Date: 2019-12-25 20:17:16 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 21163 rows and 57 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] 21163 57
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| SD:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| SD:skmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| SD:NMF | 2 | 1.000 | 0.998 | 0.999 | ** | |
| CV:kmeans | 2 | 1.000 | 0.987 | 0.994 | ** | |
| CV:NMF | 2 | 1.000 | 0.982 | 0.992 | ** | |
| MAD:hclust | 2 | 1.000 | 0.988 | 0.991 | ** | |
| MAD:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| MAD:skmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| MAD:NMF | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:skmeans | 4 | 1.000 | 0.999 | 0.998 | ** | 2,3 |
| ATC:NMF | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:hclust | 4 | 0.966 | 0.976 | 0.983 | ** | 2,3 |
| SD:pam | 2 | 0.961 | 0.954 | 0.978 | ** | |
| ATC:mclust | 6 | 0.941 | 0.862 | 0.922 | * | 4,5 |
| ATC:pam | 6 | 0.928 | 0.893 | 0.910 | * | 2,3,4,5 |
| MAD:pam | 2 | 0.927 | 0.965 | 0.981 | * | |
| SD:hclust | 2 | 0.878 | 0.955 | 0.956 | ||
| CV:mclust | 2 | 0.857 | 0.852 | 0.942 | ||
| SD:mclust | 2 | 0.829 | 0.904 | 0.956 | ||
| CV:skmeans | 2 | 0.818 | 0.948 | 0.957 | ||
| MAD:mclust | 2 | 0.781 | 0.895 | 0.950 | ||
| CV:pam | 2 | 0.384 | 0.872 | 0.892 | ||
| CV:hclust | 2 | 0.284 | 0.906 | 0.848 |
**: 1-PAC > 0.95, *: 1-PAC > 0.9
Cumulative distribution function curves of consensus matrix for all methods.
collect_plots(res_list, fun = plot_ecdf)
Consensus heatmaps for all methods. (What is a consensus heatmap?)
collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = consensus_heatmap, mc.cores = 4)
Membership heatmaps for all methods. (What is a membership heatmap?)
collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = membership_heatmap, mc.cores = 4)
Signature heatmaps for all methods. (What is a signature heatmap?)
Note in following heatmaps, rows are scaled.
collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 3, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 4, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 5, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 6, fun = get_signatures, mc.cores = 4)
The statistics used for measuring the stability of consensus partitioning. (How are they defined?)
get_stats(res_list, k = 2)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 2 1.000 0.998 0.999 0.509 0.491 0.491
#> CV:NMF 2 1.000 0.982 0.992 0.508 0.491 0.491
#> MAD:NMF 2 1.000 1.000 1.000 0.509 0.491 0.491
#> ATC:NMF 2 1.000 1.000 1.000 0.509 0.491 0.491
#> SD:skmeans 2 1.000 1.000 1.000 0.509 0.491 0.491
#> CV:skmeans 2 0.818 0.948 0.957 0.509 0.491 0.491
#> MAD:skmeans 2 1.000 1.000 1.000 0.509 0.491 0.491
#> ATC:skmeans 2 1.000 1.000 1.000 0.509 0.491 0.491
#> SD:mclust 2 0.829 0.904 0.956 0.480 0.526 0.526
#> CV:mclust 2 0.857 0.852 0.942 0.489 0.504 0.504
#> MAD:mclust 2 0.781 0.895 0.950 0.495 0.491 0.491
#> ATC:mclust 2 0.781 0.903 0.953 0.496 0.491 0.491
#> SD:kmeans 2 1.000 1.000 1.000 0.509 0.491 0.491
#> CV:kmeans 2 1.000 0.987 0.994 0.509 0.491 0.491
#> MAD:kmeans 2 1.000 1.000 1.000 0.509 0.491 0.491
#> ATC:kmeans 2 1.000 1.000 1.000 0.509 0.491 0.491
#> SD:pam 2 0.961 0.954 0.978 0.509 0.492 0.492
#> CV:pam 2 0.384 0.872 0.892 0.504 0.491 0.491
#> MAD:pam 2 0.927 0.965 0.981 0.507 0.491 0.491
#> ATC:pam 2 1.000 1.000 1.000 0.509 0.491 0.491
#> SD:hclust 2 0.878 0.955 0.956 0.491 0.491 0.491
#> CV:hclust 2 0.284 0.906 0.848 0.428 0.491 0.491
#> MAD:hclust 2 1.000 0.988 0.991 0.507 0.491 0.491
#> ATC:hclust 2 1.000 1.000 1.000 0.509 0.491 0.491
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.676 0.863 0.829 0.196 1.000 1.000
#> CV:NMF 3 0.618 0.857 0.829 0.211 1.000 1.000
#> MAD:NMF 3 0.686 0.865 0.851 0.199 1.000 1.000
#> ATC:NMF 3 0.767 0.801 0.885 0.216 0.857 0.716
#> SD:skmeans 3 0.628 0.656 0.799 0.262 0.881 0.758
#> CV:skmeans 3 0.333 0.457 0.688 0.296 0.925 0.847
#> MAD:skmeans 3 0.644 0.654 0.772 0.253 0.887 0.770
#> ATC:skmeans 3 1.000 0.998 0.997 0.163 0.917 0.832
#> SD:mclust 3 0.604 0.719 0.817 0.315 0.820 0.657
#> CV:mclust 3 0.616 0.874 0.854 0.253 0.880 0.766
#> MAD:mclust 3 0.642 0.895 0.866 0.248 0.908 0.812
#> ATC:mclust 3 0.647 0.713 0.826 0.258 0.756 0.543
#> SD:kmeans 3 0.723 0.742 0.843 0.222 0.895 0.786
#> CV:kmeans 3 0.656 0.571 0.805 0.220 0.966 0.931
#> MAD:kmeans 3 0.729 0.635 0.772 0.220 0.887 0.770
#> ATC:kmeans 3 0.760 0.822 0.833 0.207 1.000 1.000
#> SD:pam 3 0.573 0.720 0.801 0.208 0.982 0.963
#> CV:pam 3 0.329 0.488 0.700 0.262 0.918 0.834
#> MAD:pam 3 0.602 0.890 0.812 0.197 1.000 1.000
#> ATC:pam 3 1.000 0.988 0.995 0.167 0.917 0.832
#> SD:hclust 3 0.819 0.861 0.923 0.170 0.966 0.931
#> CV:hclust 3 0.368 0.799 0.843 0.269 0.982 0.964
#> MAD:hclust 3 0.811 0.869 0.910 0.130 0.982 0.964
#> ATC:hclust 3 0.911 0.987 0.972 0.144 0.917 0.832
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.623 0.686 0.815 0.1497 0.798 0.588
#> CV:NMF 4 0.539 0.519 0.732 0.1376 0.827 0.648
#> MAD:NMF 4 0.557 0.756 0.796 0.1485 0.784 0.560
#> ATC:NMF 4 0.842 0.897 0.885 0.1289 0.871 0.666
#> SD:skmeans 4 0.493 0.576 0.730 0.1454 0.845 0.610
#> CV:skmeans 4 0.391 0.367 0.610 0.1289 0.811 0.569
#> MAD:skmeans 4 0.507 0.602 0.727 0.1554 0.833 0.589
#> ATC:skmeans 4 1.000 0.999 0.998 0.2187 0.870 0.681
#> SD:mclust 4 0.702 0.775 0.855 0.1207 0.908 0.742
#> CV:mclust 4 0.623 0.687 0.795 0.1324 0.895 0.736
#> MAD:mclust 4 0.819 0.842 0.900 0.1531 0.872 0.680
#> ATC:mclust 4 0.955 0.853 0.939 0.1752 0.854 0.605
#> SD:kmeans 4 0.724 0.819 0.837 0.1276 0.859 0.648
#> CV:kmeans 4 0.644 0.663 0.760 0.1202 0.776 0.529
#> MAD:kmeans 4 0.702 0.800 0.818 0.1214 0.803 0.534
#> ATC:kmeans 4 0.678 0.906 0.835 0.1238 0.778 0.547
#> SD:pam 4 0.501 0.239 0.681 0.1069 0.896 0.781
#> CV:pam 4 0.390 0.257 0.590 0.1041 0.796 0.551
#> MAD:pam 4 0.517 0.515 0.754 0.0994 0.900 0.796
#> ATC:pam 4 1.000 0.979 0.991 0.2194 0.870 0.681
#> SD:hclust 4 0.801 0.785 0.884 0.1130 0.912 0.808
#> CV:hclust 4 0.511 0.548 0.808 0.1189 0.983 0.964
#> MAD:hclust 4 0.769 0.788 0.856 0.1281 0.883 0.753
#> ATC:hclust 4 0.966 0.976 0.983 0.0784 0.966 0.917
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.597 0.656 0.801 0.0727 0.960 0.864
#> CV:NMF 5 0.488 0.554 0.675 0.0759 0.848 0.590
#> MAD:NMF 5 0.564 0.743 0.789 0.0772 0.982 0.938
#> ATC:NMF 5 0.780 0.840 0.875 0.0544 0.971 0.893
#> SD:skmeans 5 0.498 0.548 0.652 0.0683 0.982 0.937
#> CV:skmeans 5 0.435 0.300 0.530 0.0709 0.920 0.740
#> MAD:skmeans 5 0.508 0.537 0.633 0.0712 0.982 0.937
#> ATC:skmeans 5 0.953 0.908 0.902 0.0359 1.000 1.000
#> SD:mclust 5 0.807 0.790 0.859 0.0694 0.964 0.869
#> CV:mclust 5 0.635 0.621 0.750 0.0725 0.982 0.941
#> MAD:mclust 5 0.832 0.786 0.824 0.0630 1.000 1.000
#> ATC:mclust 5 0.935 0.925 0.914 0.0366 0.945 0.800
#> SD:kmeans 5 0.676 0.784 0.837 0.0704 0.972 0.897
#> CV:kmeans 5 0.630 0.723 0.790 0.0773 0.926 0.745
#> MAD:kmeans 5 0.621 0.764 0.811 0.0818 0.958 0.850
#> ATC:kmeans 5 0.632 0.832 0.789 0.0705 1.000 1.000
#> SD:pam 5 0.489 0.318 0.641 0.0354 0.892 0.732
#> CV:pam 5 0.405 0.163 0.533 0.0388 0.862 0.615
#> MAD:pam 5 0.531 0.516 0.713 0.0363 0.981 0.951
#> ATC:pam 5 0.959 0.949 0.969 0.0275 0.982 0.937
#> SD:hclust 5 0.739 0.774 0.849 0.0606 0.964 0.904
#> CV:hclust 5 0.607 0.633 0.784 0.0708 0.897 0.777
#> MAD:hclust 5 0.700 0.725 0.830 0.0568 0.974 0.926
#> ATC:hclust 5 0.855 0.890 0.928 0.0898 0.969 0.916
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.582 0.633 0.761 0.0424 0.982 0.931
#> CV:NMF 6 0.521 0.493 0.651 0.0498 0.927 0.745
#> MAD:NMF 6 0.621 0.627 0.739 0.0435 0.993 0.975
#> ATC:NMF 6 0.824 0.808 0.848 0.0341 0.984 0.937
#> SD:skmeans 6 0.518 0.371 0.585 0.0456 0.974 0.907
#> CV:skmeans 6 0.472 0.161 0.472 0.0444 0.891 0.614
#> MAD:skmeans 6 0.512 0.500 0.583 0.0419 0.951 0.833
#> ATC:skmeans 6 0.870 0.832 0.863 0.0316 0.947 0.809
#> SD:mclust 6 0.805 0.764 0.852 0.0388 0.966 0.860
#> CV:mclust 6 0.632 0.578 0.723 0.0506 0.895 0.673
#> MAD:mclust 6 0.777 0.755 0.822 0.0411 0.935 0.765
#> ATC:mclust 6 0.941 0.862 0.922 0.0318 0.972 0.884
#> SD:kmeans 6 0.730 0.771 0.808 0.0440 0.959 0.837
#> CV:kmeans 6 0.636 0.709 0.774 0.0451 0.977 0.908
#> MAD:kmeans 6 0.672 0.753 0.789 0.0436 0.980 0.920
#> ATC:kmeans 6 0.663 0.809 0.787 0.0578 0.961 0.853
#> SD:pam 6 0.520 0.331 0.665 0.0225 0.904 0.739
#> CV:pam 6 0.420 0.157 0.541 0.0229 0.811 0.487
#> MAD:pam 6 0.516 0.506 0.703 0.0228 0.997 0.992
#> ATC:pam 6 0.928 0.893 0.910 0.0339 0.962 0.856
#> SD:hclust 6 0.719 0.636 0.841 0.0381 0.981 0.943
#> CV:hclust 6 0.645 0.620 0.783 0.0562 0.997 0.991
#> MAD:hclust 6 0.708 0.662 0.802 0.0408 0.992 0.975
#> ATC:hclust 6 0.858 0.892 0.912 0.0731 0.929 0.792
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n agent(p) dose(p) time(p) k
#> SD:NMF 57 2.57e-12 1.000 1.000 2
#> CV:NMF 57 2.57e-12 1.000 1.000 2
#> MAD:NMF 57 2.57e-12 1.000 1.000 2
#> ATC:NMF 57 2.57e-12 1.000 1.000 2
#> SD:skmeans 57 2.57e-12 1.000 1.000 2
#> CV:skmeans 57 2.57e-12 1.000 1.000 2
#> MAD:skmeans 57 2.57e-12 1.000 1.000 2
#> ATC:skmeans 57 2.57e-12 1.000 1.000 2
#> SD:mclust 56 7.87e-08 0.022 0.991 2
#> CV:mclust 51 8.42e-12 0.328 0.996 2
#> MAD:mclust 51 8.42e-12 0.328 0.996 2
#> ATC:mclust 57 2.57e-12 1.000 1.000 2
#> SD:kmeans 57 2.57e-12 1.000 1.000 2
#> CV:kmeans 57 2.57e-12 1.000 1.000 2
#> MAD:kmeans 57 2.57e-12 1.000 1.000 2
#> ATC:kmeans 57 2.57e-12 1.000 1.000 2
#> SD:pam 56 4.20e-12 0.992 1.000 2
#> CV:pam 55 6.87e-12 0.999 1.000 2
#> MAD:pam 57 2.57e-12 1.000 1.000 2
#> ATC:pam 57 2.57e-12 1.000 1.000 2
#> SD:hclust 57 2.57e-12 1.000 1.000 2
#> CV:hclust 57 2.57e-12 1.000 1.000 2
#> MAD:hclust 57 2.57e-12 1.000 1.000 2
#> ATC:hclust 57 2.57e-12 1.000 1.000 2
test_to_known_factors(res_list, k = 3)
#> n agent(p) dose(p) time(p) k
#> SD:NMF 57 2.57e-12 1.00e+00 1.0000 3
#> CV:NMF 57 2.57e-12 1.00e+00 1.0000 3
#> MAD:NMF 57 2.57e-12 1.00e+00 1.0000 3
#> ATC:NMF 52 5.11e-12 6.58e-03 0.9939 3
#> SD:skmeans 42 3.56e-08 1.94e-02 0.4836 3
#> CV:skmeans 25 NA NA NA 3
#> MAD:skmeans 45 1.10e-08 2.16e-02 0.6260 3
#> ATC:skmeans 57 4.87e-12 4.14e-03 0.9705 3
#> SD:mclust 53 1.19e-07 1.80e-04 0.9936 3
#> CV:mclust 57 9.44e-12 6.66e-04 0.9951 3
#> MAD:mclust 57 9.44e-12 6.66e-04 0.9951 3
#> ATC:mclust 45 1.69e-10 8.25e-05 0.9975 3
#> SD:kmeans 50 2.51e-09 5.88e-03 0.9291 3
#> CV:kmeans 30 1.38e-06 9.52e-02 0.2451 3
#> MAD:kmeans 48 2.84e-09 2.43e-02 0.6957 3
#> ATC:kmeans 57 2.57e-12 1.00e+00 1.0000 3
#> SD:pam 54 1.12e-11 9.97e-01 0.9991 3
#> CV:pam 27 NA NA NA 3
#> MAD:pam 57 2.57e-12 1.00e+00 1.0000 3
#> ATC:pam 57 4.87e-12 4.14e-03 0.9705 3
#> SD:hclust 53 1.40e-20 8.01e-04 0.0126 3
#> CV:hclust 54 1.88e-12 8.85e-01 0.9869 3
#> MAD:hclust 55 1.14e-12 8.89e-01 0.9893 3
#> ATC:hclust 57 4.87e-12 4.14e-03 0.9705 3
test_to_known_factors(res_list, k = 4)
#> n agent(p) dose(p) time(p) k
#> SD:NMF 51 8.66e-10 2.86e-04 0.6291 4
#> CV:NMF 33 1.61e-08 2.96e-04 0.3345 4
#> MAD:NMF 52 1.54e-09 9.08e-06 0.9584 4
#> ATC:NMF 56 8.31e-12 2.93e-06 0.9729 4
#> SD:skmeans 43 3.68e-08 5.48e-05 0.6283 4
#> CV:skmeans 17 NA 7.07e-04 0.5492 4
#> MAD:skmeans 47 8.52e-09 1.00e-05 0.9038 4
#> ATC:skmeans 57 7.72e-11 3.16e-06 0.9969 4
#> SD:mclust 51 3.39e-09 7.11e-07 0.9787 4
#> CV:mclust 45 4.70e-09 2.30e-04 0.4343 4
#> MAD:mclust 55 4.28e-10 1.32e-05 0.9613 4
#> ATC:mclust 50 3.58e-10 3.73e-07 0.9867 4
#> SD:kmeans 53 1.02e-09 5.55e-07 0.9970 4
#> CV:kmeans 40 6.03e-08 9.60e-05 0.7788 4
#> MAD:kmeans 53 1.02e-09 2.17e-06 0.9822 4
#> ATC:kmeans 57 1.45e-10 4.71e-07 0.9996 4
#> SD:pam 13 4.74e-03 3.68e-02 0.4612 4
#> CV:pam 4 NA NA NA 4
#> MAD:pam 29 9.42e-03 4.37e-01 0.5475 4
#> ATC:pam 57 7.72e-11 3.16e-06 0.9969 4
#> SD:hclust 50 1.57e-17 2.61e-04 0.0207 4
#> CV:hclust 30 8.08e-06 8.33e-02 0.7660 4
#> MAD:hclust 52 1.38e-10 2.50e-02 0.9852 4
#> ATC:hclust 57 5.82e-16 1.61e-04 0.3494 4
test_to_known_factors(res_list, k = 5)
#> n agent(p) dose(p) time(p) k
#> SD:NMF 47 1.41e-08 1.98e-05 0.821 5
#> CV:NMF 32 1.13e-07 1.73e-04 0.885 5
#> MAD:NMF 52 1.76e-09 4.20e-05 0.925 5
#> ATC:NMF 55 8.11e-14 2.26e-08 0.741 5
#> SD:skmeans 41 7.87e-08 8.83e-05 0.537 5
#> CV:skmeans 4 NA NA NA 5
#> MAD:skmeans 41 3.71e-08 2.25e-05 0.905 5
#> ATC:skmeans 57 7.72e-11 3.16e-06 0.997 5
#> SD:mclust 53 7.70e-10 1.19e-06 0.789 5
#> CV:mclust 36 4.56e-07 2.23e-04 0.712 5
#> MAD:mclust 51 2.29e-09 1.36e-05 0.947 5
#> ATC:mclust 56 3.68e-09 3.52e-06 0.857 5
#> SD:kmeans 51 2.09e-09 3.52e-06 0.733 5
#> CV:kmeans 50 1.59e-09 1.49e-06 0.735 5
#> MAD:kmeans 50 3.44e-09 1.37e-05 0.701 5
#> ATC:kmeans 57 1.45e-10 4.71e-07 1.000 5
#> SD:pam 18 NA NA NA 5
#> CV:pam 0 NA NA NA 5
#> MAD:pam 33 4.03e-07 2.07e-01 0.682 5
#> ATC:pam 57 1.83e-14 5.10e-08 0.726 5
#> SD:hclust 53 1.17e-09 2.75e-01 0.207 5
#> CV:hclust 39 3.40e-09 9.31e-02 0.425 5
#> MAD:hclust 49 7.46e-09 4.19e-03 0.939 5
#> ATC:hclust 57 1.83e-14 1.74e-04 0.419 5
test_to_known_factors(res_list, k = 6)
#> n agent(p) dose(p) time(p) k
#> SD:NMF 43 8.43e-09 6.35e-05 0.4343 6
#> CV:NMF 28 8.32e-07 1.21e-03 0.7261 6
#> MAD:NMF 45 4.58e-08 1.31e-05 0.9000 6
#> ATC:NMF 54 3.03e-13 3.63e-08 0.7222 6
#> SD:skmeans 29 1.27e-06 1.52e-04 0.8408 6
#> CV:skmeans 0 NA NA NA 6
#> MAD:skmeans 38 1.66e-07 6.93e-05 0.8472 6
#> ATC:skmeans 55 8.21e-09 2.37e-05 0.8786 6
#> SD:mclust 52 4.08e-08 3.25e-05 0.5341 6
#> CV:mclust 36 1.52e-07 5.42e-04 0.6576 6
#> MAD:mclust 51 1.15e-08 3.16e-06 0.8629 6
#> ATC:mclust 52 2.28e-11 1.37e-06 0.3975 6
#> SD:kmeans 49 1.12e-11 3.03e-07 0.6142 6
#> CV:kmeans 52 1.52e-09 3.63e-06 0.7128 6
#> MAD:kmeans 49 5.66e-09 5.01e-06 0.8834 6
#> ATC:kmeans 57 3.60e-10 2.04e-06 0.9425 6
#> SD:pam 17 4.02e-04 2.45e-01 0.0896 6
#> CV:pam 0 NA NA NA 6
#> MAD:pam 31 1.85e-06 6.27e-01 0.5569 6
#> ATC:pam 56 7.77e-13 5.69e-09 0.8013 6
#> SD:hclust 45 9.25e-10 7.75e-03 0.5577 6
#> CV:hclust 43 4.60e-10 9.03e-03 0.8700 6
#> MAD:hclust 44 1.51e-09 3.06e-03 0.8543 6
#> ATC:hclust 57 3.81e-13 1.74e-04 0.3249 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 21163 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.878 0.955 0.956 0.4907 0.491 0.491
#> 3 3 0.819 0.861 0.923 0.1702 0.966 0.931
#> 4 4 0.801 0.785 0.884 0.1130 0.912 0.808
#> 5 5 0.739 0.774 0.849 0.0606 0.964 0.904
#> 6 6 0.719 0.636 0.841 0.0381 0.981 0.943
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM148516 2 0.0000 0.998 0.000 1.000
#> GSM148517 1 0.9323 0.538 0.652 0.348
#> GSM148518 2 0.0000 0.998 0.000 1.000
#> GSM148519 2 0.0000 0.998 0.000 1.000
#> GSM148520 2 0.0000 0.998 0.000 1.000
#> GSM148521 2 0.0000 0.998 0.000 1.000
#> GSM148522 2 0.0000 0.998 0.000 1.000
#> GSM148523 2 0.0000 0.998 0.000 1.000
#> GSM148524 2 0.0000 0.998 0.000 1.000
#> GSM148525 2 0.0000 0.998 0.000 1.000
#> GSM148526 2 0.0000 0.998 0.000 1.000
#> GSM148527 2 0.0000 0.998 0.000 1.000
#> GSM148528 2 0.0000 0.998 0.000 1.000
#> GSM148529 2 0.0000 0.998 0.000 1.000
#> GSM148530 2 0.0000 0.998 0.000 1.000
#> GSM148531 2 0.0000 0.998 0.000 1.000
#> GSM148532 2 0.0000 0.998 0.000 1.000
#> GSM148533 2 0.0000 0.998 0.000 1.000
#> GSM148534 2 0.0000 0.998 0.000 1.000
#> GSM148535 2 0.0000 0.998 0.000 1.000
#> GSM148536 2 0.0000 0.998 0.000 1.000
#> GSM148537 2 0.0000 0.998 0.000 1.000
#> GSM148538 2 0.0000 0.998 0.000 1.000
#> GSM148539 2 0.0376 0.994 0.004 0.996
#> GSM148540 2 0.0000 0.998 0.000 1.000
#> GSM148541 2 0.0000 0.998 0.000 1.000
#> GSM148542 2 0.0672 0.990 0.008 0.992
#> GSM148543 2 0.0000 0.998 0.000 1.000
#> GSM148544 2 0.2236 0.959 0.036 0.964
#> GSM148545 1 0.8016 0.763 0.756 0.244
#> GSM148546 1 0.4562 0.941 0.904 0.096
#> GSM148547 1 0.4298 0.944 0.912 0.088
#> GSM148548 1 0.4562 0.941 0.904 0.096
#> GSM148549 1 0.4562 0.941 0.904 0.096
#> GSM148550 1 0.3114 0.945 0.944 0.056
#> GSM148551 1 0.3114 0.945 0.944 0.056
#> GSM148552 1 0.5629 0.920 0.868 0.132
#> GSM148553 1 0.5294 0.928 0.880 0.120
#> GSM148554 1 0.3879 0.946 0.924 0.076
#> GSM148555 1 0.4298 0.944 0.912 0.088
#> GSM148556 1 0.3114 0.944 0.944 0.056
#> GSM148557 1 0.3431 0.945 0.936 0.064
#> GSM148558 1 0.2043 0.938 0.968 0.032
#> GSM148559 1 0.5294 0.920 0.880 0.120
#> GSM148560 1 0.5737 0.907 0.864 0.136
#> GSM148561 1 0.4298 0.938 0.912 0.088
#> GSM148562 1 0.3584 0.946 0.932 0.068
#> GSM148563 1 0.2043 0.938 0.968 0.032
#> GSM148564 1 0.1414 0.932 0.980 0.020
#> GSM148565 1 0.0376 0.922 0.996 0.004
#> GSM148566 1 0.5519 0.915 0.872 0.128
#> GSM148567 1 0.3584 0.945 0.932 0.068
#> GSM148568 1 0.3431 0.945 0.936 0.064
#> GSM148569 1 0.3114 0.945 0.944 0.056
#> GSM148570 1 0.0938 0.928 0.988 0.012
#> GSM148571 1 0.0938 0.928 0.988 0.012
#> GSM148572 1 0.0000 0.920 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM148516 2 0.0592 0.988 0.000 0.988 0.012
#> GSM148517 3 0.2878 0.609 0.096 0.000 0.904
#> GSM148518 2 0.0000 0.996 0.000 1.000 0.000
#> GSM148519 2 0.0000 0.996 0.000 1.000 0.000
#> GSM148520 2 0.0237 0.994 0.004 0.996 0.000
#> GSM148521 2 0.0237 0.994 0.004 0.996 0.000
#> GSM148522 2 0.0000 0.996 0.000 1.000 0.000
#> GSM148523 2 0.0000 0.996 0.000 1.000 0.000
#> GSM148524 2 0.0000 0.996 0.000 1.000 0.000
#> GSM148525 2 0.0000 0.996 0.000 1.000 0.000
#> GSM148526 2 0.0000 0.996 0.000 1.000 0.000
#> GSM148527 2 0.0000 0.996 0.000 1.000 0.000
#> GSM148528 2 0.0000 0.996 0.000 1.000 0.000
#> GSM148529 2 0.0000 0.996 0.000 1.000 0.000
#> GSM148530 2 0.0000 0.996 0.000 1.000 0.000
#> GSM148531 2 0.0000 0.996 0.000 1.000 0.000
#> GSM148532 2 0.0000 0.996 0.000 1.000 0.000
#> GSM148533 2 0.0000 0.996 0.000 1.000 0.000
#> GSM148534 2 0.0000 0.996 0.000 1.000 0.000
#> GSM148535 2 0.0000 0.996 0.000 1.000 0.000
#> GSM148536 2 0.0000 0.996 0.000 1.000 0.000
#> GSM148537 2 0.0000 0.996 0.000 1.000 0.000
#> GSM148538 2 0.0237 0.994 0.004 0.996 0.000
#> GSM148539 2 0.0237 0.994 0.000 0.996 0.004
#> GSM148540 2 0.0000 0.996 0.000 1.000 0.000
#> GSM148541 2 0.0237 0.993 0.004 0.996 0.000
#> GSM148542 2 0.1182 0.975 0.012 0.976 0.012
#> GSM148543 2 0.0000 0.996 0.000 1.000 0.000
#> GSM148544 2 0.1411 0.955 0.036 0.964 0.000
#> GSM148545 3 0.6045 0.404 0.380 0.000 0.620
#> GSM148546 1 0.3539 0.794 0.888 0.012 0.100
#> GSM148547 1 0.3896 0.781 0.864 0.008 0.128
#> GSM148548 1 0.2446 0.822 0.936 0.012 0.052
#> GSM148549 1 0.2492 0.823 0.936 0.016 0.048
#> GSM148550 1 0.2063 0.831 0.948 0.008 0.044
#> GSM148551 1 0.2063 0.831 0.948 0.008 0.044
#> GSM148552 1 0.4862 0.741 0.820 0.020 0.160
#> GSM148553 1 0.4539 0.754 0.836 0.016 0.148
#> GSM148554 1 0.1950 0.828 0.952 0.008 0.040
#> GSM148555 1 0.2339 0.825 0.940 0.012 0.048
#> GSM148556 1 0.1950 0.830 0.952 0.008 0.040
#> GSM148557 1 0.1711 0.831 0.960 0.008 0.032
#> GSM148558 1 0.3619 0.800 0.864 0.000 0.136
#> GSM148559 1 0.6298 0.272 0.608 0.004 0.388
#> GSM148560 1 0.6451 0.281 0.608 0.008 0.384
#> GSM148561 1 0.3141 0.820 0.912 0.020 0.068
#> GSM148562 1 0.2173 0.830 0.944 0.008 0.048
#> GSM148563 1 0.3851 0.808 0.860 0.004 0.136
#> GSM148564 1 0.4110 0.792 0.844 0.004 0.152
#> GSM148565 1 0.4291 0.767 0.820 0.000 0.180
#> GSM148566 1 0.6057 0.411 0.656 0.004 0.340
#> GSM148567 1 0.4164 0.818 0.848 0.008 0.144
#> GSM148568 1 0.3896 0.818 0.864 0.008 0.128
#> GSM148569 1 0.3532 0.828 0.884 0.008 0.108
#> GSM148570 1 0.3941 0.787 0.844 0.000 0.156
#> GSM148571 1 0.4062 0.782 0.836 0.000 0.164
#> GSM148572 1 0.4291 0.767 0.820 0.000 0.180
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM148516 2 0.1584 0.9569 0.000 0.952 0.012 0.036
#> GSM148517 3 0.2281 0.5418 0.096 0.000 0.904 0.000
#> GSM148518 2 0.0000 0.9930 0.000 1.000 0.000 0.000
#> GSM148519 2 0.0000 0.9930 0.000 1.000 0.000 0.000
#> GSM148520 2 0.0188 0.9910 0.004 0.996 0.000 0.000
#> GSM148521 2 0.0188 0.9910 0.004 0.996 0.000 0.000
#> GSM148522 2 0.0000 0.9930 0.000 1.000 0.000 0.000
#> GSM148523 2 0.0000 0.9930 0.000 1.000 0.000 0.000
#> GSM148524 2 0.0000 0.9930 0.000 1.000 0.000 0.000
#> GSM148525 2 0.0000 0.9930 0.000 1.000 0.000 0.000
#> GSM148526 2 0.0188 0.9913 0.000 0.996 0.000 0.004
#> GSM148527 2 0.0000 0.9930 0.000 1.000 0.000 0.000
#> GSM148528 2 0.0000 0.9930 0.000 1.000 0.000 0.000
#> GSM148529 2 0.0000 0.9930 0.000 1.000 0.000 0.000
#> GSM148530 2 0.0000 0.9930 0.000 1.000 0.000 0.000
#> GSM148531 2 0.0000 0.9930 0.000 1.000 0.000 0.000
#> GSM148532 2 0.0000 0.9930 0.000 1.000 0.000 0.000
#> GSM148533 2 0.0000 0.9930 0.000 1.000 0.000 0.000
#> GSM148534 2 0.0000 0.9930 0.000 1.000 0.000 0.000
#> GSM148535 2 0.0000 0.9930 0.000 1.000 0.000 0.000
#> GSM148536 2 0.0000 0.9930 0.000 1.000 0.000 0.000
#> GSM148537 2 0.0000 0.9930 0.000 1.000 0.000 0.000
#> GSM148538 2 0.0188 0.9910 0.004 0.996 0.000 0.000
#> GSM148539 2 0.0524 0.9868 0.000 0.988 0.004 0.008
#> GSM148540 2 0.0188 0.9912 0.000 0.996 0.000 0.004
#> GSM148541 2 0.0844 0.9813 0.004 0.980 0.004 0.012
#> GSM148542 2 0.1884 0.9510 0.020 0.948 0.016 0.016
#> GSM148543 2 0.0188 0.9913 0.000 0.996 0.004 0.000
#> GSM148544 2 0.1388 0.9585 0.028 0.960 0.000 0.012
#> GSM148545 3 0.5112 0.3689 0.384 0.000 0.608 0.008
#> GSM148546 1 0.2088 0.7200 0.928 0.004 0.064 0.004
#> GSM148547 1 0.2334 0.7078 0.908 0.004 0.088 0.000
#> GSM148548 1 0.1369 0.7364 0.964 0.004 0.016 0.016
#> GSM148549 1 0.2039 0.7400 0.940 0.008 0.016 0.036
#> GSM148550 1 0.3043 0.7085 0.876 0.004 0.008 0.112
#> GSM148551 1 0.3730 0.6765 0.836 0.004 0.016 0.144
#> GSM148552 1 0.3128 0.6701 0.864 0.004 0.128 0.004
#> GSM148553 1 0.2839 0.6845 0.884 0.004 0.108 0.004
#> GSM148554 1 0.2570 0.7413 0.916 0.004 0.028 0.052
#> GSM148555 1 0.1920 0.7384 0.944 0.004 0.028 0.024
#> GSM148556 1 0.2983 0.7127 0.880 0.004 0.008 0.108
#> GSM148557 1 0.3172 0.7137 0.872 0.004 0.012 0.112
#> GSM148558 4 0.5476 0.5453 0.396 0.000 0.020 0.584
#> GSM148559 1 0.6374 0.0807 0.556 0.000 0.372 0.072
#> GSM148560 1 0.6277 0.1102 0.572 0.000 0.360 0.068
#> GSM148561 1 0.4477 0.6667 0.808 0.000 0.084 0.108
#> GSM148562 1 0.4532 0.6509 0.792 0.000 0.052 0.156
#> GSM148563 4 0.5452 0.6601 0.360 0.000 0.024 0.616
#> GSM148564 4 0.4933 0.7043 0.296 0.000 0.016 0.688
#> GSM148565 4 0.3695 0.7832 0.156 0.000 0.016 0.828
#> GSM148566 1 0.5847 0.2782 0.628 0.000 0.320 0.052
#> GSM148567 1 0.5990 0.2797 0.608 0.000 0.056 0.336
#> GSM148568 1 0.6180 0.2598 0.600 0.004 0.056 0.340
#> GSM148569 1 0.5452 0.2444 0.616 0.000 0.024 0.360
#> GSM148570 4 0.4086 0.8144 0.216 0.000 0.008 0.776
#> GSM148571 4 0.4049 0.8152 0.212 0.000 0.008 0.780
#> GSM148572 4 0.3161 0.7566 0.124 0.000 0.012 0.864
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM148516 2 0.3969 0.683 0.000 0.692 0.000 0.004 NA
#> GSM148517 3 0.5381 0.418 0.044 0.000 0.484 0.004 NA
#> GSM148518 2 0.0290 0.958 0.000 0.992 0.000 0.000 NA
#> GSM148519 2 0.0000 0.958 0.000 1.000 0.000 0.000 NA
#> GSM148520 2 0.0324 0.957 0.004 0.992 0.000 0.000 NA
#> GSM148521 2 0.0162 0.957 0.004 0.996 0.000 0.000 NA
#> GSM148522 2 0.0162 0.958 0.000 0.996 0.000 0.000 NA
#> GSM148523 2 0.0000 0.958 0.000 1.000 0.000 0.000 NA
#> GSM148524 2 0.0000 0.958 0.000 1.000 0.000 0.000 NA
#> GSM148525 2 0.0404 0.958 0.000 0.988 0.000 0.000 NA
#> GSM148526 2 0.0404 0.956 0.000 0.988 0.000 0.000 NA
#> GSM148527 2 0.0290 0.958 0.000 0.992 0.000 0.000 NA
#> GSM148528 2 0.0162 0.958 0.000 0.996 0.000 0.000 NA
#> GSM148529 2 0.0290 0.958 0.000 0.992 0.000 0.000 NA
#> GSM148530 2 0.0290 0.958 0.000 0.992 0.000 0.000 NA
#> GSM148531 2 0.0404 0.958 0.000 0.988 0.000 0.000 NA
#> GSM148532 2 0.0510 0.958 0.000 0.984 0.000 0.000 NA
#> GSM148533 2 0.0290 0.958 0.000 0.992 0.000 0.000 NA
#> GSM148534 2 0.0290 0.957 0.000 0.992 0.000 0.000 NA
#> GSM148535 2 0.0290 0.958 0.000 0.992 0.000 0.000 NA
#> GSM148536 2 0.0290 0.958 0.000 0.992 0.000 0.000 NA
#> GSM148537 2 0.0290 0.958 0.000 0.992 0.000 0.000 NA
#> GSM148538 2 0.0324 0.957 0.004 0.992 0.000 0.000 NA
#> GSM148539 2 0.1768 0.926 0.000 0.924 0.004 0.000 NA
#> GSM148540 2 0.1608 0.928 0.000 0.928 0.000 0.000 NA
#> GSM148541 2 0.3487 0.804 0.000 0.780 0.000 0.008 NA
#> GSM148542 2 0.4394 0.722 0.016 0.716 0.000 0.012 NA
#> GSM148543 2 0.2338 0.899 0.000 0.884 0.000 0.004 NA
#> GSM148544 2 0.2906 0.895 0.012 0.880 0.004 0.016 NA
#> GSM148545 3 0.6561 0.563 0.280 0.000 0.516 0.008 NA
#> GSM148546 1 0.1892 0.713 0.916 0.000 0.080 0.004 NA
#> GSM148547 1 0.2286 0.697 0.888 0.000 0.108 0.004 NA
#> GSM148548 1 0.1682 0.739 0.944 0.000 0.032 0.012 NA
#> GSM148549 1 0.2047 0.745 0.928 0.000 0.020 0.040 NA
#> GSM148550 1 0.2835 0.731 0.868 0.000 0.016 0.112 NA
#> GSM148551 1 0.3379 0.707 0.828 0.000 0.008 0.148 NA
#> GSM148552 1 0.3433 0.646 0.832 0.000 0.132 0.004 NA
#> GSM148553 1 0.3031 0.665 0.856 0.000 0.120 0.004 NA
#> GSM148554 1 0.2278 0.746 0.916 0.000 0.032 0.044 NA
#> GSM148555 1 0.2026 0.740 0.928 0.000 0.044 0.012 NA
#> GSM148556 1 0.2681 0.732 0.876 0.000 0.012 0.108 NA
#> GSM148557 1 0.3010 0.730 0.860 0.000 0.016 0.116 NA
#> GSM148558 4 0.4774 0.553 0.328 0.000 0.016 0.644 NA
#> GSM148559 3 0.4033 0.657 0.236 0.000 0.744 0.004 NA
#> GSM148560 3 0.4423 0.639 0.296 0.000 0.684 0.012 NA
#> GSM148561 1 0.5198 0.519 0.708 0.000 0.208 0.036 NA
#> GSM148562 1 0.4982 0.618 0.744 0.000 0.108 0.128 NA
#> GSM148563 4 0.5287 0.628 0.292 0.000 0.032 0.648 NA
#> GSM148564 4 0.4668 0.677 0.220 0.000 0.048 0.724 NA
#> GSM148565 4 0.2789 0.773 0.092 0.000 0.008 0.880 NA
#> GSM148566 3 0.4375 0.553 0.364 0.000 0.628 0.004 NA
#> GSM148567 1 0.6431 0.201 0.500 0.000 0.148 0.344 NA
#> GSM148568 1 0.6686 0.207 0.492 0.004 0.136 0.352 NA
#> GSM148569 1 0.6021 0.237 0.536 0.000 0.088 0.364 NA
#> GSM148570 4 0.3320 0.793 0.124 0.000 0.016 0.844 NA
#> GSM148571 4 0.3170 0.798 0.120 0.000 0.012 0.852 NA
#> GSM148572 4 0.1967 0.739 0.036 0.000 0.012 0.932 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM148516 3 0.4779 0.0000 0.000 0.468 0.488 0.000 0.004 0.040
#> GSM148517 6 0.3617 0.0000 0.020 0.000 0.000 0.000 0.244 0.736
#> GSM148518 2 0.0260 0.8870 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM148519 2 0.0000 0.8873 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM148520 2 0.0260 0.8850 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM148521 2 0.0146 0.8865 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM148522 2 0.0146 0.8877 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM148523 2 0.0000 0.8873 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM148524 2 0.0000 0.8873 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM148525 2 0.0363 0.8872 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM148526 2 0.0508 0.8797 0.000 0.984 0.012 0.000 0.004 0.000
#> GSM148527 2 0.0458 0.8837 0.000 0.984 0.016 0.000 0.000 0.000
#> GSM148528 2 0.0146 0.8876 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM148529 2 0.0260 0.8870 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM148530 2 0.0260 0.8870 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM148531 2 0.0363 0.8873 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM148532 2 0.0458 0.8865 0.000 0.984 0.016 0.000 0.000 0.000
#> GSM148533 2 0.0260 0.8870 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM148534 2 0.0260 0.8853 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM148535 2 0.0260 0.8870 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM148536 2 0.0458 0.8825 0.000 0.984 0.016 0.000 0.000 0.000
#> GSM148537 2 0.0363 0.8849 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM148538 2 0.0260 0.8850 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM148539 2 0.2212 0.7281 0.000 0.880 0.112 0.000 0.008 0.000
#> GSM148540 2 0.1957 0.7496 0.000 0.888 0.112 0.000 0.000 0.000
#> GSM148541 2 0.4064 -0.2311 0.000 0.644 0.336 0.000 0.000 0.020
#> GSM148542 2 0.5629 -0.5474 0.016 0.520 0.388 0.000 0.016 0.060
#> GSM148543 2 0.3385 0.4963 0.000 0.788 0.180 0.000 0.000 0.032
#> GSM148544 2 0.3338 0.6036 0.016 0.824 0.140 0.012 0.004 0.004
#> GSM148545 5 0.5998 -0.0342 0.236 0.000 0.000 0.000 0.404 0.360
#> GSM148546 1 0.1918 0.6828 0.904 0.000 0.000 0.000 0.088 0.008
#> GSM148547 1 0.2302 0.6628 0.872 0.000 0.000 0.000 0.120 0.008
#> GSM148548 1 0.1649 0.7078 0.936 0.000 0.000 0.016 0.040 0.008
#> GSM148549 1 0.1858 0.7139 0.932 0.000 0.004 0.024 0.024 0.016
#> GSM148550 1 0.2846 0.7024 0.864 0.000 0.004 0.100 0.012 0.020
#> GSM148551 1 0.3439 0.6823 0.828 0.000 0.008 0.112 0.008 0.044
#> GSM148552 1 0.3370 0.6118 0.812 0.000 0.004 0.000 0.140 0.044
#> GSM148553 1 0.2868 0.6361 0.840 0.000 0.000 0.000 0.132 0.028
#> GSM148554 1 0.2007 0.7144 0.920 0.000 0.000 0.036 0.032 0.012
#> GSM148555 1 0.2107 0.7076 0.916 0.000 0.008 0.008 0.052 0.016
#> GSM148556 1 0.2748 0.7034 0.872 0.000 0.004 0.092 0.012 0.020
#> GSM148557 1 0.2899 0.7017 0.860 0.000 0.004 0.104 0.016 0.016
#> GSM148558 4 0.5177 0.4965 0.312 0.000 0.024 0.616 0.016 0.032
#> GSM148559 5 0.3396 0.5099 0.112 0.000 0.020 0.000 0.828 0.040
#> GSM148560 5 0.3404 0.6209 0.184 0.000 0.004 0.012 0.792 0.008
#> GSM148561 1 0.7359 0.1929 0.472 0.000 0.224 0.032 0.192 0.080
#> GSM148562 1 0.6871 0.4342 0.588 0.000 0.068 0.112 0.148 0.084
#> GSM148563 4 0.5852 0.6540 0.212 0.000 0.052 0.644 0.040 0.052
#> GSM148564 4 0.4498 0.6656 0.172 0.000 0.016 0.748 0.036 0.028
#> GSM148565 4 0.3040 0.7494 0.072 0.000 0.028 0.868 0.016 0.016
#> GSM148566 5 0.3512 0.6050 0.272 0.000 0.000 0.000 0.720 0.008
#> GSM148567 1 0.6498 0.1404 0.456 0.000 0.012 0.344 0.164 0.024
#> GSM148568 1 0.6674 0.1094 0.448 0.000 0.016 0.352 0.148 0.036
#> GSM148569 1 0.5990 0.2204 0.512 0.000 0.008 0.360 0.088 0.032
#> GSM148570 4 0.2832 0.7687 0.076 0.000 0.012 0.876 0.012 0.024
#> GSM148571 4 0.2891 0.7752 0.088 0.000 0.008 0.868 0.012 0.024
#> GSM148572 4 0.1794 0.7150 0.008 0.000 0.024 0.936 0.020 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) dose(p) time(p) k
#> SD:hclust 57 2.57e-12 0.999568 1.0000 2
#> SD:hclust 53 1.40e-20 0.000801 0.0126 3
#> SD:hclust 50 1.57e-17 0.000261 0.0207 4
#> SD:hclust 53 1.17e-09 0.275130 0.2067 5
#> SD:hclust 45 9.25e-10 0.007745 0.5577 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 21163 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5093 0.491 0.491
#> 3 3 0.723 0.742 0.843 0.2221 0.895 0.786
#> 4 4 0.724 0.819 0.837 0.1276 0.859 0.648
#> 5 5 0.676 0.784 0.837 0.0704 0.972 0.897
#> 6 6 0.730 0.771 0.808 0.0440 0.959 0.837
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
#> GSM148516 2 0 1 0 1
#> GSM148517 1 0 1 1 0
#> GSM148518 2 0 1 0 1
#> GSM148519 2 0 1 0 1
#> GSM148520 2 0 1 0 1
#> GSM148521 2 0 1 0 1
#> GSM148522 2 0 1 0 1
#> GSM148523 2 0 1 0 1
#> GSM148524 2 0 1 0 1
#> GSM148525 2 0 1 0 1
#> GSM148526 2 0 1 0 1
#> GSM148527 2 0 1 0 1
#> GSM148528 2 0 1 0 1
#> GSM148529 2 0 1 0 1
#> GSM148530 2 0 1 0 1
#> GSM148531 2 0 1 0 1
#> GSM148532 2 0 1 0 1
#> GSM148533 2 0 1 0 1
#> GSM148534 2 0 1 0 1
#> GSM148535 2 0 1 0 1
#> GSM148536 2 0 1 0 1
#> GSM148537 2 0 1 0 1
#> GSM148538 2 0 1 0 1
#> GSM148539 2 0 1 0 1
#> GSM148540 2 0 1 0 1
#> GSM148541 2 0 1 0 1
#> GSM148542 2 0 1 0 1
#> GSM148543 2 0 1 0 1
#> GSM148544 2 0 1 0 1
#> GSM148545 1 0 1 1 0
#> GSM148546 1 0 1 1 0
#> GSM148547 1 0 1 1 0
#> GSM148548 1 0 1 1 0
#> GSM148549 1 0 1 1 0
#> GSM148550 1 0 1 1 0
#> GSM148551 1 0 1 1 0
#> GSM148552 1 0 1 1 0
#> GSM148553 1 0 1 1 0
#> GSM148554 1 0 1 1 0
#> GSM148555 1 0 1 1 0
#> GSM148556 1 0 1 1 0
#> GSM148557 1 0 1 1 0
#> GSM148558 1 0 1 1 0
#> GSM148559 1 0 1 1 0
#> GSM148560 1 0 1 1 0
#> GSM148561 1 0 1 1 0
#> GSM148562 1 0 1 1 0
#> GSM148563 1 0 1 1 0
#> GSM148564 1 0 1 1 0
#> GSM148565 1 0 1 1 0
#> GSM148566 1 0 1 1 0
#> GSM148567 1 0 1 1 0
#> GSM148568 1 0 1 1 0
#> GSM148569 1 0 1 1 0
#> GSM148570 1 0 1 1 0
#> GSM148571 1 0 1 1 0
#> GSM148572 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM148516 2 0.5431 0.795 0.000 0.716 0.284
#> GSM148517 1 0.1529 0.672 0.960 0.000 0.040
#> GSM148518 2 0.0237 0.935 0.000 0.996 0.004
#> GSM148519 2 0.0237 0.935 0.000 0.996 0.004
#> GSM148520 2 0.0424 0.935 0.000 0.992 0.008
#> GSM148521 2 0.0237 0.936 0.000 0.996 0.004
#> GSM148522 2 0.0000 0.936 0.000 1.000 0.000
#> GSM148523 2 0.0000 0.936 0.000 1.000 0.000
#> GSM148524 2 0.0000 0.936 0.000 1.000 0.000
#> GSM148525 2 0.0000 0.936 0.000 1.000 0.000
#> GSM148526 2 0.0000 0.936 0.000 1.000 0.000
#> GSM148527 2 0.0237 0.936 0.000 0.996 0.004
#> GSM148528 2 0.0237 0.935 0.000 0.996 0.004
#> GSM148529 2 0.0237 0.936 0.000 0.996 0.004
#> GSM148530 2 0.0424 0.935 0.000 0.992 0.008
#> GSM148531 2 0.0237 0.936 0.000 0.996 0.004
#> GSM148532 2 0.0592 0.935 0.000 0.988 0.012
#> GSM148533 2 0.0237 0.935 0.000 0.996 0.004
#> GSM148534 2 0.0237 0.935 0.000 0.996 0.004
#> GSM148535 2 0.0000 0.936 0.000 1.000 0.000
#> GSM148536 2 0.0424 0.935 0.000 0.992 0.008
#> GSM148537 2 0.0000 0.936 0.000 1.000 0.000
#> GSM148538 2 0.0237 0.936 0.000 0.996 0.004
#> GSM148539 2 0.5327 0.798 0.000 0.728 0.272
#> GSM148540 2 0.5397 0.795 0.000 0.720 0.280
#> GSM148541 2 0.5397 0.795 0.000 0.720 0.280
#> GSM148542 2 0.5431 0.792 0.000 0.716 0.284
#> GSM148543 2 0.5397 0.795 0.000 0.720 0.280
#> GSM148544 2 0.5591 0.774 0.000 0.696 0.304
#> GSM148545 1 0.1529 0.672 0.960 0.000 0.040
#> GSM148546 1 0.0000 0.697 1.000 0.000 0.000
#> GSM148547 1 0.0000 0.697 1.000 0.000 0.000
#> GSM148548 1 0.2165 0.692 0.936 0.000 0.064
#> GSM148549 1 0.2959 0.678 0.900 0.000 0.100
#> GSM148550 1 0.4399 0.601 0.812 0.000 0.188
#> GSM148551 1 0.4291 0.610 0.820 0.000 0.180
#> GSM148552 1 0.0000 0.697 1.000 0.000 0.000
#> GSM148553 1 0.0000 0.697 1.000 0.000 0.000
#> GSM148554 1 0.1411 0.698 0.964 0.000 0.036
#> GSM148555 1 0.2878 0.681 0.904 0.000 0.096
#> GSM148556 1 0.4399 0.601 0.812 0.000 0.188
#> GSM148557 1 0.4974 0.522 0.764 0.000 0.236
#> GSM148558 1 0.5650 0.341 0.688 0.000 0.312
#> GSM148559 1 0.4750 0.486 0.784 0.000 0.216
#> GSM148560 1 0.5254 0.380 0.736 0.000 0.264
#> GSM148561 1 0.6302 -0.481 0.520 0.000 0.480
#> GSM148562 3 0.6079 0.857 0.388 0.000 0.612
#> GSM148563 3 0.5733 0.970 0.324 0.000 0.676
#> GSM148564 3 0.5760 0.977 0.328 0.000 0.672
#> GSM148565 3 0.5760 0.977 0.328 0.000 0.672
#> GSM148566 1 0.5138 0.410 0.748 0.000 0.252
#> GSM148567 1 0.6286 -0.438 0.536 0.000 0.464
#> GSM148568 1 0.6302 -0.482 0.520 0.000 0.480
#> GSM148569 3 0.5810 0.966 0.336 0.000 0.664
#> GSM148570 3 0.5760 0.977 0.328 0.000 0.672
#> GSM148571 3 0.5760 0.977 0.328 0.000 0.672
#> GSM148572 3 0.5760 0.977 0.328 0.000 0.672
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM148516 3 0.5093 0.973 0.000 0.348 0.640 0.012
#> GSM148517 1 0.4818 0.633 0.748 0.000 0.216 0.036
#> GSM148518 2 0.0188 0.978 0.000 0.996 0.000 0.004
#> GSM148519 2 0.0336 0.977 0.000 0.992 0.008 0.000
#> GSM148520 2 0.1510 0.966 0.000 0.956 0.028 0.016
#> GSM148521 2 0.1406 0.966 0.000 0.960 0.024 0.016
#> GSM148522 2 0.0524 0.978 0.000 0.988 0.008 0.004
#> GSM148523 2 0.0336 0.979 0.000 0.992 0.008 0.000
#> GSM148524 2 0.0336 0.977 0.000 0.992 0.008 0.000
#> GSM148525 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM148526 2 0.0779 0.978 0.000 0.980 0.016 0.004
#> GSM148527 2 0.0657 0.978 0.000 0.984 0.012 0.004
#> GSM148528 2 0.0336 0.978 0.000 0.992 0.008 0.000
#> GSM148529 2 0.1174 0.971 0.000 0.968 0.020 0.012
#> GSM148530 2 0.1174 0.971 0.000 0.968 0.020 0.012
#> GSM148531 2 0.0657 0.977 0.000 0.984 0.012 0.004
#> GSM148532 2 0.1356 0.954 0.000 0.960 0.032 0.008
#> GSM148533 2 0.0524 0.977 0.000 0.988 0.004 0.008
#> GSM148534 2 0.0524 0.978 0.000 0.988 0.008 0.004
#> GSM148535 2 0.0188 0.978 0.000 0.996 0.000 0.004
#> GSM148536 2 0.1182 0.974 0.000 0.968 0.016 0.016
#> GSM148537 2 0.0336 0.978 0.000 0.992 0.008 0.000
#> GSM148538 2 0.1406 0.966 0.000 0.960 0.024 0.016
#> GSM148539 3 0.4936 0.954 0.000 0.372 0.624 0.004
#> GSM148540 3 0.4643 0.973 0.000 0.344 0.656 0.000
#> GSM148541 3 0.5495 0.971 0.000 0.348 0.624 0.028
#> GSM148542 3 0.5495 0.970 0.000 0.348 0.624 0.028
#> GSM148543 3 0.5075 0.971 0.000 0.344 0.644 0.012
#> GSM148544 3 0.5245 0.950 0.016 0.320 0.660 0.004
#> GSM148545 1 0.4818 0.633 0.748 0.000 0.216 0.036
#> GSM148546 1 0.1716 0.725 0.936 0.000 0.064 0.000
#> GSM148547 1 0.1716 0.725 0.936 0.000 0.064 0.000
#> GSM148548 1 0.2473 0.719 0.908 0.000 0.012 0.080
#> GSM148549 1 0.2987 0.710 0.880 0.000 0.016 0.104
#> GSM148550 1 0.3725 0.668 0.812 0.000 0.008 0.180
#> GSM148551 1 0.3810 0.664 0.804 0.000 0.008 0.188
#> GSM148552 1 0.1637 0.725 0.940 0.000 0.060 0.000
#> GSM148553 1 0.1792 0.723 0.932 0.000 0.068 0.000
#> GSM148554 1 0.1452 0.726 0.956 0.000 0.008 0.036
#> GSM148555 1 0.2987 0.707 0.880 0.000 0.016 0.104
#> GSM148556 1 0.3626 0.668 0.812 0.000 0.004 0.184
#> GSM148557 1 0.4155 0.631 0.756 0.000 0.004 0.240
#> GSM148558 1 0.4746 0.459 0.632 0.000 0.000 0.368
#> GSM148559 1 0.7490 0.277 0.496 0.000 0.284 0.220
#> GSM148560 1 0.7773 0.117 0.432 0.000 0.288 0.280
#> GSM148561 4 0.6587 0.689 0.292 0.000 0.112 0.596
#> GSM148562 4 0.5750 0.791 0.216 0.000 0.088 0.696
#> GSM148563 4 0.2988 0.856 0.112 0.000 0.012 0.876
#> GSM148564 4 0.2831 0.855 0.120 0.000 0.004 0.876
#> GSM148565 4 0.2281 0.855 0.096 0.000 0.000 0.904
#> GSM148566 1 0.7746 0.140 0.440 0.000 0.288 0.272
#> GSM148567 4 0.6587 0.694 0.292 0.000 0.112 0.596
#> GSM148568 4 0.6528 0.688 0.300 0.000 0.104 0.596
#> GSM148569 4 0.4199 0.837 0.164 0.000 0.032 0.804
#> GSM148570 4 0.2281 0.855 0.096 0.000 0.000 0.904
#> GSM148571 4 0.2281 0.855 0.096 0.000 0.000 0.904
#> GSM148572 4 0.2281 0.855 0.096 0.000 0.000 0.904
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM148516 3 0.4437 0.931 0.000 0.136 0.780 0.016 0.068
#> GSM148517 1 0.5643 -0.214 0.492 0.000 0.064 0.004 0.440
#> GSM148518 2 0.1443 0.942 0.000 0.948 0.004 0.004 0.044
#> GSM148519 2 0.1412 0.946 0.000 0.952 0.004 0.008 0.036
#> GSM148520 2 0.2748 0.923 0.000 0.880 0.016 0.008 0.096
#> GSM148521 2 0.2289 0.929 0.000 0.904 0.012 0.004 0.080
#> GSM148522 2 0.1124 0.950 0.000 0.960 0.004 0.000 0.036
#> GSM148523 2 0.1041 0.947 0.000 0.964 0.000 0.004 0.032
#> GSM148524 2 0.0865 0.950 0.000 0.972 0.000 0.004 0.024
#> GSM148525 2 0.1124 0.947 0.000 0.960 0.000 0.004 0.036
#> GSM148526 2 0.1857 0.946 0.000 0.928 0.004 0.008 0.060
#> GSM148527 2 0.1365 0.946 0.000 0.952 0.004 0.004 0.040
#> GSM148528 2 0.1644 0.944 0.000 0.940 0.004 0.008 0.048
#> GSM148529 2 0.2464 0.928 0.000 0.892 0.012 0.004 0.092
#> GSM148530 2 0.2130 0.934 0.000 0.908 0.012 0.000 0.080
#> GSM148531 2 0.1942 0.941 0.000 0.920 0.012 0.000 0.068
#> GSM148532 2 0.1965 0.938 0.000 0.924 0.024 0.000 0.052
#> GSM148533 2 0.1357 0.944 0.000 0.948 0.000 0.004 0.048
#> GSM148534 2 0.1757 0.943 0.000 0.936 0.004 0.012 0.048
#> GSM148535 2 0.1365 0.941 0.000 0.952 0.004 0.004 0.040
#> GSM148536 2 0.2295 0.930 0.000 0.900 0.008 0.004 0.088
#> GSM148537 2 0.1285 0.943 0.000 0.956 0.004 0.004 0.036
#> GSM148538 2 0.2166 0.931 0.000 0.912 0.012 0.004 0.072
#> GSM148539 3 0.3632 0.928 0.000 0.176 0.800 0.004 0.020
#> GSM148540 3 0.3044 0.955 0.000 0.148 0.840 0.004 0.008
#> GSM148541 3 0.4318 0.951 0.000 0.140 0.788 0.020 0.052
#> GSM148542 3 0.4112 0.949 0.000 0.136 0.800 0.016 0.048
#> GSM148543 3 0.3308 0.956 0.000 0.144 0.832 0.004 0.020
#> GSM148544 3 0.2660 0.952 0.008 0.128 0.864 0.000 0.000
#> GSM148545 1 0.5640 -0.205 0.496 0.000 0.064 0.004 0.436
#> GSM148546 1 0.2795 0.676 0.872 0.000 0.028 0.000 0.100
#> GSM148547 1 0.2879 0.676 0.868 0.000 0.032 0.000 0.100
#> GSM148548 1 0.1569 0.737 0.948 0.000 0.008 0.032 0.012
#> GSM148549 1 0.1569 0.737 0.944 0.000 0.004 0.044 0.008
#> GSM148550 1 0.2583 0.721 0.864 0.000 0.004 0.132 0.000
#> GSM148551 1 0.2694 0.722 0.864 0.000 0.004 0.128 0.004
#> GSM148552 1 0.3085 0.660 0.852 0.000 0.032 0.000 0.116
#> GSM148553 1 0.3002 0.661 0.856 0.000 0.028 0.000 0.116
#> GSM148554 1 0.0898 0.734 0.972 0.000 0.000 0.020 0.008
#> GSM148555 1 0.1662 0.738 0.936 0.000 0.004 0.056 0.004
#> GSM148556 1 0.2536 0.722 0.868 0.000 0.004 0.128 0.000
#> GSM148557 1 0.2966 0.694 0.816 0.000 0.000 0.184 0.000
#> GSM148558 1 0.4931 0.448 0.600 0.000 0.012 0.372 0.016
#> GSM148559 5 0.5358 0.904 0.268 0.000 0.024 0.048 0.660
#> GSM148560 5 0.5064 0.946 0.232 0.000 0.000 0.088 0.680
#> GSM148561 4 0.7614 0.333 0.208 0.000 0.060 0.412 0.320
#> GSM148562 4 0.6775 0.599 0.164 0.000 0.052 0.580 0.204
#> GSM148563 4 0.2673 0.758 0.072 0.000 0.008 0.892 0.028
#> GSM148564 4 0.2633 0.758 0.068 0.000 0.024 0.896 0.012
#> GSM148565 4 0.1883 0.751 0.048 0.000 0.008 0.932 0.012
#> GSM148566 5 0.5066 0.949 0.240 0.000 0.000 0.084 0.676
#> GSM148567 4 0.7324 0.404 0.220 0.000 0.044 0.468 0.268
#> GSM148568 4 0.7325 0.413 0.244 0.000 0.040 0.460 0.256
#> GSM148569 4 0.4406 0.722 0.136 0.000 0.020 0.784 0.060
#> GSM148570 4 0.1484 0.757 0.048 0.000 0.000 0.944 0.008
#> GSM148571 4 0.1357 0.756 0.048 0.000 0.000 0.948 0.004
#> GSM148572 4 0.1883 0.751 0.048 0.000 0.008 0.932 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM148516 3 0.4718 0.8419 0.000 0.068 0.748 0.004 0.060 0.120
#> GSM148517 6 0.5971 1.0000 0.264 0.000 0.000 0.000 0.288 0.448
#> GSM148518 2 0.1674 0.9091 0.000 0.924 0.004 0.000 0.004 0.068
#> GSM148519 2 0.1674 0.9093 0.000 0.924 0.004 0.000 0.004 0.068
#> GSM148520 2 0.2871 0.8773 0.000 0.804 0.004 0.000 0.000 0.192
#> GSM148521 2 0.2584 0.8920 0.000 0.848 0.004 0.000 0.004 0.144
#> GSM148522 2 0.0865 0.9207 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM148523 2 0.1411 0.9169 0.000 0.936 0.004 0.000 0.000 0.060
#> GSM148524 2 0.1493 0.9214 0.000 0.936 0.004 0.000 0.004 0.056
#> GSM148525 2 0.1674 0.9124 0.000 0.924 0.004 0.000 0.004 0.068
#> GSM148526 2 0.1843 0.9126 0.000 0.912 0.004 0.000 0.004 0.080
#> GSM148527 2 0.1901 0.9184 0.000 0.912 0.004 0.000 0.008 0.076
#> GSM148528 2 0.2053 0.9010 0.000 0.888 0.004 0.000 0.000 0.108
#> GSM148529 2 0.2558 0.8915 0.000 0.840 0.004 0.000 0.000 0.156
#> GSM148530 2 0.2504 0.8981 0.000 0.856 0.004 0.000 0.004 0.136
#> GSM148531 2 0.2504 0.9043 0.000 0.856 0.004 0.000 0.004 0.136
#> GSM148532 2 0.2920 0.8996 0.000 0.844 0.020 0.000 0.008 0.128
#> GSM148533 2 0.1219 0.9151 0.000 0.948 0.004 0.000 0.000 0.048
#> GSM148534 2 0.2333 0.9014 0.000 0.872 0.004 0.000 0.004 0.120
#> GSM148535 2 0.1615 0.9097 0.000 0.928 0.004 0.000 0.004 0.064
#> GSM148536 2 0.2773 0.8917 0.000 0.828 0.004 0.000 0.004 0.164
#> GSM148537 2 0.1732 0.9096 0.000 0.920 0.004 0.000 0.004 0.072
#> GSM148538 2 0.2462 0.8939 0.000 0.860 0.004 0.000 0.004 0.132
#> GSM148539 3 0.2857 0.8978 0.000 0.112 0.856 0.004 0.004 0.024
#> GSM148540 3 0.2296 0.9228 0.000 0.068 0.900 0.004 0.004 0.024
#> GSM148541 3 0.3402 0.9230 0.000 0.068 0.844 0.004 0.028 0.056
#> GSM148542 3 0.3536 0.9136 0.000 0.060 0.836 0.004 0.032 0.068
#> GSM148543 3 0.2765 0.9266 0.000 0.064 0.876 0.000 0.016 0.044
#> GSM148544 3 0.1757 0.9191 0.012 0.052 0.928 0.000 0.000 0.008
#> GSM148545 6 0.5971 1.0000 0.264 0.000 0.000 0.000 0.288 0.448
#> GSM148546 1 0.3719 0.6762 0.800 0.000 0.008 0.000 0.104 0.088
#> GSM148547 1 0.3764 0.6734 0.796 0.000 0.008 0.000 0.108 0.088
#> GSM148548 1 0.1894 0.7837 0.928 0.000 0.004 0.016 0.040 0.012
#> GSM148549 1 0.1223 0.7878 0.960 0.000 0.004 0.016 0.012 0.008
#> GSM148550 1 0.2312 0.7726 0.896 0.000 0.012 0.080 0.004 0.008
#> GSM148551 1 0.2350 0.7783 0.896 0.000 0.004 0.076 0.008 0.016
#> GSM148552 1 0.3656 0.6671 0.804 0.000 0.008 0.000 0.112 0.076
#> GSM148553 1 0.3558 0.6812 0.812 0.000 0.008 0.000 0.108 0.072
#> GSM148554 1 0.1080 0.7798 0.960 0.000 0.004 0.004 0.032 0.000
#> GSM148555 1 0.1989 0.7877 0.928 0.000 0.016 0.024 0.020 0.012
#> GSM148556 1 0.2365 0.7703 0.892 0.000 0.012 0.084 0.004 0.008
#> GSM148557 1 0.3337 0.7170 0.812 0.000 0.020 0.156 0.004 0.008
#> GSM148558 1 0.4603 0.3293 0.544 0.000 0.008 0.428 0.008 0.012
#> GSM148559 5 0.5343 0.0234 0.084 0.000 0.004 0.040 0.664 0.208
#> GSM148560 5 0.5479 0.1066 0.080 0.000 0.004 0.056 0.660 0.200
#> GSM148561 5 0.6207 0.4865 0.136 0.000 0.024 0.228 0.584 0.028
#> GSM148562 5 0.6460 0.2097 0.136 0.000 0.020 0.392 0.432 0.020
#> GSM148563 4 0.3032 0.8361 0.048 0.000 0.016 0.872 0.048 0.016
#> GSM148564 4 0.3129 0.8050 0.056 0.000 0.004 0.852 0.080 0.008
#> GSM148565 4 0.1390 0.8654 0.016 0.000 0.004 0.948 0.000 0.032
#> GSM148566 5 0.5460 0.1150 0.088 0.000 0.004 0.056 0.668 0.184
#> GSM148567 5 0.6205 0.4271 0.192 0.000 0.020 0.312 0.476 0.000
#> GSM148568 5 0.6273 0.3461 0.196 0.000 0.012 0.352 0.436 0.004
#> GSM148569 4 0.5064 0.5765 0.120 0.000 0.020 0.700 0.152 0.008
#> GSM148570 4 0.1663 0.8722 0.024 0.000 0.004 0.940 0.024 0.008
#> GSM148571 4 0.1282 0.8722 0.024 0.000 0.004 0.956 0.012 0.004
#> GSM148572 4 0.1313 0.8619 0.016 0.000 0.000 0.952 0.004 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 agent(p) dose(p) time(p) k
#> SD:kmeans 57 2.57e-12 1.00e+00 1.000 2
#> SD:kmeans 50 2.51e-09 5.88e-03 0.929 3
#> SD:kmeans 53 1.02e-09 5.55e-07 0.997 4
#> SD:kmeans 51 2.09e-09 3.52e-06 0.733 5
#> SD:kmeans 49 1.12e-11 3.03e-07 0.614 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 21163 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5093 0.491 0.491
#> 3 3 0.628 0.656 0.799 0.2625 0.881 0.758
#> 4 4 0.493 0.576 0.730 0.1454 0.845 0.610
#> 5 5 0.498 0.548 0.652 0.0683 0.982 0.937
#> 6 6 0.518 0.371 0.585 0.0456 0.974 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
#> GSM148516 2 0.0000 1.000 0.000 1.000
#> GSM148517 1 0.0000 1.000 1.000 0.000
#> GSM148518 2 0.0000 1.000 0.000 1.000
#> GSM148519 2 0.0000 1.000 0.000 1.000
#> GSM148520 2 0.0000 1.000 0.000 1.000
#> GSM148521 2 0.0000 1.000 0.000 1.000
#> GSM148522 2 0.0000 1.000 0.000 1.000
#> GSM148523 2 0.0000 1.000 0.000 1.000
#> GSM148524 2 0.0000 1.000 0.000 1.000
#> GSM148525 2 0.0000 1.000 0.000 1.000
#> GSM148526 2 0.0000 1.000 0.000 1.000
#> GSM148527 2 0.0000 1.000 0.000 1.000
#> GSM148528 2 0.0000 1.000 0.000 1.000
#> GSM148529 2 0.0000 1.000 0.000 1.000
#> GSM148530 2 0.0000 1.000 0.000 1.000
#> GSM148531 2 0.0000 1.000 0.000 1.000
#> GSM148532 2 0.0000 1.000 0.000 1.000
#> GSM148533 2 0.0000 1.000 0.000 1.000
#> GSM148534 2 0.0000 1.000 0.000 1.000
#> GSM148535 2 0.0000 1.000 0.000 1.000
#> GSM148536 2 0.0000 1.000 0.000 1.000
#> GSM148537 2 0.0000 1.000 0.000 1.000
#> GSM148538 2 0.0000 1.000 0.000 1.000
#> GSM148539 2 0.0000 1.000 0.000 1.000
#> GSM148540 2 0.0000 1.000 0.000 1.000
#> GSM148541 2 0.0000 1.000 0.000 1.000
#> GSM148542 2 0.0000 1.000 0.000 1.000
#> GSM148543 2 0.0000 1.000 0.000 1.000
#> GSM148544 2 0.0376 0.996 0.004 0.996
#> GSM148545 1 0.0000 1.000 1.000 0.000
#> GSM148546 1 0.0000 1.000 1.000 0.000
#> GSM148547 1 0.0000 1.000 1.000 0.000
#> GSM148548 1 0.0000 1.000 1.000 0.000
#> GSM148549 1 0.0000 1.000 1.000 0.000
#> GSM148550 1 0.0000 1.000 1.000 0.000
#> GSM148551 1 0.0000 1.000 1.000 0.000
#> GSM148552 1 0.0000 1.000 1.000 0.000
#> GSM148553 1 0.0000 1.000 1.000 0.000
#> GSM148554 1 0.0000 1.000 1.000 0.000
#> GSM148555 1 0.0000 1.000 1.000 0.000
#> GSM148556 1 0.0000 1.000 1.000 0.000
#> GSM148557 1 0.0000 1.000 1.000 0.000
#> GSM148558 1 0.0000 1.000 1.000 0.000
#> GSM148559 1 0.0000 1.000 1.000 0.000
#> GSM148560 1 0.0000 1.000 1.000 0.000
#> GSM148561 1 0.0000 1.000 1.000 0.000
#> GSM148562 1 0.0000 1.000 1.000 0.000
#> GSM148563 1 0.0000 1.000 1.000 0.000
#> GSM148564 1 0.0000 1.000 1.000 0.000
#> GSM148565 1 0.0000 1.000 1.000 0.000
#> GSM148566 1 0.0000 1.000 1.000 0.000
#> GSM148567 1 0.0000 1.000 1.000 0.000
#> GSM148568 1 0.0000 1.000 1.000 0.000
#> GSM148569 1 0.0000 1.000 1.000 0.000
#> GSM148570 1 0.0000 1.000 1.000 0.000
#> GSM148571 1 0.0000 1.000 1.000 0.000
#> GSM148572 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
#> GSM148516 2 0.4874 0.8673 0.028 0.828 0.144
#> GSM148517 3 0.5178 0.6929 0.256 0.000 0.744
#> GSM148518 2 0.0747 0.9378 0.000 0.984 0.016
