 0.788 0.000 0.204 0.000 0.008
#> GSM49605 2 0.0692 0.8936 0.000 0.976 0.000 0.020 0.000 0.004
#> GSM49606 2 0.0405 0.8987 0.000 0.988 0.000 0.004 0.000 0.008
#> GSM49607 2 0.0622 0.8966 0.000 0.980 0.000 0.012 0.000 0.008
#> GSM49608 2 0.0405 0.8983 0.000 0.988 0.000 0.004 0.000 0.008
#> GSM49609 2 0.0260 0.9003 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM49610 2 0.0260 0.9003 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM49611 2 0.0260 0.9003 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM49612 2 0.0146 0.8994 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM49614 3 0.0458 0.8661 0.000 0.000 0.984 0.016 0.000 0.000
#> GSM49615 3 0.0000 0.8749 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM49616 3 0.0000 0.8749 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM49617 3 0.0146 0.8731 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM49564 3 0.5234 0.6217 0.060 0.000 0.724 0.024 0.116 0.076
#> GSM49565 1 0.6818 0.3899 0.480 0.044 0.000 0.160 0.020 0.296
#> GSM49566 6 0.7887 0.2781 0.116 0.004 0.088 0.080 0.296 0.416
#> GSM49567 1 0.5266 0.4469 0.580 0.000 0.000 0.096 0.008 0.316
#> GSM49568 1 0.4254 0.5941 0.788 0.000 0.012 0.056 0.036 0.108
#> GSM49569 5 0.6685 0.2377 0.056 0.000 0.080 0.076 0.584 0.204
#> GSM49570 4 0.5506 0.4945 0.000 0.452 0.084 0.452 0.004 0.008
#> GSM49571 4 0.6650 0.4102 0.008 0.220 0.016 0.556 0.156 0.044
#> GSM49572 1 0.5272 0.5104 0.600 0.000 0.000 0.128 0.004 0.268
#> GSM49573 4 0.4305 0.5872 0.004 0.424 0.008 0.560 0.004 0.000
#> GSM49574 1 0.5418 0.5716 0.648 0.000 0.000 0.168 0.028 0.156
#> GSM49575 1 0.6366 0.4063 0.504 0.008 0.004 0.328 0.032 0.124
#> GSM49576 5 0.6844 -0.0134 0.008 0.000 0.276 0.036 0.424 0.256
#> GSM49577 6 0.8288 0.3181 0.112 0.128 0.004 0.180 0.148 0.428
#> GSM49578 1 0.1890 0.6171 0.916 0.000 0.000 0.024 0.000 0.060
#> GSM49579 6 0.6084 0.2474 0.044 0.000 0.040 0.040 0.328 0.548
#> GSM49580 1 0.6700 0.4389 0.572 0.000 0.036 0.112 0.072 0.208
#> GSM49581 1 0.5250 0.5474 0.692 0.000 0.008 0.148 0.032 0.120
#> GSM49582 1 0.1794 0.6127 0.924 0.000 0.000 0.040 0.000 0.036
#> GSM49583 2 0.1584 0.8498 0.000 0.928 0.000 0.064 0.000 0.008
#> GSM49584 1 0.3812 0.5996 0.812 0.000 0.024 0.068 0.004 0.092
#> GSM49585 1 0.8116 0.1724 0.352 0.000 0.036 0.208 0.168 0.236
#> GSM49586 5 0.4841 0.3072 0.004 0.004 0.000 0.292 0.636 0.064
#> GSM49587 1 0.4466 0.5917 0.716 0.000 0.000 0.100 0.004 0.180
#> GSM49588 1 0.6833 0.4478 0.524 0.000 0.008 0.160 0.096 0.212
#> GSM49589 3 0.6235 0.4335 0.008 0.000 0.604 0.084 0.184 0.120
#> GSM49590 5 0.5781 0.0547 0.000 0.000 0.412 0.008 0.444 0.136
#> GSM49591 1 0.6092 0.5033 0.572 0.000 0.000 0.160 0.048 0.220
#> GSM49592 1 0.4004 0.5968 0.780 0.000 0.000 0.100 0.012 0.108
#> GSM49593 5 0.3748 0.4599 0.016 0.000 0.020 0.052 0.824 0.088
#> GSM49594 5 0.7103 0.1369 0.008 0.120 0.008 0.128 0.512 0.224
#> GSM49595 5 0.5164 0.3103 0.008 0.004 0.000 0.108 0.644 0.236
#> GSM49596 5 0.7383 -0.0884 0.208 0.000 0.024 0.080 0.444 0.244
#> GSM49597 2 0.4582 0.4102 0.000 0.716 0.040 0.204 0.000 0.040
#> GSM49598 5 0.5281 0.3968 0.040 0.000 0.032 0.068 0.712 0.148
#> GSM49599 1 0.7008 0.2989 0.388 0.024 0.004 0.364 0.024 0.196
#> GSM49600 1 0.8061 0.1375 0.424 0.000 0.112 0.096 0.136 0.232
#> GSM49601 5 0.2866 0.4730 0.012 0.000 0.000 0.060 0.868 0.060
#> GSM49602 5 0.1528 0.4865 0.000 0.000 0.000 0.016 0.936 0.048
#> GSM49603 5 0.1528 0.4920 0.000 0.000 0.012 0.016 0.944 0.028
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> MAD:skmeans 51 2.44e-04 1.83e-02 2
#> MAD:skmeans 51 1.53e-05 5.42e-04 3
#> MAD:skmeans 50 1.91e-05 5.19e-08 4
#> MAD:skmeans 40 1.24e-04 3.51e-06 5
#> MAD:skmeans 27 2.09e-04 7.73e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21168 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.963 0.987 0.3379 0.669 0.669
#> 3 3 0.671 0.826 0.874 0.5489 0.834 0.754
#> 4 4 0.820 0.831 0.933 0.3548 0.741 0.513
#> 5 5 0.944 0.891 0.957 0.0429 0.941 0.806
#> 6 6 0.853 0.841 0.911 0.0324 0.983 0.936
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
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
#> GSM49613 1 0.0000 0.987 1.000 0.000
#> GSM49604 2 0.0376 0.977 0.004 0.996
#> GSM49605 2 0.0000 0.980 0.000 1.000
#> GSM49606 2 0.0000 0.980 0.000 1.000
#> GSM49607 2 0.0000 0.980 0.000 1.000
#> GSM49608 2 0.0000 0.980 0.000 1.000
#> GSM49609 2 0.0000 0.980 0.000 1.000
#> GSM49610 2 0.0000 0.980 0.000 1.000
#> GSM49611 2 0.0000 0.980 0.000 1.000
#> GSM49612 2 0.0000 0.980 0.000 1.000
#> GSM49614 1 0.0000 0.987 1.000 0.000
#> GSM49615 1 0.0000 0.987 1.000 0.000
#> GSM49616 1 0.0000 0.987 1.000 0.000
#> GSM49617 1 0.0000 0.987 1.000 0.000
#> GSM49564 1 0.0000 0.987 1.000 0.000
#> GSM49565 1 0.0000 0.987 1.000 0.000
#> GSM49566 1 0.0000 0.987 1.000 0.000
#> GSM49567 1 0.0000 0.987 1.000 0.000
#> GSM49568 1 0.0000 0.987 1.000 0.000
#> GSM49569 1 0.0000 0.987 1.000 0.000
#> GSM49570 1 1.0000 -0.025 0.504 0.496
#> GSM49571 1 0.0000 0.987 1.000 0.000
#> GSM49572 1 0.0000 0.987 1.000 0.000
#> GSM49573 1 0.1414 0.967 0.980 0.020
#> GSM49574 1 0.0000 0.987 1.000 0.000
#> GSM49575 1 0.0000 0.987 1.000 0.000
#> GSM49576 1 0.0000 0.987 1.000 0.000
#> GSM49577 1 0.0000 0.987 1.000 0.000
#> GSM49578 1 0.0000 0.987 1.000 0.000
#> GSM49579 1 0.0000 0.987 1.000 0.000
#> GSM49580 1 0.0000 0.987 1.000 0.000
#> GSM49581 1 0.0000 0.987 1.000 0.000
#> GSM49582 1 0.0000 0.987 1.000 0.000
#> GSM49583 2 0.0000 0.980 0.000 1.000
#> GSM49584 1 0.0000 0.987 1.000 0.000
#> GSM49585 1 0.0000 0.987 1.000 0.000
#> GSM49586 1 0.0000 0.987 1.000 0.000
#> GSM49587 1 0.0000 0.987 1.000 0.000
#> GSM49588 1 0.0000 0.987 1.000 0.000
#> GSM49589 1 0.0000 0.987 1.000 0.000
#> GSM49590 1 0.0000 0.987 1.000 0.000
#> GSM49591 1 0.0000 0.987 1.000 0.000
#> GSM49592 1 0.0000 0.987 1.000 0.000
#> GSM49593 1 0.0000 0.987 1.000 0.000
#> GSM49594 1 0.0000 0.987 1.000 0.000
#> GSM49595 1 0.0000 0.987 1.000 0.000
#> GSM49596 1 0.0000 0.987 1.000 0.000
#> GSM49597 2 0.6973 0.763 0.188 0.812
#> GSM49598 1 0.0000 0.987 1.000 0.000
#> GSM49599 1 0.0000 0.987 1.000 0.000
#> GSM49600 1 0.0000 0.987 1.000 0.000
#> GSM49601 1 0.0000 0.987 1.000 0.000
#> GSM49602 1 0.0000 0.987 1.000 0.000
#> GSM49603 1 0.0000 0.987 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM49613 3 0.0000 0.985 0.000 0.000 1.000
#> GSM49604 2 0.0000 0.919 0.000 1.000 0.000
#> GSM49605 2 0.0000 0.919 0.000 1.000 0.000
#> GSM49606 2 0.0000 0.919 0.000 1.000 0.000
#> GSM49607 2 0.0000 0.919 0.000 1.000 0.000
#> GSM49608 2 0.0000 0.919 0.000 1.000 0.000
#> GSM49609 2 0.0000 0.919 0.000 1.000 0.000
#> GSM49610 2 0.0000 0.919 0.000 1.000 0.000
#> GSM49611 2 0.0000 0.919 0.000 1.000 0.000
#> GSM49612 2 0.0000 0.919 0.000 1.000 0.000
#> GSM49614 3 0.0424 0.984 0.008 0.000 0.992
#> GSM49615 3 0.0424 0.985 0.008 0.000 0.992
#> GSM49616 3 0.0000 0.985 0.000 0.000 1.000
#> GSM49617 3 0.0892 0.973 0.020 0.000 0.980
#> GSM49564 1 0.5529 0.816 0.704 0.000 0.296
#> GSM49565 1 0.0000 0.791 1.000 0.000 0.000
#> GSM49566 1 0.5254 0.830 0.736 0.000 0.264
#> GSM49567 1 0.0000 0.791 1.000 0.000 0.000
#> GSM49568 1 0.0000 0.791 1.000 0.000 0.000
#> GSM49569 1 0.5431 0.826 0.716 0.000 0.284
#> GSM49570 2 0.8195 -0.099 0.072 0.492 0.436
#> GSM49571 1 0.5431 0.826 0.716 0.000 0.284
#> GSM49572 1 0.0000 0.791 1.000 0.000 0.000
#> GSM49573 1 0.7770 0.730 0.640 0.088 0.272
#> GSM49574 1 0.0000 0.791 1.000 0.000 0.000
#> GSM49575 1 0.0237 0.792 0.996 0.000 0.004
#> GSM49576 1 0.5363 0.827 0.724 0.000 0.276
#> GSM49577 1 0.5397 0.827 0.720 0.000 0.280
#> GSM49578 1 0.0000 0.791 1.000 0.000 0.000
#> GSM49579 1 0.5254 0.828 0.736 0.000 0.264
#> GSM49580 1 0.1753 0.804 0.952 0.000 0.048
#> GSM49581 1 0.0000 0.791 1.000 0.000 0.000
#> GSM49582 1 0.0000 0.791 1.000 0.000 0.000
#> GSM49583 2 0.0000 0.919 0.000 1.000 0.000
#> GSM49584 1 0.0000 0.791 1.000 0.000 0.000
#> GSM49585 1 0.2448 0.809 0.924 0.000 0.076
#> GSM49586 1 0.5431 0.826 0.716 0.000 0.284
#> GSM49587 1 0.0000 0.791 1.000 0.000 0.000
#> GSM49588 1 0.5216 0.829 0.740 0.000 0.260
#> GSM49589 1 0.5431 0.826 0.716 0.000 0.284
#> GSM49590 1 0.5431 0.826 0.716 0.000 0.284
#> GSM49591 1 0.0424 0.793 0.992 0.000 0.008
#> GSM49592 1 0.0237 0.792 0.996 0.000 0.004
#> GSM49593 1 0.5431 0.826 0.716 0.000 0.284
#> GSM49594 1 0.5431 0.826 0.716 0.000 0.284
#> GSM49595 1 0.5431 0.826 0.716 0.000 0.284
#> GSM49596 1 0.5138 0.830 0.748 0.000 0.252
#> GSM49597 2 0.4700 0.642 0.008 0.812 0.180
#> GSM49598 1 0.5431 0.826 0.716 0.000 0.284
#> GSM49599 1 0.4702 0.826 0.788 0.000 0.212
#> GSM49600 1 0.1289 0.801 0.968 0.000 0.032
#> GSM49601 1 0.5431 0.826 0.716 0.000 0.284
#> GSM49602 1 0.5431 0.826 0.716 0.000 0.284
#> GSM49603 1 0.5431 0.826 0.716 0.000 0.284
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM49613 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM49604 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM49605 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM49606 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM49607 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM49608 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM49609 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM49610 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM49611 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM49612 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM49614 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM49615 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM49616 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM49617 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM49564 1 0.0000 0.912 1.000 0.000 0.000 0.000
#> GSM49565 4 0.1389 0.836 0.048 0.000 0.000 0.952
#> GSM49566 1 0.2647 0.825 0.880 0.000 0.000 0.120
#> GSM49567 4 0.0000 0.844 0.000 0.000 0.000 1.000
#> GSM49568 4 0.1389 0.836 0.048 0.000 0.000 0.952
#> GSM49569 1 0.0000 0.912 1.000 0.000 0.000 0.000
#> GSM49570 1 0.6494 0.171 0.532 0.400 0.004 0.064
#> GSM49571 1 0.0000 0.912 1.000 0.000 0.000 0.000
#> GSM49572 4 0.0000 0.844 0.000 0.000 0.000 1.000
#> GSM49573 4 0.5850 0.103 0.456 0.032 0.000 0.512
#> GSM49574 4 0.0592 0.844 0.016 0.000 0.000 0.984
#> GSM49575 4 0.0469 0.842 0.012 0.000 0.000 0.988
#> GSM49576 1 0.2011 0.867 0.920 0.000 0.000 0.080
#> GSM49577 1 0.1474 0.890 0.948 0.000 0.000 0.052
#> GSM49578 4 0.0000 0.844 0.000 0.000 0.000 1.000
#> GSM49579 1 0.3123 0.789 0.844 0.000 0.000 0.156
#> GSM49580 4 0.1474 0.827 0.052 0.000 0.000 0.948
#> GSM49581 4 0.0000 0.844 0.000 0.000 0.000 1.000
#> GSM49582 4 0.0000 0.844 0.000 0.000 0.000 1.000
#> GSM49583 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM49584 4 0.0000 0.844 0.000 0.000 0.000 1.000
#> GSM49585 1 0.4877 0.219 0.592 0.000 0.000 0.408
#> GSM49586 1 0.0000 0.912 1.000 0.000 0.000 0.000
#> GSM49587 4 0.1211 0.839 0.040 0.000 0.000 0.960
#> GSM49588 1 0.3172 0.785 0.840 0.000 0.000 0.160
#> GSM49589 1 0.0000 0.912 1.000 0.000 0.000 0.000
#> GSM49590 1 0.0000 0.912 1.000 0.000 0.000 0.000
#> GSM49591 4 0.4933 0.238 0.432 0.000 0.000 0.568
#> GSM49592 4 0.4761 0.418 0.372 0.000 0.000 0.628
#> GSM49593 1 0.0000 0.912 1.000 0.000 0.000 0.000
#> GSM49594 1 0.0592 0.907 0.984 0.000 0.000 0.016
#> GSM49595 1 0.0000 0.912 1.000 0.000 0.000 0.000
#> GSM49596 1 0.1389 0.887 0.952 0.000 0.000 0.048
#> GSM49597 2 0.3528 0.703 0.192 0.808 0.000 0.000
#> GSM49598 1 0.0707 0.905 0.980 0.000 0.000 0.020
#> GSM49599 4 0.4522 0.491 0.320 0.000 0.000 0.680
#> GSM49600 4 0.1557 0.828 0.056 0.000 0.000 0.944
#> GSM49601 1 0.0000 0.912 1.000 0.000 0.000 0.000
#> GSM49602 1 0.0000 0.912 1.000 0.000 0.000 0.000
#> GSM49603 1 0.0000 0.912 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM49613 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM49604 2 0.0880 0.967 0.000 0.968 0 0.032 0.000
#> GSM49605 2 0.0000 0.996 0.000 1.000 0 0.000 0.000
#> GSM49606 2 0.0000 0.996 0.000 1.000 0 0.000 0.000
#> GSM49607 2 0.0000 0.996 0.000 1.000 0 0.000 0.000
#> GSM49608 2 0.0000 0.996 0.000 1.000 0 0.000 0.000
#> GSM49609 2 0.0000 0.996 0.000 1.000 0 0.000 0.000
#> GSM49610 2 0.0000 0.996 0.000 1.000 0 0.000 0.000
#> GSM49611 2 0.0000 0.996 0.000 1.000 0 0.000 0.000
#> GSM49612 2 0.0000 0.996 0.000 1.000 0 0.000 0.000
#> GSM49614 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM49615 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM49616 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM49617 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM49564 5 0.0000 0.921 0.000 0.000 0 0.000 1.000
#> GSM49565 1 0.0566 0.906 0.984 0.000 0 0.004 0.012
#> GSM49566 5 0.2516 0.807 0.140 0.000 0 0.000 0.860
#> GSM49567 1 0.0000 0.913 1.000 0.000 0 0.000 0.000
#> GSM49568 1 0.0162 0.912 0.996 0.000 0 0.004 0.000
#> GSM49569 5 0.0000 0.921 0.000 0.000 0 0.000 1.000
#> GSM49570 4 0.0162 0.965 0.000 0.000 0 0.996 0.004
#> GSM49571 5 0.0880 0.905 0.000 0.000 0 0.032 0.968
#> GSM49572 1 0.0162 0.912 0.996 0.000 0 0.004 0.000
#> GSM49573 4 0.0162 0.964 0.004 0.000 0 0.996 0.000
#> GSM49574 1 0.0162 0.912 0.996 0.000 0 0.004 0.000
#> GSM49575 1 0.0290 0.909 0.992 0.000 0 0.000 0.008
#> GSM49576 5 0.1282 0.905 0.044 0.000 0 0.004 0.952
#> GSM49577 5 0.1043 0.909 0.040 0.000 0 0.000 0.960
#> GSM49578 1 0.0000 0.913 1.000 0.000 0 0.000 0.000
#> GSM49579 5 0.1831 0.882 0.076 0.000 0 0.004 0.920
#> GSM49580 1 0.1270 0.872 0.948 0.000 0 0.000 0.052
#> GSM49581 1 0.0000 0.913 1.000 0.000 0 0.000 0.000
#> GSM49582 1 0.0000 0.913 1.000 0.000 0 0.000 0.000
#> GSM49583 2 0.0000 0.996 0.000 1.000 0 0.000 0.000
#> GSM49584 1 0.0000 0.913 1.000 0.000 0 0.000 0.000
#> GSM49585 5 0.4118 0.493 0.336 0.000 0 0.004 0.660
#> GSM49586 5 0.0162 0.920 0.000 0.000 0 0.004 0.996
#> GSM49587 1 0.0162 0.912 0.996 0.000 0 0.004 0.000
#> GSM49588 5 0.1892 0.879 0.080 0.000 0 0.004 0.916
#> GSM49589 5 0.0000 0.921 0.000 0.000 0 0.000 1.000
#> GSM49590 5 0.0000 0.921 0.000 0.000 0 0.000 1.000
#> GSM49591 5 0.4448 0.107 0.480 0.000 0 0.004 0.516
#> GSM49592 1 0.4367 0.211 0.580 0.000 0 0.004 0.416
#> GSM49593 5 0.0000 0.921 0.000 0.000 0 0.000 1.000
#> GSM49594 5 0.0451 0.919 0.008 0.000 0 0.004 0.988
#> GSM49595 5 0.0000 0.921 0.000 0.000 0 0.000 1.000
#> GSM49596 5 0.1043 0.904 0.040 0.000 0 0.000 0.960
#> GSM49597 4 0.1579 0.936 0.000 0.024 0 0.944 0.032
#> GSM49598 5 0.0609 0.916 0.020 0.000 0 0.000 0.980
#> GSM49599 1 0.3857 0.497 0.688 0.000 0 0.000 0.312
#> GSM49600 1 0.1197 0.878 0.952 0.000 0 0.000 0.048
#> GSM49601 5 0.0000 0.921 0.000 0.000 0 0.000 1.000
#> GSM49602 5 0.0000 0.921 0.000 0.000 0 0.000 1.000
#> GSM49603 5 0.0000 0.921 0.000 0.000 0 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM49613 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49604 2 0.1575 0.881 0.000 0.936 0 0.032 0.000 0.032
#> GSM49605 6 0.2597 0.868 0.000 0.176 0 0.000 0.000 0.824
#> GSM49606 2 0.2793 0.633 0.000 0.800 0 0.000 0.000 0.200
#> GSM49607 6 0.2597 0.868 0.000 0.176 0 0.000 0.000 0.824
#> GSM49608 6 0.3023 0.845 0.000 0.232 0 0.000 0.000 0.768
#> GSM49609 2 0.0000 0.928 0.000 1.000 0 0.000 0.000 0.000
#> GSM49610 2 0.0000 0.928 0.000 1.000 0 0.000 0.000 0.000
#> GSM49611 2 0.0000 0.928 0.000 1.000 0 0.000 0.000 0.000
#> GSM49612 2 0.0000 0.928 0.000 1.000 0 0.000 0.000 0.000
#> GSM49614 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49615 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49616 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49617 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM49564 5 0.0363 0.893 0.000 0.000 0 0.000 0.988 0.012
#> GSM49565 1 0.0909 0.896 0.968 0.000 0 0.000 0.012 0.020
#> GSM49566 5 0.3149 0.786 0.132 0.000 0 0.000 0.824 0.044
#> GSM49567 1 0.0937 0.890 0.960 0.000 0 0.000 0.000 0.040
#> GSM49568 1 0.0000 0.901 1.000 0.000 0 0.000 0.000 0.000
#> GSM49569 5 0.0260 0.893 0.000 0.000 0 0.000 0.992 0.008
#> GSM49570 4 0.0146 0.858 0.000 0.000 0 0.996 0.000 0.004
#> GSM49571 5 0.1789 0.880 0.000 0.000 0 0.032 0.924 0.044
#> GSM49572 1 0.1204 0.885 0.944 0.000 0 0.000 0.000 0.056
#> GSM49573 4 0.0146 0.857 0.000 0.000 0 0.996 0.000 0.004
#> GSM49574 1 0.0000 0.901 1.000 0.000 0 0.000 0.000 0.000
#> GSM49575 1 0.0405 0.899 0.988 0.000 0 0.000 0.008 0.004
#> GSM49576 5 0.3240 0.835 0.040 0.000 0 0.000 0.812 0.148
#> GSM49577 5 0.2826 0.853 0.028 0.000 0 0.000 0.844 0.128
#> GSM49578 1 0.0000 0.901 1.000 0.000 0 0.000 0.000 0.000
#> GSM49579 5 0.3680 0.813 0.072 0.000 0 0.000 0.784 0.144
#> GSM49580 1 0.1398 0.871 0.940 0.000 0 0.000 0.052 0.008
#> GSM49581 1 0.0146 0.900 0.996 0.000 0 0.000 0.000 0.004
#> GSM49582 1 0.0146 0.900 0.996 0.000 0 0.000 0.000 0.004
#> GSM49583 6 0.3747 0.584 0.000 0.396 0 0.000 0.000 0.604
#> GSM49584 1 0.0458 0.899 0.984 0.000 0 0.000 0.000 0.016
#> GSM49585 5 0.4552 0.552 0.288 0.000 0 0.000 0.648 0.064
#> GSM49586 5 0.0405 0.892 0.000 0.000 0 0.004 0.988 0.008
#> GSM49587 1 0.0937 0.890 0.960 0.000 0 0.000 0.000 0.040
#> GSM49588 5 0.2554 0.849 0.076 0.000 0 0.000 0.876 0.048
#> GSM49589 5 0.0260 0.892 0.000 0.000 0 0.000 0.992 0.008
#> GSM49590 5 0.0937 0.886 0.000 0.000 0 0.000 0.960 0.040
