cola Report for GDS4404

Date: 2019-12-25 21:35:41 CET, cola version: 1.3.2

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Summary

All available functions which can be applied to this res_list object:

res_list

#> A 'ConsensusPartitionList' object with 24 methods.
#>   On a matrix with 31632 rows and 50 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] 31632    50

Density distribution

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)

plot of chunk density-heatmap

Suggest the best k

Folowing table shows the best k (number of partitions) for each combination of top-value methods and partition methods. Clicking on the method name in the table goes to the section for a single combination of methods.

The cola vignette explains the definition of the metrics used for determining the best number of partitions.

suggest_best_k(res_list)

	The best k	1-PAC	Mean silhouette	Concordance		Optional k
SD:hclust	5	1.000	0.954	0.978	**	2,3,4
SD:kmeans	2	1.000	1.000	1.000	**
SD:pam	6	1.000	0.970	0.987	**	2,3,4,5
CV:kmeans	2	1.000	1.000	1.000	**
CV:pam	6	1.000	0.966	0.981	**	2,3,4,5
MAD:kmeans	2	1.000	1.000	1.000	**
MAD:pam	6	1.000	0.979	0.991	**	2,3,4,5
ATC:kmeans	2	1.000	1.000	1.000	**
ATC:skmeans	5	1.000	0.990	0.993	**	2,3,4
ATC:mclust	5	1.000	0.995	0.995	**	2,3,4
ATC:NMF	2	1.000	1.000	1.000	**
MAD:mclust	6	0.993	0.984	0.989	**	2,3,4,5
SD:mclust	6	0.980	0.927	0.969	**	2,3,4,5
SD:skmeans	5	0.976	0.954	0.970	**	2,3,4
MAD:skmeans	5	0.972	0.948	0.964	**	2,3,4
ATC:pam	6	0.969	0.937	0.968	**	2,3,4,5
MAD:hclust	5	0.961	0.914	0.950	**	2,3,4
MAD:NMF	5	0.960	0.944	0.952	**	2,3,4
SD:NMF	5	0.951	0.930	0.944	**	2,3,4
CV:NMF	5	0.939	0.915	0.934	*	2,3,4
ATC:hclust	6	0.918	0.833	0.914	*	2
CV:skmeans	6	0.914	0.812	0.869	*	2,3,4,5
CV:mclust	5	0.907	0.762	0.901	*	2,3,4
CV:hclust	5	0.904	0.782	0.857	*	2,3,4

**: 1-PAC > 0.95, *: 1-PAC > 0.9

CDF of consensus matrices

Cumulative distribution function curves of consensus matrix for all methods.

collect_plots(res_list, fun = plot_ecdf)

plot of chunk collect-plots

Consensus heatmap

Consensus heatmaps for all methods. (What is a consensus heatmap?)

k = 2
k = 3
k = 4
k = 5
k = 6

collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)

plot of chunk tab-collect-consensus-heatmap-1

collect_plots(res_list, k = 3, fun = consensus_heatmap, mc.cores = 4)

plot of chunk tab-collect-consensus-heatmap-2

collect_plots(res_list, k = 4, fun = consensus_heatmap, mc.cores = 4)

plot of chunk tab-collect-consensus-heatmap-3

collect_plots(res_list, k = 5, fun = consensus_heatmap, mc.cores = 4)

plot of chunk tab-collect-consensus-heatmap-4

collect_plots(res_list, k = 6, fun = consensus_heatmap, mc.cores = 4)

plot of chunk tab-collect-consensus-heatmap-5

Membership heatmap

Membership heatmaps for all methods. (What is a membership heatmap?)

k = 2
k = 3
k = 4
k = 5
k = 6

collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)

plot of chunk tab-collect-membership-heatmap-1

collect_plots(res_list, k = 3, fun = membership_heatmap, mc.cores = 4)

plot of chunk tab-collect-membership-heatmap-2

collect_plots(res_list, k = 4, fun = membership_heatmap, mc.cores = 4)

plot of chunk tab-collect-membership-heatmap-3

collect_plots(res_list, k = 5, fun = membership_heatmap, mc.cores = 4)

plot of chunk tab-collect-membership-heatmap-4

collect_plots(res_list, k = 6, fun = membership_heatmap, mc.cores = 4)

plot of chunk tab-collect-membership-heatmap-5

Signature heatmap

Signature heatmaps for all methods. (What is a signature heatmap?)