#> GSM148519 2 0.0892 0.9377 0.000 0.980 0.020
#> GSM148520 2 0.1031 0.9383 0.000 0.976 0.024
#> GSM148521 2 0.0592 0.9365 0.000 0.988 0.012
#> GSM148522 2 0.0892 0.9381 0.000 0.980 0.020
#> GSM148523 2 0.0592 0.9367 0.000 0.988 0.012
#> GSM148524 2 0.0592 0.9380 0.000 0.988 0.012
#> GSM148525 2 0.1411 0.9350 0.000 0.964 0.036
#> GSM148526 2 0.1411 0.9371 0.000 0.964 0.036
#> GSM148527 2 0.0747 0.9379 0.000 0.984 0.016
#> GSM148528 2 0.0592 0.9369 0.000 0.988 0.012
#> GSM148529 2 0.0237 0.9363 0.000 0.996 0.004
#> GSM148530 2 0.1031 0.9375 0.000 0.976 0.024
#> GSM148531 2 0.1031 0.9370 0.000 0.976 0.024
#> GSM148532 2 0.2066 0.9288 0.000 0.940 0.060
#> GSM148533 2 0.1411 0.9368 0.000 0.964 0.036
#> GSM148534 2 0.0747 0.9380 0.000 0.984 0.016
#> GSM148535 2 0.1031 0.9379 0.000 0.976 0.024
#> GSM148536 2 0.0747 0.9378 0.000 0.984 0.016
#> GSM148537 2 0.1163 0.9380 0.000 0.972 0.028
#> GSM148538 2 0.0892 0.9369 0.000 0.980 0.020
#> GSM148539 2 0.3816 0.8877 0.000 0.852 0.148
#> GSM148540 2 0.4514 0.8721 0.012 0.832 0.156
#> GSM148541 2 0.4748 0.8727 0.024 0.832 0.144
#> GSM148542 2 0.8933 0.4918 0.168 0.556 0.276
#> GSM148543 2 0.5435 0.8407 0.048 0.808 0.144
#> GSM148544 2 0.9440 0.2779 0.308 0.488 0.204
#> GSM148545 3 0.5138 0.7080 0.252 0.000 0.748
#> GSM148546 3 0.4504 0.7128 0.196 0.000 0.804
#> GSM148547 3 0.4555 0.7160 0.200 0.000 0.800
#> GSM148548 3 0.6180 0.3932 0.416 0.000 0.584
#> GSM148549 3 0.6235 0.3424 0.436 0.000 0.564
#> GSM148550 1 0.6302 -0.0652 0.520 0.000 0.480
#> GSM148551 1 0.6286 -0.0174 0.536 0.000 0.464
#> GSM148552 3 0.5020 0.6957 0.192 0.012 0.796
#> GSM148553 3 0.4702 0.6740 0.212 0.000 0.788
#> GSM148554 3 0.5859 0.5926 0.344 0.000 0.656
#> GSM148555 1 0.6291 -0.0332 0.532 0.000 0.468
#> GSM148556 1 0.6204 0.1144 0.576 0.000 0.424
#> GSM148557 1 0.5760 0.3620 0.672 0.000 0.328
#> GSM148558 1 0.5397 0.4437 0.720 0.000 0.280
#> GSM148559 3 0.6235 0.3315 0.436 0.000 0.564
#> GSM148560 1 0.6308 -0.2136 0.508 0.000 0.492
#> GSM148561 1 0.5363 0.4626 0.724 0.000 0.276
#> GSM148562 1 0.3619 0.6009 0.864 0.000 0.136
#> GSM148563 1 0.2165 0.6219 0.936 0.000 0.064
#> GSM148564 1 0.2959 0.6126 0.900 0.000 0.100
#> GSM148565 1 0.1753 0.6204 0.952 0.000 0.048
#> GSM148566 1 0.6299 -0.1596 0.524 0.000 0.476
#> GSM148567 1 0.5363 0.4305 0.724 0.000 0.276
#> GSM148568 1 0.4702 0.5243 0.788 0.000 0.212
#> GSM148569 1 0.3412 0.6113 0.876 0.000 0.124
#> GSM148570 1 0.1289 0.6160 0.968 0.000 0.032
#> GSM148571 1 0.1643 0.6183 0.956 0.000 0.044
#> GSM148572 1 0.1753 0.6213 0.952 0.000 0.048
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM148516 3 0.601 0.6241 0.044 0.320 0.628 0.008
#> GSM148517 1 0.539 0.5799 0.736 0.000 0.092 0.172
#> GSM148518 2 0.385 0.7541 0.008 0.800 0.192 0.000
#> GSM148519 2 0.300 0.7953 0.004 0.864 0.132 0.000
#> GSM148520 2 0.375 0.7613 0.004 0.800 0.196 0.000
#> GSM148521 2 0.331 0.7684 0.000 0.828 0.172 0.000
#> GSM148522 2 0.276 0.7970 0.000 0.872 0.128 0.000
#> GSM148523 2 0.363 0.7700 0.004 0.812 0.184 0.000
#> GSM148524 2 0.302 0.7986 0.000 0.852 0.148 0.000
#> GSM148525 2 0.398 0.6565 0.000 0.760 0.240 0.000
#> GSM148526 2 0.387 0.7432 0.004 0.788 0.208 0.000
#> GSM148527 2 0.331 0.7817 0.004 0.840 0.156 0.000
#> GSM148528 2 0.372 0.7875 0.008 0.812 0.180 0.000
#> GSM148529 2 0.358 0.7731 0.004 0.816 0.180 0.000
#> GSM148530 2 0.331 0.7889 0.004 0.840 0.156 0.000
#> GSM148531 2 0.409 0.7467 0.004 0.764 0.232 0.000
#> GSM148532 2 0.468 0.5739 0.004 0.680 0.316 0.000
#> GSM148533 2 0.358 0.7824 0.004 0.816 0.180 0.000
#> GSM148534 2 0.367 0.7704 0.004 0.808 0.188 0.000
#> GSM148535 2 0.326 0.7796 0.004 0.844 0.152 0.000
#> GSM148536 2 0.354 0.7640 0.004 0.820 0.176 0.000
#> GSM148537 2 0.294 0.7902 0.004 0.868 0.128 0.000
#> GSM148538 2 0.297 0.7796 0.000 0.856 0.144 0.000
#> GSM148539 3 0.531 0.4773 0.012 0.412 0.576 0.000
#> GSM148540 3 0.661 0.5550 0.040 0.360 0.572 0.028
#> GSM148541 3 0.583 0.6268 0.020 0.344 0.620 0.016
#> GSM148542 3 0.752 0.5986 0.088 0.284 0.576 0.052
#> GSM148543 3 0.610 0.6154 0.024 0.340 0.612 0.024
#> GSM148544 3 0.781 0.5421 0.024 0.248 0.540 0.188
#> GSM148545 1 0.426 0.6043 0.820 0.000 0.068 0.112
#> GSM148546 1 0.373 0.6040 0.848 0.000 0.044 0.108
#> GSM148547 1 0.374 0.6100 0.852 0.000 0.060 0.088
#> GSM148548 1 0.619 0.4573 0.644 0.000 0.096 0.260
#> GSM148549 1 0.682 0.3635 0.564 0.000 0.124 0.312
#> GSM148550 1 0.644 0.1460 0.492 0.000 0.068 0.440
#> GSM148551 1 0.692 0.0879 0.464 0.000 0.108 0.428
#> GSM148552 1 0.428 0.6008 0.832 0.008 0.068 0.092
#> GSM148553 1 0.470 0.5984 0.792 0.000 0.084 0.124
#> GSM148554 1 0.517 0.5567 0.744 0.000 0.068 0.188
#> GSM148555 4 0.640 -0.0376 0.464 0.000 0.064 0.472
#> GSM148556 4 0.664 -0.0298 0.424 0.000 0.084 0.492
#> GSM148557 4 0.578 0.2040 0.380 0.000 0.036 0.584
#> GSM148558 4 0.586 0.3088 0.340 0.000 0.048 0.612
#> GSM148559 1 0.687 0.3675 0.580 0.008 0.104 0.308
#> GSM148560 1 0.663 0.2610 0.544 0.000 0.092 0.364
#> GSM148561 4 0.619 0.4593 0.244 0.000 0.104 0.652
#> GSM148562 4 0.470 0.6129 0.164 0.000 0.056 0.780
#> GSM148563 4 0.337 0.6488 0.080 0.000 0.048 0.872
#> GSM148564 4 0.490 0.6002 0.156 0.000 0.072 0.772
#> GSM148565 4 0.323 0.6533 0.072 0.000 0.048 0.880
#> GSM148566 1 0.689 0.0595 0.452 0.000 0.104 0.444
#> GSM148567 4 0.614 0.4098 0.288 0.000 0.080 0.632
#> GSM148568 4 0.556 0.5088 0.240 0.000 0.064 0.696
#> GSM148569 4 0.331 0.6458 0.104 0.000 0.028 0.868
#> GSM148570 4 0.295 0.6548 0.088 0.000 0.024 0.888
#> GSM148571 4 0.191 0.6516 0.040 0.000 0.020 0.940
#> GSM148572 4 0.194 0.6547 0.052 0.000 0.012 0.936
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM148516 3 0.563 0.6378 0.024 0.172 0.700 0.008 NA
#> GSM148517 1 0.575 0.5019 0.668 0.000 0.020 0.136 NA
#> GSM148518 2 0.451 0.7252 0.000 0.740 0.188 0.000 NA
#> GSM148519 2 0.361 0.7527 0.000 0.824 0.112 0.000 NA
#> GSM148520 2 0.523 0.6876 0.000 0.676 0.208 0.000 NA
#> GSM148521 2 0.500 0.7136 0.000 0.700 0.196 0.000 NA
#> GSM148522 2 0.389 0.7515 0.000 0.804 0.120 0.000 NA
#> GSM148523 2 0.471 0.7198 0.004 0.736 0.180 0.000 NA
#> GSM148524 2 0.463 0.7433 0.000 0.736 0.176 0.000 NA
#> GSM148525 2 0.546 0.5791 0.000 0.644 0.256 0.004 NA
#> GSM148526 2 0.479 0.6567 0.000 0.720 0.188 0.000 NA
#> GSM148527 2 0.457 0.7366 0.000 0.748 0.148 0.000 NA
#> GSM148528 2 0.415 0.7411 0.000 0.780 0.144 0.000 NA
#> GSM148529 2 0.545 0.6973 0.004 0.668 0.200 0.000 NA
#> GSM148530 2 0.510 0.7071 0.000 0.692 0.192 0.000 NA
#> GSM148531 2 0.538 0.6964 0.000 0.656 0.224 0.000 NA
#> GSM148532 2 0.579 0.5569 0.000 0.580 0.300 0.000 NA
#> GSM148533 2 0.418 0.7362 0.000 0.776 0.152 0.000 NA
#> GSM148534 2 0.439 0.7307 0.000 0.756 0.168 0.000 NA
#> GSM148535 2 0.439 0.7262 0.000 0.764 0.140 0.000 NA
#> GSM148536 2 0.475 0.7071 0.000 0.724 0.184 0.000 NA
#> GSM148537 2 0.367 0.7478 0.000 0.812 0.140 0.000 NA
#> GSM148538 2 0.459 0.7343 0.004 0.756 0.140 0.000 NA
#> GSM148539 3 0.619 0.4714 0.024 0.316 0.576 0.004 NA
#> GSM148540 3 0.629 0.6148 0.012 0.216 0.624 0.016 NA
#> GSM148541 3 0.559 0.6617 0.020 0.164 0.696 0.004 NA
#> GSM148542 3 0.750 0.6218 0.068 0.124 0.592 0.056 NA
#> GSM148543 3 0.578 0.5962 0.012 0.212 0.656 0.004 NA
#> GSM148544 3 0.775 0.5771 0.036 0.120 0.564 0.140 NA
#> GSM148545 1 0.482 0.5368 0.744 0.000 0.016 0.072 NA
#> GSM148546 1 0.412 0.5557 0.808 0.000 0.016 0.072 NA
#> GSM148547 1 0.403 0.5557 0.812 0.000 0.012 0.076 NA
#> GSM148548 1 0.630 0.4227 0.584 0.000 0.012 0.204 NA
#> GSM148549 1 0.641 0.3690 0.564 0.000 0.012 0.236 NA
#> GSM148550 1 0.679 0.2753 0.484 0.000 0.012 0.292 NA
#> GSM148551 1 0.669 0.1314 0.452 0.000 0.012 0.372 NA
#> GSM148552 1 0.506 0.5326 0.748 0.004 0.024 0.088 NA
#> GSM148553 1 0.553 0.5303 0.712 0.004 0.032 0.100 NA
#> GSM148554 1 0.575 0.4957 0.656 0.000 0.012 0.164 NA
#> GSM148555 1 0.718 0.1529 0.404 0.000 0.024 0.352 NA
#> GSM148556 4 0.668 -0.0422 0.400 0.000 0.008 0.416 NA
#> GSM148557 4 0.668 0.2179 0.280 0.000 0.020 0.528 NA
#> GSM148558 4 0.612 0.3917 0.228 0.000 0.012 0.604 NA
#> GSM148559 1 0.715 0.3630 0.496 0.004 0.028 0.240 NA
#> GSM148560 1 0.717 0.2310 0.444 0.000 0.024 0.284 NA
#> GSM148561 4 0.661 0.3797 0.132 0.000 0.028 0.536 NA
#> GSM148562 4 0.617 0.5063 0.156 0.000 0.032 0.636 NA
#> GSM148563 4 0.391 0.6103 0.084 0.000 0.004 0.812 NA
#> GSM148564 4 0.482 0.5915 0.092 0.000 0.024 0.760 NA
#> GSM148565 4 0.388 0.6133 0.064 0.000 0.020 0.828 NA
#> GSM148566 1 0.737 0.1462 0.376 0.000 0.028 0.328 NA
#> GSM148567 4 0.715 0.2670 0.220 0.004 0.028 0.496 NA
#> GSM148568 4 0.616 0.4573 0.168 0.000 0.016 0.612 NA
#> GSM148569 4 0.519 0.5717 0.108 0.000 0.012 0.712 NA
#> GSM148570 4 0.309 0.6252 0.064 0.000 0.004 0.868 NA
#> GSM148571 4 0.223 0.6265 0.040 0.000 0.000 0.912 NA
#> GSM148572 4 0.327 0.6188 0.056 0.000 0.000 0.848 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM148516 3 0.672 0.5440 0.012 0.144 0.540 0.004 0.064 NA
#> GSM148517 1 0.533 0.3165 0.700 0.000 0.028 0.112 0.136 NA
#> GSM148518 2 0.447 0.6260 0.000 0.704 0.108 0.000 0.000 NA
#> GSM148519 2 0.340 0.6642 0.000 0.820 0.052 0.000 0.008 NA
#> GSM148520 2 0.547 0.5552 0.000 0.480 0.108 0.000 0.004 NA
#> GSM148521 2 0.540 0.5758 0.000 0.584 0.108 0.000 0.012 NA
#> GSM148522 2 0.425 0.6447 0.000 0.760 0.092 0.000 0.016 NA
#> GSM148523 2 0.478 0.6228 0.008 0.688 0.040 0.000 0.024 NA
#> GSM148524 2 0.420 0.6656 0.004 0.752 0.052 0.000 0.012 NA
#> GSM148525 2 0.614 0.5005 0.000 0.560 0.156 0.004 0.036 NA
#> GSM148526 2 0.525 0.5406 0.000 0.640 0.184 0.004 0.004 NA
#> GSM148527 2 0.531 0.6129 0.004 0.624 0.116 0.000 0.008 NA
#> GSM148528 2 0.477 0.6260 0.000 0.652 0.100 0.000 0.000 NA
#> GSM148529 2 0.536 0.6090 0.004 0.604 0.084 0.000 0.016 NA
#> GSM148530 2 0.565 0.5977 0.000 0.616 0.096 0.000 0.048 NA
#> GSM148531 2 0.606 0.5419 0.000 0.524 0.120 0.000 0.040 NA
#> GSM148532 2 0.614 0.4860 0.000 0.524 0.180 0.000 0.028 NA
#> GSM148533 2 0.540 0.6052 0.004 0.648 0.100 0.000 0.028 NA
#> GSM148534 2 0.505 0.6288 0.000 0.636 0.076 0.000 0.016 NA
#> GSM148535 2 0.488 0.6031 0.000 0.696 0.080 0.000 0.028 NA
#> GSM148536 2 0.531 0.5882 0.004 0.540 0.064 0.000 0.012 NA
#> GSM148537 2 0.488 0.5998 0.004 0.696 0.144 0.000 0.008 NA
#> GSM148538 2 0.506 0.6230 0.000 0.648 0.052 0.000 0.036 NA
#> GSM148539 3 0.694 0.4634 0.024 0.252 0.520 0.004 0.060 NA
#> GSM148540 3 0.665 0.5552 0.028 0.132 0.600 0.024 0.036 NA
#> GSM148541 3 0.577 0.5798 0.012 0.140 0.664 0.008 0.036 NA
#> GSM148542 3 0.789 0.5281 0.036 0.140 0.484 0.028 0.112 NA
#> GSM148543 3 0.632 0.5662 0.028 0.128 0.632 0.008 0.052 NA
#> GSM148544 3 0.803 0.5159 0.052 0.084 0.516 0.088 0.096 NA
#> GSM148545 1 0.418 0.3243 0.800 0.000 0.016 0.056 0.088 NA
#> GSM148546 1 0.470 0.2286 0.732 0.000 0.012 0.060 0.172 NA
#> GSM148547 1 0.449 0.2639 0.764 0.000 0.020 0.048 0.140 NA
#> GSM148548 1 0.663 -0.1410 0.444 0.000 0.024 0.116 0.380 NA
#> GSM148549 1 0.664 -0.3628 0.420 0.000 0.020 0.156 0.380 NA
#> GSM148550 1 0.689 -0.4532 0.388 0.000 0.020 0.244 0.328 NA
#> GSM148551 5 0.720 0.0000 0.312 0.000 0.028 0.292 0.340 NA
#> GSM148552 1 0.605 0.3005 0.648 0.012 0.024 0.044 0.188 NA
#> GSM148553 1 0.658 0.2766 0.576 0.000 0.036 0.084 0.228 NA
#> GSM148554 1 0.635 -0.0283 0.572 0.000 0.012 0.132 0.228 NA
#> GSM148555 1 0.726 -0.2659 0.372 0.000 0.032 0.208 0.348 NA
#> GSM148556 1 0.713 -0.5185 0.348 0.000 0.020 0.320 0.280 NA
#> GSM148557 4 0.671 -0.3437 0.276 0.000 0.004 0.440 0.244 NA
#> GSM148558 4 0.638 -0.2782 0.268 0.000 0.012 0.488 0.220 NA
#> GSM148559 1 0.715 0.2536 0.472 0.000 0.024 0.144 0.280 NA
#> GSM148560 1 0.739 0.1958 0.420 0.000 0.040 0.192 0.296 NA
#> GSM148561 4 0.754 0.3162 0.116 0.004 0.072 0.428 0.324 NA
#> GSM148562 4 0.613 0.4197 0.104 0.000 0.036 0.624 0.196 NA
#> GSM148563 4 0.507 0.4843 0.068 0.000 0.024 0.716 0.164 NA
#> GSM148564 4 0.502 0.4793 0.064 0.000 0.020 0.708 0.184 NA
#> GSM148565 4 0.470 0.4932 0.052 0.000 0.032 0.768 0.100 NA
#> GSM148566 1 0.753 0.1783 0.380 0.000 0.044 0.208 0.316 NA
#> GSM148567 4 0.728 0.3233 0.152 0.000 0.056 0.468 0.276 NA
#> GSM148568 4 0.714 0.3954 0.124 0.000 0.060 0.524 0.228 NA
#> GSM148569 4 0.556 0.4745 0.060 0.004 0.044 0.704 0.140 NA
#> GSM148570 4 0.358 0.5252 0.052 0.000 0.012 0.828 0.096 NA
#> GSM148571 4 0.359 0.5050 0.048 0.000 0.012 0.832 0.088 NA
#> GSM148572 4 0.360 0.5196 0.056 0.000 0.024 0.840 0.060 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 agent(p) dose(p) time(p) k
#> SD:skmeans 57 2.57e-12 1.00e+00 1.000 2
#> SD:skmeans 42 3.56e-08 1.94e-02 0.484 3
#> SD:skmeans 43 3.68e-08 5.48e-05 0.628 4
#> SD:skmeans 41 7.87e-08 8.83e-05 0.537 5
#> SD:skmeans 29 1.27e-06 1.52e-04 0.841 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 21163 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.961 0.954 0.978 0.5085 0.492 0.492
#> 3 3 0.573 0.720 0.801 0.2077 0.982 0.963
#> 4 4 0.501 0.239 0.681 0.1069 0.896 0.781
#> 5 5 0.489 0.318 0.641 0.0354 0.892 0.732
#> 6 6 0.520 0.331 0.665 0.0225 0.904 0.739
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
#> GSM148516 2 0.0000 0.995 0.000 1.000
#> GSM148517 1 0.0000 0.961 1.000 0.000
#> GSM148518 2 0.0000 0.995 0.000 1.000
#> GSM148519 2 0.0000 0.995 0.000 1.000
#> GSM148520 2 0.0000 0.995 0.000 1.000
#> GSM148521 2 0.0000 0.995 0.000 1.000
#> GSM148522 2 0.0000 0.995 0.000 1.000
#> GSM148523 2 0.0000 0.995 0.000 1.000
#> GSM148524 2 0.0000 0.995 0.000 1.000
#> GSM148525 2 0.0000 0.995 0.000 1.000
#> GSM148526 2 0.0000 0.995 0.000 1.000
#> GSM148527 2 0.0000 0.995 0.000 1.000
#> GSM148528 2 0.0000 0.995 0.000 1.000
#> GSM148529 2 0.0000 0.995 0.000 1.000
#> GSM148530 2 0.0000 0.995 0.000 1.000
#> GSM148531 2 0.0000 0.995 0.000 1.000
#> GSM148532 2 0.0000 0.995 0.000 1.000
#> GSM148533 2 0.0000 0.995 0.000 1.000
#> GSM148534 2 0.0000 0.995 0.000 1.000
#> GSM148535 2 0.0000 0.995 0.000 1.000
#> GSM148536 2 0.0000 0.995 0.000 1.000
#> GSM148537 2 0.0000 0.995 0.000 1.000
#> GSM148538 2 0.0000 0.995 0.000 1.000
#> GSM148539 2 0.0376 0.992 0.004 0.996
#> GSM148540 2 0.0376 0.992 0.004 0.996
#> GSM148541 2 0.0938 0.985 0.012 0.988
#> GSM148542 2 0.2603 0.954 0.044 0.956
#> GSM148543 2 0.2778 0.949 0.048 0.952
#> GSM148544 1 0.9661 0.378 0.608 0.392
#> GSM148545 1 0.0000 0.961 1.000 0.000
#> GSM148546 1 0.0376 0.959 0.996 0.004
#> GSM148547 1 0.1184 0.954 0.984 0.016
#> GSM148548 1 0.0000 0.961 1.000 0.000
#> GSM148549 1 0.0000 0.961 1.000 0.000
#> GSM148550 1 0.0000 0.961 1.000 0.000
#> GSM148551 1 0.0000 0.961 1.000 0.000
#> GSM148552 1 0.3584 0.915 0.932 0.068
#> GSM148553 1 0.5178 0.867 0.884 0.116
#> GSM148554 1 0.0000 0.961 1.000 0.000
#> GSM148555 1 0.0000 0.961 1.000 0.000
#> GSM148556 1 0.0000 0.961 1.000 0.000
#> GSM148557 1 0.0000 0.961 1.000 0.000
#> GSM148558 1 0.0000 0.961 1.000 0.000
#> GSM148559 1 0.6623 0.806 0.828 0.172
#> GSM148560 1 0.1414 0.951 0.980 0.020
#> GSM148561 1 0.1843 0.947 0.972 0.028
#> GSM148562 1 0.0000 0.961 1.000 0.000
#> GSM148563 1 0.0000 0.961 1.000 0.000
#> GSM148564 1 0.0000 0.961 1.000 0.000
#> GSM148565 1 0.0000 0.961 1.000 0.000
#> GSM148566 1 0.0938 0.956 0.988 0.012
#> GSM148567 1 0.8267 0.675 0.740 0.260
#> GSM148568 1 0.2236 0.940 0.964 0.036
#> GSM148569 1 0.0000 0.961 1.000 0.000
#> GSM148570 1 0.0000 0.961 1.000 0.000
#> GSM148571 1 0.0000 0.961 1.000 0.000
#> GSM148572 1 0.0000 0.961 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM148516 2 0.553 0.819 0.000 0.704 0.296
#> GSM148517 1 0.450 0.565 0.804 0.000 0.196
#> GSM148518 2 0.196 0.815 0.000 0.944 0.056
#> GSM148519 2 0.450 0.809 0.000 0.804 0.196
#> GSM148520 2 0.608 0.808 0.000 0.612 0.388
#> GSM148521 2 0.629 0.791 0.000 0.532 0.468
#> GSM148522 2 0.614 0.814 0.000 0.596 0.404
#> GSM148523 2 0.186 0.809 0.000 0.948 0.052
#> GSM148524 2 0.571 0.836 0.000 0.680 0.320
#> GSM148525 2 0.141 0.805 0.000 0.964 0.036
#> GSM148526 2 0.579 0.826 0.000 0.668 0.332
#> GSM148527 2 0.601 0.808 0.000 0.628 0.372
#> GSM148528 2 0.484 0.832 0.000 0.776 0.224
#> GSM148529 2 0.631 0.782 0.000 0.512 0.488
#> GSM148530 2 0.573 0.825 0.000 0.676 0.324
#> GSM148531 2 0.540 0.837 0.000 0.720 0.280
#> GSM148532 2 0.245 0.816 0.000 0.924 0.076
#> GSM148533 2 0.334 0.823 0.000 0.880 0.120
#> GSM148534 2 0.599 0.812 0.000 0.632 0.368
#> GSM148535 2 0.164 0.807 0.000 0.956 0.044
#> GSM148536 2 0.595 0.806 0.000 0.640 0.360
#> GSM148537 2 0.271 0.812 0.000 0.912 0.088
#> GSM148538 2 0.518 0.817 0.000 0.744 0.256
#> GSM148539 2 0.546 0.841 0.000 0.712 0.288
#> GSM148540 2 0.529 0.832 0.000 0.732 0.268
#> GSM148541 2 0.468 0.825 0.004 0.804 0.192
#> GSM148542 2 0.623 0.790 0.040 0.740 0.220
#> GSM148543 2 0.652 0.817 0.016 0.644 0.340
#> GSM148544 1 0.782 -0.376 0.580 0.356 0.064
#> GSM148545 1 0.455 0.631 0.800 0.000 0.200
#> GSM148546 1 0.502 0.588 0.760 0.000 0.240
#> GSM148547 1 0.465 0.604 0.792 0.000 0.208
#> GSM148548 1 0.369 0.759 0.860 0.000 0.140
#> GSM148549 1 0.334 0.749 0.880 0.000 0.120
#> GSM148550 1 0.236 0.773 0.928 0.000 0.072
#> GSM148551 1 0.288 0.779 0.904 0.000 0.096
#> GSM148552 1 0.423 0.678 0.844 0.008 0.148
#> GSM148553 1 0.572 0.564 0.744 0.016 0.240
#> GSM148554 1 0.216 0.784 0.936 0.000 0.064
#> GSM148555 1 0.207 0.776 0.940 0.000 0.060
#> GSM148556 1 0.196 0.773 0.944 0.000 0.056
#> GSM148557 1 0.175 0.773 0.952 0.000 0.048
#> GSM148558 1 0.186 0.775 0.948 0.000 0.052
#> GSM148559 1 0.693 -0.129 0.640 0.032 0.328
#> GSM148560 1 0.428 0.728 0.856 0.020 0.124
#> GSM148561 1 0.489 0.582 0.772 0.000 0.228
#> GSM148562 1 0.216 0.775 0.936 0.000 0.064
#> GSM148563 1 0.245 0.777 0.924 0.000 0.076
#> GSM148564 1 0.196 0.773 0.944 0.000 0.056
#> GSM148565 1 0.186 0.774 0.948 0.000 0.052
#> GSM148566 1 0.447 0.686 0.828 0.008 0.164
#> GSM148567 3 0.889 0.000 0.436 0.120 0.444
#> GSM148568 1 0.318 0.760 0.908 0.016 0.076
#> GSM148569 1 0.175 0.775 0.952 0.000 0.048
#> GSM148570 1 0.141 0.783 0.964 0.000 0.036
#> GSM148571 1 0.175 0.773 0.952 0.000 0.048
#> GSM148572 1 0.175 0.773 0.952 0.000 0.048
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM148516 2 0.4889 0.1751 0.000 0.636 0.360 0.004
#> GSM148517 1 0.5807 0.0967 0.636 0.000 0.052 0.312
#> GSM148518 2 0.2589 0.3934 0.000 0.884 0.116 0.000
#> GSM148519 2 0.4697 0.0772 0.000 0.644 0.356 0.000
#> GSM148520 2 0.4999 -0.1128 0.000 0.508 0.492 0.000
#> GSM148521 3 0.4543 0.5260 0.000 0.324 0.676 0.000
#> GSM148522 3 0.4925 0.5027 0.000 0.428 0.572 0.000
#> GSM148523 2 0.2814 0.3744 0.000 0.868 0.132 0.000
#> GSM148524 2 0.4830 -0.0536 0.000 0.608 0.392 0.000
#> GSM148525 2 0.1557 0.4056 0.000 0.944 0.056 0.000
#> GSM148526 3 0.4999 0.2549 0.000 0.492 0.508 0.000
#> GSM148527 2 0.4998 -0.2395 0.000 0.512 0.488 0.000
#> GSM148528 2 0.4697 0.1590 0.000 0.644 0.356 0.000
#> GSM148529 3 0.4406 0.5337 0.000 0.300 0.700 0.000
#> GSM148530 2 0.4996 -0.3760 0.000 0.516 0.484 0.000
#> GSM148531 2 0.4888 -0.1391 0.000 0.588 0.412 0.000
#> GSM148532 2 0.2216 0.4002 0.000 0.908 0.092 0.000
#> GSM148533 2 0.4008 0.2453 0.000 0.756 0.244 0.000
#> GSM148534 2 0.5000 -0.2178 0.000 0.504 0.496 0.000
#> GSM148535 2 0.1302 0.4042 0.000 0.956 0.044 0.000
#> GSM148536 2 0.4977 -0.1419 0.000 0.540 0.460 0.000
#> GSM148537 2 0.3444 0.3596 0.000 0.816 0.184 0.000
#> GSM148538 2 0.4933 -0.0575 0.000 0.568 0.432 0.000
#> GSM148539 2 0.4933 -0.1520 0.000 0.568 0.432 0.000
#> GSM148540 2 0.4948 -0.1934 0.000 0.560 0.440 0.000
#> GSM148541 2 0.4103 0.3343 0.000 0.744 0.256 0.000
#> GSM148542 2 0.5421 0.2557 0.012 0.692 0.272 0.024
#> GSM148543 3 0.4994 0.2470 0.000 0.480 0.520 0.000
#> GSM148544 1 0.7674 -0.0505 0.548 0.312 0.080 0.060
#> GSM148545 1 0.4961 -0.2448 0.552 0.000 0.000 0.448
#> GSM148546 4 0.4985 0.2256 0.468 0.000 0.000 0.532
#> GSM148547 1 0.5112 -0.2581 0.560 0.000 0.004 0.436
#> GSM148548 1 0.3444 0.4912 0.816 0.000 0.000 0.184
#> GSM148549 1 0.4790 0.2254 0.620 0.000 0.000 0.380
#> GSM148550 1 0.4193 0.4487 0.732 0.000 0.000 0.268
#> GSM148551 1 0.4193 0.4473 0.732 0.000 0.000 0.268
#> GSM148552 1 0.5713 0.2725 0.640 0.004 0.036 0.320
#> GSM148553 1 0.4800 0.2178 0.720 0.008 0.008 0.264
#> GSM148554 1 0.3074 0.5445 0.848 0.000 0.000 0.152
#> GSM148555 1 0.1118 0.5560 0.964 0.000 0.000 0.036
#> GSM148556 1 0.4382 0.3873 0.704 0.000 0.000 0.296
#> GSM148557 1 0.0188 0.5550 0.996 0.000 0.000 0.004
#> GSM148558 1 0.1022 0.5585 0.968 0.000 0.000 0.032
#> GSM148559 4 0.6809 0.4022 0.416 0.016 0.060 0.508
#> GSM148560 1 0.5253 0.1803 0.624 0.016 0.000 0.360
#> GSM148561 1 0.7332 -0.2686 0.448 0.000 0.156 0.396
#> GSM148562 1 0.4164 0.4494 0.736 0.000 0.000 0.264
#> GSM148563 1 0.2281 0.5582 0.904 0.000 0.000 0.096
#> GSM148564 1 0.4193 0.4348 0.732 0.000 0.000 0.268
#> GSM148565 1 0.4382 0.3862 0.704 0.000 0.000 0.296
#> GSM148566 1 0.5088 -0.0877 0.572 0.004 0.000 0.424
#> GSM148567 4 0.8537 0.3762 0.244 0.084 0.156 0.516
#> GSM148568 1 0.4050 0.5271 0.824 0.012 0.016 0.148
#> GSM148569 1 0.0707 0.5554 0.980 0.000 0.000 0.020
#> GSM148570 1 0.2011 0.5642 0.920 0.000 0.000 0.080
#> GSM148571 1 0.0336 0.5572 0.992 0.000 0.000 0.008
#> GSM148572 1 0.0524 0.5546 0.988 0.000 0.004 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM148516 2 0.4734 0.00597 0.000 0.604 0.372 0.000 0.024
#> GSM148517 4 0.6466 -0.30812 0.428 0.000 0.044 0.460 0.068
#> GSM148518 2 0.2377 0.42193 0.000 0.872 0.128 0.000 0.000
#> GSM148519 2 0.4196 0.21572 0.000 0.640 0.356 0.000 0.004
#> GSM148520 3 0.4452 0.12750 0.000 0.496 0.500 0.000 0.004
#> GSM148521 3 0.3949 0.44724 0.000 0.300 0.696 0.000 0.004
#> GSM148522 3 0.4201 0.42571 0.000 0.408 0.592 0.000 0.000
#> GSM148523 2 0.2753 0.42665 0.000 0.856 0.136 0.000 0.008
#> GSM148524 2 0.4350 -0.26428 0.000 0.588 0.408 0.000 0.004
#> GSM148525 2 0.1502 0.43156 0.000 0.940 0.056 0.000 0.004
#> GSM148526 3 0.4300 0.13510 0.000 0.476 0.524 0.000 0.000
#> GSM148527 3 0.4449 0.38290 0.000 0.484 0.512 0.000 0.004
#> GSM148528 2 0.4354 0.16889 0.000 0.624 0.368 0.000 0.008
#> GSM148529 3 0.3814 0.48558 0.000 0.276 0.720 0.000 0.004
#> GSM148530 3 0.4305 0.37982 0.000 0.488 0.512 0.000 0.000
#> GSM148531 2 0.4249 -0.12380 0.000 0.568 0.432 0.000 0.000
#> GSM148532 2 0.2068 0.44263 0.000 0.904 0.092 0.000 0.004
#> GSM148533 2 0.3715 0.26646 0.000 0.736 0.260 0.000 0.004
#> GSM148534 3 0.4448 0.36765 0.000 0.480 0.516 0.000 0.004
#> GSM148535 2 0.1205 0.44334 0.000 0.956 0.040 0.000 0.004
#> GSM148536 2 0.4450 -0.38379 0.000 0.508 0.488 0.000 0.004
#> GSM148537 2 0.3231 0.40948 0.000 0.800 0.196 0.000 0.004
#> GSM148538 2 0.4415 0.10095 0.000 0.552 0.444 0.000 0.004
#> GSM148539 2 0.4434 -0.21277 0.000 0.536 0.460 0.000 0.004
#> GSM148540 2 0.5468 -0.09533 0.000 0.516 0.432 0.008 0.044
#> GSM148541 2 0.4167 0.32480 0.000 0.724 0.252 0.000 0.024
#> GSM148542 2 0.5548 0.14816 0.012 0.656 0.272 0.024 0.036
#> GSM148543 3 0.4622 0.40781 0.000 0.440 0.548 0.000 0.012
#> GSM148544 1 0.7367 -0.15075 0.480 0.300 0.072 0.148 0.000
#> GSM148545 1 0.6204 0.33700 0.524 0.000 0.000 0.312 0.164
#> GSM148546 1 0.6299 0.26985 0.464 0.000 0.000 0.380 0.156
#> GSM148547 1 0.6187 0.37156 0.556 0.000 0.004 0.284 0.156
#> GSM148548 1 0.3639 0.59055 0.812 0.000 0.000 0.144 0.044
#> GSM148549 1 0.4434 0.47016 0.536 0.000 0.000 0.460 0.004
#> GSM148550 1 0.4238 0.55719 0.628 0.000 0.000 0.368 0.004
#> GSM148551 1 0.4251 0.53756 0.624 0.000 0.000 0.372 0.004
#> GSM148552 1 0.5108 0.50164 0.612 0.004 0.032 0.348 0.004
#> GSM148553 1 0.5157 0.46551 0.716 0.004 0.004 0.140 0.136
#> GSM148554 1 0.3333 0.61030 0.788 0.000 0.000 0.208 0.004
#> GSM148555 1 0.1121 0.58367 0.956 0.000 0.000 0.044 0.000
#> GSM148556 1 0.4161 0.52468 0.608 0.000 0.000 0.392 0.000
#> GSM148557 1 0.0162 0.57635 0.996 0.000 0.000 0.004 0.000
#> GSM148558 1 0.2020 0.58863 0.900 0.000 0.000 0.100 0.000
#> GSM148559 4 0.7530 -0.20317 0.368 0.008 0.084 0.436 0.104
#> GSM148560 1 0.6107 0.41744 0.564 0.008 0.020 0.344 0.064
#> GSM148561 5 0.5580 0.00000 0.256 0.000 0.008 0.096 0.640
#> GSM148562 1 0.3707 0.59661 0.716 0.000 0.000 0.284 0.000
#> GSM148563 1 0.3395 0.54930 0.844 0.000 0.004 0.104 0.048
#> GSM148564 1 0.3661 0.58980 0.724 0.000 0.000 0.276 0.000
#> GSM148565 1 0.3906 0.57305 0.704 0.000 0.000 0.292 0.004
#> GSM148566 1 0.6125 0.33263 0.492 0.004 0.024 0.424 0.056
#> GSM148567 4 0.9489 -0.06080 0.228 0.088 0.152 0.328 0.204
#> GSM148568 1 0.3867 0.59760 0.816 0.008 0.024 0.140 0.012
#> GSM148569 1 0.1830 0.58057 0.924 0.000 0.000 0.068 0.008
#> GSM148570 1 0.1792 0.60762 0.916 0.000 0.000 0.084 0.000
#> GSM148571 1 0.0404 0.58065 0.988 0.000 0.000 0.012 0.000
#> GSM148572 1 0.1518 0.54891 0.952 0.000 0.012 0.016 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM148516 3 0.5916 0.0240 0.000 0.404 0.472 0.000 0.080 0.044
#> GSM148517 4 0.7090 -0.2573 0.316 0.000 0.040 0.404 0.220 0.020
#> GSM148518 3 0.3804 0.5165 0.000 0.336 0.656 0.000 0.008 0.000
#> GSM148519 2 0.3907 -0.0348 0.000 0.588 0.408 0.000 0.000 0.004
#> GSM148520 2 0.4275 0.1872 0.000 0.644 0.328 0.000 0.020 0.008
#> GSM148521 2 0.2312 0.4504 0.000 0.876 0.112 0.000 0.012 0.000
#> GSM148522 2 0.2737 0.4734 0.000 0.832 0.160 0.000 0.004 0.004
#> GSM148523 3 0.3707 0.5122 0.000 0.312 0.680 0.000 0.008 0.000
#> GSM148524 2 0.4299 0.2799 0.000 0.620 0.356 0.000 0.012 0.012
#> GSM148525 3 0.3805 0.5559 0.000 0.248 0.728 0.000 0.016 0.008
#> GSM148526 2 0.3276 0.3614 0.000 0.764 0.228 0.000 0.004 0.004
#> GSM148527 2 0.4199 0.3821 0.000 0.712 0.244 0.000 0.028 0.016
#> GSM148528 2 0.4452 -0.0229 0.000 0.548 0.428 0.000 0.016 0.008
#> GSM148529 2 0.1340 0.4764 0.000 0.948 0.040 0.000 0.008 0.004
#> GSM148530 2 0.3384 0.4260 0.000 0.760 0.228 0.000 0.008 0.004
#> GSM148531 2 0.3805 0.2979 0.000 0.664 0.328 0.000 0.004 0.004
#> GSM148532 3 0.3468 0.5414 0.000 0.284 0.712 0.000 0.004 0.000
#> GSM148533 3 0.4128 0.1780 0.000 0.492 0.500 0.000 0.004 0.004
#> GSM148534 2 0.4222 0.3759 0.000 0.700 0.260 0.000 0.020 0.020
#> GSM148535 3 0.3290 0.5571 0.000 0.252 0.744 0.000 0.004 0.000
#> GSM148536 2 0.4288 0.2960 0.000 0.644 0.328 0.000 0.016 0.012
#> GSM148537 3 0.4356 0.4141 0.000 0.376 0.600 0.000 0.012 0.012
#> GSM148538 2 0.3659 0.0973 0.000 0.636 0.364 0.000 0.000 0.000
#> GSM148539 2 0.3916 0.3136 0.000 0.680 0.300 0.000 0.020 0.000
#> GSM148540 2 0.5467 0.2261 0.000 0.608 0.276 0.000 0.080 0.036
#> GSM148541 3 0.5076 0.3530 0.000 0.356 0.576 0.000 0.048 0.020
#> GSM148542 3 0.6143 0.2052 0.012 0.344 0.540 0.028 0.032 0.044
#> GSM148543 2 0.4217 0.3852 0.000 0.700 0.260 0.000 0.024 0.016
#> GSM148544 1 0.7072 -0.1276 0.476 0.180 0.180 0.164 0.000 0.000
#> GSM148545 1 0.6363 0.2011 0.516 0.000 0.000 0.288 0.136 0.060
#> GSM148546 1 0.6389 0.1107 0.460 0.000 0.000 0.368 0.100 0.072
#> GSM148547 1 0.6303 0.2546 0.544 0.004 0.000 0.280 0.100 0.072
#> GSM148548 1 0.3479 0.5580 0.812 0.000 0.000 0.140 0.024 0.024
#> GSM148549 1 0.3864 0.3515 0.520 0.000 0.000 0.480 0.000 0.000
#> GSM148550 1 0.3881 0.4628 0.600 0.000 0.000 0.396 0.000 0.004
#> GSM148551 1 0.3881 0.4395 0.600 0.000 0.000 0.396 0.004 0.000
#> GSM148552 1 0.4716 0.4119 0.600 0.032 0.000 0.356 0.008 0.004
#> GSM148553 1 0.5186 0.4374 0.716 0.004 0.004 0.128 0.088 0.060
#> GSM148554 1 0.3023 0.5683 0.784 0.000 0.000 0.212 0.004 0.000
#> GSM148555 1 0.0865 0.5611 0.964 0.000 0.000 0.036 0.000 0.000
#> GSM148556 1 0.3789 0.4182 0.584 0.000 0.000 0.416 0.000 0.000
#> GSM148557 1 0.0260 0.5554 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM148558 1 0.1910 0.5627 0.892 0.000 0.000 0.108 0.000 0.000
#> GSM148559 5 0.7054 0.0000 0.272 0.032 0.000 0.332 0.348 0.016
#> GSM148560 1 0.6624 0.1255 0.508 0.008 0.028 0.336 0.060 0.060
#> GSM148561 6 0.3076 0.0000 0.112 0.004 0.000 0.044 0.000 0.840
#> GSM148562 1 0.3565 0.5298 0.692 0.000 0.000 0.304 0.000 0.004
#> GSM148563 1 0.4156 0.4115 0.780 0.000 0.008 0.088 0.112 0.012
#> GSM148564 1 0.3330 0.5269 0.716 0.000 0.000 0.284 0.000 0.000
#> GSM148565 1 0.3634 0.5017 0.696 0.000 0.000 0.296 0.000 0.008
#> GSM148566 1 0.5493 0.1560 0.480 0.000 0.008 0.440 0.020 0.052
#> GSM148567 4 0.9504 -0.4224 0.236 0.160 0.088 0.284 0.100 0.132
#> GSM148568 1 0.3484 0.5617 0.812 0.024 0.008 0.148 0.004 0.004
#> GSM148569 1 0.1843 0.5584 0.912 0.000 0.004 0.080 0.000 0.004
#> GSM148570 1 0.1643 0.5751 0.924 0.000 0.000 0.068 0.008 0.000
#> GSM148571 1 0.0458 0.5589 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM148572 1 0.2510 0.4711 0.896 0.000 0.024 0.020 0.056 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) dose(p) time(p) k
#> SD:pam 56 4.20e-12 0.9921 1.0000 2
#> SD:pam 54 1.12e-11 0.9967 0.9991 3
#> SD:pam 13 4.74e-03 0.0368 0.4612 4
#> SD:pam 18 NA NA NA 5
#> SD:pam 17 4.02e-04 0.2451 0.0896 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 21163 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.829 0.904 0.956 0.4801 0.526 0.526
#> 3 3 0.604 0.719 0.817 0.3148 0.820 0.657
#> 4 4 0.702 0.775 0.855 0.1207 0.908 0.742
#> 5 5 0.807 0.790 0.859 0.0694 0.964 0.869
#> 6 6 0.805 0.764 0.852 0.0388 0.966 0.860
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
#> GSM148516 1 0.8661 0.648 0.712 0.288
#> GSM148517 1 0.0000 0.937 1.000 0.000
#> GSM148518 2 0.3431 0.914 0.064 0.936
#> GSM148519 2 0.0000 0.976 0.000 1.000
#> GSM148520 2 0.0672 0.971 0.008 0.992
#> GSM148521 2 0.0000 0.976 0.000 1.000
#> GSM148522 2 0.0000 0.976 0.000 1.000
#> GSM148523 2 0.0000 0.976 0.000 1.000
#> GSM148524 2 0.0000 0.976 0.000 1.000
#> GSM148525 2 0.0376 0.974 0.004 0.996
#> GSM148526 2 0.0376 0.974 0.004 0.996
#> GSM148527 2 0.0000 0.976 0.000 1.000
#> GSM148528 2 0.0000 0.976 0.000 1.000
#> GSM148529 2 0.0376 0.974 0.004 0.996
#> GSM148530 2 0.0000 0.976 0.000 1.000
#> GSM148531 2 0.0000 0.976 0.000 1.000
#> GSM148532 2 0.0376 0.974 0.004 0.996
#> GSM148533 2 0.0000 0.976 0.000 1.000
#> GSM148534 2 0.0376 0.974 0.004 0.996
#> GSM148535 2 0.0000 0.976 0.000 1.000
#> GSM148536 2 0.0000 0.976 0.000 1.000
#> GSM148537 2 0.9129 0.452 0.328 0.672
#> GSM148538 2 0.1414 0.961 0.020 0.980
#> GSM148539 1 0.8661 0.648 0.712 0.288
#> GSM148540 1 0.8955 0.607 0.688 0.312
#> GSM148541 1 0.8763 0.636 0.704 0.296
#> GSM148542 1 0.8608 0.654 0.716 0.284
#> GSM148543 1 0.8713 0.642 0.708 0.292
#> GSM148544 1 0.8555 0.659 0.720 0.280
#> GSM148545 1 0.0000 0.937 1.000 0.000
#> GSM148546 1 0.0000 0.937 1.000 0.000
#> GSM148547 1 0.0000 0.937 1.000 0.000
#> GSM148548 1 0.0000 0.937 1.000 0.000
#> GSM148549 1 0.0000 0.937 1.000 0.000
#> GSM148550 1 0.0000 0.937 1.000 0.000
#> GSM148551 1 0.0000 0.937 1.000 0.000
#> GSM148552 1 0.0000 0.937 1.000 0.000
#> GSM148553 1 0.0000 0.937 1.000 0.000
#> GSM148554 1 0.0000 0.937 1.000 0.000
#> GSM148555 1 0.0000 0.937 1.000 0.000
#> GSM148556 1 0.0000 0.937 1.000 0.000
#> GSM148557 1 0.0000 0.937 1.000 0.000
#> GSM148558 1 0.0000 0.937 1.000 0.000
#> GSM148559 1 0.0000 0.937 1.000 0.000
#> GSM148560 1 0.0000 0.937 1.000 0.000
#> GSM148561 1 0.0000 0.937 1.000 0.000
#> GSM148562 1 0.0000 0.937 1.000 0.000
#> GSM148563 1 0.0000 0.937 1.000 0.000
#> GSM148564 1 0.0000 0.937 1.000 0.000
#> GSM148565 1 0.0000 0.937 1.000 0.000
#> GSM148566 1 0.0000 0.937 1.000 0.000
#> GSM148567 1 0.0000 0.937 1.000 0.000
#> GSM148568 1 0.0000 0.937 1.000 0.000
#> GSM148569 1 0.0000 0.937 1.000 0.000
#> GSM148570 1 0.0000 0.937 1.000 0.000
#> GSM148571 1 0.0000 0.937 1.000 0.000
#> GSM148572 1 0.0000 0.937 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM148516 1 0.9272 0.506 0.528 0.240 0.232
#> GSM148517 1 0.2165 0.610 0.936 0.000 0.064
#> GSM148518 2 0.2550 0.926 0.040 0.936 0.024
#> GSM148519 2 0.0424 0.977 0.000 0.992 0.008
#> GSM148520 2 0.0424 0.976 0.000 0.992 0.008
#> GSM148521 2 0.0237 0.977 0.000 0.996 0.004
#> GSM148522 2 0.0237 0.977 0.004 0.996 0.000
#> GSM148523 2 0.0000 0.977 0.000 1.000 0.000
#> GSM148524 2 0.0237 0.977 0.000 0.996 0.004
#> GSM148525 2 0.0592 0.975 0.000 0.988 0.012
#> GSM148526 2 0.0237 0.977 0.000 0.996 0.004
#> GSM148527 2 0.0000 0.977 0.000 1.000 0.000
#> GSM148528 2 0.0000 0.977 0.000 1.000 0.000
#> GSM148529 2 0.0237 0.977 0.000 0.996 0.004
#> GSM148530 2 0.0661 0.975 0.004 0.988 0.008
#> GSM148531 2 0.0475 0.976 0.004 0.992 0.004
#> GSM148532 2 0.0983 0.970 0.004 0.980 0.016
#> GSM148533 2 0.0000 0.977 0.000 1.000 0.000
#> GSM148534 2 0.0237 0.977 0.000 0.996 0.004
#> GSM148535 2 0.0000 0.977 0.000 1.000 0.000
#> GSM148536 2 0.0237 0.977 0.000 0.996 0.004
#> GSM148537 2 0.6714 0.669 0.140 0.748 0.112
#> GSM148538 2 0.1751 0.953 0.012 0.960 0.028
#> GSM148539 1 0.9251 0.498 0.528 0.260 0.212
#> GSM148540 1 0.9429 0.486 0.504 0.264 0.232
#> GSM148541 1 0.9267 0.503 0.528 0.248 0.224
#> GSM148542 1 0.9182 0.515 0.536 0.204 0.260
#> GSM148543 1 0.9197 0.513 0.536 0.212 0.252
#> GSM148544 1 0.9191 0.514 0.536 0.208 0.256
#> GSM148545 1 0.2261 0.610 0.932 0.000 0.068
#> GSM148546 1 0.1964 0.617 0.944 0.000 0.056
#> GSM148547 1 0.1753 0.619 0.952 0.000 0.048
#> GSM148548 1 0.2959 0.605 0.900 0.000 0.100
#> GSM148549 1 0.3116 0.607 0.892 0.000 0.108
#> GSM148550 1 0.3482 0.597 0.872 0.000 0.128
#> GSM148551 1 0.3340 0.600 0.880 0.000 0.120
#> GSM148552 1 0.2066 0.621 0.940 0.000 0.060
#> GSM148553 1 0.2066 0.620 0.940 0.000 0.060
#> GSM148554 1 0.1289 0.624 0.968 0.000 0.032
#> GSM148555 1 0.3412 0.596 0.876 0.000 0.124
#> GSM148556 1 0.3482 0.593 0.872 0.000 0.128
#> GSM148557 1 0.3752 0.592 0.856 0.000 0.144
#> GSM148558 1 0.4178 0.580 0.828 0.000 0.172
#> GSM148559 3 0.6309 0.616 0.496 0.000 0.504
#> GSM148560 1 0.6305 -0.673 0.516 0.000 0.484
#> GSM148561 3 0.6192 0.763 0.420 0.000 0.580
#> GSM148562 3 0.6026 0.796 0.376 0.000 0.624
#> GSM148563 3 0.5098 0.843 0.248 0.000 0.752
#> GSM148564 3 0.5216 0.847 0.260 0.000 0.740
#> GSM148565 3 0.4974 0.840 0.236 0.000 0.764
#> GSM148566 1 0.6308 -0.680 0.508 0.000 0.492
#> GSM148567 3 0.6168 0.767 0.412 0.000 0.588
#> GSM148568 3 0.6154 0.756 0.408 0.000 0.592
#> GSM148569 3 0.5650 0.836 0.312 0.000 0.688
#> GSM148570 3 0.4842 0.836 0.224 0.000 0.776
#> GSM148571 3 0.4842 0.836 0.224 0.000 0.776
#> GSM148572 3 0.4887 0.838 0.228 0.000 0.772
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM148516 3 0.5555 0.9618 0.176 0.088 0.732 0.004
#> GSM148517 1 0.2401 0.6764 0.904 0.000 0.092 0.004
#> GSM148518 2 0.1975 0.9256 0.016 0.936 0.048 0.000
#> GSM148519 2 0.0000 0.9828 0.000 1.000 0.000 0.000
#> GSM148520 2 0.0188 0.9823 0.000 0.996 0.004 0.000
#> GSM148521 2 0.0336 0.9807 0.000 0.992 0.008 0.000
#> GSM148522 2 0.0336 0.9804 0.000 0.992 0.008 0.000
#> GSM148523 2 0.0000 0.9828 0.000 1.000 0.000 0.000
#> GSM148524 2 0.0000 0.9828 0.000 1.000 0.000 0.000
#> GSM148525 2 0.0188 0.9823 0.000 0.996 0.004 0.000
#> GSM148526 2 0.0188 0.9822 0.000 0.996 0.004 0.000
#> GSM148527 2 0.0000 0.9828 0.000 1.000 0.000 0.000
#> GSM148528 2 0.0000 0.9828 0.000 1.000 0.000 0.000
#> GSM148529 2 0.0000 0.9828 0.000 1.000 0.000 0.000
#> GSM148530 2 0.0336 0.9807 0.000 0.992 0.008 0.000
#> GSM148531 2 0.0188 0.9823 0.000 0.996 0.004 0.000
#> GSM148532 2 0.0817 0.9690 0.000 0.976 0.024 0.000
#> GSM148533 2 0.0188 0.9822 0.000 0.996 0.004 0.000
#> GSM148534 2 0.0188 0.9823 0.000 0.996 0.004 0.000
#> GSM148535 2 0.0000 0.9828 0.000 1.000 0.000 0.000
#> GSM148536 2 0.0000 0.9828 0.000 1.000 0.000 0.000
#> GSM148537 2 0.4017 0.7811 0.044 0.828 0.128 0.000
#> GSM148538 2 0.0336 0.9800 0.000 0.992 0.008 0.000
#> GSM148539 3 0.6178 0.9267 0.184 0.128 0.684 0.004
#> GSM148540 3 0.5815 0.9479 0.168 0.112 0.716 0.004
#> GSM148541 3 0.5674 0.9594 0.176 0.096 0.724 0.004
#> GSM148542 3 0.5380 0.9603 0.184 0.072 0.740 0.004
#> GSM148543 3 0.5446 0.9621 0.184 0.076 0.736 0.004
#> GSM148544 3 0.5242 0.9524 0.184 0.064 0.748 0.004
#> GSM148545 1 0.2053 0.6900 0.924 0.000 0.072 0.004
#> GSM148546 1 0.1209 0.7089 0.964 0.000 0.032 0.004
#> GSM148547 1 0.1209 0.7089 0.964 0.000 0.032 0.004
#> GSM148548 1 0.3707 0.6976 0.840 0.000 0.028 0.132
#> GSM148549 1 0.4462 0.6837 0.792 0.000 0.044 0.164
#> GSM148550 1 0.4839 0.6655 0.756 0.000 0.044 0.200
#> GSM148551 1 0.4839 0.6663 0.756 0.000 0.044 0.200
#> GSM148552 1 0.1798 0.7116 0.944 0.000 0.040 0.016
#> GSM148553 1 0.1724 0.7132 0.948 0.000 0.032 0.020
#> GSM148554 1 0.1151 0.7151 0.968 0.000 0.008 0.024
#> GSM148555 1 0.4638 0.6769 0.776 0.000 0.044 0.180
#> GSM148556 1 0.4707 0.6638 0.760 0.000 0.036 0.204
#> GSM148557 1 0.5055 0.6205 0.712 0.000 0.032 0.256
#> GSM148558 1 0.5522 0.5801 0.668 0.000 0.044 0.288
#> GSM148559 1 0.7632 -0.0346 0.468 0.000 0.244 0.288
#> GSM148560 1 0.7636 -0.0371 0.468 0.000 0.248 0.284
#> GSM148561 4 0.7429 0.3833 0.316 0.000 0.192 0.492
#> GSM148562 4 0.5690 0.5782 0.268 0.000 0.060 0.672
#> GSM148563 4 0.1151 0.7542 0.024 0.000 0.008 0.968
#> GSM148564 4 0.3051 0.7419 0.088 0.000 0.028 0.884
#> GSM148565 4 0.0376 0.7520 0.004 0.000 0.004 0.992
#> GSM148566 1 0.7651 -0.0439 0.464 0.000 0.248 0.288
#> GSM148567 4 0.6483 0.4817 0.324 0.000 0.092 0.584
#> GSM148568 4 0.6494 0.4533 0.340 0.000 0.088 0.572
#> GSM148569 4 0.4188 0.7099 0.148 0.000 0.040 0.812
#> GSM148570 4 0.0188 0.7508 0.000 0.000 0.004 0.996
#> GSM148571 4 0.0188 0.7508 0.000 0.000 0.004 0.996
#> GSM148572 4 0.0188 0.7508 0.000 0.000 0.004 0.996
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM148516 3 0.3910 0.854 0.040 0.140 0.808 0.000 0.012
#> GSM148517 1 0.5344 0.465 0.500 0.000 0.052 0.000 0.448
#> GSM148518 2 0.1990 0.933 0.004 0.928 0.052 0.004 0.012
#> GSM148519 2 0.0613 0.979 0.004 0.984 0.000 0.008 0.004
#> GSM148520 2 0.0566 0.980 0.000 0.984 0.000 0.012 0.004
#> GSM148521 2 0.0290 0.981 0.000 0.992 0.000 0.008 0.000
#> GSM148522 2 0.0566 0.978 0.000 0.984 0.012 0.004 0.000
#> GSM148523 2 0.0451 0.981 0.000 0.988 0.004 0.008 0.000
#> GSM148524 2 0.0290 0.981 0.000 0.992 0.000 0.008 0.000
#> GSM148525 2 0.0404 0.980 0.000 0.988 0.000 0.000 0.012
#> GSM148526 2 0.0613 0.981 0.000 0.984 0.004 0.004 0.008
#> GSM148527 2 0.0451 0.981 0.000 0.988 0.000 0.004 0.008
#> GSM148528 2 0.0451 0.980 0.000 0.988 0.000 0.004 0.008
#> GSM148529 2 0.0451 0.981 0.000 0.988 0.004 0.008 0.000
#> GSM148530 2 0.0451 0.981 0.000 0.988 0.004 0.008 0.000
#> GSM148531 2 0.0579 0.980 0.000 0.984 0.008 0.008 0.000
#> GSM148532 2 0.0727 0.980 0.000 0.980 0.004 0.004 0.012
#> GSM148533 2 0.0451 0.980 0.000 0.988 0.008 0.000 0.004
#> GSM148534 2 0.0566 0.979 0.000 0.984 0.000 0.004 0.012
#> GSM148535 2 0.0324 0.980 0.000 0.992 0.000 0.004 0.004
#> GSM148536 2 0.0451 0.981 0.000 0.988 0.000 0.008 0.004
#> GSM148537 2 0.3149 0.853 0.024 0.864 0.100 0.008 0.004
#> GSM148538 2 0.0912 0.972 0.000 0.972 0.016 0.012 0.000
#> GSM148539 3 0.3867 0.840 0.048 0.144 0.804 0.000 0.004
#> GSM148540 3 0.3543 0.867 0.040 0.128 0.828 0.000 0.004
#> GSM148541 3 0.2569 0.892 0.040 0.068 0.892 0.000 0.000
#> GSM148542 3 0.1569 0.877 0.044 0.008 0.944 0.000 0.004
#> GSM148543 3 0.1787 0.879 0.044 0.016 0.936 0.000 0.004
#> GSM148544 3 0.1443 0.873 0.044 0.004 0.948 0.000 0.004
#> GSM148545 1 0.5365 0.515 0.528 0.000 0.056 0.000 0.416
#> GSM148546 1 0.4817 0.651 0.656 0.000 0.044 0.000 0.300
#> GSM148547 1 0.4728 0.662 0.664 0.000 0.040 0.000 0.296
#> GSM148548 1 0.2395 0.715 0.904 0.000 0.016 0.008 0.072
#> GSM148549 1 0.1904 0.720 0.936 0.000 0.028 0.020 0.016
#> GSM148550 1 0.1822 0.716 0.936 0.000 0.024 0.036 0.004
#> GSM148551 1 0.1911 0.715 0.932 0.000 0.028 0.036 0.004
#> GSM148552 1 0.4227 0.679 0.692 0.000 0.016 0.000 0.292
#> GSM148553 1 0.4445 0.672 0.676 0.000 0.024 0.000 0.300
#> GSM148554 1 0.4212 0.705 0.736 0.000 0.024 0.004 0.236
#> GSM148555 1 0.1668 0.715 0.940 0.000 0.028 0.032 0.000
#> GSM148556 1 0.2523 0.721 0.908 0.000 0.024 0.040 0.028
#> GSM148557 1 0.3795 0.672 0.788 0.000 0.024 0.184 0.004
#> GSM148558 1 0.4990 0.568 0.644 0.000 0.024 0.316 0.016
#> GSM148559 5 0.2011 0.804 0.044 0.000 0.008 0.020 0.928
#> GSM148560 5 0.1772 0.805 0.032 0.000 0.008 0.020 0.940
#> GSM148561 5 0.6558 0.169 0.236 0.000 0.012 0.212 0.540
#> GSM148562 4 0.6235 0.566 0.256 0.000 0.008 0.572 0.164
#> GSM148563 4 0.3319 0.726 0.160 0.000 0.000 0.820 0.020
#> GSM148564 4 0.3667 0.728 0.140 0.000 0.000 0.812 0.048
#> GSM148565 4 0.1300 0.725 0.028 0.000 0.000 0.956 0.016
#> GSM148566 5 0.2228 0.804 0.056 0.000 0.008 0.020 0.916
#> GSM148567 4 0.7220 0.260 0.268 0.000 0.020 0.396 0.316
#> GSM148568 4 0.7144 0.236 0.264 0.000 0.016 0.396 0.324
#> GSM148569 4 0.4819 0.687 0.192 0.000 0.000 0.716 0.092
#> GSM148570 4 0.0609 0.721 0.020 0.000 0.000 0.980 0.000
#> GSM148571 4 0.0609 0.721 0.020 0.000 0.000 0.980 0.000
#> GSM148572 4 0.0609 0.721 0.020 0.000 0.000 0.980 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM148516 3 0.3552 0.8496 0.004 0.108 0.824 0.004 0.008 0.052
#> GSM148517 6 0.4634 0.6409 0.056 0.000 0.004 0.000 0.300 0.640
#> GSM148518 2 0.1860 0.9435 0.004 0.928 0.036 0.004 0.000 0.028
#> GSM148519 2 0.0603 0.9664 0.000 0.980 0.000 0.004 0.000 0.016
#> GSM148520 2 0.1364 0.9575 0.000 0.944 0.000 0.004 0.004 0.048
#> GSM148521 2 0.0713 0.9660 0.000 0.972 0.000 0.000 0.000 0.028
#> GSM148522 2 0.0922 0.9647 0.000 0.968 0.004 0.004 0.000 0.024
#> GSM148523 2 0.0777 0.9640 0.000 0.972 0.000 0.000 0.004 0.024
#> GSM148524 2 0.0748 0.9679 0.000 0.976 0.000 0.004 0.004 0.016
#> GSM148525 2 0.1080 0.9624 0.004 0.960 0.000 0.000 0.004 0.032
#> GSM148526 2 0.0837 0.9673 0.000 0.972 0.004 0.000 0.004 0.020
#> GSM148527 2 0.0692 0.9680 0.000 0.976 0.000 0.000 0.004 0.020
#> GSM148528 2 0.0692 0.9669 0.000 0.976 0.000 0.004 0.000 0.020
#> GSM148529 2 0.0935 0.9626 0.000 0.964 0.000 0.000 0.004 0.032
#> GSM148530 2 0.1265 0.9571 0.000 0.948 0.000 0.000 0.008 0.044
#> GSM148531 2 0.1080 0.9634 0.004 0.960 0.000 0.000 0.004 0.032
#> GSM148532 2 0.1096 0.9638 0.004 0.964 0.008 0.000 0.004 0.020
#> GSM148533 2 0.1080 0.9622 0.004 0.960 0.004 0.000 0.000 0.032
#> GSM148534 2 0.0837 0.9662 0.000 0.972 0.004 0.004 0.000 0.020
#> GSM148535 2 0.0713 0.9669 0.000 0.972 0.000 0.000 0.000 0.028
#> GSM148536 2 0.0291 0.9682 0.004 0.992 0.000 0.000 0.004 0.000
#> GSM148537 2 0.2663 0.8949 0.004 0.884 0.076 0.004 0.008 0.024
#> GSM148538 2 0.2257 0.9274 0.000 0.900 0.008 0.004 0.012 0.076
#> GSM148539 3 0.2747 0.8516 0.004 0.108 0.860 0.000 0.000 0.028
#> GSM148540 3 0.3407 0.8270 0.004 0.132 0.820 0.000 0.008 0.036
#> GSM148541 3 0.2152 0.8812 0.004 0.040 0.916 0.004 0.004 0.032
#> GSM148542 3 0.0922 0.8751 0.004 0.004 0.968 0.000 0.000 0.024
#> GSM148543 3 0.1477 0.8749 0.004 0.008 0.940 0.000 0.000 0.048
#> GSM148544 3 0.1440 0.8723 0.004 0.004 0.944 0.000 0.004 0.044
#> GSM148545 6 0.4484 0.6732 0.056 0.000 0.004 0.000 0.268 0.672
#> GSM148546 6 0.4490 0.7321 0.108 0.000 0.004 0.000 0.172 0.716
#> GSM148547 6 0.5224 0.7344 0.176 0.000 0.004 0.004 0.172 0.644
#> GSM148548 1 0.4124 0.4893 0.728 0.000 0.012 0.000 0.036 0.224
#> GSM148549 1 0.1957 0.7771 0.928 0.000 0.028 0.012 0.008 0.024
#> GSM148550 1 0.1346 0.7802 0.952 0.000 0.024 0.016 0.000 0.008
#> GSM148551 1 0.1684 0.7796 0.940 0.000 0.028 0.016 0.008 0.008
#> GSM148552 6 0.5995 0.5388 0.348 0.000 0.004 0.000 0.204 0.444
#> GSM148553 6 0.6039 0.5382 0.344 0.000 0.004 0.000 0.216 0.436
#> GSM148554 1 0.5843 -0.3188 0.480 0.000 0.004 0.000 0.176 0.340
#> GSM148555 1 0.1396 0.7777 0.952 0.000 0.024 0.004 0.008 0.012
#> GSM148556 1 0.1794 0.7796 0.936 0.000 0.024 0.020 0.008 0.012
#> GSM148557 1 0.3690 0.6695 0.784 0.000 0.024 0.176 0.004 0.012
#> GSM148558 1 0.4838 0.5809 0.668 0.000 0.028 0.268 0.020 0.016
#> GSM148559 5 0.1720 0.7006 0.032 0.000 0.000 0.000 0.928 0.040
#> GSM148560 5 0.1984 0.7116 0.032 0.000 0.000 0.000 0.912 0.056
#> GSM148561 5 0.6125 0.0998 0.232 0.000 0.004 0.220 0.528 0.016
#> GSM148562 4 0.5743 0.5502 0.276 0.000 0.000 0.560 0.148 0.016
#> GSM148563 4 0.3154 0.7008 0.184 0.000 0.000 0.800 0.012 0.004
#> GSM148564 4 0.3615 0.7053 0.156 0.000 0.000 0.796 0.032 0.016
#> GSM148565 4 0.1232 0.6956 0.016 0.000 0.004 0.956 0.000 0.024
#> GSM148566 5 0.2407 0.7134 0.056 0.000 0.000 0.004 0.892 0.048
#> GSM148567 4 0.6332 0.2895 0.260 0.000 0.000 0.404 0.324 0.012
#> GSM148568 4 0.6346 0.2831 0.268 0.000 0.000 0.400 0.320 0.012
#> GSM148569 4 0.4516 0.6696 0.212 0.000 0.000 0.708 0.068 0.012
#> GSM148570 4 0.0520 0.6995 0.008 0.000 0.000 0.984 0.000 0.008
#> GSM148571 4 0.1232 0.6949 0.016 0.000 0.004 0.956 0.000 0.024
#> GSM148572 4 0.1138 0.6930 0.012 0.000 0.004 0.960 0.000 0.024
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) dose(p) time(p) k
#> SD:mclust 56 7.87e-08 2.20e-02 0.991 2
#> SD:mclust 53 1.19e-07 1.80e-04 0.994 3
#> SD:mclust 51 3.39e-09 7.11e-07 0.979 4
#> SD:mclust 53 7.70e-10 1.19e-06 0.789 5
#> SD:mclust 52 4.08e-08 3.25e-05 0.534 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 21163 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.998 0.999 0.5092 0.491 0.491
#> 3 3 0.676 0.863 0.829 0.1964 1.000 1.000
#> 4 4 0.623 0.686 0.815 0.1497 0.798 0.588
#> 5 5 0.597 0.656 0.801 0.0727 0.960 0.864
#> 6 6 0.582 0.633 0.761 0.0424 0.982 0.931
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
#> GSM148516 2 0.0000 0.998 0.000 1.000
#> GSM148517 1 0.0000 1.000 1.000 0.000
#> GSM148518 2 0.0000 0.998 0.000 1.000
#> GSM148519 2 0.0000 0.998 0.000 1.000
#> GSM148520 2 0.0000 0.998 0.000 1.000
#> GSM148521 2 0.0000 0.998 0.000 1.000
#> GSM148522 2 0.0000 0.998 0.000 1.000
#> GSM148523 2 0.0000 0.998 0.000 1.000
#> GSM148524 2 0.0000 0.998 0.000 1.000
#> GSM148525 2 0.0000 0.998 0.000 1.000
#> GSM148526 2 0.0000 0.998 0.000 1.000
#> GSM148527 2 0.0000 0.998 0.000 1.000
#> GSM148528 2 0.0000 0.998 0.000 1.000
#> GSM148529 2 0.0000 0.998 0.000 1.000
#> GSM148530 2 0.0000 0.998 0.000 1.000
#> GSM148531 2 0.0000 0.998 0.000 1.000
#> GSM148532 2 0.0000 0.998 0.000 1.000
#> GSM148533 2 0.0000 0.998 0.000 1.000
#> GSM148534 2 0.0000 0.998 0.000 1.000
#> GSM148535 2 0.0000 0.998 0.000 1.000
#> GSM148536 2 0.0000 0.998 0.000 1.000
#> GSM148537 2 0.0000 0.998 0.000 1.000
#> GSM148538 2 0.0000 0.998 0.000 1.000
#> GSM148539 2 0.0000 0.998 0.000 1.000
#> GSM148540 2 0.0000 0.998 0.000 1.000
#> GSM148541 2 0.0000 0.998 0.000 1.000
#> GSM148542 2 0.0376 0.995 0.004 0.996
#> GSM148543 2 0.0000 0.998 0.000 1.000
#> GSM148544 2 0.2603 0.954 0.044 0.956
#> GSM148545 1 0.0000 1.000 1.000 0.000
#> GSM148546 1 0.0000 1.000 1.000 0.000
#> GSM148547 1 0.0000 1.000 1.000 0.000
#> GSM148548 1 0.0000 1.000 1.000 0.000
#> GSM148549 1 0.0000 1.000 1.000 0.000
#> GSM148550 1 0.0000 1.000 1.000 0.000
#> GSM148551 1 0.0000 1.000 1.000 0.000
#> GSM148552 1 0.0000 1.000 1.000 0.000
#> GSM148553 1 0.0376 0.996 0.996 0.004
#> GSM148554 1 0.0000 1.000 1.000 0.000
#> GSM148555 1 0.0000 1.000 1.000 0.000
#> GSM148556 1 0.0000 1.000 1.000 0.000
#> GSM148557 1 0.0000 1.000 1.000 0.000
#> GSM148558 1 0.0000 1.000 1.000 0.000
#> GSM148559 1 0.0000 1.000 1.000 0.000
#> GSM148560 1 0.0000 1.000 1.000 0.000
#> GSM148561 1 0.0000 1.000 1.000 0.000
#> GSM148562 1 0.0000 1.000 1.000 0.000
#> GSM148563 1 0.0000 1.000 1.000 0.000
#> GSM148564 1 0.0000 1.000 1.000 0.000
#> GSM148565 1 0.0000 1.000 1.000 0.000
#> GSM148566 1 0.0000 1.000 1.000 0.000
#> GSM148567 1 0.0000 1.000 1.000 0.000
#> GSM148568 1 0.0000 1.000 1.000 0.000
#> GSM148569 1 0.0000 1.000 1.000 0.000
#> GSM148570 1 0.0000 1.000 1.000 0.000
#> GSM148571 1 0.0000 1.000 1.000 0.000
#> GSM148572 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
#> GSM148516 2 0.5948 0.741 0.000 0.640 NA
#> GSM148517 1 0.6045 0.796 0.620 0.000 NA
#> GSM148518 2 0.0747 0.937 0.000 0.984 NA
#> GSM148519 2 0.0892 0.936 0.000 0.980 NA
#> GSM148520 2 0.1643 0.934 0.000 0.956 NA
#> GSM148521 2 0.0747 0.938 0.000 0.984 NA
#> GSM148522 2 0.0892 0.937 0.000 0.980 NA
#> GSM148523 2 0.0424 0.936 0.000 0.992 NA
#> GSM148524 2 0.1289 0.934 0.000 0.968 NA
#> GSM148525 2 0.1964 0.931 0.000 0.944 NA