#> GSM49591 5 0.4636 0.195 0.444 0.000 0 0.000 0.516 0.040
#> GSM49592 1 0.3782 0.195 0.588 0.000 0 0.000 0.412 0.000
#> GSM49593 5 0.0260 0.892 0.000 0.000 0 0.000 0.992 0.008
#> GSM49594 5 0.1806 0.876 0.004 0.000 0 0.000 0.908 0.088
#> GSM49595 5 0.1501 0.879 0.000 0.000 0 0.000 0.924 0.076
#> GSM49596 5 0.1723 0.883 0.036 0.000 0 0.000 0.928 0.036
#> GSM49597 4 0.4239 0.666 0.000 0.016 0 0.696 0.024 0.264
#> GSM49598 5 0.0806 0.891 0.020 0.000 0 0.000 0.972 0.008
#> GSM49599 1 0.4445 0.496 0.656 0.000 0 0.000 0.288 0.056
#> GSM49600 1 0.1333 0.878 0.944 0.000 0 0.000 0.048 0.008
#> GSM49601 5 0.0260 0.892 0.000 0.000 0 0.000 0.992 0.008
#> GSM49602 5 0.0260 0.893 0.000 0.000 0 0.000 0.992 0.008
#> GSM49603 5 0.0260 0.893 0.000 0.000 0 0.000 0.992 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) cell.type(p) k
#> MAD:pam 53 2.67e-08 1.83e-04 2
#> MAD:pam 53 8.86e-09 3.34e-14 3
#> MAD:pam 48 2.88e-07 1.52e-11 4
#> MAD:pam 50 5.83e-08 1.88e-11 5
#> MAD:pam 51 8.68e-08 1.09e-13 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21168 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.827 0.971 0.983 0.442 0.547 0.547
#> 3 3 1.000 0.973 0.988 0.128 0.955 0.917
#> 4 4 0.685 0.671 0.808 0.237 0.899 0.801
#> 5 5 0.796 0.746 0.871 0.114 0.800 0.542
#> 6 6 0.696 0.667 0.778 0.124 0.931 0.765
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM49613 2 0.595 0.873 0.144 0.856
#> GSM49604 2 0.000 0.951 0.000 1.000
#> GSM49605 2 0.000 0.951 0.000 1.000
#> GSM49606 2 0.000 0.951 0.000 1.000
#> GSM49607 2 0.000 0.951 0.000 1.000
#> GSM49608 2 0.000 0.951 0.000 1.000
#> GSM49609 2 0.000 0.951 0.000 1.000
#> GSM49610 2 0.000 0.951 0.000 1.000
#> GSM49611 2 0.000 0.951 0.000 1.000
#> GSM49612 2 0.000 0.951 0.000 1.000
#> GSM49614 2 0.595 0.873 0.144 0.856
#> GSM49615 2 0.595 0.873 0.144 0.856
#> GSM49616 2 0.595 0.873 0.144 0.856
#> GSM49617 2 0.595 0.873 0.144 0.856
#> GSM49564 1 0.000 0.996 1.000 0.000
#> GSM49565 1 0.000 0.996 1.000 0.000
#> GSM49566 1 0.000 0.996 1.000 0.000
#> GSM49567 1 0.000 0.996 1.000 0.000
#> GSM49568 1 0.000 0.996 1.000 0.000
#> GSM49569 1 0.000 0.996 1.000 0.000
#> GSM49570 2 0.000 0.951 0.000 1.000
#> GSM49571 1 0.358 0.923 0.932 0.068
#> GSM49572 1 0.000 0.996 1.000 0.000
#> GSM49573 2 0.416 0.902 0.084 0.916
#> GSM49574 1 0.000 0.996 1.000 0.000
#> GSM49575 1 0.000 0.996 1.000 0.000
#> GSM49576 1 0.000 0.996 1.000 0.000
#> GSM49577 1 0.000 0.996 1.000 0.000
#> GSM49578 1 0.000 0.996 1.000 0.000
#> GSM49579 1 0.000 0.996 1.000 0.000
#> GSM49580 1 0.000 0.996 1.000 0.000
#> GSM49581 1 0.000 0.996 1.000 0.000
#> GSM49582 1 0.000 0.996 1.000 0.000
#> GSM49583 2 0.000 0.951 0.000 1.000
#> GSM49584 1 0.000 0.996 1.000 0.000
#> GSM49585 1 0.000 0.996 1.000 0.000
#> GSM49586 1 0.000 0.996 1.000 0.000
#> GSM49587 1 0.000 0.996 1.000 0.000
#> GSM49588 1 0.000 0.996 1.000 0.000
#> GSM49589 1 0.000 0.996 1.000 0.000
#> GSM49590 1 0.295 0.942 0.948 0.052
#> GSM49591 1 0.000 0.996 1.000 0.000
#> GSM49592 1 0.000 0.996 1.000 0.000
#> GSM49593 1 0.000 0.996 1.000 0.000
#> GSM49594 1 0.000 0.996 1.000 0.000
#> GSM49595 1 0.000 0.996 1.000 0.000
#> GSM49596 1 0.000 0.996 1.000 0.000
#> GSM49597 2 0.000 0.951 0.000 1.000
#> GSM49598 1 0.000 0.996 1.000 0.000
#> GSM49599 1 0.000 0.996 1.000 0.000
#> GSM49600 1 0.000 0.996 1.000 0.000
#> GSM49601 1 0.000 0.996 1.000 0.000
#> GSM49602 1 0.000 0.996 1.000 0.000
#> GSM49603 1 0.000 0.996 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM49613 3 0.0000 0.999 0.000 0.000 1.000
#> GSM49604 2 0.1031 0.933 0.000 0.976 0.024
#> GSM49605 2 0.0000 0.945 0.000 1.000 0.000
#> GSM49606 2 0.0000 0.945 0.000 1.000 0.000
#> GSM49607 2 0.0000 0.945 0.000 1.000 0.000
#> GSM49608 2 0.0000 0.945 0.000 1.000 0.000
#> GSM49609 2 0.0237 0.944 0.000 0.996 0.004
#> GSM49610 2 0.0000 0.945 0.000 1.000 0.000
#> GSM49611 2 0.0237 0.944 0.000 0.996 0.004
#> GSM49612 2 0.0000 0.945 0.000 1.000 0.000
#> GSM49614 3 0.0237 0.995 0.000 0.004 0.996
#> GSM49615 3 0.0000 0.999 0.000 0.000 1.000
#> GSM49616 3 0.0000 0.999 0.000 0.000 1.000
#> GSM49617 3 0.0000 0.999 0.000 0.000 1.000
#> GSM49564 1 0.0892 0.981 0.980 0.000 0.020
#> GSM49565 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49566 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49567 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49568 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49569 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49570 2 0.4504 0.774 0.000 0.804 0.196
#> GSM49571 1 0.0592 0.987 0.988 0.000 0.012
#> GSM49572 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49573 2 0.5455 0.656 0.184 0.788 0.028
#> GSM49574 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49575 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49576 1 0.0592 0.988 0.988 0.000 0.012
#> GSM49577 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49578 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49579 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49580 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49581 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49582 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49583 2 0.0000 0.945 0.000 1.000 0.000
#> GSM49584 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49585 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49586 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49587 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49588 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49589 1 0.0892 0.981 0.980 0.000 0.020
#> GSM49590 1 0.1411 0.966 0.964 0.000 0.036
#> GSM49591 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49592 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49593 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49594 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49595 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49596 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49597 2 0.3272 0.871 0.004 0.892 0.104
#> GSM49598 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49599 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49600 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49601 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49602 1 0.0000 0.997 1.000 0.000 0.000
#> GSM49603 1 0.0000 0.997 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM49613 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM49604 2 0.1978 0.8561 0.000 0.928 0.004 0.068
#> GSM49605 2 0.0000 0.8999 0.000 1.000 0.000 0.000
#> GSM49606 2 0.0000 0.8999 0.000 1.000 0.000 0.000
#> GSM49607 2 0.0000 0.8999 0.000 1.000 0.000 0.000
#> GSM49608 2 0.0000 0.8999 0.000 1.000 0.000 0.000
#> GSM49609 2 0.0000 0.8999 0.000 1.000 0.000 0.000
#> GSM49610 2 0.0000 0.8999 0.000 1.000 0.000 0.000
#> GSM49611 2 0.0000 0.8999 0.000 1.000 0.000 0.000
#> GSM49612 2 0.0000 0.8999 0.000 1.000 0.000 0.000
#> GSM49614 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM49615 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM49616 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM49617 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM49564 4 0.4713 0.5815 0.360 0.000 0.000 0.640
#> GSM49565 1 0.0469 0.7329 0.988 0.000 0.000 0.012
#> GSM49566 1 0.4746 0.4501 0.632 0.000 0.000 0.368
#> GSM49567 1 0.0469 0.7285 0.988 0.000 0.000 0.012
#> GSM49568 1 0.1022 0.7343 0.968 0.000 0.000 0.032
#> GSM49569 1 0.4790 0.4200 0.620 0.000 0.000 0.380
#> GSM49570 2 0.7896 0.0829 0.000 0.360 0.292 0.348
#> GSM49571 1 0.0817 0.7339 0.976 0.000 0.000 0.024
#> GSM49572 1 0.0469 0.7285 0.988 0.000 0.000 0.012
#> GSM49573 4 0.9352 -0.4803 0.112 0.340 0.192 0.356
#> GSM49574 1 0.0336 0.7310 0.992 0.000 0.000 0.008
#> GSM49575 1 0.0469 0.7285 0.988 0.000 0.000 0.012
#> GSM49576 4 0.4713 0.5815 0.360 0.000 0.000 0.640
#> GSM49577 1 0.1716 0.7205 0.936 0.000 0.000 0.064
#> GSM49578 1 0.0336 0.7320 0.992 0.000 0.000 0.008
#> GSM49579 1 0.4746 0.4501 0.632 0.000 0.000 0.368
#> GSM49580 1 0.0921 0.7350 0.972 0.000 0.000 0.028
#> GSM49581 1 0.0336 0.7320 0.992 0.000 0.000 0.008
#> GSM49582 1 0.0336 0.7320 0.992 0.000 0.000 0.008
#> GSM49583 2 0.0000 0.8999 0.000 1.000 0.000 0.000
#> GSM49584 1 0.0817 0.7351 0.976 0.000 0.000 0.024
#> GSM49585 1 0.2011 0.7160 0.920 0.000 0.000 0.080
#> GSM49586 1 0.4564 0.5026 0.672 0.000 0.000 0.328
#> GSM49587 1 0.0707 0.7352 0.980 0.000 0.000 0.020
#> GSM49588 1 0.3610 0.6337 0.800 0.000 0.000 0.200
#> GSM49589 4 0.4713 0.5815 0.360 0.000 0.000 0.640
#> GSM49590 4 0.5237 0.5751 0.356 0.000 0.016 0.628
#> GSM49591 1 0.0469 0.7347 0.988 0.000 0.000 0.012
#> GSM49592 1 0.0336 0.7320 0.992 0.000 0.000 0.008
#> GSM49593 1 0.4761 0.4500 0.628 0.000 0.000 0.372
#> GSM49594 1 0.4730 0.4576 0.636 0.000 0.000 0.364
#> GSM49595 1 0.4761 0.4506 0.628 0.000 0.000 0.372
#> GSM49596 1 0.4585 0.5001 0.668 0.000 0.000 0.332
#> GSM49597 2 0.7312 0.4059 0.000 0.520 0.188 0.292
#> GSM49598 1 0.4746 0.4501 0.632 0.000 0.000 0.368
#> GSM49599 1 0.0469 0.7285 0.988 0.000 0.000 0.012
#> GSM49600 1 0.2704 0.6920 0.876 0.000 0.000 0.124
#> GSM49601 1 0.4761 0.4506 0.628 0.000 0.000 0.372
#> GSM49602 1 0.4746 0.4501 0.632 0.000 0.000 0.368
#> GSM49603 1 0.4746 0.4501 0.632 0.000 0.000 0.368
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM49613 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM49604 2 0.1341 0.9454 0.000 0.944 0.000 0.056 0.000
#> GSM49605 2 0.0000 0.9885 0.000 1.000 0.000 0.000 0.000
#> GSM49606 2 0.0000 0.9885 0.000 1.000 0.000 0.000 0.000
#> GSM49607 2 0.0000 0.9885 0.000 1.000 0.000 0.000 0.000
#> GSM49608 2 0.0000 0.9885 0.000 1.000 0.000 0.000 0.000
#> GSM49609 2 0.0000 0.9885 0.000 1.000 0.000 0.000 0.000
#> GSM49610 2 0.0000 0.9885 0.000 1.000 0.000 0.000 0.000
#> GSM49611 2 0.0000 0.9885 0.000 1.000 0.000 0.000 0.000
#> GSM49612 2 0.0000 0.9885 0.000 1.000 0.000 0.000 0.000
#> GSM49614 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM49615 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM49616 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM49617 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM49564 5 0.0162 0.3913 0.004 0.000 0.000 0.000 0.996
#> GSM49565 1 0.0404 0.8417 0.988 0.000 0.000 0.012 0.000
#> GSM49566 5 0.4242 0.6450 0.428 0.000 0.000 0.000 0.572
#> GSM49567 1 0.0162 0.8428 0.996 0.000 0.000 0.000 0.004
#> GSM49568 1 0.1043 0.8499 0.960 0.000 0.000 0.000 0.040
#> GSM49569 5 0.4138 0.6456 0.384 0.000 0.000 0.000 0.616
#> GSM49570 4 0.0609 0.9398 0.000 0.000 0.020 0.980 0.000
#> GSM49571 1 0.1012 0.8357 0.968 0.000 0.000 0.012 0.020
#> GSM49572 1 0.0162 0.8435 0.996 0.000 0.000 0.004 0.000
#> GSM49573 4 0.0671 0.9382 0.016 0.000 0.004 0.980 0.000
#> GSM49574 1 0.0290 0.8428 0.992 0.000 0.000 0.008 0.000
#> GSM49575 1 0.0162 0.8428 0.996 0.000 0.000 0.000 0.004
#> GSM49576 5 0.0162 0.3913 0.004 0.000 0.000 0.000 0.996
#> GSM49577 1 0.2006 0.7768 0.916 0.000 0.000 0.012 0.072
#> GSM49578 1 0.1410 0.8435 0.940 0.000 0.000 0.000 0.060
#> GSM49579 5 0.4242 0.6450 0.428 0.000 0.000 0.000 0.572
#> GSM49580 1 0.1282 0.8489 0.952 0.000 0.000 0.004 0.044
#> GSM49581 1 0.1638 0.8419 0.932 0.000 0.000 0.004 0.064
#> GSM49582 1 0.1571 0.8425 0.936 0.000 0.000 0.004 0.060
#> GSM49583 2 0.1121 0.9561 0.000 0.956 0.000 0.044 0.000
#> GSM49584 1 0.1571 0.8425 0.936 0.000 0.000 0.004 0.060
#> GSM49585 1 0.2136 0.7787 0.904 0.000 0.000 0.008 0.088
#> GSM49586 1 0.4597 -0.4588 0.564 0.000 0.000 0.012 0.424
#> GSM49587 1 0.0703 0.8492 0.976 0.000 0.000 0.000 0.024
#> GSM49588 1 0.4084 0.0304 0.668 0.000 0.000 0.004 0.328
#> GSM49589 5 0.0162 0.3913 0.004 0.000 0.000 0.000 0.996
#> GSM49590 5 0.0162 0.3913 0.004 0.000 0.000 0.000 0.996
#> GSM49591 1 0.1697 0.8443 0.932 0.000 0.000 0.008 0.060
#> GSM49592 1 0.1697 0.8443 0.932 0.000 0.000 0.008 0.060
#> GSM49593 5 0.4300 0.6244 0.476 0.000 0.000 0.000 0.524
#> GSM49594 5 0.4562 0.6030 0.492 0.000 0.000 0.008 0.500
#> GSM49595 5 0.4451 0.6069 0.492 0.000 0.000 0.004 0.504
#> GSM49596 1 0.4449 -0.5835 0.512 0.000 0.000 0.004 0.484
#> GSM49597 4 0.2110 0.9036 0.000 0.072 0.016 0.912 0.000
#> GSM49598 5 0.4300 0.5528 0.476 0.000 0.000 0.000 0.524
#> GSM49599 1 0.0162 0.8428 0.996 0.000 0.000 0.000 0.004
#> GSM49600 1 0.1704 0.8392 0.928 0.000 0.000 0.004 0.068
#> GSM49601 5 0.4446 0.6228 0.476 0.000 0.000 0.004 0.520
#> GSM49602 5 0.4242 0.6450 0.428 0.000 0.000 0.000 0.572
#> GSM49603 5 0.4268 0.6401 0.444 0.000 0.000 0.000 0.556
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM49613 3 0.0000 0.9990 0.000 0.000 1.000 0.000 0.000 NA
#> GSM49604 2 0.1391 0.8258 0.000 0.944 0.000 0.040 0.000 NA
#> GSM49605 2 0.2378 0.8557 0.000 0.848 0.000 0.000 0.000 NA
#> GSM49606 2 0.3244 0.8379 0.000 0.732 0.000 0.000 0.000 NA
#> GSM49607 2 0.0000 0.8561 0.000 1.000 0.000 0.000 0.000 NA
#> GSM49608 2 0.0000 0.8561 0.000 1.000 0.000 0.000 0.000 NA
#> GSM49609 2 0.3244 0.8379 0.000 0.732 0.000 0.000 0.000 NA
#> GSM49610 2 0.0000 0.8561 0.000 1.000 0.000 0.000 0.000 NA
#> GSM49611 2 0.3244 0.8379 0.000 0.732 0.000 0.000 0.000 NA
#> GSM49612 2 0.3244 0.8379 0.000 0.732 0.000 0.000 0.000 NA
#> GSM49614 3 0.0146 0.9959 0.000 0.000 0.996 0.004 0.000 NA
#> GSM49615 3 0.0000 0.9990 0.000 0.000 1.000 0.000 0.000 NA
#> GSM49616 3 0.0000 0.9990 0.000 0.000 1.000 0.000 0.000 NA
#> GSM49617 3 0.0000 0.9990 0.000 0.000 1.000 0.000 0.000 NA
#> GSM49564 5 0.2902 0.4585 0.004 0.000 0.000 0.000 0.800 NA
#> GSM49565 1 0.4310 0.6106 0.580 0.000 0.000 0.000 0.024 NA
#> GSM49566 5 0.2912 0.6816 0.216 0.000 0.000 0.000 0.784 NA
#> GSM49567 1 0.3101 0.6738 0.756 0.000 0.000 0.000 0.000 NA
#> GSM49568 1 0.3283 0.5376 0.804 0.000 0.000 0.000 0.160 NA
#> GSM49569 5 0.2793 0.6781 0.200 0.000 0.000 0.000 0.800 NA
#> GSM49570 4 0.0000 0.9198 0.000 0.000 0.000 1.000 0.000 NA
#> GSM49571 1 0.4010 0.6203 0.584 0.000 0.000 0.000 0.008 NA
#> GSM49572 1 0.3555 0.6693 0.712 0.000 0.000 0.000 0.008 NA
#> GSM49573 4 0.0000 0.9198 0.000 0.000 0.000 1.000 0.000 NA
#> GSM49574 1 0.3899 0.6404 0.628 0.000 0.000 0.000 0.008 NA
#> GSM49575 1 0.3101 0.6736 0.756 0.000 0.000 0.000 0.000 NA
#> GSM49576 5 0.2730 0.4595 0.000 0.000 0.000 0.000 0.808 NA
#> GSM49577 1 0.4726 0.5620 0.528 0.000 0.000 0.000 0.048 NA
#> GSM49578 1 0.0692 0.6678 0.976 0.000 0.000 0.000 0.020 NA
#> GSM49579 5 0.3198 0.6796 0.260 0.000 0.000 0.000 0.740 NA
#> GSM49580 1 0.4314 0.4555 0.720 0.000 0.000 0.000 0.184 NA
#> GSM49581 1 0.1970 0.6490 0.900 0.000 0.000 0.000 0.008 NA
#> GSM49582 1 0.1970 0.6490 0.900 0.000 0.000 0.000 0.008 NA
#> GSM49583 2 0.0622 0.8467 0.000 0.980 0.000 0.008 0.000 NA
#> GSM49584 1 0.4403 0.4413 0.708 0.000 0.000 0.000 0.196 NA
#> GSM49585 1 0.5042 0.1748 0.592 0.000 0.000 0.000 0.308 NA
#> GSM49586 5 0.6130 -0.0697 0.324 0.000 0.000 0.000 0.340 NA
#> GSM49587 1 0.1584 0.6736 0.928 0.000 0.000 0.000 0.008 NA
#> GSM49588 5 0.4212 0.4716 0.424 0.000 0.000 0.000 0.560 NA
#> GSM49589 5 0.2762 0.4568 0.000 0.000 0.000 0.000 0.804 NA
#> GSM49590 5 0.2762 0.4568 0.000 0.000 0.000 0.000 0.804 NA
#> GSM49591 1 0.3403 0.6697 0.768 0.000 0.000 0.000 0.020 NA
#> GSM49592 1 0.2199 0.6685 0.892 0.000 0.000 0.000 0.020 NA
#> GSM49593 5 0.3468 0.6735 0.284 0.000 0.000 0.000 0.712 NA
#> GSM49594 5 0.5944 0.2361 0.244 0.000 0.000 0.000 0.452 NA
#> GSM49595 5 0.5629 0.3635 0.224 0.000 0.000 0.000 0.540 NA
#> GSM49596 5 0.3748 0.6613 0.300 0.000 0.000 0.000 0.688 NA
#> GSM49597 4 0.2631 0.8379 0.000 0.152 0.000 0.840 0.000 NA
#> GSM49598 5 0.3830 0.5549 0.376 0.000 0.000 0.000 0.620 NA
#> GSM49599 1 0.3126 0.6729 0.752 0.000 0.000 0.000 0.000 NA
#> GSM49600 1 0.4486 0.4211 0.696 0.000 0.000 0.000 0.208 NA
#> GSM49601 5 0.3936 0.6673 0.288 0.000 0.000 0.000 0.688 NA
#> GSM49602 5 0.3244 0.6775 0.268 0.000 0.000 0.000 0.732 NA
#> GSM49603 5 0.3309 0.6740 0.280 0.000 0.000 0.000 0.720 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) cell.type(p) k
#> MAD:mclust 54 4.59e-06 2.04e-05 2
#> MAD:mclust 54 2.57e-07 8.46e-14 3
#> MAD:mclust 41 5.82e-07 6.34e-10 4
#> MAD:mclust 47 1.93e-07 1.29e-10 5
#> MAD:mclust 42 1.42e-06 3.16e-09 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21168 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.885 0.920 0.967 0.4341 0.575 0.575
#> 3 3 0.854 0.895 0.949 0.3793 0.758 0.606
#> 4 4 0.620 0.732 0.846 0.1499 0.941 0.860
#> 5 5 0.705 0.693 0.826 0.1055 0.814 0.525
#> 6 6 0.849 0.747 0.874 0.0553 0.924 0.708
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
#> GSM49613 1 0.0000 0.963 1.000 0.000
#> GSM49604 2 0.0000 0.963 0.000 1.000
#> GSM49605 2 0.0000 0.963 0.000 1.000
#> GSM49606 2 0.0000 0.963 0.000 1.000
#> GSM49607 2 0.0000 0.963 0.000 1.000
#> GSM49608 2 0.0000 0.963 0.000 1.000
#> GSM49609 2 0.0000 0.963 0.000 1.000
#> GSM49610 2 0.0000 0.963 0.000 1.000
#> GSM49611 2 0.0000 0.963 0.000 1.000
#> GSM49612 2 0.0000 0.963 0.000 1.000
#> GSM49614 1 0.8386 0.623 0.732 0.268
#> GSM49615 1 0.0000 0.963 1.000 0.000
#> GSM49616 1 0.0000 0.963 1.000 0.000
#> GSM49617 1 0.0000 0.963 1.000 0.000
#> GSM49564 1 0.0000 0.963 1.000 0.000
#> GSM49565 1 0.9954 0.142 0.540 0.460
#> GSM49566 1 0.0000 0.963 1.000 0.000