Note in following heatmaps, rows are scaled.

k = 2
k = 3
k = 4
k = 5
k = 6

collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)

plot of chunk tab-collect-get-signatures-1

collect_plots(res_list, k = 3, fun = get_signatures, mc.cores = 4)

plot of chunk tab-collect-get-signatures-2

collect_plots(res_list, k = 4, fun = get_signatures, mc.cores = 4)

plot of chunk tab-collect-get-signatures-3

collect_plots(res_list, k = 5, fun = get_signatures, mc.cores = 4)

plot of chunk tab-collect-get-signatures-4

collect_plots(res_list, k = 6, fun = get_signatures, mc.cores = 4)

plot of chunk tab-collect-get-signatures-5

Statistics table

The statistics used for measuring the stability of consensus partitioning. (How are they defined?)

k = 2
k = 3
k = 4
k = 5
k = 6

get_stats(res_list, k = 2)

#>             k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF      2     1               1           1          0.471 0.53    0.53
#> CV:NMF      2     1               1           1          0.471 0.53    0.53
#> MAD:NMF     2     1               1           1          0.471 0.53    0.53
#> ATC:NMF     2     1               1           1          0.471 0.53    0.53
#> SD:skmeans  2     1               1           1          0.471 0.53    0.53
#> CV:skmeans  2     1               1           1          0.471 0.53    0.53
#> MAD:skmeans 2     1               1           1          0.471 0.53    0.53
#> ATC:skmeans 2     1               1           1          0.471 0.53    0.53
#> SD:mclust   2     1               1           1          0.471 0.53    0.53
#> CV:mclust   2     1               1           1          0.471 0.53    0.53
#> MAD:mclust  2     1               1           1          0.471 0.53    0.53
#> ATC:mclust  2     1               1           1          0.471 0.53    0.53
#> SD:kmeans   2     1               1           1          0.471 0.53    0.53
#> CV:kmeans   2     1               1           1          0.471 0.53    0.53
#> MAD:kmeans  2     1               1           1          0.471 0.53    0.53
#> ATC:kmeans  2     1               1           1          0.471 0.53    0.53
#> SD:pam      2     1               1           1          0.471 0.53    0.53
#> CV:pam      2     1               1           1          0.471 0.53    0.53
#> MAD:pam     2     1               1           1          0.471 0.53    0.53
#> ATC:pam     2     1               1           1          0.471 0.53    0.53
#> SD:hclust   2     1               1           1          0.471 0.53    0.53
#> CV:hclust   2     1               1           1          0.471 0.53    0.53
#> MAD:hclust  2     1               1           1          0.471 0.53    0.53
#> ATC:hclust  2     1               1           1          0.471 0.53    0.53

get_stats(res_list, k = 3)