#> GSM148526 2 0.1753 0.933 0.000 0.952 NA
#> GSM148527 2 0.1289 0.937 0.000 0.968 NA
#> GSM148528 2 0.1031 0.937 0.000 0.976 NA
#> GSM148529 2 0.1289 0.935 0.000 0.968 NA
#> GSM148530 2 0.0892 0.938 0.000 0.980 NA
#> GSM148531 2 0.1163 0.937 0.000 0.972 NA
#> GSM148532 2 0.2356 0.926 0.000 0.928 NA
#> GSM148533 2 0.0892 0.936 0.000 0.980 NA
#> GSM148534 2 0.1964 0.930 0.000 0.944 NA
#> GSM148535 2 0.0892 0.936 0.000 0.980 NA
#> GSM148536 2 0.0000 0.936 0.000 1.000 NA
#> GSM148537 2 0.1289 0.935 0.000 0.968 NA
#> GSM148538 2 0.1753 0.933 0.000 0.952 NA
#> GSM148539 2 0.5016 0.838 0.000 0.760 NA
#> GSM148540 2 0.5138 0.839 0.000 0.748 NA
#> GSM148541 2 0.5529 0.803 0.000 0.704 NA
#> GSM148542 2 0.5517 0.819 0.004 0.728 NA
#> GSM148543 2 0.4504 0.867 0.000 0.804 NA
#> GSM148544 2 0.6258 0.825 0.052 0.752 NA
#> GSM148545 1 0.5988 0.800 0.632 0.000 NA
#> GSM148546 1 0.5968 0.802 0.636 0.000 NA
#> GSM148547 1 0.5859 0.810 0.656 0.000 NA
#> GSM148548 1 0.5216 0.837 0.740 0.000 NA
#> GSM148549 1 0.5016 0.842 0.760 0.000 NA
#> GSM148550 1 0.4291 0.850 0.820 0.000 NA
#> GSM148551 1 0.3752 0.854 0.856 0.000 NA
#> GSM148552 1 0.6724 0.762 0.568 0.012 NA
#> GSM148553 1 0.6111 0.786 0.604 0.000 NA
#> GSM148554 1 0.5431 0.831 0.716 0.000 NA
#> GSM148555 1 0.3619 0.853 0.864 0.000 NA
#> GSM148556 1 0.3267 0.854 0.884 0.000 NA
#> GSM148557 1 0.2711 0.845 0.912 0.000 NA
#> GSM148558 1 0.3267 0.837 0.884 0.000 NA
#> GSM148559 1 0.5948 0.806 0.640 0.000 NA
#> GSM148560 1 0.4974 0.843 0.764 0.000 NA
#> GSM148561 1 0.4235 0.829 0.824 0.000 NA
#> GSM148562 1 0.2537 0.834 0.920 0.000 NA
#> GSM148563 1 0.3340 0.823 0.880 0.000 NA
#> GSM148564 1 0.4452 0.798 0.808 0.000 NA
#> GSM148565 1 0.4452 0.800 0.808 0.000 NA
#> GSM148566 1 0.4750 0.846 0.784 0.000 NA
#> GSM148567 1 0.3267 0.842 0.884 0.000 NA
#> GSM148568 1 0.2261 0.842 0.932 0.000 NA
#> GSM148569 1 0.4235 0.802 0.824 0.000 NA
#> GSM148570 1 0.4452 0.796 0.808 0.000 NA
#> GSM148571 1 0.4399 0.799 0.812 0.000 NA
#> GSM148572 1 0.4605 0.792 0.796 0.000 NA
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM148516 3 0.5697 0.774 0.056 0.280 0.664 0.000
#> GSM148517 1 0.3266 0.761 0.876 0.000 0.084 0.040
#> GSM148518 2 0.2149 0.802 0.000 0.912 0.088 0.000
#> GSM148519 2 0.0895 0.838 0.000 0.976 0.020 0.004
#> GSM148520 2 0.2101 0.811 0.000 0.928 0.060 0.012
#> GSM148521 2 0.1807 0.833 0.000 0.940 0.052 0.008
#> GSM148522 2 0.1209 0.838 0.000 0.964 0.032 0.004
#> GSM148523 2 0.0817 0.838 0.000 0.976 0.024 0.000
#> GSM148524 2 0.1452 0.829 0.000 0.956 0.036 0.008
#> GSM148525 2 0.3710 0.618 0.000 0.804 0.192 0.004
#> GSM148526 2 0.3157 0.716 0.000 0.852 0.144 0.004
#> GSM148527 2 0.1211 0.839 0.000 0.960 0.040 0.000
#> GSM148528 2 0.1398 0.838 0.000 0.956 0.040 0.004
#> GSM148529 2 0.1389 0.820 0.000 0.952 0.048 0.000
#> GSM148530 2 0.1661 0.835 0.000 0.944 0.052 0.004
#> GSM148531 2 0.1211 0.838 0.000 0.960 0.040 0.000
#> GSM148532 2 0.3494 0.656 0.000 0.824 0.172 0.004
#> GSM148533 2 0.2011 0.808 0.000 0.920 0.080 0.000
#> GSM148534 2 0.2402 0.818 0.000 0.912 0.076 0.012
#> GSM148535 2 0.1118 0.836 0.000 0.964 0.036 0.000
#> GSM148536 2 0.1356 0.837 0.000 0.960 0.032 0.008
#> GSM148537 2 0.1398 0.834 0.000 0.956 0.040 0.004
#> GSM148538 2 0.1867 0.813 0.000 0.928 0.072 0.000
#> GSM148539 2 0.6445 -0.566 0.044 0.524 0.420 0.012
#> GSM148540 3 0.5980 0.676 0.024 0.456 0.512 0.008
#> GSM148541 3 0.5733 0.808 0.040 0.308 0.648 0.004
#> GSM148542 3 0.6420 0.804 0.028 0.352 0.588 0.032
#> GSM148543 3 0.6710 0.693 0.036 0.456 0.480 0.028
#> GSM148544 2 0.8208 -0.562 0.012 0.384 0.344 0.260
#> GSM148545 1 0.2586 0.784 0.912 0.000 0.040 0.048
#> GSM148546 1 0.2179 0.794 0.924 0.000 0.012 0.064
#> GSM148547 1 0.2300 0.794 0.920 0.000 0.016 0.064
#> GSM148548 1 0.3842 0.779 0.836 0.000 0.036 0.128
#> GSM148549 1 0.5753 0.621 0.680 0.000 0.072 0.248
#> GSM148550 1 0.4737 0.673 0.728 0.000 0.020 0.252
#> GSM148551 1 0.6176 0.186 0.524 0.000 0.052 0.424
#> GSM148552 1 0.3255 0.784 0.888 0.008 0.056 0.048
#> GSM148553 1 0.2021 0.782 0.936 0.000 0.040 0.024
#> GSM148554 1 0.3441 0.782 0.856 0.000 0.024 0.120
#> GSM148555 1 0.5596 0.532 0.632 0.000 0.036 0.332
#> GSM148556 1 0.5159 0.501 0.624 0.000 0.012 0.364
#> GSM148557 4 0.4990 0.422 0.352 0.000 0.008 0.640
#> GSM148558 4 0.4420 0.654 0.240 0.000 0.012 0.748
#> GSM148559 1 0.4161 0.741 0.832 0.004 0.108 0.056
#> GSM148560 1 0.4724 0.733 0.792 0.000 0.096 0.112
#> GSM148561 4 0.7988 0.160 0.360 0.008 0.224 0.408
#> GSM148562 4 0.4194 0.753 0.172 0.000 0.028 0.800
#> GSM148563 4 0.3441 0.777 0.120 0.000 0.024 0.856
#> GSM148564 4 0.2053 0.788 0.072 0.000 0.004 0.924
#> GSM148565 4 0.2060 0.786 0.052 0.000 0.016 0.932
#> GSM148566 1 0.4286 0.752 0.812 0.000 0.052 0.136
#> GSM148567 4 0.6637 0.444 0.324 0.000 0.104 0.572
#> GSM148568 4 0.5169 0.626 0.272 0.000 0.032 0.696
#> GSM148569 4 0.1637 0.792 0.060 0.000 0.000 0.940
#> GSM148570 4 0.1792 0.792 0.068 0.000 0.000 0.932
#> GSM148571 4 0.1890 0.789 0.056 0.000 0.008 0.936
#> GSM148572 4 0.2282 0.783 0.052 0.000 0.024 0.924
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM148516 3 0.5578 0.6299 0.024 0.112 0.688 0.000 0.176
#> GSM148517 1 0.3538 0.6948 0.832 0.000 0.028 0.012 0.128
#> GSM148518 2 0.2573 0.8664 0.000 0.880 0.104 0.000 0.016
#> GSM148519 2 0.0898 0.8971 0.000 0.972 0.020 0.000 0.008
#> GSM148520 2 0.3291 0.8417 0.000 0.848 0.064 0.000 0.088
#> GSM148521 2 0.2153 0.8919 0.000 0.916 0.040 0.000 0.044
#> GSM148522 2 0.1560 0.8973 0.000 0.948 0.028 0.004 0.020
#> GSM148523 2 0.1372 0.8983 0.000 0.956 0.024 0.004 0.016
#> GSM148524 2 0.1195 0.8976 0.000 0.960 0.028 0.000 0.012
#> GSM148525 2 0.4603 0.5355 0.000 0.668 0.300 0.000 0.032
#> GSM148526 2 0.3810 0.7703 0.000 0.792 0.168 0.000 0.040
#> GSM148527 2 0.1741 0.8990 0.000 0.936 0.040 0.000 0.024
#> GSM148528 2 0.1740 0.8988 0.000 0.932 0.056 0.000 0.012
#> GSM148529 2 0.1630 0.8864 0.004 0.944 0.016 0.000 0.036
#> GSM148530 2 0.1582 0.9010 0.000 0.944 0.028 0.000 0.028
#> GSM148531 2 0.1822 0.9009 0.004 0.936 0.036 0.000 0.024
#> GSM148532 2 0.4840 0.6102 0.000 0.688 0.248 0.000 0.064
#> GSM148533 2 0.2720 0.8711 0.000 0.880 0.096 0.004 0.020
#> GSM148534 2 0.2645 0.8815 0.000 0.888 0.068 0.000 0.044
#> GSM148535 2 0.2125 0.8949 0.000 0.920 0.052 0.004 0.024
#> GSM148536 2 0.1992 0.8954 0.000 0.924 0.044 0.000 0.032
#> GSM148537 2 0.1996 0.8958 0.000 0.928 0.036 0.004 0.032
#> GSM148538 2 0.2308 0.8865 0.004 0.912 0.036 0.000 0.048
#> GSM148539 3 0.6086 0.6214 0.032 0.316 0.580 0.000 0.072
#> GSM148540 3 0.5780 0.7031 0.016 0.224 0.656 0.004 0.100
#> GSM148541 3 0.4098 0.6898 0.016 0.112 0.808 0.000 0.064
#> GSM148542 3 0.4975 0.7073 0.016 0.148 0.760 0.024 0.052
#> GSM148543 3 0.6632 0.7074 0.024 0.216 0.620 0.032 0.108
#> GSM148544 3 0.7920 0.3658 0.008 0.176 0.392 0.348 0.076
#> GSM148545 1 0.2561 0.7163 0.884 0.000 0.020 0.000 0.096
#> GSM148546 1 0.1364 0.7349 0.952 0.000 0.012 0.000 0.036
#> GSM148547 1 0.2100 0.7366 0.924 0.000 0.012 0.016 0.048
#> GSM148548 1 0.3504 0.7181 0.844 0.000 0.012 0.044 0.100
#> GSM148549 1 0.6116 0.5631 0.668 0.000 0.080 0.160 0.092
#> GSM148550 1 0.5054 0.6565 0.744 0.000 0.032 0.140 0.084
#> GSM148551 1 0.6947 0.2038 0.496 0.000 0.044 0.328 0.132
#> GSM148552 1 0.1502 0.7340 0.940 0.004 0.000 0.000 0.056
#> GSM148553 1 0.2110 0.7314 0.912 0.000 0.016 0.000 0.072
#> GSM148554 1 0.2390 0.7350 0.908 0.000 0.008 0.024 0.060
#> GSM148555 1 0.5791 0.5760 0.676 0.000 0.032 0.172 0.120
#> GSM148556 1 0.5294 0.5478 0.680 0.000 0.016 0.236 0.068
#> GSM148557 4 0.5609 0.3145 0.292 0.000 0.016 0.624 0.068
#> GSM148558 4 0.5244 0.4393 0.212 0.000 0.024 0.700 0.064
#> GSM148559 1 0.5322 0.5749 0.692 0.016 0.040 0.016 0.236
#> GSM148560 1 0.5878 0.4419 0.636 0.004 0.044 0.048 0.268
#> GSM148561 5 0.7605 0.0000 0.156 0.000 0.100 0.264 0.480
#> GSM148562 4 0.5236 0.4285 0.120 0.000 0.004 0.692 0.184
#> GSM148563 4 0.3948 0.5949 0.056 0.000 0.008 0.808 0.128
#> GSM148564 4 0.2664 0.6438 0.040 0.000 0.004 0.892 0.064
#> GSM148565 4 0.1173 0.6634 0.012 0.000 0.004 0.964 0.020
#> GSM148566 1 0.5423 0.4986 0.672 0.000 0.028 0.056 0.244
#> GSM148567 4 0.7371 -0.6215 0.232 0.004 0.024 0.372 0.368
#> GSM148568 4 0.6098 0.0635 0.196 0.000 0.000 0.568 0.236
#> GSM148569 4 0.1668 0.6675 0.032 0.000 0.000 0.940 0.028
#> GSM148570 4 0.2331 0.6508 0.024 0.000 0.004 0.908 0.064
#> GSM148571 4 0.1498 0.6663 0.024 0.000 0.008 0.952 0.016
#> GSM148572 4 0.1095 0.6563 0.012 0.000 0.012 0.968 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM148516 3 0.585 0.58120 0.008 0.072 0.648 0.000 0.112 NA
#> GSM148517 1 0.508 0.48131 0.652 0.000 0.016 0.008 0.064 NA
#> GSM148518 2 0.303 0.83781 0.000 0.840 0.104 0.000 0.000 NA
#> GSM148519 2 0.192 0.87954 0.000 0.920 0.012 0.000 0.012 NA
#> GSM148520 2 0.405 0.78593 0.000 0.768 0.044 0.000 0.024 NA
#> GSM148521 2 0.250 0.87813 0.004 0.892 0.032 0.000 0.008 NA
#> GSM148522 2 0.215 0.87615 0.000 0.900 0.028 0.000 0.000 NA
#> GSM148523 2 0.203 0.87966 0.000 0.912 0.024 0.000 0.004 NA
#> GSM148524 2 0.194 0.87732 0.000 0.916 0.012 0.000 0.008 NA
#> GSM148525 2 0.435 0.61472 0.000 0.684 0.268 0.000 0.008 NA
#> GSM148526 2 0.438 0.77862 0.004 0.764 0.120 0.000 0.024 NA
#> GSM148527 2 0.219 0.88036 0.000 0.904 0.032 0.000 0.004 NA
#> GSM148528 2 0.221 0.87900 0.000 0.908 0.032 0.000 0.012 NA
#> GSM148529 2 0.190 0.86944 0.000 0.916 0.008 0.000 0.008 NA
#> GSM148530 2 0.201 0.88107 0.000 0.916 0.036 0.000 0.004 NA
#> GSM148531 2 0.292 0.86956 0.004 0.864 0.064 0.000 0.004 NA
#> GSM148532 2 0.536 0.49653 0.000 0.608 0.276 0.000 0.020 NA
#> GSM148533 2 0.249 0.86364 0.000 0.880 0.076 0.000 0.000 NA
#> GSM148534 2 0.304 0.86170 0.000 0.860 0.052 0.000 0.020 NA
#> GSM148535 2 0.218 0.87538 0.000 0.908 0.052 0.000 0.008 NA
#> GSM148536 2 0.242 0.87639 0.000 0.892 0.032 0.000 0.008 NA
#> GSM148537 2 0.240 0.87430 0.000 0.896 0.024 0.000 0.016 NA
#> GSM148538 2 0.276 0.85560 0.008 0.872 0.020 0.000 0.008 NA
#> GSM148539 3 0.586 0.63252 0.044 0.216 0.612 0.000 0.004 NA
#> GSM148540 3 0.596 0.64533 0.008 0.128 0.632 0.000 0.064 NA
#> GSM148541 3 0.382 0.65254 0.000 0.064 0.812 0.000 0.044 NA
#> GSM148542 3 0.575 0.64137 0.016 0.096 0.696 0.016 0.112 NA
#> GSM148543 3 0.625 0.66773 0.012 0.180 0.628 0.020 0.044 NA
#> GSM148544 3 0.791 0.31851 0.004 0.124 0.360 0.348 0.056 NA
#> GSM148545 1 0.401 0.54527 0.740 0.000 0.008 0.000 0.040 NA
#> GSM148546 1 0.222 0.62600 0.912 0.000 0.012 0.004 0.036 NA
#> GSM148547 1 0.253 0.62601 0.892 0.000 0.008 0.004 0.044 NA
#> GSM148548 1 0.380 0.61114 0.832 0.004 0.032 0.024 0.076 NA
#> GSM148549 1 0.687 0.43871 0.592 0.000 0.124 0.120 0.096 NA
#> GSM148550 1 0.469 0.57596 0.752 0.000 0.036 0.144 0.044 NA
#> GSM148551 1 0.682 0.25349 0.508 0.000 0.028 0.284 0.124 NA
#> GSM148552 1 0.366 0.61736 0.824 0.000 0.020 0.008 0.052 NA
#> GSM148553 1 0.391 0.60621 0.808 0.004 0.024 0.004 0.052 NA
#> GSM148554 1 0.236 0.63569 0.912 0.004 0.008 0.020 0.028 NA
#> GSM148555 1 0.635 0.48730 0.628 0.004 0.036 0.144 0.136 NA
#> GSM148556 1 0.494 0.48691 0.676 0.000 0.008 0.244 0.044 NA
#> GSM148557 4 0.461 0.51731 0.220 0.000 0.000 0.704 0.048 NA
#> GSM148558 4 0.459 0.55937 0.192 0.000 0.008 0.728 0.048 NA
#> GSM148559 1 0.688 0.10485 0.472 0.028 0.008 0.016 0.192 NA
#> GSM148560 5 0.701 0.00172 0.400 0.004 0.032 0.048 0.404 NA
#> GSM148561 5 0.665 0.47677 0.132 0.004 0.056 0.156 0.604 NA
#> GSM148562 4 0.533 0.45319 0.080 0.000 0.004 0.640 0.248 NA
#> GSM148563 4 0.451 0.60436 0.048 0.000 0.008 0.716 0.216 NA
#> GSM148564 4 0.266 0.72617 0.008 0.000 0.008 0.880 0.084 NA
#> GSM148565 4 0.181 0.74172 0.012 0.000 0.008 0.932 0.040 NA
#> GSM148566 1 0.684 -0.13037 0.464 0.000 0.020 0.044 0.316 NA
#> GSM148567 5 0.636 0.37918 0.148 0.000 0.016 0.276 0.532 NA
#> GSM148568 4 0.640 0.08435 0.116 0.000 0.008 0.500 0.328 NA
#> GSM148569 4 0.176 0.74062 0.000 0.000 0.000 0.916 0.076 NA
#> GSM148570 4 0.211 0.73099 0.012 0.000 0.000 0.900 0.084 NA
#> GSM148571 4 0.105 0.74591 0.012 0.000 0.000 0.964 0.020 NA
#> GSM148572 4 0.187 0.73439 0.000 0.000 0.008 0.924 0.048 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 agent(p) dose(p) time(p) k
#> SD:NMF 57 2.57e-12 1.00e+00 1.000 2
#> SD:NMF 57 2.57e-12 1.00e+00 1.000 3
#> SD:NMF 51 8.66e-10 2.86e-04 0.629 4
#> SD:NMF 47 1.41e-08 1.98e-05 0.821 5
#> SD:NMF 43 8.43e-09 6.35e-05 0.434 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 21163 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.284 0.906 0.848 0.4280 0.491 0.491
#> 3 3 0.368 0.799 0.843 0.2691 0.982 0.964
#> 4 4 0.511 0.548 0.808 0.1189 0.983 0.964
#> 5 5 0.607 0.633 0.784 0.0708 0.897 0.777
#> 6 6 0.645 0.620 0.783 0.0562 0.997 0.991
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
#> GSM148516 2 0.5737 0.849 0.136 0.864
#> GSM148517 1 0.9460 0.548 0.636 0.364
#> GSM148518 2 0.0938 0.975 0.012 0.988
#> GSM148519 2 0.0000 0.974 0.000 1.000
#> GSM148520 2 0.1414 0.970 0.020 0.980
#> GSM148521 2 0.0376 0.975 0.004 0.996
#> GSM148522 2 0.1414 0.973 0.020 0.980
#> GSM148523 2 0.0672 0.975 0.008 0.992
#> GSM148524 2 0.0376 0.974 0.004 0.996
#> GSM148525 2 0.0672 0.974 0.008 0.992
#> GSM148526 2 0.0938 0.975 0.012 0.988
#> GSM148527 2 0.0672 0.974 0.008 0.992
#> GSM148528 2 0.0672 0.975 0.008 0.992
#> GSM148529 2 0.2236 0.965 0.036 0.964
#> GSM148530 2 0.1184 0.974 0.016 0.984
#> GSM148531 2 0.1843 0.969 0.028 0.972
#> GSM148532 2 0.1414 0.973 0.020 0.980
#> GSM148533 2 0.0376 0.975 0.004 0.996
#> GSM148534 2 0.0376 0.974 0.004 0.996
#> GSM148535 2 0.0672 0.975 0.008 0.992
#> GSM148536 2 0.1843 0.971 0.028 0.972
#> GSM148537 2 0.2043 0.963 0.032 0.968
#> GSM148538 2 0.0672 0.973 0.008 0.992
#> GSM148539 2 0.2236 0.966 0.036 0.964
#> GSM148540 2 0.2603 0.963 0.044 0.956
#> GSM148541 2 0.2236 0.968 0.036 0.964
#> GSM148542 2 0.2236 0.968 0.036 0.964
#> GSM148543 2 0.2778 0.953 0.048 0.952
#> GSM148544 2 0.3879 0.923 0.076 0.924
#> GSM148545 1 0.8955 0.777 0.688 0.312
#> GSM148546 1 0.8713 0.883 0.708 0.292
#> GSM148547 1 0.8813 0.883 0.700 0.300
#> GSM148548 1 0.8813 0.885 0.700 0.300
#> GSM148549 1 0.8661 0.886 0.712 0.288
#> GSM148550 1 0.8661 0.886 0.712 0.288
#> GSM148551 1 0.8608 0.890 0.716 0.284
#> GSM148552 1 0.8813 0.879 0.700 0.300
#> GSM148553 1 0.8955 0.869 0.688 0.312
#> GSM148554 1 0.8327 0.892 0.736 0.264
#> GSM148555 1 0.8016 0.889 0.756 0.244
#> GSM148556 1 0.8713 0.885 0.708 0.292
#> GSM148557 1 0.8443 0.890 0.728 0.272
#> GSM148558 1 0.7299 0.846 0.796 0.204
#> GSM148559 1 0.8608 0.873 0.716 0.284
#> GSM148560 1 0.8661 0.871 0.712 0.288
#> GSM148561 1 0.9909 0.632 0.556 0.444
#> GSM148562 1 0.8081 0.890 0.752 0.248
#> GSM148563 1 0.8207 0.892 0.744 0.256
#> GSM148564 1 0.8016 0.871 0.756 0.244
#> GSM148565 1 0.5178 0.796 0.884 0.116
#> GSM148566 1 0.8813 0.858 0.700 0.300
#> GSM148567 1 0.8081 0.885 0.752 0.248
#> GSM148568 1 0.8861 0.880 0.696 0.304
#> GSM148569 1 0.7883 0.881 0.764 0.236
#> GSM148570 1 0.7139 0.854 0.804 0.196
#> GSM148571 1 0.6801 0.847 0.820 0.180
#> GSM148572 1 0.5294 0.796 0.880 0.120
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM148516 2 0.7024 0.621 0.072 0.704 0.224
#> GSM148517 3 0.6341 0.000 0.252 0.032 0.716
#> GSM148518 2 0.1129 0.963 0.020 0.976 0.004
#> GSM148519 2 0.0747 0.963 0.016 0.984 0.000
#> GSM148520 2 0.2187 0.952 0.028 0.948 0.024
#> GSM148521 2 0.0592 0.963 0.012 0.988 0.000
#> GSM148522 2 0.1647 0.960 0.036 0.960 0.004
#> GSM148523 2 0.0829 0.964 0.012 0.984 0.004
#> GSM148524 2 0.0747 0.963 0.016 0.984 0.000
#> GSM148525 2 0.0892 0.963 0.020 0.980 0.000
#> GSM148526 2 0.1163 0.964 0.028 0.972 0.000
#> GSM148527 2 0.0892 0.962 0.020 0.980 0.000
#> GSM148528 2 0.1129 0.964 0.020 0.976 0.004
#> GSM148529 2 0.1950 0.956 0.040 0.952 0.008
#> GSM148530 2 0.1525 0.962 0.032 0.964 0.004
#> GSM148531 2 0.2173 0.955 0.048 0.944 0.008
#> GSM148532 2 0.1765 0.961 0.040 0.956 0.004
#> GSM148533 2 0.0829 0.963 0.012 0.984 0.004
#> GSM148534 2 0.1337 0.961 0.016 0.972 0.012
#> GSM148535 2 0.0983 0.963 0.016 0.980 0.004
#> GSM148536 2 0.1411 0.962 0.036 0.964 0.000
#> GSM148537 2 0.1878 0.956 0.044 0.952 0.004
#> GSM148538 2 0.0829 0.962 0.012 0.984 0.004
#> GSM148539 2 0.2152 0.950 0.036 0.948 0.016
#> GSM148540 2 0.2269 0.947 0.040 0.944 0.016
#> GSM148541 2 0.2056 0.950 0.024 0.952 0.024
#> GSM148542 2 0.2313 0.947 0.032 0.944 0.024
#> GSM148543 2 0.2384 0.940 0.056 0.936 0.008
#> GSM148544 2 0.3886 0.895 0.096 0.880 0.024
#> GSM148545 1 0.7715 -0.166 0.524 0.048 0.428
#> GSM148546 1 0.5573 0.763 0.796 0.160 0.044
#> GSM148547 1 0.6254 0.749 0.756 0.188 0.056
#> GSM148548 1 0.5757 0.776 0.792 0.152 0.056
#> GSM148549 1 0.5558 0.775 0.800 0.152 0.048
#> GSM148550 1 0.5598 0.776 0.800 0.148 0.052
#> GSM148551 1 0.5173 0.782 0.816 0.148 0.036
#> GSM148552 1 0.6511 0.753 0.760 0.136 0.104
#> GSM148553 1 0.6239 0.746 0.768 0.160 0.072
#> GSM148554 1 0.4591 0.785 0.848 0.120 0.032
#> GSM148555 1 0.5093 0.760 0.836 0.076 0.088
#> GSM148556 1 0.5558 0.775 0.800 0.152 0.048
#> GSM148557 1 0.5069 0.783 0.828 0.128 0.044
#> GSM148558 1 0.6703 0.499 0.692 0.040 0.268
#> GSM148559 1 0.7666 0.562 0.636 0.076 0.288
#> GSM148560 1 0.6990 0.686 0.728 0.108 0.164
#> GSM148561 1 0.8371 0.540 0.624 0.212 0.164
#> GSM148562 1 0.5260 0.774 0.828 0.092 0.080
#> GSM148563 1 0.5179 0.774 0.832 0.088 0.080
#> GSM148564 1 0.6425 0.730 0.764 0.096 0.140
#> GSM148565 1 0.5585 0.587 0.772 0.024 0.204
#> GSM148566 1 0.7447 0.667 0.696 0.120 0.184
#> GSM148567 1 0.6168 0.775 0.780 0.124 0.096
#> GSM148568 1 0.7180 0.746 0.716 0.168 0.116
#> GSM148569 1 0.5426 0.755 0.820 0.088 0.092
#> GSM148570 1 0.5346 0.691 0.808 0.040 0.152
#> GSM148571 1 0.5357 0.705 0.820 0.064 0.116
#> GSM148572 1 0.5849 0.580 0.756 0.028 0.216
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM148516 2 0.7320 0.167 0.012 0.492 0.384 0.112
#> GSM148517 3 0.5849 0.000 0.132 0.000 0.704 0.164
#> GSM148518 2 0.0779 0.951 0.016 0.980 0.000 0.004
#> GSM148519 2 0.0895 0.951 0.020 0.976 0.004 0.000
#> GSM148520 2 0.1958 0.940 0.028 0.944 0.020 0.008
#> GSM148521 2 0.0524 0.950 0.008 0.988 0.004 0.000
#> GSM148522 2 0.1209 0.947 0.032 0.964 0.000 0.004
#> GSM148523 2 0.0712 0.951 0.008 0.984 0.004 0.004
#> GSM148524 2 0.0657 0.951 0.012 0.984 0.004 0.000
#> GSM148525 2 0.0779 0.951 0.016 0.980 0.004 0.000
#> GSM148526 2 0.0817 0.951 0.024 0.976 0.000 0.000
#> GSM148527 2 0.0779 0.950 0.016 0.980 0.004 0.000
#> GSM148528 2 0.0657 0.951 0.012 0.984 0.004 0.000
#> GSM148529 2 0.1406 0.945 0.024 0.960 0.016 0.000
#> GSM148530 2 0.1174 0.950 0.020 0.968 0.000 0.012
#> GSM148531 2 0.1697 0.945 0.028 0.952 0.004 0.016
#> GSM148532 2 0.1388 0.949 0.028 0.960 0.000 0.012
#> GSM148533 2 0.0712 0.950 0.008 0.984 0.004 0.004
#> GSM148534 2 0.1271 0.949 0.012 0.968 0.012 0.008
#> GSM148535 2 0.0712 0.950 0.008 0.984 0.004 0.004
#> GSM148536 2 0.1339 0.948 0.024 0.964 0.004 0.008
#> GSM148537 2 0.1598 0.947 0.020 0.956 0.004 0.020
#> GSM148538 2 0.0712 0.950 0.008 0.984 0.004 0.004
#> GSM148539 2 0.2531 0.929 0.032 0.924 0.020 0.024
#> GSM148540 2 0.2486 0.928 0.048 0.920 0.004 0.028
#> GSM148541 2 0.2301 0.932 0.028 0.932 0.012 0.028
#> GSM148542 2 0.2364 0.930 0.036 0.928 0.008 0.028
#> GSM148543 2 0.2695 0.921 0.056 0.912 0.008 0.024
#> GSM148544 2 0.3898 0.863 0.092 0.852 0.008 0.048
#> GSM148545 1 0.7440 -0.176 0.440 0.000 0.388 0.172
#> GSM148546 1 0.4053 0.510 0.844 0.108 0.020 0.028
#> GSM148547 1 0.5599 0.485 0.752 0.164 0.048 0.036
#> GSM148548 1 0.4342 0.503 0.820 0.128 0.008 0.044
#> GSM148549 1 0.3706 0.501 0.848 0.112 0.000 0.040
#> GSM148550 1 0.4583 0.489 0.808 0.112 0.004 0.076
#> GSM148551 1 0.4413 0.478 0.820 0.096 0.004 0.080
#> GSM148552 1 0.6201 0.459 0.720 0.100 0.032 0.148
#> GSM148553 1 0.5125 0.499 0.792 0.108 0.024 0.076
#> GSM148554 1 0.3623 0.489 0.864 0.084 0.004 0.048
#> GSM148555 1 0.4832 0.421 0.812 0.036 0.048 0.104
#> GSM148556 1 0.4734 0.488 0.796 0.128 0.004 0.072
#> GSM148557 1 0.4932 0.479 0.792 0.096 0.008 0.104
#> GSM148558 1 0.7503 -0.472 0.468 0.020 0.108 0.404
#> GSM148559 1 0.7487 0.108 0.472 0.032 0.084 0.412
#> GSM148560 1 0.6945 0.313 0.652 0.056 0.072 0.220
#> GSM148561 1 0.8177 0.177 0.520 0.080 0.100 0.300
#> GSM148562 1 0.5658 0.372 0.756 0.056 0.040 0.148
#> GSM148563 1 0.5509 0.225 0.724 0.048 0.012 0.216
#> GSM148564 1 0.6652 0.114 0.604 0.064 0.020 0.312
#> GSM148565 1 0.5464 -0.935 0.496 0.004 0.008 0.492
#> GSM148566 1 0.7330 0.300 0.628 0.068 0.084 0.220
#> GSM148567 1 0.6583 0.336 0.660 0.096 0.020 0.224
#> GSM148568 1 0.7172 0.340 0.636 0.132 0.036 0.196
#> GSM148569 1 0.5914 0.202 0.704 0.056 0.020 0.220
#> GSM148570 1 0.5212 -0.551 0.572 0.008 0.000 0.420
#> GSM148571 1 0.6120 -0.526 0.564 0.036 0.008 0.392
#> GSM148572 4 0.5675 0.000 0.472 0.004 0.016 0.508
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM148516 3 0.5516 0.0000 0.004 0.388 0.548 0.000 0.060
#> GSM148517 5 0.2204 0.4853 0.036 0.000 0.008 0.036 0.920
#> GSM148518 2 0.1059 0.9304 0.020 0.968 0.008 0.004 0.000
#> GSM148519 2 0.1130 0.9294 0.012 0.968 0.012 0.004 0.004
#> GSM148520 2 0.1847 0.9116 0.028 0.940 0.020 0.004 0.008
#> GSM148521 2 0.0566 0.9295 0.004 0.984 0.012 0.000 0.000
#> GSM148522 2 0.1766 0.9172 0.040 0.940 0.012 0.004 0.004
#> GSM148523 2 0.0898 0.9309 0.008 0.972 0.020 0.000 0.000
#> GSM148524 2 0.0613 0.9291 0.008 0.984 0.004 0.000 0.004
#> GSM148525 2 0.0932 0.9301 0.020 0.972 0.004 0.004 0.000
#> GSM148526 2 0.1059 0.9309 0.020 0.968 0.008 0.004 0.000
#> GSM148527 2 0.0693 0.9296 0.012 0.980 0.008 0.000 0.000
#> GSM148528 2 0.0727 0.9303 0.012 0.980 0.004 0.004 0.000
#> GSM148529 2 0.1441 0.9196 0.024 0.956 0.008 0.004 0.008
#> GSM148530 2 0.1369 0.9285 0.028 0.956 0.000 0.008 0.008
#> GSM148531 2 0.1748 0.9222 0.028 0.944 0.016 0.008 0.004
#> GSM148532 2 0.1742 0.9271 0.032 0.944 0.008 0.008 0.008
#> GSM148533 2 0.1074 0.9305 0.012 0.968 0.016 0.004 0.000
#> GSM148534 2 0.1235 0.9264 0.012 0.964 0.016 0.004 0.004
#> GSM148535 2 0.0854 0.9302 0.008 0.976 0.012 0.004 0.000
#> GSM148536 2 0.1153 0.9268 0.024 0.964 0.000 0.008 0.004
#> GSM148537 2 0.1924 0.9199 0.016 0.940 0.016 0.016 0.012
#> GSM148538 2 0.0833 0.9318 0.016 0.976 0.004 0.004 0.000
#> GSM148539 2 0.2933 0.8658 0.032 0.892 0.052 0.012 0.012
#> GSM148540 2 0.2834 0.8543 0.060 0.888 0.040 0.012 0.000
#> GSM148541 2 0.2830 0.8586 0.036 0.896 0.048 0.012 0.008
#> GSM148542 2 0.2985 0.8559 0.048 0.888 0.044 0.012 0.008
#> GSM148543 2 0.3088 0.8474 0.056 0.880 0.048 0.008 0.008
#> GSM148544 2 0.3913 0.7381 0.108 0.824 0.036 0.032 0.000
#> GSM148545 5 0.6508 0.3164 0.280 0.000 0.052 0.092 0.576
#> GSM148546 1 0.3546 0.5931 0.860 0.064 0.016 0.012 0.048
#> GSM148547 1 0.4926 0.5728 0.772 0.124 0.036 0.012 0.056
#> GSM148548 1 0.3777 0.5940 0.844 0.092 0.016 0.024 0.024
#> GSM148549 1 0.3011 0.5919 0.876 0.076 0.012 0.036 0.000
#> GSM148550 1 0.4582 0.5774 0.800 0.072 0.024 0.088 0.016
#> GSM148551 1 0.4170 0.5416 0.820 0.048 0.016 0.100 0.016
#> GSM148552 1 0.7142 0.4919 0.632 0.076 0.092 0.140 0.060
#> GSM148553 1 0.5479 0.5594 0.760 0.068 0.048 0.064 0.060
#> GSM148554 1 0.3519 0.5808 0.856 0.048 0.008 0.076 0.012
#> GSM148555 1 0.6187 0.4956 0.700 0.028 0.072 0.120 0.080
#> GSM148556 1 0.4621 0.5759 0.792 0.088 0.020 0.088 0.012
#> GSM148557 1 0.4522 0.5696 0.796 0.052 0.012 0.116 0.024
#> GSM148558 4 0.7306 0.3681 0.300 0.004 0.044 0.480 0.172
#> GSM148559 4 0.8839 -0.3597 0.228 0.016 0.220 0.340 0.196
#> GSM148560 1 0.8062 0.2501 0.516 0.028 0.128 0.168 0.160
#> GSM148561 1 0.7143 0.0407 0.460 0.028 0.364 0.136 0.012
#> GSM148562 1 0.5202 0.4125 0.740 0.020 0.056 0.164 0.020
#> GSM148563 1 0.6247 0.2069 0.620 0.024 0.048 0.272 0.036
#> GSM148564 1 0.7106 0.1126 0.492 0.056 0.064 0.364 0.024
#> GSM148565 4 0.4905 0.5311 0.344 0.000 0.008 0.624 0.024
#> GSM148566 1 0.8246 0.2151 0.508 0.040 0.136 0.160 0.156
#> GSM148567 1 0.6401 0.3523 0.620 0.068 0.044 0.252 0.016
#> GSM148568 1 0.7581 0.3756 0.560 0.116 0.060 0.216 0.048
#> GSM148569 1 0.5683 0.2791 0.620 0.036 0.044 0.300 0.000
#> GSM148570 4 0.5084 0.3724 0.452 0.000 0.016 0.520 0.012
#> GSM148571 4 0.5503 0.3671 0.440 0.016 0.020 0.516 0.008
#> GSM148572 4 0.4625 0.5352 0.324 0.000 0.004 0.652 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM148516 3 0.3709 0.0000 0.000 0.204 0.756 0.000 0.000 0.040
#> GSM148517 6 0.0692 0.2186 0.020 0.000 0.000 0.004 0.000 0.976
#> GSM148518 2 0.1180 0.9241 0.004 0.960 0.008 0.004 0.024 0.000
#> GSM148519 2 0.1312 0.9210 0.008 0.956 0.012 0.000 0.020 0.004
#> GSM148520 2 0.2072 0.9118 0.016 0.924 0.024 0.000 0.024 0.012
#> GSM148521 2 0.1262 0.9228 0.008 0.956 0.020 0.000 0.016 0.000
#> GSM148522 2 0.2148 0.9162 0.036 0.920 0.020 0.004 0.016 0.004
#> GSM148523 2 0.1498 0.9235 0.012 0.948 0.024 0.004 0.012 0.000
#> GSM148524 2 0.0810 0.9211 0.008 0.976 0.004 0.000 0.008 0.004
#> GSM148525 2 0.1078 0.9248 0.016 0.964 0.008 0.000 0.012 0.000
#> GSM148526 2 0.1718 0.9211 0.024 0.936 0.020 0.000 0.020 0.000
#> GSM148527 2 0.1078 0.9231 0.016 0.964 0.012 0.000 0.008 0.000
#> GSM148528 2 0.0767 0.9238 0.004 0.976 0.008 0.000 0.012 0.000
#> GSM148529 2 0.1734 0.9150 0.028 0.940 0.012 0.004 0.008 0.008
#> GSM148530 2 0.1515 0.9207 0.020 0.944 0.008 0.000 0.028 0.000
#> GSM148531 2 0.1596 0.9188 0.020 0.944 0.012 0.004 0.020 0.000
#> GSM148532 2 0.1562 0.9200 0.024 0.940 0.004 0.000 0.032 0.000
#> GSM148533 2 0.1261 0.9236 0.004 0.956 0.008 0.004 0.028 0.000
#> GSM148534 2 0.0951 0.9228 0.004 0.968 0.008 0.000 0.020 0.000
#> GSM148535 2 0.0912 0.9232 0.004 0.972 0.012 0.004 0.008 0.000
#> GSM148536 2 0.1121 0.9231 0.016 0.964 0.000 0.008 0.008 0.004
#> GSM148537 2 0.1963 0.9140 0.012 0.928 0.016 0.012 0.032 0.000
#> GSM148538 2 0.1007 0.9241 0.008 0.968 0.004 0.004 0.016 0.000
#> GSM148539 2 0.3705 0.8357 0.036 0.824 0.100 0.004 0.032 0.004
#> GSM148540 2 0.3776 0.8256 0.064 0.824 0.068 0.008 0.036 0.000
#> GSM148541 2 0.4516 0.7615 0.040 0.784 0.104 0.020 0.044 0.008
#> GSM148542 2 0.4663 0.7574 0.048 0.776 0.100 0.020 0.048 0.008
#> GSM148543 2 0.3941 0.8138 0.060 0.812 0.088 0.004 0.032 0.004
#> GSM148544 2 0.4397 0.7620 0.104 0.784 0.056 0.028 0.028 0.000
#> GSM148545 6 0.5886 0.0548 0.252 0.000 0.004 0.012 0.176 0.556
#> GSM148546 1 0.3472 0.5993 0.856 0.048 0.016 0.012 0.048 0.020
#> GSM148547 1 0.4849 0.5872 0.772 0.080 0.052 0.016 0.060 0.020
#> GSM148548 1 0.3310 0.5984 0.860 0.072 0.012 0.012 0.024 0.020
#> GSM148549 1 0.2860 0.5951 0.872 0.068 0.000 0.028 0.032 0.000
#> GSM148550 1 0.4391 0.5810 0.792 0.056 0.008 0.080 0.056 0.008
#> GSM148551 1 0.4361 0.5398 0.788 0.032 0.008 0.100 0.064 0.008
#> GSM148552 1 0.6479 0.5081 0.616 0.064 0.012 0.068 0.200 0.040
#> GSM148553 1 0.4760 0.5747 0.764 0.044 0.012 0.020 0.124 0.036
#> GSM148554 1 0.3459 0.5856 0.848 0.036 0.004 0.072 0.032 0.008
#> GSM148555 1 0.5740 0.5164 0.680 0.008 0.016 0.096 0.148 0.052
#> GSM148556 1 0.4443 0.5810 0.788 0.064 0.012 0.076 0.056 0.004
#> GSM148557 1 0.4343 0.5747 0.792 0.032 0.008 0.100 0.056 0.012
#> GSM148558 4 0.7679 0.3422 0.216 0.004 0.012 0.412 0.220 0.136
#> GSM148559 5 0.4886 0.0000 0.096 0.012 0.004 0.032 0.744 0.112
#> GSM148560 1 0.7096 0.1398 0.496 0.012 0.028 0.048 0.284 0.132
#> GSM148561 1 0.7820 -0.0631 0.376 0.016 0.256 0.128 0.220 0.004
#> GSM148562 1 0.6205 0.3341 0.608 0.008 0.036 0.184 0.152 0.012
#> GSM148563 1 0.6586 0.1035 0.520 0.012 0.020 0.316 0.096 0.036
#> GSM148564 1 0.7007 -0.0332 0.388 0.052 0.008 0.372 0.176 0.004
#> GSM148565 4 0.3616 0.6798 0.184 0.000 0.012 0.780 0.024 0.000
#> GSM148566 1 0.7074 0.0552 0.476 0.016 0.028 0.044 0.324 0.112
#> GSM148567 1 0.6670 0.2312 0.528 0.048 0.016 0.284 0.116 0.008
#> GSM148568 1 0.7754 0.3406 0.492 0.104 0.020 0.208 0.136 0.040
#> GSM148569 1 0.6235 0.1863 0.528 0.036 0.012 0.328 0.092 0.004
#> GSM148570 4 0.5556 0.5657 0.292 0.000 0.012 0.592 0.092 0.012
#> GSM148571 4 0.5265 0.5959 0.268 0.020 0.012 0.644 0.052 0.004
#> GSM148572 4 0.3232 0.6557 0.140 0.000 0.020 0.824 0.016 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) dose(p) time(p) k
#> CV:hclust 57 2.57e-12 0.99957 1.000 2
#> CV:hclust 54 1.88e-12 0.88492 0.987 3
#> CV:hclust 30 8.08e-06 0.08332 0.766 4
#> CV:hclust 39 3.40e-09 0.09311 0.425 5
#> CV:hclust 43 4.60e-10 0.00903 0.870 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 21163 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.987 0.994 0.5087 0.491 0.491
#> 3 3 0.656 0.571 0.805 0.2199 0.966 0.931
#> 4 4 0.644 0.663 0.760 0.1202 0.776 0.529
#> 5 5 0.630 0.723 0.790 0.0773 0.926 0.745
#> 6 6 0.636 0.709 0.774 0.0451 0.977 0.908
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
#> GSM148516 2 0.0938 0.979 0.012 0.988
#> GSM148517 1 0.0000 0.999 1.000 0.000
#> GSM148518 2 0.0000 0.988 0.000 1.000
#> GSM148519 2 0.0000 0.988 0.000 1.000
#> GSM148520 2 0.0000 0.988 0.000 1.000
#> GSM148521 2 0.0000 0.988 0.000 1.000
#> GSM148522 2 0.0000 0.988 0.000 1.000
#> GSM148523 2 0.0000 0.988 0.000 1.000
#> GSM148524 2 0.0000 0.988 0.000 1.000
#> GSM148525 2 0.0000 0.988 0.000 1.000
#> GSM148526 2 0.0000 0.988 0.000 1.000
#> GSM148527 2 0.0000 0.988 0.000 1.000
#> GSM148528 2 0.0000 0.988 0.000 1.000
#> GSM148529 2 0.0000 0.988 0.000 1.000
#> GSM148530 2 0.0000 0.988 0.000 1.000
#> GSM148531 2 0.0000 0.988 0.000 1.000
#> GSM148532 2 0.0000 0.988 0.000 1.000
#> GSM148533 2 0.0000 0.988 0.000 1.000
#> GSM148534 2 0.0000 0.988 0.000 1.000
#> GSM148535 2 0.0000 0.988 0.000 1.000
#> GSM148536 2 0.0000 0.988 0.000 1.000
#> GSM148537 2 0.0000 0.988 0.000 1.000
#> GSM148538 2 0.0000 0.988 0.000 1.000
#> GSM148539 2 0.0000 0.988 0.000 1.000
#> GSM148540 2 0.5059 0.876 0.112 0.888
#> GSM148541 2 0.0376 0.985 0.004 0.996
#> GSM148542 2 0.0000 0.988 0.000 1.000
#> GSM148543 2 0.0000 0.988 0.000 1.000
#> GSM148544 2 0.6973 0.777 0.188 0.812
#> GSM148545 1 0.0000 0.999 1.000 0.000
#> GSM148546 1 0.0000 0.999 1.000 0.000
#> GSM148547 1 0.0000 0.999 1.000 0.000
#> GSM148548 1 0.0376 0.996 0.996 0.004
#> GSM148549 1 0.0376 0.996 0.996 0.004
#> GSM148550 1 0.0000 0.999 1.000 0.000
#> GSM148551 1 0.0938 0.989 0.988 0.012
#> GSM148552 1 0.0000 0.999 1.000 0.000
#> GSM148553 1 0.0376 0.996 0.996 0.004
#> GSM148554 1 0.0000 0.999 1.000 0.000
#> GSM148555 1 0.0000 0.999 1.000 0.000
#> GSM148556 1 0.0000 0.999 1.000 0.000
#> GSM148557 1 0.0000 0.999 1.000 0.000
#> GSM148558 1 0.0000 0.999 1.000 0.000
#> GSM148559 1 0.0000 0.999 1.000 0.000
#> GSM148560 1 0.0000 0.999 1.000 0.000
#> GSM148561 1 0.0000 0.999 1.000 0.000
#> GSM148562 1 0.0000 0.999 1.000 0.000
#> GSM148563 1 0.0000 0.999 1.000 0.000
#> GSM148564 1 0.0000 0.999 1.000 0.000
#> GSM148565 1 0.0000 0.999 1.000 0.000
#> GSM148566 1 0.0000 0.999 1.000 0.000
#> GSM148567 1 0.0672 0.993 0.992 0.008
#> GSM148568 1 0.0000 0.999 1.000 0.000
#> GSM148569 1 0.0000 0.999 1.000 0.000
#> GSM148570 1 0.0000 0.999 1.000 0.000
#> GSM148571 1 0.0000 0.999 1.000 0.000
#> GSM148572 1 0.0000 0.999 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM148516 2 0.6297 0.7102 0.008 0.640 0.352
#> GSM148517 3 0.6168 0.9339 0.412 0.000 0.588
#> GSM148518 2 0.0892 0.9200 0.000 0.980 0.020
#> GSM148519 2 0.0237 0.9221 0.000 0.996 0.004
#> GSM148520 2 0.0829 0.9194 0.004 0.984 0.012
#> GSM148521 2 0.0237 0.9223 0.000 0.996 0.004
#> GSM148522 2 0.0000 0.9223 0.000 1.000 0.000
#> GSM148523 2 0.0424 0.9222 0.000 0.992 0.008
#> GSM148524 2 0.0237 0.9221 0.000 0.996 0.004
#> GSM148525 2 0.1031 0.9188 0.000 0.976 0.024
#> GSM148526 2 0.0424 0.9224 0.000 0.992 0.008
#> GSM148527 2 0.0237 0.9223 0.000 0.996 0.004
#> GSM148528 2 0.0424 0.9218 0.000 0.992 0.008
#> GSM148529 2 0.0237 0.9223 0.000 0.996 0.004
#> GSM148530 2 0.0237 0.9228 0.000 0.996 0.004
#> GSM148531 2 0.0424 0.9222 0.000 0.992 0.008
#> GSM148532 2 0.2301 0.9007 0.004 0.936 0.060
#> GSM148533 2 0.0237 0.9226 0.000 0.996 0.004
#> GSM148534 2 0.0424 0.9218 0.000 0.992 0.008
#> GSM148535 2 0.0424 0.9222 0.000 0.992 0.008
#> GSM148536 2 0.0424 0.9218 0.000 0.992 0.008
#> GSM148537 2 0.0829 0.9181 0.012 0.984 0.004
#> GSM148538 2 0.0237 0.9223 0.000 0.996 0.004
#> GSM148539 2 0.5404 0.7899 0.004 0.740 0.256
#> GSM148540 2 0.7941 0.6866 0.096 0.628 0.276
#> GSM148541 2 0.6224 0.7549 0.016 0.688 0.296
#> GSM148542 2 0.5728 0.7804 0.008 0.720 0.272
#> GSM148543 2 0.5692 0.7794 0.008 0.724 0.268
#> GSM148544 2 0.8750 0.6115 0.164 0.580 0.256
#> GSM148545 3 0.6225 0.9330 0.432 0.000 0.568
#> GSM148546 1 0.5926 0.0737 0.644 0.000 0.356
#> GSM148547 1 0.5926 0.0513 0.644 0.000 0.356
#> GSM148548 1 0.5650 0.2132 0.688 0.000 0.312
#> GSM148549 1 0.4504 0.3775 0.804 0.000 0.196
#> GSM148550 1 0.4750 0.3527 0.784 0.000 0.216
#> GSM148551 1 0.4861 0.3844 0.800 0.008 0.192
#> GSM148552 1 0.6062 -0.1358 0.616 0.000 0.384
#> GSM148553 1 0.6264 -0.0168 0.616 0.004 0.380
#> GSM148554 1 0.5178 0.2528 0.744 0.000 0.256
#> GSM148555 1 0.5363 0.2461 0.724 0.000 0.276
#> GSM148556 1 0.4235 0.3835 0.824 0.000 0.176
#> GSM148557 1 0.4750 0.3540 0.784 0.000 0.216
#> GSM148558 1 0.5926 0.1243 0.644 0.000 0.356
#> GSM148559 1 0.6267 -0.5926 0.548 0.000 0.452
#> GSM148560 1 0.5810 -0.1022 0.664 0.000 0.336
#> GSM148561 1 0.4235 0.4215 0.824 0.000 0.176
#> GSM148562 1 0.3340 0.4544 0.880 0.000 0.120
#> GSM148563 1 0.5058 0.3631 0.756 0.000 0.244
#> GSM148564 1 0.4452 0.4022 0.808 0.000 0.192
#> GSM148565 1 0.5254 0.2984 0.736 0.000 0.264
#> GSM148566 1 0.5733 -0.0736 0.676 0.000 0.324
#> GSM148567 1 0.3941 0.4457 0.844 0.000 0.156
#> GSM148568 1 0.3340 0.4487 0.880 0.000 0.120
#> GSM148569 1 0.3267 0.4517 0.884 0.000 0.116
#> GSM148570 1 0.4291 0.3981 0.820 0.000 0.180
#> GSM148571 1 0.4346 0.3865 0.816 0.000 0.184
#> GSM148572 1 0.5178 0.2913 0.744 0.000 0.256
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM148516 3 0.6140 0.8217 0.064 0.340 0.596 0.000
#> GSM148517 1 0.6139 0.2988 0.656 0.000 0.244 0.100
#> GSM148518 2 0.1151 0.9502 0.008 0.968 0.024 0.000
#> GSM148519 2 0.0657 0.9553 0.004 0.984 0.012 0.000
#> GSM148520 2 0.0817 0.9535 0.000 0.976 0.024 0.000
#> GSM148521 2 0.0469 0.9577 0.000 0.988 0.012 0.000
#> GSM148522 2 0.1042 0.9523 0.008 0.972 0.020 0.000
#> GSM148523 2 0.0895 0.9533 0.004 0.976 0.020 0.000
#> GSM148524 2 0.0376 0.9575 0.004 0.992 0.004 0.000
#> GSM148525 2 0.1452 0.9459 0.008 0.956 0.036 0.000
#> GSM148526 2 0.1256 0.9462 0.008 0.964 0.028 0.000
#> GSM148527 2 0.0657 0.9576 0.004 0.984 0.012 0.000
#> GSM148528 2 0.0817 0.9509 0.000 0.976 0.024 0.000
#> GSM148529 2 0.0707 0.9534 0.000 0.980 0.020 0.000
#> GSM148530 2 0.1004 0.9552 0.004 0.972 0.024 0.000
#> GSM148531 2 0.0657 0.9570 0.004 0.984 0.012 0.000
#> GSM148532 2 0.3306 0.7119 0.004 0.840 0.156 0.000
#> GSM148533 2 0.1356 0.9459 0.008 0.960 0.032 0.000
#> GSM148534 2 0.1022 0.9472 0.000 0.968 0.032 0.000
#> GSM148535 2 0.1356 0.9468 0.008 0.960 0.032 0.000
#> GSM148536 2 0.0817 0.9528 0.000 0.976 0.024 0.000
#> GSM148537 2 0.1296 0.9487 0.004 0.964 0.028 0.004
#> GSM148538 2 0.0336 0.9570 0.000 0.992 0.008 0.000
#> GSM148539 3 0.5353 0.8445 0.012 0.432 0.556 0.000
#> GSM148540 3 0.6393 0.8679 0.044 0.332 0.604 0.020
#> GSM148541 3 0.5040 0.8818 0.008 0.364 0.628 0.000
#> GSM148542 3 0.5070 0.8712 0.004 0.416 0.580 0.000
#> GSM148543 3 0.5203 0.8714 0.008 0.416 0.576 0.000
#> GSM148544 3 0.7550 0.8279 0.064 0.324 0.548 0.064
#> GSM148545 1 0.5956 0.3263 0.680 0.000 0.220 0.100
#> GSM148546 1 0.4853 0.5447 0.744 0.000 0.036 0.220
#> GSM148547 1 0.4888 0.5419 0.740 0.000 0.036 0.224
#> GSM148548 1 0.5903 0.4839 0.616 0.000 0.052 0.332
#> GSM148549 1 0.6784 0.3979 0.528 0.000 0.104 0.368
#> GSM148550 1 0.5883 0.4206 0.572 0.000 0.040 0.388
#> GSM148551 1 0.6898 0.3793 0.512 0.008 0.084 0.396
#> GSM148552 1 0.4839 0.5239 0.756 0.000 0.044 0.200
#> GSM148553 1 0.5361 0.5385 0.724 0.000 0.068 0.208
#> GSM148554 1 0.4889 0.4639 0.636 0.000 0.004 0.360
#> GSM148555 1 0.5969 0.4227 0.564 0.000 0.044 0.392
#> GSM148556 1 0.5775 0.3992 0.560 0.000 0.032 0.408
#> GSM148557 4 0.5408 -0.3162 0.488 0.000 0.012 0.500
#> GSM148558 4 0.6586 0.0926 0.368 0.000 0.088 0.544
#> GSM148559 1 0.5990 0.3317 0.688 0.000 0.188 0.124
#> GSM148560 1 0.7225 0.1635 0.512 0.000 0.160 0.328
#> GSM148561 4 0.6684 0.3703 0.336 0.000 0.104 0.560
#> GSM148562 4 0.5883 0.4211 0.288 0.000 0.064 0.648
#> GSM148563 4 0.5031 0.5195 0.212 0.000 0.048 0.740
#> GSM148564 4 0.4761 0.5825 0.184 0.000 0.048 0.768
#> GSM148565 4 0.3239 0.5771 0.052 0.000 0.068 0.880
#> GSM148566 1 0.7363 0.1312 0.492 0.000 0.176 0.332
#> GSM148567 4 0.5429 0.5518 0.196 0.004 0.068 0.732
#> GSM148568 4 0.5025 0.4550 0.252 0.000 0.032 0.716
#> GSM148569 4 0.4234 0.6045 0.132 0.000 0.052 0.816
#> GSM148570 4 0.2335 0.6183 0.060 0.000 0.020 0.920
#> GSM148571 4 0.1936 0.6186 0.032 0.000 0.028 0.940
#> GSM148572 4 0.3621 0.5680 0.068 0.000 0.072 0.860
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM148516 3 0.5928 0.789 0.004 0.148 0.680 0.036 0.132
#> GSM148517 5 0.4679 0.616 0.156 0.000 0.040 0.040 0.764
#> GSM148518 2 0.2339 0.924 0.000 0.912 0.052 0.008 0.028
#> GSM148519 2 0.0693 0.941 0.000 0.980 0.000 0.008 0.012
#> GSM148520 2 0.1815 0.934 0.000 0.940 0.016 0.024 0.020
#> GSM148521 2 0.0898 0.939 0.000 0.972 0.000 0.020 0.008
#> GSM148522 2 0.1202 0.939 0.000 0.960 0.032 0.004 0.004
#> GSM148523 2 0.1186 0.941 0.000 0.964 0.020 0.008 0.008
#> GSM148524 2 0.0727 0.942 0.000 0.980 0.004 0.012 0.004
#> GSM148525 2 0.2795 0.901 0.000 0.884 0.080 0.008 0.028
#> GSM148526 2 0.1805 0.931 0.012 0.944 0.020 0.008 0.016
#> GSM148527 2 0.0867 0.943 0.000 0.976 0.008 0.008 0.008
#> GSM148528 2 0.1597 0.936 0.000 0.948 0.020 0.008 0.024
#> GSM148529 2 0.1220 0.937 0.004 0.964 0.004 0.020 0.008
#> GSM148530 2 0.2363 0.928 0.000 0.912 0.052 0.012 0.024
#> GSM148531 2 0.2270 0.930 0.000 0.916 0.052 0.012 0.020
#> GSM148532 2 0.4650 0.676 0.008 0.736 0.216 0.012 0.028
#> GSM148533 2 0.1914 0.926 0.000 0.924 0.060 0.000 0.016
#> GSM148534 2 0.1997 0.933 0.000 0.932 0.024 0.016 0.028
#> GSM148535 2 0.1978 0.930 0.000 0.928 0.044 0.004 0.024
#> GSM148536 2 0.1518 0.938 0.000 0.952 0.012 0.020 0.016
#> GSM148537 2 0.1554 0.940 0.004 0.952 0.012 0.008 0.024
#> GSM148538 2 0.1074 0.942 0.000 0.968 0.004 0.016 0.012
#> GSM148539 3 0.4134 0.874 0.008 0.224 0.752 0.008 0.008
#> GSM148540 3 0.4746 0.889 0.040 0.156 0.768 0.012 0.024
#> GSM148541 3 0.4384 0.883 0.020 0.152 0.788 0.012 0.028
#> GSM148542 3 0.4325 0.892 0.012 0.164 0.784 0.016 0.024
#> GSM148543 3 0.3421 0.888 0.008 0.204 0.788 0.000 0.000
#> GSM148544 3 0.5913 0.853 0.084 0.164 0.696 0.040 0.016
#> GSM148545 5 0.4879 0.610 0.204 0.000 0.036 0.032 0.728
#> GSM148546 1 0.3764 0.639 0.828 0.000 0.032 0.024 0.116
#> GSM148547 1 0.3898 0.624 0.820 0.000 0.032 0.028 0.120
#> GSM148548 1 0.2756 0.707 0.900 0.004 0.036 0.020 0.040
#> GSM148549 1 0.3428 0.672 0.848 0.000 0.092 0.052 0.008
#> GSM148550 1 0.2607 0.705 0.904 0.000 0.032 0.040 0.024
#> GSM148551 1 0.3634 0.683 0.840 0.000 0.072 0.076 0.012
#> GSM148552 1 0.4779 0.473 0.704 0.000 0.016 0.032 0.248
#> GSM148553 1 0.5121 0.572 0.736 0.000 0.080 0.032 0.152
#> GSM148554 1 0.3175 0.694 0.872 0.000 0.020 0.044 0.064
#> GSM148555 1 0.4371 0.650 0.796 0.000 0.024 0.080 0.100
#> GSM148556 1 0.2445 0.703 0.908 0.000 0.016 0.056 0.020
#> GSM148557 1 0.3613 0.623 0.812 0.000 0.012 0.160 0.016
#> GSM148558 1 0.7152 -0.101 0.400 0.000 0.020 0.348 0.232
#> GSM148559 5 0.6073 0.592 0.248 0.000 0.044 0.080 0.628
#> GSM148560 5 0.7136 0.507 0.220 0.000 0.044 0.224 0.512
#> GSM148561 4 0.7760 0.320 0.336 0.004 0.088 0.424 0.148
#> GSM148562 1 0.6599 -0.394 0.456 0.000 0.036 0.416 0.092
#> GSM148563 4 0.6347 0.491 0.344 0.000 0.036 0.540 0.080
#> GSM148564 4 0.5495 0.659 0.236 0.000 0.020 0.668 0.076
#> GSM148565 4 0.4531 0.643 0.128 0.000 0.024 0.780 0.068
#> GSM148566 5 0.7003 0.483 0.228 0.000 0.032 0.228 0.512
#> GSM148567 4 0.6046 0.629 0.260 0.000 0.048 0.624 0.068
#> GSM148568 4 0.6317 0.375 0.424 0.000 0.024 0.468 0.084
#> GSM148569 4 0.4954 0.633 0.336 0.000 0.008 0.628 0.028
#> GSM148570 4 0.4382 0.666 0.228 0.000 0.012 0.736 0.024
#> GSM148571 4 0.3003 0.688 0.188 0.000 0.000 0.812 0.000
#> GSM148572 4 0.4703 0.648 0.140 0.000 0.032 0.768 0.060
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM148516 3 0.565 0.6388 0.000 0.060 0.580 0.012 0.032 NA
#> GSM148517 5 0.599 0.5238 0.096 0.000 0.004 0.036 0.520 NA
#> GSM148518 2 0.281 0.8818 0.000 0.864 0.052 0.004 0.000 NA
#> GSM148519 2 0.115 0.8993 0.000 0.952 0.004 0.000 0.000 NA
#> GSM148520 2 0.325 0.8612 0.008 0.832 0.032 0.000 0.004 NA
#> GSM148521 2 0.130 0.9004 0.000 0.948 0.012 0.000 0.000 NA
#> GSM148522 2 0.148 0.8994 0.000 0.944 0.032 0.004 0.000 NA
#> GSM148523 2 0.208 0.8969 0.000 0.912 0.040 0.004 0.000 NA
#> GSM148524 2 0.112 0.9037 0.000 0.956 0.008 0.000 0.000 NA
#> GSM148525 2 0.312 0.8642 0.000 0.836 0.084 0.000 0.000 NA
#> GSM148526 2 0.327 0.8574 0.004 0.840 0.044 0.004 0.004 NA
#> GSM148527 2 0.082 0.9019 0.000 0.972 0.012 0.000 0.000 NA
#> GSM148528 2 0.267 0.8703 0.000 0.864 0.024 0.004 0.000 NA
#> GSM148529 2 0.218 0.8884 0.004 0.900 0.020 0.000 0.000 NA
#> GSM148530 2 0.302 0.8820 0.000 0.844 0.072 0.000 0.000 NA
#> GSM148531 2 0.287 0.8869 0.000 0.860 0.052 0.004 0.000 NA
#> GSM148532 2 0.446 0.7129 0.000 0.708 0.204 0.004 0.000 NA
#> GSM148533 2 0.258 0.8804 0.000 0.880 0.068 0.004 0.000 NA
#> GSM148534 2 0.307 0.8590 0.004 0.840 0.028 0.004 0.000 NA
#> GSM148535 2 0.265 0.8811 0.000 0.876 0.052 0.004 0.000 NA
#> GSM148536 2 0.272 0.8715 0.004 0.860 0.024 0.000 0.000 NA
#> GSM148537 2 0.229 0.8931 0.008 0.900 0.016 0.004 0.000 NA
#> GSM148538 2 0.130 0.9013 0.000 0.948 0.012 0.000 0.000 NA
#> GSM148539 3 0.363 0.7939 0.004 0.160 0.792 0.004 0.000 NA
#> GSM148540 3 0.339 0.8234 0.028 0.068 0.856 0.008 0.028 NA
#> GSM148541 3 0.381 0.8182 0.008 0.068 0.816 0.004 0.012 NA
#> GSM148542 3 0.401 0.8252 0.008 0.104 0.796 0.004 0.008 NA
#> GSM148543 3 0.255 0.8376 0.004 0.112 0.868 0.000 0.000 NA
#> GSM148544 3 0.521 0.7698 0.104 0.088 0.736 0.032 0.008 NA
#> GSM148545 5 0.607 0.5287 0.132 0.000 0.000 0.036 0.524 NA
#> GSM148546 1 0.338 0.7252 0.812 0.000 0.008 0.004 0.152 NA
#> GSM148547 1 0.372 0.7106 0.804 0.000 0.012 0.012 0.140 NA
#> GSM148548 1 0.248 0.7711 0.908 0.004 0.020 0.020 0.028 NA
#> GSM148549 1 0.294 0.7534 0.876 0.000 0.060 0.032 0.016 NA
#> GSM148550 1 0.252 0.7584 0.896 0.000 0.020 0.060 0.012 NA
#> GSM148551 1 0.266 0.7546 0.888 0.000 0.020 0.064 0.008 NA
#> GSM148552 1 0.489 0.6090 0.684 0.000 0.016 0.020 0.240 NA
#> GSM148553 1 0.473 0.6493 0.720 0.000 0.028 0.020 0.200 NA
#> GSM148554 1 0.282 0.7667 0.876 0.000 0.000 0.036 0.060 NA
#> GSM148555 1 0.428 0.7142 0.772 0.000 0.004 0.048 0.136 NA
#> GSM148556 1 0.269 0.7527 0.884 0.000 0.012 0.072 0.012 NA
#> GSM148557 1 0.349 0.6967 0.804 0.000 0.000 0.152 0.012 NA
#> GSM148558 1 0.746 -0.0573 0.360 0.000 0.012 0.340 0.108 NA
#> GSM148559 5 0.568 0.5446 0.140 0.000 0.044 0.020 0.672 NA
#> GSM148560 5 0.413 0.5262 0.072 0.000 0.020 0.104 0.792 NA
#> GSM148561 5 0.782 -0.1675 0.196 0.000 0.008 0.268 0.324 NA
#> GSM148562 4 0.676 0.3969 0.360 0.000 0.004 0.436 0.112 NA
#> GSM148563 4 0.690 0.4238 0.244 0.000 0.012 0.496 0.180 NA
#> GSM148564 4 0.549 0.5895 0.140 0.000 0.012 0.684 0.116 NA
#> GSM148565 4 0.339 0.6081 0.052 0.000 0.008 0.848 0.028 NA
#> GSM148566 5 0.412 0.5140 0.088 0.000 0.000 0.108 0.780 NA
#> GSM148567 4 0.652 0.5433 0.172 0.004 0.036 0.596 0.152 NA
#> GSM148568 4 0.691 0.4233 0.300 0.004 0.008 0.460 0.176 NA
#> GSM148569 4 0.467 0.5916 0.296 0.000 0.004 0.652 0.032 NA
#> GSM148570 4 0.502 0.6204 0.148 0.000 0.004 0.716 0.080 NA
#> GSM148571 4 0.259 0.6535 0.116 0.000 0.000 0.864 0.004 NA
#> GSM148572 4 0.347 0.6065 0.052 0.000 0.008 0.844 0.032 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 agent(p) dose(p) time(p) k
#> CV:kmeans 57 2.57e-12 1.00e+00 1.000 2
#> CV:kmeans 30 1.38e-06 9.52e-02 0.245 3
#> CV:kmeans 40 6.03e-08 9.60e-05 0.779 4
#> CV:kmeans 50 1.59e-09 1.49e-06 0.735 5
#> CV:kmeans 52 1.52e-09 3.63e-06 0.713 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 21163 rows and 57 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 0.818 0.948 0.957 0.5087 0.491 0.491
#> 3 3 0.333 0.457 0.688 0.2965 0.925 0.847
#> 4 4 0.391 0.367 0.610 0.1289 0.811 0.569
#> 5 5 0.435 0.300 0.530 0.0709 0.920 0.740
#> 6 6 0.472 0.161 0.472 0.0444 0.891 0.614
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
#> GSM148516 2 0.5178 0.905 0.116 0.884
#> GSM148517 1 0.0672 0.964 0.992 0.008
#> GSM148518 2 0.0000 0.960 0.000 1.000
#> GSM148519 2 0.0000 0.960 0.000 1.000
#> GSM148520 2 0.2423 0.953 0.040 0.960
#> GSM148521 2 0.0000 0.960 0.000 1.000
#> GSM148522 2 0.0000 0.960 0.000 1.000
#> GSM148523 2 0.0376 0.960 0.004 0.996
#> GSM148524 2 0.0672 0.960 0.008 0.992
#> GSM148525 2 0.0000 0.960 0.000 1.000
#> GSM148526 2 0.1843 0.959 0.028 0.972
#> GSM148527 2 0.0672 0.960 0.008 0.992
#> GSM148528 2 0.0376 0.960 0.004 0.996
#> GSM148529 2 0.1184 0.960 0.016 0.984
#> GSM148530 2 0.0938 0.960 0.012 0.988
#> GSM148531 2 0.1414 0.960 0.020 0.980
#> GSM148532 2 0.2603 0.955 0.044 0.956
#> GSM148533 2 0.0000 0.960 0.000 1.000
#> GSM148534 2 0.0938 0.961 0.012 0.988
#> GSM148535 2 0.0376 0.960 0.004 0.996
#> GSM148536 2 0.2603 0.953 0.044 0.956
#> GSM148537 2 0.2236 0.956 0.036 0.964
#> GSM148538 2 0.2043 0.957 0.032 0.968
#> GSM148539 2 0.3114 0.944 0.056 0.944
#> GSM148540 2 0.7299 0.801 0.204 0.796
#> GSM148541 2 0.3274 0.946 0.060 0.940
#> GSM148542 2 0.6712 0.829 0.176 0.824
#> GSM148543 2 0.4161 0.928 0.084 0.916
#> GSM148544 2 0.7219 0.813 0.200 0.800
#> GSM148545 1 0.0938 0.966 0.988 0.012
#> GSM148546 1 0.3114 0.959 0.944 0.056
#> GSM148547 1 0.2423 0.966 0.960 0.040
#> GSM148548 1 0.3274 0.958 0.940 0.060
#> GSM148549 1 0.3584 0.955 0.932 0.068
#> GSM148550 1 0.2043 0.967 0.968 0.032
#> GSM148551 1 0.4298 0.940 0.912 0.088
#> GSM148552 1 0.5178 0.899 0.884 0.116
#> GSM148553 1 0.4022 0.945 0.920 0.080
#> GSM148554 1 0.2778 0.964 0.952 0.048
#> GSM148555 1 0.1184 0.966 0.984 0.016
#> GSM148556 1 0.2423 0.965 0.960 0.040
#> GSM148557 1 0.0000 0.960 1.000 0.000
#> GSM148558 1 0.0376 0.962 0.996 0.004
#> GSM148559 1 0.5519 0.893 0.872 0.128
#> GSM148560 1 0.1414 0.967 0.980 0.020
#> GSM148561 1 0.3274 0.955 0.940 0.060
#> GSM148562 1 0.2236 0.967 0.964 0.036
#> GSM148563 1 0.2423 0.965 0.960 0.040
#> GSM148564 1 0.2778 0.963 0.952 0.048
#> GSM148565 1 0.1414 0.966 0.980 0.020
#> GSM148566 1 0.1843 0.967 0.972 0.028
#> GSM148567 1 0.2236 0.967 0.964 0.036
#> GSM148568 1 0.5059 0.915 0.888 0.112
#> GSM148569 1 0.0672 0.964 0.992 0.008
#> GSM148570 1 0.0672 0.963 0.992 0.008
#> GSM148571 1 0.0938 0.965 0.988 0.012
#> GSM148572 1 0.0376 0.962 0.996 0.004
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM148516 2 0.868 0.546097 0.124 0.548 0.328
#> GSM148517 3 0.682 -0.000132 0.488 0.012 0.500
#> GSM148518 2 0.245 0.837747 0.012 0.936 0.052
#> GSM148519 2 0.196 0.835344 0.000 0.944 0.056
#> GSM148520 2 0.566 0.805196 0.052 0.796 0.152
#> GSM148521 2 0.338 0.841702 0.008 0.892 0.100
#> GSM148522 2 0.199 0.836226 0.004 0.948 0.048
#> GSM148523 2 0.338 0.842572 0.008 0.892 0.100
#> GSM148524 2 0.311 0.841372 0.004 0.900 0.096
#> GSM148525 2 0.329 0.841285 0.008 0.896 0.096
#> GSM148526 2 0.439 0.835137 0.012 0.840 0.148
#> GSM148527 2 0.287 0.839868 0.008 0.916 0.076
#> GSM148528 2 0.338 0.841255 0.012 0.896 0.092
#> GSM148529 2 0.420 0.836984 0.024 0.864 0.112
#> GSM148530 2 0.421 0.838035 0.020 0.860 0.120
#> GSM148531 2 0.474 0.833371 0.048 0.848 0.104
#> GSM148532 2 0.421 0.839109 0.016 0.856 0.128
#> GSM148533 2 0.280 0.840816 0.000 0.908 0.092
#> GSM148534 2 0.341 0.841988 0.028 0.904 0.068