#> GSM49567 1 0.0938 0.955 0.988 0.012
#> GSM49568 1 0.0000 0.963 1.000 0.000
#> GSM49569 1 0.0000 0.963 1.000 0.000
#> GSM49570 2 0.0000 0.963 0.000 1.000
#> GSM49571 2 0.3431 0.911 0.064 0.936
#> GSM49572 1 0.0672 0.958 0.992 0.008
#> GSM49573 2 0.0000 0.963 0.000 1.000
#> GSM49574 1 0.7056 0.760 0.808 0.192
#> GSM49575 1 0.2043 0.939 0.968 0.032
#> GSM49576 1 0.0000 0.963 1.000 0.000
#> GSM49577 2 0.5946 0.823 0.144 0.856
#> GSM49578 1 0.0000 0.963 1.000 0.000
#> GSM49579 1 0.0000 0.963 1.000 0.000
#> GSM49580 1 0.0000 0.963 1.000 0.000
#> GSM49581 1 0.0000 0.963 1.000 0.000
#> GSM49582 1 0.0000 0.963 1.000 0.000
#> GSM49583 2 0.0000 0.963 0.000 1.000
#> GSM49584 1 0.0000 0.963 1.000 0.000
#> GSM49585 1 0.0000 0.963 1.000 0.000
#> GSM49586 1 0.7602 0.718 0.780 0.220
#> GSM49587 1 0.0000 0.963 1.000 0.000
#> GSM49588 1 0.0000 0.963 1.000 0.000
#> GSM49589 1 0.0000 0.963 1.000 0.000
#> GSM49590 1 0.0000 0.963 1.000 0.000
#> GSM49591 1 0.0000 0.963 1.000 0.000
#> GSM49592 1 0.0000 0.963 1.000 0.000
#> GSM49593 1 0.0000 0.963 1.000 0.000
#> GSM49594 2 0.8909 0.545 0.308 0.692
#> GSM49595 1 0.4431 0.881 0.908 0.092
#> GSM49596 1 0.0000 0.963 1.000 0.000
#> GSM49597 2 0.0000 0.963 0.000 1.000
#> GSM49598 1 0.0000 0.963 1.000 0.000
#> GSM49599 1 0.0672 0.958 0.992 0.008
#> GSM49600 1 0.0000 0.963 1.000 0.000
#> GSM49601 1 0.0000 0.963 1.000 0.000
#> GSM49602 1 0.0000 0.963 1.000 0.000
#> GSM49603 1 0.0000 0.963 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM49613 3 0.0000 0.943 0.000 0.000 1.000
#> GSM49604 2 0.0000 0.953 0.000 1.000 0.000
#> GSM49605 2 0.0000 0.953 0.000 1.000 0.000
#> GSM49606 2 0.0000 0.953 0.000 1.000 0.000
#> GSM49607 2 0.0000 0.953 0.000 1.000 0.000
#> GSM49608 2 0.0424 0.947 0.000 0.992 0.008
#> GSM49609 2 0.0000 0.953 0.000 1.000 0.000
#> GSM49610 2 0.0000 0.953 0.000 1.000 0.000
#> GSM49611 2 0.0000 0.953 0.000 1.000 0.000
#> GSM49612 2 0.0000 0.953 0.000 1.000 0.000
#> GSM49614 3 0.0892 0.934 0.000 0.020 0.980
#> GSM49615 3 0.0000 0.943 0.000 0.000 1.000
#> GSM49616 3 0.0424 0.940 0.000 0.008 0.992
#> GSM49617 3 0.0892 0.934 0.000 0.020 0.980
#> GSM49564 3 0.1289 0.937 0.032 0.000 0.968
#> GSM49565 1 0.1753 0.913 0.952 0.048 0.000
#> GSM49566 1 0.3192 0.878 0.888 0.000 0.112
#> GSM49567 1 0.0747 0.929 0.984 0.016 0.000
#> GSM49568 1 0.0592 0.934 0.988 0.000 0.012
#> GSM49569 1 0.3267 0.874 0.884 0.000 0.116
#> GSM49570 2 0.5254 0.629 0.000 0.736 0.264
#> GSM49571 2 0.4974 0.645 0.236 0.764 0.000
#> GSM49572 1 0.0892 0.928 0.980 0.020 0.000
#> GSM49573 2 0.0237 0.950 0.004 0.996 0.000
#> GSM49574 1 0.1163 0.925 0.972 0.028 0.000
#> GSM49575 1 0.1163 0.925 0.972 0.028 0.000
#> GSM49576 3 0.4504 0.750 0.196 0.000 0.804
#> GSM49577 1 0.5926 0.458 0.644 0.356 0.000
#> GSM49578 1 0.0237 0.934 0.996 0.000 0.004
#> GSM49579 1 0.0747 0.934 0.984 0.000 0.016
#> GSM49580 1 0.1289 0.929 0.968 0.000 0.032
#> GSM49581 1 0.0592 0.934 0.988 0.000 0.012
#> GSM49582 1 0.0592 0.934 0.988 0.000 0.012
#> GSM49583 2 0.0000 0.953 0.000 1.000 0.000
#> GSM49584 1 0.2448 0.906 0.924 0.000 0.076
#> GSM49585 1 0.0237 0.934 0.996 0.000 0.004
#> GSM49586 1 0.2537 0.887 0.920 0.080 0.000
#> GSM49587 1 0.0237 0.934 0.996 0.000 0.004
#> GSM49588 1 0.0747 0.934 0.984 0.000 0.016
#> GSM49589 3 0.1964 0.918 0.056 0.000 0.944
#> GSM49590 3 0.1031 0.940 0.024 0.000 0.976
#> GSM49591 1 0.0000 0.933 1.000 0.000 0.000
#> GSM49592 1 0.0000 0.933 1.000 0.000 0.000
#> GSM49593 1 0.2066 0.916 0.940 0.000 0.060
#> GSM49594 1 0.6225 0.255 0.568 0.432 0.000
#> GSM49595 1 0.1411 0.920 0.964 0.036 0.000
#> GSM49596 1 0.0892 0.933 0.980 0.000 0.020
#> GSM49597 2 0.0237 0.950 0.000 0.996 0.004
#> GSM49598 1 0.2625 0.902 0.916 0.000 0.084
#> GSM49599 1 0.1163 0.925 0.972 0.028 0.000
#> GSM49600 1 0.2711 0.897 0.912 0.000 0.088
#> GSM49601 1 0.0892 0.933 0.980 0.000 0.020
#> GSM49602 1 0.1031 0.932 0.976 0.000 0.024
#> GSM49603 1 0.3267 0.876 0.884 0.000 0.116
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM49613 3 0.0672 0.891 0.008 0.000 0.984 0.008
#> GSM49604 4 0.4522 0.681 0.000 0.320 0.000 0.680
#> GSM49605 2 0.1118 0.846 0.000 0.964 0.000 0.036
#> GSM49606 2 0.0188 0.847 0.000 0.996 0.000 0.004
#> GSM49607 2 0.2466 0.816 0.000 0.900 0.004 0.096
#> GSM49608 2 0.2334 0.823 0.000 0.908 0.004 0.088
#> GSM49609 2 0.0657 0.841 0.000 0.984 0.004 0.012
#> GSM49610 2 0.2011 0.832 0.000 0.920 0.000 0.080
#> GSM49611 2 0.0657 0.841 0.000 0.984 0.004 0.012
#> GSM49612 2 0.0000 0.847 0.000 1.000 0.000 0.000
#> GSM49614 3 0.3545 0.759 0.000 0.008 0.828 0.164
#> GSM49615 3 0.0657 0.890 0.004 0.000 0.984 0.012
#> GSM49616 3 0.1576 0.875 0.004 0.000 0.948 0.048
#> GSM49617 3 0.2611 0.832 0.000 0.008 0.896 0.096
#> GSM49564 3 0.0672 0.889 0.008 0.000 0.984 0.008
#> GSM49565 1 0.2125 0.784 0.920 0.076 0.004 0.000
#> GSM49566 1 0.5653 0.699 0.712 0.000 0.192 0.096
#> GSM49567 1 0.2530 0.748 0.888 0.000 0.000 0.112
#> GSM49568 1 0.0000 0.809 1.000 0.000 0.000 0.000
#> GSM49569 1 0.6198 0.649 0.660 0.000 0.224 0.116
#> GSM49570 4 0.4462 0.763 0.000 0.132 0.064 0.804
#> GSM49571 4 0.5920 0.633 0.168 0.120 0.004 0.708
#> GSM49572 1 0.0524 0.808 0.988 0.004 0.000 0.008
#> GSM49573 4 0.3821 0.776 0.040 0.120 0.000 0.840
#> GSM49574 1 0.0336 0.808 0.992 0.000 0.000 0.008
#> GSM49575 1 0.4898 0.212 0.584 0.000 0.000 0.416
#> GSM49576 3 0.4231 0.766 0.080 0.000 0.824 0.096
#> GSM49577 1 0.4644 0.712 0.788 0.164 0.004 0.044
#> GSM49578 1 0.0188 0.809 0.996 0.000 0.000 0.004
#> GSM49579 1 0.4773 0.750 0.788 0.000 0.092 0.120
#> GSM49580 1 0.1557 0.790 0.944 0.000 0.000 0.056
#> GSM49581 1 0.1716 0.786 0.936 0.000 0.000 0.064
#> GSM49582 1 0.0707 0.805 0.980 0.000 0.000 0.020
#> GSM49583 2 0.4072 0.584 0.000 0.748 0.000 0.252
#> GSM49584 1 0.0524 0.809 0.988 0.000 0.004 0.008
#> GSM49585 1 0.1388 0.810 0.960 0.000 0.012 0.028
#> GSM49586 1 0.6935 0.513 0.552 0.112 0.004 0.332
#> GSM49587 1 0.0188 0.809 0.996 0.000 0.000 0.004
#> GSM49588 1 0.1388 0.808 0.960 0.000 0.028 0.012
#> GSM49589 3 0.2402 0.861 0.012 0.000 0.912 0.076
#> GSM49590 3 0.2737 0.842 0.008 0.000 0.888 0.104
#> GSM49591 1 0.0336 0.810 0.992 0.000 0.000 0.008
#> GSM49592 1 0.0376 0.810 0.992 0.004 0.000 0.004
#> GSM49593 1 0.6204 0.679 0.672 0.000 0.160 0.168
#> GSM49594 2 0.6725 0.318 0.184 0.632 0.004 0.180
#> GSM49595 1 0.7668 0.479 0.532 0.276 0.016 0.176
#> GSM49596 1 0.3301 0.786 0.876 0.000 0.048 0.076
#> GSM49597 4 0.4428 0.711 0.000 0.276 0.004 0.720
#> GSM49598 1 0.5208 0.738 0.748 0.000 0.080 0.172
#> GSM49599 1 0.4998 -0.038 0.512 0.000 0.000 0.488
#> GSM49600 1 0.0927 0.811 0.976 0.000 0.016 0.008
#> GSM49601 1 0.7686 0.625 0.604 0.056 0.148 0.192
#> GSM49602 1 0.6808 0.649 0.632 0.008 0.160 0.200
#> GSM49603 1 0.7318 0.485 0.524 0.000 0.280 0.196
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM49613 3 0.0880 0.89873 0.000 0.000 0.968 0.000 0.032
#> GSM49604 4 0.3578 0.64453 0.000 0.132 0.000 0.820 0.048
#> GSM49605 2 0.0992 0.85103 0.000 0.968 0.000 0.024 0.008
#> GSM49606 2 0.0324 0.85034 0.000 0.992 0.000 0.004 0.004
#> GSM49607 2 0.4657 0.75110 0.000 0.752 0.004 0.116 0.128
#> GSM49608 2 0.4400 0.77207 0.000 0.780 0.008 0.108 0.104
#> GSM49609 2 0.1732 0.82184 0.000 0.920 0.000 0.000 0.080
#> GSM49610 2 0.2141 0.84295 0.000 0.916 0.004 0.064 0.016
#> GSM49611 2 0.1732 0.82184 0.000 0.920 0.000 0.000 0.080
#> GSM49612 2 0.1041 0.84473 0.000 0.964 0.004 0.000 0.032
#> GSM49614 3 0.3682 0.74770 0.000 0.012 0.836 0.088 0.064
#> GSM49615 3 0.0703 0.89886 0.000 0.000 0.976 0.000 0.024
#> GSM49616 3 0.0609 0.89810 0.000 0.000 0.980 0.000 0.020
#> GSM49617 3 0.0566 0.88382 0.000 0.000 0.984 0.012 0.004
#> GSM49564 3 0.1121 0.88843 0.000 0.000 0.956 0.000 0.044
#> GSM49565 1 0.2130 0.82397 0.908 0.080 0.000 0.000 0.012
#> GSM49566 1 0.5647 0.04772 0.548 0.000 0.072 0.004 0.376
#> GSM49567 1 0.1372 0.85836 0.956 0.004 0.000 0.016 0.024
#> GSM49568 1 0.0000 0.87588 1.000 0.000 0.000 0.000 0.000
#> GSM49569 5 0.6206 0.62318 0.252 0.000 0.200 0.000 0.548
#> GSM49570 4 0.0727 0.69208 0.000 0.004 0.004 0.980 0.012
#> GSM49571 4 0.4476 0.67276 0.048 0.016 0.000 0.764 0.172
#> GSM49572 1 0.0740 0.87250 0.980 0.008 0.000 0.004 0.008
#> GSM49573 4 0.2570 0.70045 0.004 0.008 0.000 0.880 0.108
#> GSM49574 1 0.0000 0.87588 1.000 0.000 0.000 0.000 0.000
#> GSM49575 1 0.5113 0.30874 0.620 0.000 0.000 0.324 0.056
#> GSM49576 5 0.5587 0.42604 0.072 0.000 0.428 0.000 0.500
#> GSM49577 1 0.6813 0.16111 0.504 0.240 0.000 0.016 0.240
#> GSM49578 1 0.0000 0.87588 1.000 0.000 0.000 0.000 0.000
#> GSM49579 5 0.4803 0.30427 0.444 0.000 0.020 0.000 0.536
#> GSM49580 1 0.0404 0.87494 0.988 0.000 0.000 0.000 0.012
#> GSM49581 1 0.0898 0.86963 0.972 0.000 0.000 0.020 0.008
#> GSM49582 1 0.0162 0.87544 0.996 0.000 0.000 0.000 0.004
#> GSM49583 2 0.6534 0.53467 0.008 0.568 0.012 0.256 0.156
#> GSM49584 1 0.0579 0.87527 0.984 0.000 0.008 0.000 0.008
#> GSM49585 1 0.2741 0.77416 0.860 0.000 0.004 0.004 0.132
#> GSM49586 5 0.4188 0.45882 0.020 0.008 0.000 0.228 0.744
#> GSM49587 1 0.0000 0.87588 1.000 0.000 0.000 0.000 0.000
#> GSM49588 1 0.0898 0.87156 0.972 0.000 0.008 0.000 0.020
#> GSM49589 3 0.3305 0.60508 0.000 0.000 0.776 0.000 0.224
#> GSM49590 5 0.4283 0.32821 0.000 0.000 0.456 0.000 0.544
#> GSM49591 1 0.0880 0.86685 0.968 0.000 0.000 0.000 0.032
#> GSM49592 1 0.0162 0.87550 0.996 0.000 0.000 0.000 0.004
#> GSM49593 5 0.5628 0.67307 0.220 0.000 0.148 0.000 0.632
#> GSM49594 5 0.4752 0.50159 0.036 0.316 0.000 0.000 0.648
#> GSM49595 5 0.4876 0.62614 0.080 0.220 0.000 0.000 0.700
#> GSM49596 1 0.3586 0.53706 0.736 0.000 0.000 0.000 0.264
#> GSM49597 4 0.5743 0.40116 0.000 0.156 0.016 0.664 0.164
#> GSM49598 5 0.5054 0.62153 0.184 0.000 0.004 0.104 0.708
#> GSM49599 4 0.4655 0.00372 0.476 0.000 0.000 0.512 0.012
#> GSM49600 1 0.0992 0.86886 0.968 0.000 0.008 0.000 0.024
#> GSM49601 5 0.5775 0.66011 0.084 0.068 0.152 0.000 0.696
#> GSM49602 5 0.4884 0.69244 0.128 0.000 0.152 0.000 0.720
#> GSM49603 5 0.4519 0.63707 0.052 0.000 0.228 0.000 0.720
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM49613 3 0.0777 0.9062 0.000 0.000 0.972 0.000 0.024 0.004
#> GSM49604 4 0.3254 0.6664 0.000 0.124 0.000 0.820 0.000 0.056
#> GSM49605 2 0.2053 0.8314 0.000 0.888 0.000 0.000 0.004 0.108
#> GSM49606 2 0.1141 0.8573 0.000 0.948 0.000 0.000 0.000 0.052
#> GSM49607 2 0.3652 0.5455 0.000 0.672 0.004 0.000 0.000 0.324
#> GSM49608 2 0.3368 0.6999 0.000 0.756 0.012 0.000 0.000 0.232
#> GSM49609 2 0.0937 0.8316 0.000 0.960 0.000 0.000 0.000 0.040
#> GSM49610 2 0.0937 0.8589 0.000 0.960 0.000 0.000 0.000 0.040
#> GSM49611 2 0.0790 0.8376 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM49612 2 0.0000 0.8524 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM49614 3 0.1701 0.8590 0.000 0.000 0.920 0.008 0.000 0.072
#> GSM49615 3 0.0458 0.9075 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM49616 3 0.0291 0.9046 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM49617 3 0.0713 0.8958 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM49564 3 0.1080 0.9011 0.004 0.000 0.960 0.000 0.032 0.004
#> GSM49565 1 0.1398 0.8618 0.940 0.008 0.000 0.000 0.000 0.052
#> GSM49566 5 0.5212 0.5273 0.124 0.004 0.004 0.000 0.632 0.236
#> GSM49567 1 0.1471 0.8558 0.932 0.000 0.000 0.000 0.004 0.064
#> GSM49568 1 0.0146 0.8718 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM49569 5 0.1483 0.8509 0.036 0.000 0.008 0.000 0.944 0.012
#> GSM49570 4 0.3772 0.5413 0.000 0.004 0.004 0.672 0.000 0.320
#> GSM49571 4 0.1340 0.7126 0.000 0.004 0.000 0.948 0.008 0.040
#> GSM49572 1 0.1075 0.8635 0.952 0.000 0.000 0.000 0.000 0.048
#> GSM49573 4 0.1814 0.7188 0.000 0.000 0.000 0.900 0.000 0.100
#> GSM49574 1 0.0622 0.8713 0.980 0.000 0.000 0.008 0.000 0.012
#> GSM49575 1 0.4161 0.2740 0.540 0.000 0.000 0.448 0.000 0.012
#> GSM49576 5 0.1616 0.8504 0.000 0.000 0.020 0.000 0.932 0.048
#> GSM49577 5 0.6755 0.0195 0.156 0.072 0.000 0.000 0.424 0.348
#> GSM49578 1 0.0000 0.8714 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM49579 5 0.2537 0.8091 0.032 0.000 0.000 0.000 0.872 0.096
#> GSM49580 1 0.0858 0.8691 0.968 0.000 0.000 0.004 0.000 0.028
#> GSM49581 1 0.1167 0.8707 0.960 0.000 0.000 0.020 0.008 0.012
#> GSM49582 1 0.0622 0.8708 0.980 0.000 0.000 0.008 0.000 0.012
#> GSM49583 6 0.3862 0.4999 0.004 0.268 0.000 0.004 0.012 0.712
#> GSM49584 1 0.0653 0.8721 0.980 0.000 0.004 0.004 0.000 0.012
#> GSM49585 1 0.4783 0.6997 0.740 0.008 0.008 0.136 0.016 0.092
#> GSM49586 4 0.5025 0.5080 0.000 0.016 0.004 0.684 0.192 0.104
#> GSM49587 1 0.0260 0.8715 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM49588 1 0.1503 0.8626 0.944 0.000 0.000 0.008 0.016 0.032
#> GSM49589 3 0.3512 0.5992 0.000 0.000 0.720 0.000 0.272 0.008
#> GSM49590 5 0.1088 0.8566 0.000 0.000 0.016 0.000 0.960 0.024
#> GSM49591 1 0.2680 0.8305 0.880 0.000 0.000 0.060 0.012 0.048
#> GSM49592 1 0.2121 0.8476 0.916 0.000 0.008 0.040 0.004 0.032
#> GSM49593 5 0.1401 0.8510 0.020 0.000 0.028 0.004 0.948 0.000
#> GSM49594 5 0.1092 0.8512 0.000 0.020 0.000 0.000 0.960 0.020
#> GSM49595 5 0.0405 0.8563 0.000 0.004 0.000 0.000 0.988 0.008
#> GSM49596 1 0.4097 -0.0233 0.504 0.000 0.000 0.000 0.488 0.008
#> GSM49597 6 0.3880 0.5115 0.000 0.024 0.000 0.132 0.052 0.792
#> GSM49598 5 0.1908 0.8433 0.020 0.000 0.012 0.044 0.924 0.000
#> GSM49599 1 0.4855 0.2806 0.556 0.000 0.000 0.380 0.000 0.064
#> GSM49600 1 0.1390 0.8637 0.948 0.000 0.000 0.004 0.032 0.016
#> GSM49601 5 0.5045 0.6761 0.000 0.056 0.068 0.040 0.748 0.088
#> GSM49602 5 0.0291 0.8570 0.004 0.000 0.000 0.000 0.992 0.004
#> GSM49603 5 0.1440 0.8477 0.004 0.000 0.032 0.012 0.948 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) cell.type(p) k
#> MAD:NMF 53 2.77e-05 3.04e-03 2
#> MAD:NMF 52 2.78e-06 1.35e-07 3
#> MAD:NMF 49 3.02e-07 9.05e-08 4
#> MAD:NMF 45 3.77e-06 1.19e-07 5
#> MAD:NMF 49 2.61e-07 2.78e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "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 21168 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.978 0.987 0.3655 0.628 0.628
#> 3 3 0.908 0.920 0.951 0.1163 0.971 0.953
#> 4 4 1.000 0.966 0.986 0.0308 0.992 0.986
#> 5 5 0.656 0.835 0.890 0.3216 0.874 0.787
#> 6 6 0.695 0.844 0.886 0.0682 0.971 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
#> GSM49613 1 0.000 0.994 1.000 0.000
#> GSM49604 2 0.506 0.910 0.112 0.888
#> GSM49605 2 0.000 0.958 0.000 1.000
#> GSM49606 2 0.456 0.927 0.096 0.904
#> GSM49607 2 0.000 0.958 0.000 1.000
#> GSM49608 2 0.000 0.958 0.000 1.000
#> GSM49609 2 0.456 0.927 0.096 0.904
#> GSM49610 2 0.000 0.958 0.000 1.000
#> GSM49611 2 0.456 0.927 0.096 0.904
#> GSM49612 2 0.456 0.927 0.096 0.904
#> GSM49614 1 0.000 0.994 1.000 0.000
#> GSM49615 1 0.000 0.994 1.000 0.000
#> GSM49616 1 0.000 0.994 1.000 0.000
#> GSM49617 1 0.000 0.994 1.000 0.000
#> GSM49564 1 0.000 0.994 1.000 0.000
#> GSM49565 1 0.000 0.994 1.000 0.000
#> GSM49566 1 0.000 0.994 1.000 0.000
#> GSM49567 1 0.000 0.994 1.000 0.000
#> GSM49568 1 0.000 0.994 1.000 0.000
#> GSM49569 1 0.000 0.994 1.000 0.000
#> GSM49570 2 0.000 0.958 0.000 1.000
#> GSM49571 1 0.482 0.880 0.896 0.104
#> GSM49572 1 0.000 0.994 1.000 0.000
#> GSM49573 2 0.000 0.958 0.000 1.000
#> GSM49574 1 0.000 0.994 1.000 0.000
#> GSM49575 1 0.000 0.994 1.000 0.000
#> GSM49576 1 0.000 0.994 1.000 0.000
#> GSM49577 1 0.000 0.994 1.000 0.000
#> GSM49578 1 0.000 0.994 1.000 0.000
#> GSM49579 1 0.000 0.994 1.000 0.000
#> GSM49580 1 0.000 0.994 1.000 0.000
#> GSM49581 1 0.000 0.994 1.000 0.000
#> GSM49582 1 0.000 0.994 1.000 0.000
#> GSM49583 2 0.000 0.958 0.000 1.000
#> GSM49584 1 0.000 0.994 1.000 0.000
#> GSM49585 1 0.000 0.994 1.000 0.000
#> GSM49586 1 0.482 0.880 0.896 0.104
#> GSM49587 1 0.000 0.994 1.000 0.000
#> GSM49588 1 0.000 0.994 1.000 0.000
#> GSM49589 1 0.000 0.994 1.000 0.000
#> GSM49590 1 0.000 0.994 1.000 0.000
#> GSM49591 1 0.000 0.994 1.000 0.000
#> GSM49592 1 0.000 0.994 1.000 0.000
#> GSM49593 1 0.000 0.994 1.000 0.000
#> GSM49594 1 0.000 0.994 1.000 0.000
#> GSM49595 1 0.000 0.994 1.000 0.000
#> GSM49596 1 0.000 0.994 1.000 0.000
#> GSM49597 2 0.000 0.958 0.000 1.000
#> GSM49598 1 0.000 0.994 1.000 0.000
#> GSM49599 1 0.000 0.994 1.000 0.000
#> GSM49600 1 0.000 0.994 1.000 0.000
#> GSM49601 1 0.000 0.994 1.000 0.000
#> GSM49602 1 0.000 0.994 1.000 0.000
#> GSM49603 1 0.000 0.994 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM49613 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49604 2 0.0237 0.543 0.000 0.996 0.004
#> GSM49605 3 0.0000 1.000 0.000 0.000 1.000
#> GSM49606 2 0.6308 0.496 0.000 0.508 0.492
#> GSM49607 3 0.0000 1.000 0.000 0.000 1.000
#> GSM49608 3 0.0000 1.000 0.000 0.000 1.000
#> GSM49609 2 0.6302 0.520 0.000 0.520 0.480
#> GSM49610 3 0.0000 1.000 0.000 0.000 1.000
#> GSM49611 2 0.6302 0.520 0.000 0.520 0.480
#> GSM49612 2 0.6302 0.520 0.000 0.520 0.480