#>             k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> SD:NMF      3 0.927           0.922       0.966          0.434 0.792   0.607
#> CV:NMF      3 0.949           0.933       0.969          0.436 0.792   0.607
#> MAD:NMF     3 0.966           0.972       0.974          0.415 0.794   0.612
#> ATC:NMF     3 0.809           0.964       0.927          0.321 0.804   0.630
#> SD:skmeans  3 0.950           0.905       0.965          0.435 0.794   0.612
#> CV:skmeans  3 1.000           0.966       0.984          0.440 0.792   0.607
#> MAD:skmeans 3 1.000           0.989       0.995          0.438 0.794   0.612
#> ATC:skmeans 3 1.000           0.984       0.994          0.395 0.811   0.644
#> SD:mclust   3 1.000           1.000       1.000          0.416 0.804   0.630
#> CV:mclust   3 1.000           1.000       1.000          0.416 0.804   0.630
#> MAD:mclust  3 1.000           1.000       1.000          0.416 0.804   0.630
#> ATC:mclust  3 1.000           1.000       1.000          0.416 0.804   0.630
#> SD:kmeans   3 0.704           0.906       0.878          0.344 0.794   0.612
#> CV:kmeans   3 0.707           0.921       0.860          0.338 0.794   0.612
#> MAD:kmeans  3 0.699           0.874       0.856          0.338 0.794   0.612
#> ATC:kmeans  3 0.775           0.952       0.907          0.303 0.811   0.644
#> SD:pam      3 0.956           0.969       0.985          0.426 0.798   0.619
#> CV:pam      3 0.974           0.953       0.976          0.438 0.792   0.607
#> MAD:pam     3 0.952           0.959       0.981          0.436 0.794   0.612
#> ATC:pam     3 0.974           0.913       0.968          0.409 0.811   0.644
#> SD:hclust   3 1.000           0.958       0.982          0.432 0.794   0.612
#> CV:hclust   3 0.971           0.944       0.969          0.435 0.794   0.612
#> MAD:hclust  3 1.000           0.962       0.981          0.431 0.794   0.612
#> ATC:hclust  3 0.846           0.908       0.950          0.378 0.804   0.630

get_stats(res_list, k = 4)

#>             k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> SD:NMF      4 0.996           0.966       0.979         0.0990 0.909   0.729
#> CV:NMF      4 0.985           0.921       0.966         0.0935 0.922   0.762
#> MAD:NMF     4 1.000           0.975       0.981         0.1144 0.912   0.736
#> ATC:NMF     4 0.869           0.883       0.867         0.1320 0.919   0.758
#> SD:skmeans  4 1.000           0.985       0.993         0.1030 0.912   0.736
#> CV:skmeans  4 0.958           0.894       0.949         0.0974 0.899   0.700
#> MAD:skmeans 4 1.000           0.975       0.991         0.1020 0.912   0.736
#> ATC:skmeans 4 1.000           0.890       0.956         0.1358 0.882   0.670
#> SD:mclust   4 0.971           0.919       0.967         0.1192 0.919   0.758
#> CV:mclust   4 0.966           0.920       0.966         0.1189 0.918   0.756
#> MAD:mclust  4 0.959           0.920       0.966         0.1176 0.922   0.765
#> ATC:mclust  4 1.000           1.000       1.000         0.1174 0.922   0.765
#> SD:kmeans   4 0.794           0.794       0.824         0.1277 0.939   0.814
#> CV:kmeans   4 0.619           0.866       0.836         0.1225 0.928   0.783
#> MAD:kmeans  4 0.635           0.881       0.831         0.1311 0.912   0.736
#> ATC:kmeans  4 0.645           0.532       0.805         0.1402 0.984   0.952
#> SD:pam      4 1.000           0.987       0.994         0.1135 0.912   0.737
#> CV:pam      4 0.975           0.939       0.972         0.1002 0.899   0.700
#> MAD:pam     4 1.000           0.991       0.995         0.1049 0.900   0.704
#> ATC:pam     4 1.000           0.986       0.994         0.1247 0.900   0.714
#> SD:hclust   4 1.000           0.957       0.983         0.0933 0.941   0.819
#> CV:hclust   4 0.982           0.944       0.969         0.0511 0.980   0.940
#> MAD:hclust  4 1.000           0.956       0.976         0.0916 0.941   0.819
#> ATC:hclust  4 0.815           0.874       0.929         0.0799 0.974   0.922

get_stats(res_list, k = 5)