#> GSM148535 2 0.345 0.841686 0.008 0.888 0.104
#> GSM148536 2 0.621 0.795260 0.088 0.776 0.136
#> GSM148537 2 0.547 0.814161 0.040 0.800 0.160
#> GSM148538 2 0.428 0.834000 0.020 0.856 0.124
#> GSM148539 2 0.715 0.727207 0.060 0.676 0.264
#> GSM148540 2 0.928 0.328573 0.164 0.468 0.368
#> GSM148541 2 0.800 0.628709 0.076 0.580 0.344
#> GSM148542 2 0.941 0.341342 0.196 0.488 0.316
#> GSM148543 2 0.834 0.607448 0.112 0.592 0.296
#> GSM148544 2 0.979 0.256264 0.256 0.428 0.316
#> GSM148545 1 0.628 -0.016816 0.540 0.000 0.460
#> GSM148546 1 0.748 -0.040128 0.508 0.036 0.456
#> GSM148547 1 0.749 -0.094894 0.496 0.036 0.468
#> GSM148548 3 0.864 0.087877 0.444 0.100 0.456
#> GSM148549 1 0.728 0.101820 0.564 0.032 0.404
#> GSM148550 1 0.663 0.247340 0.644 0.020 0.336
#> GSM148551 1 0.704 0.223353 0.648 0.040 0.312
#> GSM148552 3 0.864 0.258912 0.400 0.104 0.496
#> GSM148553 3 0.750 0.223806 0.360 0.048 0.592
#> GSM148554 1 0.707 0.067344 0.568 0.024 0.408
#> GSM148555 1 0.688 0.128220 0.592 0.020 0.388
#> GSM148556 1 0.636 0.230610 0.652 0.012 0.336
#> GSM148557 1 0.520 0.329102 0.760 0.004 0.236
#> GSM148558 1 0.524 0.308564 0.756 0.004 0.240
#> GSM148559 3 0.803 0.214150 0.424 0.064 0.512
#> GSM148560 1 0.706 0.027538 0.520 0.020 0.460
#> GSM148561 1 0.800 0.041789 0.552 0.068 0.380
#> GSM148562 1 0.534 0.334051 0.760 0.008 0.232
#> GSM148563 1 0.492 0.357956 0.816 0.020 0.164
#> GSM148564 1 0.752 0.088377 0.568 0.044 0.388
#> GSM148565 1 0.484 0.337827 0.776 0.000 0.224
#> GSM148566 1 0.675 0.056012 0.556 0.012 0.432
#> GSM148567 1 0.755 0.152269 0.580 0.048 0.372
#> GSM148568 1 0.774 0.038115 0.568 0.056 0.376
#> GSM148569 1 0.590 0.307950 0.736 0.020 0.244
#> GSM148570 1 0.493 0.348588 0.784 0.004 0.212
#> GSM148571 1 0.441 0.372584 0.844 0.016 0.140
#> GSM148572 1 0.388 0.350943 0.848 0.000 0.152
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM148516 3 0.796 0.42438 0.128 0.308 0.520 0.044
#> GSM148517 1 0.731 0.15747 0.524 0.012 0.120 0.344
#> GSM148518 2 0.493 0.62920 0.028 0.760 0.200 0.012
#> GSM148519 2 0.371 0.66604 0.024 0.852 0.116 0.008
#> GSM148520 2 0.717 0.40254 0.048 0.568 0.328 0.056
#> GSM148521 2 0.567 0.59387 0.040 0.692 0.256 0.012
#> GSM148522 2 0.349 0.66372 0.036 0.868 0.092 0.004
#> GSM148523 2 0.446 0.63434 0.024 0.800 0.164 0.012
#> GSM148524 2 0.496 0.63133 0.020 0.760 0.200 0.020
#> GSM148525 2 0.602 0.49867 0.028 0.668 0.272 0.032
#> GSM148526 2 0.655 0.44493 0.060 0.640 0.272 0.028
#> GSM148527 2 0.493 0.64793 0.028 0.768 0.188 0.016
#> GSM148528 2 0.479 0.63455 0.020 0.740 0.236 0.004
#> GSM148529 2 0.636 0.57240 0.052 0.680 0.228 0.040
#> GSM148530 2 0.585 0.58873 0.064 0.712 0.208 0.016
#> GSM148531 2 0.669 0.48568 0.064 0.644 0.256 0.036
#> GSM148532 2 0.637 0.43772 0.068 0.616 0.308 0.008
#> GSM148533 2 0.415 0.64293 0.016 0.800 0.180 0.004
#> GSM148534 2 0.548 0.61167 0.024 0.696 0.264 0.016
#> GSM148535 2 0.404 0.64789 0.024 0.820 0.152 0.004
#> GSM148536 2 0.732 0.51517 0.076 0.616 0.244 0.064
#> GSM148537 2 0.539 0.61571 0.036 0.760 0.168 0.036
#> GSM148538 2 0.540 0.63716 0.052 0.760 0.164 0.024
#> GSM148539 3 0.808 0.36309 0.096 0.400 0.444 0.060
#> GSM148540 3 0.884 0.50476 0.148 0.244 0.492 0.116
#> GSM148541 3 0.754 0.40990 0.104 0.356 0.512 0.028
#> GSM148542 3 0.888 0.42051 0.104 0.352 0.416 0.128
#> GSM148543 3 0.840 0.37141 0.104 0.364 0.452 0.080
#> GSM148544 3 0.955 0.43887 0.144 0.244 0.392 0.220
#> GSM148545 1 0.703 0.16760 0.508 0.008 0.096 0.388
#> GSM148546 1 0.709 0.30616 0.624 0.036 0.096 0.244
#> GSM148547 1 0.699 0.23222 0.604 0.016 0.112 0.268
#> GSM148548 1 0.786 0.23589 0.564 0.056 0.120 0.260
#> GSM148549 1 0.857 0.18057 0.432 0.048 0.188 0.332
#> GSM148550 1 0.705 0.09255 0.464 0.004 0.104 0.428
#> GSM148551 1 0.774 0.10653 0.468 0.032 0.108 0.392
#> GSM148552 1 0.847 0.23094 0.520 0.084 0.144 0.252
#> GSM148553 1 0.666 0.32289 0.680 0.028 0.136 0.156
#> GSM148554 1 0.729 0.22848 0.548 0.024 0.096 0.332
#> GSM148555 4 0.722 -0.09162 0.432 0.008 0.108 0.452
#> GSM148556 4 0.737 -0.01527 0.408 0.024 0.088 0.480
#> GSM148557 4 0.657 0.00286 0.408 0.004 0.068 0.520
#> GSM148558 4 0.637 0.15332 0.336 0.000 0.080 0.584
#> GSM148559 1 0.865 0.16594 0.444 0.060 0.176 0.320
#> GSM148560 4 0.776 0.08950 0.404 0.028 0.116 0.452
#> GSM148561 4 0.823 0.17842 0.264 0.048 0.172 0.516
#> GSM148562 4 0.665 0.25281 0.284 0.016 0.080 0.620
#> GSM148563 4 0.647 0.27875 0.284 0.016 0.068 0.632
#> GSM148564 4 0.749 0.18822 0.324 0.024 0.116 0.536
#> GSM148565 4 0.513 0.35249 0.212 0.004 0.044 0.740
#> GSM148566 4 0.757 0.10458 0.368 0.028 0.104 0.500
#> GSM148567 4 0.762 0.23889 0.244 0.048 0.120 0.588
#> GSM148568 4 0.748 0.20466 0.268 0.020 0.148 0.564
#> GSM148569 4 0.660 0.29824 0.220 0.012 0.116 0.652
#> GSM148570 4 0.541 0.35448 0.168 0.000 0.096 0.736
#> GSM148571 4 0.522 0.36801 0.136 0.016 0.072 0.776
#> GSM148572 4 0.387 0.38466 0.096 0.000 0.060 0.844
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM148516 3 0.865 0.31078 0.068 0.216 0.440 0.076 NA
#> GSM148517 1 0.750 0.14921 0.476 0.008 0.044 0.268 NA
#> GSM148518 2 0.557 0.46881 0.000 0.624 0.276 0.004 NA
#> GSM148519 2 0.470 0.52882 0.016 0.756 0.156 0.000 NA
#> GSM148520 2 0.802 0.33834 0.052 0.484 0.220 0.040 NA
#> GSM148521 2 0.666 0.42704 0.036 0.536 0.308 0.000 NA
#> GSM148522 2 0.555 0.49909 0.020 0.696 0.192 0.008 NA
#> GSM148523 2 0.631 0.47073 0.016 0.616 0.244 0.016 NA
#> GSM148524 2 0.609 0.50591 0.024 0.672 0.188 0.024 NA
#> GSM148525 2 0.634 0.27872 0.012 0.492 0.400 0.008 NA
#> GSM148526 2 0.703 0.39900 0.044 0.592 0.208 0.024 NA
#> GSM148527 2 0.542 0.51481 0.008 0.688 0.196 0.004 NA
#> GSM148528 2 0.592 0.50896 0.020 0.684 0.176 0.020 NA
#> GSM148529 2 0.646 0.45828 0.056 0.656 0.168 0.016 NA
#> GSM148530 2 0.656 0.45747 0.024 0.528 0.352 0.012 NA
#> GSM148531 2 0.686 0.34535 0.020 0.492 0.372 0.024 NA
#> GSM148532 3 0.752 -0.21894 0.040 0.368 0.452 0.036 NA
#> GSM148533 2 0.551 0.41653 0.012 0.548 0.396 0.000 NA
#> GSM148534 2 0.585 0.49841 0.008 0.664 0.188 0.012 NA
#> GSM148535 2 0.578 0.47502 0.016 0.632 0.256 0.000 NA
#> GSM148536 2 0.741 0.39529 0.044 0.512 0.268 0.016 NA
#> GSM148537 2 0.620 0.45197 0.016 0.656 0.184 0.024 NA
#> GSM148538 2 0.672 0.45545 0.056 0.592 0.248 0.008 NA
#> GSM148539 3 0.758 0.19433 0.036 0.324 0.444 0.016 NA
#> GSM148540 3 0.877 0.37158 0.092 0.160 0.448 0.084 NA
#> GSM148541 3 0.820 0.37283 0.056 0.220 0.428 0.032 NA
#> GSM148542 3 0.882 0.34194 0.068 0.208 0.432 0.100 NA
#> GSM148543 3 0.737 0.34747 0.036 0.180 0.560 0.036 NA
#> GSM148544 3 0.904 0.36281 0.092 0.112 0.420 0.164 NA
#> GSM148545 1 0.755 0.17792 0.496 0.012 0.052 0.256 NA
#> GSM148546 1 0.646 0.29997 0.652 0.024 0.032 0.136 NA
#> GSM148547 1 0.761 0.25270 0.548 0.028 0.068 0.156 NA
#> GSM148548 1 0.864 0.20679 0.464 0.068 0.108 0.212 NA
#> GSM148549 1 0.827 0.20740 0.468 0.032 0.112 0.248 NA
#> GSM148550 1 0.738 0.21422 0.480 0.012 0.040 0.312 NA
#> GSM148551 1 0.810 0.11876 0.464 0.044 0.064 0.288 NA
#> GSM148552 1 0.873 0.19552 0.440 0.068 0.092 0.180 NA
#> GSM148553 1 0.782 0.23068 0.512 0.020 0.080 0.180 NA
#> GSM148554 1 0.664 0.26000 0.624 0.020 0.048 0.216 NA
#> GSM148555 1 0.774 0.17721 0.460 0.020 0.044 0.288 NA
#> GSM148556 1 0.701 0.19490 0.540 0.016 0.044 0.300 NA
#> GSM148557 1 0.630 0.04293 0.464 0.004 0.020 0.436 NA
#> GSM148558 4 0.716 0.02348 0.384 0.012 0.020 0.428 NA
#> GSM148559 1 0.867 0.13302 0.372 0.036 0.096 0.200 NA
#> GSM148560 1 0.802 0.00668 0.380 0.016 0.048 0.276 NA
#> GSM148561 4 0.814 0.16939 0.252 0.016 0.076 0.428 NA
#> GSM148562 4 0.749 0.16909 0.312 0.008 0.044 0.456 NA
#> GSM148563 4 0.731 0.26785 0.260 0.012 0.052 0.528 NA
#> GSM148564 4 0.697 0.31471 0.156 0.024 0.072 0.624 NA
#> GSM148565 4 0.643 0.33113 0.136 0.024 0.048 0.668 NA
#> GSM148566 4 0.818 0.09587 0.280 0.028 0.044 0.372 NA
#> GSM148567 4 0.785 0.29172 0.176 0.032 0.072 0.524 NA
#> GSM148568 4 0.813 0.23266 0.212 0.036 0.080 0.492 NA
#> GSM148569 4 0.691 0.27727 0.204 0.008 0.052 0.588 NA
#> GSM148570 4 0.604 0.34303 0.200 0.000 0.036 0.648 NA
#> GSM148571 4 0.529 0.35644 0.148 0.000 0.032 0.724 NA
#> GSM148572 4 0.407 0.36629 0.104 0.012 0.020 0.824 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM148516 3 0.836 0.2871 0.052 0.124 0.420 0.048 0.096 0.260
#> GSM148517 5 0.760 0.2299 0.184 0.024 0.024 0.236 0.468 0.064
#> GSM148518 2 0.622 0.1891 0.032 0.624 0.160 0.012 0.020 0.152
#> GSM148519 2 0.503 0.1475 0.020 0.700 0.072 0.000 0.016 0.192
#> GSM148520 6 0.801 0.1541 0.048 0.328 0.136 0.032 0.064 0.392
#> GSM148521 2 0.718 -0.0771 0.020 0.456 0.140 0.024 0.036 0.324
#> GSM148522 2 0.616 0.0646 0.032 0.624 0.116 0.004 0.032 0.192
#> GSM148523 2 0.624 0.1735 0.020 0.616 0.176 0.012 0.028 0.148
#> GSM148524 2 0.642 0.0164 0.020 0.572 0.100 0.012 0.036 0.260
#> GSM148525 2 0.710 0.0733 0.024 0.460 0.224 0.000 0.048 0.244
#> GSM148526 2 0.696 0.0696 0.048 0.520 0.172 0.004 0.028 0.228
#> GSM148527 2 0.620 0.0213 0.012 0.552 0.140 0.004 0.020 0.272
#> GSM148528 2 0.660 0.0452 0.032 0.564 0.104 0.008 0.040 0.252
#> GSM148529 6 0.669 0.1200 0.032 0.408 0.084 0.012 0.028 0.436
#> GSM148530 2 0.712 -0.0469 0.024 0.452 0.148 0.020 0.028 0.328
#> GSM148531 2 0.733 0.0679 0.040 0.484 0.180 0.020 0.028 0.248
#> GSM148532 2 0.804 0.0127 0.064 0.336 0.284 0.008 0.052 0.256
#> GSM148533 2 0.635 0.1448 0.028 0.604 0.180 0.004 0.036 0.148
#> GSM148534 2 0.687 -0.1223 0.024 0.508 0.100 0.016 0.044 0.308
#> GSM148535 2 0.618 0.2165 0.024 0.648 0.160 0.016 0.044 0.108
#> GSM148536 6 0.684 0.1454 0.036 0.400 0.092 0.020 0.020 0.432
#> GSM148537 2 0.649 0.1286 0.036 0.636 0.084 0.036 0.040 0.168
#> GSM148538 2 0.691 -0.1174 0.032 0.440 0.092 0.024 0.024 0.388
#> GSM148539 3 0.763 0.2554 0.056 0.264 0.484 0.028 0.052 0.116
#> GSM148540 3 0.800 0.3938 0.060 0.124 0.528 0.068 0.104 0.116
#> GSM148541 3 0.763 0.3822 0.052 0.164 0.528 0.028 0.072 0.156
#> GSM148542 3 0.889 0.3278 0.064 0.180 0.408 0.112 0.088 0.148
#> GSM148543 3 0.628 0.3714 0.052 0.188 0.640 0.024 0.028 0.068
#> GSM148544 3 0.892 0.3640 0.124 0.120 0.424 0.140 0.076 0.116
#> GSM148545 5 0.743 0.2117 0.256 0.000 0.056 0.156 0.468 0.064
#> GSM148546 1 0.713 0.0730 0.480 0.012 0.052 0.096 0.320 0.040
#> GSM148547 1 0.786 0.0117 0.412 0.008 0.060 0.152 0.296 0.072
#> GSM148548 1 0.820 0.1590 0.484 0.060 0.084 0.136 0.180 0.056
#> GSM148549 1 0.732 0.2502 0.556 0.024 0.072 0.200 0.068 0.080
#> GSM148550 1 0.695 0.2430 0.552 0.008 0.060 0.224 0.120 0.036
#> GSM148551 1 0.787 0.2139 0.464 0.012 0.072 0.232 0.148 0.072
#> GSM148552 5 0.829 0.1311 0.300 0.032 0.044 0.116 0.384 0.124
#> GSM148553 5 0.859 0.0578 0.296 0.032 0.140 0.100 0.356 0.076
#> GSM148554 1 0.730 0.2445 0.532 0.012 0.032 0.188 0.152 0.084
#> GSM148555 1 0.799 0.0851 0.400 0.008 0.052 0.276 0.180 0.084
#> GSM148556 1 0.697 0.1561 0.500 0.008 0.028 0.296 0.116 0.052
#> GSM148557 4 0.723 -0.0896 0.376 0.008 0.032 0.408 0.124 0.052
#> GSM148558 4 0.696 0.1613 0.232 0.000 0.040 0.516 0.168 0.044
#> GSM148559 5 0.891 0.1953 0.216 0.040 0.100 0.160 0.372 0.112
#> GSM148560 5 0.736 0.2227 0.144 0.020 0.072 0.216 0.520 0.028
#> GSM148561 4 0.874 0.0613 0.176 0.028 0.104 0.352 0.256 0.084
#> GSM148562 4 0.721 0.2010 0.244 0.004 0.028 0.504 0.136 0.084
#> GSM148563 4 0.747 0.2240 0.164 0.004 0.060 0.492 0.220 0.060
#> GSM148564 4 0.741 0.1935 0.136 0.008 0.076 0.504 0.232 0.044
#> GSM148565 4 0.632 0.3427 0.108 0.012 0.052 0.640 0.156 0.032
#> GSM148566 5 0.723 0.1866 0.132 0.032 0.036 0.212 0.544 0.044
#> GSM148567 4 0.782 0.2352 0.140 0.024 0.096 0.492 0.204 0.044
#> GSM148568 4 0.793 0.1179 0.104 0.024 0.052 0.432 0.296 0.092
#> GSM148569 4 0.719 0.2042 0.232 0.020 0.052 0.524 0.144 0.028
#> GSM148570 4 0.589 0.3266 0.116 0.004 0.028 0.660 0.156 0.036
#> GSM148571 4 0.484 0.3563 0.108 0.004 0.028 0.760 0.064 0.036
#> GSM148572 4 0.519 0.3654 0.108 0.004 0.040 0.728 0.100 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 agent(p) dose(p) time(p) k
#> CV:skmeans 57 2.57e-12 0.999568 1.000 2
#> CV:skmeans 25 NA NA NA 3
#> CV:skmeans 17 NA 0.000707 0.549 4
#> CV:skmeans 4 NA NA NA 5
#> CV:skmeans 0 NA NA NA 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "pam"]
# you can also extract it by
# res = res_list["CV:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21163 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.384 0.872 0.892 0.5037 0.491 0.491
#> 3 3 0.329 0.488 0.700 0.2622 0.918 0.834
#> 4 4 0.390 0.257 0.590 0.1041 0.796 0.551
#> 5 5 0.405 0.163 0.533 0.0388 0.862 0.615
#> 6 6 0.420 0.157 0.541 0.0229 0.811 0.487
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
#> GSM148516 2 0.295 0.916 0.052 0.948
#> GSM148517 1 0.714 0.870 0.804 0.196
#> GSM148518 2 0.295 0.919 0.052 0.948
#> GSM148519 2 0.295 0.921 0.052 0.948
#> GSM148520 2 0.358 0.918 0.068 0.932
#> GSM148521 2 0.343 0.915 0.064 0.936
#> GSM148522 2 0.343 0.916 0.064 0.936
#> GSM148523 2 0.204 0.922 0.032 0.968
#> GSM148524 2 0.278 0.917 0.048 0.952
#> GSM148525 2 0.260 0.916 0.044 0.956
#> GSM148526 2 0.644 0.857 0.164 0.836
#> GSM148527 2 0.388 0.913 0.076 0.924
#> GSM148528 2 0.260 0.919 0.044 0.956
#> GSM148529 2 0.388 0.916 0.076 0.924
#> GSM148530 2 0.295 0.921 0.052 0.948
#> GSM148531 2 0.430 0.909 0.088 0.912
#> GSM148532 2 0.163 0.916 0.024 0.976
#> GSM148533 2 0.224 0.923 0.036 0.964
#> GSM148534 2 0.430 0.917 0.088 0.912
#> GSM148535 2 0.184 0.917 0.028 0.972
#> GSM148536 2 0.529 0.888 0.120 0.880
#> GSM148537 2 0.260 0.921 0.044 0.956
#> GSM148538 2 0.295 0.924 0.052 0.948
#> GSM148539 2 0.343 0.917 0.064 0.936
#> GSM148540 2 0.552 0.893 0.128 0.872
#> GSM148541 2 0.327 0.910 0.060 0.940
#> GSM148542 2 0.327 0.918 0.060 0.940
#> GSM148543 2 0.358 0.915 0.068 0.932
#> GSM148544 2 0.975 0.415 0.408 0.592
#> GSM148545 1 0.373 0.904 0.928 0.072
#> GSM148546 1 0.753 0.856 0.784 0.216
#> GSM148547 1 0.494 0.907 0.892 0.108
#> GSM148548 1 0.788 0.774 0.764 0.236
#> GSM148549 1 0.469 0.906 0.900 0.100
#> GSM148550 1 0.242 0.902 0.960 0.040
#> GSM148551 1 0.469 0.906 0.900 0.100
#> GSM148552 1 0.529 0.902 0.880 0.120
#> GSM148553 1 0.781 0.826 0.768 0.232
#> GSM148554 1 0.456 0.905 0.904 0.096
#> GSM148555 1 0.388 0.913 0.924 0.076
#> GSM148556 1 0.242 0.904 0.960 0.040
#> GSM148557 1 0.373 0.901 0.928 0.072
#> GSM148558 1 0.204 0.899 0.968 0.032
#> GSM148559 1 0.730 0.839 0.796 0.204
#> GSM148560 1 0.615 0.886 0.848 0.152
#> GSM148561 1 0.775 0.816 0.772 0.228
#> GSM148562 1 0.388 0.907 0.924 0.076
#> GSM148563 1 0.574 0.888 0.864 0.136
#> GSM148564 1 0.671 0.887 0.824 0.176
#> GSM148565 1 0.388 0.913 0.924 0.076
#> GSM148566 1 0.653 0.885 0.832 0.168
#> GSM148567 2 1.000 -0.144 0.488 0.512
#> GSM148568 1 0.680 0.886 0.820 0.180
#> GSM148569 1 0.506 0.896 0.888 0.112
#> GSM148570 1 0.358 0.905 0.932 0.068
#> GSM148571 1 0.358 0.907 0.932 0.068
#> GSM148572 1 0.260 0.901 0.956 0.044
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM148516 2 0.343 0.47415 0.004 0.884 0.112
#> GSM148517 1 0.851 0.64814 0.604 0.152 0.244
#> GSM148518 2 0.572 0.42987 0.016 0.744 0.240
#> GSM148519 2 0.603 0.23145 0.000 0.624 0.376
#> GSM148520 2 0.546 0.44418 0.020 0.776 0.204
#> GSM148521 2 0.668 0.02433 0.008 0.508 0.484
#> GSM148522 2 0.698 -0.03351 0.020 0.560 0.420
#> GSM148523 2 0.385 0.48400 0.004 0.860 0.136
#> GSM148524 2 0.598 0.30858 0.004 0.668 0.328
#> GSM148525 2 0.483 0.42076 0.004 0.792 0.204
#> GSM148526 3 0.742 0.05267 0.040 0.388 0.572
#> GSM148527 2 0.677 0.23835 0.028 0.652 0.320
#> GSM148528 2 0.619 0.23110 0.000 0.580 0.420
#> GSM148529 3 0.707 -0.06193 0.020 0.476 0.504
#> GSM148530 2 0.480 0.42280 0.020 0.824 0.156
#> GSM148531 3 0.737 -0.04835 0.032 0.444 0.524
#> GSM148532 2 0.484 0.45486 0.016 0.816 0.168
#> GSM148533 2 0.304 0.47377 0.008 0.908 0.084
#> GSM148534 2 0.675 0.15803 0.016 0.596 0.388
#> GSM148535 2 0.566 0.37958 0.004 0.712 0.284
#> GSM148536 2 0.531 0.42671 0.048 0.816 0.136
#> GSM148537 2 0.623 0.27981 0.004 0.624 0.372
#> GSM148538 2 0.680 0.09752 0.012 0.532 0.456
#> GSM148539 2 0.625 0.33179 0.024 0.708 0.268
#> GSM148540 3 0.749 0.00611 0.036 0.480 0.484
#> GSM148541 2 0.655 0.34890 0.020 0.656 0.324
#> GSM148542 2 0.512 0.45598 0.012 0.788 0.200
#> GSM148543 2 0.517 0.41299 0.024 0.804 0.172
#> GSM148544 2 0.969 0.00997 0.276 0.460 0.264
#> GSM148545 1 0.392 0.81087 0.872 0.016 0.112
#> GSM148546 1 0.792 0.72786 0.664 0.184 0.152
#> GSM148547 1 0.646 0.80261 0.756 0.080 0.164
#> GSM148548 3 0.758 -0.43273 0.460 0.040 0.500
#> GSM148549 1 0.634 0.78619 0.736 0.044 0.220
#> GSM148550 1 0.341 0.81573 0.876 0.000 0.124
#> GSM148551 1 0.529 0.82208 0.824 0.064 0.112
#> GSM148552 1 0.677 0.78025 0.724 0.068 0.208
#> GSM148553 1 0.814 0.69260 0.644 0.152 0.204
#> GSM148554 1 0.471 0.82193 0.848 0.044 0.108
#> GSM148555 1 0.551 0.80935 0.808 0.056 0.136
#> GSM148556 1 0.487 0.81063 0.832 0.032 0.136
#> GSM148557 1 0.369 0.79934 0.884 0.016 0.100
#> GSM148558 1 0.371 0.79975 0.868 0.004 0.128
#> GSM148559 1 0.737 0.74761 0.688 0.092 0.220
#> GSM148560 1 0.782 0.68500 0.648 0.100 0.252
#> GSM148561 1 0.835 0.67835 0.628 0.196 0.176
#> GSM148562 1 0.557 0.81123 0.784 0.032 0.184
#> GSM148563 1 0.687 0.71844 0.672 0.040 0.288
#> GSM148564 1 0.733 0.77113 0.708 0.156 0.136
#> GSM148565 1 0.570 0.81440 0.800 0.064 0.136
#> GSM148566 1 0.823 0.69440 0.632 0.144 0.224
#> GSM148567 2 0.988 -0.07742 0.340 0.396 0.264
#> GSM148568 1 0.635 0.79247 0.768 0.140 0.092
#> GSM148569 1 0.554 0.79736 0.812 0.072 0.116
#> GSM148570 1 0.460 0.80531 0.852 0.040 0.108
#> GSM148571 1 0.449 0.80425 0.856 0.036 0.108
#> GSM148572 1 0.371 0.81212 0.868 0.004 0.128
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM148516 2 0.624 0.35329 0.044 0.620 0.320 0.016
#> GSM148517 1 0.519 0.13714 0.780 0.128 0.016 0.076
#> GSM148518 2 0.482 0.37274 0.020 0.784 0.168 0.028
#> GSM148519 2 0.511 0.13217 0.012 0.688 0.292 0.008
#> GSM148520 2 0.687 0.28150 0.060 0.556 0.360 0.024
#> GSM148521 3 0.569 0.27752 0.008 0.368 0.604 0.020
#> GSM148522 3 0.583 0.38433 0.020 0.304 0.652 0.024
#> GSM148523 2 0.461 0.41784 0.004 0.752 0.228 0.016
#> GSM148524 3 0.625 0.09724 0.040 0.416 0.536 0.008
#> GSM148525 2 0.123 0.43293 0.004 0.968 0.008 0.020
#> GSM148526 3 0.730 0.26588 0.052 0.396 0.504 0.048
#> GSM148527 3 0.570 0.14713 0.012 0.364 0.608 0.016
#> GSM148528 2 0.644 0.01635 0.044 0.528 0.416 0.012
#> GSM148529 3 0.571 0.39632 0.012 0.304 0.656 0.028
#> GSM148530 2 0.629 0.20756 0.020 0.556 0.396 0.028
#> GSM148531 2 0.641 -0.14604 0.012 0.544 0.400 0.044
#> GSM148532 2 0.366 0.43747 0.008 0.852 0.120 0.020
#> GSM148533 2 0.515 0.37159 0.016 0.696 0.280 0.008
#> GSM148534 3 0.625 0.29643 0.064 0.232 0.680 0.024
#> GSM148535 2 0.317 0.37725 0.004 0.876 0.104 0.016
#> GSM148536 2 0.763 0.28519 0.052 0.544 0.320 0.084
#> GSM148537 2 0.516 0.22206 0.016 0.720 0.248 0.016
#> GSM148538 2 0.595 -0.06482 0.016 0.552 0.416 0.016
#> GSM148539 3 0.654 0.00308 0.020 0.460 0.484 0.036
#> GSM148540 3 0.707 0.32920 0.048 0.388 0.524 0.040
#> GSM148541 2 0.543 0.33242 0.016 0.712 0.244 0.028
#> GSM148542 2 0.559 0.39529 0.032 0.724 0.216 0.028
#> GSM148543 2 0.645 0.22519 0.028 0.556 0.388 0.028
#> GSM148544 2 0.873 0.08450 0.120 0.516 0.148 0.216
#> GSM148545 4 0.318 0.43167 0.132 0.004 0.004 0.860
#> GSM148546 4 0.572 0.45693 0.052 0.168 0.036 0.744
#> GSM148547 4 0.625 0.38587 0.188 0.056 0.048 0.708
#> GSM148548 3 0.862 -0.28817 0.176 0.052 0.388 0.384
#> GSM148549 4 0.490 0.46959 0.060 0.016 0.128 0.796
#> GSM148550 4 0.447 0.37110 0.180 0.000 0.036 0.784
#> GSM148551 4 0.580 0.27505 0.224 0.020 0.048 0.708
#> GSM148552 4 0.486 0.47350 0.052 0.020 0.128 0.800
#> GSM148553 4 0.869 -0.04927 0.356 0.096 0.116 0.432
#> GSM148554 4 0.627 -0.05394 0.360 0.024 0.028 0.588
#> GSM148555 1 0.692 0.48619 0.472 0.048 0.028 0.452
#> GSM148556 4 0.331 0.45618 0.084 0.028 0.008 0.880
#> GSM148557 1 0.500 0.55543 0.516 0.000 0.000 0.484
#> GSM148558 1 0.557 0.57714 0.540 0.000 0.020 0.440
#> GSM148559 4 0.485 0.48388 0.032 0.060 0.096 0.812
#> GSM148560 4 0.702 0.34044 0.128 0.204 0.028 0.640
#> GSM148561 4 0.894 0.15084 0.224 0.104 0.192 0.480
#> GSM148562 4 0.466 0.45356 0.128 0.004 0.068 0.800
#> GSM148563 4 0.788 -0.02184 0.304 0.024 0.164 0.508
#> GSM148564 4 0.593 0.44706 0.092 0.160 0.020 0.728
#> GSM148565 4 0.483 0.46870 0.116 0.032 0.044 0.808
#> GSM148566 4 0.593 0.40569 0.064 0.232 0.012 0.692
#> GSM148567 4 0.836 0.10870 0.044 0.376 0.156 0.424
#> GSM148568 4 0.731 -0.23962 0.372 0.104 0.016 0.508
#> GSM148569 4 0.676 -0.39596 0.420 0.032 0.036 0.512
#> GSM148570 1 0.622 0.52828 0.500 0.036 0.008 0.456
#> GSM148571 1 0.601 0.54742 0.500 0.020 0.012 0.468
#> GSM148572 4 0.571 -0.24914 0.384 0.004 0.024 0.588
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM148516 2 0.6781 0.2813 0.036 0.548 0.256 0.000 NA
#> GSM148517 4 0.6276 0.1346 0.012 0.104 0.000 0.448 NA
#> GSM148518 2 0.4387 0.3100 0.004 0.744 0.208 0.000 NA
#> GSM148519 2 0.4643 0.0769 0.012 0.656 0.320 0.000 NA
#> GSM148520 2 0.6886 0.2080 0.024 0.508 0.308 0.004 NA
#> GSM148521 3 0.5760 0.3210 0.012 0.340 0.576 0.000 NA
#> GSM148522 3 0.4181 0.4151 0.008 0.240 0.736 0.000 NA
#> GSM148523 2 0.4771 0.3442 0.004 0.712 0.224 0.000 NA
#> GSM148524 3 0.6285 0.1797 0.012 0.372 0.504 0.000 NA
#> GSM148525 2 0.0854 0.3831 0.008 0.976 0.004 0.000 NA
#> GSM148526 3 0.6326 0.2866 0.036 0.356 0.540 0.004 NA
#> GSM148527 3 0.5371 0.2158 0.008 0.308 0.624 0.000 NA
#> GSM148528 2 0.6314 -0.0480 0.008 0.500 0.364 0.000 NA
#> GSM148529 3 0.4903 0.4262 0.012 0.236 0.708 0.004 NA
#> GSM148530 2 0.5742 0.1361 0.012 0.496 0.436 0.000 NA
#> GSM148531 2 0.5441 -0.2089 0.012 0.504 0.456 0.012 NA
#> GSM148532 2 0.2622 0.3808 0.004 0.884 0.100 0.004 NA
#> GSM148533 2 0.5116 0.2931 0.004 0.640 0.304 0.000 NA
#> GSM148534 3 0.6137 0.3325 0.020 0.192 0.636 0.004 NA
#> GSM148535 2 0.2517 0.3248 0.004 0.884 0.104 0.000 NA
#> GSM148536 2 0.7476 0.2230 0.072 0.492 0.280 0.004 NA
#> GSM148537 2 0.4479 0.1816 0.004 0.720 0.240 0.000 NA
#> GSM148538 2 0.5659 -0.1470 0.008 0.528 0.404 0.000 NA
#> GSM148539 3 0.5870 0.0827 0.020 0.400 0.524 0.000 NA
#> GSM148540 3 0.5587 0.3606 0.024 0.336 0.604 0.008 NA
#> GSM148541 2 0.6735 0.2415 0.080 0.624 0.180 0.008 NA
#> GSM148542 2 0.5176 0.3270 0.016 0.688 0.236 0.000 NA
#> GSM148543 2 0.5781 0.1627 0.008 0.508 0.416 0.000 NA
#> GSM148544 2 0.7815 0.1176 0.116 0.516 0.164 0.192 NA
#> GSM148545 4 0.4818 -0.4753 0.460 0.000 0.000 0.520 NA
#> GSM148546 1 0.7502 0.4179 0.404 0.176 0.020 0.376 NA
#> GSM148547 4 0.7383 -0.1824 0.324 0.044 0.048 0.508 NA
#> GSM148548 3 0.7507 -0.2230 0.176 0.028 0.452 0.324 NA
#> GSM148549 1 0.6945 0.4927 0.456 0.000 0.128 0.376 NA
#> GSM148550 4 0.5149 -0.3304 0.388 0.000 0.036 0.572 NA
#> GSM148551 4 0.6195 -0.1130 0.312 0.016 0.036 0.592 NA
#> GSM148552 1 0.7362 0.4916 0.424 0.008 0.080 0.400 NA
#> GSM148553 4 0.7194 0.1907 0.104 0.064 0.080 0.632 NA
#> GSM148554 4 0.4844 0.1699 0.224 0.016 0.004 0.720 NA
#> GSM148555 4 0.3631 0.3608 0.060 0.036 0.028 0.860 NA
#> GSM148556 1 0.5539 0.4512 0.492 0.032 0.004 0.460 NA
#> GSM148557 4 0.0671 0.3705 0.016 0.000 0.000 0.980 NA
#> GSM148558 4 0.1300 0.3761 0.028 0.000 0.016 0.956 NA
#> GSM148559 1 0.8029 0.3502 0.484 0.052 0.060 0.276 NA
#> GSM148560 4 0.7800 -0.2370 0.320 0.208 0.048 0.412 NA
#> GSM148561 4 0.9099 0.0188 0.272 0.072 0.128 0.372 NA
#> GSM148562 4 0.6733 -0.4813 0.408 0.004 0.044 0.464 NA
#> GSM148563 4 0.6368 0.1593 0.164 0.008 0.168 0.632 NA
#> GSM148564 4 0.7573 -0.4155 0.380 0.136 0.008 0.412 NA
#> GSM148565 1 0.6957 0.4695 0.436 0.024 0.044 0.436 NA
#> GSM148566 4 0.7457 -0.3276 0.348 0.248 0.012 0.376 NA
#> GSM148567 2 0.9315 -0.1197 0.264 0.352 0.132 0.160 NA
#> GSM148568 4 0.5364 0.2524 0.132 0.104 0.016 0.732 NA
#> GSM148569 4 0.5360 0.2988 0.156 0.028 0.020 0.736 NA
#> GSM148570 4 0.3003 0.3643 0.096 0.020 0.008 0.872 NA
#> GSM148571 4 0.2470 0.3749 0.036 0.020 0.012 0.916 NA
#> GSM148572 4 0.4426 0.2565 0.188 0.000 0.028 0.760 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM148516 2 0.5680 0.3665 0.008 0.640 0.108 0.000 0.204 0.040
#> GSM148517 6 0.5096 0.0000 0.000 0.012 0.056 0.388 0.000 0.544
#> GSM148518 2 0.4721 0.1578 0.000 0.592 0.356 0.000 0.048 0.004
#> GSM148519 3 0.4271 0.2756 0.004 0.300 0.664 0.000 0.032 0.000
#> GSM148520 2 0.5463 0.3887 0.008 0.632 0.176 0.008 0.176 0.000
#> GSM148521 3 0.5976 0.1233 0.000 0.392 0.456 0.000 0.132 0.020
#> GSM148522 2 0.5220 -0.0567 0.004 0.544 0.384 0.000 0.056 0.012
#> GSM148523 2 0.4402 0.3437 0.000 0.672 0.268 0.000 0.060 0.000
#> GSM148524 2 0.5609 0.1160 0.000 0.496 0.368 0.004 0.132 0.000
#> GSM148525 3 0.4348 -0.0464 0.004 0.464 0.520 0.000 0.008 0.004
#> GSM148526 3 0.6209 0.2591 0.024 0.272 0.556 0.004 0.132 0.012
#> GSM148527 2 0.5011 0.2687 0.000 0.672 0.204 0.000 0.108 0.016
#> GSM148528 3 0.5675 0.1047 0.000 0.344 0.488 0.000 0.168 0.000
#> GSM148529 3 0.6218 0.1205 0.012 0.384 0.476 0.008 0.104 0.016
#> GSM148530 2 0.1382 0.4738 0.008 0.948 0.036 0.000 0.008 0.000
#> GSM148531 3 0.4776 0.3143 0.008 0.284 0.660 0.012 0.032 0.004
#> GSM148532 2 0.4455 0.0236 0.008 0.500 0.480 0.004 0.008 0.000
#> GSM148533 2 0.2402 0.4558 0.000 0.856 0.140 0.000 0.000 0.004
#> GSM148534 2 0.6245 0.1246 0.008 0.484 0.276 0.008 0.224 0.000
#> GSM148535 3 0.3782 0.1366 0.000 0.360 0.636 0.000 0.000 0.004
#> GSM148536 2 0.4968 0.4397 0.056 0.732 0.064 0.012 0.136 0.000
#> GSM148537 3 0.4202 0.2591 0.000 0.300 0.668 0.000 0.028 0.004
#> GSM148538 3 0.5305 0.2395 0.000 0.328 0.568 0.000 0.096 0.008
#> GSM148539 2 0.4829 0.2982 0.012 0.668 0.260 0.000 0.052 0.008
#> GSM148540 3 0.5912 0.1704 0.016 0.416 0.488 0.016 0.048 0.016
#> GSM148541 3 0.7572 0.1250 0.072 0.196 0.500 0.004 0.156 0.072
#> GSM148542 2 0.4109 0.3758 0.012 0.736 0.212 0.000 0.040 0.000
#> GSM148543 2 0.0909 0.4805 0.000 0.968 0.020 0.000 0.012 0.000
#> GSM148544 3 0.7669 0.0946 0.144 0.288 0.380 0.172 0.016 0.000
#> GSM148545 4 0.5422 -0.3203 0.436 0.000 0.000 0.472 0.012 0.080
#> GSM148546 1 0.7267 0.2462 0.396 0.056 0.152 0.360 0.000 0.036
#> GSM148547 4 0.7122 -0.0457 0.316 0.056 0.024 0.496 0.064 0.044
#> GSM148548 4 0.9172 -0.1276 0.176 0.168 0.236 0.296 0.084 0.040
#> GSM148549 1 0.6764 0.3221 0.496 0.048 0.024 0.348 0.056 0.028
#> GSM148550 4 0.4827 -0.1847 0.412 0.020 0.000 0.548 0.012 0.008
#> GSM148551 4 0.5862 0.0380 0.336 0.032 0.004 0.560 0.044 0.024
#> GSM148552 1 0.7120 0.2885 0.408 0.020 0.036 0.400 0.104 0.032
#> GSM148553 4 0.6595 0.2353 0.092 0.080 0.048 0.632 0.136 0.012
#> GSM148554 4 0.4623 0.2585 0.220 0.016 0.004 0.716 0.020 0.024
#> GSM148555 4 0.3432 0.3833 0.052 0.028 0.020 0.860 0.012 0.028
#> GSM148556 1 0.5282 0.2255 0.484 0.004 0.032 0.456 0.016 0.008
#> GSM148557 4 0.0603 0.3877 0.016 0.000 0.000 0.980 0.000 0.004
#> GSM148558 4 0.1737 0.3889 0.040 0.008 0.000 0.932 0.000 0.020
#> GSM148559 1 0.7551 0.0397 0.536 0.052 0.036 0.196 0.064 0.116
#> GSM148560 4 0.7716 -0.1461 0.308 0.044 0.208 0.388 0.032 0.020
#> GSM148561 5 0.7065 0.0000 0.084 0.100 0.008 0.276 0.508 0.024
#> GSM148562 4 0.6603 -0.2909 0.380 0.028 0.008 0.456 0.108 0.020
#> GSM148563 4 0.6878 0.2008 0.144 0.028 0.112 0.612 0.052 0.052
#> GSM148564 4 0.7626 -0.2897 0.372 0.028 0.104 0.392 0.028 0.076
#> GSM148565 4 0.6729 -0.3198 0.396 0.032 0.020 0.436 0.012 0.104
#> GSM148566 4 0.7011 -0.2278 0.344 0.012 0.264 0.352 0.020 0.008
#> GSM148567 3 0.9260 -0.2282 0.224 0.184 0.300 0.160 0.072 0.060
#> GSM148568 4 0.4921 0.3023 0.136 0.056 0.076 0.728 0.004 0.000
#> GSM148569 4 0.5300 0.3186 0.168 0.048 0.004 0.708 0.028 0.044
#> GSM148570 4 0.3443 0.3651 0.096 0.000 0.044 0.836 0.008 0.016
#> GSM148571 4 0.2074 0.3924 0.036 0.048 0.000 0.912 0.004 0.000
#> GSM148572 4 0.4453 0.3046 0.184 0.012 0.000 0.732 0.004 0.068
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) dose(p) time(p) k
#> CV:pam 55 6.87e-12 0.999 1 2
#> CV:pam 27 NA NA NA 3
#> CV:pam 4 NA NA NA 4
#> CV:pam 0 NA NA NA 5
#> CV:pam 0 NA NA NA 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 21163 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.857 0.852 0.942 0.4887 0.504 0.504
#> 3 3 0.616 0.874 0.854 0.2526 0.880 0.766
#> 4 4 0.623 0.687 0.795 0.1324 0.895 0.736
#> 5 5 0.635 0.621 0.750 0.0725 0.982 0.941
#> 6 6 0.632 0.578 0.723 0.0506 0.895 0.673
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM148516 1 0.9775 0.2473 0.588 0.412
#> GSM148517 1 0.0000 0.9385 1.000 0.000
#> GSM148518 2 0.0376 0.9291 0.004 0.996
#> GSM148519 2 0.0672 0.9313 0.008 0.992
#> GSM148520 2 0.0938 0.9321 0.012 0.988
#> GSM148521 2 0.0672 0.9310 0.008 0.992
#> GSM148522 2 0.0672 0.9314 0.008 0.992
#> GSM148523 2 0.0376 0.9296 0.004 0.996
#> GSM148524 2 0.0672 0.9313 0.008 0.992
#> GSM148525 2 0.0672 0.9311 0.008 0.992
#> GSM148526 2 0.3584 0.9058 0.068 0.932
#> GSM148527 2 0.1843 0.9292 0.028 0.972
#> GSM148528 2 0.1843 0.9292 0.028 0.972
#> GSM148529 2 0.2948 0.9182 0.052 0.948
#> GSM148530 2 0.1184 0.9321 0.016 0.984
#> GSM148531 2 0.0000 0.9272 0.000 1.000
#> GSM148532 2 0.2423 0.9242 0.040 0.960
#> GSM148533 2 0.0000 0.9272 0.000 1.000
#> GSM148534 2 0.1414 0.9317 0.020 0.980
#> GSM148535 2 0.0672 0.9314 0.008 0.992
#> GSM148536 2 0.1843 0.9298 0.028 0.972
#> GSM148537 2 0.4431 0.8858 0.092 0.908
#> GSM148538 2 0.2423 0.9245 0.040 0.960
#> GSM148539 2 0.7815 0.7072 0.232 0.768
#> GSM148540 1 0.9795 0.2352 0.584 0.416
#> GSM148541 1 0.9996 -0.0290 0.512 0.488
#> GSM148542 2 1.0000 0.0184 0.496 0.504
#> GSM148543 2 0.9427 0.4534 0.360 0.640
#> GSM148544 1 0.9686 0.2925 0.604 0.396
#> GSM148545 1 0.0000 0.9385 1.000 0.000
#> GSM148546 1 0.0000 0.9385 1.000 0.000
#> GSM148547 1 0.0000 0.9385 1.000 0.000
#> GSM148548 1 0.0000 0.9385 1.000 0.000
#> GSM148549 1 0.0000 0.9385 1.000 0.000
#> GSM148550 1 0.0000 0.9385 1.000 0.000
#> GSM148551 1 0.0000 0.9385 1.000 0.000
#> GSM148552 1 0.0000 0.9385 1.000 0.000
#> GSM148553 1 0.0000 0.9385 1.000 0.000
#> GSM148554 1 0.0376 0.9354 0.996 0.004
#> GSM148555 1 0.0000 0.9385 1.000 0.000
#> GSM148556 1 0.0000 0.9385 1.000 0.000
#> GSM148557 1 0.0000 0.9385 1.000 0.000
#> GSM148558 1 0.0000 0.9385 1.000 0.000
#> GSM148559 1 0.0376 0.9354 0.996 0.004
#> GSM148560 1 0.0000 0.9385 1.000 0.000
#> GSM148561 1 0.0000 0.9385 1.000 0.000
#> GSM148562 1 0.0000 0.9385 1.000 0.000
#> GSM148563 1 0.0000 0.9385 1.000 0.000
#> GSM148564 1 0.0000 0.9385 1.000 0.000
#> GSM148565 1 0.0000 0.9385 1.000 0.000
#> GSM148566 1 0.0000 0.9385 1.000 0.000
#> GSM148567 1 0.0376 0.9354 0.996 0.004
#> GSM148568 1 0.0000 0.9385 1.000 0.000
#> GSM148569 1 0.0000 0.9385 1.000 0.000
#> GSM148570 1 0.0000 0.9385 1.000 0.000
#> GSM148571 1 0.0000 0.9385 1.000 0.000
#> GSM148572 1 0.0000 0.9385 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM148516 3 0.8643 0.819 0.212 0.188 0.600
#> GSM148517 1 0.5138 0.806 0.748 0.000 0.252
#> GSM148518 2 0.1170 0.970 0.008 0.976 0.016
#> GSM148519 2 0.0661 0.972 0.004 0.988 0.008
#> GSM148520 2 0.0829 0.971 0.004 0.984 0.012
#> GSM148521 2 0.0747 0.970 0.000 0.984 0.016
#> GSM148522 2 0.1170 0.970 0.008 0.976 0.016
#> GSM148523 2 0.0237 0.968 0.000 0.996 0.004
#> GSM148524 2 0.0237 0.971 0.004 0.996 0.000
#> GSM148525 2 0.1315 0.965 0.008 0.972 0.020
#> GSM148526 2 0.2527 0.942 0.020 0.936 0.044
#> GSM148527 2 0.0829 0.971 0.012 0.984 0.004
#> GSM148528 2 0.1015 0.970 0.008 0.980 0.012
#> GSM148529 2 0.1711 0.952 0.032 0.960 0.008
#> GSM148530 2 0.1015 0.971 0.012 0.980 0.008
#> GSM148531 2 0.0424 0.969 0.000 0.992 0.008
#> GSM148532 2 0.1905 0.951 0.028 0.956 0.016
#> GSM148533 2 0.0237 0.970 0.004 0.996 0.000
#> GSM148534 2 0.0661 0.971 0.004 0.988 0.008
#> GSM148535 2 0.0475 0.970 0.004 0.992 0.004
#> GSM148536 2 0.1337 0.969 0.012 0.972 0.016
#> GSM148537 2 0.3148 0.905 0.048 0.916 0.036
#> GSM148538 2 0.1636 0.958 0.020 0.964 0.016
#> GSM148539 3 0.8140 0.512 0.068 0.456 0.476
#> GSM148540 3 0.8361 0.801 0.216 0.160 0.624
#> GSM148541 3 0.8349 0.829 0.128 0.264 0.608
#> GSM148542 3 0.8292 0.827 0.124 0.264 0.612
#> GSM148543 3 0.8297 0.739 0.092 0.348 0.560
#> GSM148544 3 0.8210 0.760 0.240 0.132 0.628
#> GSM148545 1 0.5016 0.812 0.760 0.000 0.240
#> GSM148546 1 0.3752 0.832 0.856 0.000 0.144
#> GSM148547 1 0.3752 0.834 0.856 0.000 0.144
#> GSM148548 1 0.2796 0.857 0.908 0.000 0.092
#> GSM148549 1 0.3340 0.852 0.880 0.000 0.120
#> GSM148550 1 0.2959 0.852 0.900 0.000 0.100
#> GSM148551 1 0.2711 0.865 0.912 0.000 0.088
#> GSM148552 1 0.3686 0.838 0.860 0.000 0.140
#> GSM148553 1 0.3686 0.837 0.860 0.000 0.140
#> GSM148554 1 0.2711 0.859 0.912 0.000 0.088
#> GSM148555 1 0.3038 0.854 0.896 0.000 0.104
#> GSM148556 1 0.3038 0.851 0.896 0.000 0.104
#> GSM148557 1 0.4346 0.837 0.816 0.000 0.184
#> GSM148558 1 0.4842 0.814 0.776 0.000 0.224
#> GSM148559 1 0.4399 0.828 0.812 0.000 0.188
#> GSM148560 1 0.4399 0.829 0.812 0.000 0.188
#> GSM148561 1 0.3551 0.847 0.868 0.000 0.132
#> GSM148562 1 0.2356 0.865 0.928 0.000 0.072
#> GSM148563 1 0.3192 0.858 0.888 0.000 0.112
#> GSM148564 1 0.4121 0.849 0.832 0.000 0.168
#> GSM148565 1 0.5016 0.800 0.760 0.000 0.240
#> GSM148566 1 0.4452 0.829 0.808 0.000 0.192
#> GSM148567 1 0.2796 0.857 0.908 0.000 0.092
#> GSM148568 1 0.2711 0.864 0.912 0.000 0.088
#> GSM148569 1 0.4178 0.844 0.828 0.000 0.172
#> GSM148570 1 0.4796 0.813 0.780 0.000 0.220
#> GSM148571 1 0.4931 0.804 0.768 0.000 0.232
#> GSM148572 1 0.5058 0.801 0.756 0.000 0.244
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM148516 3 0.6761 0.7628 0.112 0.108 0.700 0.080
#> GSM148517 1 0.5963 0.4658 0.688 0.000 0.196 0.116
#> GSM148518 2 0.0712 0.9769 0.004 0.984 0.004 0.008
#> GSM148519 2 0.0672 0.9756 0.000 0.984 0.008 0.008
#> GSM148520 2 0.0707 0.9755 0.000 0.980 0.020 0.000
#> GSM148521 2 0.0817 0.9756 0.000 0.976 0.024 0.000
#> GSM148522 2 0.0712 0.9755 0.004 0.984 0.008 0.004
#> GSM148523 2 0.0188 0.9753 0.000 0.996 0.004 0.000
#> GSM148524 2 0.0188 0.9753 0.000 0.996 0.000 0.004
#> GSM148525 2 0.0804 0.9736 0.000 0.980 0.012 0.008
#> GSM148526 2 0.2408 0.9288 0.016 0.920 0.060 0.004
#> GSM148527 2 0.0844 0.9754 0.004 0.980 0.012 0.004
#> GSM148528 2 0.1339 0.9704 0.004 0.964 0.024 0.008
#> GSM148529 2 0.1114 0.9747 0.008 0.972 0.016 0.004
#> GSM148530 2 0.0657 0.9763 0.000 0.984 0.012 0.004
#> GSM148531 2 0.0469 0.9764 0.000 0.988 0.012 0.000
#> GSM148532 2 0.1305 0.9676 0.000 0.960 0.036 0.004
#> GSM148533 2 0.0188 0.9750 0.000 0.996 0.000 0.004
#> GSM148534 2 0.0672 0.9764 0.000 0.984 0.008 0.008
#> GSM148535 2 0.0657 0.9744 0.000 0.984 0.012 0.004
#> GSM148536 2 0.1209 0.9696 0.004 0.964 0.032 0.000
#> GSM148537 2 0.2438 0.9319 0.012 0.924 0.048 0.016
#> GSM148538 2 0.1471 0.9678 0.012 0.960 0.024 0.004
#> GSM148539 3 0.6149 0.5392 0.036 0.404 0.552 0.008
#> GSM148540 3 0.6441 0.8125 0.096 0.132 0.716 0.056
#> GSM148541 3 0.6115 0.8312 0.052 0.148 0.732 0.068
#> GSM148542 3 0.5870 0.8284 0.036 0.168 0.736 0.060
#> GSM148543 3 0.6063 0.7882 0.044 0.256 0.676 0.024
#> GSM148544 3 0.6534 0.7842 0.104 0.104 0.716 0.076
#> GSM148545 1 0.5820 0.4742 0.700 0.000 0.192 0.108
#> GSM148546 1 0.3876 0.5956 0.836 0.000 0.124 0.040
#> GSM148547 1 0.3612 0.6094 0.856 0.000 0.100 0.044
#> GSM148548 1 0.4685 0.6013 0.784 0.000 0.060 0.156
#> GSM148549 1 0.5977 0.5132 0.680 0.000 0.104 0.216
#> GSM148550 1 0.5590 0.4985 0.692 0.000 0.064 0.244
#> GSM148551 1 0.6329 0.4320 0.616 0.000 0.092 0.292
#> GSM148552 1 0.3542 0.6065 0.864 0.000 0.060 0.076
#> GSM148553 1 0.4428 0.6073 0.808 0.000 0.124 0.068
#> GSM148554 1 0.3583 0.5765 0.816 0.000 0.004 0.180
#> GSM148555 1 0.4988 0.5355 0.728 0.000 0.036 0.236
#> GSM148556 1 0.4904 0.5519 0.744 0.000 0.040 0.216
#> GSM148557 1 0.5472 0.0481 0.544 0.000 0.016 0.440
#> GSM148558 4 0.4908 0.5250 0.292 0.000 0.016 0.692
#> GSM148559 1 0.5483 0.5385 0.736 0.000 0.136 0.128
#> GSM148560 1 0.5058 0.5782 0.768 0.000 0.128 0.104
#> GSM148561 1 0.6766 0.3785 0.596 0.004 0.116 0.284
#> GSM148562 1 0.5543 0.1449 0.556 0.000 0.020 0.424
#> GSM148563 4 0.6080 0.0480 0.468 0.000 0.044 0.488
#> GSM148564 4 0.4972 0.1438 0.456 0.000 0.000 0.544
#> GSM148565 4 0.2730 0.6604 0.088 0.000 0.016 0.896
#> GSM148566 1 0.5280 0.5506 0.752 0.000 0.124 0.124
#> GSM148567 1 0.6627 0.0750 0.516 0.004 0.072 0.408
#> GSM148568 1 0.5271 0.4297 0.640 0.000 0.020 0.340
#> GSM148569 4 0.5398 0.2612 0.404 0.000 0.016 0.580
#> GSM148570 4 0.3812 0.6595 0.140 0.000 0.028 0.832
#> GSM148571 4 0.2987 0.6639 0.104 0.000 0.016 0.880
#> GSM148572 4 0.2730 0.6541 0.088 0.000 0.016 0.896
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM148516 3 0.576 0.7415 0.116 0.092 0.720 0.012 NA
#> GSM148517 1 0.504 0.3077 0.544 0.000 0.008 0.020 NA
#> GSM148518 2 0.190 0.9408 0.000 0.932 0.024 0.004 NA
#> GSM148519 2 0.182 0.9412 0.000 0.932 0.024 0.000 NA
#> GSM148520 2 0.220 0.9307 0.004 0.916 0.024 0.000 NA
#> GSM148521 2 0.215 0.9380 0.000 0.916 0.048 0.000 NA
#> GSM148522 2 0.140 0.9435 0.000 0.952 0.028 0.000 NA
#> GSM148523 2 0.102 0.9445 0.000 0.968 0.016 0.000 NA
#> GSM148524 2 0.120 0.9434 0.000 0.956 0.004 0.000 NA
#> GSM148525 2 0.136 0.9403 0.000 0.952 0.036 0.000 NA
#> GSM148526 2 0.284 0.9064 0.008 0.876 0.096 0.000 NA
#> GSM148527 2 0.199 0.9317 0.000 0.924 0.044 0.000 NA
#> GSM148528 2 0.223 0.9334 0.000 0.916 0.044 0.004 NA
#> GSM148529 2 0.239 0.9274 0.000 0.900 0.028 0.000 NA
#> GSM148530 2 0.155 0.9412 0.000 0.944 0.016 0.000 NA
#> GSM148531 2 0.160 0.9362 0.000 0.940 0.012 0.000 NA
#> GSM148532 2 0.141 0.9419 0.004 0.952 0.036 0.000 NA
#> GSM148533 2 0.117 0.9400 0.000 0.960 0.008 0.000 NA
#> GSM148534 2 0.163 0.9410 0.000 0.944 0.016 0.004 NA
#> GSM148535 2 0.122 0.9429 0.000 0.960 0.020 0.000 NA
#> GSM148536 2 0.240 0.9306 0.004 0.912 0.040 0.004 NA
#> GSM148537 2 0.315 0.9018 0.004 0.864 0.100 0.008 NA
#> GSM148538 2 0.230 0.9253 0.000 0.904 0.024 0.000 NA
#> GSM148539 3 0.472 0.5863 0.016 0.340 0.636 0.000 NA
#> GSM148540 3 0.354 0.8070 0.056 0.080 0.848 0.016 NA
#> GSM148541 3 0.335 0.8144 0.020 0.080 0.864 0.004 NA
#> GSM148542 3 0.279 0.8169 0.004 0.088 0.884 0.008 NA
#> GSM148543 3 0.335 0.7913 0.004 0.192 0.800 0.004 NA
#> GSM148544 3 0.434 0.7898 0.072 0.088 0.808 0.028 NA
#> GSM148545 1 0.503 0.3115 0.548 0.000 0.008 0.020 NA
#> GSM148546 1 0.201 0.5078 0.924 0.000 0.016 0.004 NA
#> GSM148547 1 0.181 0.5167 0.936 0.000 0.020 0.004 NA
#> GSM148548 1 0.542 0.4979 0.668 0.000 0.032 0.048 NA
#> GSM148549 1 0.744 0.3754 0.460 0.000 0.120 0.092 NA
#> GSM148550 1 0.755 0.3102 0.448 0.000 0.068 0.184 NA
#> GSM148551 1 0.795 0.2771 0.432 0.000 0.116 0.192 NA
#> GSM148552 1 0.474 0.5158 0.736 0.000 0.020 0.044 NA
#> GSM148553 1 0.319 0.5263 0.872 0.000 0.040 0.024 NA
#> GSM148554 1 0.569 0.4711 0.628 0.000 0.008 0.104 NA
#> GSM148555 1 0.638 0.3608 0.476 0.000 0.004 0.148 NA
#> GSM148556 1 0.681 0.3368 0.476 0.000 0.024 0.152 NA
#> GSM148557 4 0.715 0.0709 0.300 0.000 0.016 0.400 NA
#> GSM148558 4 0.561 0.4848 0.156 0.000 0.008 0.664 NA
#> GSM148559 1 0.586 0.3660 0.512 0.000 0.048 0.024 NA
#> GSM148560 1 0.430 0.4904 0.804 0.000 0.084 0.028 NA
#> GSM148561 1 0.695 0.3732 0.600 0.004 0.104 0.180 NA
#> GSM148562 1 0.705 -0.0199 0.408 0.000 0.024 0.384 NA
#> GSM148563 4 0.650 0.0493 0.412 0.000 0.028 0.464 NA
#> GSM148564 4 0.701 0.1056 0.328 0.000 0.012 0.416 NA
#> GSM148565 4 0.130 0.5796 0.008 0.000 0.012 0.960 NA
#> GSM148566 1 0.471 0.4850 0.780 0.000 0.084 0.044 NA
#> GSM148567 1 0.791 0.0147 0.380 0.000 0.120 0.352 NA
#> GSM148568 1 0.734 0.1299 0.420 0.000 0.032 0.300 NA
#> GSM148569 4 0.675 0.2520 0.268 0.000 0.012 0.500 NA
#> GSM148570 4 0.274 0.5861 0.068 0.000 0.016 0.892 NA
#> GSM148571 4 0.149 0.5871 0.040 0.000 0.008 0.948 NA
#> GSM148572 4 0.120 0.5774 0.008 0.000 0.012 0.964 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM148516 3 0.660 0.642 0.060 0.096 0.576 0.004 0.232 0.032
#> GSM148517 6 0.143 0.538 0.048 0.000 0.000 0.012 0.000 0.940
#> GSM148518 2 0.133 0.906 0.000 0.944 0.008 0.000 0.048 0.000
#> GSM148519 2 0.166 0.906 0.000 0.928 0.016 0.000 0.056 0.000
#> GSM148520 2 0.313 0.872 0.000 0.820 0.024 0.004 0.152 0.000
#> GSM148521 2 0.292 0.897 0.000 0.848 0.052 0.000 0.100 0.000
#> GSM148522 2 0.181 0.908 0.000 0.920 0.020 0.000 0.060 0.000
#> GSM148523 2 0.143 0.911 0.000 0.940 0.012 0.000 0.048 0.000
#> GSM148524 2 0.206 0.903 0.000 0.900 0.008 0.004 0.088 0.000
#> GSM148525 2 0.118 0.909 0.000 0.956 0.020 0.000 0.024 0.000
#> GSM148526 2 0.336 0.858 0.000 0.828 0.108 0.004 0.056 0.004
#> GSM148527 2 0.253 0.877 0.000 0.884 0.056 0.000 0.056 0.004
#> GSM148528 2 0.238 0.884 0.000 0.888 0.064 0.000 0.048 0.000
#> GSM148529 2 0.360 0.857 0.000 0.788 0.032 0.004 0.172 0.004
#> GSM148530 2 0.240 0.898 0.000 0.872 0.016 0.000 0.112 0.000
#> GSM148531 2 0.257 0.886 0.000 0.856 0.008 0.004 0.132 0.000
#> GSM148532 2 0.214 0.902 0.004 0.908 0.048 0.000 0.040 0.000
#> GSM148533 2 0.115 0.901 0.000 0.956 0.004 0.000 0.036 0.004
#> GSM148534 2 0.191 0.905 0.000 0.920 0.024 0.004 0.052 0.000
#> GSM148535 2 0.139 0.906 0.000 0.944 0.016 0.000 0.040 0.000
#> GSM148536 2 0.317 0.888 0.004 0.836 0.036 0.004 0.120 0.000
#> GSM148537 2 0.362 0.850 0.008 0.804 0.124 0.000 0.064 0.000
#> GSM148538 2 0.338 0.857 0.000 0.792 0.016 0.004 0.184 0.004
#> GSM148539 3 0.464 0.597 0.008 0.268 0.664 0.000 0.060 0.000
#> GSM148540 3 0.274 0.743 0.028 0.032 0.888 0.008 0.044 0.000
#> GSM148541 3 0.428 0.751 0.020 0.052 0.764 0.000 0.156 0.008
#> GSM148542 3 0.356 0.763 0.008 0.056 0.816 0.004 0.116 0.000
#> GSM148543 3 0.326 0.741 0.012 0.144 0.820 0.000 0.024 0.000
#> GSM148544 3 0.432 0.734 0.048 0.056 0.796 0.024 0.076 0.000
#> GSM148545 6 0.167 0.538 0.060 0.000 0.000 0.008 0.004 0.928
#> GSM148546 6 0.662 -0.597 0.292 0.000 0.020 0.004 0.292 0.392
#> GSM148547 1 0.641 -0.618 0.364 0.000 0.008 0.004 0.264 0.360
#> GSM148548 1 0.457 0.206 0.716 0.000 0.000 0.008 0.112 0.164
#> GSM148549 1 0.558 0.411 0.696 0.000 0.092 0.048 0.128 0.036
#> GSM148550 1 0.494 0.471 0.756 0.000 0.040 0.084 0.064 0.056
#> GSM148551 1 0.675 0.368 0.584 0.000 0.096 0.104 0.176 0.040
#> GSM148552 1 0.606 -0.160 0.468 0.000 0.008 0.012 0.136 0.376
#> GSM148553 1 0.665 -0.453 0.388 0.000 0.032 0.000 0.256 0.324
#> GSM148554 1 0.479 0.310 0.684 0.000 0.000 0.044 0.036 0.236
#> GSM148555 1 0.385 0.450 0.804 0.000 0.000 0.072 0.028 0.096
#> GSM148556 1 0.333 0.458 0.852 0.000 0.004 0.048 0.048 0.048
#> GSM148557 1 0.441 0.355 0.692 0.000 0.000 0.256 0.016 0.036
#> GSM148558 4 0.451 0.358 0.372 0.000 0.000 0.596 0.020 0.012
#> GSM148559 6 0.513 0.377 0.228 0.000 0.016 0.016 0.068 0.672
#> GSM148560 5 0.704 0.874 0.272 0.000 0.044 0.008 0.364 0.312
#> GSM148561 1 0.786 -0.368 0.388 0.000 0.052 0.124 0.304 0.132
#> GSM148562 1 0.618 0.370 0.568 0.000 0.012 0.244 0.144 0.032
#> GSM148563 1 0.667 0.168 0.444 0.000 0.020 0.344 0.168 0.024
#> GSM148564 1 0.505 0.276 0.592 0.000 0.000 0.328 0.072 0.008
#> GSM148565 4 0.079 0.796 0.032 0.000 0.000 0.968 0.000 0.000
#> GSM148566 5 0.711 0.881 0.296 0.000 0.044 0.012 0.372 0.276
#> GSM148567 1 0.734 0.342 0.456 0.000 0.084 0.248 0.188 0.024
#> GSM148568 1 0.480 0.473 0.724 0.000 0.008 0.176 0.052 0.040
#> GSM148569 1 0.538 0.177 0.544 0.000 0.004 0.368 0.072 0.012
#> GSM148570 4 0.394 0.721 0.120 0.000 0.016 0.800 0.052 0.012
#> GSM148571 4 0.229 0.795 0.072 0.000 0.004 0.900 0.016 0.008
#> GSM148572 4 0.120 0.791 0.040 0.000 0.000 0.952 0.008 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) dose(p) time(p) k
#> CV:mclust 51 8.42e-12 0.327825 0.996 2
#> CV:mclust 57 9.44e-12 0.000666 0.995 3
#> CV:mclust 45 4.70e-09 0.000230 0.434 4
#> CV:mclust 36 4.56e-07 0.000223 0.712 5
#> CV:mclust 36 1.52e-07 0.000542 0.658 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 21163 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.982 0.992 0.5085 0.491 0.491
#> 3 3 0.618 0.857 0.829 0.2108 1.000 1.000
#> 4 4 0.539 0.519 0.732 0.1376 0.827 0.648
#> 5 5 0.488 0.554 0.675 0.0759 0.848 0.590
#> 6 6 0.521 0.493 0.651 0.0498 0.927 0.745
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
#> GSM148516 2 0.1414 0.967 0.020 0.980
#> GSM148517 1 0.0000 0.999 1.000 0.000
#> GSM148518 2 0.0000 0.983 0.000 1.000
#> GSM148519 2 0.0000 0.983 0.000 1.000
#> GSM148520 2 0.0000 0.983 0.000 1.000
#> GSM148521 2 0.0000 0.983 0.000 1.000
#> GSM148522 2 0.0000 0.983 0.000 1.000
#> GSM148523 2 0.0000 0.983 0.000 1.000
#> GSM148524 2 0.0000 0.983 0.000 1.000
#> GSM148525 2 0.0000 0.983 0.000 1.000
#> GSM148526 2 0.0000 0.983 0.000 1.000
#> GSM148527 2 0.0000 0.983 0.000 1.000
#> GSM148528 2 0.0000 0.983 0.000 1.000
#> GSM148529 2 0.0000 0.983 0.000 1.000
#> GSM148530 2 0.0000 0.983 0.000 1.000
#> GSM148531 2 0.0000 0.983 0.000 1.000
#> GSM148532 2 0.0000 0.983 0.000 1.000
#> GSM148533 2 0.0000 0.983 0.000 1.000
#> GSM148534 2 0.0000 0.983 0.000 1.000
#> GSM148535 2 0.0000 0.983 0.000 1.000
#> GSM148536 2 0.0000 0.983 0.000 1.000
#> GSM148537 2 0.0000 0.983 0.000 1.000
#> GSM148538 2 0.0000 0.983 0.000 1.000
#> GSM148539 2 0.0000 0.983 0.000 1.000
#> GSM148540 2 0.7139 0.767 0.196 0.804
#> GSM148541 2 0.0000 0.983 0.000 1.000
#> GSM148542 2 0.1184 0.970 0.016 0.984
#> GSM148543 2 0.0000 0.983 0.000 1.000
#> GSM148544 2 0.7528 0.738 0.216 0.784
#> GSM148545 1 0.0000 0.999 1.000 0.000
#> GSM148546 1 0.0000 0.999 1.000 0.000
#> GSM148547 1 0.0000 0.999 1.000 0.000
#> GSM148548 1 0.0376 0.995 0.996 0.004
#> GSM148549 1 0.0376 0.995 0.996 0.004
#> GSM148550 1 0.0000 0.999 1.000 0.000
#> GSM148551 1 0.0938 0.988 0.988 0.012
#> GSM148552 1 0.0000 0.999 1.000 0.000
#> GSM148553 1 0.1184 0.984 0.984 0.016
#> GSM148554 1 0.0000 0.999 1.000 0.000
#> GSM148555 1 0.0000 0.999 1.000 0.000
#> GSM148556 1 0.0000 0.999 1.000 0.000
#> GSM148557 1 0.0000 0.999 1.000 0.000
#> GSM148558 1 0.0000 0.999 1.000 0.000
#> GSM148559 1 0.0000 0.999 1.000 0.000
#> GSM148560 1 0.0000 0.999 1.000 0.000
#> GSM148561 1 0.0000 0.999 1.000 0.000
#> GSM148562 1 0.0000 0.999 1.000 0.000
#> GSM148563 1 0.0000 0.999 1.000 0.000
#> GSM148564 1 0.0000 0.999 1.000 0.000
#> GSM148565 1 0.0000 0.999 1.000 0.000
#> GSM148566 1 0.0000 0.999 1.000 0.000
#> GSM148567 1 0.0000 0.999 1.000 0.000
#> GSM148568 1 0.0000 0.999 1.000 0.000
#> GSM148569 1 0.0000 0.999 1.000 0.000
#> GSM148570 1 0.0000 0.999 1.000 0.000
#> GSM148571 1 0.0000 0.999 1.000 0.000
#> GSM148572 1 0.0000 0.999 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM148516 2 0.7366 0.624 0.032 0.524 NA
#> GSM148517 1 0.5529 0.837 0.704 0.000 NA
#> GSM148518 2 0.1411 0.906 0.000 0.964 NA
#> GSM148519 2 0.0892 0.908 0.000 0.980 NA
#> GSM148520 2 0.2796 0.898 0.000 0.908 NA
#> GSM148521 2 0.0747 0.908 0.000 0.984 NA
#> GSM148522 2 0.1031 0.909 0.000 0.976 NA
#> GSM148523 2 0.0747 0.907 0.000 0.984 NA
#> GSM148524 2 0.1529 0.904 0.000 0.960 NA
#> GSM148525 2 0.2537 0.899 0.000 0.920 NA
#> GSM148526 2 0.2959 0.891 0.000 0.900 NA
#> GSM148527 2 0.1031 0.908 0.000 0.976 NA
#> GSM148528 2 0.1529 0.909 0.000 0.960 NA
#> GSM148529 2 0.2356 0.894 0.000 0.928 NA
#> GSM148530 2 0.1163 0.909 0.000 0.972 NA
#> GSM148531 2 0.1753 0.906 0.000 0.952 NA
#> GSM148532 2 0.2959 0.898 0.000 0.900 NA
#> GSM148533 2 0.1411 0.907 0.000 0.964 NA
#> GSM148534 2 0.1753 0.908 0.000 0.952 NA
#> GSM148535 2 0.0747 0.907 0.000 0.984 NA
#> GSM148536 2 0.1411 0.908 0.000 0.964 NA
#> GSM148537 2 0.1647 0.903 0.004 0.960 NA
#> GSM148538 2 0.2711 0.891 0.000 0.912 NA
#> GSM148539 2 0.4963 0.847 0.008 0.792 NA
#> GSM148540 2 0.8700 0.597 0.120 0.536 NA
#> GSM148541 2 0.6745 0.667 0.012 0.560 NA
#> GSM148542 2 0.6427 0.734 0.012 0.640 NA
#> GSM148543 2 0.5843 0.809 0.016 0.732 NA
#> GSM148544 2 0.8799 0.610 0.196 0.584 NA