#> GSM49614 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49615 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49616 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49617 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49564 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49565 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49566 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49567 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49568 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49569 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49570 2 0.3619 0.531 0.000 0.864 0.136
#> GSM49571 1 0.4750 0.734 0.784 0.216 0.000
#> GSM49572 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49573 2 0.3619 0.531 0.000 0.864 0.136
#> GSM49574 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49575 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49576 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49577 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49578 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49579 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49580 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49581 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49582 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49583 3 0.0000 1.000 0.000 0.000 1.000
#> GSM49584 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49585 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49586 1 0.4750 0.734 0.784 0.216 0.000
#> GSM49587 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49588 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49589 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49590 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49591 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49592 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49593 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49594 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49595 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49596 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49597 3 0.0000 1.000 0.000 0.000 1.000
#> GSM49598 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49599 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49600 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49601 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49602 1 0.0000 0.989 1.000 0.000 0.000
#> GSM49603 1 0.0000 0.989 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM49613 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49604 4 0.4406 0.539 0.000 0.000 0.300 0.700
#> GSM49605 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM49606 3 0.0469 0.982 0.000 0.012 0.988 0.000
#> GSM49607 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM49608 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM49609 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM49610 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM49611 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM49612 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM49614 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49615 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49616 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49617 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49564 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49565 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49566 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49567 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49568 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49569 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49570 4 0.0592 0.828 0.000 0.000 0.016 0.984
#> GSM49571 1 0.4175 0.731 0.784 0.000 0.200 0.016
#> GSM49572 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49573 4 0.0592 0.828 0.000 0.000 0.016 0.984
#> GSM49574 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49575 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49576 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49577 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49578 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49579 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49580 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49581 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49582 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49583 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM49584 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49585 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49586 1 0.4175 0.731 0.784 0.000 0.200 0.016
#> GSM49587 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49588 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49589 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49590 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49591 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49592 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49593 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49594 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49595 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49596 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49597 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM49598 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49599 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49600 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49601 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49602 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM49603 1 0.0000 0.989 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM49613 3 0.4192 1.000 0.404 0.000 0.596 0.000 0.000
#> GSM49604 4 0.4121 0.709 0.000 0.000 0.112 0.788 0.100
#> GSM49605 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM49606 5 0.0404 0.984 0.000 0.012 0.000 0.000 0.988
#> GSM49607 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM49608 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM49609 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000
#> GSM49610 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM49611 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000
#> GSM49612 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000
#> GSM49614 3 0.4192 1.000 0.404 0.000 0.596 0.000 0.000
#> GSM49615 3 0.4192 1.000 0.404 0.000 0.596 0.000 0.000
#> GSM49616 3 0.4192 1.000 0.404 0.000 0.596 0.000 0.000
#> GSM49617 3 0.4192 1.000 0.404 0.000 0.596 0.000 0.000
#> GSM49564 1 0.4192 -0.548 0.596 0.000 0.404 0.000 0.000
#> GSM49565 1 0.2891 0.816 0.824 0.000 0.000 0.176 0.000
#> GSM49566 1 0.2773 0.822 0.836 0.000 0.000 0.164 0.000
#> GSM49567 1 0.2891 0.816 0.824 0.000 0.000 0.176 0.000
#> GSM49568 1 0.0162 0.832 0.996 0.000 0.000 0.004 0.000
#> GSM49569 1 0.2773 0.822 0.836 0.000 0.000 0.164 0.000
#> GSM49570 4 0.4192 0.869 0.000 0.000 0.404 0.596 0.000
#> GSM49571 1 0.4192 0.494 0.596 0.000 0.000 0.404 0.000
#> GSM49572 1 0.2891 0.816 0.824 0.000 0.000 0.176 0.000
#> GSM49573 4 0.4192 0.869 0.000 0.000 0.404 0.596 0.000
#> GSM49574 1 0.2773 0.822 0.836 0.000 0.000 0.164 0.000
#> GSM49575 1 0.3003 0.806 0.812 0.000 0.000 0.188 0.000
#> GSM49576 1 0.2329 0.829 0.876 0.000 0.000 0.124 0.000
#> GSM49577 1 0.2966 0.810 0.816 0.000 0.000 0.184 0.000
#> GSM49578 1 0.0000 0.831 1.000 0.000 0.000 0.000 0.000
#> GSM49579 1 0.2852 0.818 0.828 0.000 0.000 0.172 0.000
#> GSM49580 1 0.0000 0.831 1.000 0.000 0.000 0.000 0.000
#> GSM49581 1 0.0000 0.831 1.000 0.000 0.000 0.000 0.000
#> GSM49582 1 0.0000 0.831 1.000 0.000 0.000 0.000 0.000
#> GSM49583 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM49584 1 0.0000 0.831 1.000 0.000 0.000 0.000 0.000
#> GSM49585 1 0.0000 0.831 1.000 0.000 0.000 0.000 0.000
#> GSM49586 1 0.4192 0.494 0.596 0.000 0.000 0.404 0.000
#> GSM49587 1 0.0510 0.834 0.984 0.000 0.000 0.016 0.000
#> GSM49588 1 0.0000 0.831 1.000 0.000 0.000 0.000 0.000
#> GSM49589 1 0.2329 0.829 0.876 0.000 0.000 0.124 0.000
#> GSM49590 1 0.2773 0.822 0.836 0.000 0.000 0.164 0.000
#> GSM49591 1 0.0000 0.831 1.000 0.000 0.000 0.000 0.000
#> GSM49592 1 0.0000 0.831 1.000 0.000 0.000 0.000 0.000
#> GSM49593 1 0.0000 0.831 1.000 0.000 0.000 0.000 0.000
#> GSM49594 1 0.2891 0.816 0.824 0.000 0.000 0.176 0.000
#> GSM49595 1 0.2891 0.816 0.824 0.000 0.000 0.176 0.000
#> GSM49596 1 0.0794 0.834 0.972 0.000 0.000 0.028 0.000
#> GSM49597 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM49598 1 0.0000 0.831 1.000 0.000 0.000 0.000 0.000
#> GSM49599 1 0.2891 0.816 0.824 0.000 0.000 0.176 0.000
#> GSM49600 1 0.0000 0.831 1.000 0.000 0.000 0.000 0.000
#> GSM49601 1 0.0000 0.831 1.000 0.000 0.000 0.000 0.000
#> GSM49602 1 0.0290 0.833 0.992 0.000 0.000 0.008 0.000
#> GSM49603 1 0.0290 0.833 0.992 0.000 0.000 0.008 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM49613 3 0.2697 0.760 0.188 0.000 0.812 0.000 0.000 0.000
#> GSM49604 5 0.5157 0.000 0.000 0.000 0.024 0.284 0.624 0.068
#> GSM49605 2 0.0000 0.948 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM49606 6 0.0363 0.981 0.000 0.012 0.000 0.000 0.000 0.988
#> GSM49607 2 0.0000 0.948 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM49608 2 0.0000 0.948 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM49609 6 0.0000 0.994 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM49610 2 0.0000 0.948 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM49611 6 0.0000 0.994 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM49612 6 0.0000 0.994 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM49614 3 0.0632 0.625 0.024 0.000 0.976 0.000 0.000 0.000
#> GSM49615 3 0.2697 0.760 0.188 0.000 0.812 0.000 0.000 0.000
#> GSM49616 3 0.2664 0.760 0.184 0.000 0.816 0.000 0.000 0.000
#> GSM49617 3 0.0632 0.625 0.024 0.000 0.976 0.000 0.000 0.000
#> GSM49564 3 0.3817 0.408 0.432 0.000 0.568 0.000 0.000 0.000
#> GSM49565 1 0.2738 0.866 0.820 0.000 0.004 0.000 0.176 0.000
#> GSM49566 1 0.2595 0.872 0.836 0.000 0.004 0.000 0.160 0.000
#> GSM49567 1 0.2738 0.866 0.820 0.000 0.004 0.000 0.176 0.000
#> GSM49568 1 0.0603 0.879 0.980 0.000 0.016 0.000 0.004 0.000
#> GSM49569 1 0.2595 0.872 0.836 0.000 0.004 0.000 0.160 0.000
#> GSM49570 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM49571 1 0.3890 0.615 0.596 0.000 0.004 0.000 0.400 0.000
#> GSM49572 1 0.2738 0.866 0.820 0.000 0.004 0.000 0.176 0.000
#> GSM49573 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM49574 1 0.2595 0.872 0.836 0.000 0.004 0.000 0.160 0.000
#> GSM49575 1 0.2730 0.858 0.808 0.000 0.000 0.000 0.192 0.000
#> GSM49576 1 0.2191 0.879 0.876 0.000 0.004 0.000 0.120 0.000
#> GSM49577 1 0.2838 0.858 0.808 0.000 0.004 0.000 0.188 0.000
#> GSM49578 1 0.0363 0.879 0.988 0.000 0.012 0.000 0.000 0.000
#> GSM49579 1 0.2703 0.867 0.824 0.000 0.004 0.000 0.172 0.000
#> GSM49580 1 0.0363 0.879 0.988 0.000 0.012 0.000 0.000 0.000
#> GSM49581 1 0.0146 0.883 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM49582 1 0.0458 0.876 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM49583 2 0.1910 0.901 0.000 0.892 0.000 0.000 0.108 0.000
#> GSM49584 1 0.0458 0.876 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM49585 1 0.0146 0.883 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM49586 1 0.3890 0.615 0.596 0.000 0.004 0.000 0.400 0.000
#> GSM49587 1 0.0363 0.885 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM49588 1 0.0146 0.883 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM49589 1 0.2048 0.880 0.880 0.000 0.000 0.000 0.120 0.000
#> GSM49590 1 0.2595 0.872 0.836 0.000 0.004 0.000 0.160 0.000
#> GSM49591 1 0.0146 0.883 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM49592 1 0.0146 0.883 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM49593 1 0.0146 0.883 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM49594 1 0.2738 0.866 0.820 0.000 0.004 0.000 0.176 0.000
#> GSM49595 1 0.2738 0.866 0.820 0.000 0.004 0.000 0.176 0.000
#> GSM49596 1 0.0632 0.886 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM49597 2 0.2664 0.847 0.000 0.816 0.000 0.000 0.184 0.000
#> GSM49598 1 0.0146 0.883 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM49599 1 0.2738 0.866 0.820 0.000 0.004 0.000 0.176 0.000
#> GSM49600 1 0.0146 0.883 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM49601 1 0.0146 0.883 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM49602 1 0.0405 0.885 0.988 0.000 0.004 0.000 0.008 0.000
#> GSM49603 1 0.0405 0.885 0.988 0.000 0.004 0.000 0.008 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> ATC:hclust 54 5.97e-07 6.72e-04 2
#> ATC:hclust 53 1.26e-06 4.07e-04 3
#> ATC:hclust 54 1.73e-07 1.60e-05 4
#> ATC:hclust 51 1.07e-06 5.14e-14 5
#> ATC:hclust 52 1.72e-07 2.44e-14 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "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 21168 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.997 0.994 0.3705 0.628 0.628
#> 3 3 0.633 0.788 0.857 0.4126 0.874 0.800
#> 4 4 0.615 0.747 0.814 0.1741 0.830 0.662
#> 5 5 0.638 0.731 0.814 0.1362 0.932 0.801
#> 6 6 0.705 0.730 0.837 0.0783 0.886 0.644
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
#> GSM49613 1 0.118 0.986 0.984 0.016
#> GSM49604 2 0.118 1.000 0.016 0.984
#> GSM49605 2 0.118 1.000 0.016 0.984
#> GSM49606 2 0.118 1.000 0.016 0.984
#> GSM49607 2 0.118 1.000 0.016 0.984
#> GSM49608 2 0.118 1.000 0.016 0.984
#> GSM49609 2 0.118 1.000 0.016 0.984
#> GSM49610 2 0.118 1.000 0.016 0.984
#> GSM49611 2 0.118 1.000 0.016 0.984
#> GSM49612 2 0.118 1.000 0.016 0.984
#> GSM49614 1 0.118 0.986 0.984 0.016
#> GSM49615 1 0.118 0.986 0.984 0.016
#> GSM49616 1 0.118 0.986 0.984 0.016
#> GSM49617 1 0.118 0.986 0.984 0.016
#> GSM49564 1 0.118 0.986 0.984 0.016
#> GSM49565 1 0.000 0.998 1.000 0.000
#> GSM49566 1 0.000 0.998 1.000 0.000
#> GSM49567 1 0.000 0.998 1.000 0.000
#> GSM49568 1 0.000 0.998 1.000 0.000
#> GSM49569 1 0.000 0.998 1.000 0.000
#> GSM49570 2 0.118 1.000 0.016 0.984
#> GSM49571 1 0.000 0.998 1.000 0.000
#> GSM49572 1 0.000 0.998 1.000 0.000
#> GSM49573 2 0.118 1.000 0.016 0.984
#> GSM49574 1 0.000 0.998 1.000 0.000
#> GSM49575 1 0.000 0.998 1.000 0.000
#> GSM49576 1 0.000 0.998 1.000 0.000
#> GSM49577 1 0.000 0.998 1.000 0.000
#> GSM49578 1 0.000 0.998 1.000 0.000
#> GSM49579 1 0.000 0.998 1.000 0.000
#> GSM49580 1 0.000 0.998 1.000 0.000
#> GSM49581 1 0.000 0.998 1.000 0.000
#> GSM49582 1 0.000 0.998 1.000 0.000
#> GSM49583 2 0.118 1.000 0.016 0.984
#> GSM49584 1 0.000 0.998 1.000 0.000
#> GSM49585 1 0.000 0.998 1.000 0.000
#> GSM49586 1 0.000 0.998 1.000 0.000
#> GSM49587 1 0.000 0.998 1.000 0.000
#> GSM49588 1 0.000 0.998 1.000 0.000
#> GSM49589 1 0.000 0.998 1.000 0.000
#> GSM49590 1 0.000 0.998 1.000 0.000
#> GSM49591 1 0.000 0.998 1.000 0.000
#> GSM49592 1 0.000 0.998 1.000 0.000
#> GSM49593 1 0.000 0.998 1.000 0.000
#> GSM49594 1 0.000 0.998 1.000 0.000
#> GSM49595 1 0.000 0.998 1.000 0.000
#> GSM49596 1 0.000 0.998 1.000 0.000
#> GSM49597 2 0.118 1.000 0.016 0.984
#> GSM49598 1 0.000 0.998 1.000 0.000
#> GSM49599 1 0.000 0.998 1.000 0.000
#> GSM49600 1 0.000 0.998 1.000 0.000
#> GSM49601 1 0.000 0.998 1.000 0.000
#> GSM49602 1 0.000 0.998 1.000 0.000
#> GSM49603 1 0.000 0.998 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM49613 3 0.470 0.951 0.212 0.000 0.788
#> GSM49604 2 0.470 0.885 0.000 0.788 0.212
#> GSM49605 2 0.000 0.953 0.000 1.000 0.000
#> GSM49606 2 0.116 0.949 0.000 0.972 0.028
#> GSM49607 2 0.000 0.953 0.000 1.000 0.000
#> GSM49608 2 0.000 0.953 0.000 1.000 0.000
#> GSM49609 2 0.296 0.939 0.008 0.912 0.080
#> GSM49610 2 0.000 0.953 0.000 1.000 0.000
#> GSM49611 2 0.254 0.942 0.000 0.920 0.080
#> GSM49612 2 0.254 0.942 0.000 0.920 0.080
#> GSM49614 3 0.559 0.824 0.304 0.000 0.696
#> GSM49615 3 0.470 0.951 0.212 0.000 0.788
#> GSM49616 3 0.470 0.951 0.212 0.000 0.788
#> GSM49617 3 0.480 0.947 0.220 0.000 0.780
#> GSM49564 1 0.565 0.759 0.688 0.000 0.312
#> GSM49565 1 0.000 0.648 1.000 0.000 0.000
#> GSM49566 1 0.480 0.755 0.780 0.000 0.220
#> GSM49567 1 0.000 0.648 1.000 0.000 0.000
#> GSM49568 1 0.518 0.765 0.744 0.000 0.256
#> GSM49569 1 0.465 0.750 0.792 0.000 0.208
#> GSM49570 2 0.382 0.900 0.000 0.852 0.148
#> GSM49571 1 0.429 0.333 0.820 0.000 0.180
#> GSM49572 1 0.000 0.648 1.000 0.000 0.000
#> GSM49573 2 0.429 0.892 0.000 0.820 0.180
#> GSM49574 1 0.000 0.648 1.000 0.000 0.000
#> GSM49575 1 0.000 0.648 1.000 0.000 0.000
#> GSM49576 1 0.550 0.767 0.708 0.000 0.292
#> GSM49577 1 0.000 0.648 1.000 0.000 0.000
#> GSM49578 1 0.565 0.759 0.688 0.000 0.312
#> GSM49579 1 0.460 0.751 0.796 0.000 0.204
#> GSM49580 1 0.559 0.764 0.696 0.000 0.304
#> GSM49581 1 0.245 0.679 0.924 0.000 0.076
#> GSM49582 1 0.565 0.759 0.688 0.000 0.312
#> GSM49583 2 0.000 0.953 0.000 1.000 0.000
#> GSM49584 1 0.565 0.759 0.688 0.000 0.312
#> GSM49585 1 0.559 0.763 0.696 0.000 0.304
#> GSM49586 1 0.000 0.648 1.000 0.000 0.000
#> GSM49587 1 0.565 0.759 0.688 0.000 0.312
#> GSM49588 1 0.565 0.759 0.688 0.000 0.312
#> GSM49589 1 0.565 0.759 0.688 0.000 0.312
#> GSM49590 1 0.480 0.755 0.780 0.000 0.220
#> GSM49591 1 0.493 0.758 0.768 0.000 0.232
#> GSM49592 1 0.565 0.759 0.688 0.000 0.312
#> GSM49593 1 0.559 0.764 0.696 0.000 0.304
#> GSM49594 1 0.000 0.648 1.000 0.000 0.000
#> GSM49595 1 0.000 0.648 1.000 0.000 0.000