#>             k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> SD:NMF      5 0.951           0.930       0.944         0.0348 0.958   0.838
#> CV:NMF      5 0.939           0.915       0.934         0.0389 0.958   0.842
#> MAD:NMF     5 0.960           0.944       0.952         0.0360 0.958   0.838
#> ATC:NMF     5 0.846           0.904       0.897         0.0439 0.984   0.941
#> SD:skmeans  5 0.976           0.954       0.970         0.0372 0.958   0.838
#> CV:skmeans  5 0.971           0.870       0.924         0.0341 0.985   0.942
#> MAD:skmeans 5 0.972           0.948       0.964         0.0361 0.958   0.838
#> ATC:skmeans 5 1.000           0.990       0.993         0.0341 0.971   0.888
#> SD:mclust   5 1.000           0.992       0.996         0.0377 0.958   0.840
#> CV:mclust   5 0.907           0.762       0.901         0.0344 0.987   0.948
#> MAD:mclust  5 1.000           0.944       0.980         0.0395 0.965   0.864
#> ATC:mclust  5 1.000           0.995       0.995         0.0381 0.971   0.888
#> SD:kmeans   5 0.693           0.697       0.811         0.0628 0.958   0.850
#> CV:kmeans   5 0.736           0.691       0.822         0.0795 0.974   0.902
#> MAD:kmeans  5 0.693           0.756       0.820         0.0692 0.974   0.898
#> ATC:kmeans  5 0.764           0.840       0.823         0.0741 0.878   0.633
#> SD:pam      5 0.968           0.960       0.971         0.0348 0.958   0.840
#> CV:pam      5 0.999           0.966       0.984         0.0286 0.977   0.910
#> MAD:pam     5 1.000           0.966       0.980         0.0372 0.958   0.840
#> ATC:pam     5 0.926           0.880       0.909         0.0446 0.945   0.792
#> SD:hclust   5 1.000           0.954       0.978         0.0483 0.961   0.852
#> CV:hclust   5 0.904           0.782       0.857         0.0615 0.948   0.832
#> MAD:hclust  5 0.961           0.914       0.950         0.0457 0.963   0.862
#> ATC:hclust  5 0.863           0.796       0.866         0.0717 0.922   0.745

get_stats(res_list, k = 6)

#>             k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> SD:NMF      6 0.924           0.926       0.944         0.0139 1.000   1.000
#> CV:NMF      6 0.902           0.914       0.934         0.0198 1.000   1.000
#> MAD:NMF     6 0.973           0.934       0.951         0.0107 1.000   1.000
#> ATC:NMF     6 0.807           0.860       0.887         0.0263 1.000   1.000
#> SD:skmeans  6 0.962           0.901       0.926         0.0156 1.000   1.000
#> CV:skmeans  6 0.914           0.812       0.869         0.0239 0.980   0.918
#> MAD:skmeans 6 0.972           0.911       0.917         0.0164 1.000   1.000
#> ATC:skmeans 6 0.982           0.930       0.946         0.0143 0.990   0.957
#> SD:mclust   6 0.980           0.927       0.969         0.0279 0.978   0.903
#> CV:mclust   6 0.855           0.679       0.851         0.0342 0.984   0.932
#> MAD:mclust  6 0.993           0.984       0.989         0.0272 0.969   0.866
#> ATC:mclust  6 0.989           0.950       0.956         0.0268 0.990   0.957
#> SD:kmeans   6 0.762           0.693       0.803         0.0584 0.971   0.882
#> CV:kmeans   6 0.715           0.703       0.785         0.0485 0.974   0.892
#> MAD:kmeans  6 0.751           0.699       0.804         0.0509 1.000   1.000
#> ATC:kmeans  6 0.747           0.771       0.777         0.0570 0.962   0.832
#> SD:pam      6 1.000           0.970       0.987         0.0173 0.988   0.946
#> CV:pam      6 1.000           0.966       0.981         0.0297 0.953   0.810
#> MAD:pam     6 1.000           0.979       0.991         0.0162 0.988   0.946
#> ATC:pam     6 0.969           0.937       0.968         0.0397 0.971   0.869
#> SD:hclust   6 0.924           0.893       0.926         0.0239 1.000   1.000
#> CV:hclust   6 0.890           0.873       0.871         0.0398 0.947   0.802
#> MAD:hclust  6 0.936           0.787       0.871         0.0227 0.993   0.971
#> ATC:hclust  6 0.918           0.833       0.914         0.0588 0.949   0.780

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.