#> GSM148545 1 0.5591 0.839 0.696 0.000 NA
#> GSM148546 1 0.5650 0.849 0.688 0.000 NA
#> GSM148547 1 0.5690 0.862 0.708 0.004 NA
#> GSM148548 1 0.5325 0.873 0.748 0.004 NA
#> GSM148549 1 0.4047 0.886 0.848 0.004 NA
#> GSM148550 1 0.3482 0.887 0.872 0.000 NA
#> GSM148551 1 0.4555 0.879 0.800 0.000 NA
#> GSM148552 1 0.6102 0.828 0.672 0.008 NA
#> GSM148553 1 0.5926 0.832 0.644 0.000 NA
#> GSM148554 1 0.4645 0.877 0.816 0.008 NA
#> GSM148555 1 0.3340 0.888 0.880 0.000 NA
#> GSM148556 1 0.3412 0.887 0.876 0.000 NA
#> GSM148557 1 0.1964 0.884 0.944 0.000 NA
#> GSM148558 1 0.3551 0.879 0.868 0.000 NA
#> GSM148559 1 0.6111 0.797 0.604 0.000 NA
#> GSM148560 1 0.5058 0.869 0.756 0.000 NA
#> GSM148561 1 0.6062 0.772 0.616 0.000 NA
#> GSM148562 1 0.4291 0.875 0.820 0.000 NA
#> GSM148563 1 0.4452 0.876 0.808 0.000 NA
#> GSM148564 1 0.2959 0.878 0.900 0.000 NA
#> GSM148565 1 0.3340 0.869 0.880 0.000 NA
#> GSM148566 1 0.5650 0.850 0.688 0.000 NA
#> GSM148567 1 0.4346 0.865 0.816 0.000 NA
#> GSM148568 1 0.2959 0.882 0.900 0.000 NA
#> GSM148569 1 0.3267 0.872 0.884 0.000 NA
#> GSM148570 1 0.3412 0.878 0.876 0.000 NA
#> GSM148571 1 0.3340 0.871 0.880 0.000 NA
#> GSM148572 1 0.3267 0.869 0.884 0.000 NA
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM148516 3 0.6917 0.7533 0.144 0.236 0.612 0.008
#> GSM148517 1 0.5754 0.5106 0.636 0.000 0.048 0.316
#> GSM148518 2 0.1888 0.8302 0.016 0.940 0.044 0.000
#> GSM148519 2 0.0657 0.8322 0.004 0.984 0.012 0.000
#> GSM148520 2 0.3687 0.7763 0.080 0.856 0.064 0.000
#> GSM148521 2 0.2060 0.8330 0.016 0.932 0.052 0.000
#> GSM148522 2 0.1706 0.8368 0.016 0.948 0.036 0.000
#> GSM148523 2 0.1510 0.8351 0.016 0.956 0.028 0.000
#> GSM148524 2 0.1610 0.8303 0.016 0.952 0.032 0.000
#> GSM148525 2 0.3638 0.7487 0.032 0.848 0.120 0.000
#> GSM148526 2 0.4095 0.6828 0.024 0.804 0.172 0.000
#> GSM148527 2 0.1798 0.8349 0.016 0.944 0.040 0.000
#> GSM148528 2 0.1677 0.8308 0.012 0.948 0.040 0.000
#> GSM148529 2 0.2124 0.8230 0.040 0.932 0.028 0.000
#> GSM148530 2 0.1733 0.8365 0.024 0.948 0.028 0.000
#> GSM148531 2 0.1488 0.8366 0.032 0.956 0.012 0.000
#> GSM148532 2 0.4416 0.7063 0.052 0.812 0.132 0.004
#> GSM148533 2 0.1706 0.8322 0.016 0.948 0.036 0.000
#> GSM148534 2 0.2300 0.8255 0.028 0.924 0.048 0.000
#> GSM148535 2 0.0804 0.8349 0.008 0.980 0.012 0.000
#> GSM148536 2 0.1510 0.8365 0.016 0.956 0.028 0.000
#> GSM148537 2 0.2643 0.8169 0.016 0.916 0.052 0.016
#> GSM148538 2 0.3198 0.7856 0.080 0.880 0.040 0.000
#> GSM148539 2 0.5955 0.1676 0.056 0.616 0.328 0.000
#> GSM148540 3 0.7451 0.7042 0.068 0.316 0.560 0.056
#> GSM148541 3 0.4789 0.7878 0.020 0.236 0.740 0.004
#> GSM148542 3 0.6602 0.7094 0.052 0.348 0.580 0.020
#> GSM148543 2 0.6314 -0.4224 0.048 0.484 0.464 0.004
#> GSM148544 2 0.8592 -0.4295 0.052 0.448 0.312 0.188
#> GSM148545 1 0.5947 0.5262 0.628 0.000 0.060 0.312
#> GSM148546 1 0.7694 0.4629 0.448 0.000 0.244 0.308
#> GSM148547 1 0.7332 0.3896 0.468 0.000 0.160 0.372
#> GSM148548 4 0.7342 -0.2729 0.412 0.000 0.156 0.432
#> GSM148549 4 0.6967 0.2657 0.244 0.000 0.176 0.580
#> GSM148550 4 0.6367 0.1475 0.336 0.000 0.080 0.584
#> GSM148551 4 0.6513 0.3672 0.180 0.000 0.180 0.640
#> GSM148552 1 0.6291 0.4823 0.600 0.012 0.048 0.340
#> GSM148553 1 0.7408 0.4912 0.512 0.000 0.276 0.212
#> GSM148554 4 0.6008 -0.1474 0.464 0.000 0.040 0.496
#> GSM148555 4 0.5884 0.2213 0.328 0.000 0.052 0.620
#> GSM148556 4 0.6069 0.0900 0.356 0.000 0.056 0.588
#> GSM148557 4 0.4262 0.4307 0.236 0.000 0.008 0.756
#> GSM148558 4 0.5256 0.4016 0.260 0.000 0.040 0.700
#> GSM148559 1 0.6653 0.4905 0.636 0.016 0.092 0.256
#> GSM148560 1 0.7775 0.3370 0.384 0.000 0.240 0.376
#> GSM148561 4 0.7852 -0.0879 0.268 0.000 0.360 0.372
#> GSM148562 4 0.5719 0.4207 0.132 0.000 0.152 0.716
#> GSM148563 4 0.6373 0.3469 0.148 0.000 0.200 0.652
#> GSM148564 4 0.4452 0.5009 0.156 0.000 0.048 0.796
#> GSM148565 4 0.3099 0.5187 0.104 0.000 0.020 0.876
#> GSM148566 1 0.7832 0.3997 0.392 0.000 0.264 0.344
#> GSM148567 4 0.5913 0.4124 0.124 0.000 0.180 0.696
#> GSM148568 4 0.4638 0.4898 0.180 0.000 0.044 0.776
#> GSM148569 4 0.3286 0.5387 0.080 0.000 0.044 0.876
#> GSM148570 4 0.3691 0.5303 0.068 0.000 0.076 0.856
#> GSM148571 4 0.2411 0.5375 0.040 0.000 0.040 0.920
#> GSM148572 4 0.3421 0.5174 0.088 0.000 0.044 0.868
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM148516 3 0.666 0.49224 0.060 0.104 0.600 0.004 NA
#> GSM148517 1 0.639 0.39626 0.496 0.000 0.020 0.104 NA
#> GSM148518 2 0.304 0.82643 0.000 0.864 0.100 0.004 NA
#> GSM148519 2 0.198 0.85548 0.004 0.928 0.024 0.000 NA
#> GSM148520 2 0.486 0.73788 0.016 0.756 0.064 0.008 NA
#> GSM148521 2 0.254 0.85383 0.004 0.900 0.048 0.000 NA
#> GSM148522 2 0.313 0.83876 0.008 0.868 0.092 0.004 NA
#> GSM148523 2 0.262 0.85081 0.000 0.888 0.076 0.000 NA
#> GSM148524 2 0.223 0.85402 0.004 0.916 0.032 0.000 NA
#> GSM148525 2 0.436 0.63732 0.000 0.736 0.224 0.004 NA
#> GSM148526 2 0.488 0.70370 0.044 0.764 0.124 0.000 NA
#> GSM148527 2 0.214 0.85686 0.004 0.924 0.044 0.004 NA
#> GSM148528 2 0.321 0.84130 0.024 0.872 0.056 0.000 NA
#> GSM148529 2 0.287 0.83579 0.020 0.884 0.020 0.000 NA
#> GSM148530 2 0.254 0.85563 0.004 0.900 0.044 0.000 NA
#> GSM148531 2 0.275 0.85223 0.004 0.888 0.052 0.000 NA
#> GSM148532 2 0.533 0.51901 0.012 0.672 0.240 0.000 NA
#> GSM148533 2 0.197 0.84844 0.000 0.924 0.060 0.004 NA
#> GSM148534 2 0.348 0.83829 0.004 0.848 0.084 0.004 NA
#> GSM148535 2 0.212 0.85628 0.008 0.924 0.036 0.000 NA
#> GSM148536 2 0.261 0.85211 0.004 0.896 0.056 0.000 NA
#> GSM148537 2 0.363 0.82771 0.024 0.860 0.052 0.016 NA
#> GSM148538 2 0.408 0.79737 0.048 0.816 0.032 0.000 NA
#> GSM148539 3 0.681 0.40233 0.064 0.412 0.464 0.012 NA
#> GSM148540 3 0.718 0.64798 0.072 0.204 0.604 0.064 NA
#> GSM148541 3 0.582 0.59187 0.056 0.132 0.716 0.016 NA
#> GSM148542 3 0.634 0.66655 0.012 0.240 0.628 0.076 NA
#> GSM148543 3 0.680 0.56158 0.032 0.348 0.528 0.032 NA
#> GSM148544 3 0.841 0.48276 0.040 0.332 0.348 0.228 NA
#> GSM148545 1 0.621 0.41019 0.512 0.000 0.028 0.072 NA
#> GSM148546 1 0.577 0.45451 0.700 0.000 0.140 0.072 NA
#> GSM148547 1 0.575 0.42867 0.704 0.000 0.092 0.128 NA
#> GSM148548 1 0.605 0.40798 0.668 0.004 0.040 0.168 NA
#> GSM148549 1 0.747 0.04736 0.412 0.000 0.180 0.352 NA
#> GSM148550 1 0.645 0.20732 0.552 0.000 0.056 0.324 NA
#> GSM148551 1 0.742 -0.00532 0.464 0.004 0.104 0.340 NA
#> GSM148552 1 0.596 0.43908 0.620 0.012 0.012 0.080 NA
#> GSM148553 1 0.607 0.45148 0.672 0.000 0.144 0.064 NA
#> GSM148554 1 0.544 0.34028 0.660 0.000 0.008 0.240 NA
#> GSM148555 1 0.649 0.19300 0.516 0.000 0.016 0.332 NA
#> GSM148556 1 0.565 0.20950 0.584 0.000 0.012 0.340 NA
#> GSM148557 4 0.587 0.18172 0.416 0.000 0.028 0.512 NA
#> GSM148558 4 0.599 0.35667 0.300 0.000 0.020 0.592 NA
#> GSM148559 1 0.693 0.38182 0.468 0.016 0.036 0.084 NA
#> GSM148560 1 0.795 0.30704 0.456 0.000 0.148 0.172 NA
#> GSM148561 1 0.873 0.11240 0.324 0.008 0.220 0.200 NA
#> GSM148562 4 0.726 0.31394 0.332 0.000 0.104 0.476 NA
#> GSM148563 4 0.708 0.20711 0.348 0.000 0.116 0.476 NA
#> GSM148564 4 0.521 0.57714 0.128 0.004 0.028 0.740 NA
#> GSM148565 4 0.252 0.62054 0.068 0.000 0.008 0.900 NA
#> GSM148566 1 0.787 0.34023 0.460 0.000 0.160 0.136 NA
#> GSM148567 4 0.617 0.51795 0.172 0.000 0.092 0.660 NA
#> GSM148568 4 0.628 0.45148 0.252 0.004 0.016 0.596 NA
#> GSM148569 4 0.407 0.62156 0.128 0.000 0.036 0.808 NA
#> GSM148570 4 0.493 0.59583 0.192 0.000 0.044 0.732 NA
#> GSM148571 4 0.346 0.62277 0.120 0.000 0.024 0.840 NA
#> GSM148572 4 0.306 0.59912 0.052 0.000 0.024 0.880 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM148516 3 0.762 0.2968 0.076 0.084 0.412 0.000 0.328 0.100
#> GSM148517 6 0.594 0.4738 0.308 0.000 0.032 0.056 0.032 0.572
#> GSM148518 2 0.382 0.7541 0.000 0.772 0.180 0.000 0.032 0.016
#> GSM148519 2 0.200 0.8123 0.000 0.920 0.040 0.000 0.028 0.012
#> GSM148520 2 0.525 0.7045 0.000 0.716 0.072 0.012 0.112 0.088
#> GSM148521 2 0.295 0.8133 0.024 0.872 0.060 0.000 0.040 0.004
#> GSM148522 2 0.360 0.7932 0.004 0.808 0.140 0.000 0.032 0.016
#> GSM148523 2 0.334 0.8056 0.008 0.840 0.104 0.000 0.028 0.020
#> GSM148524 2 0.336 0.8033 0.004 0.852 0.036 0.004 0.068 0.036
#> GSM148525 2 0.528 0.6237 0.000 0.656 0.220 0.000 0.084 0.040
#> GSM148526 2 0.606 0.6380 0.072 0.664 0.140 0.004 0.084 0.036
#> GSM148527 2 0.302 0.8117 0.012 0.872 0.052 0.000 0.044 0.020
#> GSM148528 2 0.337 0.7981 0.020 0.852 0.056 0.000 0.056 0.016
#> GSM148529 2 0.376 0.7759 0.012 0.820 0.016 0.000 0.076 0.076
#> GSM148530 2 0.369 0.8023 0.004 0.820 0.096 0.000 0.056 0.024
#> GSM148531 2 0.406 0.8018 0.008 0.796 0.112 0.000 0.056 0.028
#> GSM148532 2 0.637 0.3941 0.004 0.532 0.308 0.008 0.060 0.088
#> GSM148533 2 0.336 0.7937 0.000 0.820 0.136 0.000 0.024 0.020
#> GSM148534 2 0.344 0.7967 0.000 0.836 0.048 0.000 0.080 0.036
#> GSM148535 2 0.293 0.8049 0.000 0.856 0.104 0.000 0.024 0.016
#> GSM148536 2 0.326 0.8022 0.000 0.848 0.036 0.000 0.076 0.040
#> GSM148537 2 0.456 0.7813 0.032 0.792 0.088 0.024 0.040 0.024
#> GSM148538 2 0.399 0.7678 0.008 0.800 0.040 0.000 0.036 0.116
#> GSM148539 3 0.689 0.4514 0.056 0.296 0.516 0.004 0.076 0.052
#> GSM148540 3 0.688 0.5032 0.064 0.104 0.636 0.064 0.072 0.060
#> GSM148541 3 0.584 0.4845 0.052 0.076 0.660 0.004 0.184 0.024
#> GSM148542 3 0.677 0.4838 0.036 0.128 0.596 0.044 0.176 0.020
#> GSM148543 3 0.599 0.5792 0.048 0.232 0.628 0.008 0.060 0.024
#> GSM148544 3 0.807 0.4311 0.072 0.200 0.412 0.248 0.048 0.020
#> GSM148545 6 0.560 0.4676 0.336 0.000 0.032 0.040 0.020 0.572
#> GSM148546 1 0.641 0.2249 0.628 0.000 0.092 0.044 0.092 0.144
#> GSM148547 1 0.521 0.3123 0.732 0.000 0.048 0.036 0.096 0.088
#> GSM148548 1 0.511 0.3974 0.744 0.000 0.040 0.064 0.072 0.080
#> GSM148549 1 0.685 0.3913 0.544 0.000 0.160 0.204 0.060 0.032
#> GSM148550 1 0.531 0.4453 0.676 0.000 0.044 0.200 0.008 0.072
#> GSM148551 1 0.685 0.3603 0.556 0.000 0.076 0.220 0.104 0.044
#> GSM148552 1 0.641 -0.1951 0.520 0.016 0.032 0.036 0.048 0.348
#> GSM148553 1 0.691 0.0495 0.552 0.000 0.136 0.020 0.132 0.160
#> GSM148554 1 0.593 0.3904 0.636 0.000 0.020 0.152 0.036 0.156
#> GSM148555 1 0.693 0.3453 0.532 0.004 0.016 0.212 0.076 0.160
#> GSM148556 1 0.646 0.3875 0.568 0.000 0.032 0.248 0.048 0.104
#> GSM148557 1 0.549 0.0704 0.468 0.000 0.000 0.440 0.020 0.072
#> GSM148558 4 0.646 0.1813 0.276 0.000 0.044 0.528 0.012 0.140
#> GSM148559 6 0.684 0.3855 0.284 0.016 0.024 0.040 0.112 0.524
#> GSM148560 5 0.810 0.0584 0.316 0.000 0.088 0.068 0.320 0.208
#> GSM148561 5 0.721 0.3015 0.240 0.008 0.068 0.132 0.516 0.036
#> GSM148562 4 0.698 0.2759 0.280 0.000 0.044 0.476 0.172 0.028
#> GSM148563 1 0.815 -0.2097 0.324 0.000 0.072 0.312 0.200 0.092
#> GSM148564 4 0.526 0.5614 0.068 0.000 0.028 0.728 0.092 0.084
#> GSM148565 4 0.254 0.6280 0.044 0.000 0.004 0.896 0.020 0.036
#> GSM148566 6 0.776 -0.3296 0.300 0.000 0.052 0.052 0.296 0.300
#> GSM148567 4 0.672 0.2815 0.204 0.000 0.048 0.508 0.228 0.012
#> GSM148568 4 0.732 0.3536 0.208 0.008 0.016 0.504 0.140 0.124
#> GSM148569 4 0.356 0.6292 0.100 0.000 0.020 0.832 0.032 0.016
#> GSM148570 4 0.544 0.5456 0.180 0.000 0.016 0.680 0.084 0.040
#> GSM148571 4 0.402 0.6107 0.124 0.000 0.012 0.796 0.044 0.024
#> GSM148572 4 0.276 0.6170 0.036 0.000 0.020 0.888 0.012 0.044
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) dose(p) time(p) k
#> CV:NMF 57 2.57e-12 0.999568 1.000 2
#> CV:NMF 57 2.57e-12 0.999568 1.000 3
#> CV:NMF 33 1.61e-08 0.000296 0.335 4
#> CV:NMF 32 1.13e-07 0.000173 0.885 5
#> CV:NMF 28 8.32e-07 0.001205 0.726 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 21163 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.988 0.991 0.5075 0.491 0.491
#> 3 3 0.811 0.869 0.910 0.1303 0.982 0.964
#> 4 4 0.769 0.788 0.856 0.1281 0.883 0.753
#> 5 5 0.700 0.725 0.830 0.0568 0.974 0.926
#> 6 6 0.708 0.662 0.802 0.0408 0.992 0.975
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
#> GSM148516 2 0.0376 0.993 0.004 0.996
#> GSM148517 1 0.1633 0.983 0.976 0.024
#> GSM148518 2 0.0000 0.996 0.000 1.000
#> GSM148519 2 0.0000 0.996 0.000 1.000
#> GSM148520 2 0.0000 0.996 0.000 1.000
#> GSM148521 2 0.0000 0.996 0.000 1.000
#> GSM148522 2 0.0000 0.996 0.000 1.000
#> GSM148523 2 0.0000 0.996 0.000 1.000
#> GSM148524 2 0.0000 0.996 0.000 1.000
#> GSM148525 2 0.0000 0.996 0.000 1.000
#> GSM148526 2 0.0000 0.996 0.000 1.000
#> GSM148527 2 0.0000 0.996 0.000 1.000
#> GSM148528 2 0.0000 0.996 0.000 1.000
#> GSM148529 2 0.0000 0.996 0.000 1.000
#> GSM148530 2 0.0000 0.996 0.000 1.000
#> GSM148531 2 0.0000 0.996 0.000 1.000
#> GSM148532 2 0.0000 0.996 0.000 1.000
#> GSM148533 2 0.0000 0.996 0.000 1.000
#> GSM148534 2 0.0000 0.996 0.000 1.000
#> GSM148535 2 0.0000 0.996 0.000 1.000
#> GSM148536 2 0.0000 0.996 0.000 1.000
#> GSM148537 2 0.0000 0.996 0.000 1.000
#> GSM148538 2 0.0000 0.996 0.000 1.000
#> GSM148539 2 0.0000 0.996 0.000 1.000
#> GSM148540 2 0.0000 0.996 0.000 1.000
#> GSM148541 2 0.0376 0.993 0.004 0.996
#> GSM148542 2 0.3733 0.922 0.072 0.928
#> GSM148543 2 0.1184 0.982 0.016 0.984
#> GSM148544 2 0.0000 0.996 0.000 1.000
#> GSM148545 1 0.1414 0.985 0.980 0.020
#> GSM148546 1 0.1843 0.982 0.972 0.028
#> GSM148547 1 0.1843 0.982 0.972 0.028
#> GSM148548 1 0.0938 0.988 0.988 0.012
#> GSM148549 1 0.0938 0.988 0.988 0.012
#> GSM148550 1 0.0000 0.986 1.000 0.000
#> GSM148551 1 0.0938 0.987 0.988 0.012
#> GSM148552 1 0.1633 0.983 0.976 0.024
#> GSM148553 1 0.1633 0.984 0.976 0.024
#> GSM148554 1 0.0376 0.987 0.996 0.004
#> GSM148555 1 0.0672 0.988 0.992 0.008
#> GSM148556 1 0.0376 0.987 0.996 0.004
#> GSM148557 1 0.0376 0.987 0.996 0.004
#> GSM148558 1 0.0000 0.986 1.000 0.000
#> GSM148559 1 0.2043 0.978 0.968 0.032
#> GSM148560 1 0.1414 0.985 0.980 0.020
#> GSM148561 1 0.3584 0.946 0.932 0.068
#> GSM148562 1 0.2603 0.964 0.956 0.044
#> GSM148563 1 0.0000 0.986 1.000 0.000
#> GSM148564 1 0.1184 0.985 0.984 0.016
#> GSM148565 1 0.0000 0.986 1.000 0.000
#> GSM148566 1 0.0938 0.987 0.988 0.012
#> GSM148567 1 0.0938 0.986 0.988 0.012
#> GSM148568 1 0.0938 0.987 0.988 0.012
#> GSM148569 1 0.0376 0.987 0.996 0.004
#> GSM148570 1 0.0000 0.986 1.000 0.000
#> GSM148571 1 0.0000 0.986 1.000 0.000
#> GSM148572 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
#> GSM148516 2 0.1289 0.971 0.000 0.968 0.032
#> GSM148517 3 0.3619 0.000 0.136 0.000 0.864
#> GSM148518 2 0.0000 0.992 0.000 1.000 0.000
#> GSM148519 2 0.0000 0.992 0.000 1.000 0.000
#> GSM148520 2 0.0424 0.989 0.000 0.992 0.008
#> GSM148521 2 0.0237 0.991 0.000 0.996 0.004
#> GSM148522 2 0.0000 0.992 0.000 1.000 0.000
#> GSM148523 2 0.0000 0.992 0.000 1.000 0.000
#> GSM148524 2 0.0000 0.992 0.000 1.000 0.000
#> GSM148525 2 0.0000 0.992 0.000 1.000 0.000
#> GSM148526 2 0.0000 0.992 0.000 1.000 0.000
#> GSM148527 2 0.0000 0.992 0.000 1.000 0.000
#> GSM148528 2 0.0237 0.991 0.000 0.996 0.004
#> GSM148529 2 0.0000 0.992 0.000 1.000 0.000
#> GSM148530 2 0.0000 0.992 0.000 1.000 0.000
#> GSM148531 2 0.0000 0.992 0.000 1.000 0.000
#> GSM148532 2 0.0000 0.992 0.000 1.000 0.000
#> GSM148533 2 0.0000 0.992 0.000 1.000 0.000
#> GSM148534 2 0.0000 0.992 0.000 1.000 0.000
#> GSM148535 2 0.0000 0.992 0.000 1.000 0.000
#> GSM148536 2 0.0000 0.992 0.000 1.000 0.000
#> GSM148537 2 0.0000 0.992 0.000 1.000 0.000
#> GSM148538 2 0.0000 0.992 0.000 1.000 0.000
#> GSM148539 2 0.0424 0.988 0.000 0.992 0.008
#> GSM148540 2 0.0424 0.989 0.000 0.992 0.008
#> GSM148541 2 0.0592 0.986 0.000 0.988 0.012
#> GSM148542 2 0.3472 0.896 0.040 0.904 0.056
#> GSM148543 2 0.1399 0.971 0.004 0.968 0.028
#> GSM148544 2 0.0592 0.986 0.000 0.988 0.012
#> GSM148545 1 0.6095 0.495 0.608 0.000 0.392
#> GSM148546 1 0.5115 0.758 0.768 0.004 0.228
#> GSM148547 1 0.4978 0.762 0.780 0.004 0.216
#> GSM148548 1 0.2772 0.830 0.916 0.004 0.080
#> GSM148549 1 0.2496 0.831 0.928 0.004 0.068
#> GSM148550 1 0.3116 0.828 0.892 0.000 0.108
#> GSM148551 1 0.3193 0.834 0.896 0.004 0.100
#> GSM148552 1 0.5728 0.694 0.720 0.008 0.272
#> GSM148553 1 0.5536 0.741 0.752 0.012 0.236
#> GSM148554 1 0.3349 0.823 0.888 0.004 0.108
#> GSM148555 1 0.2945 0.833 0.908 0.004 0.088
#> GSM148556 1 0.2860 0.828 0.912 0.004 0.084
#> GSM148557 1 0.3272 0.826 0.892 0.004 0.104
#> GSM148558 1 0.3879 0.815 0.848 0.000 0.152
#> GSM148559 1 0.6228 0.626 0.672 0.012 0.316
#> GSM148560 1 0.5650 0.649 0.688 0.000 0.312
#> GSM148561 1 0.4915 0.803 0.832 0.036 0.132
#> GSM148562 1 0.4209 0.810 0.860 0.020 0.120
#> GSM148563 1 0.3340 0.821 0.880 0.000 0.120
#> GSM148564 1 0.3454 0.823 0.888 0.008 0.104
#> GSM148565 1 0.3619 0.808 0.864 0.000 0.136
#> GSM148566 1 0.4842 0.751 0.776 0.000 0.224
#> GSM148567 1 0.3377 0.823 0.896 0.012 0.092
#> GSM148568 1 0.3043 0.830 0.908 0.008 0.084
#> GSM148569 1 0.3112 0.822 0.900 0.004 0.096
#> GSM148570 1 0.3192 0.813 0.888 0.000 0.112
#> GSM148571 1 0.3686 0.809 0.860 0.000 0.140
#> GSM148572 1 0.3551 0.811 0.868 0.000 0.132
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM148516 2 0.2089 0.943 0.000 0.932 0.048 0.020
#> GSM148517 3 0.3743 0.000 0.160 0.000 0.824 0.016
#> GSM148518 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM148519 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM148520 2 0.0592 0.980 0.000 0.984 0.016 0.000
#> GSM148521 2 0.0188 0.985 0.000 0.996 0.004 0.000
#> GSM148522 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM148523 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM148524 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM148525 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM148526 2 0.0188 0.985 0.000 0.996 0.000 0.004
#> GSM148527 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM148528 2 0.0188 0.985 0.000 0.996 0.004 0.000
#> GSM148529 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM148530 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM148531 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM148532 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM148533 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM148534 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM148535 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM148536 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM148537 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM148538 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM148539 2 0.0967 0.976 0.004 0.976 0.004 0.016
#> GSM148540 2 0.1174 0.971 0.000 0.968 0.020 0.012
#> GSM148541 2 0.1362 0.969 0.004 0.964 0.020 0.012
#> GSM148542 2 0.3668 0.867 0.056 0.872 0.056 0.016
#> GSM148543 2 0.1871 0.957 0.012 0.948 0.024 0.016
#> GSM148544 2 0.1182 0.971 0.000 0.968 0.016 0.016
#> GSM148545 1 0.5639 0.462 0.636 0.000 0.324 0.040
#> GSM148546 1 0.3377 0.718 0.848 0.000 0.140 0.012
#> GSM148547 1 0.3324 0.720 0.852 0.000 0.136 0.012
#> GSM148548 1 0.3384 0.698 0.860 0.000 0.024 0.116
#> GSM148549 1 0.3659 0.683 0.840 0.000 0.024 0.136
#> GSM148550 1 0.3497 0.680 0.852 0.000 0.024 0.124
#> GSM148551 1 0.4194 0.626 0.800 0.000 0.028 0.172
#> GSM148552 1 0.4514 0.671 0.788 0.004 0.176 0.032
#> GSM148553 1 0.4331 0.705 0.808 0.004 0.152 0.036
#> GSM148554 1 0.3876 0.706 0.836 0.000 0.040 0.124
#> GSM148555 1 0.3156 0.704 0.884 0.000 0.048 0.068
#> GSM148556 1 0.3428 0.671 0.844 0.000 0.012 0.144
#> GSM148557 1 0.3495 0.685 0.844 0.000 0.016 0.140
#> GSM148558 4 0.5592 0.386 0.404 0.000 0.024 0.572
#> GSM148559 1 0.6644 0.501 0.624 0.004 0.248 0.124
#> GSM148560 1 0.6181 0.560 0.668 0.000 0.204 0.128
#> GSM148561 1 0.6730 0.337 0.628 0.004 0.156 0.212
#> GSM148562 4 0.6929 0.404 0.440 0.000 0.108 0.452
#> GSM148563 4 0.5754 0.654 0.316 0.000 0.048 0.636
#> GSM148564 4 0.5823 0.644 0.344 0.004 0.036 0.616
#> GSM148565 4 0.3105 0.700 0.140 0.000 0.004 0.856
#> GSM148566 1 0.5842 0.647 0.704 0.000 0.168 0.128
#> GSM148567 4 0.5959 0.621 0.388 0.000 0.044 0.568
#> GSM148568 4 0.6182 0.570 0.428 0.000 0.052 0.520
#> GSM148569 4 0.5213 0.682 0.328 0.000 0.020 0.652
#> GSM148570 4 0.4139 0.716 0.176 0.000 0.024 0.800
#> GSM148571 4 0.3306 0.714 0.156 0.000 0.004 0.840
#> GSM148572 4 0.3088 0.687 0.128 0.000 0.008 0.864
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM148516 2 0.4375 0.7920 0.000 0.772 0.156 0.008 0.064
#> GSM148517 3 0.4872 0.0000 0.120 0.000 0.720 0.000 0.160
#> GSM148518 2 0.0000 0.9598 0.000 1.000 0.000 0.000 0.000
#> GSM148519 2 0.0000 0.9598 0.000 1.000 0.000 0.000 0.000
#> GSM148520 2 0.0912 0.9505 0.000 0.972 0.012 0.000 0.016
#> GSM148521 2 0.0162 0.9593 0.000 0.996 0.004 0.000 0.000
#> GSM148522 2 0.0162 0.9593 0.000 0.996 0.004 0.000 0.000
#> GSM148523 2 0.0162 0.9592 0.000 0.996 0.004 0.000 0.000
#> GSM148524 2 0.0000 0.9598 0.000 1.000 0.000 0.000 0.000
#> GSM148525 2 0.0000 0.9598 0.000 1.000 0.000 0.000 0.000
#> GSM148526 2 0.0404 0.9568 0.000 0.988 0.012 0.000 0.000
#> GSM148527 2 0.0162 0.9593 0.000 0.996 0.004 0.000 0.000
#> GSM148528 2 0.0290 0.9581 0.000 0.992 0.008 0.000 0.000
#> GSM148529 2 0.0000 0.9598 0.000 1.000 0.000 0.000 0.000
#> GSM148530 2 0.0000 0.9598 0.000 1.000 0.000 0.000 0.000
#> GSM148531 2 0.0000 0.9598 0.000 1.000 0.000 0.000 0.000
#> GSM148532 2 0.0000 0.9598 0.000 1.000 0.000 0.000 0.000
#> GSM148533 2 0.0162 0.9592 0.000 0.996 0.004 0.000 0.000
#> GSM148534 2 0.0000 0.9598 0.000 1.000 0.000 0.000 0.000
#> GSM148535 2 0.0000 0.9598 0.000 1.000 0.000 0.000 0.000
#> GSM148536 2 0.0451 0.9573 0.000 0.988 0.008 0.000 0.004
#> GSM148537 2 0.0290 0.9583 0.000 0.992 0.008 0.000 0.000
#> GSM148538 2 0.0000 0.9598 0.000 1.000 0.000 0.000 0.000
#> GSM148539 2 0.2189 0.9102 0.000 0.904 0.084 0.000 0.012
#> GSM148540 2 0.2722 0.8896 0.000 0.872 0.108 0.000 0.020
#> GSM148541 2 0.3529 0.8619 0.004 0.836 0.120 0.004 0.036
#> GSM148542 2 0.4628 0.7833 0.036 0.792 0.108 0.008 0.056
#> GSM148543 2 0.3218 0.8713 0.012 0.848 0.124 0.000 0.016
#> GSM148544 2 0.2625 0.8919 0.000 0.876 0.108 0.000 0.016
#> GSM148545 1 0.6327 -0.3656 0.484 0.000 0.168 0.000 0.348
#> GSM148546 1 0.3845 0.5321 0.812 0.000 0.060 0.004 0.124
#> GSM148547 1 0.3798 0.5406 0.816 0.000 0.060 0.004 0.120
#> GSM148548 1 0.3152 0.6692 0.868 0.000 0.016 0.084 0.032
#> GSM148549 1 0.3325 0.6681 0.852 0.000 0.012 0.104 0.032
#> GSM148550 1 0.3834 0.6538 0.816 0.000 0.008 0.124 0.052
#> GSM148551 1 0.3818 0.6385 0.812 0.000 0.016 0.144 0.028
#> GSM148552 1 0.5040 0.3874 0.716 0.004 0.072 0.008 0.200
#> GSM148553 1 0.4908 0.4812 0.748 0.004 0.064 0.020 0.164
#> GSM148554 1 0.3658 0.6681 0.832 0.000 0.016 0.116 0.036
#> GSM148555 1 0.3426 0.6348 0.852 0.000 0.012 0.052 0.084
#> GSM148556 1 0.3022 0.6616 0.848 0.000 0.004 0.136 0.012
#> GSM148557 1 0.3127 0.6670 0.848 0.000 0.004 0.128 0.020
#> GSM148558 4 0.5117 0.3211 0.348 0.000 0.016 0.612 0.024
#> GSM148559 5 0.4501 0.6300 0.276 0.000 0.020 0.008 0.696
#> GSM148560 5 0.4774 0.7009 0.340 0.000 0.024 0.004 0.632
#> GSM148561 1 0.7012 0.0782 0.500 0.000 0.088 0.080 0.332
#> GSM148562 4 0.7825 0.3858 0.340 0.000 0.076 0.372 0.212
#> GSM148563 4 0.6200 0.6128 0.252 0.000 0.036 0.612 0.100
#> GSM148564 4 0.6294 0.6261 0.252 0.004 0.020 0.600 0.124
#> GSM148565 4 0.2243 0.6567 0.056 0.000 0.012 0.916 0.016
#> GSM148566 5 0.5644 0.4973 0.472 0.000 0.024 0.032 0.472
#> GSM148567 4 0.6331 0.5983 0.300 0.000 0.008 0.540 0.152
#> GSM148568 4 0.6591 0.5686 0.312 0.000 0.016 0.516 0.156
#> GSM148569 4 0.5267 0.6674 0.232 0.000 0.004 0.672 0.092
#> GSM148570 4 0.3707 0.6774 0.108 0.000 0.008 0.828 0.056
#> GSM148571 4 0.2748 0.6744 0.096 0.000 0.008 0.880 0.016
#> GSM148572 4 0.1522 0.6464 0.044 0.000 0.012 0.944 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM148516 2 0.4450 0.406 0.000 0.528 0.448 0.000 0.004 0.020
#> GSM148517 6 0.3435 0.000 0.060 0.000 0.000 0.000 0.136 0.804
#> GSM148518 2 0.0000 0.925 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM148519 2 0.0146 0.925 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM148520 2 0.1464 0.906 0.000 0.944 0.036 0.000 0.016 0.004
#> GSM148521 2 0.0260 0.925 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM148522 2 0.0146 0.925 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM148523 2 0.0260 0.925 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM148524 2 0.0291 0.926 0.000 0.992 0.004 0.000 0.000 0.004
#> GSM148525 2 0.0146 0.925 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM148526 2 0.0458 0.922 0.000 0.984 0.016 0.000 0.000 0.000
#> GSM148527 2 0.0146 0.925 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM148528 2 0.0632 0.921 0.000 0.976 0.024 0.000 0.000 0.000
#> GSM148529 2 0.0000 0.925 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM148530 2 0.0000 0.925 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM148531 2 0.0000 0.925 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM148532 2 0.0146 0.925 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM148533 2 0.0260 0.925 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM148534 2 0.0000 0.925 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM148535 2 0.0000 0.925 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM148536 2 0.1010 0.915 0.000 0.960 0.036 0.000 0.004 0.000
#> GSM148537 2 0.0260 0.925 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM148538 2 0.0146 0.925 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM148539 2 0.2300 0.847 0.000 0.856 0.144 0.000 0.000 0.000
#> GSM148540 2 0.3074 0.799 0.000 0.792 0.200 0.000 0.004 0.004
#> GSM148541 2 0.3665 0.706 0.000 0.696 0.296 0.000 0.004 0.004
#> GSM148542 2 0.4962 0.500 0.012 0.608 0.320 0.000 0.000 0.060
#> GSM148543 2 0.3519 0.765 0.008 0.752 0.232 0.000 0.000 0.008
#> GSM148544 2 0.2964 0.798 0.000 0.792 0.204 0.000 0.000 0.004
#> GSM148545 1 0.5901 -0.216 0.408 0.000 0.000 0.000 0.388 0.204
#> GSM148546 1 0.4089 0.631 0.768 0.000 0.008 0.004 0.152 0.068
#> GSM148547 1 0.4052 0.634 0.772 0.000 0.008 0.004 0.148 0.068
#> GSM148548 1 0.2351 0.689 0.908 0.000 0.008 0.040 0.028 0.016
#> GSM148549 1 0.2503 0.682 0.896 0.000 0.008 0.060 0.024 0.012
#> GSM148550 1 0.3606 0.672 0.832 0.000 0.012 0.084 0.052 0.020
#> GSM148551 1 0.3410 0.632 0.836 0.000 0.012 0.108 0.024 0.020
#> GSM148552 1 0.5234 0.534 0.660 0.004 0.012 0.004 0.216 0.104
#> GSM148553 1 0.5267 0.574 0.692 0.004 0.020 0.016 0.180 0.088
#> GSM148554 1 0.3161 0.699 0.856 0.000 0.004 0.080 0.036 0.024
#> GSM148555 1 0.3920 0.626 0.820 0.000 0.044 0.028 0.080 0.028
#> GSM148556 1 0.2597 0.682 0.880 0.000 0.004 0.088 0.020 0.008
#> GSM148557 1 0.2697 0.692 0.876 0.000 0.004 0.088 0.020 0.012
#> GSM148558 4 0.5335 0.171 0.368 0.000 0.012 0.560 0.032 0.028
#> GSM148559 5 0.2988 0.627 0.140 0.000 0.004 0.004 0.836 0.016
#> GSM148560 5 0.4167 0.672 0.176 0.000 0.028 0.004 0.760 0.032
#> GSM148561 3 0.8067 0.000 0.308 0.000 0.348 0.076 0.184 0.084
#> GSM148562 4 0.8361 -0.192 0.280 0.000 0.164 0.340 0.124 0.092
#> GSM148563 4 0.6235 0.391 0.172 0.000 0.096 0.632 0.048 0.052
#> GSM148564 4 0.6573 0.427 0.228 0.004 0.064 0.576 0.104 0.024
#> GSM148565 4 0.2890 0.566 0.036 0.000 0.024 0.884 0.024 0.032
#> GSM148566 5 0.5938 0.476 0.292 0.000 0.096 0.008 0.568 0.036
#> GSM148567 4 0.6852 0.375 0.260 0.000 0.088 0.524 0.104 0.024
#> GSM148568 4 0.7064 0.320 0.268 0.000 0.100 0.496 0.112 0.024
#> GSM148569 4 0.5679 0.494 0.240 0.000 0.056 0.628 0.068 0.008
#> GSM148570 4 0.4155 0.556 0.092 0.000 0.036 0.804 0.036 0.032
#> GSM148571 4 0.3296 0.566 0.084 0.000 0.024 0.852 0.020 0.020
#> GSM148572 4 0.2622 0.561 0.040 0.000 0.028 0.896 0.012 0.024
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) dose(p) time(p) k
#> MAD:hclust 57 2.57e-12 0.99957 1.000 2
#> MAD:hclust 55 1.14e-12 0.88851 0.989 3
#> MAD:hclust 52 1.38e-10 0.02496 0.985 4
#> MAD:hclust 49 7.46e-09 0.00419 0.939 5
#> MAD:hclust 44 1.51e-09 0.00306 0.854 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 21163 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5093 0.491 0.491
#> 3 3 0.729 0.635 0.772 0.2200 0.887 0.770
#> 4 4 0.702 0.800 0.818 0.1214 0.803 0.534
#> 5 5 0.621 0.764 0.811 0.0818 0.958 0.850
#> 6 6 0.672 0.753 0.789 0.0436 0.980 0.920
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
#> GSM148516 2 0 1 0 1
#> GSM148517 1 0 1 1 0
#> GSM148518 2 0 1 0 1
#> GSM148519 2 0 1 0 1
#> GSM148520 2 0 1 0 1
#> GSM148521 2 0 1 0 1
#> GSM148522 2 0 1 0 1
#> GSM148523 2 0 1 0 1
#> GSM148524 2 0 1 0 1
#> GSM148525 2 0 1 0 1
#> GSM148526 2 0 1 0 1
#> GSM148527 2 0 1 0 1
#> GSM148528 2 0 1 0 1
#> GSM148529 2 0 1 0 1
#> GSM148530 2 0 1 0 1
#> GSM148531 2 0 1 0 1
#> GSM148532 2 0 1 0 1
#> GSM148533 2 0 1 0 1
#> GSM148534 2 0 1 0 1
#> GSM148535 2 0 1 0 1
#> GSM148536 2 0 1 0 1
#> GSM148537 2 0 1 0 1
#> GSM148538 2 0 1 0 1
#> GSM148539 2 0 1 0 1
#> GSM148540 2 0 1 0 1
#> GSM148541 2 0 1 0 1
#> GSM148542 2 0 1 0 1
#> GSM148543 2 0 1 0 1
#> GSM148544 2 0 1 0 1
#> GSM148545 1 0 1 1 0
#> GSM148546 1 0 1 1 0
#> GSM148547 1 0 1 1 0
#> GSM148548 1 0 1 1 0
#> GSM148549 1 0 1 1 0
#> GSM148550 1 0 1 1 0
#> GSM148551 1 0 1 1 0
#> GSM148552 1 0 1 1 0
#> GSM148553 1 0 1 1 0
#> GSM148554 1 0 1 1 0
#> GSM148555 1 0 1 1 0
#> GSM148556 1 0 1 1 0
#> GSM148557 1 0 1 1 0
#> GSM148558 1 0 1 1 0
#> GSM148559 1 0 1 1 0
#> GSM148560 1 0 1 1 0
#> GSM148561 1 0 1 1 0
#> GSM148562 1 0 1 1 0
#> GSM148563 1 0 1 1 0
#> GSM148564 1 0 1 1 0
#> GSM148565 1 0 1 1 0
#> GSM148566 1 0 1 1 0
#> GSM148567 1 0 1 1 0
#> GSM148568 1 0 1 1 0
#> GSM148569 1 0 1 1 0
#> GSM148570 1 0 1 1 0
#> GSM148571 1 0 1 1 0
#> GSM148572 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM148516 2 0.5835 0.7541 0.000 0.660 0.340
#> GSM148517 3 0.5882 0.8681 0.348 0.000 0.652
#> GSM148518 2 0.0424 0.9264 0.000 0.992 0.008
#> GSM148519 2 0.0000 0.9274 0.000 1.000 0.000
#> GSM148520 2 0.0424 0.9264 0.000 0.992 0.008
#> GSM148521 2 0.0000 0.9274 0.000 1.000 0.000
#> GSM148522 2 0.0000 0.9274 0.000 1.000 0.000
#> GSM148523 2 0.0237 0.9271 0.000 0.996 0.004
#> GSM148524 2 0.0237 0.9271 0.000 0.996 0.004
#> GSM148525 2 0.0592 0.9256 0.000 0.988 0.012
#> GSM148526 2 0.0000 0.9274 0.000 1.000 0.000
#> GSM148527 2 0.0000 0.9274 0.000 1.000 0.000
#> GSM148528 2 0.0237 0.9268 0.000 0.996 0.004
#> GSM148529 2 0.0000 0.9274 0.000 1.000 0.000
#> GSM148530 2 0.0000 0.9274 0.000 1.000 0.000
#> GSM148531 2 0.0237 0.9271 0.000 0.996 0.004
#> GSM148532 2 0.0424 0.9264 0.000 0.992 0.008
#> GSM148533 2 0.0237 0.9271 0.000 0.996 0.004
#> GSM148534 2 0.0237 0.9268 0.000 0.996 0.004
#> GSM148535 2 0.0237 0.9271 0.000 0.996 0.004
#> GSM148536 2 0.0424 0.9259 0.000 0.992 0.008
#> GSM148537 2 0.0237 0.9271 0.000 0.996 0.004
#> GSM148538 2 0.0000 0.9274 0.000 1.000 0.000
#> GSM148539 2 0.5497 0.7837 0.000 0.708 0.292
#> GSM148540 2 0.5785 0.7584 0.000 0.668 0.332
#> GSM148541 2 0.5810 0.7556 0.000 0.664 0.336
#> GSM148542 2 0.6057 0.7530 0.004 0.656 0.340
#> GSM148543 2 0.5760 0.7609 0.000 0.672 0.328
#> GSM148544 2 0.5785 0.7603 0.000 0.668 0.332
#> GSM148545 3 0.5926 0.8778 0.356 0.000 0.644
#> GSM148546 3 0.5988 0.8912 0.368 0.000 0.632
#> GSM148547 3 0.5988 0.8912 0.368 0.000 0.632
#> GSM148548 3 0.6299 0.6336 0.476 0.000 0.524
#> GSM148549 1 0.6280 -0.4704 0.540 0.000 0.460
#> GSM148550 1 0.6291 -0.4892 0.532 0.000 0.468
#> GSM148551 1 0.6008 -0.1529 0.628 0.000 0.372
#> GSM148552 3 0.5988 0.8904 0.368 0.000 0.632
#> GSM148553 3 0.6008 0.8892 0.372 0.000 0.628
#> GSM148554 3 0.6204 0.8091 0.424 0.000 0.576
#> GSM148555 1 0.6302 -0.5375 0.520 0.000 0.480
#> GSM148556 1 0.6286 -0.4740 0.536 0.000 0.464
#> GSM148557 1 0.6260 -0.4341 0.552 0.000 0.448
#> GSM148558 1 0.5678 0.0418 0.684 0.000 0.316
#> GSM148559 3 0.6267 0.6507 0.452 0.000 0.548
#> GSM148560 1 0.6192 -0.2686 0.580 0.000 0.420
#> GSM148561 1 0.2165 0.6060 0.936 0.000 0.064
#> GSM148562 1 0.1163 0.6215 0.972 0.000 0.028
#> GSM148563 1 0.0892 0.6212 0.980 0.000 0.020
#> GSM148564 1 0.0892 0.6220 0.980 0.000 0.020
#> GSM148565 1 0.0237 0.6185 0.996 0.000 0.004
#> GSM148566 1 0.5882 0.0218 0.652 0.000 0.348
#> GSM148567 1 0.1411 0.6189 0.964 0.000 0.036
#> GSM148568 1 0.1860 0.6063 0.948 0.000 0.052
#> GSM148569 1 0.0747 0.6226 0.984 0.000 0.016
#> GSM148570 1 0.0237 0.6195 0.996 0.000 0.004
#> GSM148571 1 0.0424 0.6186 0.992 0.000 0.008
#> GSM148572 1 0.0424 0.6183 0.992 0.000 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM148516 3 0.5453 0.952 0.032 0.320 0.648 0.000
#> GSM148517 1 0.5326 0.643 0.748 0.000 0.116 0.136
#> GSM148518 2 0.1452 0.956 0.036 0.956 0.008 0.000
#> GSM148519 2 0.1004 0.964 0.024 0.972 0.004 0.000
#> GSM148520 2 0.1584 0.952 0.036 0.952 0.012 0.000
#> GSM148521 2 0.0657 0.965 0.012 0.984 0.004 0.000
#> GSM148522 2 0.0336 0.966 0.008 0.992 0.000 0.000
#> GSM148523 2 0.1452 0.960 0.036 0.956 0.008 0.000
#> GSM148524 2 0.1151 0.960 0.024 0.968 0.008 0.000
#> GSM148525 2 0.1833 0.942 0.032 0.944 0.024 0.000
#> GSM148526 2 0.0895 0.965 0.020 0.976 0.004 0.000
#> GSM148527 2 0.0657 0.965 0.012 0.984 0.004 0.000
#> GSM148528 2 0.1584 0.961 0.036 0.952 0.012 0.000
#> GSM148529 2 0.0592 0.964 0.016 0.984 0.000 0.000
#> GSM148530 2 0.0592 0.967 0.016 0.984 0.000 0.000
#> GSM148531 2 0.1151 0.965 0.024 0.968 0.008 0.000
#> GSM148532 2 0.1610 0.963 0.032 0.952 0.016 0.000
#> GSM148533 2 0.1488 0.957 0.032 0.956 0.012 0.000
#> GSM148534 2 0.1256 0.962 0.028 0.964 0.008 0.000
#> GSM148535 2 0.1356 0.956 0.032 0.960 0.008 0.000
#> GSM148536 2 0.1610 0.950 0.032 0.952 0.016 0.000
#> GSM148537 2 0.1356 0.956 0.032 0.960 0.008 0.000
#> GSM148538 2 0.0657 0.965 0.012 0.984 0.004 0.000
#> GSM148539 3 0.5560 0.878 0.024 0.392 0.584 0.000
#> GSM148540 3 0.5271 0.957 0.020 0.340 0.640 0.000
#> GSM148541 3 0.4741 0.957 0.004 0.328 0.668 0.000
#> GSM148542 3 0.5557 0.935 0.040 0.308 0.652 0.000
#> GSM148543 3 0.4605 0.959 0.000 0.336 0.664 0.000
#> GSM148544 3 0.4897 0.959 0.008 0.332 0.660 0.000
#> GSM148545 1 0.5092 0.654 0.764 0.000 0.096 0.140
#> GSM148546 1 0.3495 0.688 0.844 0.000 0.016 0.140
#> GSM148547 1 0.3300 0.688 0.848 0.000 0.008 0.144
#> GSM148548 1 0.6585 0.626 0.584 0.000 0.104 0.312
#> GSM148549 1 0.6773 0.582 0.532 0.000 0.104 0.364
#> GSM148550 1 0.6784 0.584 0.528 0.000 0.104 0.368
#> GSM148551 1 0.6887 0.444 0.456 0.000 0.104 0.440
#> GSM148552 1 0.3958 0.683 0.824 0.000 0.032 0.144
#> GSM148553 1 0.3913 0.689 0.824 0.000 0.028 0.148
#> GSM148554 1 0.5537 0.668 0.688 0.000 0.056 0.256
#> GSM148555 1 0.6887 0.591 0.528 0.000 0.116 0.356
#> GSM148556 1 0.6804 0.576 0.520 0.000 0.104 0.376
#> GSM148557 1 0.6542 0.525 0.496 0.000 0.076 0.428
#> GSM148558 4 0.6500 -0.286 0.376 0.000 0.080 0.544
#> GSM148559 1 0.6616 0.546 0.624 0.000 0.156 0.220
#> GSM148560 1 0.7228 0.361 0.504 0.000 0.156 0.340
#> GSM148561 4 0.4150 0.800 0.056 0.000 0.120 0.824
#> GSM148562 4 0.3149 0.840 0.032 0.000 0.088 0.880
#> GSM148563 4 0.2271 0.852 0.008 0.000 0.076 0.916
#> GSM148564 4 0.1820 0.865 0.020 0.000 0.036 0.944
#> GSM148565 4 0.0707 0.863 0.000 0.000 0.020 0.980
#> GSM148566 1 0.7312 0.225 0.436 0.000 0.152 0.412
#> GSM148567 4 0.2596 0.852 0.024 0.000 0.068 0.908
#> GSM148568 4 0.3400 0.822 0.064 0.000 0.064 0.872
#> GSM148569 4 0.1624 0.862 0.020 0.000 0.028 0.952
#> GSM148570 4 0.1022 0.865 0.000 0.000 0.032 0.968
#> GSM148571 4 0.0817 0.860 0.000 0.000 0.024 0.976
#> GSM148572 4 0.0707 0.862 0.000 0.000 0.020 0.980
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM148516 3 0.436 0.920 0.000 0.148 0.776 0.008 0.068
#> GSM148517 1 0.530 -0.361 0.476 0.000 0.048 0.000 0.476
#> GSM148518 2 0.198 0.927 0.000 0.920 0.016 0.000 0.064
#> GSM148519 2 0.225 0.919 0.000 0.896 0.008 0.000 0.096
#> GSM148520 2 0.272 0.900 0.000 0.868 0.008 0.004 0.120
#> GSM148521 2 0.148 0.928 0.000 0.936 0.000 0.000 0.064
#> GSM148522 2 0.144 0.932 0.000 0.948 0.012 0.000 0.040
#> GSM148523 2 0.167 0.930 0.000 0.936 0.012 0.000 0.052
#> GSM148524 2 0.174 0.928 0.000 0.932 0.012 0.000 0.056
#> GSM148525 2 0.285 0.904 0.000 0.872 0.036 0.000 0.092
#> GSM148526 2 0.219 0.921 0.000 0.900 0.008 0.000 0.092
#> GSM148527 2 0.163 0.930 0.000 0.936 0.008 0.000 0.056
#> GSM148528 2 0.265 0.904 0.000 0.868 0.004 0.004 0.124
#> GSM148529 2 0.141 0.934 0.000 0.948 0.008 0.000 0.044
#> GSM148530 2 0.152 0.930 0.000 0.944 0.012 0.000 0.044
#> GSM148531 2 0.170 0.927 0.000 0.936 0.016 0.000 0.048
#> GSM148532 2 0.205 0.928 0.000 0.916 0.016 0.000 0.068
#> GSM148533 2 0.174 0.929 0.000 0.932 0.012 0.000 0.056
#> GSM148534 2 0.265 0.907 0.000 0.868 0.004 0.004 0.124
#> GSM148535 2 0.198 0.923 0.000 0.920 0.016 0.000 0.064
#> GSM148536 2 0.252 0.914 0.000 0.884 0.016 0.000 0.100
#> GSM148537 2 0.221 0.922 0.000 0.908 0.020 0.000 0.072
#> GSM148538 2 0.104 0.934 0.000 0.964 0.004 0.000 0.032
#> GSM148539 3 0.491 0.837 0.000 0.232 0.692 0.000 0.076
#> GSM148540 3 0.345 0.938 0.000 0.148 0.820 0.000 0.032
#> GSM148541 3 0.337 0.939 0.000 0.148 0.824 0.000 0.028
#> GSM148542 3 0.494 0.907 0.004 0.152 0.752 0.024 0.068
#> GSM148543 3 0.293 0.941 0.000 0.152 0.840 0.000 0.008
#> GSM148544 3 0.284 0.940 0.000 0.144 0.848 0.000 0.008
#> GSM148545 1 0.473 -0.215 0.532 0.000 0.016 0.000 0.452
#> GSM148546 1 0.311 0.495 0.800 0.000 0.000 0.000 0.200
#> GSM148547 1 0.324 0.477 0.784 0.000 0.000 0.000 0.216
#> GSM148548 1 0.275 0.649 0.880 0.000 0.000 0.080 0.040
#> GSM148549 1 0.246 0.656 0.880 0.000 0.000 0.112 0.008
#> GSM148550 1 0.261 0.654 0.868 0.000 0.000 0.124 0.008
#> GSM148551 1 0.421 0.579 0.756 0.000 0.004 0.204 0.036
#> GSM148552 1 0.379 0.380 0.724 0.000 0.004 0.000 0.272
#> GSM148553 1 0.327 0.467 0.780 0.000 0.000 0.000 0.220
#> GSM148554 1 0.291 0.615 0.872 0.000 0.000 0.052 0.076
#> GSM148555 1 0.325 0.640 0.852 0.000 0.004 0.104 0.040
#> GSM148556 1 0.249 0.654 0.872 0.000 0.000 0.124 0.004
#> GSM148557 1 0.297 0.636 0.828 0.000 0.000 0.168 0.004
#> GSM148558 1 0.506 0.383 0.584 0.000 0.016 0.384 0.016
#> GSM148559 5 0.572 0.662 0.360 0.000 0.008 0.072 0.560
#> GSM148560 5 0.659 0.796 0.288 0.000 0.020 0.156 0.536
#> GSM148561 4 0.625 0.693 0.128 0.000 0.052 0.644 0.176
#> GSM148562 4 0.547 0.777 0.144 0.000 0.036 0.712 0.108
#> GSM148563 4 0.316 0.831 0.072 0.000 0.028 0.872 0.028
#> GSM148564 4 0.435 0.832 0.104 0.000 0.032 0.800 0.064
#> GSM148565 4 0.191 0.833 0.044 0.000 0.016 0.932 0.008
#> GSM148566 5 0.695 0.728 0.252 0.000 0.024 0.224 0.500
#> GSM148567 4 0.526 0.801 0.124 0.000 0.036 0.732 0.108
#> GSM148568 4 0.539 0.789 0.120 0.000 0.040 0.724 0.116
#> GSM148569 4 0.416 0.831 0.128 0.000 0.016 0.800 0.056
#> GSM148570 4 0.295 0.841 0.076 0.000 0.028 0.880 0.016
#> GSM148571 4 0.220 0.831 0.056 0.000 0.024 0.916 0.004
#> GSM148572 4 0.289 0.820 0.084 0.000 0.020 0.880 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM148516 3 0.443 0.843 0.004 0.064 0.772 0.004 0.036 NA
#> GSM148517 5 0.626 0.498 0.284 0.000 0.012 0.004 0.476 NA
#> GSM148518 2 0.281 0.876 0.000 0.824 0.004 0.000 0.004 NA
#> GSM148519 2 0.305 0.881 0.000 0.812 0.012 0.000 0.004 NA
#> GSM148520 2 0.321 0.855 0.000 0.816 0.016 0.000 0.012 NA
#> GSM148521 2 0.202 0.886 0.000 0.900 0.012 0.000 0.000 NA
#> GSM148522 2 0.221 0.892 0.000 0.892 0.012 0.004 0.000 NA
#> GSM148523 2 0.264 0.882 0.000 0.868 0.016 0.004 0.004 NA
#> GSM148524 2 0.215 0.890 0.000 0.904 0.012 0.004 0.004 NA
#> GSM148525 2 0.373 0.849 0.000 0.768 0.032 0.000 0.008 NA
#> GSM148526 2 0.325 0.875 0.000 0.812 0.016 0.000 0.012 NA
#> GSM148527 2 0.211 0.890 0.000 0.896 0.016 0.000 0.000 NA
#> GSM148528 2 0.333 0.864 0.000 0.788 0.008 0.000 0.012 NA
#> GSM148529 2 0.211 0.886 0.000 0.900 0.012 0.000 0.004 NA
#> GSM148530 2 0.220 0.891 0.000 0.896 0.016 0.000 0.004 NA
#> GSM148531 2 0.240 0.887 0.000 0.892 0.016 0.004 0.008 NA
#> GSM148532 2 0.256 0.886 0.000 0.864 0.008 0.000 0.008 NA
#> GSM148533 2 0.264 0.881 0.000 0.860 0.016 0.004 0.000 NA
#> GSM148534 2 0.349 0.862 0.000 0.776 0.012 0.000 0.012 NA
#> GSM148535 2 0.329 0.862 0.000 0.796 0.012 0.004 0.004 NA
#> GSM148536 2 0.330 0.871 0.000 0.820 0.028 0.000 0.012 NA
#> GSM148537 2 0.318 0.869 0.000 0.804 0.016 0.004 0.000 NA
#> GSM148538 2 0.207 0.893 0.000 0.908 0.020 0.000 0.004 NA
#> GSM148539 3 0.471 0.807 0.000 0.124 0.740 0.004 0.032 NA
#> GSM148540 3 0.329 0.886 0.004 0.052 0.856 0.004 0.024 NA
#> GSM148541 3 0.253 0.893 0.004 0.052 0.896 0.000 0.028 NA
#> GSM148542 3 0.486 0.825 0.000 0.072 0.740 0.004 0.108 NA
#> GSM148543 3 0.143 0.898 0.000 0.052 0.940 0.000 0.004 NA
#> GSM148544 3 0.219 0.896 0.000 0.056 0.908 0.000 0.012 NA
#> GSM148545 5 0.586 0.331 0.384 0.000 0.000 0.004 0.444 NA
#> GSM148546 1 0.430 0.498 0.708 0.000 0.000 0.000 0.216 NA
#> GSM148547 1 0.448 0.452 0.680 0.000 0.000 0.000 0.244 NA
#> GSM148548 1 0.193 0.717 0.928 0.000 0.004 0.032 0.016 NA
#> GSM148549 1 0.147 0.730 0.932 0.000 0.000 0.064 0.004 NA
#> GSM148550 1 0.156 0.729 0.920 0.000 0.000 0.080 0.000 NA
#> GSM148551 1 0.331 0.696 0.836 0.000 0.004 0.112 0.016 NA
#> GSM148552 1 0.518 0.278 0.608 0.000 0.008 0.000 0.284 NA
#> GSM148553 1 0.492 0.427 0.660 0.000 0.008 0.000 0.232 NA
#> GSM148554 1 0.328 0.667 0.844 0.000 0.000 0.032 0.088 NA
#> GSM148555 1 0.257 0.705 0.888 0.000 0.004 0.072 0.024 NA
#> GSM148556 1 0.161 0.729 0.916 0.000 0.000 0.084 0.000 NA
#> GSM148557 1 0.219 0.718 0.876 0.000 0.000 0.120 0.000 NA
#> GSM148558 1 0.511 0.367 0.536 0.000 0.008 0.400 0.004 NA
#> GSM148559 5 0.472 0.656 0.188 0.000 0.004 0.052 0.720 NA
#> GSM148560 5 0.421 0.639 0.124 0.000 0.000 0.112 0.756 NA
#> GSM148561 4 0.729 0.568 0.144 0.000 0.008 0.456 0.236 NA
#> GSM148562 4 0.596 0.718 0.168 0.000 0.000 0.620 0.084 NA
#> GSM148563 4 0.410 0.770 0.104 0.000 0.008 0.796 0.032 NA
#> GSM148564 4 0.505 0.766 0.096 0.000 0.020 0.740 0.064 NA
#> GSM148565 4 0.188 0.771 0.020 0.000 0.008 0.928 0.004 NA
#> GSM148566 5 0.563 0.470 0.124 0.000 0.004 0.172 0.652 NA
#> GSM148567 4 0.596 0.721 0.112 0.000 0.004 0.632 0.164 NA
#> GSM148568 4 0.614 0.698 0.128 0.000 0.004 0.612 0.168 NA
#> GSM148569 4 0.431 0.780 0.120 0.000 0.000 0.768 0.036 NA
#> GSM148570 4 0.280 0.789 0.052 0.000 0.008 0.884 0.024 NA
#> GSM148571 4 0.207 0.773 0.028 0.000 0.012 0.916 0.000 NA
#> GSM148572 4 0.227 0.768 0.056 0.000 0.004 0.904 0.004 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 agent(p) dose(p) time(p) k
#> MAD:kmeans 57 2.57e-12 1.00e+00 1.000 2
#> MAD:kmeans 48 2.84e-09 2.43e-02 0.696 3
#> MAD:kmeans 53 1.02e-09 2.17e-06 0.982 4
#> MAD:kmeans 50 3.44e-09 1.37e-05 0.701 5
#> MAD:kmeans 49 5.66e-09 5.01e-06 0.883 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 21163 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5093 0.491 0.491
#> 3 3 0.644 0.654 0.772 0.2525 0.887 0.770
#> 4 4 0.507 0.602 0.727 0.1554 0.833 0.589
#> 5 5 0.508 0.537 0.633 0.0712 0.982 0.937
#> 6 6 0.512 0.500 0.583 0.0419 0.951 0.833
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
#> GSM148516 2 0 1 0 1
#> GSM148517 1 0 1 1 0
#> GSM148518 2 0 1 0 1
#> GSM148519 2 0 1 0 1
#> GSM148520 2 0 1 0 1
#> GSM148521 2 0 1 0 1
#> GSM148522 2 0 1 0 1
#> GSM148523 2 0 1 0 1
#> GSM148524 2 0 1 0 1
#> GSM148525 2 0 1 0 1
#> GSM148526 2 0 1 0 1
#> GSM148527 2 0 1 0 1
#> GSM148528 2 0 1 0 1
#> GSM148529 2 0 1 0 1
#> GSM148530 2 0 1 0 1
#> GSM148531 2 0 1 0 1
#> GSM148532 2 0 1 0 1
#> GSM148533 2 0 1 0 1
#> GSM148534 2 0 1 0 1
#> GSM148535 2 0 1 0 1
#> GSM148536 2 0 1 0 1
#> GSM148537 2 0 1 0 1
#> GSM148538 2 0 1 0 1
#> GSM148539 2 0 1 0 1
#> GSM148540 2 0 1 0 1
#> GSM148541 2 0 1 0 1
#> GSM148542 2 0 1 0 1
#> GSM148543 2 0 1 0 1
#> GSM148544 2 0 1 0 1
#> GSM148545 1 0 1 1 0
#> GSM148546 1 0 1 1 0
#> GSM148547 1 0 1 1 0
#> GSM148548 1 0 1 1 0
#> GSM148549 1 0 1 1 0
#> GSM148550 1 0 1 1 0
#> GSM148551 1 0 1 1 0
#> GSM148552 1 0 1 1 0
#> GSM148553 1 0 1 1 0
#> GSM148554 1 0 1 1 0
#> GSM148555 1 0 1 1 0
#> GSM148556 1 0 1 1 0
#> GSM148557 1 0 1 1 0
#> GSM148558 1 0 1 1 0
#> GSM148559 1 0 1 1 0
#> GSM148560 1 0 1 1 0
#> GSM148561 1 0 1 1 0
#> GSM148562 1 0 1 1 0
#> GSM148563 1 0 1 1 0
#> GSM148564 1 0 1 1 0
#> GSM148565 1 0 1 1 0
#> GSM148566 1 0 1 1 0
#> GSM148567 1 0 1 1 0
#> GSM148568 1 0 1 1 0
#> GSM148569 1 0 1 1 0
#> GSM148570 1 0 1 1 0
#> GSM148571 1 0 1 1 0
#> GSM148572 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM148516 2 0.4784 0.8761 0.004 0.796 0.200
#> GSM148517 3 0.6008 0.6507 0.372 0.000 0.628
#> GSM148518 2 0.1289 0.9409 0.000 0.968 0.032
#> GSM148519 2 0.0424 0.9386 0.000 0.992 0.008
#> GSM148520 2 0.1964 0.9380 0.000 0.944 0.056
#> GSM148521 2 0.0892 0.9402 0.000 0.980 0.020
#> GSM148522 2 0.1163 0.9407 0.000 0.972 0.028
#> GSM148523 2 0.1163 0.9406 0.000 0.972 0.028
#> GSM148524 2 0.1031 0.9416 0.000 0.976 0.024
#> GSM148525 2 0.1643 0.9388 0.000 0.956 0.044
#> GSM148526 2 0.2165 0.9371 0.000 0.936 0.064
#> GSM148527 2 0.1643 0.9396 0.000 0.956 0.044
#> GSM148528 2 0.1163 0.9410 0.000 0.972 0.028
#> GSM148529 2 0.1163 0.9404 0.000 0.972 0.028
#> GSM148530 2 0.1643 0.9403 0.000 0.956 0.044
#> GSM148531 2 0.1163 0.9394 0.000 0.972 0.028
#> GSM148532 2 0.1529 0.9405 0.000 0.960 0.040
#> GSM148533 2 0.0747 0.9396 0.000 0.984 0.016
#> GSM148534 2 0.0892 0.9414 0.000 0.980 0.020
#> GSM148535 2 0.1163 0.9401 0.000 0.972 0.028
#> GSM148536 2 0.1031 0.9405 0.000 0.976 0.024
#> GSM148537 2 0.1163 0.9404 0.000 0.972 0.028
#> GSM148538 2 0.0892 0.9411 0.000 0.980 0.020
#> GSM148539 2 0.4834 0.8735 0.004 0.792 0.204
#> GSM148540 2 0.5982 0.8362 0.028 0.744 0.228
#> GSM148541 2 0.5903 0.8420 0.024 0.744 0.232
#> GSM148542 2 0.8665 0.5858 0.124 0.552 0.324
#> GSM148543 2 0.5305 0.8682 0.020 0.788 0.192
#> GSM148544 2 0.7226 0.7848 0.080 0.692 0.228
#> GSM148545 3 0.5810 0.6916 0.336 0.000 0.664
#> GSM148546 3 0.5706 0.6980 0.320 0.000 0.680
#> GSM148547 3 0.5431 0.7129 0.284 0.000 0.716
#> GSM148548 3 0.6168 0.5551 0.412 0.000 0.588
#> GSM148549 1 0.6307 -0.2571 0.512 0.000 0.488
#> GSM148550 1 0.6235 -0.1101 0.564 0.000 0.436
#> GSM148551 1 0.6095 0.1563 0.608 0.000 0.392
#> GSM148552 3 0.5560 0.6982 0.300 0.000 0.700
#> GSM148553 3 0.5560 0.6526 0.300 0.000 0.700
#> GSM148554 3 0.6252 0.5126 0.444 0.000 0.556
#> GSM148555 1 0.6215 -0.0171 0.572 0.000 0.428
#> GSM148556 1 0.6215 -0.0291 0.572 0.000 0.428
#> GSM148557 1 0.5859 0.2573 0.656 0.000 0.344
#> GSM148558 1 0.5926 0.2642 0.644 0.000 0.356
#> GSM148559 3 0.6295 0.3736 0.472 0.000 0.528
#> GSM148560 1 0.6244 -0.1329 0.560 0.000 0.440
#> GSM148561 1 0.4931 0.4629 0.768 0.000 0.232
#> GSM148562 1 0.3941 0.5522 0.844 0.000 0.156
#> GSM148563 1 0.2878 0.5760 0.904 0.000 0.096
#> GSM148564 1 0.4121 0.5539 0.832 0.000 0.168
#> GSM148565 1 0.3038 0.5723 0.896 0.000 0.104
#> GSM148566 1 0.6079 0.0844 0.612 0.000 0.388
#> GSM148567 1 0.3879 0.5634 0.848 0.000 0.152
#> GSM148568 1 0.4654 0.4991 0.792 0.000 0.208
#> GSM148569 1 0.3267 0.5748 0.884 0.000 0.116
#> GSM148570 1 0.3192 0.5770 0.888 0.000 0.112
#> GSM148571 1 0.3038 0.5791 0.896 0.000 0.104
#> GSM148572 1 0.2625 0.5763 0.916 0.000 0.084
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM148516 3 0.538 0.6790 0.008 0.300 0.672 0.020
#> GSM148517 1 0.496 0.5271 0.732 0.000 0.036 0.232
#> GSM148518 2 0.395 0.7444 0.004 0.780 0.216 0.000
#> GSM148519 2 0.326 0.7924 0.004 0.844 0.152 0.000
#> GSM148520 2 0.401 0.7164 0.000 0.756 0.244 0.000
#> GSM148521 2 0.349 0.7783 0.004 0.824 0.172 0.000
#> GSM148522 2 0.253 0.7995 0.000 0.888 0.112 0.000
#> GSM148523 2 0.363 0.7894 0.004 0.812 0.184 0.000
#> GSM148524 2 0.349 0.7881 0.004 0.824 0.172 0.000
#> GSM148525 2 0.453 0.6678 0.004 0.704 0.292 0.000
#> GSM148526 2 0.383 0.7529 0.004 0.792 0.204 0.000
#> GSM148527 2 0.335 0.7785 0.004 0.836 0.160 0.000
#> GSM148528 2 0.371 0.7792 0.004 0.804 0.192 0.000
#> GSM148529 2 0.276 0.7975 0.000 0.872 0.128 0.000
#> GSM148530 2 0.297 0.7984 0.000 0.856 0.144 0.000
#> GSM148531 2 0.369 0.7729 0.000 0.792 0.208 0.000
#> GSM148532 2 0.373 0.7686 0.000 0.788 0.212 0.000