#> GSM49596 1 0.550 0.768 0.708 0.000 0.292
#> GSM49597 2 0.000 0.953 0.000 1.000 0.000
#> GSM49598 1 0.497 0.759 0.764 0.000 0.236
#> GSM49599 1 0.000 0.648 1.000 0.000 0.000
#> GSM49600 1 0.559 0.764 0.696 0.000 0.304
#> GSM49601 1 0.565 0.759 0.688 0.000 0.312
#> GSM49602 1 0.550 0.768 0.708 0.000 0.292
#> GSM49603 1 0.556 0.766 0.700 0.000 0.300
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM49613 3 0.4605 0.879 0.336 0.000 0.664 0.000
#> GSM49604 2 0.7745 0.541 0.000 0.396 0.232 0.372
#> GSM49605 2 0.0000 0.838 0.000 1.000 0.000 0.000
#> GSM49606 2 0.2329 0.824 0.000 0.916 0.072 0.012
#> GSM49607 2 0.0000 0.838 0.000 1.000 0.000 0.000
#> GSM49608 2 0.0000 0.838 0.000 1.000 0.000 0.000
#> GSM49609 2 0.5140 0.783 0.000 0.760 0.144 0.096
#> GSM49610 2 0.0000 0.838 0.000 1.000 0.000 0.000
#> GSM49611 2 0.4465 0.800 0.000 0.800 0.144 0.056
#> GSM49612 2 0.4614 0.798 0.000 0.792 0.144 0.064
#> GSM49614 3 0.5891 0.790 0.168 0.000 0.700 0.132
#> GSM49615 3 0.4605 0.879 0.336 0.000 0.664 0.000
#> GSM49616 3 0.4250 0.892 0.276 0.000 0.724 0.000
#> GSM49617 3 0.5279 0.876 0.232 0.000 0.716 0.052
#> GSM49564 1 0.0469 0.866 0.988 0.000 0.012 0.000
#> GSM49565 4 0.5000 0.679 0.496 0.000 0.000 0.504
#> GSM49566 1 0.2814 0.720 0.868 0.000 0.000 0.132
#> GSM49567 4 0.4888 0.845 0.412 0.000 0.000 0.588
#> GSM49568 1 0.1474 0.831 0.948 0.000 0.000 0.052
#> GSM49569 1 0.3123 0.670 0.844 0.000 0.000 0.156
#> GSM49570 2 0.7106 0.582 0.000 0.528 0.148 0.324
#> GSM49571 4 0.2759 0.209 0.052 0.000 0.044 0.904
#> GSM49572 1 0.5000 -0.715 0.500 0.000 0.000 0.500
#> GSM49573 2 0.7591 0.554 0.000 0.444 0.204 0.352
#> GSM49574 1 0.5000 -0.704 0.504 0.000 0.000 0.496
#> GSM49575 4 0.4843 0.848 0.396 0.000 0.000 0.604
#> GSM49576 1 0.1302 0.837 0.956 0.000 0.000 0.044
#> GSM49577 4 0.4843 0.848 0.396 0.000 0.000 0.604
#> GSM49578 1 0.0188 0.874 0.996 0.000 0.004 0.000
#> GSM49579 1 0.2973 0.696 0.856 0.000 0.000 0.144
#> GSM49580 1 0.0000 0.874 1.000 0.000 0.000 0.000
#> GSM49581 1 0.2921 0.666 0.860 0.000 0.000 0.140
#> GSM49582 1 0.0188 0.874 0.996 0.000 0.004 0.000
#> GSM49583 2 0.0000 0.838 0.000 1.000 0.000 0.000
#> GSM49584 1 0.0188 0.874 0.996 0.000 0.004 0.000
#> GSM49585 1 0.0188 0.874 0.996 0.000 0.004 0.000
#> GSM49586 4 0.4948 0.797 0.440 0.000 0.000 0.560
#> GSM49587 1 0.0188 0.874 0.996 0.000 0.004 0.000
#> GSM49588 1 0.0188 0.874 0.996 0.000 0.004 0.000
#> GSM49589 1 0.0188 0.874 0.996 0.000 0.004 0.000
#> GSM49590 1 0.2814 0.720 0.868 0.000 0.000 0.132
#> GSM49591 1 0.0921 0.851 0.972 0.000 0.000 0.028
#> GSM49592 1 0.0188 0.874 0.996 0.000 0.004 0.000
#> GSM49593 1 0.0000 0.874 1.000 0.000 0.000 0.000
#> GSM49594 4 0.4843 0.848 0.396 0.000 0.000 0.604
#> GSM49595 4 0.4933 0.822 0.432 0.000 0.000 0.568
#> GSM49596 1 0.0000 0.874 1.000 0.000 0.000 0.000
#> GSM49597 2 0.0000 0.838 0.000 1.000 0.000 0.000
#> GSM49598 1 0.0921 0.851 0.972 0.000 0.000 0.028
#> GSM49599 4 0.4898 0.843 0.416 0.000 0.000 0.584
#> GSM49600 1 0.0000 0.874 1.000 0.000 0.000 0.000
#> GSM49601 1 0.0188 0.874 0.996 0.000 0.004 0.000
#> GSM49602 1 0.0000 0.874 1.000 0.000 0.000 0.000
#> GSM49603 1 0.0000 0.874 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM49613 3 0.3355 0.847 0.000 0.000 0.804 0.012 0.184
#> GSM49604 4 0.3564 0.784 0.028 0.100 0.028 0.844 0.000
#> GSM49605 2 0.0000 0.791 0.000 1.000 0.000 0.000 0.000
#> GSM49606 2 0.4088 0.710 0.060 0.824 0.052 0.064 0.000
#> GSM49607 2 0.0162 0.790 0.004 0.996 0.000 0.000 0.000
#> GSM49608 2 0.0000 0.791 0.000 1.000 0.000 0.000 0.000
#> GSM49609 2 0.6645 0.475 0.072 0.560 0.076 0.292 0.000
#> GSM49610 2 0.0000 0.791 0.000 1.000 0.000 0.000 0.000
#> GSM49611 2 0.6593 0.481 0.068 0.564 0.076 0.292 0.000
#> GSM49612 2 0.6593 0.481 0.068 0.564 0.076 0.292 0.000
#> GSM49614 3 0.3905 0.812 0.080 0.000 0.832 0.036 0.052
#> GSM49615 3 0.3355 0.847 0.000 0.000 0.804 0.012 0.184
#> GSM49616 3 0.2074 0.870 0.000 0.000 0.896 0.000 0.104
#> GSM49617 3 0.3073 0.857 0.052 0.000 0.868 0.004 0.076
#> GSM49564 5 0.2430 0.836 0.028 0.000 0.020 0.040 0.912
#> GSM49565 1 0.3990 0.744 0.688 0.000 0.000 0.004 0.308
#> GSM49566 5 0.5298 0.206 0.396 0.000 0.004 0.044 0.556
#> GSM49567 1 0.3048 0.819 0.820 0.000 0.000 0.004 0.176
#> GSM49568 5 0.1251 0.841 0.036 0.000 0.000 0.008 0.956
#> GSM49569 5 0.5383 0.161 0.408 0.000 0.004 0.048 0.540
#> GSM49570 4 0.3774 0.724 0.000 0.296 0.000 0.704 0.000
#> GSM49571 1 0.4937 0.102 0.604 0.000 0.028 0.364 0.004
#> GSM49572 1 0.4290 0.744 0.680 0.000 0.000 0.016 0.304
#> GSM49573 4 0.2773 0.833 0.000 0.164 0.000 0.836 0.000
#> GSM49574 1 0.4066 0.726 0.672 0.000 0.000 0.004 0.324
#> GSM49575 1 0.3398 0.782 0.828 0.000 0.024 0.004 0.144
#> GSM49576 5 0.4713 0.517 0.280 0.000 0.000 0.044 0.676
#> GSM49577 1 0.2773 0.813 0.836 0.000 0.000 0.000 0.164
#> GSM49578 5 0.0404 0.855 0.000 0.000 0.000 0.012 0.988
#> GSM49579 5 0.5118 0.174 0.412 0.000 0.000 0.040 0.548
#> GSM49580 5 0.0290 0.856 0.000 0.000 0.000 0.008 0.992
#> GSM49581 5 0.1444 0.832 0.040 0.000 0.000 0.012 0.948
#> GSM49582 5 0.0404 0.855 0.000 0.000 0.000 0.012 0.988
#> GSM49583 2 0.0290 0.789 0.008 0.992 0.000 0.000 0.000
#> GSM49584 5 0.0510 0.855 0.000 0.000 0.000 0.016 0.984
#> GSM49585 5 0.0566 0.856 0.004 0.000 0.000 0.012 0.984
#> GSM49586 1 0.4970 0.532 0.624 0.000 0.028 0.008 0.340
#> GSM49587 5 0.0290 0.855 0.000 0.000 0.000 0.008 0.992
#> GSM49588 5 0.0566 0.856 0.004 0.000 0.000 0.012 0.984
#> GSM49589 5 0.1915 0.843 0.032 0.000 0.000 0.040 0.928
#> GSM49590 5 0.5261 0.266 0.380 0.000 0.004 0.044 0.572
#> GSM49591 5 0.0807 0.855 0.012 0.000 0.000 0.012 0.976
#> GSM49592 5 0.0290 0.855 0.000 0.000 0.000 0.008 0.992
#> GSM49593 5 0.1668 0.847 0.032 0.000 0.000 0.028 0.940
#> GSM49594 1 0.2629 0.804 0.860 0.000 0.000 0.004 0.136
#> GSM49595 1 0.3456 0.803 0.800 0.000 0.000 0.016 0.184
#> GSM49596 5 0.0898 0.858 0.008 0.000 0.000 0.020 0.972
#> GSM49597 2 0.0290 0.789 0.008 0.992 0.000 0.000 0.000
#> GSM49598 5 0.1830 0.847 0.040 0.000 0.000 0.028 0.932
#> GSM49599 1 0.3086 0.820 0.816 0.000 0.000 0.004 0.180
#> GSM49600 5 0.0771 0.857 0.004 0.000 0.000 0.020 0.976
#> GSM49601 5 0.1668 0.848 0.032 0.000 0.000 0.028 0.940
#> GSM49602 5 0.1997 0.843 0.036 0.000 0.000 0.040 0.924
#> GSM49603 5 0.1997 0.843 0.036 0.000 0.000 0.040 0.924
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM49613 3 0.2869 0.798 0.148 0.000 0.832 0.000 0.000 0.020
#> GSM49604 4 0.3254 0.719 0.000 0.008 0.020 0.828 0.008 0.136
#> GSM49605 2 0.0000 0.739 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM49606 2 0.4332 0.599 0.000 0.672 0.000 0.052 0.000 0.276
#> GSM49607 2 0.0146 0.738 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM49608 2 0.0000 0.739 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM49609 2 0.6300 0.400 0.000 0.416 0.012 0.248 0.000 0.324
#> GSM49610 2 0.0000 0.739 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM49611 2 0.6300 0.400 0.000 0.416 0.012 0.248 0.000 0.324
#> GSM49612 2 0.6300 0.400 0.000 0.416 0.012 0.248 0.000 0.324
#> GSM49614 3 0.3361 0.777 0.012 0.000 0.832 0.004 0.040 0.112
#> GSM49615 3 0.2869 0.798 0.148 0.000 0.832 0.000 0.000 0.020
#> GSM49616 3 0.0865 0.834 0.036 0.000 0.964 0.000 0.000 0.000
#> GSM49617 3 0.1585 0.817 0.012 0.000 0.940 0.000 0.036 0.012
#> GSM49564 1 0.2575 0.906 0.884 0.000 0.020 0.000 0.020 0.076
#> GSM49565 5 0.2146 0.635 0.116 0.000 0.000 0.000 0.880 0.004
#> GSM49566 5 0.5063 0.552 0.284 0.000 0.000 0.000 0.604 0.112
#> GSM49567 5 0.1364 0.606 0.048 0.000 0.000 0.004 0.944 0.004
#> GSM49568 1 0.2058 0.895 0.908 0.000 0.000 0.000 0.056 0.036
#> GSM49569 5 0.5066 0.555 0.276 0.000 0.000 0.000 0.608 0.116
#> GSM49570 4 0.2491 0.754 0.000 0.164 0.000 0.836 0.000 0.000
#> GSM49571 6 0.6221 0.469 0.000 0.000 0.012 0.212 0.360 0.416
#> GSM49572 5 0.2480 0.640 0.104 0.000 0.000 0.000 0.872 0.024
#> GSM49573 4 0.1267 0.812 0.000 0.060 0.000 0.940 0.000 0.000
#> GSM49574 5 0.2234 0.633 0.124 0.000 0.000 0.000 0.872 0.004
#> GSM49575 5 0.4556 -0.263 0.036 0.000 0.004 0.004 0.636 0.320
#> GSM49576 5 0.5325 0.476 0.328 0.000 0.000 0.000 0.548 0.124
#> GSM49577 5 0.1511 0.600 0.044 0.000 0.000 0.004 0.940 0.012
#> GSM49578 1 0.0632 0.938 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM49579 5 0.4969 0.557 0.280 0.000 0.000 0.000 0.616 0.104
#> GSM49580 1 0.1225 0.931 0.952 0.000 0.000 0.000 0.012 0.036
#> GSM49581 1 0.0717 0.940 0.976 0.000 0.000 0.000 0.016 0.008
#> GSM49582 1 0.0547 0.938 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM49583 2 0.0520 0.736 0.000 0.984 0.008 0.000 0.008 0.000
#> GSM49584 1 0.1265 0.931 0.948 0.000 0.000 0.000 0.008 0.044
#> GSM49585 1 0.1010 0.939 0.960 0.000 0.000 0.000 0.004 0.036
#> GSM49586 6 0.6066 0.548 0.196 0.000 0.008 0.000 0.356 0.440
#> GSM49587 1 0.0603 0.939 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM49588 1 0.1010 0.939 0.960 0.000 0.000 0.000 0.004 0.036
#> GSM49589 1 0.2826 0.873 0.844 0.000 0.000 0.000 0.028 0.128
#> GSM49590 5 0.5117 0.544 0.288 0.000 0.000 0.000 0.596 0.116
#> GSM49591 1 0.0972 0.939 0.964 0.000 0.000 0.000 0.008 0.028
#> GSM49592 1 0.0777 0.939 0.972 0.000 0.000 0.000 0.004 0.024
#> GSM49593 1 0.1461 0.934 0.940 0.000 0.000 0.000 0.016 0.044
#> GSM49594 5 0.1492 0.609 0.036 0.000 0.000 0.000 0.940 0.024
#> GSM49595 5 0.1644 0.615 0.040 0.000 0.000 0.000 0.932 0.028
#> GSM49596 1 0.1003 0.942 0.964 0.000 0.000 0.000 0.020 0.016
#> GSM49597 2 0.0622 0.735 0.000 0.980 0.012 0.000 0.008 0.000
#> GSM49598 1 0.1320 0.936 0.948 0.000 0.000 0.000 0.016 0.036
#> GSM49599 5 0.1644 0.605 0.052 0.000 0.000 0.004 0.932 0.012
#> GSM49600 1 0.1225 0.931 0.952 0.000 0.000 0.000 0.012 0.036
#> GSM49601 1 0.1657 0.936 0.928 0.000 0.000 0.000 0.016 0.056
#> GSM49602 1 0.2432 0.898 0.876 0.000 0.000 0.000 0.024 0.100
#> GSM49603 1 0.2301 0.903 0.884 0.000 0.000 0.000 0.020 0.096
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) cell.type(p) k
#> ATC:kmeans 54 5.97e-07 6.72e-04 2
#> ATC:kmeans 53 3.58e-07 1.61e-13 3
#> ATC:kmeans 51 3.06e-06 9.46e-12 4
#> ATC:kmeans 46 9.79e-05 2.02e-08 5
#> ATC:kmeans 48 1.55e-04 5.11e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "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 21168 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.974 0.991 0.433 0.560 0.560
#> 3 3 0.658 0.808 0.836 0.381 0.781 0.615
#> 4 4 0.624 0.762 0.863 0.139 0.924 0.791
#> 5 5 0.613 0.630 0.821 0.077 0.896 0.700
#> 6 6 0.631 0.586 0.764 0.055 0.977 0.922
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
#> GSM49613 1 0.000 1.0000 1.00 0.00
#> GSM49604 2 0.000 0.9697 0.00 1.00
#> GSM49605 2 0.000 0.9697 0.00 1.00
#> GSM49606 2 0.000 0.9697 0.00 1.00
#> GSM49607 2 0.000 0.9697 0.00 1.00
#> GSM49608 2 0.000 0.9697 0.00 1.00
#> GSM49609 2 0.000 0.9697 0.00 1.00
#> GSM49610 2 0.000 0.9697 0.00 1.00
#> GSM49611 2 0.000 0.9697 0.00 1.00
#> GSM49612 2 0.000 0.9697 0.00 1.00
#> GSM49614 1 0.000 1.0000 1.00 0.00
#> GSM49615 1 0.000 1.0000 1.00 0.00
#> GSM49616 1 0.000 1.0000 1.00 0.00
#> GSM49617 1 0.000 1.0000 1.00 0.00
#> GSM49564 1 0.000 1.0000 1.00 0.00
#> GSM49565 1 0.000 1.0000 1.00 0.00
#> GSM49566 1 0.000 1.0000 1.00 0.00
#> GSM49567 1 0.000 1.0000 1.00 0.00
#> GSM49568 1 0.000 1.0000 1.00 0.00
#> GSM49569 1 0.000 1.0000 1.00 0.00
#> GSM49570 2 0.000 0.9697 0.00 1.00
#> GSM49571 2 0.000 0.9697 0.00 1.00
#> GSM49572 1 0.000 1.0000 1.00 0.00
#> GSM49573 2 0.000 0.9697 0.00 1.00
#> GSM49574 1 0.000 1.0000 1.00 0.00
#> GSM49575 2 0.000 0.9697 0.00 1.00
#> GSM49576 1 0.000 1.0000 1.00 0.00
#> GSM49577 2 0.000 0.9697 0.00 1.00
#> GSM49578 1 0.000 1.0000 1.00 0.00
#> GSM49579 1 0.000 1.0000 1.00 0.00
#> GSM49580 1 0.000 1.0000 1.00 0.00
#> GSM49581 1 0.000 1.0000 1.00 0.00
#> GSM49582 1 0.000 1.0000 1.00 0.00
#> GSM49583 2 0.000 0.9697 0.00 1.00
#> GSM49584 1 0.000 1.0000 1.00 0.00
#> GSM49585 1 0.000 1.0000 1.00 0.00
#> GSM49586 1 0.000 1.0000 1.00 0.00
#> GSM49587 1 0.000 1.0000 1.00 0.00
#> GSM49588 1 0.000 1.0000 1.00 0.00
#> GSM49589 1 0.000 1.0000 1.00 0.00
#> GSM49590 1 0.000 1.0000 1.00 0.00
#> GSM49591 1 0.000 1.0000 1.00 0.00
#> GSM49592 1 0.000 1.0000 1.00 0.00
#> GSM49593 1 0.000 1.0000 1.00 0.00
#> GSM49594 2 0.999 0.0769 0.48 0.52
#> GSM49595 1 0.000 1.0000 1.00 0.00
#> GSM49596 1 0.000 1.0000 1.00 0.00
#> GSM49597 2 0.000 0.9697 0.00 1.00
#> GSM49598 1 0.000 1.0000 1.00 0.00
#> GSM49599 1 0.000 1.0000 1.00 0.00
#> GSM49600 1 0.000 1.0000 1.00 0.00
#> GSM49601 1 0.000 1.0000 1.00 0.00
#> GSM49602 1 0.000 1.0000 1.00 0.00
#> GSM49603 1 0.000 1.0000 1.00 0.00
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM49613 3 0.6280 0.8291 0.460 0.000 0.540
#> GSM49604 2 0.0237 0.9400 0.000 0.996 0.004
#> GSM49605 2 0.0000 0.9412 0.000 1.000 0.000
#> GSM49606 2 0.0000 0.9412 0.000 1.000 0.000
#> GSM49607 2 0.0000 0.9412 0.000 1.000 0.000
#> GSM49608 2 0.0000 0.9412 0.000 1.000 0.000
#> GSM49609 2 0.0000 0.9412 0.000 1.000 0.000
#> GSM49610 2 0.0000 0.9412 0.000 1.000 0.000
#> GSM49611 2 0.0000 0.9412 0.000 1.000 0.000
#> GSM49612 2 0.0000 0.9412 0.000 1.000 0.000
#> GSM49614 3 0.6483 0.8251 0.392 0.008 0.600
#> GSM49615 3 0.6280 0.8291 0.460 0.000 0.540
#> GSM49616 3 0.6225 0.8361 0.432 0.000 0.568
#> GSM49617 3 0.6126 0.8315 0.400 0.000 0.600
#> GSM49564 3 0.6309 0.7844 0.496 0.000 0.504
#> GSM49565 1 0.3340 0.7640 0.880 0.000 0.120
#> GSM49566 3 0.6307 0.7183 0.488 0.000 0.512
#> GSM49567 1 0.5905 0.4575 0.648 0.000 0.352
#> GSM49568 1 0.1031 0.8530 0.976 0.000 0.024
#> GSM49569 3 0.6111 0.8289 0.396 0.000 0.604
#> GSM49570 2 0.0237 0.9400 0.000 0.996 0.004
#> GSM49571 2 0.5363 0.7653 0.000 0.724 0.276
#> GSM49572 1 0.4555 0.6842 0.800 0.000 0.200
#> GSM49573 2 0.0237 0.9400 0.000 0.996 0.004
#> GSM49574 1 0.2261 0.8195 0.932 0.000 0.068
#> GSM49575 2 0.8013 0.6042 0.072 0.564 0.364
#> GSM49576 3 0.6280 0.8199 0.460 0.000 0.540
#> GSM49577 2 0.6587 0.6793 0.016 0.632 0.352
#> GSM49578 1 0.0000 0.8661 1.000 0.000 0.000
#> GSM49579 1 0.4178 0.6519 0.828 0.000 0.172
#> GSM49580 1 0.0592 0.8604 0.988 0.000 0.012
#> GSM49581 1 0.0892 0.8595 0.980 0.000 0.020
#> GSM49582 1 0.0000 0.8661 1.000 0.000 0.000
#> GSM49583 2 0.0000 0.9412 0.000 1.000 0.000
#> GSM49584 1 0.2537 0.7588 0.920 0.000 0.080
#> GSM49585 1 0.0000 0.8661 1.000 0.000 0.000
#> GSM49586 1 0.5465 0.4977 0.712 0.000 0.288
#> GSM49587 1 0.0424 0.8637 0.992 0.000 0.008
#> GSM49588 1 0.0000 0.8661 1.000 0.000 0.000
#> GSM49589 3 0.6295 0.8186 0.472 0.000 0.528
#> GSM49590 3 0.6154 0.8345 0.408 0.000 0.592
#> GSM49591 1 0.0237 0.8661 0.996 0.000 0.004
#> GSM49592 1 0.0000 0.8661 1.000 0.000 0.000
#> GSM49593 1 0.0424 0.8638 0.992 0.000 0.008
#> GSM49594 3 0.8772 -0.0908 0.364 0.120 0.516
#> GSM49595 1 0.5882 0.4640 0.652 0.000 0.348
#> GSM49596 1 0.0424 0.8655 0.992 0.000 0.008
#> GSM49597 2 0.0000 0.9412 0.000 1.000 0.000
#> GSM49598 1 0.0892 0.8626 0.980 0.000 0.020
#> GSM49599 1 0.4121 0.7112 0.832 0.000 0.168
#> GSM49600 1 0.0592 0.8615 0.988 0.000 0.012
#> GSM49601 1 0.0592 0.8617 0.988 0.000 0.012
#> GSM49602 1 0.0892 0.8559 0.980 0.000 0.020
#> GSM49603 1 0.0892 0.8559 0.980 0.000 0.020
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM49613 3 0.3837 0.747 0.224 0.000 0.776 0.000
#> GSM49604 2 0.2589 0.876 0.000 0.884 0.000 0.116
#> GSM49605 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM49606 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM49607 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM49608 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM49609 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM49610 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM49611 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM49612 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM49614 3 0.1557 0.637 0.056 0.000 0.944 0.000
#> GSM49615 3 0.3837 0.747 0.224 0.000 0.776 0.000
#> GSM49616 3 0.2281 0.676 0.096 0.000 0.904 0.000
#> GSM49617 3 0.1637 0.643 0.060 0.000 0.940 0.000
#> GSM49564 3 0.4898 0.610 0.416 0.000 0.584 0.000
#> GSM49565 1 0.4323 0.716 0.788 0.000 0.028 0.184
#> GSM49566 3 0.5784 0.540 0.412 0.000 0.556 0.032
#> GSM49567 1 0.6458 0.150 0.520 0.000 0.072 0.408
#> GSM49568 1 0.1902 0.848 0.932 0.000 0.064 0.004
#> GSM49569 3 0.4245 0.710 0.196 0.000 0.784 0.020
#> GSM49570 2 0.2530 0.880 0.000 0.888 0.000 0.112
#> GSM49571 4 0.4382 0.407 0.000 0.296 0.000 0.704
#> GSM49572 1 0.5977 0.576 0.680 0.000 0.104 0.216
#> GSM49573 2 0.2647 0.872 0.000 0.880 0.000 0.120
#> GSM49574 1 0.2909 0.820 0.888 0.000 0.020 0.092
#> GSM49575 4 0.3037 0.615 0.020 0.100 0.000 0.880
#> GSM49576 3 0.5821 0.535 0.432 0.000 0.536 0.032
#> GSM49577 4 0.6554 0.404 0.008 0.336 0.072 0.584
#> GSM49578 1 0.0000 0.875 1.000 0.000 0.000 0.000
#> GSM49579 1 0.5705 0.596 0.712 0.000 0.180 0.108
#> GSM49580 1 0.1118 0.868 0.964 0.000 0.036 0.000
#> GSM49581 1 0.1022 0.867 0.968 0.000 0.000 0.032
#> GSM49582 1 0.0000 0.875 1.000 0.000 0.000 0.000
#> GSM49583 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM49584 1 0.2469 0.796 0.892 0.000 0.108 0.000
#> GSM49585 1 0.0188 0.875 0.996 0.000 0.000 0.004
#> GSM49586 4 0.4040 0.487 0.248 0.000 0.000 0.752