#> GSM148533 2 0.344 0.7720 0.000 0.816 0.184 0.000
#> GSM148534 2 0.367 0.7811 0.004 0.808 0.188 0.000
#> GSM148535 2 0.363 0.7669 0.004 0.812 0.184 0.000
#> GSM148536 2 0.402 0.7530 0.004 0.772 0.224 0.000
#> GSM148537 2 0.379 0.7592 0.004 0.796 0.200 0.000
#> GSM148538 2 0.305 0.7966 0.004 0.860 0.136 0.000
#> GSM148539 3 0.533 0.5937 0.016 0.380 0.604 0.000
#> GSM148540 3 0.562 0.7014 0.028 0.256 0.696 0.020
#> GSM148541 3 0.511 0.7019 0.016 0.296 0.684 0.004
#> GSM148542 3 0.740 0.6174 0.056 0.280 0.588 0.076
#> GSM148543 3 0.550 0.6949 0.028 0.312 0.656 0.004
#> GSM148544 3 0.593 0.7096 0.020 0.276 0.668 0.036
#> GSM148545 1 0.420 0.5853 0.808 0.000 0.036 0.156
#> GSM148546 1 0.442 0.6090 0.796 0.000 0.044 0.160
#> GSM148547 1 0.379 0.6104 0.844 0.000 0.044 0.112
#> GSM148548 1 0.542 0.5528 0.692 0.000 0.048 0.260
#> GSM148549 1 0.648 0.4149 0.564 0.000 0.084 0.352
#> GSM148550 1 0.597 0.4647 0.600 0.000 0.052 0.348
#> GSM148551 1 0.652 0.2667 0.512 0.000 0.076 0.412
#> GSM148552 1 0.356 0.5791 0.856 0.000 0.036 0.108
#> GSM148553 1 0.503 0.5590 0.752 0.000 0.060 0.188
#> GSM148554 1 0.551 0.5647 0.692 0.000 0.056 0.252
#> GSM148555 1 0.622 0.3627 0.532 0.000 0.056 0.412
#> GSM148556 1 0.615 0.3723 0.540 0.000 0.052 0.408
#> GSM148557 4 0.621 -0.1593 0.468 0.000 0.052 0.480
#> GSM148558 4 0.633 0.1240 0.404 0.000 0.064 0.532
#> GSM148559 1 0.610 0.3750 0.624 0.000 0.072 0.304
#> GSM148560 4 0.621 0.0145 0.468 0.000 0.052 0.480
#> GSM148561 4 0.573 0.5467 0.200 0.000 0.096 0.704
#> GSM148562 4 0.546 0.5674 0.212 0.000 0.072 0.716
#> GSM148563 4 0.417 0.6094 0.140 0.000 0.044 0.816
#> GSM148564 4 0.529 0.5717 0.224 0.000 0.056 0.720
#> GSM148565 4 0.476 0.6038 0.192 0.000 0.044 0.764
#> GSM148566 4 0.645 0.1384 0.448 0.000 0.068 0.484
#> GSM148567 4 0.482 0.5630 0.216 0.000 0.036 0.748
#> GSM148568 4 0.507 0.5707 0.208 0.000 0.052 0.740
#> GSM148569 4 0.415 0.6111 0.160 0.000 0.032 0.808
#> GSM148570 4 0.418 0.6095 0.180 0.000 0.024 0.796
#> GSM148571 4 0.429 0.6096 0.164 0.000 0.036 0.800
#> GSM148572 4 0.401 0.6164 0.148 0.000 0.032 0.820
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM148516 3 0.547 0.5772 0.004 0.232 0.664 0.004 NA
#> GSM148517 1 0.627 0.4114 0.596 0.000 0.016 0.172 NA
#> GSM148518 2 0.444 0.6921 0.000 0.760 0.136 0.000 NA
#> GSM148519 2 0.370 0.7168 0.000 0.820 0.080 0.000 NA
#> GSM148520 2 0.613 0.5847 0.000 0.556 0.264 0.000 NA
#> GSM148521 2 0.548 0.6606 0.000 0.644 0.232 0.000 NA
#> GSM148522 2 0.480 0.7086 0.000 0.728 0.120 0.000 NA
#> GSM148523 2 0.488 0.6730 0.000 0.720 0.152 0.000 NA
#> GSM148524 2 0.491 0.7055 0.004 0.728 0.148 0.000 NA
#> GSM148525 2 0.590 0.4678 0.000 0.584 0.268 0.000 NA
#> GSM148526 2 0.475 0.6860 0.000 0.728 0.172 0.000 NA
#> GSM148527 2 0.520 0.6860 0.000 0.688 0.164 0.000 NA
#> GSM148528 2 0.480 0.6792 0.000 0.720 0.184 0.000 NA
#> GSM148529 2 0.537 0.6769 0.000 0.668 0.180 0.000 NA
#> GSM148530 2 0.548 0.6800 0.000 0.656 0.172 0.000 NA
#> GSM148531 2 0.558 0.6672 0.000 0.640 0.208 0.000 NA
#> GSM148532 2 0.554 0.6580 0.000 0.644 0.212 0.000 NA
#> GSM148533 2 0.417 0.7077 0.000 0.784 0.112 0.000 NA
#> GSM148534 2 0.503 0.6839 0.000 0.704 0.168 0.000 NA
#> GSM148535 2 0.454 0.6848 0.000 0.752 0.136 0.000 NA
#> GSM148536 2 0.555 0.6262 0.000 0.644 0.204 0.000 NA
#> GSM148537 2 0.473 0.6642 0.000 0.732 0.160 0.000 NA
#> GSM148538 2 0.541 0.6879 0.000 0.664 0.156 0.000 NA
#> GSM148539 3 0.584 0.6101 0.020 0.260 0.636 0.004 NA
#> GSM148540 3 0.557 0.6538 0.024 0.160 0.716 0.016 NA
#> GSM148541 3 0.523 0.6584 0.012 0.164 0.728 0.012 NA
#> GSM148542 3 0.781 0.5463 0.036 0.192 0.520 0.056 NA
#> GSM148543 3 0.524 0.6468 0.020 0.188 0.720 0.008 NA
#> GSM148544 3 0.639 0.6339 0.012 0.180 0.644 0.036 NA
#> GSM148545 1 0.514 0.5065 0.708 0.000 0.008 0.104 NA
#> GSM148546 1 0.408 0.5446 0.804 0.000 0.008 0.108 NA
#> GSM148547 1 0.478 0.5296 0.748 0.000 0.008 0.124 NA
#> GSM148548 1 0.605 0.5043 0.640 0.000 0.024 0.152 NA
#> GSM148549 1 0.643 0.4474 0.572 0.000 0.020 0.252 NA
#> GSM148550 1 0.630 0.4134 0.556 0.000 0.012 0.292 NA
#> GSM148551 1 0.660 0.3510 0.524 0.000 0.020 0.308 NA
#> GSM148552 1 0.595 0.4936 0.656 0.004 0.024 0.112 NA
#> GSM148553 1 0.671 0.4496 0.576 0.000 0.056 0.120 NA
#> GSM148554 1 0.542 0.5192 0.696 0.000 0.016 0.168 NA
#> GSM148555 1 0.659 0.3751 0.500 0.000 0.012 0.324 NA
#> GSM148556 1 0.628 0.3868 0.540 0.000 0.008 0.312 NA
#> GSM148557 1 0.634 0.2272 0.488 0.000 0.008 0.376 NA
#> GSM148558 4 0.624 -0.0244 0.376 0.000 0.000 0.476 NA
#> GSM148559 1 0.740 0.2247 0.448 0.004 0.032 0.248 NA
#> GSM148560 4 0.698 0.0445 0.376 0.000 0.012 0.388 NA
#> GSM148561 4 0.664 0.4525 0.132 0.000 0.044 0.576 NA
#> GSM148562 4 0.593 0.4786 0.180 0.000 0.036 0.664 NA
#> GSM148563 4 0.465 0.5542 0.156 0.000 0.004 0.748 NA
#> GSM148564 4 0.528 0.5409 0.116 0.000 0.020 0.716 NA
#> GSM148565 4 0.477 0.5672 0.108 0.000 0.028 0.768 NA
#> GSM148566 4 0.690 0.0581 0.380 0.000 0.012 0.404 NA
#> GSM148567 4 0.612 0.5128 0.172 0.000 0.024 0.632 NA
#> GSM148568 4 0.622 0.5123 0.156 0.000 0.040 0.640 NA
#> GSM148569 4 0.572 0.5097 0.168 0.000 0.028 0.680 NA
#> GSM148570 4 0.445 0.5780 0.136 0.000 0.004 0.768 NA
#> GSM148571 4 0.395 0.5678 0.112 0.000 0.008 0.812 NA
#> GSM148572 4 0.386 0.5766 0.096 0.000 0.004 0.816 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM148516 3 0.635 0.5283 0.012 0.196 0.564 0.004 0.028 NA
#> GSM148517 1 0.651 0.4076 0.600 0.000 0.028 0.164 0.132 NA
#> GSM148518 2 0.432 0.6456 0.000 0.724 0.080 0.000 0.004 NA
#> GSM148519 2 0.356 0.6683 0.000 0.780 0.044 0.000 0.000 NA
#> GSM148520 2 0.562 0.5849 0.000 0.512 0.076 0.000 0.028 NA
#> GSM148521 2 0.554 0.6128 0.000 0.568 0.076 0.000 0.032 NA
#> GSM148522 2 0.399 0.6624 0.004 0.752 0.044 0.000 0.004 NA
#> GSM148523 2 0.536 0.6197 0.000 0.636 0.084 0.000 0.036 NA
#> GSM148524 2 0.483 0.6371 0.000 0.656 0.080 0.000 0.008 NA
#> GSM148525 2 0.585 0.5017 0.000 0.560 0.200 0.000 0.016 NA
#> GSM148526 2 0.484 0.6290 0.000 0.660 0.064 0.000 0.016 NA
#> GSM148527 2 0.446 0.6334 0.000 0.688 0.064 0.000 0.004 NA
#> GSM148528 2 0.507 0.6279 0.000 0.604 0.080 0.000 0.008 NA
#> GSM148529 2 0.467 0.6502 0.000 0.648 0.040 0.000 0.016 NA
#> GSM148530 2 0.566 0.5994 0.000 0.568 0.100 0.000 0.028 NA
#> GSM148531 2 0.524 0.6263 0.000 0.612 0.080 0.000 0.020 NA
#> GSM148532 2 0.522 0.5683 0.000 0.552 0.108 0.000 0.000 NA
#> GSM148533 2 0.473 0.6478 0.000 0.648 0.072 0.000 0.004 NA
#> GSM148534 2 0.465 0.6468 0.000 0.688 0.080 0.000 0.008 NA
#> GSM148535 2 0.467 0.6286 0.000 0.676 0.072 0.000 0.008 NA
#> GSM148536 2 0.573 0.6036 0.000 0.540 0.116 0.000 0.020 NA
#> GSM148537 2 0.508 0.6174 0.000 0.680 0.116 0.000 0.024 NA
#> GSM148538 2 0.493 0.6591 0.000 0.668 0.060 0.000 0.028 NA
#> GSM148539 3 0.689 0.5287 0.012 0.208 0.520 0.008 0.052 NA
#> GSM148540 3 0.658 0.5996 0.044 0.116 0.604 0.012 0.036 NA
#> GSM148541 3 0.514 0.6290 0.008 0.112 0.724 0.004 0.048 NA
#> GSM148542 3 0.792 0.5022 0.036 0.184 0.492 0.040 0.092 NA
#> GSM148543 3 0.589 0.6015 0.000 0.144 0.628 0.016 0.032 NA
#> GSM148544 3 0.710 0.6029 0.012 0.108 0.564 0.044 0.080 NA
#> GSM148545 1 0.523 0.4723 0.720 0.000 0.032 0.096 0.120 NA
#> GSM148546 1 0.427 0.5095 0.784 0.000 0.020 0.060 0.116 NA
#> GSM148547 1 0.449 0.5023 0.760 0.000 0.012 0.080 0.128 NA
#> GSM148548 1 0.631 0.4512 0.552 0.000 0.020 0.100 0.284 NA
#> GSM148549 1 0.702 0.3429 0.416 0.000 0.044 0.124 0.376 NA
#> GSM148550 1 0.694 0.2928 0.404 0.000 0.032 0.228 0.320 NA
#> GSM148551 1 0.726 0.2627 0.392 0.000 0.036 0.212 0.324 NA
#> GSM148552 1 0.679 0.4438 0.548 0.000 0.052 0.060 0.248 NA
#> GSM148553 1 0.711 0.4170 0.536 0.004 0.048 0.092 0.232 NA
#> GSM148554 1 0.579 0.4768 0.632 0.000 0.016 0.112 0.208 NA
#> GSM148555 1 0.699 0.2432 0.368 0.000 0.020 0.264 0.324 NA
#> GSM148556 1 0.762 0.1926 0.340 0.000 0.048 0.296 0.272 NA
#> GSM148557 4 0.683 -0.0422 0.272 0.000 0.016 0.404 0.288 NA
#> GSM148558 4 0.699 0.1961 0.248 0.000 0.036 0.488 0.192 NA
#> GSM148559 1 0.751 0.3499 0.500 0.012 0.040 0.160 0.212 NA
#> GSM148560 1 0.730 0.1924 0.388 0.000 0.028 0.240 0.300 NA
#> GSM148561 4 0.708 0.3651 0.088 0.000 0.064 0.404 0.396 NA
#> GSM148562 4 0.634 0.4781 0.100 0.000 0.036 0.552 0.284 NA
#> GSM148563 4 0.576 0.5256 0.092 0.000 0.024 0.616 0.248 NA
#> GSM148564 4 0.603 0.5266 0.088 0.000 0.040 0.644 0.180 NA
#> GSM148565 4 0.365 0.5830 0.032 0.000 0.020 0.824 0.108 NA
#> GSM148566 1 0.715 0.0784 0.380 0.000 0.032 0.276 0.288 NA
#> GSM148567 4 0.602 0.5267 0.080 0.000 0.036 0.608 0.244 NA
#> GSM148568 4 0.692 0.4209 0.100 0.000 0.068 0.480 0.320 NA
#> GSM148569 4 0.534 0.5368 0.084 0.000 0.032 0.708 0.140 NA
#> GSM148570 4 0.490 0.5541 0.100 0.000 0.012 0.716 0.156 NA
#> GSM148571 4 0.404 0.5785 0.072 0.000 0.012 0.800 0.096 NA
#> GSM148572 4 0.390 0.5766 0.056 0.000 0.020 0.804 0.112 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 agent(p) dose(p) time(p) k
#> MAD:skmeans 57 2.57e-12 1.00e+00 1.000 2
#> MAD:skmeans 45 1.10e-08 2.16e-02 0.626 3
#> MAD:skmeans 47 8.52e-09 1.00e-05 0.904 4
#> MAD:skmeans 41 3.71e-08 2.25e-05 0.905 5
#> MAD:skmeans 38 1.66e-07 6.93e-05 0.847 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 21163 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.927 0.965 0.981 0.5072 0.491 0.491
#> 3 3 0.602 0.890 0.812 0.1975 1.000 1.000
#> 4 4 0.517 0.515 0.754 0.0994 0.900 0.796
#> 5 5 0.531 0.516 0.713 0.0363 0.981 0.951
#> 6 6 0.516 0.506 0.703 0.0228 0.997 0.992
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
#> GSM148516 2 0.0000 0.992 0.000 1.000
#> GSM148517 1 0.5519 0.878 0.872 0.128
#> GSM148518 2 0.0000 0.992 0.000 1.000
#> GSM148519 2 0.0000 0.992 0.000 1.000
#> GSM148520 2 0.0000 0.992 0.000 1.000
#> GSM148521 2 0.0000 0.992 0.000 1.000
#> GSM148522 2 0.0000 0.992 0.000 1.000
#> GSM148523 2 0.0000 0.992 0.000 1.000
#> GSM148524 2 0.0000 0.992 0.000 1.000
#> GSM148525 2 0.0000 0.992 0.000 1.000
#> GSM148526 2 0.0000 0.992 0.000 1.000
#> GSM148527 2 0.0000 0.992 0.000 1.000
#> GSM148528 2 0.0000 0.992 0.000 1.000
#> GSM148529 2 0.0000 0.992 0.000 1.000
#> GSM148530 2 0.0000 0.992 0.000 1.000
#> GSM148531 2 0.0000 0.992 0.000 1.000
#> GSM148532 2 0.0000 0.992 0.000 1.000
#> GSM148533 2 0.0000 0.992 0.000 1.000
#> GSM148534 2 0.0000 0.992 0.000 1.000
#> GSM148535 2 0.0000 0.992 0.000 1.000
#> GSM148536 2 0.0000 0.992 0.000 1.000
#> GSM148537 2 0.0000 0.992 0.000 1.000
#> GSM148538 2 0.0000 0.992 0.000 1.000
#> GSM148539 2 0.0376 0.989 0.004 0.996
#> GSM148540 2 0.0672 0.985 0.008 0.992
#> GSM148541 2 0.0000 0.992 0.000 1.000
#> GSM148542 2 0.0000 0.992 0.000 1.000
#> GSM148543 2 0.0672 0.986 0.008 0.992
#> GSM148544 2 0.6887 0.769 0.184 0.816
#> GSM148545 1 0.0672 0.967 0.992 0.008
#> GSM148546 1 0.0000 0.969 1.000 0.000
#> GSM148547 1 0.5408 0.883 0.876 0.124
#> GSM148548 1 0.0672 0.967 0.992 0.008
#> GSM148549 1 0.0000 0.969 1.000 0.000
#> GSM148550 1 0.0000 0.969 1.000 0.000
#> GSM148551 1 0.0000 0.969 1.000 0.000
#> GSM148552 1 0.7219 0.792 0.800 0.200
#> GSM148553 1 0.3733 0.929 0.928 0.072
#> GSM148554 1 0.0938 0.966 0.988 0.012
#> GSM148555 1 0.0376 0.968 0.996 0.004
#> GSM148556 1 0.0000 0.969 1.000 0.000
#> GSM148557 1 0.0000 0.969 1.000 0.000
#> GSM148558 1 0.1843 0.958 0.972 0.028
#> GSM148559 1 0.6343 0.844 0.840 0.160
#> GSM148560 1 0.0376 0.968 0.996 0.004
#> GSM148561 1 0.2778 0.946 0.952 0.048
#> GSM148562 1 0.0376 0.968 0.996 0.004
#> GSM148563 1 0.0000 0.969 1.000 0.000
#> GSM148564 1 0.0000 0.969 1.000 0.000
#> GSM148565 1 0.0000 0.969 1.000 0.000
#> GSM148566 1 0.0000 0.969 1.000 0.000
#> GSM148567 1 0.4161 0.919 0.916 0.084
#> GSM148568 1 0.0000 0.969 1.000 0.000
#> GSM148569 1 0.0000 0.969 1.000 0.000
#> GSM148570 1 0.0000 0.969 1.000 0.000
#> GSM148571 1 0.0000 0.969 1.000 0.000
#> GSM148572 1 0.0376 0.968 0.996 0.004
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM148516 2 0.6045 0.852 0.000 0.620 NA
#> GSM148517 1 0.7128 0.769 0.620 0.036 NA
#> GSM148518 2 0.6260 0.853 0.000 0.552 NA
#> GSM148519 2 0.5216 0.866 0.000 0.740 NA
#> GSM148520 2 0.5216 0.869 0.000 0.740 NA
#> GSM148521 2 0.4504 0.878 0.000 0.804 NA
#> GSM148522 2 0.2066 0.876 0.000 0.940 NA
#> GSM148523 2 0.6295 0.844 0.000 0.528 NA
#> GSM148524 2 0.2959 0.878 0.000 0.900 NA
#> GSM148525 2 0.6295 0.842 0.000 0.528 NA
#> GSM148526 2 0.3192 0.884 0.000 0.888 NA
#> GSM148527 2 0.2165 0.877 0.000 0.936 NA
#> GSM148528 2 0.3686 0.885 0.000 0.860 NA
#> GSM148529 2 0.1860 0.876 0.000 0.948 NA
#> GSM148530 2 0.2165 0.878 0.000 0.936 NA
#> GSM148531 2 0.4931 0.882 0.000 0.768 NA
#> GSM148532 2 0.6168 0.862 0.000 0.588 NA
#> GSM148533 2 0.5465 0.868 0.000 0.712 NA
#> GSM148534 2 0.3551 0.884 0.000 0.868 NA
#> GSM148535 2 0.6079 0.850 0.000 0.612 NA
#> GSM148536 2 0.5529 0.879 0.000 0.704 NA
#> GSM148537 2 0.5497 0.864 0.000 0.708 NA
#> GSM148538 2 0.5254 0.884 0.000 0.736 NA
#> GSM148539 2 0.3686 0.885 0.000 0.860 NA
#> GSM148540 2 0.3267 0.882 0.000 0.884 NA
#> GSM148541 2 0.5397 0.873 0.000 0.720 NA
#> GSM148542 2 0.6026 0.857 0.000 0.624 NA
#> GSM148543 2 0.4842 0.877 0.000 0.776 NA
#> GSM148544 2 0.8693 0.730 0.108 0.496 NA
#> GSM148545 1 0.4409 0.916 0.824 0.004 NA
#> GSM148546 1 0.1163 0.930 0.972 0.000 NA
#> GSM148547 1 0.5581 0.902 0.788 0.036 NA
#> GSM148548 1 0.3030 0.933 0.904 0.004 NA
#> GSM148549 1 0.1411 0.930 0.964 0.000 NA
#> GSM148550 1 0.0592 0.927 0.988 0.000 NA
#> GSM148551 1 0.3192 0.931 0.888 0.000 NA
#> GSM148552 1 0.5851 0.840 0.792 0.140 NA
#> GSM148553 1 0.4937 0.915 0.824 0.028 NA
#> GSM148554 1 0.4233 0.916 0.836 0.004 NA
#> GSM148555 1 0.3340 0.930 0.880 0.000 NA
#> GSM148556 1 0.0592 0.927 0.988 0.000 NA
#> GSM148557 1 0.2066 0.928 0.940 0.000 NA
#> GSM148558 1 0.4682 0.908 0.804 0.004 NA
#> GSM148559 1 0.5576 0.875 0.812 0.104 NA
#> GSM148560 1 0.1163 0.932 0.972 0.000 NA
#> GSM148561 1 0.2339 0.919 0.940 0.048 NA
#> GSM148562 1 0.0592 0.930 0.988 0.000 NA
#> GSM148563 1 0.1163 0.931 0.972 0.000 NA
#> GSM148564 1 0.1411 0.930 0.964 0.000 NA
#> GSM148565 1 0.0747 0.929 0.984 0.000 NA
#> GSM148566 1 0.1289 0.930 0.968 0.000 NA
#> GSM148567 1 0.5263 0.907 0.824 0.060 NA
#> GSM148568 1 0.3619 0.922 0.864 0.000 NA
#> GSM148569 1 0.4452 0.910 0.808 0.000 NA
#> GSM148570 1 0.1860 0.930 0.948 0.000 NA
#> GSM148571 1 0.4178 0.916 0.828 0.000 NA
#> GSM148572 1 0.2165 0.928 0.936 0.000 NA
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM148516 3 0.5628 0.0274 0.024 0.420 0.556 0.000
#> GSM148517 1 0.2635 0.0000 0.908 0.004 0.016 0.072
#> GSM148518 3 0.5080 0.4630 0.004 0.420 0.576 0.000
#> GSM148519 2 0.4697 -0.0281 0.000 0.644 0.356 0.000
#> GSM148520 2 0.5186 0.2255 0.016 0.640 0.344 0.000
#> GSM148521 2 0.4072 0.3888 0.000 0.748 0.252 0.000
#> GSM148522 2 0.1474 0.4839 0.000 0.948 0.052 0.000
#> GSM148523 3 0.4713 0.5078 0.000 0.360 0.640 0.000
#> GSM148524 2 0.2760 0.4839 0.000 0.872 0.128 0.000
#> GSM148525 3 0.4855 0.4440 0.000 0.400 0.600 0.000
#> GSM148526 2 0.2973 0.4410 0.000 0.856 0.144 0.000
#> GSM148527 2 0.2011 0.4993 0.000 0.920 0.080 0.000
#> GSM148528 2 0.4720 0.3375 0.016 0.720 0.264 0.000
#> GSM148529 2 0.1557 0.4979 0.000 0.944 0.056 0.000
#> GSM148530 2 0.1867 0.4972 0.000 0.928 0.072 0.000
#> GSM148531 2 0.4356 0.2280 0.000 0.708 0.292 0.000
#> GSM148532 3 0.5060 0.3448 0.004 0.412 0.584 0.000
#> GSM148533 2 0.4925 -0.2121 0.000 0.572 0.428 0.000
#> GSM148534 2 0.4364 0.3944 0.016 0.764 0.220 0.000
#> GSM148535 3 0.4955 0.3490 0.000 0.444 0.556 0.000
#> GSM148536 2 0.5364 0.0533 0.016 0.592 0.392 0.000
#> GSM148537 2 0.4907 -0.2090 0.000 0.580 0.420 0.000
#> GSM148538 2 0.4382 0.2197 0.000 0.704 0.296 0.000
#> GSM148539 2 0.3791 0.3994 0.004 0.796 0.200 0.000
#> GSM148540 2 0.3052 0.4641 0.004 0.860 0.136 0.000
#> GSM148541 2 0.4699 0.2244 0.004 0.676 0.320 0.000
#> GSM148542 2 0.5771 -0.1279 0.028 0.512 0.460 0.000
#> GSM148543 2 0.4661 0.3453 0.004 0.708 0.284 0.004
#> GSM148544 2 0.8787 -0.1234 0.164 0.416 0.348 0.072
#> GSM148545 4 0.4917 0.7277 0.336 0.000 0.008 0.656
#> GSM148546 4 0.0779 0.8113 0.016 0.000 0.004 0.980
#> GSM148547 4 0.5237 0.7079 0.356 0.016 0.000 0.628
#> GSM148548 4 0.4126 0.8024 0.216 0.004 0.004 0.776
#> GSM148549 4 0.2281 0.8152 0.096 0.000 0.000 0.904
#> GSM148550 4 0.0188 0.8074 0.000 0.000 0.004 0.996
#> GSM148551 4 0.3837 0.8080 0.224 0.000 0.000 0.776
#> GSM148552 4 0.4965 0.7310 0.100 0.112 0.004 0.784
#> GSM148553 4 0.4458 0.7846 0.208 0.012 0.008 0.772
#> GSM148554 4 0.4331 0.7600 0.288 0.000 0.000 0.712
#> GSM148555 4 0.4608 0.7432 0.304 0.000 0.004 0.692
#> GSM148556 4 0.0188 0.8074 0.000 0.000 0.004 0.996
#> GSM148557 4 0.4122 0.7562 0.236 0.000 0.004 0.760
#> GSM148558 4 0.4898 0.6583 0.416 0.000 0.000 0.584
#> GSM148559 4 0.4469 0.7612 0.112 0.080 0.000 0.808
#> GSM148560 4 0.1022 0.8170 0.032 0.000 0.000 0.968
#> GSM148561 4 0.3301 0.8008 0.044 0.040 0.024 0.892
#> GSM148562 4 0.1305 0.8177 0.036 0.000 0.004 0.960
#> GSM148563 4 0.2480 0.8203 0.088 0.000 0.008 0.904
#> GSM148564 4 0.1109 0.8123 0.028 0.000 0.004 0.968
#> GSM148565 4 0.0657 0.8097 0.012 0.000 0.004 0.984
#> GSM148566 4 0.1978 0.8203 0.068 0.000 0.004 0.928
#> GSM148567 4 0.5139 0.7829 0.196 0.052 0.004 0.748
#> GSM148568 4 0.3402 0.7902 0.164 0.000 0.004 0.832
#> GSM148569 4 0.4830 0.6779 0.392 0.000 0.000 0.608
#> GSM148570 4 0.3257 0.8072 0.152 0.000 0.004 0.844
#> GSM148571 4 0.4277 0.7643 0.280 0.000 0.000 0.720
#> GSM148572 4 0.4155 0.7574 0.240 0.000 0.004 0.756
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM148516 3 0.6810 0.00000 0.000 0.300 0.356 0.344 0.000
#> GSM148517 5 0.3246 0.00000 0.008 0.000 0.184 0.000 0.808
#> GSM148518 4 0.4610 0.44717 0.000 0.388 0.016 0.596 0.000
#> GSM148519 2 0.4613 -0.00926 0.000 0.620 0.020 0.360 0.000
#> GSM148520 2 0.5620 0.24691 0.000 0.612 0.116 0.272 0.000
#> GSM148521 2 0.4998 0.38761 0.000 0.700 0.104 0.196 0.000
#> GSM148522 2 0.1484 0.50229 0.000 0.944 0.008 0.048 0.000
#> GSM148523 4 0.4451 0.49226 0.000 0.340 0.016 0.644 0.000
#> GSM148524 2 0.3146 0.50493 0.000 0.856 0.052 0.092 0.000
#> GSM148525 4 0.4151 0.47188 0.000 0.344 0.004 0.652 0.000
#> GSM148526 2 0.3432 0.45937 0.000 0.828 0.040 0.132 0.000
#> GSM148527 2 0.2144 0.51652 0.000 0.912 0.020 0.068 0.000
#> GSM148528 2 0.5314 0.37008 0.000 0.672 0.136 0.192 0.000
#> GSM148529 2 0.1502 0.51270 0.000 0.940 0.004 0.056 0.000
#> GSM148530 2 0.1809 0.51383 0.000 0.928 0.012 0.060 0.000
#> GSM148531 2 0.4329 0.21402 0.000 0.672 0.016 0.312 0.000
#> GSM148532 4 0.5607 0.26627 0.000 0.380 0.080 0.540 0.000
#> GSM148533 2 0.4610 -0.13841 0.000 0.556 0.012 0.432 0.000
#> GSM148534 2 0.4648 0.43774 0.000 0.740 0.104 0.156 0.000
#> GSM148535 4 0.4242 0.34651 0.000 0.428 0.000 0.572 0.000
#> GSM148536 2 0.5896 0.12367 0.000 0.564 0.128 0.308 0.000
#> GSM148537 2 0.5272 -0.17170 0.000 0.552 0.052 0.396 0.000
#> GSM148538 2 0.4360 0.22462 0.000 0.680 0.020 0.300 0.000
#> GSM148539 2 0.3812 0.40911 0.000 0.772 0.024 0.204 0.000
#> GSM148540 2 0.3651 0.45742 0.000 0.812 0.032 0.152 0.004
#> GSM148541 2 0.5461 0.21620 0.000 0.620 0.096 0.284 0.000
#> GSM148542 4 0.6587 -0.35743 0.000 0.368 0.164 0.460 0.008
#> GSM148543 2 0.4650 0.34825 0.004 0.684 0.032 0.280 0.000
#> GSM148544 2 0.8250 -0.14049 0.072 0.396 0.028 0.328 0.176
#> GSM148545 1 0.4703 0.74834 0.632 0.000 0.028 0.000 0.340
#> GSM148546 1 0.0898 0.80789 0.972 0.000 0.020 0.000 0.008
#> GSM148547 1 0.4874 0.72036 0.588 0.016 0.008 0.000 0.388
#> GSM148548 1 0.4646 0.79314 0.712 0.000 0.060 0.000 0.228
#> GSM148549 1 0.2669 0.81561 0.876 0.000 0.020 0.000 0.104
#> GSM148550 1 0.0290 0.80265 0.992 0.000 0.008 0.000 0.000
#> GSM148551 1 0.3807 0.80973 0.748 0.000 0.012 0.000 0.240
#> GSM148552 1 0.4648 0.75918 0.780 0.100 0.032 0.000 0.088
#> GSM148553 1 0.4185 0.79643 0.752 0.000 0.024 0.008 0.216
#> GSM148554 1 0.3837 0.77366 0.692 0.000 0.000 0.000 0.308
#> GSM148555 1 0.4655 0.74257 0.644 0.000 0.028 0.000 0.328
#> GSM148556 1 0.0290 0.80265 0.992 0.000 0.008 0.000 0.000
#> GSM148557 1 0.3885 0.75539 0.724 0.000 0.008 0.000 0.268
#> GSM148558 1 0.4425 0.67772 0.544 0.000 0.004 0.000 0.452
#> GSM148559 1 0.4360 0.77659 0.800 0.068 0.032 0.000 0.100
#> GSM148560 1 0.1041 0.81173 0.964 0.000 0.004 0.000 0.032
#> GSM148561 1 0.4483 0.67521 0.740 0.024 0.216 0.000 0.020
#> GSM148562 1 0.1408 0.81395 0.948 0.000 0.008 0.000 0.044
#> GSM148563 1 0.3427 0.81720 0.836 0.000 0.056 0.000 0.108
#> GSM148564 1 0.1877 0.80742 0.924 0.000 0.064 0.000 0.012
#> GSM148565 1 0.1168 0.80596 0.960 0.000 0.032 0.000 0.008
#> GSM148566 1 0.2331 0.81594 0.900 0.000 0.020 0.000 0.080
#> GSM148567 1 0.5161 0.79179 0.720 0.024 0.076 0.000 0.180
#> GSM148568 1 0.3812 0.79417 0.800 0.000 0.036 0.004 0.160
#> GSM148569 1 0.4597 0.69755 0.564 0.000 0.012 0.000 0.424
#> GSM148570 1 0.3655 0.80997 0.804 0.000 0.036 0.000 0.160
#> GSM148571 1 0.4206 0.77760 0.696 0.000 0.016 0.000 0.288
#> GSM148572 1 0.4268 0.75623 0.708 0.000 0.024 0.000 0.268
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM148516 3 0.5444 0.00000 0.000 0.208 0.576 0.216 0.000 0.000
#> GSM148517 6 0.4994 0.00000 0.004 0.000 0.096 0.016 0.200 0.684
#> GSM148518 4 0.4301 0.60945 0.000 0.392 0.024 0.584 0.000 0.000
#> GSM148519 2 0.4406 -0.12294 0.000 0.624 0.040 0.336 0.000 0.000
#> GSM148520 2 0.5303 0.25777 0.000 0.596 0.172 0.232 0.000 0.000
#> GSM148521 2 0.4631 0.36684 0.000 0.692 0.140 0.168 0.000 0.000
#> GSM148522 2 0.1296 0.47374 0.000 0.948 0.004 0.044 0.004 0.000
#> GSM148523 4 0.4292 0.64932 0.000 0.340 0.032 0.628 0.000 0.000
#> GSM148524 2 0.2994 0.48378 0.000 0.852 0.064 0.080 0.004 0.000
#> GSM148525 4 0.3852 0.62766 0.000 0.324 0.012 0.664 0.000 0.000
#> GSM148526 2 0.3352 0.41610 0.000 0.820 0.056 0.120 0.004 0.000
#> GSM148527 2 0.2249 0.48950 0.000 0.900 0.032 0.064 0.004 0.000
#> GSM148528 2 0.5051 0.33462 0.000 0.652 0.188 0.156 0.004 0.000
#> GSM148529 2 0.1219 0.49071 0.000 0.948 0.004 0.048 0.000 0.000
#> GSM148530 2 0.1787 0.48568 0.000 0.920 0.008 0.068 0.004 0.000
#> GSM148531 2 0.4074 0.06593 0.000 0.656 0.016 0.324 0.004 0.000
#> GSM148532 4 0.5471 0.31450 0.000 0.380 0.112 0.504 0.004 0.000
#> GSM148533 2 0.4634 -0.26575 0.000 0.556 0.044 0.400 0.000 0.000
#> GSM148534 2 0.4528 0.40732 0.000 0.716 0.148 0.132 0.004 0.000
#> GSM148535 4 0.3950 0.52233 0.000 0.432 0.004 0.564 0.000 0.000
#> GSM148536 2 0.5646 0.07031 0.000 0.548 0.176 0.272 0.004 0.000
#> GSM148537 2 0.4864 -0.32439 0.000 0.552 0.064 0.384 0.000 0.000
#> GSM148538 2 0.4065 0.14752 0.000 0.672 0.028 0.300 0.000 0.000
#> GSM148539 2 0.3885 0.35277 0.000 0.756 0.048 0.192 0.004 0.000
#> GSM148540 2 0.3935 0.41303 0.000 0.784 0.048 0.144 0.024 0.000
#> GSM148541 2 0.5762 -0.00772 0.000 0.516 0.112 0.352 0.020 0.000
#> GSM148542 5 0.6721 0.00000 0.000 0.304 0.036 0.204 0.448 0.008
#> GSM148543 2 0.4723 0.33213 0.004 0.684 0.060 0.240 0.012 0.000
#> GSM148544 2 0.7690 -0.12251 0.068 0.400 0.040 0.320 0.008 0.164
#> GSM148545 1 0.4538 0.74833 0.612 0.000 0.000 0.000 0.048 0.340
#> GSM148546 1 0.1666 0.80068 0.936 0.000 0.008 0.000 0.036 0.020
#> GSM148547 1 0.4631 0.72801 0.572 0.008 0.008 0.000 0.016 0.396
#> GSM148548 1 0.4380 0.79135 0.700 0.000 0.000 0.000 0.080 0.220
#> GSM148549 1 0.2527 0.80780 0.868 0.000 0.000 0.000 0.024 0.108
#> GSM148550 1 0.0291 0.79130 0.992 0.000 0.004 0.000 0.004 0.000
#> GSM148551 1 0.3558 0.80608 0.736 0.000 0.000 0.000 0.016 0.248
#> GSM148552 1 0.4196 0.76509 0.780 0.100 0.000 0.000 0.036 0.084
#> GSM148553 1 0.4124 0.79625 0.740 0.000 0.008 0.004 0.040 0.208
#> GSM148554 1 0.3482 0.77978 0.684 0.000 0.000 0.000 0.000 0.316
#> GSM148555 1 0.4453 0.73831 0.624 0.000 0.000 0.000 0.044 0.332
#> GSM148556 1 0.0291 0.79130 0.992 0.000 0.004 0.000 0.004 0.000
#> GSM148557 1 0.3586 0.75331 0.712 0.000 0.004 0.000 0.004 0.280
#> GSM148558 1 0.3989 0.68749 0.528 0.000 0.004 0.000 0.000 0.468
#> GSM148559 1 0.4547 0.76977 0.784 0.060 0.012 0.008 0.056 0.080
#> GSM148560 1 0.1829 0.79648 0.928 0.000 0.028 0.000 0.008 0.036
#> GSM148561 1 0.6626 0.41814 0.572 0.024 0.076 0.060 0.252 0.016
#> GSM148562 1 0.1340 0.80416 0.948 0.000 0.004 0.000 0.008 0.040
#> GSM148563 1 0.3953 0.80183 0.792 0.000 0.012 0.004 0.084 0.108
#> GSM148564 1 0.2001 0.80020 0.912 0.000 0.008 0.000 0.068 0.012
#> GSM148565 1 0.1976 0.79237 0.924 0.000 0.032 0.004 0.032 0.008
#> GSM148566 1 0.2617 0.80491 0.884 0.000 0.012 0.008 0.016 0.080
#> GSM148567 1 0.4969 0.78107 0.692 0.024 0.000 0.000 0.108 0.176
#> GSM148568 1 0.3595 0.79627 0.796 0.000 0.012 0.000 0.036 0.156
#> GSM148569 1 0.4377 0.70298 0.540 0.000 0.000 0.000 0.024 0.436
#> GSM148570 1 0.4334 0.79109 0.752 0.000 0.028 0.000 0.060 0.160
#> GSM148571 1 0.4302 0.78306 0.684 0.000 0.016 0.000 0.024 0.276
#> GSM148572 1 0.4505 0.74884 0.676 0.000 0.020 0.000 0.032 0.272
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) dose(p) time(p) k
#> MAD:pam 57 2.57e-12 1.000 1.000 2
#> MAD:pam 57 2.57e-12 1.000 1.000 3
#> MAD:pam 29 9.42e-03 0.437 0.547 4
#> MAD:pam 33 4.03e-07 0.207 0.682 5
#> MAD:pam 31 1.85e-06 0.627 0.557 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 21163 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.781 0.895 0.950 0.4948 0.491 0.491
#> 3 3 0.642 0.895 0.866 0.2482 0.908 0.812
#> 4 4 0.819 0.842 0.900 0.1531 0.872 0.680
#> 5 5 0.832 0.786 0.824 0.0630 1.000 1.000
#> 6 6 0.777 0.755 0.822 0.0411 0.935 0.765
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
#> GSM148516 2 0.9661 0.500 0.392 0.608
#> GSM148517 1 0.0000 1.000 1.000 0.000
#> GSM148518 2 0.0938 0.883 0.012 0.988
#> GSM148519 2 0.0000 0.888 0.000 1.000
#> GSM148520 2 0.0000 0.888 0.000 1.000
#> GSM148521 2 0.0000 0.888 0.000 1.000
#> GSM148522 2 0.0000 0.888 0.000 1.000
#> GSM148523 2 0.0000 0.888 0.000 1.000
#> GSM148524 2 0.0000 0.888 0.000 1.000
#> GSM148525 2 0.0672 0.885 0.008 0.992
#> GSM148526 2 0.0376 0.887 0.004 0.996
#> GSM148527 2 0.0000 0.888 0.000 1.000
#> GSM148528 2 0.0000 0.888 0.000 1.000
#> GSM148529 2 0.0000 0.888 0.000 1.000
#> GSM148530 2 0.0376 0.887 0.004 0.996
#> GSM148531 2 0.0000 0.888 0.000 1.000
#> GSM148532 2 0.0000 0.888 0.000 1.000
#> GSM148533 2 0.0000 0.888 0.000 1.000
#> GSM148534 2 0.0000 0.888 0.000 1.000
#> GSM148535 2 0.0000 0.888 0.000 1.000
#> GSM148536 2 0.0000 0.888 0.000 1.000
#> GSM148537 2 0.0672 0.885 0.008 0.992
#> GSM148538 2 0.1633 0.876 0.024 0.976
#> GSM148539 2 0.9635 0.505 0.388 0.612
#> GSM148540 2 0.9710 0.486 0.400 0.600
#> GSM148541 2 0.9732 0.478 0.404 0.596
#> GSM148542 2 0.9732 0.478 0.404 0.596
#> GSM148543 2 0.9732 0.478 0.404 0.596
#> GSM148544 2 0.9732 0.478 0.404 0.596
#> GSM148545 1 0.0000 1.000 1.000 0.000
#> GSM148546 1 0.0000 1.000 1.000 0.000
#> GSM148547 1 0.0000 1.000 1.000 0.000
#> GSM148548 1 0.0000 1.000 1.000 0.000
#> GSM148549 1 0.0000 1.000 1.000 0.000
#> GSM148550 1 0.0000 1.000 1.000 0.000
#> GSM148551 1 0.0000 1.000 1.000 0.000
#> GSM148552 1 0.0000 1.000 1.000 0.000
#> GSM148553 1 0.0000 1.000 1.000 0.000
#> GSM148554 1 0.0000 1.000 1.000 0.000
#> GSM148555 1 0.0000 1.000 1.000 0.000
#> GSM148556 1 0.0000 1.000 1.000 0.000
#> GSM148557 1 0.0000 1.000 1.000 0.000
#> GSM148558 1 0.0000 1.000 1.000 0.000
#> GSM148559 1 0.0000 1.000 1.000 0.000
#> GSM148560 1 0.0000 1.000 1.000 0.000
#> GSM148561 1 0.0000 1.000 1.000 0.000
#> GSM148562 1 0.0000 1.000 1.000 0.000
#> GSM148563 1 0.0000 1.000 1.000 0.000
#> GSM148564 1 0.0000 1.000 1.000 0.000
#> GSM148565 1 0.0000 1.000 1.000 0.000
#> GSM148566 1 0.0000 1.000 1.000 0.000
#> GSM148567 1 0.0000 1.000 1.000 0.000
#> GSM148568 1 0.0000 1.000 1.000 0.000
#> GSM148569 1 0.0000 1.000 1.000 0.000
#> GSM148570 1 0.0000 1.000 1.000 0.000
#> GSM148571 1 0.0000 1.000 1.000 0.000
#> GSM148572 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
#> GSM148516 3 0.6414 0.985 0.036 0.248 0.716
#> GSM148517 1 0.6111 0.793 0.604 0.000 0.396
#> GSM148518 2 0.1289 0.960 0.000 0.968 0.032
#> GSM148519 2 0.0000 0.990 0.000 1.000 0.000
#> GSM148520 2 0.0000 0.990 0.000 1.000 0.000
#> GSM148521 2 0.0000 0.990 0.000 1.000 0.000
#> GSM148522 2 0.0000 0.990 0.000 1.000 0.000
#> GSM148523 2 0.0237 0.989 0.000 0.996 0.004
#> GSM148524 2 0.0000 0.990 0.000 1.000 0.000
#> GSM148525 2 0.1878 0.939 0.004 0.952 0.044
#> GSM148526 2 0.0000 0.990 0.000 1.000 0.000
#> GSM148527 2 0.0000 0.990 0.000 1.000 0.000
#> GSM148528 2 0.0000 0.990 0.000 1.000 0.000
#> GSM148529 2 0.0237 0.988 0.000 0.996 0.004
#> GSM148530 2 0.0237 0.988 0.000 0.996 0.004
#> GSM148531 2 0.0000 0.990 0.000 1.000 0.000
#> GSM148532 2 0.0237 0.989 0.000 0.996 0.004
#> GSM148533 2 0.0592 0.983 0.000 0.988 0.012
#> GSM148534 2 0.0000 0.990 0.000 1.000 0.000
#> GSM148535 2 0.0237 0.989 0.000 0.996 0.004
#> GSM148536 2 0.0237 0.988 0.000 0.996 0.004
#> GSM148537 2 0.0983 0.976 0.004 0.980 0.016
#> GSM148538 2 0.0829 0.978 0.004 0.984 0.012
#> GSM148539 3 0.6601 0.928 0.028 0.296 0.676
#> GSM148540 3 0.6414 0.985 0.036 0.248 0.716
#> GSM148541 3 0.6375 0.987 0.036 0.244 0.720
#> GSM148542 3 0.6375 0.987 0.036 0.244 0.720
#> GSM148543 3 0.6375 0.987 0.036 0.244 0.720
#> GSM148544 3 0.6375 0.987 0.036 0.244 0.720
#> GSM148545 1 0.6126 0.790 0.600 0.000 0.400
#> GSM148546 1 0.6045 0.799 0.620 0.000 0.380
#> GSM148547 1 0.6062 0.797 0.616 0.000 0.384
#> GSM148548 1 0.5431 0.831 0.716 0.000 0.284
#> GSM148549 1 0.5216 0.834 0.740 0.000 0.260
#> GSM148550 1 0.5098 0.835 0.752 0.000 0.248
#> GSM148551 1 0.4796 0.834 0.780 0.000 0.220
#> GSM148552 1 0.6095 0.796 0.608 0.000 0.392
#> GSM148553 1 0.6062 0.799 0.616 0.000 0.384
#> GSM148554 1 0.5905 0.811 0.648 0.000 0.352
#> GSM148555 1 0.5058 0.835 0.756 0.000 0.244
#> GSM148556 1 0.5058 0.838 0.756 0.000 0.244
#> GSM148557 1 0.5058 0.835 0.756 0.000 0.244
#> GSM148558 1 0.4750 0.833 0.784 0.000 0.216
#> GSM148559 1 0.5465 0.809 0.712 0.000 0.288
#> GSM148560 1 0.5431 0.809 0.716 0.000 0.284
#> GSM148561 1 0.2537 0.814 0.920 0.000 0.080
#> GSM148562 1 0.0747 0.810 0.984 0.000 0.016
#> GSM148563 1 0.0892 0.800 0.980 0.000 0.020
#> GSM148564 1 0.1031 0.804 0.976 0.000 0.024
#> GSM148565 1 0.1529 0.789 0.960 0.000 0.040
#> GSM148566 1 0.5254 0.814 0.736 0.000 0.264
#> GSM148567 1 0.1860 0.813 0.948 0.000 0.052
#> GSM148568 1 0.1753 0.818 0.952 0.000 0.048
#> GSM148569 1 0.0592 0.806 0.988 0.000 0.012
#> GSM148570 1 0.1289 0.801 0.968 0.000 0.032
#> GSM148571 1 0.1529 0.789 0.960 0.000 0.040
#> GSM148572 1 0.1529 0.791 0.960 0.000 0.040
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM148516 3 0.2125 0.948 0.012 0.052 0.932 0.004
#> GSM148517 1 0.0804 0.785 0.980 0.000 0.008 0.012
#> GSM148518 2 0.0657 0.985 0.004 0.984 0.012 0.000
#> GSM148519 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM148520 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM148521 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM148522 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM148523 2 0.0188 0.995 0.000 0.996 0.004 0.000
#> GSM148524 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM148525 2 0.0895 0.977 0.000 0.976 0.020 0.004
#> GSM148526 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM148527 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM148528 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM148529 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM148530 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM148531 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM148532 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM148533 2 0.0188 0.995 0.000 0.996 0.004 0.000
#> GSM148534 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM148535 2 0.0188 0.995 0.000 0.996 0.004 0.000
#> GSM148536 2 0.0188 0.994 0.000 0.996 0.004 0.000
#> GSM148537 2 0.0336 0.992 0.000 0.992 0.008 0.000
#> GSM148538 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM148539 3 0.3529 0.839 0.012 0.152 0.836 0.000
#> GSM148540 3 0.1471 0.967 0.012 0.024 0.960 0.004
#> GSM148541 3 0.1471 0.967 0.012 0.024 0.960 0.004
#> GSM148542 3 0.1471 0.967 0.012 0.024 0.960 0.004
#> GSM148543 3 0.1471 0.967 0.012 0.024 0.960 0.004
#> GSM148544 3 0.1471 0.967 0.012 0.024 0.960 0.004
#> GSM148545 1 0.0804 0.785 0.980 0.000 0.008 0.012
#> GSM148546 1 0.1042 0.789 0.972 0.000 0.008 0.020
#> GSM148547 1 0.1151 0.789 0.968 0.000 0.008 0.024
#> GSM148548 1 0.3718 0.748 0.820 0.000 0.012 0.168
#> GSM148549 1 0.4978 0.602 0.664 0.000 0.012 0.324
#> GSM148550 1 0.4820 0.643 0.692 0.000 0.012 0.296
#> GSM148551 1 0.5112 0.465 0.608 0.000 0.008 0.384
#> GSM148552 1 0.1042 0.789 0.972 0.000 0.008 0.020
#> GSM148553 1 0.1356 0.791 0.960 0.000 0.008 0.032
#> GSM148554 1 0.2124 0.788 0.924 0.000 0.008 0.068
#> GSM148555 1 0.5130 0.587 0.652 0.000 0.016 0.332
#> GSM148556 1 0.4795 0.648 0.696 0.000 0.012 0.292
#> GSM148557 1 0.5018 0.592 0.656 0.000 0.012 0.332
#> GSM148558 4 0.5636 0.113 0.424 0.000 0.024 0.552
#> GSM148559 1 0.2060 0.756 0.932 0.000 0.016 0.052
#> GSM148560 1 0.2775 0.750 0.896 0.000 0.020 0.084
#> GSM148561 4 0.4844 0.657 0.300 0.000 0.012 0.688
#> GSM148562 4 0.3681 0.774 0.176 0.000 0.008 0.816
#> GSM148563 4 0.2060 0.799 0.052 0.000 0.016 0.932
#> GSM148564 4 0.3105 0.798 0.140 0.000 0.004 0.856
#> GSM148565 4 0.0779 0.780 0.004 0.000 0.016 0.980
#> GSM148566 1 0.3900 0.717 0.816 0.000 0.020 0.164
#> GSM148567 4 0.4453 0.713 0.244 0.000 0.012 0.744
#> GSM148568 4 0.4663 0.676 0.272 0.000 0.012 0.716
#> GSM148569 4 0.3052 0.797 0.136 0.000 0.004 0.860
#> GSM148570 4 0.1284 0.791 0.024 0.000 0.012 0.964
#> GSM148571 4 0.0592 0.777 0.000 0.000 0.016 0.984
#> GSM148572 4 0.0469 0.778 0.000 0.000 0.012 0.988
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM148516 3 0.1568 0.941 0.000 0.036 0.944 0.000 0.020
#> GSM148517 1 0.2536 0.635 0.868 0.000 0.004 0.000 0.128
#> GSM148518 2 0.1942 0.946 0.000 0.920 0.012 0.000 0.068
#> GSM148519 2 0.0404 0.982 0.000 0.988 0.000 0.000 0.012
#> GSM148520 2 0.1041 0.978 0.000 0.964 0.004 0.000 0.032
#> GSM148521 2 0.0290 0.982 0.000 0.992 0.000 0.000 0.008
#> GSM148522 2 0.0404 0.982 0.000 0.988 0.000 0.000 0.012
#> GSM148523 2 0.0290 0.981 0.000 0.992 0.008 0.000 0.000
#> GSM148524 2 0.0703 0.980 0.000 0.976 0.000 0.000 0.024
#> GSM148525 2 0.1965 0.950 0.000 0.924 0.024 0.000 0.052
#> GSM148526 2 0.0963 0.979 0.000 0.964 0.000 0.000 0.036
#> GSM148527 2 0.0880 0.980 0.000 0.968 0.000 0.000 0.032
#> GSM148528 2 0.0290 0.982 0.000 0.992 0.000 0.000 0.008
#> GSM148529 2 0.0955 0.977 0.000 0.968 0.004 0.000 0.028
#> GSM148530 2 0.0162 0.982 0.000 0.996 0.000 0.000 0.004
#> GSM148531 2 0.0162 0.982 0.000 0.996 0.000 0.000 0.004
#> GSM148532 2 0.0880 0.975 0.000 0.968 0.000 0.000 0.032
#> GSM148533 2 0.0992 0.977 0.000 0.968 0.008 0.000 0.024
#> GSM148534 2 0.0404 0.982 0.000 0.988 0.000 0.000 0.012
#> GSM148535 2 0.0771 0.978 0.000 0.976 0.004 0.000 0.020
#> GSM148536 2 0.0898 0.980 0.000 0.972 0.008 0.000 0.020
#> GSM148537 2 0.0912 0.978 0.000 0.972 0.012 0.000 0.016
#> GSM148538 2 0.0404 0.982 0.000 0.988 0.000 0.000 0.012
#> GSM148539 3 0.3400 0.813 0.000 0.136 0.828 0.000 0.036
#> GSM148540 3 0.1018 0.955 0.000 0.016 0.968 0.000 0.016
#> GSM148541 3 0.0898 0.952 0.000 0.008 0.972 0.000 0.020
#> GSM148542 3 0.0290 0.954 0.000 0.008 0.992 0.000 0.000
#> GSM148543 3 0.0566 0.955 0.000 0.012 0.984 0.000 0.004
#> GSM148544 3 0.0613 0.953 0.000 0.008 0.984 0.004 0.004
#> GSM148545 1 0.2233 0.644 0.892 0.000 0.004 0.000 0.104
#> GSM148546 1 0.1956 0.654 0.916 0.000 0.000 0.008 0.076
#> GSM148547 1 0.1956 0.654 0.916 0.000 0.000 0.008 0.076
#> GSM148548 1 0.5338 0.618 0.700 0.000 0.012 0.160 0.128
#> GSM148549 1 0.6981 0.458 0.456 0.000 0.016 0.296 0.232
#> GSM148550 1 0.6845 0.512 0.496 0.000 0.016 0.256 0.232
#> GSM148551 1 0.7052 0.374 0.416 0.000 0.016 0.340 0.228
#> GSM148552 1 0.1924 0.664 0.924 0.000 0.008 0.004 0.064
#> GSM148553 1 0.1617 0.671 0.948 0.000 0.012 0.020 0.020
#> GSM148554 1 0.3749 0.666 0.828 0.000 0.012 0.052 0.108
#> GSM148555 1 0.7028 0.470 0.448 0.000 0.016 0.280 0.256
#> GSM148556 1 0.6741 0.522 0.512 0.000 0.016 0.272 0.200
#> GSM148557 1 0.7043 0.463 0.444 0.000 0.016 0.276 0.264
#> GSM148558 4 0.7143 -0.110 0.316 0.000 0.016 0.400 0.268
#> GSM148559 1 0.4474 0.524 0.652 0.000 0.004 0.012 0.332
#> GSM148560 1 0.5016 0.530 0.616 0.000 0.004 0.036 0.344
#> GSM148561 4 0.4991 0.678 0.092 0.000 0.008 0.720 0.180
#> GSM148562 4 0.2291 0.779 0.036 0.000 0.000 0.908 0.056
#> GSM148563 4 0.2351 0.794 0.016 0.000 0.000 0.896 0.088
#> GSM148564 4 0.2144 0.791 0.020 0.000 0.000 0.912 0.068
#> GSM148565 4 0.2890 0.772 0.004 0.000 0.000 0.836 0.160
#> GSM148566 1 0.6379 0.462 0.504 0.000 0.004 0.160 0.332
#> GSM148567 4 0.3821 0.733 0.052 0.000 0.000 0.800 0.148
#> GSM148568 4 0.4372 0.699 0.072 0.000 0.000 0.756 0.172
#> GSM148569 4 0.1498 0.790 0.024 0.000 0.008 0.952 0.016
#> GSM148570 4 0.2798 0.781 0.008 0.000 0.000 0.852 0.140
#> GSM148571 4 0.2891 0.762 0.000 0.000 0.000 0.824 0.176
#> GSM148572 4 0.2813 0.766 0.000 0.000 0.000 0.832 0.168
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM148516 3 0.2455 0.911 0.016 0.016 0.888 0.000 0.080 0.000
#> GSM148517 6 0.2136 0.552 0.048 0.000 0.000 0.000 0.048 0.904
#> GSM148518 2 0.2362 0.919 0.000 0.860 0.000 0.000 0.136 0.004
#> GSM148519 2 0.1007 0.957 0.000 0.956 0.000 0.000 0.044 0.000
#> GSM148520 2 0.1745 0.947 0.000 0.920 0.012 0.000 0.068 0.000
#> GSM148521 2 0.0858 0.956 0.000 0.968 0.004 0.000 0.028 0.000
#> GSM148522 2 0.0858 0.957 0.000 0.968 0.004 0.000 0.028 0.000
#> GSM148523 2 0.0790 0.957 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM148524 2 0.1141 0.956 0.000 0.948 0.000 0.000 0.052 0.000
#> GSM148525 2 0.2531 0.909 0.000 0.856 0.012 0.000 0.132 0.000
#> GSM148526 2 0.1588 0.948 0.000 0.924 0.004 0.000 0.072 0.000
#> GSM148527 2 0.0937 0.958 0.000 0.960 0.000 0.000 0.040 0.000
#> GSM148528 2 0.1010 0.956 0.000 0.960 0.000 0.000 0.036 0.004
#> GSM148529 2 0.1701 0.944 0.000 0.920 0.008 0.000 0.072 0.000
#> GSM148530 2 0.1010 0.957 0.000 0.960 0.004 0.000 0.036 0.000
#> GSM148531 2 0.1285 0.955 0.000 0.944 0.004 0.000 0.052 0.000
#> GSM148532 2 0.1765 0.938 0.000 0.904 0.000 0.000 0.096 0.000
#> GSM148533 2 0.1588 0.950 0.000 0.924 0.004 0.000 0.072 0.000
#> GSM148534 2 0.1531 0.952 0.000 0.928 0.000 0.000 0.068 0.004
#> GSM148535 2 0.1327 0.953 0.000 0.936 0.000 0.000 0.064 0.000
#> GSM148536 2 0.1075 0.955 0.000 0.952 0.000 0.000 0.048 0.000
#> GSM148537 2 0.1644 0.949 0.000 0.920 0.004 0.000 0.076 0.000
#> GSM148538 2 0.1349 0.954 0.000 0.940 0.004 0.000 0.056 0.000
#> GSM148539 3 0.3270 0.797 0.000 0.120 0.820 0.000 0.060 0.000
#> GSM148540 3 0.1679 0.927 0.016 0.012 0.936 0.000 0.036 0.000
#> GSM148541 3 0.1657 0.918 0.016 0.000 0.928 0.000 0.056 0.000
#> GSM148542 3 0.0725 0.928 0.000 0.012 0.976 0.000 0.012 0.000
#> GSM148543 3 0.1074 0.926 0.000 0.012 0.960 0.000 0.028 0.000
#> GSM148544 3 0.1151 0.925 0.000 0.012 0.956 0.000 0.032 0.000
#> GSM148545 6 0.1657 0.590 0.056 0.000 0.000 0.000 0.016 0.928
#> GSM148546 6 0.2312 0.593 0.112 0.000 0.000 0.000 0.012 0.876
#> GSM148547 6 0.2070 0.601 0.100 0.000 0.000 0.000 0.008 0.892
#> GSM148548 1 0.4306 0.470 0.700 0.000 0.000 0.044 0.008 0.248
#> GSM148549 1 0.3184 0.646 0.832 0.000 0.004 0.132 0.008 0.024
#> GSM148550 1 0.2814 0.669 0.864 0.000 0.000 0.080 0.004 0.052
#> GSM148551 1 0.4073 0.568 0.724 0.000 0.004 0.240 0.020 0.012
#> GSM148552 6 0.4648 0.290 0.340 0.000 0.000 0.000 0.056 0.604
#> GSM148553 6 0.4434 0.232 0.428 0.000 0.000 0.000 0.028 0.544
#> GSM148554 1 0.4601 -0.106 0.556 0.000 0.000 0.004 0.032 0.408
#> GSM148555 1 0.2795 0.669 0.864 0.000 0.004 0.100 0.004 0.028
#> GSM148556 1 0.3095 0.657 0.856 0.000 0.000 0.072 0.020 0.052
#> GSM148557 1 0.2812 0.658 0.860 0.000 0.000 0.104 0.008 0.028
#> GSM148558 1 0.4828 0.487 0.640 0.000 0.000 0.276 0.080 0.004
#> GSM148559 5 0.5709 0.593 0.108 0.000 0.004 0.008 0.456 0.424
#> GSM148560 5 0.6242 0.633 0.264 0.000 0.000 0.008 0.416 0.312
#> GSM148561 4 0.5815 0.701 0.148 0.000 0.016 0.644 0.156 0.036
#> GSM148562 4 0.3349 0.802 0.164 0.000 0.008 0.804 0.024 0.000
#> GSM148563 4 0.2631 0.820 0.076 0.000 0.004 0.876 0.044 0.000
#> GSM148564 4 0.3017 0.819 0.108 0.000 0.000 0.840 0.052 0.000
#> GSM148565 4 0.2398 0.783 0.020 0.000 0.000 0.876 0.104 0.000
#> GSM148566 1 0.6610 -0.627 0.372 0.000 0.004 0.024 0.372 0.228
#> GSM148567 4 0.4515 0.761 0.160 0.000 0.004 0.716 0.120 0.000
#> GSM148568 4 0.4908 0.725 0.188 0.000 0.004 0.680 0.124 0.004
#> GSM148569 4 0.2730 0.814 0.152 0.000 0.000 0.836 0.012 0.000
#> GSM148570 4 0.2249 0.803 0.032 0.000 0.004 0.900 0.064 0.000
#> GSM148571 4 0.2491 0.772 0.020 0.000 0.000 0.868 0.112 0.000
#> GSM148572 4 0.2573 0.775 0.024 0.000 0.000 0.864 0.112 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) dose(p) time(p) k
#> MAD:mclust 51 8.42e-12 3.28e-01 0.996 2
#> MAD:mclust 57 9.44e-12 6.66e-04 0.995 3
#> MAD:mclust 55 4.28e-10 1.32e-05 0.961 4
#> MAD:mclust 51 2.29e-09 1.36e-05 0.947 5
#> MAD:mclust 51 1.15e-08 3.16e-06 0.863 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 21163 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5093 0.491 0.491
#> 3 3 0.686 0.865 0.851 0.1993 1.000 1.000
#> 4 4 0.557 0.756 0.796 0.1485 0.784 0.560
#> 5 5 0.564 0.743 0.789 0.0772 0.982 0.938
#> 6 6 0.621 0.627 0.739 0.0435 0.993 0.975
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 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
#> GSM148516 2 0 1 0 1
#> GSM148517 1 0 1 1 0
#> GSM148518 2 0 1 0 1
#> GSM148519 2 0 1 0 1
#> GSM148520 2 0 1 0 1
#> GSM148521 2 0 1 0 1
#> GSM148522 2 0 1 0 1
#> GSM148523 2 0 1 0 1
#> GSM148524 2 0 1 0 1
#> GSM148525 2 0 1 0 1
#> GSM148526 2 0 1 0 1
#> GSM148527 2 0 1 0 1
#> GSM148528 2 0 1 0 1
#> GSM148529 2 0 1 0 1
#> GSM148530 2 0 1 0 1
#> GSM148531 2 0 1 0 1
#> GSM148532 2 0 1 0 1
#> GSM148533 2 0 1 0 1
#> GSM148534 2 0 1 0 1
#> GSM148535 2 0 1 0 1
#> GSM148536 2 0 1 0 1
#> GSM148537 2 0 1 0 1
#> GSM148538 2 0 1 0 1
#> GSM148539 2 0 1 0 1
#> GSM148540 2 0 1 0 1
#> GSM148541 2 0 1 0 1
#> GSM148542 2 0 1 0 1
#> GSM148543 2 0 1 0 1
#> GSM148544 2 0 1 0 1
#> GSM148545 1 0 1 1 0
#> GSM148546 1 0 1 1 0
#> GSM148547 1 0 1 1 0
#> GSM148548 1 0 1 1 0
#> GSM148549 1 0 1 1 0
#> GSM148550 1 0 1 1 0
#> GSM148551 1 0 1 1 0
#> GSM148552 1 0 1 1 0
#> GSM148553 1 0 1 1 0
#> GSM148554 1 0 1 1 0
#> GSM148555 1 0 1 1 0
#> GSM148556 1 0 1 1 0
#> GSM148557 1 0 1 1 0
#> GSM148558 1 0 1 1 0
#> GSM148559 1 0 1 1 0
#> GSM148560 1 0 1 1 0
#> GSM148561 1 0 1 1 0
#> GSM148562 1 0 1 1 0
#> GSM148563 1 0 1 1 0
#> GSM148564 1 0 1 1 0
#> GSM148565 1 0 1 1 0
#> GSM148566 1 0 1 1 0
#> GSM148567 1 0 1 1 0
#> GSM148568 1 0 1 1 0
#> GSM148569 1 0 1 1 0
#> GSM148570 1 0 1 1 0
#> GSM148571 1 0 1 1 0
#> GSM148572 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM148516 2 0.661 0.715 0.008 0.560 NA
#> GSM148517 1 0.341 0.863 0.876 0.000 NA
#> GSM148518 2 0.153 0.911 0.000 0.960 NA
#> GSM148519 2 0.129 0.910 0.000 0.968 NA
#> GSM148520 2 0.245 0.905 0.000 0.924 NA
#> GSM148521 2 0.186 0.910 0.000 0.948 NA
#> GSM148522 2 0.186 0.909 0.000 0.948 NA
#> GSM148523 2 0.129 0.911 0.000 0.968 NA
#> GSM148524 2 0.141 0.908 0.000 0.964 NA
#> GSM148525 2 0.254 0.904 0.000 0.920 NA
#> GSM148526 2 0.245 0.909 0.000 0.924 NA
#> GSM148527 2 0.103 0.910 0.000 0.976 NA
#> GSM148528 2 0.103 0.910 0.000 0.976 NA
#> GSM148529 2 0.196 0.903 0.000 0.944 NA
#> GSM148530 2 0.175 0.911 0.000 0.952 NA
#> GSM148531 2 0.153 0.910 0.000 0.960 NA
#> GSM148532 2 0.236 0.908 0.000 0.928 NA
#> GSM148533 2 0.153 0.911 0.000 0.960 NA
#> GSM148534 2 0.175 0.910 0.000 0.952 NA
#> GSM148535 2 0.129 0.910 0.000 0.968 NA
#> GSM148536 2 0.175 0.910 0.000 0.952 NA
#> GSM148537 2 0.186 0.909 0.000 0.948 NA
#> GSM148538 2 0.216 0.906 0.000 0.936 NA
#> GSM148539 2 0.625 0.798 0.016 0.684 NA
#> GSM148540 2 0.615 0.742 0.000 0.592 NA
#> GSM148541 2 0.650 0.690 0.004 0.532 NA
#> GSM148542 2 0.639 0.731 0.004 0.584 NA
#> GSM148543 2 0.633 0.746 0.004 0.600 NA
#> GSM148544 2 0.581 0.785 0.000 0.664 NA
#> GSM148545 1 0.327 0.866 0.884 0.000 NA
#> GSM148546 1 0.304 0.869 0.896 0.000 NA
#> GSM148547 1 0.304 0.870 0.896 0.000 NA
#> GSM148548 1 0.263 0.875 0.916 0.000 NA
#> GSM148549 1 0.216 0.887 0.936 0.000 NA
#> GSM148550 1 0.226 0.884 0.932 0.000 NA
#> GSM148551 1 0.245 0.889 0.924 0.000 NA
#> GSM148552 1 0.520 0.818 0.796 0.020 NA
#> GSM148553 1 0.418 0.843 0.828 0.000 NA
#> GSM148554 1 0.263 0.874 0.916 0.000 NA
#> GSM148555 1 0.254 0.887 0.920 0.000 NA
#> GSM148556 1 0.129 0.888 0.968 0.000 NA
#> GSM148557 1 0.263 0.888 0.916 0.000 NA
#> GSM148558 1 0.271 0.886 0.912 0.000 NA
#> GSM148559 1 0.435 0.855 0.836 0.008 NA
#> GSM148560 1 0.245 0.888 0.924 0.000 NA
#> GSM148561 1 0.583 0.804 0.660 0.000 NA
#> GSM148562 1 0.506 0.862 0.756 0.000 NA
#> GSM148563 1 0.529 0.851 0.732 0.000 NA
#> GSM148564 1 0.525 0.852 0.736 0.000 NA
#> GSM148565 1 0.497 0.859 0.764 0.000 NA
#> GSM148566 1 0.271 0.888 0.912 0.000 NA
#> GSM148567 1 0.562 0.833 0.692 0.000 NA
#> GSM148568 1 0.455 0.869 0.800 0.000 NA
#> GSM148569 1 0.529 0.851 0.732 0.000 NA
#> GSM148570 1 0.550 0.839 0.708 0.000 NA
#> GSM148571 1 0.529 0.848 0.732 0.000 NA
#> GSM148572 1 0.556 0.836 0.700 0.000 NA
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM148516 3 0.631 0.818 0.028 0.268 0.656 0.048
#> GSM148517 1 0.267 0.715 0.908 0.000 0.044 0.048
#> GSM148518 2 0.247 0.856 0.000 0.900 0.096 0.004
#> GSM148519 2 0.180 0.903 0.000 0.944 0.040 0.016
#> GSM148520 2 0.361 0.835 0.000 0.840 0.140 0.020
#> GSM148521 2 0.254 0.894 0.000 0.904 0.084 0.012
#> GSM148522 2 0.172 0.892 0.000 0.944 0.048 0.008
#> GSM148523 2 0.131 0.902 0.000 0.960 0.036 0.004
#> GSM148524 2 0.227 0.894 0.000 0.916 0.076 0.008
#> GSM148525 2 0.458 0.591 0.000 0.748 0.232 0.020
#> GSM148526 2 0.350 0.827 0.000 0.844 0.140 0.016
#> GSM148527 2 0.149 0.903 0.000 0.952 0.044 0.004
#> GSM148528 2 0.271 0.890 0.000 0.900 0.080 0.020
#> GSM148529 2 0.214 0.889 0.000 0.928 0.056 0.016
#> GSM148530 2 0.168 0.903 0.000 0.948 0.040 0.012
#> GSM148531 2 0.131 0.901 0.000 0.960 0.036 0.004
#> GSM148532 2 0.371 0.828 0.000 0.840 0.132 0.028
#> GSM148533 2 0.222 0.874 0.000 0.908 0.092 0.000
#> GSM148534 2 0.180 0.901 0.000 0.944 0.040 0.016
#> GSM148535 2 0.161 0.898 0.000 0.952 0.032 0.016
#> GSM148536 2 0.286 0.883 0.000 0.888 0.096 0.016
#> GSM148537 2 0.177 0.901 0.000 0.944 0.044 0.012
#> GSM148538 2 0.283 0.875 0.000 0.900 0.060 0.040
#> GSM148539 3 0.718 0.667 0.068 0.404 0.500 0.028
#> GSM148540 3 0.584 0.827 0.024 0.248 0.692 0.036
#> GSM148541 3 0.559 0.804 0.020 0.200 0.732 0.048
#> GSM148542 3 0.617 0.809 0.012 0.300 0.636 0.052
#> GSM148543 3 0.734 0.821 0.040 0.292 0.580 0.088
#> GSM148544 3 0.744 0.750 0.024 0.368 0.508 0.100
#> GSM148545 1 0.231 0.726 0.924 0.000 0.032 0.044
#> GSM148546 1 0.198 0.736 0.936 0.000 0.016 0.048
#> GSM148547 1 0.244 0.735 0.916 0.000 0.024 0.060
#> GSM148548 1 0.234 0.737 0.912 0.000 0.008 0.080
#> GSM148549 1 0.568 0.435 0.640 0.000 0.044 0.316
#> GSM148550 1 0.331 0.713 0.840 0.000 0.004 0.156
#> GSM148551 1 0.509 0.425 0.640 0.000 0.012 0.348
#> GSM148552 1 0.309 0.675 0.888 0.000 0.060 0.052
#> GSM148553 1 0.330 0.681 0.876 0.004 0.092 0.028
#> GSM148554 1 0.227 0.738 0.912 0.000 0.004 0.084
#> GSM148555 1 0.445 0.637 0.744 0.000 0.012 0.244
#> GSM148556 1 0.376 0.658 0.784 0.000 0.000 0.216
#> GSM148557 1 0.481 0.496 0.676 0.000 0.008 0.316
#> GSM148558 1 0.550 -0.130 0.520 0.000 0.016 0.464
#> GSM148559 1 0.483 0.669 0.792 0.004 0.084 0.120
#> GSM148560 1 0.514 0.625 0.716 0.000 0.040 0.244
#> GSM148561 4 0.700 0.558 0.264 0.004 0.148 0.584
#> GSM148562 4 0.520 0.792 0.252 0.000 0.040 0.708
#> GSM148563 4 0.440 0.837 0.212 0.000 0.020 0.768
#> GSM148564 4 0.446 0.843 0.208 0.000 0.024 0.768
#> GSM148565 4 0.439 0.833 0.252 0.000 0.008 0.740
#> GSM148566 1 0.515 0.496 0.664 0.000 0.020 0.316
#> GSM148567 4 0.477 0.804 0.256 0.000 0.020 0.724
#> GSM148568 4 0.561 0.602 0.380 0.000 0.028 0.592
#> GSM148569 4 0.419 0.833 0.228 0.000 0.008 0.764
#> GSM148570 4 0.418 0.841 0.200 0.000 0.016 0.784
#> GSM148571 4 0.394 0.842 0.236 0.000 0.000 0.764
#> GSM148572 4 0.416 0.828 0.188 0.000 0.020 0.792
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM148516 3 0.531 0.798 0.020 0.080 0.736 0.016 NA
#> GSM148517 1 0.382 0.718 0.820 0.000 0.020 0.032 NA
#> GSM148518 2 0.308 0.856 0.000 0.860 0.092 0.000 NA
#> GSM148519 2 0.199 0.891 0.000 0.924 0.032 0.000 NA
#> GSM148520 2 0.461 0.795 0.004 0.756 0.116 0.000 NA
#> GSM148521 2 0.327 0.871 0.008 0.860 0.064 0.000 NA
#> GSM148522 2 0.232 0.882 0.008 0.916 0.020 0.004 NA
#> GSM148523 2 0.226 0.883 0.000 0.908 0.028 0.000 NA
#> GSM148524 2 0.267 0.882 0.004 0.892 0.044 0.000 NA
#> GSM148525 2 0.543 0.517 0.000 0.632 0.268 0.000 NA
#> GSM148526 2 0.442 0.803 0.012 0.772 0.156 0.000 NA
#> GSM148527 2 0.175 0.891 0.000 0.936 0.028 0.000 NA
#> GSM148528 2 0.304 0.876 0.000 0.864 0.056 0.000 NA
#> GSM148529 2 0.228 0.889 0.000 0.908 0.032 0.000 NA
#> GSM148530 2 0.144 0.890 0.000 0.948 0.012 0.000 NA
#> GSM148531 2 0.197 0.891 0.004 0.932 0.020 0.004 NA
#> GSM148532 2 0.391 0.814 0.000 0.796 0.144 0.000 NA
#> GSM148533 2 0.279 0.877 0.000 0.880 0.052 0.000 NA
#> GSM148534 2 0.340 0.859 0.000 0.840 0.040 0.004 NA
#> GSM148535 2 0.221 0.884 0.000 0.912 0.032 0.000 NA
#> GSM148536 2 0.292 0.878 0.000 0.872 0.072 0.000 NA
#> GSM148537 2 0.194 0.886 0.000 0.924 0.020 0.000 NA
#> GSM148538 2 0.305 0.878 0.008 0.876 0.024 0.008 NA
#> GSM148539 3 0.681 0.709 0.036 0.228 0.552 0.000 NA
#> GSM148540 3 0.497 0.819 0.008 0.100 0.752 0.012 NA
#> GSM148541 3 0.442 0.806 0.012 0.068 0.808 0.024 NA
#> GSM148542 3 0.632 0.785 0.016 0.120 0.672 0.052 NA
#> GSM148543 3 0.512 0.817 0.008 0.124 0.756 0.036 NA
#> GSM148544 3 0.642 0.772 0.000 0.184 0.636 0.088 NA
#> GSM148545 1 0.282 0.733 0.884 0.000 0.012 0.024 NA
#> GSM148546 1 0.208 0.744 0.928 0.000 0.016 0.032 NA
#> GSM148547 1 0.234 0.744 0.916 0.000 0.020 0.024 NA
#> GSM148548 1 0.331 0.738 0.860 0.000 0.016 0.084 NA
#> GSM148549 1 0.713 0.290 0.480 0.000 0.084 0.344 NA
#> GSM148550 1 0.438 0.663 0.740 0.000 0.008 0.220 NA
#> GSM148551 1 0.685 0.266 0.484 0.000 0.060 0.368 NA
#> GSM148552 1 0.327 0.730 0.860 0.004 0.020 0.016 NA
#> GSM148553 1 0.347 0.720 0.844 0.000 0.048 0.008 NA
#> GSM148554 1 0.282 0.738 0.884 0.000 0.012 0.080 NA
#> GSM148555 1 0.616 0.512 0.580 0.000 0.028 0.304 NA
#> GSM148556 1 0.447 0.636 0.720 0.000 0.008 0.244 NA
#> GSM148557 1 0.569 0.411 0.556 0.000 0.012 0.372 NA
#> GSM148558 4 0.570 0.199 0.376 0.000 0.012 0.552 NA
#> GSM148559 1 0.494 0.669 0.732 0.004 0.016 0.056 NA
#> GSM148560 1 0.520 0.631 0.692 0.000 0.004 0.108 NA
#> GSM148561 4 0.790 0.404 0.152 0.004 0.108 0.436 NA
#> GSM148562 4 0.484 0.745 0.092 0.000 0.048 0.772 NA
#> GSM148563 4 0.436 0.785 0.096 0.000 0.012 0.788 NA
#> GSM148564 4 0.321 0.804 0.092 0.000 0.008 0.860 NA
#> GSM148565 4 0.311 0.800 0.096 0.000 0.008 0.864 NA
#> GSM148566 1 0.508 0.617 0.700 0.000 0.000 0.160 NA
#> GSM148567 4 0.424 0.781 0.108 0.000 0.008 0.792 NA
#> GSM148568 4 0.502 0.674 0.212 0.000 0.004 0.700 NA
#> GSM148569 4 0.263 0.803 0.056 0.000 0.020 0.900 NA
#> GSM148570 4 0.290 0.808 0.064 0.000 0.012 0.884 NA
#> GSM148571 4 0.245 0.805 0.076 0.000 0.000 0.896 NA
#> GSM148572 4 0.258 0.795 0.040 0.000 0.008 0.900 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM148516 3 0.656 0.624 0.012 0.060 0.560 0.004 0.132 NA
#> GSM148517 1 0.557 0.541 0.632 0.000 0.024 0.016 0.244 NA
#> GSM148518 2 0.368 0.844 0.000 0.812 0.064 0.000 0.020 NA
#> GSM148519 2 0.191 0.878 0.000 0.920 0.016 0.000 0.008 NA
#> GSM148520 2 0.488 0.741 0.000 0.672 0.064 0.000 0.024 NA
#> GSM148521 2 0.335 0.868 0.000 0.832 0.040 0.000 0.020 NA
#> GSM148522 2 0.261 0.871 0.000 0.884 0.044 0.000 0.012 NA
#> GSM148523 2 0.256 0.871 0.000 0.880 0.040 0.000 0.004 NA
#> GSM148524 2 0.313 0.868 0.000 0.848 0.032 0.004 0.012 NA
#> GSM148525 2 0.490 0.624 0.000 0.656 0.200 0.000 0.000 NA
#> GSM148526 2 0.391 0.849 0.000 0.792 0.068 0.000 0.020 NA
#> GSM148527 2 0.292 0.878 0.000 0.856 0.052 0.000 0.004 NA
#> GSM148528 2 0.300 0.873 0.000 0.848 0.028 0.000 0.012 NA
#> GSM148529 2 0.261 0.874 0.000 0.864 0.008 0.000 0.012 NA
#> GSM148530 2 0.178 0.880 0.000 0.920 0.016 0.000 0.000 NA
#> GSM148531 2 0.335 0.866 0.000 0.824 0.028 0.000 0.020 NA
#> GSM148532 2 0.453 0.761 0.000 0.700 0.088 0.000 0.004 NA
#> GSM148533 2 0.325 0.862 0.000 0.836 0.060 0.000 0.008 NA
#> GSM148534 2 0.302 0.874 0.000 0.840 0.016 0.000 0.016 NA
#> GSM148535 2 0.224 0.870 0.000 0.900 0.020 0.000 0.008 NA
#> GSM148536 2 0.366 0.854 0.000 0.804 0.060 0.000 0.012 NA
#> GSM148537 2 0.201 0.874 0.000 0.916 0.012 0.000 0.016 NA
#> GSM148538 2 0.304 0.861 0.000 0.828 0.008 0.000 0.016 NA
#> GSM148539 3 0.607 0.599 0.016 0.188 0.604 0.000 0.032 NA
#> GSM148540 3 0.474 0.676 0.000 0.028 0.732 0.012 0.060 NA
#> GSM148541 3 0.454 0.676 0.004 0.016 0.752 0.012 0.060 NA
#> GSM148542 3 0.666 0.607 0.004 0.060 0.580 0.036 0.104 NA
#> GSM148543 3 0.466 0.692 0.012 0.040 0.788 0.040 0.052 NA
#> GSM148544 3 0.590 0.641 0.004 0.064 0.692 0.092 0.068 NA
#> GSM148545 1 0.360 0.629 0.788 0.000 0.000 0.008 0.168 NA
#> GSM148546 1 0.282 0.656 0.880 0.000 0.012 0.020 0.068 NA
#> GSM148547 1 0.301 0.655 0.872 0.000 0.020 0.016 0.064 NA
#> GSM148548 1 0.311 0.656 0.860 0.000 0.000 0.052 0.052 NA
#> GSM148549 1 0.727 0.370 0.508 0.000 0.124 0.208 0.128 NA
#> GSM148550 1 0.484 0.603 0.732 0.000 0.016 0.140 0.092 NA
#> GSM148551 1 0.707 0.289 0.492 0.000 0.052 0.276 0.136 NA
#> GSM148552 1 0.402 0.639 0.792 0.008 0.016 0.000 0.120 NA
#> GSM148553 1 0.445 0.622 0.764 0.004 0.036 0.008 0.148 NA
#> GSM148554 1 0.207 0.660 0.916 0.000 0.000 0.044 0.028 NA
#> GSM148555 1 0.708 0.446 0.548 0.004 0.072 0.164 0.172 NA
#> GSM148556 1 0.453 0.610 0.740 0.000 0.004 0.152 0.088 NA
#> GSM148557 1 0.587 0.312 0.532 0.000 0.016 0.332 0.112 NA
#> GSM148558 4 0.592 0.123 0.368 0.000 0.008 0.504 0.100 NA
#> GSM148559 1 0.609 0.488 0.596 0.004 0.012 0.044 0.248 NA
#> GSM148560 1 0.645 0.192 0.468 0.000 0.012 0.144 0.348 NA
#> GSM148561 5 0.764 0.000 0.096 0.012 0.060 0.352 0.408 NA
#> GSM148562 4 0.575 0.312 0.076 0.000 0.052 0.664 0.180 NA
#> GSM148563 4 0.394 0.517 0.068 0.000 0.008 0.784 0.136 NA
#> GSM148564 4 0.390 0.551 0.036 0.000 0.020 0.808 0.116 NA
#> GSM148565 4 0.358 0.593 0.072 0.000 0.008 0.832 0.068 NA
#> GSM148566 1 0.628 0.249 0.532 0.000 0.008 0.192 0.244 NA
#> GSM148567 4 0.516 0.310 0.072 0.004 0.004 0.680 0.212 NA
#> GSM148568 4 0.568 0.108 0.160 0.000 0.004 0.612 0.204 NA
#> GSM148569 4 0.357 0.598 0.056 0.000 0.020 0.840 0.064 NA
#> GSM148570 4 0.347 0.561 0.052 0.000 0.008 0.836 0.088 NA
#> GSM148571 4 0.179 0.617 0.040 0.000 0.000 0.928 0.028 NA
#> GSM148572 4 0.269 0.601 0.032 0.000 0.016 0.888 0.056 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) dose(p) time(p) k
#> MAD:NMF 57 2.57e-12 1.00e+00 1.000 2
#> MAD:NMF 57 2.57e-12 1.00e+00 1.000 3
#> MAD:NMF 52 1.54e-09 9.08e-06 0.958 4
#> MAD:NMF 52 1.76e-09 4.20e-05 0.925 5
#> MAD:NMF 45 4.58e-08 1.31e-05 0.900 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 21163 rows and 57 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5093 0.491 0.491
#> 3 3 0.911 0.987 0.972 0.1435 0.917 0.832
#> 4 4 0.966 0.976 0.983 0.0784 0.966 0.917
#> 5 5 0.855 0.890 0.928 0.0898 0.969 0.916
#> 6 6 0.858 0.892 0.912 0.0731 0.929 0.792
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
#> GSM148516 2 0 1 0 1
#> GSM148517 1 0 1 1 0
#> GSM148518 2 0 1 0 1
#> GSM148519 2 0 1 0 1
#> GSM148520 2 0 1 0 1
#> GSM148521 2 0 1 0 1
#> GSM148522 2 0 1 0 1
#> GSM148523 2 0 1 0 1
#> GSM148524 2 0 1 0 1
#> GSM148525 2 0 1 0 1
#> GSM148526 2 0 1 0 1
#> GSM148527 2 0 1 0 1
#> GSM148528 2 0 1 0 1
#> GSM148529 2 0 1 0 1
#> GSM148530 2 0 1 0 1
#> GSM148531 2 0 1 0 1
#> GSM148532 2 0 1 0 1
#> GSM148533 2 0 1 0 1
#> GSM148534 2 0 1 0 1
#> GSM148535 2 0 1 0 1
#> GSM148536 2 0 1 0 1
#> GSM148537 2 0 1 0 1
#> GSM148538 2 0 1 0 1
#> GSM148539 2 0 1 0 1
#> GSM148540 2 0 1 0 1
#> GSM148541 2 0 1 0 1
#> GSM148542 2 0 1 0 1
#> GSM148543 2 0 1 0 1
#> GSM148544 2 0 1 0 1
#> GSM148545 1 0 1 1 0
#> GSM148546 1 0 1 1 0
#> GSM148547 1 0 1 1 0
#> GSM148548 1 0 1 1 0
#> GSM148549 1 0 1 1 0
#> GSM148550 1 0 1 1 0
#> GSM148551 1 0 1 1 0
#> GSM148552 1 0 1 1 0
#> GSM148553 1 0 1 1 0
#> GSM148554 1 0 1 1 0
#> GSM148555 1 0 1 1 0
#> GSM148556 1 0 1 1 0
#> GSM148557 1 0 1 1 0
#> GSM148558 1 0 1 1 0
#> GSM148559 1 0 1 1 0
#> GSM148560 1 0 1 1 0
#> GSM148561 1 0 1 1 0
#> GSM148562 1 0 1 1 0
#> GSM148563 1 0 1 1 0
#> GSM148564 1 0 1 1 0
#> GSM148565 1 0 1 1 0
#> GSM148566 1 0 1 1 0
#> GSM148567 1 0 1 1 0
#> GSM148568 1 0 1 1 0
#> GSM148569 1 0 1 1 0
#> GSM148570 1 0 1 1 0
#> GSM148571 1 0 1 1 0
#> GSM148572 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM148516 3 0.45 1.000 0.000 0.196 0.804
#> GSM148517 1 0.45 0.802 0.804 0.000 0.196
#> GSM148518 2 0.00 1.000 0.000 1.000 0.000
#> GSM148519 2 0.00 1.000 0.000 1.000 0.000
#> GSM148520 2 0.00 1.000 0.000 1.000 0.000
#> GSM148521 2 0.00 1.000 0.000 1.000 0.000
#> GSM148522 2 0.00 1.000 0.000 1.000 0.000
#> GSM148523 2 0.00 1.000 0.000 1.000 0.000
#> GSM148524 2 0.00 1.000 0.000 1.000 0.000
#> GSM148525 2 0.00 1.000 0.000 1.000 0.000
#> GSM148526 2 0.00 1.000 0.000 1.000 0.000
#> GSM148527 2 0.00 1.000 0.000 1.000 0.000
#> GSM148528 2 0.00 1.000 0.000 1.000 0.000
#> GSM148529 2 0.00 1.000 0.000 1.000 0.000
#> GSM148530 2 0.00 1.000 0.000 1.000 0.000
#> GSM148531 2 0.00 1.000 0.000 1.000 0.000
#> GSM148532 2 0.00 1.000 0.000 1.000 0.000
#> GSM148533 2 0.00 1.000 0.000 1.000 0.000
#> GSM148534 2 0.00 1.000 0.000 1.000 0.000
#> GSM148535 2 0.00 1.000 0.000 1.000 0.000
#> GSM148536 2 0.00 1.000 0.000 1.000 0.000
#> GSM148537 2 0.00 1.000 0.000 1.000 0.000
#> GSM148538 2 0.00 1.000 0.000 1.000 0.000
#> GSM148539 3 0.45 1.000 0.000 0.196 0.804
#> GSM148540 3 0.45 1.000 0.000 0.196 0.804
#> GSM148541 3 0.45 1.000 0.000 0.196 0.804
#> GSM148542 2 0.00 1.000 0.000 1.000 0.000
#> GSM148543 3 0.45 1.000 0.000 0.196 0.804
#> GSM148544 3 0.45 1.000 0.000 0.196 0.804
#> GSM148545 1 0.45 0.802 0.804 0.000 0.196
#> GSM148546 1 0.00 0.987 1.000 0.000 0.000
#> GSM148547 1 0.00 0.987 1.000 0.000 0.000
#> GSM148548 1 0.00 0.987 1.000 0.000 0.000
#> GSM148549 1 0.00 0.987 1.000 0.000 0.000
#> GSM148550 1 0.00 0.987 1.000 0.000 0.000
#> GSM148551 1 0.00 0.987 1.000 0.000 0.000
#> GSM148552 1 0.00 0.987 1.000 0.000 0.000
#> GSM148553 1 0.00 0.987 1.000 0.000 0.000
#> GSM148554 1 0.00 0.987 1.000 0.000 0.000
#> GSM148555 1 0.00 0.987 1.000 0.000 0.000
#> GSM148556 1 0.00 0.987 1.000 0.000 0.000
#> GSM148557 1 0.00 0.987 1.000 0.000 0.000
#> GSM148558 1 0.00 0.987 1.000 0.000 0.000
#> GSM148559 1 0.00 0.987 1.000 0.000 0.000
#> GSM148560 1 0.00 0.987 1.000 0.000 0.000
#> GSM148561 1 0.00 0.987 1.000 0.000 0.000
#> GSM148562 1 0.00 0.987 1.000 0.000 0.000
#> GSM148563 1 0.00 0.987 1.000 0.000 0.000
#> GSM148564 1 0.00 0.987 1.000 0.000 0.000
#> GSM148565 1 0.00 0.987 1.000 0.000 0.000
#> GSM148566 1 0.00 0.987 1.000 0.000 0.000
#> GSM148567 1 0.00 0.987 1.000 0.000 0.000
#> GSM148568 1 0.00 0.987 1.000 0.000 0.000
#> GSM148569 1 0.00 0.987 1.000 0.000 0.000
#> GSM148570 1 0.00 0.987 1.000 0.000 0.000
#> GSM148571 1 0.00 0.987 1.000 0.000 0.000
#> GSM148572 1 0.00 0.987 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM148516 3 0.0000 1.000 0.000 0 1 0.000
#> GSM148517 1 0.3649 1.000 0.796 0 0 0.204
#> GSM148518 2 0.0000 1.000 0.000 1 0 0.000
#> GSM148519 2 0.0000 1.000 0.000 1 0 0.000
#> GSM148520 2 0.0000 1.000 0.000 1 0 0.000
#> GSM148521 2 0.0000 1.000 0.000 1 0 0.000
#> GSM148522 2 0.0000 1.000 0.000 1 0 0.000
#> GSM148523 2 0.0000 1.000 0.000 1 0 0.000
#> GSM148524 2 0.0000 1.000 0.000 1 0 0.000
#> GSM148525 2 0.0000 1.000 0.000 1 0 0.000
#> GSM148526 2 0.0000 1.000 0.000 1 0 0.000
#> GSM148527 2 0.0000 1.000 0.000 1 0 0.000
#> GSM148528 2 0.0000 1.000 0.000 1 0 0.000
#> GSM148529 2 0.0000 1.000 0.000 1 0 0.000
#> GSM148530 2 0.0000 1.000 0.000 1 0 0.000
#> GSM148531 2 0.0000 1.000 0.000 1 0 0.000
#> GSM148532 2 0.0000 1.000 0.000 1 0 0.000
#> GSM148533 2 0.0000 1.000 0.000 1 0 0.000
#> GSM148534 2 0.0000 1.000 0.000 1 0 0.000
#> GSM148535 2 0.0000 1.000 0.000 1 0 0.000
#> GSM148536 2 0.0000 1.000 0.000 1 0 0.000
#> GSM148537 2 0.0000 1.000 0.000 1 0 0.000
#> GSM148538 2 0.0000 1.000 0.000 1 0 0.000
#> GSM148539 3 0.0000 1.000 0.000 0 1 0.000
#> GSM148540 3 0.0000 1.000 0.000 0 1 0.000
#> GSM148541 3 0.0000 1.000 0.000 0 1 0.000
#> GSM148542 2 0.0000 1.000 0.000 1 0 0.000
#> GSM148543 3 0.0000 1.000 0.000 0 1 0.000
#> GSM148544 3 0.0000 1.000 0.000 0 1 0.000
#> GSM148545 1 0.3649 1.000 0.796 0 0 0.204
#> GSM148546 4 0.0000 0.973 0.000 0 0 1.000
#> GSM148547 4 0.0000 0.973 0.000 0 0 1.000
#> GSM148548 4 0.0188 0.971 0.004 0 0 0.996
#> GSM148549 4 0.0000 0.973 0.000 0 0 1.000
#> GSM148550 4 0.0000 0.973 0.000 0 0 1.000
#> GSM148551 4 0.0000 0.973 0.000 0 0 1.000
#> GSM148552 4 0.3649 0.731 0.204 0 0 0.796
#> GSM148553 4 0.3649 0.731 0.204 0 0 0.796
#> GSM148554 4 0.1867 0.905 0.072 0 0 0.928
#> GSM148555 4 0.0188 0.971 0.004 0 0 0.996
#> GSM148556 4 0.0188 0.971 0.004 0 0 0.996
#> GSM148557 4 0.0188 0.971 0.004 0 0 0.996
#> GSM148558 4 0.0000 0.973 0.000 0 0 1.000
#> GSM148559 4 0.0000 0.973 0.000 0 0 1.000
#> GSM148560 4 0.0000 0.973 0.000 0 0 1.000
#> GSM148561 4 0.0921 0.952 0.028 0 0 0.972
#> GSM148562 4 0.0000 0.973 0.000 0 0 1.000
#> GSM148563 4 0.0000 0.973 0.000 0 0 1.000
#> GSM148564 4 0.0000 0.973 0.000 0 0 1.000
#> GSM148565 4 0.0000 0.973 0.000 0 0 1.000
#> GSM148566 4 0.0000 0.973 0.000 0 0 1.000
#> GSM148567 4 0.0921 0.952 0.028 0 0 0.972
#> GSM148568 4 0.0921 0.952 0.028 0 0 0.972
#> GSM148569 4 0.0000 0.973 0.000 0 0 1.000
#> GSM148570 4 0.0000 0.973 0.000 0 0 1.000
#> GSM148571 4 0.0000 0.973 0.000 0 0 1.000
#> GSM148572 4 0.0000 0.973 0.000 0 0 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM148516 3 0.000 1.000 0.000 0 1 0.000 0.000
#> GSM148517 4 0.000 1.000 0.000 0 0 1.000 0.000
#> GSM148518 2 0.000 1.000 0.000 1 0 0.000 0.000
#> GSM148519 2 0.000 1.000 0.000 1 0 0.000 0.000
#> GSM148520 2 0.000 1.000 0.000 1 0 0.000 0.000
#> GSM148521 2 0.000 1.000 0.000 1 0 0.000 0.000
#> GSM148522 2 0.000 1.000 0.000 1 0 0.000 0.000
#> GSM148523 2 0.000 1.000 0.000 1 0 0.000 0.000
#> GSM148524 2 0.000 1.000 0.000 1 0 0.000 0.000
#> GSM148525 2 0.000 1.000 0.000 1 0 0.000 0.000
#> GSM148526 2 0.000 1.000 0.000 1 0 0.000 0.000
#> GSM148527 2 0.000 1.000 0.000 1 0 0.000 0.000
#> GSM148528 2 0.000 1.000 0.000 1 0 0.000 0.000
#> GSM148529 2 0.000 1.000 0.000 1 0 0.000 0.000
#> GSM148530 2 0.000 1.000 0.000 1 0 0.000 0.000
#> GSM148531 2 0.000 1.000 0.000 1 0 0.000 0.000
#> GSM148532 2 0.000 1.000 0.000 1 0 0.000 0.000
#> GSM148533 2 0.000 1.000 0.000 1 0 0.000 0.000
#> GSM148534 2 0.000 1.000 0.000 1 0 0.000 0.000
#> GSM148535 2 0.000 1.000 0.000 1 0 0.000 0.000
#> GSM148536 2 0.000 1.000 0.000 1 0 0.000 0.000
#> GSM148537 2 0.000 1.000 0.000 1 0 0.000 0.000
#> GSM148538 2 0.000 1.000 0.000 1 0 0.000 0.000
#> GSM148539 3 0.000 1.000 0.000 0 1 0.000 0.000
#> GSM148540 3 0.000 1.000 0.000 0 1 0.000 0.000
#> GSM148541 3 0.000 1.000 0.000 0 1 0.000 0.000
#> GSM148542 2 0.000 1.000 0.000 1 0 0.000 0.000
#> GSM148543 3 0.000 1.000 0.000 0 1 0.000 0.000
#> GSM148544 3 0.000 1.000 0.000 0 1 0.000 0.000
#> GSM148545 4 0.000 1.000 0.000 0 0 1.000 0.000
#> GSM148546 1 0.000 0.772 1.000 0 0 0.000 0.000
#> GSM148547 1 0.000 0.772 1.000 0 0 0.000 0.000
#> GSM148548 1 0.088 0.742 0.968 0 0 0.000 0.032
#> GSM148549 1 0.000 0.772 1.000 0 0 0.000 0.000
#> GSM148550 1 0.000 0.772 1.000 0 0 0.000 0.000
#> GSM148551 1 0.000 0.772 1.000 0 0 0.000 0.000
#> GSM148552 5 0.405 1.000 0.356 0 0 0.000 0.644
#> GSM148553 5 0.405 1.000 0.356 0 0 0.000 0.644
#> GSM148554 1 0.202 0.649 0.900 0 0 0.000 0.100
#> GSM148555 1 0.088 0.742 0.968 0 0 0.000 0.032
#> GSM148556 1 0.029 0.766 0.992 0 0 0.000 0.008
#> GSM148557 1 0.029 0.766 0.992 0 0 0.000 0.008
#> GSM148558 1 0.000 0.772 1.000 0 0 0.000 0.000
#> GSM148559 1 0.285 0.801 0.828 0 0 0.000 0.172
#> GSM148560 1 0.285 0.801 0.828 0 0 0.000 0.172
#> GSM148561 1 0.311 0.793 0.800 0 0 0.000 0.200
#> GSM148562 1 0.285 0.801 0.828 0 0 0.000 0.172
#> GSM148563 1 0.405 0.689 0.644 0 0 0.000 0.356
#> GSM148564 1 0.491 0.658 0.608 0 0 0.036 0.356
#> GSM148565 1 0.491 0.658 0.608 0 0 0.036 0.356
#> GSM148566 1 0.285 0.801 0.828 0 0 0.000 0.172
#> GSM148567 1 0.311 0.793 0.800 0 0 0.000 0.200
#> GSM148568 1 0.311 0.793 0.800 0 0 0.000 0.200
#> GSM148569 1 0.285 0.801 0.828 0 0 0.000 0.172
#> GSM148570 1 0.405 0.689 0.644 0 0 0.000 0.356
#> GSM148571 1 0.405 0.689 0.644 0 0 0.000 0.356
#> GSM148572 1 0.491 0.658 0.608 0 0 0.036 0.356
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM148516 3 0.0000 1.000 0.000 0.00 1 0.000 0.000 0.000
#> GSM148517 6 0.0790 1.000 0.000 0.00 0 0.032 0.000 0.968
#> GSM148518 2 0.0000 0.992 0.000 1.00 0 0.000 0.000 0.000
#> GSM148519 2 0.0000 0.992 0.000 1.00 0 0.000 0.000 0.000
#> GSM148520 2 0.0000 0.992 0.000 1.00 0 0.000 0.000 0.000
#> GSM148521 2 0.0000 0.992 0.000 1.00 0 0.000 0.000 0.000
#> GSM148522 2 0.0000 0.992 0.000 1.00 0 0.000 0.000 0.000
#> GSM148523 2 0.0000 0.992 0.000 1.00 0 0.000 0.000 0.000
#> GSM148524 2 0.0000 0.992 0.000 1.00 0 0.000 0.000 0.000
#> GSM148525 2 0.0000 0.992 0.000 1.00 0 0.000 0.000 0.000
#> GSM148526 2 0.0000 0.992 0.000 1.00 0 0.000 0.000 0.000
#> GSM148527 2 0.0000 0.992 0.000 1.00 0 0.000 0.000 0.000
#> GSM148528 2 0.0000 0.992 0.000 1.00 0 0.000 0.000 0.000
#> GSM148529 2 0.0000 0.992 0.000 1.00 0 0.000 0.000 0.000
#> GSM148530 2 0.0000 0.992 0.000 1.00 0 0.000 0.000 0.000
#> GSM148531 2 0.0000 0.992 0.000 1.00 0 0.000 0.000 0.000
#> GSM148532 2 0.0000 0.992 0.000 1.00 0 0.000 0.000 0.000
#> GSM148533 2 0.0000 0.992 0.000 1.00 0 0.000 0.000 0.000
#> GSM148534 2 0.0000 0.992 0.000 1.00 0 0.000 0.000 0.000
#> GSM148535 2 0.0000 0.992 0.000 1.00 0 0.000 0.000 0.000
#> GSM148536 2 0.0000 0.992 0.000 1.00 0 0.000 0.000 0.000
#> GSM148537 2 0.0000 0.992 0.000 1.00 0 0.000 0.000 0.000
#> GSM148538 2 0.0000 0.992 0.000 1.00 0 0.000 0.000 0.000
#> GSM148539 3 0.0000 1.000 0.000 0.00 1 0.000 0.000 0.000
#> GSM148540 3 0.0000 1.000 0.000 0.00 1 0.000 0.000 0.000
#> GSM148541 3 0.0000 1.000 0.000 0.00 1 0.000 0.000 0.000
#> GSM148542 2 0.3101 0.796 0.000 0.82 0 0.148 0.000 0.032
#> GSM148543 3 0.0000 1.000 0.000 0.00 1 0.000 0.000 0.000
#> GSM148544 3 0.0000 1.000 0.000 0.00 1 0.000 0.000 0.000
#> GSM148545 6 0.0790 1.000 0.000 0.00 0 0.032 0.000 0.968
#> GSM148546 1 0.0458 0.768 0.984 0.00 0 0.000 0.016 0.000
#> GSM148547 1 0.0458 0.768 0.984 0.00 0 0.000 0.016 0.000
#> GSM148548 1 0.0790 0.740 0.968 0.00 0 0.000 0.032 0.000
#> GSM148549 1 0.0000 0.766 1.000 0.00 0 0.000 0.000 0.000
#> GSM148550 1 0.0000 0.766 1.000 0.00 0 0.000 0.000 0.000
#> GSM148551 1 0.0000 0.766 1.000 0.00 0 0.000 0.000 0.000
#> GSM148552 5 0.3499 1.000 0.320 0.00 0 0.000 0.680 0.000
#> GSM148553 5 0.3499 1.000 0.320 0.00 0 0.000 0.680 0.000
#> GSM148554 1 0.1814 0.642 0.900 0.00 0 0.000 0.100 0.000
#> GSM148555 1 0.0790 0.740 0.968 0.00 0 0.000 0.032 0.000
#> GSM148556 1 0.0260 0.761 0.992 0.00 0 0.000 0.008 0.000
#> GSM148557 1 0.0260 0.761 0.992 0.00 0 0.000 0.008 0.000
#> GSM148558 1 0.0000 0.766 1.000 0.00 0 0.000 0.000 0.000
#> GSM148559 1 0.3499 0.721 0.680 0.00 0 0.000 0.320 0.000
#> GSM148560 1 0.3499 0.721 0.680 0.00 0 0.000 0.320 0.000
#> GSM148561 1 0.3607 0.707 0.652 0.00 0 0.000 0.348 0.000
#> GSM148562 1 0.3741 0.716 0.672 0.00 0 0.008 0.320 0.000
#> GSM148563 4 0.5135 0.688 0.240 0.00 0 0.616 0.144 0.000
#> GSM148564 4 0.2340 0.910 0.148 0.00 0 0.852 0.000 0.000
#> GSM148565 4 0.2340 0.910 0.148 0.00 0 0.852 0.000 0.000
#> GSM148566 1 0.3499 0.721 0.680 0.00 0 0.000 0.320 0.000
#> GSM148567 1 0.3607 0.707 0.652 0.00 0 0.000 0.348 0.000
#> GSM148568 1 0.3607 0.707 0.652 0.00 0 0.000 0.348 0.000
#> GSM148569 1 0.3741 0.716 0.672 0.00 0 0.008 0.320 0.000
#> GSM148570 4 0.2664 0.907 0.184 0.00 0 0.816 0.000 0.000
#> GSM148571 4 0.2664 0.907 0.184 0.00 0 0.816 0.000 0.000
#> GSM148572 4 0.2340 0.910 0.148 0.00 0 0.852 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) dose(p) time(p) k
#> ATC:hclust 57 2.57e-12 0.999568 1.000 2
#> ATC:hclust 57 4.87e-12 0.004143 0.970 3
#> ATC:hclust 57 5.82e-16 0.000161 0.349 4
#> ATC:hclust 57 1.83e-14 0.000174 0.419 5
#> ATC:hclust 57 3.81e-13 0.000174 0.325 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 21163 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5093 0.491 0.491
#> 3 3 0.760 0.822 0.833 0.2072 1.000 1.000
#> 4 4 0.678 0.906 0.835 0.1238 0.778 0.547
#> 5 5 0.632 0.832 0.789 0.0705 1.000 1.000
#> 6 6 0.663 0.809 0.787 0.0578 0.961 0.853
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
#> GSM148516 2 0 1 0 1
#> GSM148517 1 0 1 1 0
#> GSM148518 2 0 1 0 1
#> GSM148519 2 0 1 0 1
#> GSM148520 2 0 1 0 1
#> GSM148521 2 0 1 0 1
#> GSM148522 2 0 1 0 1
#> GSM148523 2 0 1 0 1
#> GSM148524 2 0 1 0 1
#> GSM148525 2 0 1 0 1
#> GSM148526 2 0 1 0 1
#> GSM148527 2 0 1 0 1
#> GSM148528 2 0 1 0 1
#> GSM148529 2 0 1 0 1
#> GSM148530 2 0 1 0 1
#> GSM148531 2 0 1 0 1
#> GSM148532 2 0 1 0 1
#> GSM148533 2 0 1 0 1
#> GSM148534 2 0 1 0 1
#> GSM148535 2 0 1 0 1
#> GSM148536 2 0 1 0 1
#> GSM148537 2 0 1 0 1
#> GSM148538 2 0 1 0 1
#> GSM148539 2 0 1 0 1
#> GSM148540 2 0 1 0 1
#> GSM148541 2 0 1 0 1
#> GSM148542 2 0 1 0 1
#> GSM148543 2 0 1 0 1
#> GSM148544 2 0 1 0 1
#> GSM148545 1 0 1 1 0
#> GSM148546 1 0 1 1 0
#> GSM148547 1 0 1 1 0
#> GSM148548 1 0 1 1 0
#> GSM148549 1 0 1 1 0
#> GSM148550 1 0 1 1 0
#> GSM148551 1 0 1 1 0
#> GSM148552 1 0 1 1 0
#> GSM148553 1 0 1 1 0
#> GSM148554 1 0 1 1 0
#> GSM148555 1 0 1 1 0
#> GSM148556 1 0 1 1 0
#> GSM148557 1 0 1 1 0
#> GSM148558 1 0 1 1 0
#> GSM148559 1 0 1 1 0
#> GSM148560 1 0 1 1 0
#> GSM148561 1 0 1 1 0
#> GSM148562 1 0 1 1 0
#> GSM148563 1 0 1 1 0
#> GSM148564 1 0 1 1 0
#> GSM148565 1 0 1 1 0
#> GSM148566 1 0 1 1 0
#> GSM148567 1 0 1 1 0
#> GSM148568 1 0 1 1 0
#> GSM148569 1 0 1 1 0
#> GSM148570 1 0 1 1 0
#> GSM148571 1 0 1 1 0
#> GSM148572 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM148516 2 0.0000 0.660 0.000 1.00 NA
#> GSM148517 1 0.4002 0.801 0.840 0.00 NA
#> GSM148518 2 0.6280 0.901 0.000 0.54 NA
#> GSM148519 2 0.6280 0.901 0.000 0.54 NA
#> GSM148520 2 0.6280 0.901 0.000 0.54 NA
#> GSM148521 2 0.6280 0.901 0.000 0.54 NA
#> GSM148522 2 0.6280 0.901 0.000 0.54 NA
#> GSM148523 2 0.6280 0.901 0.000 0.54 NA
#> GSM148524 2 0.6280 0.901 0.000 0.54 NA
#> GSM148525 2 0.6280 0.901 0.000 0.54 NA
#> GSM148526 2 0.6280 0.901 0.000 0.54 NA
#> GSM148527 2 0.6280 0.901 0.000 0.54 NA
#> GSM148528 2 0.6280 0.901 0.000 0.54 NA
#> GSM148529 2 0.6280 0.901 0.000 0.54 NA
#> GSM148530 2 0.6280 0.901 0.000 0.54 NA
#> GSM148531 2 0.6280 0.901 0.000 0.54 NA
#> GSM148532 2 0.6280 0.901 0.000 0.54 NA
#> GSM148533 2 0.6280 0.901 0.000 0.54 NA
#> GSM148534 2 0.6280 0.901 0.000 0.54 NA
#> GSM148535 2 0.6280 0.901 0.000 0.54 NA
#> GSM148536 2 0.6280 0.901 0.000 0.54 NA
#> GSM148537 2 0.6280 0.901 0.000 0.54 NA
#> GSM148538 2 0.6280 0.901 0.000 0.54 NA
#> GSM148539 2 0.0000 0.660 0.000 1.00 NA
#> GSM148540 2 0.0000 0.660 0.000 1.00 NA
#> GSM148541 2 0.0000 0.660 0.000 1.00 NA
#> GSM148542 2 0.0000 0.660 0.000 1.00 NA
#> GSM148543 2 0.0000 0.660 0.000 1.00 NA
#> GSM148544 2 0.0000 0.660 0.000 1.00 NA
#> GSM148545 1 0.4002 0.801 0.840 0.00 NA
#> GSM148546 1 0.6192 0.794 0.580 0.00 NA
#> GSM148547 1 0.6192 0.794 0.580 0.00 NA
#> GSM148548 1 0.6192 0.794 0.580 0.00 NA
#> GSM148549 1 0.6192 0.794 0.580 0.00 NA
#> GSM148550 1 0.6192 0.794 0.580 0.00 NA
#> GSM148551 1 0.6192 0.794 0.580 0.00 NA
#> GSM148552 1 0.6192 0.794 0.580 0.00 NA
#> GSM148553 1 0.6192 0.794 0.580 0.00 NA
#> GSM148554 1 0.6192 0.794 0.580 0.00 NA
#> GSM148555 1 0.6192 0.794 0.580 0.00 NA
#> GSM148556 1 0.6192 0.794 0.580 0.00 NA
#> GSM148557 1 0.6192 0.793 0.580 0.00 NA
#> GSM148558 1 0.6267 0.785 0.548 0.00 NA
#> GSM148559 1 0.0424 0.820 0.992 0.00 NA
#> GSM148560 1 0.0424 0.820 0.992 0.00 NA
#> GSM148561 1 0.0424 0.820 0.992 0.00 NA
#> GSM148562 1 0.0000 0.819 1.000 0.00 NA
#> GSM148563 1 0.1411 0.811 0.964 0.00 NA
#> GSM148564 1 0.2261 0.801 0.932 0.00 NA
#> GSM148565 1 0.2261 0.801 0.932 0.00 NA
#> GSM148566 1 0.0424 0.820 0.992 0.00 NA
#> GSM148567 1 0.0424 0.820 0.992 0.00 NA
#> GSM148568 1 0.0424 0.820 0.992 0.00 NA
#> GSM148569 1 0.0892 0.815 0.980 0.00 NA
#> GSM148570 1 0.2261 0.801 0.932 0.00 NA
#> GSM148571 1 0.2261 0.801 0.932 0.00 NA
#> GSM148572 1 0.2261 0.801 0.932 0.00 NA
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM148516 3 0.4040 0.990 0.000 0.248 0.752 0.000
#> GSM148517 4 0.5855 0.726 0.100 0.000 0.208 0.692
#> GSM148518 2 0.2530 0.868 0.112 0.888 0.000 0.000
#> GSM148519 2 0.2530 0.868 0.112 0.888 0.000 0.000
#> GSM148520 2 0.2149 0.887 0.088 0.912 0.000 0.000
#> GSM148521 2 0.2149 0.887 0.088 0.912 0.000 0.000
#> GSM148522 2 0.2011 0.889 0.080 0.920 0.000 0.000
#> GSM148523 2 0.2149 0.887 0.088 0.912 0.000 0.000
#> GSM148524 2 0.2216 0.887 0.092 0.908 0.000 0.000
#> GSM148525 2 0.2647 0.865 0.120 0.880 0.000 0.000
#> GSM148526 2 0.2647 0.865 0.120 0.880 0.000 0.000
#> GSM148527 2 0.1022 0.893 0.032 0.968 0.000 0.000
#> GSM148528 2 0.2530 0.868 0.112 0.888 0.000 0.000
#> GSM148529 2 0.2216 0.887 0.092 0.908 0.000 0.000
#> GSM148530 2 0.2149 0.887 0.088 0.912 0.000 0.000
#> GSM148531 2 0.2149 0.887 0.088 0.912 0.000 0.000
#> GSM148532 2 0.0921 0.895 0.028 0.972 0.000 0.000
#> GSM148533 2 0.2647 0.865 0.120 0.880 0.000 0.000
#> GSM148534 2 0.2530 0.868 0.112 0.888 0.000 0.000
#> GSM148535 2 0.1940 0.882 0.076 0.924 0.000 0.000
#> GSM148536 2 0.0817 0.894 0.024 0.976 0.000 0.000
#> GSM148537 2 0.2216 0.887 0.092 0.908 0.000 0.000
#> GSM148538 2 0.0188 0.895 0.004 0.996 0.000 0.000
#> GSM148539 3 0.4220 0.990 0.004 0.248 0.748 0.000
#> GSM148540 3 0.4220 0.990 0.004 0.248 0.748 0.000
#> GSM148541 3 0.4220 0.990 0.004 0.248 0.748 0.000
#> GSM148542 3 0.5687 0.949 0.068 0.248 0.684 0.000
#> GSM148543 3 0.4040 0.990 0.000 0.248 0.752 0.000
#> GSM148544 3 0.4040 0.990 0.000 0.248 0.752 0.000
#> GSM148545 4 0.5855 0.726 0.100 0.000 0.208 0.692
#> GSM148546 1 0.4608 0.986 0.692 0.000 0.004 0.304
#> GSM148547 1 0.4608 0.986 0.692 0.000 0.004 0.304
#> GSM148548 1 0.4584 0.987 0.696 0.000 0.004 0.300
#> GSM148549 1 0.4584 0.986 0.696 0.000 0.004 0.300
#> GSM148550 1 0.4608 0.986 0.692 0.000 0.004 0.304
#> GSM148551 1 0.4608 0.986 0.692 0.000 0.004 0.304
#> GSM148552 1 0.4957 0.981 0.684 0.000 0.016 0.300
#> GSM148553 1 0.4957 0.981 0.684 0.000 0.016 0.300
#> GSM148554 1 0.4957 0.981 0.684 0.000 0.016 0.300
#> GSM148555 1 0.4584 0.987 0.696 0.000 0.004 0.300
#> GSM148556 1 0.4584 0.987 0.696 0.000 0.004 0.300
#> GSM148557 1 0.4431 0.985 0.696 0.000 0.000 0.304
#> GSM148558 1 0.4761 0.953 0.664 0.000 0.004 0.332
#> GSM148559 4 0.1661 0.868 0.052 0.000 0.004 0.944
#> GSM148560 4 0.1474 0.868 0.052 0.000 0.000 0.948
#> GSM148561 4 0.2060 0.863 0.052 0.000 0.016 0.932
#> GSM148562 4 0.1211 0.871 0.040 0.000 0.000 0.960
#> GSM148563 4 0.0927 0.865 0.008 0.000 0.016 0.976
#> GSM148564 4 0.3074 0.842 0.000 0.000 0.152 0.848
#> GSM148565 4 0.3024 0.842 0.000 0.000 0.148 0.852
#> GSM148566 4 0.1661 0.867 0.052 0.000 0.004 0.944
#> GSM148567 4 0.2060 0.863 0.052 0.000 0.016 0.932
#> GSM148568 4 0.2060 0.863 0.052 0.000 0.016 0.932
#> GSM148569 4 0.1004 0.872 0.024 0.000 0.004 0.972
#> GSM148570 4 0.3024 0.842 0.000 0.000 0.148 0.852
#> GSM148571 4 0.3024 0.842 0.000 0.000 0.148 0.852
#> GSM148572 4 0.3024 0.842 0.000 0.000 0.148 0.852
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM148516 3 0.3048 0.973 0.004 0.176 0.820 0.000 0.000
#> GSM148517 4 0.6095 0.605 0.056 0.000 0.120 0.664 0.160
#> GSM148518 2 0.3661 0.748 0.000 0.724 0.000 0.000 0.276
#> GSM148519 2 0.3661 0.748 0.000 0.724 0.000 0.000 0.276
#> GSM148520 2 0.1965 0.800 0.000 0.904 0.000 0.000 0.096
#> GSM148521 2 0.2127 0.795 0.000 0.892 0.000 0.000 0.108
#> GSM148522 2 0.2513 0.802 0.008 0.876 0.000 0.000 0.116
#> GSM148523 2 0.2127 0.795 0.000 0.892 0.000 0.000 0.108
#> GSM148524 2 0.2127 0.795 0.000 0.892 0.000 0.000 0.108
#> GSM148525 2 0.4655 0.728 0.052 0.700 0.000 0.000 0.248
#> GSM148526 2 0.4655 0.728 0.052 0.700 0.000 0.000 0.248
#> GSM148527 2 0.2448 0.806 0.020 0.892 0.000 0.000 0.088
#> GSM148528 2 0.3661 0.748 0.000 0.724 0.000 0.000 0.276
#> GSM148529 2 0.2127 0.795 0.000 0.892 0.000 0.000 0.108
#> GSM148530 2 0.2127 0.795 0.000 0.892 0.000 0.000 0.108
#> GSM148531 2 0.2127 0.795 0.000 0.892 0.000 0.000 0.108
#> GSM148532 2 0.1012 0.810 0.020 0.968 0.000 0.000 0.012
#> GSM148533 2 0.4655 0.728 0.052 0.700 0.000 0.000 0.248
#> GSM148534 2 0.3661 0.748 0.000 0.724 0.000 0.000 0.276
#> GSM148535 2 0.3399 0.785 0.020 0.812 0.000 0.000 0.168
#> GSM148536 2 0.2505 0.804 0.020 0.888 0.000 0.000 0.092
#> GSM148537 2 0.2522 0.796 0.012 0.880 0.000 0.000 0.108
#> GSM148538 2 0.2012 0.808 0.020 0.920 0.000 0.000 0.060
#> GSM148539 3 0.2891 0.974 0.000 0.176 0.824 0.000 0.000
#> GSM148540 3 0.2891 0.974 0.000 0.176 0.824 0.000 0.000
#> GSM148541 3 0.3171 0.972 0.008 0.176 0.816 0.000 0.000
#> GSM148542 3 0.6589 0.845 0.104 0.176 0.624 0.000 0.096
#> GSM148543 3 0.2891 0.974 0.000 0.176 0.824 0.000 0.000
#> GSM148544 3 0.2891 0.974 0.000 0.176 0.824 0.000 0.000
#> GSM148545 4 0.6095 0.605 0.056 0.000 0.120 0.664 0.160
#> GSM148546 1 0.3888 0.951 0.788 0.000 0.004 0.176 0.032
#> GSM148547 1 0.3888 0.951 0.788 0.000 0.004 0.176 0.032
#> GSM148548 1 0.3769 0.950 0.796 0.000 0.016 0.176 0.012
#> GSM148549 1 0.3048 0.954 0.820 0.000 0.004 0.176 0.000
#> GSM148550 1 0.3888 0.951 0.788 0.000 0.004 0.176 0.032
#> GSM148551 1 0.3888 0.951 0.788 0.000 0.004 0.176 0.032
#> GSM148552 1 0.5278 0.911 0.720 0.000 0.048 0.176 0.056
#> GSM148553 1 0.5278 0.911 0.720 0.000 0.048 0.176 0.056
#> GSM148554 1 0.5074 0.919 0.732 0.000 0.040 0.176 0.052
#> GSM148555 1 0.3769 0.950 0.796 0.000 0.016 0.176 0.012
#> GSM148556 1 0.3171 0.954 0.816 0.000 0.008 0.176 0.000
#> GSM148557 1 0.2891 0.955 0.824 0.000 0.000 0.176 0.000
#> GSM148558 1 0.3961 0.947 0.780 0.000 0.004 0.184 0.032
#> GSM148559 4 0.4671 0.803 0.028 0.000 0.000 0.640 0.332
#> GSM148560 4 0.4822 0.801 0.028 0.000 0.004 0.636 0.332
#> GSM148561 4 0.5166 0.784 0.028 0.000 0.012 0.592 0.368
#> GSM148562 4 0.4608 0.803 0.024 0.000 0.000 0.640 0.336
#> GSM148563 4 0.4337 0.800 0.016 0.000 0.004 0.696 0.284
#> GSM148564 4 0.0162 0.745 0.000 0.000 0.000 0.996 0.004
#> GSM148565 4 0.0000 0.745 0.000 0.000 0.000 1.000 0.000
#> GSM148566 4 0.4929 0.797 0.032 0.000 0.004 0.624 0.340
#> GSM148567 4 0.5052 0.788 0.028 0.000 0.008 0.600 0.364
#> GSM148568 4 0.5052 0.788 0.028 0.000 0.008 0.600 0.364
#> GSM148569 4 0.4418 0.805 0.016 0.000 0.000 0.652 0.332
#> GSM148570 4 0.0000 0.745 0.000 0.000 0.000 1.000 0.000
#> GSM148571 4 0.0000 0.745 0.000 0.000 0.000 1.000 0.000
#> GSM148572 4 0.0000 0.745 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM148516 3 0.2261 0.961 0.000 0.104 0.884 0.004 0.000 NA
#> GSM148517 4 0.7907 0.539 0.100 0.000 0.068 0.428 0.236 NA
#> GSM148518 2 0.3999 0.683 0.000 0.500 0.000 0.004 0.000 NA
#> GSM148519 2 0.3999 0.683 0.000 0.500 0.000 0.004 0.000 NA
#> GSM148520 2 0.0622 0.745 0.000 0.980 0.000 0.000 0.008 NA
#> GSM148521 2 0.0260 0.742 0.000 0.992 0.000 0.000 0.008 NA
#> GSM148522 2 0.1196 0.751 0.000 0.952 0.000 0.008 0.000 NA
#> GSM148523 2 0.0000 0.743 0.000 1.000 0.000 0.000 0.000 NA
#> GSM148524 2 0.0000 0.743 0.000 1.000 0.000 0.000 0.000 NA
#> GSM148525 2 0.5358 0.659 0.000 0.484 0.000 0.032 0.044 NA
#> GSM148526 2 0.5358 0.659 0.000 0.484 0.000 0.032 0.044 NA
#> GSM148527 2 0.4325 0.752 0.000 0.692 0.000 0.064 0.000 NA
#> GSM148528 2 0.3999 0.683 0.000 0.500 0.000 0.004 0.000 NA
#> GSM148529 2 0.0000 0.743 0.000 1.000 0.000 0.000 0.000 NA
#> GSM148530 2 0.0000 0.743 0.000 1.000 0.000 0.000 0.000 NA
#> GSM148531 2 0.0000 0.743 0.000 1.000 0.000 0.000 0.000 NA
#> GSM148532 2 0.3874 0.756 0.000 0.776 0.000 0.060 0.008 NA
#> GSM148533 2 0.5358 0.659 0.000 0.484 0.000 0.032 0.044 NA
#> GSM148534 2 0.3999 0.683 0.000 0.500 0.000 0.004 0.000 NA
#> GSM148535 2 0.4621 0.738 0.000 0.632 0.000 0.064 0.000 NA
#> GSM148536 2 0.4392 0.749 0.000 0.680 0.000 0.064 0.000 NA
#> GSM148537 2 0.1007 0.744 0.000 0.956 0.000 0.044 0.000 NA
#> GSM148538 2 0.4149 0.754 0.000 0.720 0.000 0.064 0.000 NA
#> GSM148539 3 0.2006 0.962 0.000 0.104 0.892 0.000 0.000 NA
#> GSM148540 3 0.2006 0.962 0.000 0.104 0.892 0.000 0.000 NA
#> GSM148541 3 0.2361 0.961 0.000 0.104 0.880 0.004 0.000 NA
#> GSM148542 3 0.6472 0.783 0.000 0.104 0.624 0.144 0.056 NA
#> GSM148543 3 0.2006 0.962 0.000 0.104 0.892 0.000 0.004 NA
#> GSM148544 3 0.2149 0.962 0.000 0.104 0.888 0.004 0.004 NA
#> GSM148545 4 0.7886 0.539 0.100 0.000 0.068 0.432 0.236 NA
#> GSM148546 1 0.1065 0.900 0.964 0.000 0.000 0.008 0.008 NA
#> GSM148547 1 0.1065 0.900 0.964 0.000 0.000 0.008 0.008 NA
#> GSM148548 1 0.2431 0.881 0.860 0.000 0.000 0.008 0.000 NA
#> GSM148549 1 0.0146 0.902 0.996 0.000 0.000 0.000 0.000 NA
#> GSM148550 1 0.0665 0.896 0.980 0.000 0.000 0.008 0.008 NA
#> GSM148551 1 0.0810 0.896 0.976 0.000 0.004 0.008 0.008 NA
#> GSM148552 1 0.3975 0.806 0.716 0.000 0.000 0.040 0.000 NA
#> GSM148553 1 0.3975 0.806 0.716 0.000 0.000 0.040 0.000 NA
#> GSM148554 1 0.3975 0.806 0.716 0.000 0.000 0.040 0.000 NA
#> GSM148555 1 0.2473 0.880 0.856 0.000 0.000 0.008 0.000 NA
#> GSM148556 1 0.1462 0.898 0.936 0.000 0.000 0.008 0.000 NA
#> GSM148557 1 0.1138 0.902 0.960 0.000 0.000 0.012 0.004 NA
#> GSM148558 1 0.1363 0.882 0.952 0.000 0.004 0.028 0.012 NA
#> GSM148559 5 0.2053 0.920 0.108 0.000 0.004 0.000 0.888 NA
#> GSM148560 5 0.2563 0.918 0.108 0.000 0.008 0.008 0.872 NA
#> GSM148561 5 0.3278 0.902 0.108 0.000 0.004 0.028 0.840 NA
#> GSM148562 5 0.2565 0.913 0.104 0.000 0.016 0.008 0.872 NA
#> GSM148563 5 0.4277 0.719 0.080 0.000 0.028 0.112 0.776 NA
#> GSM148564 4 0.4950 0.793 0.080 0.000 0.000 0.576 0.344 NA
#> GSM148565 4 0.4926 0.797 0.080 0.000 0.000 0.584 0.336 NA
#> GSM148566 5 0.2754 0.914 0.116 0.000 0.008 0.012 0.860 NA
#> GSM148567 5 0.3237 0.899 0.112 0.000 0.004 0.028 0.840 NA
#> GSM148568 5 0.3192 0.901 0.108 0.000 0.004 0.028 0.844 NA
#> GSM148569 5 0.2405 0.911 0.100 0.000 0.016 0.004 0.880 NA
#> GSM148570 4 0.5335 0.794 0.080 0.000 0.016 0.568 0.336 NA
#> GSM148571 4 0.5335 0.794 0.080 0.000 0.016 0.568 0.336 NA
#> GSM148572 4 0.4926 0.797 0.080 0.000 0.000 0.584 0.336 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 agent(p) dose(p) time(p) k
#> ATC:kmeans 57 2.57e-12 1.00e+00 1.000 2
#> ATC:kmeans 57 2.57e-12 1.00e+00 1.000 3
#> ATC:kmeans 57 1.45e-10 4.71e-07 1.000 4
#> ATC:kmeans 57 1.45e-10 4.71e-07 1.000 5
#> ATC:kmeans 57 3.60e-10 2.04e-06 0.943 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21163 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5093 0.491 0.491
#> 3 3 1.000 0.998 0.997 0.1629 0.917 0.832
#> 4 4 1.000 0.999 0.998 0.2187 0.870 0.681
#> 5 5 0.953 0.908 0.902 0.0359 1.000 1.000
#> 6 6 0.870 0.832 0.863 0.0316 0.947 0.809
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
#> GSM148516 2 0 1 0 1
#> GSM148517 1 0 1 1 0
#> GSM148518 2 0 1 0 1
#> GSM148519 2 0 1 0 1
#> GSM148520 2 0 1 0 1
#> GSM148521 2 0 1 0 1
#> GSM148522 2 0 1 0 1
#> GSM148523 2 0 1 0 1
#> GSM148524 2 0 1 0 1
#> GSM148525 2 0 1 0 1
#> GSM148526 2 0 1 0 1
#> GSM148527 2 0 1 0 1
#> GSM148528 2 0 1 0 1
#> GSM148529 2 0 1 0 1
#> GSM148530 2 0 1 0 1
#> GSM148531 2 0 1 0 1
#> GSM148532 2 0 1 0 1
#> GSM148533 2 0 1 0 1
#> GSM148534 2 0 1 0 1
#> GSM148535 2 0 1 0 1
#> GSM148536 2 0 1 0 1
#> GSM148537 2 0 1 0 1
#> GSM148538 2 0 1 0 1
#> GSM148539 2 0 1 0 1
#> GSM148540 2 0 1 0 1
#> GSM148541 2 0 1 0 1
#> GSM148542 2 0 1 0 1
#> GSM148543 2 0 1 0 1
#> GSM148544 2 0 1 0 1
#> GSM148545 1 0 1 1 0
#> GSM148546 1 0 1 1 0
#> GSM148547 1 0 1 1 0
#> GSM148548 1 0 1 1 0
#> GSM148549 1 0 1 1 0
#> GSM148550 1 0 1 1 0
#> GSM148551 1 0 1 1 0
#> GSM148552 1 0 1 1 0
#> GSM148553 1 0 1 1 0
#> GSM148554 1 0 1 1 0
#> GSM148555 1 0 1 1 0
#> GSM148556 1 0 1 1 0
#> GSM148557 1 0 1 1 0
#> GSM148558 1 0 1 1 0
#> GSM148559 1 0 1 1 0
#> GSM148560 1 0 1 1 0
#> GSM148561 1 0 1 1 0
#> GSM148562 1 0 1 1 0
#> GSM148563 1 0 1 1 0
#> GSM148564 1 0 1 1 0
#> GSM148565 1 0 1 1 0
#> GSM148566 1 0 1 1 0
#> GSM148567 1 0 1 1 0
#> GSM148568 1 0 1 1 0
#> GSM148569 1 0 1 1 0
#> GSM148570 1 0 1 1 0
#> GSM148571 1 0 1 1 0
#> GSM148572 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM148516 3 0.0424 1.000 0.000 0.008 0.992
#> GSM148517 1 0.0000 0.997 1.000 0.000 0.000
#> GSM148518 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148519 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148520 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148521 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148522 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148523 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148524 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148525 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148526 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148527 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148528 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148529 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148530 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148531 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148532 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148533 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148534 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148535 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148536 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148537 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148538 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148539 3 0.0424 1.000 0.000 0.008 0.992
#> GSM148540 3 0.0424 1.000 0.000 0.008 0.992
#> GSM148541 3 0.0424 1.000 0.000 0.008 0.992
#> GSM148542 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148543 3 0.0424 1.000 0.000 0.008 0.992
#> GSM148544 3 0.0424 1.000 0.000 0.008 0.992
#> GSM148545 1 0.0000 0.997 1.000 0.000 0.000
#> GSM148546 1 0.0424 0.996 0.992 0.000 0.008
#> GSM148547 1 0.0424 0.996 0.992 0.000 0.008
#> GSM148548 1 0.0424 0.996 0.992 0.000 0.008
#> GSM148549 1 0.0424 0.996 0.992 0.000 0.008
#> GSM148550 1 0.0424 0.996 0.992 0.000 0.008
#> GSM148551 1 0.0424 0.996 0.992 0.000 0.008
#> GSM148552 1 0.0424 0.996 0.992 0.000 0.008
#> GSM148553 1 0.0424 0.996 0.992 0.000 0.008
#> GSM148554 1 0.0424 0.996 0.992 0.000 0.008
#> GSM148555 1 0.0424 0.996 0.992 0.000 0.008
#> GSM148556 1 0.0424 0.996 0.992 0.000 0.008
#> GSM148557 1 0.0424 0.996 0.992 0.000 0.008
#> GSM148558 1 0.0424 0.996 0.992 0.000 0.008
#> GSM148559 1 0.0000 0.997 1.000 0.000 0.000
#> GSM148560 1 0.0000 0.997 1.000 0.000 0.000
#> GSM148561 1 0.0000 0.997 1.000 0.000 0.000
#> GSM148562 1 0.0000 0.997 1.000 0.000 0.000
#> GSM148563 1 0.0000 0.997 1.000 0.000 0.000
#> GSM148564 1 0.0000 0.997 1.000 0.000 0.000
#> GSM148565 1 0.0000 0.997 1.000 0.000 0.000
#> GSM148566 1 0.0000 0.997 1.000 0.000 0.000
#> GSM148567 1 0.0000 0.997 1.000 0.000 0.000
#> GSM148568 1 0.0000 0.997 1.000 0.000 0.000
#> GSM148569 1 0.0000 0.997 1.000 0.000 0.000
#> GSM148570 1 0.0000 0.997 1.000 0.000 0.000
#> GSM148571 1 0.0000 0.997 1.000 0.000 0.000
#> GSM148572 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
#> GSM148516 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM148517 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM148518 2 0.0188 0.998 0.004 0.996 0 0.000
#> GSM148519 2 0.0188 0.998 0.004 0.996 0 0.000
#> GSM148520 2 0.0000 0.999 0.000 1.000 0 0.000
#> GSM148521 2 0.0000 0.999 0.000 1.000 0 0.000
#> GSM148522 2 0.0000 0.999 0.000 1.000 0 0.000
#> GSM148523 2 0.0000 0.999 0.000 1.000 0 0.000
#> GSM148524 2 0.0000 0.999 0.000 1.000 0 0.000
#> GSM148525 2 0.0188 0.998 0.004 0.996 0 0.000
#> GSM148526 2 0.0188 0.998 0.004 0.996 0 0.000
#> GSM148527 2 0.0000 0.999 0.000 1.000 0 0.000
#> GSM148528 2 0.0188 0.998 0.004 0.996 0 0.000
#> GSM148529 2 0.0000 0.999 0.000 1.000 0 0.000
#> GSM148530 2 0.0000 0.999 0.000 1.000 0 0.000
#> GSM148531 2 0.0000 0.999 0.000 1.000 0 0.000
#> GSM148532 2 0.0000 0.999 0.000 1.000 0 0.000
#> GSM148533 2 0.0188 0.998 0.004 0.996 0 0.000
#> GSM148534 2 0.0188 0.998 0.004 0.996 0 0.000
#> GSM148535 2 0.0000 0.999 0.000 1.000 0 0.000
#> GSM148536 2 0.0000 0.999 0.000 1.000 0 0.000
#> GSM148537 2 0.0000 0.999 0.000 1.000 0 0.000
#> GSM148538 2 0.0000 0.999 0.000 1.000 0 0.000
#> GSM148539 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM148540 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM148541 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM148542 2 0.0188 0.998 0.004 0.996 0 0.000
#> GSM148543 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM148544 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM148545 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM148546 1 0.0336 0.997 0.992 0.000 0 0.008
#> GSM148547 1 0.0336 0.997 0.992 0.000 0 0.008
#> GSM148548 1 0.0188 0.998 0.996 0.000 0 0.004
#> GSM148549 1 0.0188 0.998 0.996 0.000 0 0.004
#> GSM148550 1 0.0336 0.997 0.992 0.000 0 0.008
#> GSM148551 1 0.0336 0.997 0.992 0.000 0 0.008
#> GSM148552 1 0.0188 0.998 0.996 0.000 0 0.004
#> GSM148553 1 0.0188 0.998 0.996 0.000 0 0.004
#> GSM148554 1 0.0188 0.998 0.996 0.000 0 0.004
#> GSM148555 1 0.0188 0.998 0.996 0.000 0 0.004
#> GSM148556 1 0.0188 0.998 0.996 0.000 0 0.004
#> GSM148557 1 0.0336 0.997 0.992 0.000 0 0.008
#> GSM148558 1 0.0336 0.997 0.992 0.000 0 0.008
#> GSM148559 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM148560 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM148561 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM148562 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM148563 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM148564 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM148565 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM148566 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM148567 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM148568 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM148569 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM148570 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM148571 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM148572 4 0.0000 1.000 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
#> GSM148516 3 0.0290 0.976 0.000 0.000 0.992 0.000 NA
#> GSM148517 4 0.4718 0.721 0.016 0.000 0.000 0.540 NA
#> GSM148518 2 0.0703 0.982 0.000 0.976 0.000 0.000 NA
#> GSM148519 2 0.0703 0.982 0.000 0.976 0.000 0.000 NA
#> GSM148520 2 0.0000 0.988 0.000 1.000 0.000 0.000 NA
#> GSM148521 2 0.0290 0.987 0.000 0.992 0.000 0.000 NA
#> GSM148522 2 0.0290 0.987 0.000 0.992 0.000 0.000 NA
#> GSM148523 2 0.0290 0.987 0.000 0.992 0.000 0.000 NA
#> GSM148524 2 0.0290 0.987 0.000 0.992 0.000 0.000 NA
#> GSM148525 2 0.0703 0.982 0.000 0.976 0.000 0.000 NA
#> GSM148526 2 0.0703 0.982 0.000 0.976 0.000 0.000 NA
#> GSM148527 2 0.0000 0.988 0.000 1.000 0.000 0.000 NA
#> GSM148528 2 0.0703 0.982 0.000 0.976 0.000 0.000 NA
#> GSM148529 2 0.0290 0.987 0.000 0.992 0.000 0.000 NA
#> GSM148530 2 0.0290 0.987 0.000 0.992 0.000 0.000 NA
#> GSM148531 2 0.0290 0.987 0.000 0.992 0.000 0.000 NA
#> GSM148532 2 0.0000 0.988 0.000 1.000 0.000 0.000 NA
#> GSM148533 2 0.0703 0.982 0.000 0.976 0.000 0.000 NA
#> GSM148534 2 0.0703 0.982 0.000 0.976 0.000 0.000 NA
#> GSM148535 2 0.0000 0.988 0.000 1.000 0.000 0.000 NA
#> GSM148536 2 0.0000 0.988 0.000 1.000 0.000 0.000 NA
#> GSM148537 2 0.0290 0.987 0.000 0.992 0.000 0.000 NA
#> GSM148538 2 0.0162 0.988 0.000 0.996 0.000 0.000 NA
#> GSM148539 3 0.2605 0.912 0.000 0.000 0.852 0.000 NA
#> GSM148540 3 0.0404 0.978 0.000 0.000 0.988 0.000 NA
#> GSM148541 3 0.0404 0.978 0.000 0.000 0.988 0.000 NA
#> GSM148542 2 0.1549 0.960 0.000 0.944 0.016 0.000 NA
#> GSM148543 3 0.0000 0.978 0.000 0.000 1.000 0.000 NA
#> GSM148544 3 0.0000 0.978 0.000 0.000 1.000 0.000 NA
#> GSM148545 4 0.4942 0.716 0.028 0.000 0.000 0.540 NA
#> GSM148546 1 0.0000 0.942 1.000 0.000 0.000 0.000 NA
#> GSM148547 1 0.0000 0.942 1.000 0.000 0.000 0.000 NA
#> GSM148548 1 0.0000 0.942 1.000 0.000 0.000 0.000 NA
#> GSM148549 1 0.0000 0.942 1.000 0.000 0.000 0.000 NA
#> GSM148550 1 0.0000 0.942 1.000 0.000 0.000 0.000 NA
#> GSM148551 1 0.0000 0.942 1.000 0.000 0.000 0.000 NA
#> GSM148552 1 0.4030 0.667 0.648 0.000 0.000 0.000 NA
#> GSM148553 1 0.3949 0.687 0.668 0.000 0.000 0.000 NA
#> GSM148554 1 0.0162 0.941 0.996 0.000 0.000 0.000 NA
#> GSM148555 1 0.0000 0.942 1.000 0.000 0.000 0.000 NA
#> GSM148556 1 0.0880 0.928 0.968 0.000 0.000 0.000 NA
#> GSM148557 1 0.0880 0.928 0.968 0.000 0.000 0.000 NA
#> GSM148558 1 0.0880 0.928 0.968 0.000 0.000 0.000 NA
#> GSM148559 4 0.0162 0.811 0.000 0.000 0.000 0.996 NA
#> GSM148560 4 0.0162 0.811 0.000 0.000 0.000 0.996 NA
#> GSM148561 4 0.0162 0.811 0.000 0.000 0.000 0.996 NA
#> GSM148562 4 0.0290 0.814 0.000 0.000 0.000 0.992 NA
#> GSM148563 4 0.1544 0.812 0.000 0.000 0.000 0.932 NA
#> GSM148564 4 0.4210 0.768 0.000 0.000 0.000 0.588 NA
#> GSM148565 4 0.4210 0.768 0.000 0.000 0.000 0.588 NA
#> GSM148566 4 0.0162 0.811 0.000 0.000 0.000 0.996 NA
#> GSM148567 4 0.1478 0.823 0.000 0.000 0.000 0.936 NA
#> GSM148568 4 0.1270 0.822 0.000 0.000 0.000 0.948 NA
#> GSM148569 4 0.1671 0.824 0.000 0.000 0.000 0.924 NA
#> GSM148570 4 0.4192 0.771 0.000 0.000 0.000 0.596 NA
#> GSM148571 4 0.4192 0.771 0.000 0.000 0.000 0.596 NA
#> GSM148572 4 0.4210 0.768 0.000 0.000 0.000 0.588 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM148516 3 0.1176 0.925 0.000 0.000 0.956 0.000 0.020 0.024
#> GSM148517 4 0.4161 0.577 0.012 0.000 0.000 0.764 0.092 0.132
#> GSM148518 2 0.2328 0.918 0.000 0.892 0.000 0.000 0.052 0.056
#> GSM148519 2 0.2328 0.918 0.000 0.892 0.000 0.000 0.052 0.056
#> GSM148520 2 0.0520 0.942 0.000 0.984 0.000 0.000 0.008 0.008
#> GSM148521 2 0.0972 0.938 0.000 0.964 0.000 0.000 0.008 0.028
#> GSM148522 2 0.0891 0.939 0.000 0.968 0.000 0.000 0.008 0.024
#> GSM148523 2 0.0972 0.938 0.000 0.964 0.000 0.000 0.008 0.028
#> GSM148524 2 0.0972 0.938 0.000 0.964 0.000 0.000 0.008 0.028
#> GSM148525 2 0.2328 0.918 0.000 0.892 0.000 0.000 0.052 0.056
#> GSM148526 2 0.2328 0.918 0.000 0.892 0.000 0.000 0.052 0.056
#> GSM148527 2 0.0291 0.943 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM148528 2 0.2328 0.918 0.000 0.892 0.000 0.000 0.052 0.056
#> GSM148529 2 0.0972 0.938 0.000 0.964 0.000 0.000 0.008 0.028
#> GSM148530 2 0.0972 0.938 0.000 0.964 0.000 0.000 0.008 0.028
#> GSM148531 2 0.0972 0.938 0.000 0.964 0.000 0.000 0.008 0.028
#> GSM148532 2 0.0622 0.941 0.000 0.980 0.000 0.000 0.012 0.008
#> GSM148533 2 0.2328 0.918 0.000 0.892 0.000 0.000 0.052 0.056
#> GSM148534 2 0.2328 0.918 0.000 0.892 0.000 0.000 0.052 0.056
#> GSM148535 2 0.0622 0.941 0.000 0.980 0.000 0.000 0.012 0.008
#> GSM148536 2 0.0260 0.942 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM148537 2 0.0891 0.939 0.000 0.968 0.000 0.000 0.008 0.024
#> GSM148538 2 0.0146 0.942 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM148539 3 0.3920 0.759 0.000 0.000 0.736 0.000 0.216 0.048