#> GSM49587 1 0.0707 0.873 0.980 0.000 0.020 0.000
#> GSM49588 1 0.0188 0.875 0.996 0.000 0.000 0.004
#> GSM49589 3 0.4889 0.697 0.360 0.000 0.636 0.004
#> GSM49590 3 0.5578 0.698 0.312 0.000 0.648 0.040
#> GSM49591 1 0.0336 0.876 0.992 0.000 0.000 0.008
#> GSM49592 1 0.0000 0.875 1.000 0.000 0.000 0.000
#> GSM49593 1 0.1388 0.868 0.960 0.000 0.012 0.028
#> GSM49594 4 0.5655 0.563 0.056 0.052 0.128 0.764
#> GSM49595 4 0.7156 0.111 0.388 0.000 0.136 0.476
#> GSM49596 1 0.0657 0.877 0.984 0.000 0.004 0.012
#> GSM49597 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM49598 1 0.1938 0.859 0.936 0.000 0.012 0.052
#> GSM49599 1 0.4853 0.655 0.744 0.000 0.036 0.220
#> GSM49600 1 0.1389 0.862 0.952 0.000 0.048 0.000
#> GSM49601 1 0.1256 0.870 0.964 0.000 0.008 0.028
#> GSM49602 1 0.2399 0.849 0.920 0.000 0.032 0.048
#> GSM49603 1 0.2124 0.855 0.932 0.000 0.028 0.040
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM49613 3 0.3480 0.6518 0.248 0.000 0.752 0.000 0.000
#> GSM49604 2 0.3636 0.6659 0.000 0.728 0.000 0.272 0.000
#> GSM49605 2 0.0000 0.9290 0.000 1.000 0.000 0.000 0.000
#> GSM49606 2 0.0000 0.9290 0.000 1.000 0.000 0.000 0.000
#> GSM49607 2 0.0000 0.9290 0.000 1.000 0.000 0.000 0.000
#> GSM49608 2 0.0000 0.9290 0.000 1.000 0.000 0.000 0.000
#> GSM49609 2 0.0000 0.9290 0.000 1.000 0.000 0.000 0.000
#> GSM49610 2 0.0000 0.9290 0.000 1.000 0.000 0.000 0.000
#> GSM49611 2 0.0000 0.9290 0.000 1.000 0.000 0.000 0.000
#> GSM49612 2 0.0000 0.9290 0.000 1.000 0.000 0.000 0.000
#> GSM49614 3 0.0162 0.5913 0.004 0.000 0.996 0.000 0.000
#> GSM49615 3 0.3508 0.6495 0.252 0.000 0.748 0.000 0.000
#> GSM49616 3 0.1341 0.6318 0.056 0.000 0.944 0.000 0.000
#> GSM49617 3 0.0609 0.6082 0.020 0.000 0.980 0.000 0.000
#> GSM49564 1 0.5014 -0.0569 0.536 0.000 0.432 0.000 0.032
#> GSM49565 1 0.4557 0.0840 0.552 0.000 0.004 0.004 0.440
#> GSM49566 1 0.7031 -0.2079 0.372 0.000 0.328 0.008 0.292
#> GSM49567 5 0.5545 0.5001 0.212 0.000 0.016 0.100 0.672
#> GSM49568 1 0.2899 0.7405 0.872 0.000 0.028 0.004 0.096
#> GSM49569 3 0.5934 0.5108 0.156 0.000 0.648 0.020 0.176
#> GSM49570 2 0.3177 0.7461 0.000 0.792 0.000 0.208 0.000
#> GSM49571 4 0.2074 0.7911 0.000 0.104 0.000 0.896 0.000
#> GSM49572 5 0.5078 0.4112 0.336 0.000 0.020 0.020 0.624
#> GSM49573 2 0.3707 0.6467 0.000 0.716 0.000 0.284 0.000
#> GSM49574 1 0.4348 0.6262 0.768 0.000 0.020 0.032 0.180
#> GSM49575 4 0.1862 0.8153 0.004 0.016 0.000 0.932 0.048
#> GSM49576 1 0.7015 -0.1511 0.428 0.000 0.336 0.016 0.220
#> GSM49577 5 0.5799 0.2949 0.004 0.160 0.008 0.172 0.656
#> GSM49578 1 0.0510 0.7698 0.984 0.000 0.000 0.000 0.016
#> GSM49579 1 0.5723 0.1502 0.532 0.000 0.076 0.004 0.388
#> GSM49580 1 0.2206 0.7593 0.912 0.000 0.016 0.004 0.068
#> GSM49581 1 0.2922 0.7467 0.872 0.000 0.000 0.072 0.056
#> GSM49582 1 0.0703 0.7690 0.976 0.000 0.000 0.000 0.024
#> GSM49583 2 0.0000 0.9290 0.000 1.000 0.000 0.000 0.000
#> GSM49584 1 0.2954 0.7381 0.876 0.000 0.056 0.004 0.064
#> GSM49585 1 0.0932 0.7727 0.972 0.000 0.004 0.004 0.020
#> GSM49586 4 0.2388 0.7794 0.072 0.000 0.000 0.900 0.028
#> GSM49587 1 0.0865 0.7719 0.972 0.000 0.004 0.000 0.024
#> GSM49588 1 0.0671 0.7725 0.980 0.000 0.004 0.000 0.016
#> GSM49589 3 0.5431 0.2805 0.448 0.000 0.500 0.004 0.048
#> GSM49590 3 0.6670 0.3707 0.316 0.000 0.464 0.004 0.216
#> GSM49591 1 0.0898 0.7731 0.972 0.000 0.000 0.008 0.020
#> GSM49592 1 0.0566 0.7710 0.984 0.000 0.004 0.000 0.012
#> GSM49593 1 0.2517 0.7502 0.884 0.000 0.004 0.008 0.104
#> GSM49594 5 0.6246 0.3701 0.036 0.032 0.056 0.224 0.652
#> GSM49595 5 0.6380 0.4403 0.160 0.000 0.052 0.156 0.632
#> GSM49596 1 0.1608 0.7717 0.928 0.000 0.000 0.000 0.072
#> GSM49597 2 0.0000 0.9290 0.000 1.000 0.000 0.000 0.000
#> GSM49598 1 0.3178 0.7428 0.860 0.000 0.004 0.048 0.088
#> GSM49599 1 0.7278 -0.0874 0.444 0.000 0.052 0.156 0.348
#> GSM49600 1 0.3037 0.7543 0.864 0.000 0.032 0.004 0.100
#> GSM49601 1 0.2284 0.7566 0.896 0.000 0.004 0.004 0.096
#> GSM49602 1 0.3870 0.7143 0.816 0.000 0.024 0.028 0.132
#> GSM49603 1 0.3458 0.7258 0.840 0.000 0.016 0.024 0.120
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM49613 3 0.3680 0.5937 0.232 0.000 0.744 0.000 0.004 0.020
#> GSM49604 2 0.3819 0.4974 0.000 0.624 0.000 0.372 0.000 0.004
#> GSM49605 2 0.0000 0.9034 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM49606 2 0.0000 0.9034 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM49607 2 0.0000 0.9034 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM49608 2 0.0000 0.9034 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM49609 2 0.0146 0.9022 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM49610 2 0.0000 0.9034 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM49611 2 0.0146 0.9022 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM49612 2 0.0146 0.9022 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM49614 3 0.0837 0.5380 0.004 0.000 0.972 0.000 0.020 0.004
#> GSM49615 3 0.3679 0.5835 0.260 0.000 0.724 0.000 0.004 0.012
#> GSM49616 3 0.0790 0.5704 0.032 0.000 0.968 0.000 0.000 0.000
#> GSM49617 3 0.0622 0.5505 0.008 0.000 0.980 0.000 0.012 0.000
#> GSM49564 1 0.5808 0.2102 0.540 0.000 0.344 0.008 0.028 0.080
#> GSM49565 1 0.6191 -0.2147 0.448 0.000 0.004 0.004 0.300 0.244
#> GSM49566 1 0.7483 -0.1070 0.320 0.000 0.244 0.004 0.112 0.320
#> GSM49567 6 0.5862 0.3952 0.128 0.000 0.012 0.048 0.172 0.640
#> GSM49568 1 0.4191 0.6461 0.760 0.000 0.028 0.000 0.048 0.164
#> GSM49569 3 0.7461 0.2332 0.140 0.000 0.392 0.004 0.196 0.268
#> GSM49570 2 0.3468 0.6305 0.000 0.712 0.000 0.284 0.000 0.004
#> GSM49571 4 0.0777 0.8837 0.000 0.024 0.000 0.972 0.004 0.000
#> GSM49572 6 0.5668 0.4289 0.240 0.000 0.024 0.004 0.124 0.608
#> GSM49573 2 0.3881 0.4488 0.000 0.600 0.000 0.396 0.000 0.004
#> GSM49574 1 0.6444 0.1698 0.528 0.000 0.016 0.024 0.208 0.224
#> GSM49575 4 0.2677 0.8755 0.000 0.016 0.000 0.876 0.024 0.084
#> GSM49576 1 0.7327 -0.0284 0.412 0.000 0.284 0.004 0.164 0.136
#> GSM49577 6 0.6256 -0.0766 0.004 0.080 0.004 0.052 0.384 0.476
#> GSM49578 1 0.1230 0.7012 0.956 0.000 0.008 0.000 0.008 0.028
#> GSM49579 1 0.6911 -0.0822 0.412 0.000 0.076 0.000 0.184 0.328
#> GSM49580 1 0.3424 0.6824 0.816 0.000 0.016 0.000 0.032 0.136
#> GSM49581 1 0.4208 0.6578 0.768 0.000 0.000 0.064 0.028 0.140
#> GSM49582 1 0.1471 0.6987 0.932 0.000 0.000 0.000 0.004 0.064
#> GSM49583 2 0.0000 0.9034 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM49584 1 0.3539 0.6726 0.808 0.000 0.044 0.000 0.012 0.136
#> GSM49585 1 0.2520 0.6947 0.896 0.000 0.012 0.012 0.020 0.060
#> GSM49586 4 0.1974 0.8724 0.012 0.000 0.000 0.920 0.020 0.048
#> GSM49587 1 0.2414 0.7003 0.896 0.000 0.012 0.000 0.036 0.056
#> GSM49588 1 0.1628 0.7020 0.940 0.000 0.012 0.004 0.008 0.036
#> GSM49589 3 0.5843 0.2684 0.388 0.000 0.504 0.008 0.036 0.064
#> GSM49590 3 0.7688 0.2398 0.272 0.000 0.360 0.008 0.172 0.188
#> GSM49591 1 0.2514 0.6978 0.896 0.000 0.004 0.016 0.032 0.052
#> GSM49592 1 0.1565 0.6994 0.944 0.000 0.008 0.008 0.008 0.032
#> GSM49593 1 0.3883 0.6927 0.792 0.000 0.004 0.008 0.076 0.120
#> GSM49594 5 0.2821 0.8654 0.008 0.000 0.020 0.064 0.880 0.028
#> GSM49595 5 0.2895 0.8640 0.044 0.000 0.020 0.044 0.880 0.012
#> GSM49596 1 0.3565 0.6976 0.820 0.000 0.008 0.004 0.076 0.092
#> GSM49597 2 0.0000 0.9034 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM49598 1 0.5173 0.6653 0.700 0.000 0.004 0.048 0.092 0.156
#> GSM49599 6 0.7740 0.2078 0.272 0.000 0.036 0.104 0.184 0.404
#> GSM49600 1 0.5011 0.6543 0.712 0.000 0.060 0.008 0.048 0.172
#> GSM49601 1 0.3739 0.6876 0.812 0.000 0.012 0.008 0.060 0.108
#> GSM49602 1 0.5478 0.6074 0.660 0.000 0.012 0.020 0.148 0.160
#> GSM49603 1 0.4871 0.6480 0.720 0.000 0.008 0.020 0.108 0.144
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> ATC:skmeans 53 2.77e-05 3.04e-03 2
#> ATC:skmeans 50 5.25e-05 1.11e-05 3
#> ATC:skmeans 49 8.04e-06 3.00e-05 4
#> ATC:skmeans 42 1.88e-04 7.59e-07 5
#> ATC:skmeans 39 1.83e-04 4.32e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "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 21168 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.999 0.999 0.372 0.628 0.628
#> 3 3 0.573 0.634 0.847 0.378 0.945 0.913
#> 4 4 0.582 0.635 0.798 0.129 0.876 0.793
#> 5 5 0.539 0.605 0.774 0.182 0.742 0.497
#> 6 6 0.721 0.732 0.885 0.104 0.869 0.587
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
#> GSM49613 1 0.000 1.000 1.000 0.000
#> GSM49604 2 0.000 0.997 0.000 1.000
#> GSM49605 2 0.000 0.997 0.000 1.000
#> GSM49606 2 0.000 0.997 0.000 1.000
#> GSM49607 2 0.000 0.997 0.000 1.000
#> GSM49608 2 0.000 0.997 0.000 1.000
#> GSM49609 2 0.224 0.963 0.036 0.964
#> GSM49610 2 0.000 0.997 0.000 1.000
#> GSM49611 2 0.000 0.997 0.000 1.000
#> GSM49612 2 0.000 0.997 0.000 1.000
#> GSM49614 1 0.000 1.000 1.000 0.000
#> GSM49615 1 0.000 1.000 1.000 0.000
#> GSM49616 1 0.000 1.000 1.000 0.000
#> GSM49617 1 0.000 1.000 1.000 0.000
#> GSM49564 1 0.000 1.000 1.000 0.000
#> GSM49565 1 0.000 1.000 1.000 0.000
#> GSM49566 1 0.000 1.000 1.000 0.000
#> GSM49567 1 0.000 1.000 1.000 0.000
#> GSM49568 1 0.000 1.000 1.000 0.000
#> GSM49569 1 0.000 1.000 1.000 0.000
#> GSM49570 2 0.000 0.997 0.000 1.000
#> GSM49571 1 0.000 1.000 1.000 0.000
#> GSM49572 1 0.000 1.000 1.000 0.000
#> GSM49573 2 0.000 0.997 0.000 1.000
#> GSM49574 1 0.000 1.000 1.000 0.000
#> GSM49575 1 0.000 1.000 1.000 0.000
#> GSM49576 1 0.000 1.000 1.000 0.000
#> GSM49577 1 0.000 1.000 1.000 0.000
#> GSM49578 1 0.000 1.000 1.000 0.000
#> GSM49579 1 0.000 1.000 1.000 0.000
#> GSM49580 1 0.000 1.000 1.000 0.000
#> GSM49581 1 0.000 1.000 1.000 0.000
#> GSM49582 1 0.000 1.000 1.000 0.000
#> GSM49583 2 0.000 0.997 0.000 1.000
#> GSM49584 1 0.000 1.000 1.000 0.000
#> GSM49585 1 0.000 1.000 1.000 0.000
#> GSM49586 1 0.000 1.000 1.000 0.000
#> GSM49587 1 0.000 1.000 1.000 0.000
#> GSM49588 1 0.000 1.000 1.000 0.000
#> GSM49589 1 0.000 1.000 1.000 0.000
#> GSM49590 1 0.000 1.000 1.000 0.000
#> GSM49591 1 0.000 1.000 1.000 0.000
#> GSM49592 1 0.000 1.000 1.000 0.000
#> GSM49593 1 0.000 1.000 1.000 0.000
#> GSM49594 1 0.000 1.000 1.000 0.000
#> GSM49595 1 0.000 1.000 1.000 0.000
#> GSM49596 1 0.000 1.000 1.000 0.000
#> GSM49597 2 0.000 0.997 0.000 1.000
#> GSM49598 1 0.000 1.000 1.000 0.000
#> GSM49599 1 0.000 1.000 1.000 0.000
#> GSM49600 1 0.000 1.000 1.000 0.000
#> GSM49601 1 0.000 1.000 1.000 0.000
#> GSM49602 1 0.000 1.000 1.000 0.000
#> GSM49603 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM49613 1 0.5948 -0.271 0.640 0.000 0.360
#> GSM49604 2 0.5560 0.809 0.000 0.700 0.300
#> GSM49605 2 0.0000 0.905 0.000 1.000 0.000
#> GSM49606 2 0.0000 0.905 0.000 1.000 0.000
#> GSM49607 2 0.0000 0.905 0.000 1.000 0.000
#> GSM49608 2 0.0000 0.905 0.000 1.000 0.000
#> GSM49609 2 0.6299 0.452 0.000 0.524 0.476
#> GSM49610 2 0.0000 0.905 0.000 1.000 0.000
#> GSM49611 2 0.3879 0.854 0.000 0.848 0.152
#> GSM49612 2 0.5058 0.797 0.000 0.756 0.244
#> GSM49614 3 0.5591 0.808 0.304 0.000 0.696
#> GSM49615 1 0.5948 -0.271 0.640 0.000 0.360
#> GSM49616 1 0.5948 -0.271 0.640 0.000 0.360
#> GSM49617 3 0.6095 0.783 0.392 0.000 0.608
#> GSM49564 1 0.0000 0.728 1.000 0.000 0.000
#> GSM49565 1 0.5216 0.515 0.740 0.000 0.260
#> GSM49566 1 0.3619 0.653 0.864 0.000 0.136
#> GSM49567 1 0.5431 0.465 0.716 0.000 0.284
#> GSM49568 1 0.0592 0.728 0.988 0.000 0.012
#> GSM49569 1 0.5810 0.393 0.664 0.000 0.336
#> GSM49570 2 0.3879 0.854 0.000 0.848 0.152
#> GSM49571 1 0.5810 0.393 0.664 0.000 0.336
#> GSM49572 1 0.4002 0.629 0.840 0.000 0.160
#> GSM49573 2 0.3879 0.854 0.000 0.848 0.152
#> GSM49574 1 0.3551 0.654 0.868 0.000 0.132
#> GSM49575 1 0.5810 0.393 0.664 0.000 0.336
#> GSM49576 1 0.5216 0.523 0.740 0.000 0.260
#> GSM49577 1 0.5810 0.393 0.664 0.000 0.336
#> GSM49578 1 0.0000 0.728 1.000 0.000 0.000
#> GSM49579 1 0.5785 0.401 0.668 0.000 0.332
#> GSM49580 1 0.0237 0.728 0.996 0.000 0.004
#> GSM49581 1 0.0000 0.728 1.000 0.000 0.000
#> GSM49582 1 0.0000 0.728 1.000 0.000 0.000
#> GSM49583 2 0.0000 0.905 0.000 1.000 0.000
#> GSM49584 1 0.0424 0.728 0.992 0.000 0.008
#> GSM49585 1 0.0000 0.728 1.000 0.000 0.000
#> GSM49586 1 0.3482 0.658 0.872 0.000 0.128
#> GSM49587 1 0.0000 0.728 1.000 0.000 0.000
#> GSM49588 1 0.0000 0.728 1.000 0.000 0.000
#> GSM49589 1 0.2066 0.710 0.940 0.000 0.060
#> GSM49590 1 0.3619 0.655 0.864 0.000 0.136
#> GSM49591 1 0.0000 0.728 1.000 0.000 0.000
#> GSM49592 1 0.0000 0.728 1.000 0.000 0.000
#> GSM49593 1 0.0592 0.728 0.988 0.000 0.012
#> GSM49594 1 0.5810 0.393 0.664 0.000 0.336
#> GSM49595 1 0.5810 0.393 0.664 0.000 0.336
#> GSM49596 1 0.0747 0.728 0.984 0.000 0.016
#> GSM49597 2 0.0000 0.905 0.000 1.000 0.000
#> GSM49598 1 0.0592 0.728 0.988 0.000 0.012
#> GSM49599 1 0.5216 0.523 0.740 0.000 0.260
#> GSM49600 1 0.0000 0.728 1.000 0.000 0.000
#> GSM49601 1 0.0424 0.728 0.992 0.000 0.008
#> GSM49602 1 0.3686 0.647 0.860 0.000 0.140
#> GSM49603 1 0.0592 0.728 0.988 0.000 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM49613 3 0.2081 0.768 0.084 0.000 0.916 0.000
#> GSM49604 4 0.1474 0.552 0.000 0.052 0.000 0.948
#> GSM49605 2 0.0000 0.825 0.000 1.000 0.000 0.000
#> GSM49606 2 0.0000 0.825 0.000 1.000 0.000 0.000
#> GSM49607 2 0.0000 0.825 0.000 1.000 0.000 0.000
#> GSM49608 2 0.0000 0.825 0.000 1.000 0.000 0.000
#> GSM49609 2 0.7148 0.382 0.128 0.524 0.004 0.344
#> GSM49610 2 0.0000 0.825 0.000 1.000 0.000 0.000
#> GSM49611 2 0.4819 0.556 0.000 0.652 0.004 0.344
#> GSM49612 2 0.5464 0.539 0.020 0.632 0.004 0.344
#> GSM49614 1 0.4999 -0.509 0.508 0.000 0.492 0.000
#> GSM49615 3 0.1867 0.772 0.072 0.000 0.928 0.000
#> GSM49616 3 0.1867 0.772 0.072 0.000 0.928 0.000
#> GSM49617 3 0.4981 0.273 0.464 0.000 0.536 0.000
#> GSM49564 1 0.4888 0.676 0.588 0.000 0.412 0.000
#> GSM49565 1 0.1389 0.574 0.952 0.000 0.048 0.000
#> GSM49566 1 0.3726 0.634 0.788 0.000 0.212 0.000
#> GSM49567 1 0.2011 0.594 0.920 0.000 0.080 0.000
#> GSM49568 1 0.4907 0.676 0.580 0.000 0.420 0.000
#> GSM49569 1 0.0000 0.564 1.000 0.000 0.000 0.000
#> GSM49570 4 0.5877 0.767 0.000 0.276 0.068 0.656
#> GSM49571 1 0.0000 0.564 1.000 0.000 0.000 0.000
#> GSM49572 1 0.3486 0.623 0.812 0.000 0.188 0.000
#> GSM49573 4 0.5877 0.767 0.000 0.276 0.068 0.656
#> GSM49574 1 0.3873 0.644 0.772 0.000 0.228 0.000
#> GSM49575 1 0.0000 0.564 1.000 0.000 0.000 0.000
#> GSM49576 1 0.0188 0.567 0.996 0.000 0.004 0.000
#> GSM49577 1 0.0000 0.564 1.000 0.000 0.000 0.000
#> GSM49578 1 0.4941 0.670 0.564 0.000 0.436 0.000
#> GSM49579 1 0.0336 0.569 0.992 0.000 0.008 0.000
#> GSM49580 1 0.4933 0.672 0.568 0.000 0.432 0.000
#> GSM49581 1 0.4941 0.670 0.564 0.000 0.436 0.000
#> GSM49582 1 0.4941 0.670 0.564 0.000 0.436 0.000
#> GSM49583 2 0.0000 0.825 0.000 1.000 0.000 0.000
#> GSM49584 1 0.4925 0.673 0.572 0.000 0.428 0.000
#> GSM49585 1 0.4941 0.670 0.564 0.000 0.436 0.000
#> GSM49586 1 0.3801 0.642 0.780 0.000 0.220 0.000
#> GSM49587 1 0.4941 0.670 0.564 0.000 0.436 0.000
#> GSM49588 1 0.4941 0.670 0.564 0.000 0.436 0.000
#> GSM49589 1 0.4543 0.675 0.676 0.000 0.324 0.000
#> GSM49590 1 0.3266 0.633 0.832 0.000 0.168 0.000
#> GSM49591 1 0.4941 0.670 0.564 0.000 0.436 0.000
#> GSM49592 1 0.4941 0.670 0.564 0.000 0.436 0.000
#> GSM49593 1 0.4761 0.680 0.628 0.000 0.372 0.000
#> GSM49594 1 0.0000 0.564 1.000 0.000 0.000 0.000
#> GSM49595 1 0.0000 0.564 1.000 0.000 0.000 0.000
#> GSM49596 1 0.4866 0.680 0.596 0.000 0.404 0.000
#> GSM49597 2 0.0000 0.825 0.000 1.000 0.000 0.000
#> GSM49598 1 0.4761 0.680 0.628 0.000 0.372 0.000
#> GSM49599 1 0.0921 0.579 0.972 0.000 0.028 0.000
#> GSM49600 1 0.4941 0.670 0.564 0.000 0.436 0.000
#> GSM49601 1 0.4898 0.675 0.584 0.000 0.416 0.000
#> GSM49602 1 0.3649 0.637 0.796 0.000 0.204 0.000
#> GSM49603 1 0.4761 0.680 0.628 0.000 0.372 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM49613 3 0.4668 0.664 0.352 0.000 0.624 0.000 0.024
#> GSM49604 4 0.2930 0.500 0.000 0.032 0.032 0.888 0.048
#> GSM49605 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM49606 2 0.0703 0.968 0.000 0.976 0.000 0.024 0.000
#> GSM49607 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM49608 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM49609 4 0.6071 0.328 0.000 0.300 0.000 0.548 0.152
#> GSM49610 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM49611 4 0.4278 0.154 0.000 0.452 0.000 0.548 0.000
#> GSM49612 4 0.5281 0.255 0.000 0.400 0.000 0.548 0.052
#> GSM49614 3 0.4114 0.434 0.000 0.000 0.624 0.000 0.376
#> GSM49615 3 0.4114 0.661 0.376 0.000 0.624 0.000 0.000
#> GSM49616 3 0.4114 0.661 0.376 0.000 0.624 0.000 0.000
#> GSM49617 3 0.4794 0.474 0.032 0.000 0.624 0.000 0.344
#> GSM49564 1 0.3366 0.547 0.768 0.000 0.000 0.000 0.232
#> GSM49565 5 0.4268 0.420 0.444 0.000 0.000 0.000 0.556
#> GSM49566 1 0.3949 0.260 0.668 0.000 0.000 0.000 0.332
#> GSM49567 1 0.4294 -0.276 0.532 0.000 0.000 0.000 0.468
#> GSM49568 1 0.1410 0.718 0.940 0.000 0.000 0.000 0.060
#> GSM49569 5 0.3109 0.777 0.200 0.000 0.000 0.000 0.800
#> GSM49570 4 0.6396 0.401 0.000 0.000 0.376 0.452 0.172
#> GSM49571 5 0.3242 0.766 0.216 0.000 0.000 0.000 0.784
#> GSM49572 1 0.3816 0.269 0.696 0.000 0.000 0.000 0.304