#> GSM148540 3 0.0520 0.938 0.000 0.000 0.984 0.000 0.008 0.008
#> GSM148541 3 0.0891 0.936 0.000 0.000 0.968 0.000 0.024 0.008
#> GSM148542 2 0.3755 0.848 0.000 0.804 0.016 0.000 0.076 0.104
#> GSM148543 3 0.0291 0.939 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM148544 3 0.0405 0.939 0.000 0.000 0.988 0.000 0.008 0.004
#> GSM148545 4 0.5071 0.531 0.056 0.000 0.000 0.708 0.104 0.132
#> GSM148546 1 0.0146 0.962 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM148547 1 0.0000 0.963 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM148548 1 0.0363 0.958 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM148549 1 0.0000 0.963 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM148550 1 0.0000 0.963 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM148551 1 0.0000 0.963 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM148552 6 0.3464 0.917 0.312 0.000 0.000 0.000 0.000 0.688
#> GSM148553 6 0.3371 0.919 0.292 0.000 0.000 0.000 0.000 0.708
#> GSM148554 1 0.0937 0.932 0.960 0.000 0.000 0.000 0.000 0.040
#> GSM148555 1 0.0458 0.956 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM148556 1 0.1124 0.931 0.956 0.000 0.000 0.036 0.008 0.000
#> GSM148557 1 0.1398 0.912 0.940 0.000 0.000 0.052 0.008 0.000
#> GSM148558 1 0.1327 0.902 0.936 0.000 0.000 0.064 0.000 0.000
#> GSM148559 5 0.3659 0.915 0.000 0.000 0.000 0.364 0.636 0.000
#> GSM148560 5 0.3672 0.917 0.000 0.000 0.000 0.368 0.632 0.000
#> GSM148561 5 0.3807 0.917 0.004 0.000 0.000 0.368 0.628 0.000
#> GSM148562 5 0.3717 0.910 0.000 0.000 0.000 0.384 0.616 0.000
#> GSM148563 5 0.3862 0.754 0.000 0.000 0.000 0.476 0.524 0.000
#> GSM148564 4 0.0000 0.700 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM148565 4 0.0000 0.700 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM148566 5 0.3899 0.913 0.008 0.000 0.000 0.364 0.628 0.000
#> GSM148567 4 0.3998 -0.689 0.000 0.000 0.000 0.504 0.492 0.004
#> GSM148568 5 0.3857 0.741 0.000 0.000 0.000 0.468 0.532 0.000
#> GSM148569 4 0.3857 -0.668 0.000 0.000 0.000 0.532 0.468 0.000
#> GSM148570 4 0.0260 0.697 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM148571 4 0.0458 0.690 0.000 0.000 0.000 0.984 0.016 0.000
#> GSM148572 4 0.0000 0.700 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) dose(p) time(p) k
#> ATC:skmeans 57 2.57e-12 1.00e+00 1.000 2
#> ATC:skmeans 57 4.87e-12 4.14e-03 0.970 3
#> ATC:skmeans 57 7.72e-11 3.16e-06 0.997 4
#> ATC:skmeans 57 7.72e-11 3.16e-06 0.997 5
#> ATC:skmeans 55 8.21e-09 2.37e-05 0.879 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 21163 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5093 0.491 0.491
#> 3 3 1.000 0.988 0.995 0.1674 0.917 0.832
#> 4 4 1.000 0.979 0.991 0.2194 0.870 0.681
#> 5 5 0.959 0.949 0.969 0.0275 0.982 0.937
#> 6 6 0.928 0.893 0.910 0.0339 0.962 0.856
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 4 5
There is also optional best \(k\) = 2 3 4 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM148516 2 0 1 0 1
#> GSM148517 1 0 1 1 0
#> GSM148518 2 0 1 0 1
#> GSM148519 2 0 1 0 1
#> GSM148520 2 0 1 0 1
#> GSM148521 2 0 1 0 1
#> GSM148522 2 0 1 0 1
#> GSM148523 2 0 1 0 1
#> GSM148524 2 0 1 0 1
#> GSM148525 2 0 1 0 1
#> GSM148526 2 0 1 0 1
#> GSM148527 2 0 1 0 1
#> GSM148528 2 0 1 0 1
#> GSM148529 2 0 1 0 1
#> GSM148530 2 0 1 0 1
#> GSM148531 2 0 1 0 1
#> GSM148532 2 0 1 0 1
#> GSM148533 2 0 1 0 1
#> GSM148534 2 0 1 0 1
#> GSM148535 2 0 1 0 1
#> GSM148536 2 0 1 0 1
#> GSM148537 2 0 1 0 1
#> GSM148538 2 0 1 0 1
#> GSM148539 2 0 1 0 1
#> GSM148540 2 0 1 0 1
#> GSM148541 2 0 1 0 1
#> GSM148542 2 0 1 0 1
#> GSM148543 2 0 1 0 1
#> GSM148544 2 0 1 0 1
#> GSM148545 1 0 1 1 0
#> GSM148546 1 0 1 1 0
#> GSM148547 1 0 1 1 0
#> GSM148548 1 0 1 1 0
#> GSM148549 1 0 1 1 0
#> GSM148550 1 0 1 1 0
#> GSM148551 1 0 1 1 0
#> GSM148552 1 0 1 1 0
#> GSM148553 1 0 1 1 0
#> GSM148554 1 0 1 1 0
#> GSM148555 1 0 1 1 0
#> GSM148556 1 0 1 1 0
#> GSM148557 1 0 1 1 0
#> GSM148558 1 0 1 1 0
#> GSM148559 1 0 1 1 0
#> GSM148560 1 0 1 1 0
#> GSM148561 1 0 1 1 0
#> GSM148562 1 0 1 1 0
#> GSM148563 1 0 1 1 0
#> GSM148564 1 0 1 1 0
#> GSM148565 1 0 1 1 0
#> GSM148566 1 0 1 1 0
#> GSM148567 1 0 1 1 0
#> GSM148568 1 0 1 1 0
#> GSM148569 1 0 1 1 0
#> GSM148570 1 0 1 1 0
#> GSM148571 1 0 1 1 0
#> GSM148572 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM148516 3 0.00 1.000 0 0.00 1.00
#> GSM148517 1 0.00 1.000 1 0.00 0.00
#> GSM148518 2 0.00 0.986 0 1.00 0.00
#> GSM148519 2 0.00 0.986 0 1.00 0.00
#> GSM148520 2 0.00 0.986 0 1.00 0.00
#> GSM148521 2 0.00 0.986 0 1.00 0.00
#> GSM148522 2 0.00 0.986 0 1.00 0.00
#> GSM148523 2 0.00 0.986 0 1.00 0.00
#> GSM148524 2 0.00 0.986 0 1.00 0.00
#> GSM148525 2 0.00 0.986 0 1.00 0.00
#> GSM148526 2 0.00 0.986 0 1.00 0.00
#> GSM148527 2 0.00 0.986 0 1.00 0.00
#> GSM148528 2 0.00 0.986 0 1.00 0.00
#> GSM148529 2 0.00 0.986 0 1.00 0.00
#> GSM148530 2 0.00 0.986 0 1.00 0.00
#> GSM148531 2 0.00 0.986 0 1.00 0.00
#> GSM148532 2 0.00 0.986 0 1.00 0.00
#> GSM148533 2 0.00 0.986 0 1.00 0.00
#> GSM148534 2 0.00 0.986 0 1.00 0.00
#> GSM148535 2 0.00 0.986 0 1.00 0.00
#> GSM148536 2 0.00 0.986 0 1.00 0.00
#> GSM148537 2 0.00 0.986 0 1.00 0.00
#> GSM148538 2 0.00 0.986 0 1.00 0.00
#> GSM148539 3 0.00 1.000 0 0.00 1.00
#> GSM148540 3 0.00 1.000 0 0.00 1.00
#> GSM148541 3 0.00 1.000 0 0.00 1.00
#> GSM148542 2 0.54 0.611 0 0.72 0.28
#> GSM148543 3 0.00 1.000 0 0.00 1.00
#> GSM148544 3 0.00 1.000 0 0.00 1.00
#> GSM148545 1 0.00 1.000 1 0.00 0.00
#> GSM148546 1 0.00 1.000 1 0.00 0.00
#> GSM148547 1 0.00 1.000 1 0.00 0.00
#> GSM148548 1 0.00 1.000 1 0.00 0.00
#> GSM148549 1 0.00 1.000 1 0.00 0.00
#> GSM148550 1 0.00 1.000 1 0.00 0.00
#> GSM148551 1 0.00 1.000 1 0.00 0.00
#> GSM148552 1 0.00 1.000 1 0.00 0.00
#> GSM148553 1 0.00 1.000 1 0.00 0.00
#> GSM148554 1 0.00 1.000 1 0.00 0.00
#> GSM148555 1 0.00 1.000 1 0.00 0.00
#> GSM148556 1 0.00 1.000 1 0.00 0.00
#> GSM148557 1 0.00 1.000 1 0.00 0.00
#> GSM148558 1 0.00 1.000 1 0.00 0.00
#> GSM148559 1 0.00 1.000 1 0.00 0.00
#> GSM148560 1 0.00 1.000 1 0.00 0.00
#> GSM148561 1 0.00 1.000 1 0.00 0.00
#> GSM148562 1 0.00 1.000 1 0.00 0.00
#> GSM148563 1 0.00 1.000 1 0.00 0.00
#> GSM148564 1 0.00 1.000 1 0.00 0.00
#> GSM148565 1 0.00 1.000 1 0.00 0.00
#> GSM148566 1 0.00 1.000 1 0.00 0.00
#> GSM148567 1 0.00 1.000 1 0.00 0.00
#> GSM148568 1 0.00 1.000 1 0.00 0.00
#> GSM148569 1 0.00 1.000 1 0.00 0.00
#> GSM148570 1 0.00 1.000 1 0.00 0.00
#> GSM148571 1 0.00 1.000 1 0.00 0.00
#> GSM148572 1 0.00 1.000 1 0.00 0.00
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM148516 3 0.0000 1.000 0.000 0.00 1.00 0.000
#> GSM148517 4 0.0469 0.975 0.012 0.00 0.00 0.988
#> GSM148518 2 0.0000 0.986 0.000 1.00 0.00 0.000
#> GSM148519 2 0.0000 0.986 0.000 1.00 0.00 0.000
#> GSM148520 2 0.0000 0.986 0.000 1.00 0.00 0.000
#> GSM148521 2 0.0000 0.986 0.000 1.00 0.00 0.000
#> GSM148522 2 0.0000 0.986 0.000 1.00 0.00 0.000
#> GSM148523 2 0.0000 0.986 0.000 1.00 0.00 0.000
#> GSM148524 2 0.0000 0.986 0.000 1.00 0.00 0.000
#> GSM148525 2 0.0000 0.986 0.000 1.00 0.00 0.000
#> GSM148526 2 0.0000 0.986 0.000 1.00 0.00 0.000
#> GSM148527 2 0.0000 0.986 0.000 1.00 0.00 0.000
#> GSM148528 2 0.0000 0.986 0.000 1.00 0.00 0.000
#> GSM148529 2 0.0000 0.986 0.000 1.00 0.00 0.000
#> GSM148530 2 0.0000 0.986 0.000 1.00 0.00 0.000
#> GSM148531 2 0.0000 0.986 0.000 1.00 0.00 0.000
#> GSM148532 2 0.0000 0.986 0.000 1.00 0.00 0.000
#> GSM148533 2 0.0000 0.986 0.000 1.00 0.00 0.000
#> GSM148534 2 0.0000 0.986 0.000 1.00 0.00 0.000
#> GSM148535 2 0.0000 0.986 0.000 1.00 0.00 0.000
#> GSM148536 2 0.0000 0.986 0.000 1.00 0.00 0.000
#> GSM148537 2 0.0000 0.986 0.000 1.00 0.00 0.000
#> GSM148538 2 0.0000 0.986 0.000 1.00 0.00 0.000
#> GSM148539 3 0.0000 1.000 0.000 0.00 1.00 0.000
#> GSM148540 3 0.0000 1.000 0.000 0.00 1.00 0.000
#> GSM148541 3 0.0000 1.000 0.000 0.00 1.00 0.000
#> GSM148542 2 0.4277 0.611 0.000 0.72 0.28 0.000
#> GSM148543 3 0.0000 1.000 0.000 0.00 1.00 0.000
#> GSM148544 3 0.0000 1.000 0.000 0.00 1.00 0.000
#> GSM148545 4 0.0469 0.975 0.012 0.00 0.00 0.988
#> GSM148546 1 0.0000 1.000 1.000 0.00 0.00 0.000
#> GSM148547 1 0.0000 1.000 1.000 0.00 0.00 0.000
#> GSM148548 1 0.0000 1.000 1.000 0.00 0.00 0.000
#> GSM148549 1 0.0000 1.000 1.000 0.00 0.00 0.000
#> GSM148550 1 0.0000 1.000 1.000 0.00 0.00 0.000
#> GSM148551 1 0.0000 1.000 1.000 0.00 0.00 0.000
#> GSM148552 1 0.0000 1.000 1.000 0.00 0.00 0.000
#> GSM148553 1 0.0000 1.000 1.000 0.00 0.00 0.000
#> GSM148554 1 0.0000 1.000 1.000 0.00 0.00 0.000
#> GSM148555 1 0.0000 1.000 1.000 0.00 0.00 0.000
#> GSM148556 1 0.0000 1.000 1.000 0.00 0.00 0.000
#> GSM148557 1 0.0000 1.000 1.000 0.00 0.00 0.000
#> GSM148558 1 0.0000 1.000 1.000 0.00 0.00 0.000
#> GSM148559 4 0.0000 0.982 0.000 0.00 0.00 1.000
#> GSM148560 4 0.0000 0.982 0.000 0.00 0.00 1.000
#> GSM148561 4 0.0000 0.982 0.000 0.00 0.00 1.000
#> GSM148562 4 0.0000 0.982 0.000 0.00 0.00 1.000
#> GSM148563 4 0.0000 0.982 0.000 0.00 0.00 1.000
#> GSM148564 4 0.0000 0.982 0.000 0.00 0.00 1.000
#> GSM148565 4 0.0188 0.981 0.004 0.00 0.00 0.996
#> GSM148566 4 0.3569 0.748 0.196 0.00 0.00 0.804
#> GSM148567 4 0.0000 0.982 0.000 0.00 0.00 1.000
#> GSM148568 4 0.0000 0.982 0.000 0.00 0.00 1.000
#> GSM148569 4 0.0000 0.982 0.000 0.00 0.00 1.000
#> GSM148570 4 0.0000 0.982 0.000 0.00 0.00 1.000
#> GSM148571 4 0.0188 0.981 0.004 0.00 0.00 0.996
#> GSM148572 4 0.0188 0.981 0.004 0.00 0.00 0.996
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM148516 3 0.0000 1.000 0.000 0.00 1.00 0.000 0.000
#> GSM148517 5 0.2127 0.956 0.000 0.00 0.00 0.108 0.892
#> GSM148518 2 0.0000 0.986 0.000 1.00 0.00 0.000 0.000
#> GSM148519 2 0.0000 0.986 0.000 1.00 0.00 0.000 0.000
#> GSM148520 2 0.0000 0.986 0.000 1.00 0.00 0.000 0.000
#> GSM148521 2 0.0000 0.986 0.000 1.00 0.00 0.000 0.000
#> GSM148522 2 0.0000 0.986 0.000 1.00 0.00 0.000 0.000
#> GSM148523 2 0.0000 0.986 0.000 1.00 0.00 0.000 0.000
#> GSM148524 2 0.0000 0.986 0.000 1.00 0.00 0.000 0.000
#> GSM148525 2 0.0000 0.986 0.000 1.00 0.00 0.000 0.000
#> GSM148526 2 0.0000 0.986 0.000 1.00 0.00 0.000 0.000
#> GSM148527 2 0.0000 0.986 0.000 1.00 0.00 0.000 0.000
#> GSM148528 2 0.0000 0.986 0.000 1.00 0.00 0.000 0.000
#> GSM148529 2 0.0000 0.986 0.000 1.00 0.00 0.000 0.000
#> GSM148530 2 0.0000 0.986 0.000 1.00 0.00 0.000 0.000
#> GSM148531 2 0.0000 0.986 0.000 1.00 0.00 0.000 0.000
#> GSM148532 2 0.0000 0.986 0.000 1.00 0.00 0.000 0.000
#> GSM148533 2 0.0000 0.986 0.000 1.00 0.00 0.000 0.000
#> GSM148534 2 0.0000 0.986 0.000 1.00 0.00 0.000 0.000
#> GSM148535 2 0.0000 0.986 0.000 1.00 0.00 0.000 0.000
#> GSM148536 2 0.0000 0.986 0.000 1.00 0.00 0.000 0.000
#> GSM148537 2 0.0000 0.986 0.000 1.00 0.00 0.000 0.000
#> GSM148538 2 0.0000 0.986 0.000 1.00 0.00 0.000 0.000
#> GSM148539 3 0.0000 1.000 0.000 0.00 1.00 0.000 0.000
#> GSM148540 3 0.0000 1.000 0.000 0.00 1.00 0.000 0.000
#> GSM148541 3 0.0000 1.000 0.000 0.00 1.00 0.000 0.000
#> GSM148542 2 0.3684 0.611 0.000 0.72 0.28 0.000 0.000
#> GSM148543 3 0.0000 1.000 0.000 0.00 1.00 0.000 0.000
#> GSM148544 3 0.0000 1.000 0.000 0.00 1.00 0.000 0.000
#> GSM148545 5 0.2516 0.956 0.000 0.00 0.00 0.140 0.860
#> GSM148546 1 0.0000 0.942 1.000 0.00 0.00 0.000 0.000
#> GSM148547 1 0.0000 0.942 1.000 0.00 0.00 0.000 0.000
#> GSM148548 1 0.0290 0.943 0.992 0.00 0.00 0.000 0.008
#> GSM148549 1 0.0609 0.942 0.980 0.00 0.00 0.000 0.020
#> GSM148550 1 0.0703 0.942 0.976 0.00 0.00 0.000 0.024
#> GSM148551 1 0.0703 0.942 0.976 0.00 0.00 0.000 0.024
#> GSM148552 1 0.2179 0.918 0.888 0.00 0.00 0.000 0.112
#> GSM148553 1 0.2179 0.918 0.888 0.00 0.00 0.000 0.112
#> GSM148554 1 0.2179 0.918 0.888 0.00 0.00 0.000 0.112
#> GSM148555 1 0.2179 0.918 0.888 0.00 0.00 0.000 0.112
#> GSM148556 1 0.2471 0.916 0.864 0.00 0.00 0.000 0.136
#> GSM148557 1 0.0794 0.942 0.972 0.00 0.00 0.000 0.028
#> GSM148558 1 0.0703 0.942 0.976 0.00 0.00 0.000 0.024
#> GSM148559 4 0.0000 0.947 0.000 0.00 0.00 1.000 0.000
#> GSM148560 4 0.0000 0.947 0.000 0.00 0.00 1.000 0.000
#> GSM148561 4 0.0000 0.947 0.000 0.00 0.00 1.000 0.000
#> GSM148562 4 0.0000 0.947 0.000 0.00 0.00 1.000 0.000
#> GSM148563 4 0.0290 0.945 0.000 0.00 0.00 0.992 0.008
#> GSM148564 4 0.0963 0.936 0.000 0.00 0.00 0.964 0.036
#> GSM148565 4 0.1410 0.923 0.000 0.00 0.00 0.940 0.060
#> GSM148566 4 0.3661 0.516 0.276 0.00 0.00 0.724 0.000
#> GSM148567 4 0.0000 0.947 0.000 0.00 0.00 1.000 0.000
#> GSM148568 4 0.0000 0.947 0.000 0.00 0.00 1.000 0.000
#> GSM148569 4 0.0000 0.947 0.000 0.00 0.00 1.000 0.000
#> GSM148570 4 0.0963 0.936 0.000 0.00 0.00 0.964 0.036
#> GSM148571 4 0.1410 0.923 0.000 0.00 0.00 0.940 0.060
#> GSM148572 4 0.1410 0.923 0.000 0.00 0.00 0.940 0.060
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM148516 3 0.0000 1.000 0.000 0.00 1.00 0.000 0.000 0.000
#> GSM148517 6 0.0000 0.951 0.000 0.00 0.00 0.000 0.000 1.000
#> GSM148518 2 0.0000 0.985 0.000 1.00 0.00 0.000 0.000 0.000
#> GSM148519 2 0.0000 0.985 0.000 1.00 0.00 0.000 0.000 0.000
#> GSM148520 2 0.0000 0.985 0.000 1.00 0.00 0.000 0.000 0.000
#> GSM148521 2 0.0000 0.985 0.000 1.00 0.00 0.000 0.000 0.000
#> GSM148522 2 0.0000 0.985 0.000 1.00 0.00 0.000 0.000 0.000
#> GSM148523 2 0.0000 0.985 0.000 1.00 0.00 0.000 0.000 0.000
#> GSM148524 2 0.0000 0.985 0.000 1.00 0.00 0.000 0.000 0.000
#> GSM148525 2 0.0000 0.985 0.000 1.00 0.00 0.000 0.000 0.000
#> GSM148526 2 0.0000 0.985 0.000 1.00 0.00 0.000 0.000 0.000
#> GSM148527 2 0.0000 0.985 0.000 1.00 0.00 0.000 0.000 0.000
#> GSM148528 2 0.0000 0.985 0.000 1.00 0.00 0.000 0.000 0.000
#> GSM148529 2 0.0000 0.985 0.000 1.00 0.00 0.000 0.000 0.000
#> GSM148530 2 0.0000 0.985 0.000 1.00 0.00 0.000 0.000 0.000
#> GSM148531 2 0.0000 0.985 0.000 1.00 0.00 0.000 0.000 0.000
#> GSM148532 2 0.0000 0.985 0.000 1.00 0.00 0.000 0.000 0.000
#> GSM148533 2 0.0000 0.985 0.000 1.00 0.00 0.000 0.000 0.000
#> GSM148534 2 0.0000 0.985 0.000 1.00 0.00 0.000 0.000 0.000
#> GSM148535 2 0.0000 0.985 0.000 1.00 0.00 0.000 0.000 0.000
#> GSM148536 2 0.0000 0.985 0.000 1.00 0.00 0.000 0.000 0.000
#> GSM148537 2 0.0000 0.985 0.000 1.00 0.00 0.000 0.000 0.000
#> GSM148538 2 0.0000 0.985 0.000 1.00 0.00 0.000 0.000 0.000
#> GSM148539 3 0.0000 1.000 0.000 0.00 1.00 0.000 0.000 0.000
#> GSM148540 3 0.0000 1.000 0.000 0.00 1.00 0.000 0.000 0.000
#> GSM148541 3 0.0000 1.000 0.000 0.00 1.00 0.000 0.000 0.000
#> GSM148542 2 0.3309 0.608 0.000 0.72 0.28 0.000 0.000 0.000
#> GSM148543 3 0.0000 1.000 0.000 0.00 1.00 0.000 0.000 0.000
#> GSM148544 3 0.0000 1.000 0.000 0.00 1.00 0.000 0.000 0.000
#> GSM148545 6 0.0865 0.951 0.000 0.00 0.00 0.036 0.000 0.964
#> GSM148546 1 0.0000 0.873 1.000 0.00 0.00 0.000 0.000 0.000
#> GSM148547 1 0.0000 0.873 1.000 0.00 0.00 0.000 0.000 0.000
#> GSM148548 1 0.1327 0.760 0.936 0.00 0.00 0.000 0.064 0.000
#> GSM148549 1 0.0000 0.873 1.000 0.00 0.00 0.000 0.000 0.000
#> GSM148550 1 0.0000 0.873 1.000 0.00 0.00 0.000 0.000 0.000
#> GSM148551 1 0.0000 0.873 1.000 0.00 0.00 0.000 0.000 0.000
#> GSM148552 5 0.3833 0.998 0.444 0.00 0.00 0.000 0.556 0.000
#> GSM148553 5 0.3961 0.991 0.440 0.00 0.00 0.004 0.556 0.000
#> GSM148554 5 0.3833 0.998 0.444 0.00 0.00 0.000 0.556 0.000
#> GSM148555 5 0.3833 0.998 0.444 0.00 0.00 0.000 0.556 0.000
#> GSM148556 5 0.3833 0.998 0.444 0.00 0.00 0.000 0.556 0.000
#> GSM148557 1 0.0000 0.873 1.000 0.00 0.00 0.000 0.000 0.000
#> GSM148558 1 0.0000 0.873 1.000 0.00 0.00 0.000 0.000 0.000
#> GSM148559 4 0.0000 0.812 0.000 0.00 0.00 1.000 0.000 0.000
#> GSM148560 4 0.0000 0.812 0.000 0.00 0.00 1.000 0.000 0.000
#> GSM148561 4 0.0000 0.812 0.000 0.00 0.00 1.000 0.000 0.000
#> GSM148562 4 0.0000 0.812 0.000 0.00 0.00 1.000 0.000 0.000
#> GSM148563 4 0.0508 0.809 0.000 0.00 0.00 0.984 0.012 0.004
#> GSM148564 4 0.4578 0.575 0.000 0.00 0.00 0.520 0.444 0.036
#> GSM148565 4 0.4578 0.575 0.000 0.00 0.00 0.520 0.444 0.036
#> GSM148566 1 0.3737 0.290 0.608 0.00 0.00 0.392 0.000 0.000
#> GSM148567 4 0.0000 0.812 0.000 0.00 0.00 1.000 0.000 0.000
#> GSM148568 4 0.0000 0.812 0.000 0.00 0.00 1.000 0.000 0.000
#> GSM148569 4 0.0000 0.812 0.000 0.00 0.00 1.000 0.000 0.000
#> GSM148570 4 0.3283 0.737 0.000 0.00 0.00 0.804 0.160 0.036
#> GSM148571 4 0.4578 0.575 0.000 0.00 0.00 0.520 0.444 0.036
#> GSM148572 4 0.4578 0.575 0.000 0.00 0.00 0.520 0.444 0.036
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) dose(p) time(p) k
#> ATC:pam 57 2.57e-12 1.00e+00 1.000 2
#> ATC:pam 57 4.87e-12 4.14e-03 0.970 3
#> ATC:pam 57 7.72e-11 3.16e-06 0.997 4
#> ATC:pam 57 1.83e-14 5.10e-08 0.726 5
#> ATC:pam 56 7.77e-13 5.69e-09 0.801 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 21163 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.781 0.903 0.953 0.4960 0.491 0.491
#> 3 3 0.647 0.713 0.826 0.2584 0.756 0.543
#> 4 4 0.955 0.853 0.939 0.1752 0.854 0.605
#> 5 5 0.935 0.925 0.914 0.0366 0.945 0.800
#> 6 6 0.941 0.862 0.922 0.0318 0.972 0.884
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 4 5
There is also optional best \(k\) = 4 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM148516 2 0.958 0.523 0.38 0.62
#> GSM148517 1 0.000 1.000 1.00 0.00
#> GSM148518 2 0.000 0.895 0.00 1.00
#> GSM148519 2 0.000 0.895 0.00 1.00
#> GSM148520 2 0.000 0.895 0.00 1.00
#> GSM148521 2 0.000 0.895 0.00 1.00
#> GSM148522 2 0.000 0.895 0.00 1.00
#> GSM148523 2 0.000 0.895 0.00 1.00
#> GSM148524 2 0.000 0.895 0.00 1.00
#> GSM148525 2 0.000 0.895 0.00 1.00
#> GSM148526 2 0.000 0.895 0.00 1.00
#> GSM148527 2 0.000 0.895 0.00 1.00
#> GSM148528 2 0.000 0.895 0.00 1.00
#> GSM148529 2 0.000 0.895 0.00 1.00
#> GSM148530 2 0.000 0.895 0.00 1.00
#> GSM148531 2 0.000 0.895 0.00 1.00
#> GSM148532 2 0.000 0.895 0.00 1.00
#> GSM148533 2 0.000 0.895 0.00 1.00
#> GSM148534 2 0.000 0.895 0.00 1.00
#> GSM148535 2 0.000 0.895 0.00 1.00
#> GSM148536 2 0.000 0.895 0.00 1.00
#> GSM148537 2 0.000 0.895 0.00 1.00
#> GSM148538 2 0.000 0.895 0.00 1.00
#> GSM148539 2 0.958 0.523 0.38 0.62
#> GSM148540 2 0.958 0.523 0.38 0.62
#> GSM148541 2 0.958 0.523 0.38 0.62
#> GSM148542 2 0.958 0.523 0.38 0.62
#> GSM148543 2 0.958 0.523 0.38 0.62
#> GSM148544 2 0.958 0.523 0.38 0.62
#> GSM148545 1 0.000 1.000 1.00 0.00
#> GSM148546 1 0.000 1.000 1.00 0.00
#> GSM148547 1 0.000 1.000 1.00 0.00
#> GSM148548 1 0.000 1.000 1.00 0.00
#> GSM148549 1 0.000 1.000 1.00 0.00
#> GSM148550 1 0.000 1.000 1.00 0.00
#> GSM148551 1 0.000 1.000 1.00 0.00
#> GSM148552 1 0.000 1.000 1.00 0.00
#> GSM148553 1 0.000 1.000 1.00 0.00
#> GSM148554 1 0.000 1.000 1.00 0.00
#> GSM148555 1 0.000 1.000 1.00 0.00
#> GSM148556 1 0.000 1.000 1.00 0.00
#> GSM148557 1 0.000 1.000 1.00 0.00
#> GSM148558 1 0.000 1.000 1.00 0.00
#> GSM148559 1 0.000 1.000 1.00 0.00
#> GSM148560 1 0.000 1.000 1.00 0.00
#> GSM148561 1 0.000 1.000 1.00 0.00
#> GSM148562 1 0.000 1.000 1.00 0.00
#> GSM148563 1 0.000 1.000 1.00 0.00
#> GSM148564 1 0.000 1.000 1.00 0.00
#> GSM148565 1 0.000 1.000 1.00 0.00
#> GSM148566 1 0.000 1.000 1.00 0.00
#> GSM148567 1 0.000 1.000 1.00 0.00
#> GSM148568 1 0.000 1.000 1.00 0.00
#> GSM148569 1 0.000 1.000 1.00 0.00
#> GSM148570 1 0.000 1.000 1.00 0.00
#> GSM148571 1 0.000 1.000 1.00 0.00
#> GSM148572 1 0.000 1.000 1.00 0.00
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM148516 3 0.9329 0.205 0.400 0.164 0.436
#> GSM148517 1 0.5926 0.413 0.644 0.000 0.356
#> GSM148518 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148519 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148520 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148521 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148522 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148523 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148524 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148525 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148526 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148527 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148528 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148529 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148530 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148531 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148532 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148533 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148534 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148535 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148536 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148537 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148538 2 0.0000 1.000 0.000 1.000 0.000
#> GSM148539 3 0.9329 0.205 0.400 0.164 0.436
#> GSM148540 3 0.9293 0.204 0.400 0.160 0.440
#> GSM148541 3 0.9293 0.204 0.400 0.160 0.440
#> GSM148542 1 0.9602 -0.270 0.400 0.200 0.400
#> GSM148543 3 0.9364 0.203 0.400 0.168 0.432
#> GSM148544 3 0.9329 0.205 0.400 0.164 0.436
#> GSM148545 1 0.5926 0.413 0.644 0.000 0.356
#> GSM148546 3 0.5397 0.518 0.280 0.000 0.720
#> GSM148547 3 0.5397 0.518 0.280 0.000 0.720
#> GSM148548 3 0.5397 0.518 0.280 0.000 0.720
#> GSM148549 3 0.5397 0.518 0.280 0.000 0.720
#> GSM148550 3 0.5397 0.518 0.280 0.000 0.720
#> GSM148551 3 0.5397 0.518 0.280 0.000 0.720
#> GSM148552 1 0.5760 0.417 0.672 0.000 0.328
#> GSM148553 1 0.4346 0.626 0.816 0.000 0.184
#> GSM148554 3 0.5397 0.518 0.280 0.000 0.720
#> GSM148555 3 0.5397 0.518 0.280 0.000 0.720
#> GSM148556 1 0.5621 0.455 0.692 0.000 0.308
#> GSM148557 1 0.5621 0.455 0.692 0.000 0.308
#> GSM148558 1 0.4702 0.595 0.788 0.000 0.212
#> GSM148559 1 0.0000 0.798 1.000 0.000 0.000
#> GSM148560 1 0.0000 0.798 1.000 0.000 0.000
#> GSM148561 1 0.0237 0.796 0.996 0.000 0.004
#> GSM148562 1 0.0000 0.798 1.000 0.000 0.000
#> GSM148563 1 0.0000 0.798 1.000 0.000 0.000
#> GSM148564 1 0.0000 0.798 1.000 0.000 0.000
#> GSM148565 1 0.0237 0.796 0.996 0.000 0.004
#> GSM148566 1 0.0237 0.796 0.996 0.000 0.004
#> GSM148567 1 0.0000 0.798 1.000 0.000 0.000
#> GSM148568 1 0.0000 0.798 1.000 0.000 0.000
#> GSM148569 1 0.0000 0.798 1.000 0.000 0.000
#> GSM148570 1 0.0237 0.796 0.996 0.000 0.004
#> GSM148571 1 0.0000 0.798 1.000 0.000 0.000
#> GSM148572 1 0.0237 0.796 0.996 0.000 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM148516 3 0.000 0.8138 0.000 0.00 1.000 0.000
#> GSM148517 3 0.771 -0.0895 0.376 0.00 0.400 0.224
#> GSM148518 2 0.000 1.0000 0.000 1.00 0.000 0.000
#> GSM148519 2 0.000 1.0000 0.000 1.00 0.000 0.000
#> GSM148520 2 0.000 1.0000 0.000 1.00 0.000 0.000
#> GSM148521 2 0.000 1.0000 0.000 1.00 0.000 0.000
#> GSM148522 2 0.000 1.0000 0.000 1.00 0.000 0.000
#> GSM148523 2 0.000 1.0000 0.000 1.00 0.000 0.000
#> GSM148524 2 0.000 1.0000 0.000 1.00 0.000 0.000
#> GSM148525 2 0.000 1.0000 0.000 1.00 0.000 0.000
#> GSM148526 2 0.000 1.0000 0.000 1.00 0.000 0.000
#> GSM148527 2 0.000 1.0000 0.000 1.00 0.000 0.000
#> GSM148528 2 0.000 1.0000 0.000 1.00 0.000 0.000
#> GSM148529 2 0.000 1.0000 0.000 1.00 0.000 0.000
#> GSM148530 2 0.000 1.0000 0.000 1.00 0.000 0.000
#> GSM148531 2 0.000 1.0000 0.000 1.00 0.000 0.000
#> GSM148532 2 0.000 1.0000 0.000 1.00 0.000 0.000
#> GSM148533 2 0.000 1.0000 0.000 1.00 0.000 0.000
#> GSM148534 2 0.000 1.0000 0.000 1.00 0.000 0.000
#> GSM148535 2 0.000 1.0000 0.000 1.00 0.000 0.000
#> GSM148536 2 0.000 1.0000 0.000 1.00 0.000 0.000
#> GSM148537 2 0.000 1.0000 0.000 1.00 0.000 0.000
#> GSM148538 2 0.000 1.0000 0.000 1.00 0.000 0.000
#> GSM148539 3 0.000 0.8138 0.000 0.00 1.000 0.000
#> GSM148540 3 0.000 0.8138 0.000 0.00 1.000 0.000
#> GSM148541 3 0.000 0.8138 0.000 0.00 1.000 0.000
#> GSM148542 3 0.164 0.7557 0.000 0.06 0.940 0.000
#> GSM148543 3 0.000 0.8138 0.000 0.00 1.000 0.000
#> GSM148544 3 0.000 0.8138 0.000 0.00 1.000 0.000
#> GSM148545 3 0.771 -0.0895 0.376 0.00 0.400 0.224
#> GSM148546 1 0.000 0.7769 1.000 0.00 0.000 0.000
#> GSM148547 1 0.000 0.7769 1.000 0.00 0.000 0.000
#> GSM148548 1 0.000 0.7769 1.000 0.00 0.000 0.000
#> GSM148549 1 0.000 0.7769 1.000 0.00 0.000 0.000
#> GSM148550 1 0.000 0.7769 1.000 0.00 0.000 0.000
#> GSM148551 1 0.000 0.7769 1.000 0.00 0.000 0.000
#> GSM148552 1 0.529 0.4334 0.584 0.00 0.404 0.012
#> GSM148553 1 0.527 0.4463 0.592 0.00 0.396 0.012
#> GSM148554 1 0.000 0.7769 1.000 0.00 0.000 0.000
#> GSM148555 1 0.000 0.7769 1.000 0.00 0.000 0.000
#> GSM148556 1 0.555 0.4486 0.588 0.00 0.388 0.024
#> GSM148557 1 0.555 0.4486 0.588 0.00 0.388 0.024
#> GSM148558 1 0.651 0.3746 0.540 0.00 0.380 0.080
#> GSM148559 4 0.000 0.9914 0.000 0.00 0.000 1.000
#> GSM148560 4 0.000 0.9914 0.000 0.00 0.000 1.000
#> GSM148561 4 0.000 0.9914 0.000 0.00 0.000 1.000
#> GSM148562 4 0.000 0.9914 0.000 0.00 0.000 1.000
#> GSM148563 4 0.000 0.9914 0.000 0.00 0.000 1.000
#> GSM148564 4 0.000 0.9914 0.000 0.00 0.000 1.000
#> GSM148565 4 0.000 0.9914 0.000 0.00 0.000 1.000
#> GSM148566 4 0.222 0.8814 0.092 0.00 0.000 0.908
#> GSM148567 4 0.000 0.9914 0.000 0.00 0.000 1.000
#> GSM148568 4 0.000 0.9914 0.000 0.00 0.000 1.000
#> GSM148569 4 0.000 0.9914 0.000 0.00 0.000 1.000
#> GSM148570 4 0.000 0.9914 0.000 0.00 0.000 1.000
#> GSM148571 4 0.000 0.9914 0.000 0.00 0.000 1.000
#> GSM148572 4 0.000 0.9914 0.000 0.00 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM148516 3 0.0000 0.982 0.000 0.000 1.000 0.000 0.000
#> GSM148517 1 0.6323 0.572 0.508 0.000 0.060 0.388 0.044
#> GSM148518 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM148519 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM148520 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM148521 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM148522 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM148523 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM148524 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM148525 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM148526 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM148527 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM148528 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM148529 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM148530 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM148531 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM148532 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM148533 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM148534 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM148535 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM148536 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM148537 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM148538 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM148539 3 0.0000 0.982 0.000 0.000 1.000 0.000 0.000
#> GSM148540 3 0.0000 0.982 0.000 0.000 1.000 0.000 0.000
#> GSM148541 3 0.0000 0.982 0.000 0.000 1.000 0.000 0.000
#> GSM148542 3 0.2597 0.891 0.000 0.024 0.884 0.092 0.000
#> GSM148543 3 0.0000 0.982 0.000 0.000 1.000 0.000 0.000
#> GSM148544 3 0.0162 0.980 0.000 0.000 0.996 0.004 0.000
#> GSM148545 1 0.6323 0.572 0.508 0.000 0.060 0.388 0.044
#> GSM148546 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> GSM148547 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> GSM148548 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> GSM148549 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> GSM148550 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> GSM148551 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> GSM148552 1 0.3527 0.825 0.828 0.000 0.056 0.116 0.000
#> GSM148553 1 0.3446 0.834 0.840 0.000 0.036 0.116 0.008
#> GSM148554 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> GSM148555 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> GSM148556 1 0.3012 0.839 0.860 0.000 0.036 0.104 0.000
#> GSM148557 1 0.3012 0.839 0.860 0.000 0.036 0.104 0.000
#> GSM148558 1 0.6691 0.360 0.492 0.000 0.036 0.108 0.364
#> GSM148559 5 0.0000 0.978 0.000 0.000 0.000 0.000 1.000
#> GSM148560 5 0.0000 0.978 0.000 0.000 0.000 0.000 1.000
#> GSM148561 5 0.0290 0.971 0.000 0.000 0.000 0.008 0.992
#> GSM148562 5 0.0000 0.978 0.000 0.000 0.000 0.000 1.000
#> GSM148563 4 0.4307 0.849 0.000 0.000 0.000 0.500 0.500
#> GSM148564 4 0.4201 0.934 0.000 0.000 0.000 0.592 0.408
#> GSM148565 4 0.4201 0.934 0.000 0.000 0.000 0.592 0.408
#> GSM148566 5 0.1430 0.871 0.052 0.000 0.000 0.004 0.944
#> GSM148567 5 0.0162 0.975 0.000 0.000 0.000 0.004 0.996
#> GSM148568 5 0.0000 0.978 0.000 0.000 0.000 0.000 1.000
#> GSM148569 5 0.0000 0.978 0.000 0.000 0.000 0.000 1.000
#> GSM148570 4 0.4210 0.933 0.000 0.000 0.000 0.588 0.412
#> GSM148571 4 0.4307 0.855 0.000 0.000 0.000 0.500 0.500
#> GSM148572 4 0.4201 0.934 0.000 0.000 0.000 0.592 0.408
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM148516 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM148517 6 0.2739 0.647 0.084 0.000 0.032 0.000 0.012 0.872
#> GSM148518 2 0.0458 0.988 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM148519 2 0.0458 0.988 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM148520 2 0.0458 0.988 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM148521 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM148522 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM148523 2 0.0146 0.989 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM148524 2 0.0363 0.987 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM148525 2 0.0458 0.988 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM148526 2 0.0458 0.988 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM148527 2 0.0363 0.987 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM148528 2 0.0458 0.988 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM148529 2 0.0363 0.987 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM148530 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM148531 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM148532 2 0.0363 0.987 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM148533 2 0.0458 0.988 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM148534 2 0.0458 0.988 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM148535 2 0.0363 0.987 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM148536 2 0.0458 0.988 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM148537 2 0.0363 0.987 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM148538 2 0.0363 0.987 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM148539 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM148540 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM148541 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM148542 3 0.1933 0.926 0.000 0.012 0.924 0.032 0.000 0.032
#> GSM148543 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM148544 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM148545 6 0.2739 0.647 0.084 0.000 0.032 0.000 0.012 0.872
#> GSM148546 1 0.0000 0.829 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM148547 1 0.0000 0.829 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM148548 1 0.0000 0.829 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM148549 1 0.0000 0.829 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM148550 1 0.0000 0.829 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM148551 1 0.0000 0.829 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM148552 1 0.5655 0.313 0.604 0.000 0.032 0.120 0.000 0.244
#> GSM148553 1 0.5228 0.346 0.620 0.000 0.008 0.120 0.000 0.252
#> GSM148554 1 0.0000 0.829 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM148555 1 0.0000 0.829 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM148556 1 0.4098 -0.321 0.496 0.000 0.008 0.000 0.000 0.496
#> GSM148557 6 0.4086 0.147 0.464 0.000 0.008 0.000 0.000 0.528
#> GSM148558 6 0.6021 0.384 0.276 0.000 0.000 0.000 0.296 0.428
#> GSM148559 5 0.0000 0.979 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM148560 5 0.0000 0.979 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM148561 5 0.0000 0.979 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM148562 5 0.0000 0.979 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM148563 4 0.3737 0.685 0.000 0.000 0.000 0.608 0.392 0.000
#> GSM148564 4 0.2416 0.899 0.000 0.000 0.000 0.844 0.156 0.000
#> GSM148565 4 0.2416 0.899 0.000 0.000 0.000 0.844 0.156 0.000
#> GSM148566 5 0.2119 0.852 0.060 0.000 0.000 0.000 0.904 0.036
#> GSM148567 5 0.0000 0.979 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM148568 5 0.0000 0.979 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM148569 5 0.0000 0.979 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM148570 4 0.2416 0.899 0.000 0.000 0.000 0.844 0.156 0.000
#> GSM148571 4 0.3563 0.768 0.000 0.000 0.000 0.664 0.336 0.000
#> GSM148572 4 0.2416 0.899 0.000 0.000 0.000 0.844 0.156 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) dose(p) time(p) k
#> ATC:mclust 57 2.57e-12 1.00e+00 1.000 2
#> ATC:mclust 45 1.69e-10 8.25e-05 0.997 3
#> ATC:mclust 50 3.58e-10 3.73e-07 0.987 4
#> ATC:mclust 56 3.68e-09 3.52e-06 0.857 5
#> ATC:mclust 52 2.28e-11 1.37e-06 0.397 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 21163 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5093 0.491 0.491
#> 3 3 0.767 0.801 0.885 0.2157 0.857 0.716
#> 4 4 0.842 0.897 0.885 0.1289 0.871 0.666
#> 5 5 0.780 0.840 0.875 0.0544 0.971 0.893
#> 6 6 0.824 0.808 0.848 0.0341 0.984 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
#> GSM148516 2 0 1 0 1
#> GSM148517 1 0 1 1 0
#> GSM148518 2 0 1 0 1
#> GSM148519 2 0 1 0 1
#> GSM148520 2 0 1 0 1
#> GSM148521 2 0 1 0 1
#> GSM148522 2 0 1 0 1
#> GSM148523 2 0 1 0 1
#> GSM148524 2 0 1 0 1
#> GSM148525 2 0 1 0 1
#> GSM148526 2 0 1 0 1
#> GSM148527 2 0 1 0 1
#> GSM148528 2 0 1 0 1
#> GSM148529 2 0 1 0 1
#> GSM148530 2 0 1 0 1
#> GSM148531 2 0 1 0 1
#> GSM148532 2 0 1 0 1
#> GSM148533 2 0 1 0 1
#> GSM148534 2 0 1 0 1
#> GSM148535 2 0 1 0 1
#> GSM148536 2 0 1 0 1
#> GSM148537 2 0 1 0 1
#> GSM148538 2 0 1 0 1
#> GSM148539 2 0 1 0 1
#> GSM148540 2 0 1 0 1
#> GSM148541 2 0 1 0 1
#> GSM148542 2 0 1 0 1
#> GSM148543 2 0 1 0 1
#> GSM148544 2 0 1 0 1
#> GSM148545 1 0 1 1 0
#> GSM148546 1 0 1 1 0
#> GSM148547 1 0 1 1 0
#> GSM148548 1 0 1 1 0
#> GSM148549 1 0 1 1 0
#> GSM148550 1 0 1 1 0
#> GSM148551 1 0 1 1 0
#> GSM148552 1 0 1 1 0
#> GSM148553 1 0 1 1 0
#> GSM148554 1 0 1 1 0
#> GSM148555 1 0 1 1 0
#> GSM148556 1 0 1 1 0
#> GSM148557 1 0 1 1 0
#> GSM148558 1 0 1 1 0
#> GSM148559 1 0 1 1 0
#> GSM148560 1 0 1 1 0
#> GSM148561 1 0 1 1 0
#> GSM148562 1 0 1 1 0
#> GSM148563 1 0 1 1 0
#> GSM148564 1 0 1 1 0
#> GSM148565 1 0 1 1 0
#> GSM148566 1 0 1 1 0
#> GSM148567 1 0 1 1 0
#> GSM148568 1 0 1 1 0
#> GSM148569 1 0 1 1 0
#> GSM148570 1 0 1 1 0
#> GSM148571 1 0 1 1 0
#> GSM148572 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM148516 3 0.6126 0.473 0.000 0.400 0.600
#> GSM148517 3 0.5178 0.316 0.256 0.000 0.744
#> GSM148518 2 0.0237 0.979 0.000 0.996 0.004
#> GSM148519 2 0.0237 0.980 0.000 0.996 0.004
#> GSM148520 2 0.0237 0.979 0.000 0.996 0.004
#> GSM148521 2 0.0000 0.980 0.000 1.000 0.000
#> GSM148522 2 0.0000 0.980 0.000 1.000 0.000
#> GSM148523 2 0.0237 0.980 0.000 0.996 0.004
#> GSM148524 2 0.0592 0.978 0.000 0.988 0.012
#> GSM148525 2 0.0592 0.976 0.000 0.988 0.012
#> GSM148526 2 0.0747 0.977 0.000 0.984 0.016
#> GSM148527 2 0.1031 0.972 0.000 0.976 0.024
#> GSM148528 2 0.0747 0.973 0.000 0.984 0.016
#> GSM148529 2 0.0592 0.978 0.000 0.988 0.012
#> GSM148530 2 0.0592 0.976 0.000 0.988 0.012
#> GSM148531 2 0.0424 0.978 0.000 0.992 0.008
#> GSM148532 2 0.1643 0.957 0.000 0.956 0.044
#> GSM148533 2 0.0592 0.980 0.000 0.988 0.012
#> GSM148534 2 0.0424 0.978 0.000 0.992 0.008
#> GSM148535 2 0.1411 0.964 0.000 0.964 0.036
#> GSM148536 2 0.0237 0.980 0.000 0.996 0.004
#> GSM148537 2 0.1643 0.957 0.000 0.956 0.044
#> GSM148538 2 0.1643 0.957 0.000 0.956 0.044
#> GSM148539 3 0.5621 0.592 0.000 0.308 0.692
#> GSM148540 3 0.5968 0.535 0.000 0.364 0.636
#> GSM148541 3 0.4750 0.609 0.000 0.216 0.784
#> GSM148542 2 0.1860 0.945 0.000 0.948 0.052
#> GSM148543 3 0.5650 0.589 0.000 0.312 0.688
#> GSM148544 3 0.6215 0.421 0.000 0.428 0.572
#> GSM148545 3 0.6295 -0.217 0.472 0.000 0.528
#> GSM148546 1 0.2066 0.861 0.940 0.000 0.060
#> GSM148547 1 0.2165 0.859 0.936 0.000 0.064
#> GSM148548 1 0.2356 0.856 0.928 0.000 0.072
#> GSM148549 1 0.2448 0.854 0.924 0.000 0.076
#> GSM148550 1 0.2448 0.854 0.924 0.000 0.076
#> GSM148551 1 0.2448 0.854 0.924 0.000 0.076
#> GSM148552 1 0.0747 0.868 0.984 0.000 0.016
#> GSM148553 1 0.0424 0.868 0.992 0.000 0.008
#> GSM148554 1 0.2165 0.859 0.936 0.000 0.064
#> GSM148555 1 0.2448 0.854 0.924 0.000 0.076
#> GSM148556 1 0.0892 0.867 0.980 0.000 0.020
#> GSM148557 1 0.0892 0.867 0.980 0.000 0.020
#> GSM148558 1 0.1964 0.862 0.944 0.000 0.056
#> GSM148559 1 0.4555 0.776 0.800 0.000 0.200
#> GSM148560 1 0.2711 0.846 0.912 0.000 0.088
#> GSM148561 1 0.0747 0.869 0.984 0.000 0.016
#> GSM148562 1 0.2959 0.841 0.900 0.000 0.100
#> GSM148563 1 0.0424 0.868 0.992 0.000 0.008
#> GSM148564 3 0.6299 -0.231 0.476 0.000 0.524
#> GSM148565 1 0.5835 0.601 0.660 0.000 0.340
#> GSM148566 1 0.1643 0.864 0.956 0.000 0.044
#> GSM148567 1 0.5254 0.714 0.736 0.000 0.264
#> GSM148568 1 0.4931 0.749 0.768 0.000 0.232
#> GSM148569 1 0.4887 0.753 0.772 0.000 0.228
#> GSM148570 1 0.5216 0.719 0.740 0.000 0.260
#> GSM148571 1 0.3116 0.837 0.892 0.000 0.108
#> GSM148572 1 0.6045 0.522 0.620 0.000 0.380
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM148516 3 0.2111 0.905 0.024 0.044 0.932 0.000
#> GSM148517 3 0.5320 0.198 0.012 0.000 0.572 0.416
#> GSM148518 2 0.0336 0.968 0.008 0.992 0.000 0.000
#> GSM148519 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM148520 2 0.1305 0.959 0.036 0.960 0.004 0.000
#> GSM148521 2 0.1118 0.960 0.036 0.964 0.000 0.000
#> GSM148522 2 0.0188 0.968 0.004 0.996 0.000 0.000
#> GSM148523 2 0.0817 0.968 0.024 0.976 0.000 0.000
#> GSM148524 2 0.0469 0.967 0.012 0.988 0.000 0.000
#> GSM148525 2 0.1284 0.961 0.024 0.964 0.012 0.000
#> GSM148526 2 0.0524 0.968 0.004 0.988 0.008 0.000
#> GSM148527 2 0.0469 0.967 0.012 0.988 0.000 0.000
#> GSM148528 2 0.1767 0.952 0.044 0.944 0.012 0.000
#> GSM148529 2 0.0469 0.967 0.012 0.988 0.000 0.000
#> GSM148530 2 0.1305 0.959 0.036 0.960 0.004 0.000
#> GSM148531 2 0.1211 0.959 0.040 0.960 0.000 0.000
#> GSM148532 2 0.0707 0.966 0.020 0.980 0.000 0.000
#> GSM148533 2 0.1059 0.965 0.016 0.972 0.012 0.000
#> GSM148534 2 0.0524 0.968 0.004 0.988 0.008 0.000
#> GSM148535 2 0.0592 0.967 0.016 0.984 0.000 0.000
#> GSM148536 2 0.0804 0.967 0.012 0.980 0.008 0.000
#> GSM148537 2 0.0779 0.966 0.016 0.980 0.004 0.000
#> GSM148538 2 0.1004 0.963 0.024 0.972 0.004 0.000
#> GSM148539 3 0.2021 0.908 0.024 0.040 0.936 0.000
#> GSM148540 3 0.1913 0.906 0.020 0.040 0.940 0.000
#> GSM148541 3 0.2023 0.901 0.028 0.028 0.940 0.004
#> GSM148542 2 0.6049 0.590 0.120 0.680 0.200 0.000
#> GSM148543 3 0.1767 0.908 0.012 0.044 0.944 0.000
#> GSM148544 3 0.1637 0.898 0.000 0.060 0.940 0.000
#> GSM148545 4 0.5322 0.503 0.028 0.000 0.312 0.660
#> GSM148546 1 0.4522 0.900 0.680 0.000 0.000 0.320
#> GSM148547 1 0.4382 0.907 0.704 0.000 0.000 0.296
#> GSM148548 1 0.4103 0.902 0.744 0.000 0.000 0.256
#> GSM148549 1 0.3486 0.836 0.812 0.000 0.000 0.188
#> GSM148550 1 0.4164 0.905 0.736 0.000 0.000 0.264
#> GSM148551 1 0.4103 0.902 0.744 0.000 0.000 0.256
#> GSM148552 1 0.5083 0.886 0.716 0.000 0.036 0.248
#> GSM148553 1 0.4697 0.880 0.644 0.000 0.000 0.356
#> GSM148554 1 0.4250 0.907 0.724 0.000 0.000 0.276
#> GSM148555 1 0.3907 0.884 0.768 0.000 0.000 0.232
#> GSM148556 1 0.5220 0.878 0.632 0.000 0.016 0.352
#> GSM148557 1 0.5217 0.848 0.608 0.000 0.012 0.380
#> GSM148558 1 0.4730 0.872 0.636 0.000 0.000 0.364
#> GSM148559 4 0.0336 0.935 0.008 0.000 0.000 0.992
#> GSM148560 4 0.0592 0.930 0.016 0.000 0.000 0.984
#> GSM148561 4 0.2402 0.855 0.076 0.000 0.012 0.912
#> GSM148562 4 0.0469 0.932 0.012 0.000 0.000 0.988
#> GSM148563 4 0.2266 0.838 0.084 0.000 0.004 0.912
#> GSM148564 4 0.0707 0.924 0.000 0.000 0.020 0.980
#> GSM148565 4 0.0469 0.931 0.000 0.000 0.012 0.988
#> GSM148566 1 0.4977 0.710 0.540 0.000 0.000 0.460
#> GSM148567 4 0.0657 0.935 0.004 0.000 0.012 0.984
#> GSM148568 4 0.0000 0.936 0.000 0.000 0.000 1.000
#> GSM148569 4 0.0188 0.936 0.004 0.000 0.000 0.996
#> GSM148570 4 0.0524 0.935 0.004 0.000 0.008 0.988
#> GSM148571 4 0.0188 0.936 0.004 0.000 0.000 0.996
#> GSM148572 4 0.0592 0.928 0.000 0.000 0.016 0.984
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM148516 3 0.1059 0.821 0.004 0.008 0.968 0.000 0.020
#> GSM148517 5 0.7976 0.593 0.116 0.000 0.336 0.168 0.380
#> GSM148518 2 0.0798 0.983 0.000 0.976 0.016 0.000 0.008
#> GSM148519 2 0.0579 0.985 0.000 0.984 0.008 0.000 0.008
#> GSM148520 2 0.0510 0.983 0.000 0.984 0.000 0.000 0.016
#> GSM148521 2 0.0609 0.982 0.000 0.980 0.000 0.000 0.020
#> GSM148522 2 0.0162 0.985 0.000 0.996 0.000 0.000 0.004
#> GSM148523 2 0.0404 0.984 0.000 0.988 0.000 0.000 0.012
#> GSM148524 2 0.0510 0.985 0.000 0.984 0.000 0.000 0.016
#> GSM148525 2 0.0613 0.985 0.004 0.984 0.004 0.000 0.008
#> GSM148526 2 0.0727 0.984 0.004 0.980 0.004 0.000 0.012
#> GSM148527 2 0.0510 0.985 0.000 0.984 0.000 0.000 0.016
#> GSM148528 2 0.0566 0.985 0.000 0.984 0.004 0.000 0.012
#> GSM148529 2 0.0404 0.985 0.000 0.988 0.000 0.000 0.012
#> GSM148530 2 0.0566 0.984 0.004 0.984 0.000 0.000 0.012
#> GSM148531 2 0.0865 0.978 0.004 0.972 0.000 0.000 0.024
#> GSM148532 2 0.0693 0.984 0.000 0.980 0.008 0.000 0.012
#> GSM148533 2 0.1808 0.955 0.008 0.936 0.012 0.000 0.044
#> GSM148534 2 0.0451 0.985 0.000 0.988 0.008 0.000 0.004
#> GSM148535 2 0.0798 0.983 0.000 0.976 0.008 0.000 0.016
#> GSM148536 2 0.0324 0.986 0.000 0.992 0.004 0.000 0.004
#> GSM148537 2 0.0324 0.986 0.000 0.992 0.004 0.000 0.004
#> GSM148538 2 0.0807 0.983 0.000 0.976 0.012 0.000 0.012
#> GSM148539 3 0.0579 0.822 0.008 0.000 0.984 0.000 0.008
#> GSM148540 3 0.0865 0.823 0.000 0.004 0.972 0.000 0.024
#> GSM148541 3 0.0880 0.814 0.000 0.000 0.968 0.000 0.032
#> GSM148542 3 0.7198 0.218 0.024 0.336 0.456 0.008 0.176
#> GSM148543 3 0.1082 0.823 0.000 0.008 0.964 0.000 0.028
#> GSM148544 3 0.0955 0.810 0.000 0.028 0.968 0.000 0.004
#> GSM148545 5 0.8251 0.605 0.176 0.000 0.160 0.300 0.364
#> GSM148546 1 0.4404 0.762 0.760 0.000 0.000 0.152 0.088
#> GSM148547 1 0.4260 0.785 0.784 0.000 0.004 0.124 0.088
#> GSM148548 1 0.2473 0.812 0.896 0.000 0.000 0.072 0.032
#> GSM148549 1 0.2885 0.791 0.880 0.000 0.004 0.064 0.052
#> GSM148550 1 0.2423 0.810 0.896 0.000 0.000 0.080 0.024
#> GSM148551 1 0.2694 0.803 0.884 0.000 0.000 0.076 0.040
#> GSM148552 1 0.4784 0.758 0.772 0.000 0.044 0.068 0.116
#> GSM148553 1 0.4985 0.694 0.728 0.000 0.008 0.116 0.148
#> GSM148554 1 0.3512 0.803 0.840 0.000 0.004 0.088 0.068
#> GSM148555 1 0.2270 0.810 0.908 0.000 0.004 0.072 0.016
#> GSM148556 1 0.4746 0.742 0.744 0.000 0.004 0.132 0.120
#> GSM148557 1 0.4888 0.741 0.728 0.000 0.004 0.160 0.108
#> GSM148558 1 0.4065 0.771 0.772 0.000 0.000 0.180 0.048
#> GSM148559 4 0.3494 0.801 0.096 0.000 0.004 0.840 0.060
#> GSM148560 4 0.4149 0.727 0.128 0.000 0.000 0.784 0.088
#> GSM148561 4 0.4316 0.657 0.120 0.000 0.000 0.772 0.108
#> GSM148562 4 0.2248 0.854 0.088 0.000 0.000 0.900 0.012
#> GSM148563 4 0.1942 0.862 0.068 0.000 0.000 0.920 0.012
#> GSM148564 4 0.3012 0.806 0.036 0.000 0.000 0.860 0.104
#> GSM148565 4 0.3146 0.823 0.052 0.000 0.000 0.856 0.092
#> GSM148566 1 0.6028 0.211 0.468 0.000 0.000 0.416 0.116
#> GSM148567 4 0.2304 0.860 0.068 0.000 0.004 0.908 0.020
#> GSM148568 4 0.1914 0.855 0.060 0.000 0.000 0.924 0.016
#> GSM148569 4 0.1981 0.863 0.064 0.000 0.000 0.920 0.016
#> GSM148570 4 0.2514 0.852 0.060 0.000 0.000 0.896 0.044
#> GSM148571 4 0.2989 0.842 0.072 0.000 0.000 0.868 0.060
#> GSM148572 4 0.3130 0.821 0.048 0.000 0.000 0.856 0.096
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM148516 3 0.1426 0.915 0.000 0.016 0.948 0.000 NA 0.028
#> GSM148517 6 0.6075 0.851 0.212 0.000 0.084 0.096 NA 0.604
#> GSM148518 2 0.0951 0.976 0.000 0.968 0.004 0.000 NA 0.008
#> GSM148519 2 0.0837 0.976 0.000 0.972 0.004 0.000 NA 0.004
#> GSM148520 2 0.0260 0.979 0.000 0.992 0.000 0.000 NA 0.008
#> GSM148521 2 0.0363 0.979 0.000 0.988 0.000 0.000 NA 0.012
#> GSM148522 2 0.0146 0.979 0.000 0.996 0.000 0.000 NA 0.004
#> GSM148523 2 0.1067 0.971 0.004 0.964 0.004 0.000 NA 0.024
#> GSM148524 2 0.0777 0.976 0.000 0.972 0.000 0.000 NA 0.024
#> GSM148525 2 0.0891 0.977 0.000 0.968 0.000 0.000 NA 0.008
#> GSM148526 2 0.0935 0.976 0.000 0.964 0.000 0.000 NA 0.004
#> GSM148527 2 0.0622 0.980 0.000 0.980 0.000 0.000 NA 0.008
#> GSM148528 2 0.0508 0.979 0.000 0.984 0.000 0.000 NA 0.004
#> GSM148529 2 0.0692 0.977 0.000 0.976 0.000 0.000 NA 0.020
#> GSM148530 2 0.0951 0.973 0.008 0.968 0.000 0.000 NA 0.020
#> GSM148531 2 0.1198 0.969 0.012 0.960 0.004 0.000 NA 0.020
#> GSM148532 2 0.0665 0.979 0.000 0.980 0.004 0.000 NA 0.008
#> GSM148533 2 0.1769 0.954 0.000 0.924 0.004 0.000 NA 0.012
#> GSM148534 2 0.0951 0.976 0.000 0.968 0.004 0.000 NA 0.008
#> GSM148535 2 0.1116 0.975 0.000 0.960 0.004 0.000 NA 0.008
#> GSM148536 2 0.0405 0.979 0.000 0.988 0.000 0.000 NA 0.008
#> GSM148537 2 0.0551 0.979 0.000 0.984 0.004 0.000 NA 0.008
#> GSM148538 2 0.0984 0.977 0.000 0.968 0.008 0.000 NA 0.012
#> GSM148539 3 0.1810 0.907 0.004 0.008 0.932 0.000 NA 0.020
#> GSM148540 3 0.0508 0.915 0.000 0.000 0.984 0.000 NA 0.012
#> GSM148541 3 0.0858 0.912 0.000 0.000 0.968 0.000 NA 0.028
#> GSM148542 3 0.5580 0.669 0.012 0.100 0.684 0.000 NA 0.132
#> GSM148543 3 0.1230 0.914 0.000 0.008 0.956 0.000 NA 0.028
#> GSM148544 3 0.0692 0.917 0.000 0.020 0.976 0.000 NA 0.004
#> GSM148545 6 0.6733 0.843 0.232 0.000 0.048 0.164 NA 0.532
#> GSM148546 1 0.4928 0.561 0.680 0.000 0.000 0.100 NA 0.016
#> GSM148547 1 0.3912 0.685 0.784 0.000 0.000 0.060 NA 0.016
#> GSM148548 1 0.1793 0.754 0.928 0.000 0.000 0.032 NA 0.004
#> GSM148549 1 0.1851 0.754 0.928 0.000 0.000 0.036 NA 0.012
#> GSM148550 1 0.1957 0.759 0.920 0.000 0.000 0.048 NA 0.008
#> GSM148551 1 0.2602 0.750 0.888 0.000 0.000 0.052 NA 0.020
#> GSM148552 1 0.4829 0.480 0.692 0.000 0.004 0.008 NA 0.196
#> GSM148553 1 0.5968 0.280 0.528 0.000 0.012 0.040 NA 0.068
#> GSM148554 1 0.3381 0.716 0.828 0.000 0.000 0.032 NA 0.024
#> GSM148555 1 0.1196 0.758 0.952 0.000 0.000 0.040 NA 0.008
#> GSM148556 1 0.3879 0.684 0.808 0.000 0.000 0.072 NA 0.044
#> GSM148557 1 0.4018 0.656 0.768 0.000 0.000 0.112 NA 0.004
#> GSM148558 1 0.4338 0.618 0.732 0.000 0.000 0.164 NA 0.004
#> GSM148559 4 0.4011 0.668 0.060 0.000 0.000 0.736 NA 0.000
#> GSM148560 4 0.4500 0.617 0.076 0.000 0.000 0.676 NA 0.000
#> GSM148561 4 0.4945 0.512 0.068 0.000 0.000 0.584 NA 0.004
#> GSM148562 4 0.3138 0.733 0.060 0.000 0.000 0.832 NA 0.000
#> GSM148563 4 0.2001 0.747 0.040 0.000 0.000 0.912 NA 0.000
#> GSM148564 4 0.3606 0.663 0.016 0.000 0.000 0.788 NA 0.024
#> GSM148565 4 0.3621 0.659 0.032 0.000 0.000 0.772 NA 0.004
#> GSM148566 4 0.5725 0.389 0.208 0.000 0.000 0.512 NA 0.000
#> GSM148567 4 0.3634 0.727 0.060 0.000 0.000 0.820 NA 0.028
#> GSM148568 4 0.2420 0.743 0.040 0.000 0.000 0.884 NA 0.000
#> GSM148569 4 0.1204 0.745 0.056 0.000 0.000 0.944 NA 0.000
#> GSM148570 4 0.2822 0.713 0.040 0.000 0.000 0.852 NA 0.000
#> GSM148571 4 0.3651 0.680 0.048 0.000 0.000 0.772 NA 0.000
#> GSM148572 4 0.3682 0.653 0.032 0.000 0.000 0.764 NA 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) dose(p) time(p) k
#> ATC:NMF 57 2.57e-12 1.00e+00 1.000 2
#> ATC:NMF 52 5.11e-12 6.58e-03 0.994 3
#> ATC:NMF 56 8.31e-12 2.93e-06 0.973 4
#> ATC:NMF 55 8.11e-14 2.26e-08 0.741 5
#> ATC:NMF 54 3.03e-13 3.63e-08 0.722 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