#> GSM49573 4 0.6396 0.401 0.000 0.000 0.376 0.452 0.172
#> GSM49574 1 0.3999 0.145 0.656 0.000 0.000 0.000 0.344
#> GSM49575 5 0.2852 0.787 0.172 0.000 0.000 0.000 0.828
#> GSM49576 5 0.2852 0.787 0.172 0.000 0.000 0.000 0.828
#> GSM49577 5 0.2852 0.787 0.172 0.000 0.000 0.000 0.828
#> GSM49578 1 0.0000 0.752 1.000 0.000 0.000 0.000 0.000
#> GSM49579 5 0.3395 0.745 0.236 0.000 0.000 0.000 0.764
#> GSM49580 1 0.0609 0.743 0.980 0.000 0.000 0.000 0.020
#> GSM49581 1 0.0000 0.752 1.000 0.000 0.000 0.000 0.000
#> GSM49582 1 0.0000 0.752 1.000 0.000 0.000 0.000 0.000
#> GSM49583 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM49584 1 0.1270 0.722 0.948 0.000 0.000 0.000 0.052
#> GSM49585 1 0.0000 0.752 1.000 0.000 0.000 0.000 0.000
#> GSM49586 5 0.4273 0.336 0.448 0.000 0.000 0.000 0.552
#> GSM49587 1 0.0000 0.752 1.000 0.000 0.000 0.000 0.000
#> GSM49588 1 0.0000 0.752 1.000 0.000 0.000 0.000 0.000
#> GSM49589 1 0.3999 0.354 0.656 0.000 0.000 0.000 0.344
#> GSM49590 5 0.4242 0.333 0.428 0.000 0.000 0.000 0.572
#> GSM49591 1 0.0000 0.752 1.000 0.000 0.000 0.000 0.000
#> GSM49592 1 0.0000 0.752 1.000 0.000 0.000 0.000 0.000
#> GSM49593 1 0.3837 0.427 0.692 0.000 0.000 0.000 0.308
#> GSM49594 5 0.2852 0.787 0.172 0.000 0.000 0.000 0.828
#> GSM49595 5 0.2891 0.787 0.176 0.000 0.000 0.000 0.824
#> GSM49596 1 0.1851 0.708 0.912 0.000 0.000 0.000 0.088
#> GSM49597 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM49598 1 0.4088 0.278 0.632 0.000 0.000 0.000 0.368
#> GSM49599 5 0.4242 0.469 0.428 0.000 0.000 0.000 0.572
#> GSM49600 1 0.0000 0.752 1.000 0.000 0.000 0.000 0.000
#> GSM49601 1 0.3305 0.557 0.776 0.000 0.000 0.000 0.224
#> GSM49602 5 0.4249 0.381 0.432 0.000 0.000 0.000 0.568
#> GSM49603 1 0.3837 0.427 0.692 0.000 0.000 0.000 0.308
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM49613 3 0.0146 0.996 0.004 0.000 0.996 0.0 0.000 0.000
#> GSM49604 6 0.3409 0.570 0.000 0.000 0.000 0.3 0.000 0.700
#> GSM49605 2 0.0000 0.983 0.000 1.000 0.000 0.0 0.000 0.000
#> GSM49606 2 0.1765 0.892 0.000 0.904 0.000 0.0 0.000 0.096
#> GSM49607 2 0.0000 0.983 0.000 1.000 0.000 0.0 0.000 0.000
#> GSM49608 2 0.0000 0.983 0.000 1.000 0.000 0.0 0.000 0.000
#> GSM49609 6 0.0000 0.892 0.000 0.000 0.000 0.0 0.000 1.000
#> GSM49610 2 0.0000 0.983 0.000 1.000 0.000 0.0 0.000 0.000
#> GSM49611 6 0.0000 0.892 0.000 0.000 0.000 0.0 0.000 1.000
#> GSM49612 6 0.0000 0.892 0.000 0.000 0.000 0.0 0.000 1.000
#> GSM49614 3 0.0000 0.994 0.000 0.000 1.000 0.0 0.000 0.000
#> GSM49615 3 0.0146 0.996 0.004 0.000 0.996 0.0 0.000 0.000
#> GSM49616 3 0.0146 0.996 0.004 0.000 0.996 0.0 0.000 0.000
#> GSM49617 3 0.0000 0.994 0.000 0.000 1.000 0.0 0.000 0.000
#> GSM49564 5 0.3868 0.302 0.492 0.000 0.000 0.0 0.508 0.000
#> GSM49565 1 0.3930 0.374 0.576 0.000 0.004 0.0 0.420 0.000
#> GSM49566 1 0.3782 0.463 0.636 0.000 0.004 0.0 0.360 0.000
#> GSM49567 1 0.3907 0.398 0.588 0.000 0.004 0.0 0.408 0.000
#> GSM49568 1 0.1765 0.774 0.904 0.000 0.000 0.0 0.096 0.000
#> GSM49569 5 0.0865 0.742 0.036 0.000 0.000 0.0 0.964 0.000
#> GSM49570 4 0.0000 1.000 0.000 0.000 0.000 1.0 0.000 0.000
#> GSM49571 5 0.1387 0.744 0.068 0.000 0.000 0.0 0.932 0.000
#> GSM49572 1 0.2838 0.682 0.808 0.000 0.004 0.0 0.188 0.000
#> GSM49573 4 0.0000 1.000 0.000 0.000 0.000 1.0 0.000 0.000
#> GSM49574 1 0.3737 0.295 0.608 0.000 0.000 0.0 0.392 0.000
#> GSM49575 5 0.0146 0.733 0.000 0.000 0.004 0.0 0.996 0.000
#> GSM49576 5 0.0405 0.734 0.008 0.000 0.004 0.0 0.988 0.000
#> GSM49577 5 0.0146 0.733 0.000 0.000 0.004 0.0 0.996 0.000
#> GSM49578 1 0.0000 0.812 1.000 0.000 0.000 0.0 0.000 0.000
#> GSM49579 5 0.2668 0.607 0.168 0.000 0.004 0.0 0.828 0.000
#> GSM49580 1 0.0547 0.807 0.980 0.000 0.000 0.0 0.020 0.000
#> GSM49581 1 0.0458 0.807 0.984 0.000 0.000 0.0 0.016 0.000
#> GSM49582 1 0.0000 0.812 1.000 0.000 0.000 0.0 0.000 0.000
#> GSM49583 2 0.0000 0.983 0.000 1.000 0.000 0.0 0.000 0.000
#> GSM49584 1 0.1387 0.783 0.932 0.000 0.000 0.0 0.068 0.000
#> GSM49585 1 0.0000 0.812 1.000 0.000 0.000 0.0 0.000 0.000
#> GSM49586 5 0.2562 0.718 0.172 0.000 0.000 0.0 0.828 0.000
#> GSM49587 1 0.0000 0.812 1.000 0.000 0.000 0.0 0.000 0.000
#> GSM49588 1 0.0000 0.812 1.000 0.000 0.000 0.0 0.000 0.000
#> GSM49589 5 0.3797 0.448 0.420 0.000 0.000 0.0 0.580 0.000
#> GSM49590 5 0.2703 0.691 0.172 0.000 0.004 0.0 0.824 0.000
#> GSM49591 1 0.0000 0.812 1.000 0.000 0.000 0.0 0.000 0.000
#> GSM49592 1 0.0000 0.812 1.000 0.000 0.000 0.0 0.000 0.000
#> GSM49593 5 0.3578 0.596 0.340 0.000 0.000 0.0 0.660 0.000
#> GSM49594 5 0.0146 0.733 0.000 0.000 0.004 0.0 0.996 0.000
#> GSM49595 5 0.0291 0.735 0.004 0.000 0.004 0.0 0.992 0.000
#> GSM49596 1 0.2562 0.662 0.828 0.000 0.000 0.0 0.172 0.000
#> GSM49597 2 0.0000 0.983 0.000 1.000 0.000 0.0 0.000 0.000
#> GSM49598 5 0.3446 0.628 0.308 0.000 0.000 0.0 0.692 0.000
#> GSM49599 5 0.3860 -0.205 0.472 0.000 0.000 0.0 0.528 0.000
#> GSM49600 1 0.0260 0.809 0.992 0.000 0.000 0.0 0.008 0.000
#> GSM49601 1 0.3857 -0.274 0.532 0.000 0.000 0.0 0.468 0.000
#> GSM49602 5 0.2454 0.723 0.160 0.000 0.000 0.0 0.840 0.000
#> GSM49603 5 0.3531 0.607 0.328 0.000 0.000 0.0 0.672 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) cell.type(p) k
#> ATC:pam 54 5.97e-07 6.72e-04 2
#> ATC:pam 42 4.32e-06 3.71e-10 3
#> ATC:pam 51 8.01e-07 3.06e-12 4
#> ATC:pam 34 2.91e-04 7.90e-06 5
#> ATC:pam 46 3.94e-06 2.25e-11 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 21168 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.977 0.989 0.4786 0.516 0.516
#> 3 3 0.792 0.911 0.922 0.2233 0.893 0.796
#> 4 4 0.806 0.925 0.937 0.0454 0.976 0.942
#> 5 5 0.725 0.859 0.873 0.1410 0.878 0.694
#> 6 6 0.675 0.838 0.872 0.0759 0.992 0.970
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
#> GSM49613 2 0.7219 0.775 0.200 0.800
#> GSM49604 2 0.0000 0.970 0.000 1.000
#> GSM49605 2 0.0000 0.970 0.000 1.000
#> GSM49606 2 0.0000 0.970 0.000 1.000
#> GSM49607 2 0.0000 0.970 0.000 1.000
#> GSM49608 2 0.0000 0.970 0.000 1.000
#> GSM49609 2 0.0000 0.970 0.000 1.000
#> GSM49610 2 0.0000 0.970 0.000 1.000
#> GSM49611 2 0.0000 0.970 0.000 1.000
#> GSM49612 2 0.0000 0.970 0.000 1.000
#> GSM49614 2 0.0000 0.970 0.000 1.000
#> GSM49615 2 0.7219 0.775 0.200 0.800
#> GSM49616 2 0.0376 0.967 0.004 0.996
#> GSM49617 2 0.0000 0.970 0.000 1.000
#> GSM49564 1 0.0672 0.992 0.992 0.008
#> GSM49565 1 0.0000 1.000 1.000 0.000
#> GSM49566 1 0.0000 1.000 1.000 0.000
#> GSM49567 1 0.0000 1.000 1.000 0.000
#> GSM49568 1 0.0000 1.000 1.000 0.000
#> GSM49569 1 0.0000 1.000 1.000 0.000
#> GSM49570 2 0.0000 0.970 0.000 1.000
#> GSM49571 2 0.0000 0.970 0.000 1.000
#> GSM49572 1 0.0000 1.000 1.000 0.000
#> GSM49573 2 0.0000 0.970 0.000 1.000
#> GSM49574 1 0.0000 1.000 1.000 0.000
#> GSM49575 2 0.7056 0.785 0.192 0.808
#> GSM49576 1 0.0000 1.000 1.000 0.000
#> GSM49577 1 0.0000 1.000 1.000 0.000
#> GSM49578 1 0.0000 1.000 1.000 0.000
#> GSM49579 1 0.0000 1.000 1.000 0.000
#> GSM49580 1 0.0000 1.000 1.000 0.000
#> GSM49581 1 0.0000 1.000 1.000 0.000
#> GSM49582 1 0.0000 1.000 1.000 0.000
#> GSM49583 2 0.0000 0.970 0.000 1.000
#> GSM49584 1 0.0000 1.000 1.000 0.000
#> GSM49585 1 0.0000 1.000 1.000 0.000
#> GSM49586 2 0.0000 0.970 0.000 1.000
#> GSM49587 1 0.0000 1.000 1.000 0.000
#> GSM49588 1 0.0000 1.000 1.000 0.000
#> GSM49589 1 0.0000 1.000 1.000 0.000
#> GSM49590 1 0.0000 1.000 1.000 0.000
#> GSM49591 1 0.0000 1.000 1.000 0.000
#> GSM49592 1 0.0000 1.000 1.000 0.000
#> GSM49593 1 0.0000 1.000 1.000 0.000
#> GSM49594 1 0.0000 1.000 1.000 0.000
#> GSM49595 1 0.0000 1.000 1.000 0.000
#> GSM49596 1 0.0000 1.000 1.000 0.000
#> GSM49597 2 0.0000 0.970 0.000 1.000
#> GSM49598 1 0.0000 1.000 1.000 0.000
#> GSM49599 1 0.0000 1.000 1.000 0.000
#> GSM49600 1 0.0000 1.000 1.000 0.000
#> GSM49601 1 0.0000 1.000 1.000 0.000
#> GSM49602 1 0.0000 1.000 1.000 0.000
#> GSM49603 1 0.0000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM49613 3 0.2878 0.834 0.000 0.096 0.904
#> GSM49604 3 0.0000 0.892 0.000 0.000 1.000
#> GSM49605 2 0.4555 1.000 0.000 0.800 0.200
#> GSM49606 2 0.4555 1.000 0.000 0.800 0.200
#> GSM49607 2 0.4555 1.000 0.000 0.800 0.200
#> GSM49608 2 0.4555 1.000 0.000 0.800 0.200
#> GSM49609 2 0.4555 1.000 0.000 0.800 0.200
#> GSM49610 2 0.4555 1.000 0.000 0.800 0.200
#> GSM49611 2 0.4555 1.000 0.000 0.800 0.200
#> GSM49612 2 0.4555 1.000 0.000 0.800 0.200
#> GSM49614 3 0.0000 0.892 0.000 0.000 1.000
#> GSM49615 3 0.2878 0.834 0.000 0.096 0.904
#> GSM49616 3 0.0000 0.892 0.000 0.000 1.000
#> GSM49617 3 0.0000 0.892 0.000 0.000 1.000
#> GSM49564 1 0.7592 0.641 0.680 0.112 0.208
#> GSM49565 1 0.0000 0.947 1.000 0.000 0.000
#> GSM49566 1 0.0000 0.947 1.000 0.000 0.000
#> GSM49567 1 0.0000 0.947 1.000 0.000 0.000
#> GSM49568 1 0.0000 0.947 1.000 0.000 0.000
#> GSM49569 1 0.0000 0.947 1.000 0.000 0.000
#> GSM49570 3 0.0000 0.892 0.000 0.000 1.000
#> GSM49571 3 0.0000 0.892 0.000 0.000 1.000
#> GSM49572 1 0.0000 0.947 1.000 0.000 0.000
#> GSM49573 3 0.0000 0.892 0.000 0.000 1.000
#> GSM49574 1 0.0000 0.947 1.000 0.000 0.000
#> GSM49575 3 0.4121 0.724 0.168 0.000 0.832
#> GSM49576 1 0.0000 0.947 1.000 0.000 0.000
#> GSM49577 1 0.1411 0.925 0.964 0.000 0.036
#> GSM49578 1 0.2625 0.911 0.916 0.084 0.000
#> GSM49579 1 0.0000 0.947 1.000 0.000 0.000
#> GSM49580 1 0.0000 0.947 1.000 0.000 0.000
#> GSM49581 3 0.6264 0.430 0.380 0.004 0.616
#> GSM49582 1 0.0237 0.946 0.996 0.004 0.000
#> GSM49583 2 0.4555 1.000 0.000 0.800 0.200
#> GSM49584 1 0.0000 0.947 1.000 0.000 0.000
#> GSM49585 1 0.4555 0.841 0.800 0.200 0.000
#> GSM49586 3 0.0000 0.892 0.000 0.000 1.000
#> GSM49587 1 0.0000 0.947 1.000 0.000 0.000
#> GSM49588 1 0.4555 0.841 0.800 0.200 0.000
#> GSM49589 1 0.4555 0.841 0.800 0.200 0.000
#> GSM49590 1 0.0000 0.947 1.000 0.000 0.000
#> GSM49591 1 0.4121 0.863 0.832 0.168 0.000
#> GSM49592 1 0.4555 0.841 0.800 0.200 0.000
#> GSM49593 1 0.0237 0.946 0.996 0.004 0.000
#> GSM49594 1 0.0000 0.947 1.000 0.000 0.000
#> GSM49595 1 0.0000 0.947 1.000 0.000 0.000
#> GSM49596 1 0.0000 0.947 1.000 0.000 0.000
#> GSM49597 2 0.4555 1.000 0.000 0.800 0.200
#> GSM49598 1 0.0237 0.946 0.996 0.004 0.000
#> GSM49599 1 0.0000 0.947 1.000 0.000 0.000
#> GSM49600 1 0.0000 0.947 1.000 0.000 0.000
#> GSM49601 1 0.4555 0.841 0.800 0.200 0.000
#> GSM49602 1 0.1529 0.932 0.960 0.040 0.000
#> GSM49603 1 0.3619 0.883 0.864 0.136 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM49613 3 0.0188 1.000 0.000 0.004 0.996 0.000
#> GSM49604 4 0.3569 0.855 0.000 0.196 0.000 0.804
#> GSM49605 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM49606 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM49607 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM49608 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM49609 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM49610 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM49611 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM49612 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM49614 3 0.0188 1.000 0.000 0.004 0.996 0.000
#> GSM49615 3 0.0188 1.000 0.000 0.004 0.996 0.000
#> GSM49616 3 0.0188 1.000 0.000 0.004 0.996 0.000
#> GSM49617 3 0.0188 1.000 0.000 0.004 0.996 0.000
#> GSM49564 1 0.3257 0.867 0.844 0.000 0.004 0.152
#> GSM49565 1 0.0188 0.945 0.996 0.000 0.000 0.004
#> GSM49566 1 0.0188 0.945 0.996 0.000 0.000 0.004
#> GSM49567 1 0.0188 0.945 0.996 0.000 0.000 0.004
#> GSM49568 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM49569 1 0.0188 0.945 0.996 0.000 0.000 0.004
#> GSM49570 4 0.3569 0.855 0.000 0.196 0.000 0.804
#> GSM49571 4 0.3710 0.854 0.000 0.192 0.004 0.804
#> GSM49572 1 0.0188 0.945 0.996 0.000 0.000 0.004
#> GSM49573 4 0.3569 0.855 0.000 0.196 0.000 0.804
#> GSM49574 1 0.0188 0.945 0.996 0.000 0.000 0.004
#> GSM49575 4 0.5459 0.828 0.072 0.192 0.004 0.732
#> GSM49576 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM49577 1 0.0895 0.933 0.976 0.020 0.004 0.000
#> GSM49578 1 0.3052 0.877 0.860 0.000 0.004 0.136
#> GSM49579 1 0.0188 0.945 0.996 0.000 0.000 0.004
#> GSM49580 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM49581 4 0.4585 0.470 0.332 0.000 0.000 0.668
#> GSM49582 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM49583 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM49584 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM49585 1 0.3710 0.839 0.804 0.000 0.004 0.192
#> GSM49586 4 0.5429 0.830 0.068 0.196 0.004 0.732
#> GSM49587 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM49588 1 0.3710 0.839 0.804 0.000 0.004 0.192
#> GSM49589 1 0.3583 0.848 0.816 0.000 0.004 0.180
#> GSM49590 1 0.0188 0.945 0.996 0.000 0.000 0.004
#> GSM49591 1 0.3583 0.848 0.816 0.000 0.004 0.180
#> GSM49592 1 0.3710 0.839 0.804 0.000 0.004 0.192
#> GSM49593 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM49594 1 0.0188 0.945 0.996 0.000 0.000 0.004
#> GSM49595 1 0.0188 0.945 0.996 0.000 0.000 0.004
#> GSM49596 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM49597 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM49598 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM49599 1 0.0188 0.945 0.996 0.000 0.000 0.004
#> GSM49600 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM49601 1 0.3710 0.839 0.804 0.000 0.004 0.192
#> GSM49602 1 0.0469 0.942 0.988 0.000 0.000 0.012
#> GSM49603 1 0.3355 0.862 0.836 0.000 0.004 0.160
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM49613 3 0.1082 0.954 0.028 0.000 0.964 0.000 0.008
#> GSM49604 4 0.0000 0.791 0.000 0.000 0.000 1.000 0.000
#> GSM49605 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM49606 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM49607 2 0.0162 0.988 0.000 0.996 0.000 0.004 0.000
#> GSM49608 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM49609 2 0.0794 0.979 0.000 0.972 0.000 0.028 0.000
#> GSM49610 2 0.0162 0.988 0.000 0.996 0.000 0.004 0.000
#> GSM49611 2 0.0794 0.979 0.000 0.972 0.000 0.028 0.000
#> GSM49612 2 0.0794 0.979 0.000 0.972 0.000 0.028 0.000
#> GSM49614 3 0.0162 0.967 0.000 0.000 0.996 0.004 0.000
#> GSM49615 3 0.1082 0.954 0.028 0.000 0.964 0.000 0.008
#> GSM49616 3 0.0000 0.968 0.000 0.000 1.000 0.000 0.000
#> GSM49617 3 0.0000 0.968 0.000 0.000 1.000 0.000 0.000
#> GSM49564 5 0.4015 0.916 0.348 0.000 0.000 0.000 0.652
#> GSM49565 1 0.1792 0.842 0.916 0.000 0.000 0.000 0.084
#> GSM49566 5 0.4088 0.949 0.368 0.000 0.000 0.000 0.632
#> GSM49567 1 0.2068 0.837 0.904 0.000 0.000 0.004 0.092
#> GSM49568 1 0.1341 0.835 0.944 0.000 0.000 0.000 0.056
#> GSM49569 5 0.4088 0.949 0.368 0.000 0.000 0.000 0.632
#> GSM49570 4 0.0693 0.786 0.000 0.012 0.000 0.980 0.008
#> GSM49571 4 0.0794 0.789 0.000 0.000 0.000 0.972 0.028
#> GSM49572 1 0.1792 0.842 0.916 0.000 0.000 0.000 0.084
#> GSM49573 4 0.0290 0.790 0.000 0.000 0.000 0.992 0.008
#> GSM49574 1 0.1792 0.842 0.916 0.000 0.000 0.000 0.084
#> GSM49575 4 0.5324 0.645 0.128 0.000 0.000 0.668 0.204
#> GSM49576 5 0.4150 0.946 0.388 0.000 0.000 0.000 0.612
#> GSM49577 1 0.2260 0.841 0.908 0.000 0.000 0.028 0.064
#> GSM49578 1 0.1671 0.834 0.924 0.000 0.000 0.000 0.076
#> GSM49579 1 0.2424 0.778 0.868 0.000 0.000 0.000 0.132
#> GSM49580 1 0.1270 0.839 0.948 0.000 0.000 0.000 0.052
#> GSM49581 4 0.6362 0.137 0.368 0.000 0.000 0.464 0.168
#> GSM49582 1 0.0794 0.857 0.972 0.000 0.000 0.000 0.028
#> GSM49583 2 0.0290 0.988 0.000 0.992 0.000 0.008 0.000
#> GSM49584 5 0.4273 0.866 0.448 0.000 0.000 0.000 0.552
#> GSM49585 1 0.2773 0.752 0.836 0.000 0.000 0.000 0.164
#> GSM49586 4 0.3318 0.745 0.008 0.000 0.000 0.800 0.192
#> GSM49587 1 0.0609 0.861 0.980 0.000 0.000 0.000 0.020
#> GSM49588 1 0.2929 0.739 0.820 0.000 0.000 0.000 0.180
#> GSM49589 5 0.4225 0.938 0.364 0.000 0.004 0.000 0.632
#> GSM49590 5 0.4101 0.948 0.372 0.000 0.000 0.000 0.628
#> GSM49591 1 0.2690 0.782 0.844 0.000 0.000 0.000 0.156
#> GSM49592 1 0.2891 0.743 0.824 0.000 0.000 0.000 0.176
#> GSM49593 1 0.0963 0.860 0.964 0.000 0.000 0.000 0.036
#> GSM49594 1 0.1732 0.844 0.920 0.000 0.000 0.000 0.080
#> GSM49595 1 0.1608 0.845 0.928 0.000 0.000 0.000 0.072
#> GSM49596 1 0.0404 0.860 0.988 0.000 0.000 0.000 0.012
#> GSM49597 2 0.0290 0.988 0.000 0.992 0.000 0.008 0.000
#> GSM49598 1 0.1357 0.850 0.948 0.000 0.000 0.004 0.048
#> GSM49599 1 0.1732 0.844 0.920 0.000 0.000 0.000 0.080
#> GSM49600 1 0.1544 0.823 0.932 0.000 0.000 0.000 0.068
#> GSM49601 1 0.2929 0.739 0.820 0.000 0.000 0.000 0.180
#> GSM49602 1 0.0703 0.857 0.976 0.000 0.000 0.000 0.024
#> GSM49603 1 0.2471 0.792 0.864 0.000 0.000 0.000 0.136
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM49613 3 0.1036 0.958 0.024 0.000 0.964 0.000 0.004 0.008
#> GSM49604 4 0.0405 0.935 0.000 0.004 0.000 0.988 0.000 0.008
#> GSM49605 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM49606 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM49607 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM49608 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM49609 2 0.0547 0.984 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM49610 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM49611 2 0.0547 0.984 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM49612 2 0.0547 0.984 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM49614 3 0.0000 0.973 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM49615 3 0.1036 0.958 0.024 0.000 0.964 0.000 0.004 0.008
#> GSM49616 3 0.0000 0.973 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM49617 3 0.0000 0.973 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM49564 5 0.2278 0.877 0.128 0.000 0.000 0.004 0.868 0.000
#> GSM49565 1 0.5333 0.721 0.564 0.000 0.000 0.000 0.300 0.136
#> GSM49566 5 0.1007 0.942 0.044 0.000 0.000 0.000 0.956 0.000
#> GSM49567 1 0.4765 0.764 0.676 0.000 0.000 0.000 0.152 0.172
#> GSM49568 1 0.3221 0.776 0.736 0.000 0.000 0.000 0.264 0.000
#> GSM49569 5 0.1265 0.942 0.044 0.000 0.008 0.000 0.948 0.000
#> GSM49570 4 0.0363 0.933 0.000 0.012 0.000 0.988 0.000 0.000
#> GSM49571 4 0.2260 0.825 0.000 0.000 0.000 0.860 0.000 0.140
#> GSM49572 1 0.5319 0.722 0.568 0.000 0.000 0.000 0.296 0.136
#> GSM49573 4 0.0146 0.937 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM49574 1 0.5350 0.721 0.564 0.000 0.000 0.000 0.296 0.140
#> GSM49575 6 0.2979 0.585 0.032 0.000 0.000 0.112 0.008 0.848
#> GSM49576 5 0.1141 0.943 0.052 0.000 0.000 0.000 0.948 0.000
#> GSM49577 1 0.4707 0.756 0.676 0.000 0.000 0.000 0.120 0.204
#> GSM49578 1 0.1010 0.778 0.960 0.000 0.000 0.000 0.036 0.004
#> GSM49579 1 0.4273 0.680 0.596 0.000 0.000 0.000 0.380 0.024
#> GSM49580 1 0.3221 0.776 0.736 0.000 0.000 0.000 0.264 0.000
#> GSM49581 6 0.4117 0.489 0.256 0.000 0.000 0.004 0.036 0.704
#> GSM49582 1 0.2948 0.781 0.848 0.000 0.000 0.000 0.060 0.092
#> GSM49583 2 0.0405 0.986 0.000 0.988 0.000 0.004 0.000 0.008
#> GSM49584 5 0.1387 0.937 0.068 0.000 0.000 0.000 0.932 0.000
#> GSM49585 1 0.0603 0.753 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM49586 6 0.3428 0.340 0.000 0.000 0.000 0.304 0.000 0.696
#> GSM49587 1 0.2854 0.802 0.792 0.000 0.000 0.000 0.208 0.000
#> GSM49588 1 0.0520 0.752 0.984 0.000 0.000 0.000 0.008 0.008
#> GSM49589 5 0.2540 0.884 0.104 0.000 0.020 0.000 0.872 0.004
#> GSM49590 5 0.0937 0.941 0.040 0.000 0.000 0.000 0.960 0.000
#> GSM49591 1 0.2633 0.756 0.864 0.000 0.000 0.000 0.104 0.032
#> GSM49592 1 0.0508 0.750 0.984 0.000 0.000 0.000 0.004 0.012
#> GSM49593 1 0.3013 0.784 0.844 0.000 0.000 0.000 0.068 0.088
#> GSM49594 1 0.4774 0.769 0.672 0.000 0.000 0.000 0.192 0.136
#> GSM49595 1 0.4809 0.768 0.668 0.000 0.000 0.000 0.192 0.140
#> GSM49596 1 0.2948 0.809 0.804 0.000 0.000 0.000 0.188 0.008
#> GSM49597 2 0.0405 0.986 0.000 0.988 0.000 0.004 0.000 0.008
#> GSM49598 1 0.3172 0.767 0.824 0.000 0.000 0.000 0.048 0.128
#> GSM49599 1 0.4781 0.770 0.672 0.000 0.000 0.000 0.188 0.140
#> GSM49600 1 0.3244 0.774 0.732 0.000 0.000 0.000 0.268 0.000
#> GSM49601 1 0.0508 0.750 0.984 0.000 0.000 0.000 0.004 0.012
#> GSM49602 1 0.3076 0.780 0.760 0.000 0.000 0.000 0.240 0.000
#> GSM49603 1 0.2006 0.754 0.892 0.000 0.000 0.000 0.104 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) cell.type(p) k
#> ATC:mclust 54 5.52e-05 2.06e-04 2
#> ATC:mclust 53 1.21e-07 6.60e-08 3
#> ATC:mclust 53 5.55e-07 2.20e-13 4
#> ATC:mclust 53 2.03e-06 2.70e-12 5
#> ATC:mclust 52 6.75e-06 4.64e-11 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 21168 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.3731 0.628 0.628
#> 3 3 0.968 0.961 0.976 0.2600 0.893 0.831
#> 4 4 0.710 0.839 0.903 0.2901 0.823 0.681
#> 5 5 0.668 0.736 0.865 0.0548 0.994 0.984
#> 6 6 0.568 0.662 0.790 0.0862 0.956 0.891
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
#> GSM49613 1 0 1 1 0
#> GSM49604 2 0 1 0 1
#> GSM49605 2 0 1 0 1
#> GSM49606 2 0 1 0 1
#> GSM49607 2 0 1 0 1
#> GSM49608 2 0 1 0 1
#> GSM49609 2 0 1 0 1
#> GSM49610 2 0 1 0 1
#> GSM49611 2 0 1 0 1
#> GSM49612 2 0 1 0 1
#> GSM49614 1 0 1 1 0
#> GSM49615 1 0 1 1 0
#> GSM49616 1 0 1 1 0
#> GSM49617 1 0 1 1 0
#> GSM49564 1 0 1 1 0
#> GSM49565 1 0 1 1 0
#> GSM49566 1 0 1 1 0
#> GSM49567 1 0 1 1 0
#> GSM49568 1 0 1 1 0
#> GSM49569 1 0 1 1 0
#> GSM49570 2 0 1 0 1
#> GSM49571 1 0 1 1 0
#> GSM49572 1 0 1 1 0
#> GSM49573 2 0 1 0 1
#> GSM49574 1 0 1 1 0
#> GSM49575 1 0 1 1 0
#> GSM49576 1 0 1 1 0
#> GSM49577 1 0 1 1 0
#> GSM49578 1 0 1 1 0
#> GSM49579 1 0 1 1 0
#> GSM49580 1 0 1 1 0
#> GSM49581 1 0 1 1 0
#> GSM49582 1 0 1 1 0
#> GSM49583 2 0 1 0 1
#> GSM49584 1 0 1 1 0
#> GSM49585 1 0 1 1 0
#> GSM49586 1 0 1 1 0
#> GSM49587 1 0 1 1 0
#> GSM49588 1 0 1 1 0
#> GSM49589 1 0 1 1 0
#> GSM49590 1 0 1 1 0
#> GSM49591 1 0 1 1 0
#> GSM49592 1 0 1 1 0
#> GSM49593 1 0 1 1 0
#> GSM49594 1 0 1 1 0
#> GSM49595 1 0 1 1 0
#> GSM49596 1 0 1 1 0
#> GSM49597 2 0 1 0 1
#> GSM49598 1 0 1 1 0
#> GSM49599 1 0 1 1 0
#> GSM49600 1 0 1 1 0
#> GSM49601 1 0 1 1 0
#> GSM49602 1 0 1 1 0
#> GSM49603 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM49613 1 0.1289 0.971 0.968 0.000 0.032
#> GSM49604 3 0.3267 0.822 0.000 0.116 0.884
#> GSM49605 2 0.0000 1.000 0.000 1.000 0.000
#> GSM49606 2 0.0000 1.000 0.000 1.000 0.000
#> GSM49607 2 0.0000 1.000 0.000 1.000 0.000
#> GSM49608 2 0.0000 1.000 0.000 1.000 0.000
#> GSM49609 2 0.0000 1.000 0.000 1.000 0.000
#> GSM49610 2 0.0000 1.000 0.000 1.000 0.000
#> GSM49611 2 0.0000 1.000 0.000 1.000 0.000
#> GSM49612 2 0.0000 1.000 0.000 1.000 0.000
#> GSM49614 1 0.1411 0.968 0.964 0.000 0.036
#> GSM49615 1 0.1289 0.971 0.968 0.000 0.032
#> GSM49616 1 0.1289 0.971 0.968 0.000 0.032
#> GSM49617 1 0.1289 0.971 0.968 0.000 0.032
#> GSM49564 1 0.1289 0.971 0.968 0.000 0.032
#> GSM49565 1 0.0237 0.985 0.996 0.000 0.004
#> GSM49566 1 0.0000 0.985 1.000 0.000 0.000
#> GSM49567 1 0.0747 0.981 0.984 0.000 0.016
#> GSM49568 1 0.0424 0.985 0.992 0.000 0.008
#> GSM49569 1 0.0000 0.985 1.000 0.000 0.000
#> GSM49570 3 0.4931 0.716 0.000 0.232 0.768
#> GSM49571 3 0.0000 0.826 0.000 0.000 1.000
#> GSM49572 1 0.0000 0.985 1.000 0.000 0.000
#> GSM49573 3 0.2711 0.834 0.000 0.088 0.912
#> GSM49574 1 0.0000 0.985 1.000 0.000 0.000
#> GSM49575 3 0.4235 0.713 0.176 0.000 0.824
#> GSM49576 1 0.0237 0.985 0.996 0.000 0.004
#> GSM49577 1 0.0000 0.985 1.000 0.000 0.000
#> GSM49578 1 0.0424 0.984 0.992 0.000 0.008
#> GSM49579 1 0.0000 0.985 1.000 0.000 0.000
#> GSM49580 1 0.0237 0.985 0.996 0.000 0.004
#> GSM49581 1 0.3192 0.890 0.888 0.000 0.112
#> GSM49582 1 0.1031 0.979 0.976 0.000 0.024
#> GSM49583 2 0.0000 1.000 0.000 1.000 0.000
#> GSM49584 1 0.0237 0.985 0.996 0.000 0.004
#> GSM49585 1 0.0592 0.984 0.988 0.000 0.012
#> GSM49586 3 0.2711 0.805 0.088 0.000 0.912
#> GSM49587 1 0.0000 0.985 1.000 0.000 0.000
#> GSM49588 1 0.1031 0.979 0.976 0.000 0.024
#> GSM49589 1 0.0892 0.978 0.980 0.000 0.020
#> GSM49590 1 0.0424 0.984 0.992 0.000 0.008
#> GSM49591 1 0.0892 0.979 0.980 0.000 0.020
#> GSM49592 1 0.0892 0.981 0.980 0.000 0.020
#> GSM49593 1 0.0592 0.983 0.988 0.000 0.012
#> GSM49594 1 0.0000 0.985 1.000 0.000 0.000
#> GSM49595 1 0.0000 0.985 1.000 0.000 0.000
#> GSM49596 1 0.0000 0.985 1.000 0.000 0.000
#> GSM49597 2 0.0000 1.000 0.000 1.000 0.000
#> GSM49598 1 0.1753 0.961 0.952 0.000 0.048
#> GSM49599 1 0.0237 0.985 0.996 0.000 0.004
#> GSM49600 1 0.0237 0.985 0.996 0.000 0.004
#> GSM49601 1 0.0747 0.981 0.984 0.000 0.016
#> GSM49602 1 0.0237 0.985 0.996 0.000 0.004
#> GSM49603 1 0.1163 0.974 0.972 0.000 0.028
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM49613 3 0.3610 0.927 0.200 0.000 0.800 0.000
#> GSM49604 4 0.0817 0.869 0.000 0.024 0.000 0.976
#> GSM49605 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> GSM49606 2 0.0592 0.977 0.000 0.984 0.016 0.000
#> GSM49607 2 0.0817 0.974 0.000 0.976 0.024 0.000
#> GSM49608 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> GSM49609 2 0.1732 0.961 0.004 0.948 0.040 0.008
#> GSM49610 2 0.0336 0.978 0.000 0.992 0.008 0.000
#> GSM49611 2 0.1109 0.972 0.000 0.968 0.028 0.004
#> GSM49612 2 0.1109 0.972 0.000 0.968 0.028 0.004
#> GSM49614 3 0.3950 0.913 0.184 0.008 0.804 0.004
#> GSM49615 3 0.3610 0.927 0.200 0.000 0.800 0.000
#> GSM49616 3 0.3528 0.925 0.192 0.000 0.808 0.000
#> GSM49617 3 0.3668 0.921 0.188 0.004 0.808 0.000
#> GSM49564 3 0.4406 0.843 0.300 0.000 0.700 0.000
#> GSM49565 1 0.1118 0.880 0.964 0.000 0.036 0.000
#> GSM49566 1 0.3074 0.764 0.848 0.000 0.152 0.000
#> GSM49567 1 0.1118 0.880 0.964 0.000 0.036 0.000
#> GSM49568 1 0.1389 0.884 0.952 0.000 0.048 0.000
#> GSM49569 1 0.4730 0.248 0.636 0.000 0.364 0.000
#> GSM49570 4 0.4888 0.786 0.000 0.124 0.096 0.780
#> GSM49571 4 0.0188 0.868 0.000 0.000 0.004 0.996
#> GSM49572 1 0.0469 0.890 0.988 0.000 0.012 0.000
#> GSM49573 4 0.2596 0.864 0.000 0.024 0.068 0.908
#> GSM49574 1 0.0592 0.888 0.984 0.000 0.016 0.000
#> GSM49575 1 0.6698 0.245 0.556 0.000 0.104 0.340
#> GSM49576 1 0.4331 0.503 0.712 0.000 0.288 0.000
#> GSM49577 1 0.1474 0.870 0.948 0.000 0.052 0.000
#> GSM49578 1 0.0592 0.888 0.984 0.000 0.016 0.000
#> GSM49579 1 0.1389 0.875 0.952 0.000 0.048 0.000
#> GSM49580 1 0.1637 0.880 0.940 0.000 0.060 0.000
#> GSM49581 1 0.2494 0.855 0.916 0.000 0.036 0.048
#> GSM49582 1 0.0376 0.891 0.992 0.000 0.004 0.004
#> GSM49583 2 0.0707 0.975 0.000 0.980 0.020 0.000
#> GSM49584 1 0.2760 0.795 0.872 0.000 0.128 0.000
#> GSM49585 1 0.2255 0.861 0.920 0.000 0.068 0.012
#> GSM49586 4 0.3946 0.675 0.168 0.000 0.020 0.812
#> GSM49587 1 0.1022 0.885 0.968 0.000 0.032 0.000
#> GSM49588 1 0.1398 0.881 0.956 0.000 0.040 0.004
#> GSM49589 3 0.4454 0.828 0.308 0.000 0.692 0.000
#> GSM49590 1 0.4989 -0.246 0.528 0.000 0.472 0.000
#> GSM49591 1 0.1297 0.886 0.964 0.000 0.020 0.016
#> GSM49592 1 0.2101 0.873 0.928 0.000 0.060 0.012
#> GSM49593 1 0.0336 0.889 0.992 0.000 0.008 0.000
#> GSM49594 1 0.0921 0.884 0.972 0.000 0.028 0.000
#> GSM49595 1 0.0469 0.889 0.988 0.000 0.012 0.000
#> GSM49596 1 0.0336 0.889 0.992 0.000 0.008 0.000
#> GSM49597 2 0.1211 0.965 0.000 0.960 0.040 0.000
#> GSM49598 1 0.1520 0.883 0.956 0.000 0.020 0.024
#> GSM49599 1 0.0817 0.885 0.976 0.000 0.024 0.000
#> GSM49600 1 0.1792 0.863 0.932 0.000 0.068 0.000
#> GSM49601 1 0.2256 0.871 0.924 0.000 0.056 0.020
#> GSM49602 1 0.0469 0.890 0.988 0.000 0.012 0.000
#> GSM49603 1 0.1297 0.888 0.964 0.000 0.020 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM49613 3 0.1662 0.9036 0.056 0.000 0.936 0.004 0.004
#> GSM49604 4 0.2654 0.7979 0.000 0.032 0.000 0.884 0.084
#> GSM49605 2 0.0000 0.6519 0.000 1.000 0.000 0.000 0.000
#> GSM49606 2 0.2280 0.4958 0.000 0.880 0.000 0.000 0.120
#> GSM49607 2 0.1478 0.6408 0.000 0.936 0.000 0.000 0.064
#> GSM49608 2 0.0404 0.6460 0.000 0.988 0.000 0.000 0.012
#> GSM49609 5 0.5608 0.0000 0.012 0.472 0.004 0.036 0.476
#> GSM49610 2 0.0703 0.6516 0.000 0.976 0.000 0.000 0.024
#> GSM49611 2 0.4276 -0.5578 0.000 0.616 0.000 0.004 0.380
#> GSM49612 2 0.4973 -0.7019 0.000 0.564 0.024 0.004 0.408
#> GSM49614 3 0.1282 0.8979 0.044 0.000 0.952 0.004 0.000
#> GSM49615 3 0.1662 0.9036 0.056 0.000 0.936 0.004 0.004
#> GSM49616 3 0.1282 0.8998 0.044 0.000 0.952 0.000 0.004
#> GSM49617 3 0.1121 0.8999 0.044 0.000 0.956 0.000 0.000
#> GSM49564 3 0.3210 0.7347 0.212 0.000 0.788 0.000 0.000
#> GSM49565 1 0.1012 0.8971 0.968 0.000 0.020 0.000 0.012
#> GSM49566 1 0.3242 0.8205 0.816 0.000 0.172 0.000 0.012
#> GSM49567 1 0.1914 0.8875 0.932 0.000 0.032 0.004 0.032
#> GSM49568 1 0.1818 0.9046 0.932 0.000 0.044 0.000 0.024
#> GSM49569 1 0.3807 0.7387 0.748 0.000 0.240 0.000 0.012
#> GSM49570 4 0.4486 0.7622 0.000 0.080 0.000 0.748 0.172
#> GSM49571 4 0.0324 0.8202 0.004 0.000 0.000 0.992 0.004
#> GSM49572 1 0.1211 0.8975 0.960 0.000 0.016 0.000 0.024
#> GSM49573 4 0.3236 0.8016 0.000 0.020 0.000 0.828 0.152
#> GSM49574 1 0.0404 0.9009 0.988 0.000 0.012 0.000 0.000
#> GSM49575 1 0.5444 0.6607 0.712 0.000 0.032 0.144 0.112
#> GSM49576 1 0.3561 0.7132 0.740 0.000 0.260 0.000 0.000
#> GSM49577 1 0.2227 0.8805 0.916 0.004 0.032 0.000 0.048
#> GSM49578 1 0.1518 0.9007 0.944 0.000 0.048 0.004 0.004
#> GSM49579 1 0.1597 0.9025 0.940 0.000 0.048 0.000 0.012
#> GSM49580 1 0.1741 0.9042 0.936 0.000 0.040 0.000 0.024
#> GSM49581 1 0.2273 0.8906 0.920 0.000 0.032 0.024 0.024
#> GSM49582 1 0.0671 0.9054 0.980 0.000 0.016 0.000 0.004
#> GSM49583 2 0.1792 0.6286 0.000 0.916 0.000 0.000 0.084
#> GSM49584 1 0.2723 0.8639 0.864 0.000 0.124 0.000 0.012
#> GSM49585 1 0.3047 0.8660 0.868 0.000 0.096 0.012 0.024
#> GSM49586 4 0.4802 0.6648 0.068 0.000 0.004 0.716 0.212
#> GSM49587 1 0.1608 0.8967 0.928 0.000 0.072 0.000 0.000
#> GSM49588 1 0.1991 0.8903 0.916 0.000 0.076 0.004 0.004
#> GSM49589 3 0.2773 0.8044 0.164 0.000 0.836 0.000 0.000
#> GSM49590 1 0.4307 0.0401 0.504 0.000 0.496 0.000 0.000
#> GSM49591 1 0.1314 0.8996 0.960 0.000 0.012 0.012 0.016
#> GSM49592 1 0.2241 0.8877 0.908 0.000 0.076 0.008 0.008
#> GSM49593 1 0.0798 0.9019 0.976 0.000 0.016 0.000 0.008
#> GSM49594 1 0.0798 0.8997 0.976 0.000 0.016 0.000 0.008
#> GSM49595 1 0.0566 0.9043 0.984 0.000 0.012 0.000 0.004
#> GSM49596 1 0.0898 0.9049 0.972 0.000 0.020 0.000 0.008
#> GSM49597 2 0.3707 0.3981 0.000 0.716 0.000 0.000 0.284
#> GSM49598 1 0.0740 0.9034 0.980 0.000 0.008 0.004 0.008
#> GSM49599 1 0.2278 0.8829 0.908 0.000 0.032 0.000 0.060
#> GSM49600 1 0.2344 0.8961 0.904 0.000 0.064 0.000 0.032
#> GSM49601 1 0.4711 0.7772 0.772 0.000 0.052 0.044 0.132
#> GSM49602 1 0.1569 0.9027 0.944 0.000 0.044 0.004 0.008
#> GSM49603 1 0.2199 0.8964 0.916 0.000 0.060 0.008 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM49613 3 0.1693 0.775 0.044 0.000 0.932 0.000 0.020 0.004
#> GSM49604 4 0.5329 0.330 0.012 0.076 0.000 0.576 0.332 0.004
#> GSM49605 2 0.3819 0.473 0.000 0.652 0.000 0.000 0.008 0.340
#> GSM49606 2 0.3388 0.575 0.000 0.804 0.004 0.000 0.036 0.156
#> GSM49607 2 0.3911 0.410 0.000 0.624 0.000 0.000 0.008 0.368
#> GSM49608 2 0.3816 0.547 0.000 0.728 0.000 0.000 0.032 0.240
#> GSM49609 2 0.3199 0.438 0.004 0.840 0.008 0.004 0.120 0.024
#> GSM49610 2 0.3547 0.490 0.000 0.668 0.000 0.000 0.000 0.332
#> GSM49611 2 0.1340 0.547 0.000 0.948 0.000 0.004 0.040 0.008
#> GSM49612 2 0.2340 0.511 0.000 0.900 0.016 0.000 0.060 0.024
#> GSM49614 3 0.1964 0.731 0.012 0.008 0.920 0.004 0.056 0.000
#> GSM49615 3 0.1265 0.778 0.044 0.000 0.948 0.000 0.008 0.000
#> GSM49616 3 0.1092 0.764 0.020 0.000 0.960 0.000 0.020 0.000
#> GSM49617 3 0.1232 0.756 0.016 0.004 0.956 0.000 0.024 0.000
#> GSM49564 3 0.3273 0.616 0.212 0.000 0.776 0.000 0.008 0.004
#> GSM49565 1 0.3522 0.764 0.784 0.000 0.000 0.000 0.172 0.044
#> GSM49566 1 0.4941 0.734 0.720 0.000 0.116 0.000 0.112 0.052
#> GSM49567 1 0.2605 0.808 0.864 0.000 0.000 0.000 0.108 0.028
#> GSM49568 1 0.2136 0.824 0.908 0.000 0.016 0.000 0.064 0.012
#> GSM49569 1 0.4306 0.665 0.700 0.000 0.248 0.000 0.044 0.008
#> GSM49570 4 0.1542 0.621 0.000 0.008 0.000 0.936 0.004 0.052
#> GSM49571 4 0.3929 0.496 0.000 0.028 0.000 0.700 0.272 0.000
#> GSM49572 1 0.3860 0.755 0.764 0.000 0.000 0.000 0.164 0.072
#> GSM49573 4 0.0405 0.641 0.000 0.004 0.000 0.988 0.000 0.008
#> GSM49574 1 0.0922 0.823 0.968 0.000 0.004 0.000 0.024 0.004
#> GSM49575 1 0.6062 0.246 0.536 0.000 0.004 0.320 0.092 0.048
#> GSM49576 1 0.4566 0.440 0.596 0.000 0.364 0.000 0.036 0.004
#> GSM49577 1 0.4902 0.689 0.708 0.012 0.008 0.000 0.144 0.128
#> GSM49578 1 0.2063 0.822 0.912 0.000 0.020 0.000 0.060 0.008
#> GSM49579 1 0.2771 0.811 0.852 0.000 0.032 0.000 0.116 0.000
#> GSM49580 1 0.1873 0.827 0.924 0.000 0.008 0.000 0.048 0.020
#> GSM49581 1 0.2901 0.808 0.868 0.000 0.004 0.012 0.080 0.036
#> GSM49582 1 0.0891 0.826 0.968 0.000 0.008 0.000 0.024 0.000
#> GSM49583 6 0.4506 0.470 0.000 0.348 0.000 0.000 0.044 0.608
#> GSM49584 1 0.4576 0.763 0.752 0.000 0.092 0.000 0.108 0.048
#> GSM49585 1 0.3759 0.779 0.792 0.012 0.024 0.000 0.160 0.012
#> GSM49586 5 0.7081 0.000 0.132 0.128 0.008 0.252 0.480 0.000
#> GSM49587 1 0.3123 0.808 0.852 0.000 0.024 0.000 0.088 0.036
#> GSM49588 1 0.2249 0.824 0.900 0.000 0.032 0.000 0.064 0.004
#> GSM49589 3 0.2889 0.730 0.116 0.000 0.852 0.000 0.020 0.012
#> GSM49590 3 0.4777 0.157 0.416 0.000 0.540 0.000 0.036 0.008
#> GSM49591 1 0.1644 0.822 0.920 0.000 0.004 0.000 0.076 0.000
#> GSM49592 1 0.2958 0.815 0.852 0.000 0.028 0.000 0.108 0.012
#> GSM49593 1 0.3031 0.808 0.852 0.000 0.016 0.000 0.100 0.032
#> GSM49594 1 0.3629 0.783 0.816 0.000 0.012 0.004 0.108 0.060
#> GSM49595 1 0.2554 0.810 0.880 0.000 0.020 0.000 0.088 0.012
#> GSM49596 1 0.0951 0.826 0.968 0.000 0.004 0.000 0.020 0.008
#> GSM49597 6 0.2773 0.607 0.000 0.164 0.000 0.004 0.004 0.828
#> GSM49598 1 0.4005 0.775 0.796 0.000 0.028 0.012 0.128 0.036
#> GSM49599 1 0.4583 0.715 0.716 0.008 0.008 0.000 0.068 0.200
#> GSM49600 1 0.3409 0.814 0.840 0.000 0.060 0.000 0.064 0.036
#> GSM49601 1 0.5232 0.568 0.636 0.052 0.036 0.000 0.272 0.004
#> GSM49602 1 0.3718 0.774 0.804 0.000 0.052 0.000 0.124 0.020
#> GSM49603 1 0.4128 0.753 0.768 0.000 0.064 0.000 0.148 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) cell.type(p) k
#> ATC:NMF 54 5.97e-07 6.72e-04 2
#> ATC:NMF 54 1.50e-07 3.78e-04 3
#> ATC:NMF 51 1.17e-06 1.72e-09 4
#> ATC:NMF 48 1.19e-05 2.48e-07 5
#> ATC:NMF 43 5.46e-07 5.54e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
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