k = 2
k = 3
k = 4
k = 5
k = 6

collect_stats(res_list, k = 2)

plot of chunk tab-collect-stats-from-consensus-partition-list-1

collect_stats(res_list, k = 3)

plot of chunk tab-collect-stats-from-consensus-partition-list-2

collect_stats(res_list, k = 4)

plot of chunk tab-collect-stats-from-consensus-partition-list-3

collect_stats(res_list, k = 5)

plot of chunk tab-collect-stats-from-consensus-partition-list-4

collect_stats(res_list, k = 6)

plot of chunk tab-collect-stats-from-consensus-partition-list-5

Partition from all methods

Collect partitions from all methods:

k = 2
k = 3
k = 4
k = 5
k = 6

collect_classes(res_list, k = 2)

#> Error in valid.viewport(x, y, width, height, just, gp, clip, xscale, yscale, : invalid 'xscale' in viewport

plot of chunk tab-collect-classes-from-consensus-partition-list-1

collect_classes(res_list, k = 3)

plot of chunk tab-collect-classes-from-consensus-partition-list-2

collect_classes(res_list, k = 4)

plot of chunk tab-collect-classes-from-consensus-partition-list-3

collect_classes(res_list, k = 5)

plot of chunk tab-collect-classes-from-consensus-partition-list-4

collect_classes(res_list, k = 6)

plot of chunk tab-collect-classes-from-consensus-partition-list-5

Top rows overlap

Overlap of top rows from different top-row methods:

top_n = 1000
top_n = 2000
top_n = 3000
top_n = 4000
top_n = 5000

top_rows_overlap(res_list, top_n = 1000, method = "euler")

plot of chunk tab-top-rows-overlap-by-euler-1

top_rows_overlap(res_list, top_n = 2000, method = "euler")

plot of chunk tab-top-rows-overlap-by-euler-2

top_rows_overlap(res_list, top_n = 3000, method = "euler")

plot of chunk tab-top-rows-overlap-by-euler-3

top_rows_overlap(res_list, top_n = 4000, method = "euler")

plot of chunk tab-top-rows-overlap-by-euler-4

top_rows_overlap(res_list, top_n = 5000, method = "euler")

plot of chunk tab-top-rows-overlap-by-euler-5

Also visualize the correspondance of rankings between different top-row methods:

top_n = 1000
top_n = 2000
top_n = 3000
top_n = 4000
top_n = 5000

top_rows_overlap(res_list, top_n = 1000, method = "correspondance")

plot of chunk tab-top-rows-overlap-by-correspondance-1

top_rows_overlap(res_list, top_n = 2000, method = "correspondance")

plot of chunk tab-top-rows-overlap-by-correspondance-2

top_rows_overlap(res_list, top_n = 3000, method = "correspondance")

plot of chunk tab-top-rows-overlap-by-correspondance-3

top_rows_overlap(res_list, top_n = 4000, method = "correspondance")

plot of chunk tab-top-rows-overlap-by-correspondance-4

top_rows_overlap(res_list, top_n = 5000, method = "correspondance")

plot of chunk tab-top-rows-overlap-by-correspondance-5

Heatmaps of the top rows:

top_n = 1000
top_n = 2000
top_n = 3000
top_n = 4000
top_n = 5000

top_rows_heatmap(res_list, top_n = 1000)

plot of chunk tab-top-rows-heatmap-1

top_rows_heatmap(res_list, top_n = 2000)

plot of chunk tab-top-rows-heatmap-2

top_rows_heatmap(res_list, top_n = 3000)

plot of chunk tab-top-rows-heatmap-3

top_rows_heatmap(res_list, top_n = 4000)

plot of chunk tab-top-rows-heatmap-4

top_rows_heatmap(res_list, top_n = 5000)

plot of chunk tab-top-rows-heatmap-5

Test to known annotations

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.

k = 2
k = 3
k = 4
k = 5
k = 6

test_to_known_factors(res_list, k = 2)

#>              n tissue(p) disease.state(p) other(p) individual(p) k
#> SD:NMF      50         1            0.934 2.67e-07       0.00142 2
#> CV:NMF      50         1            0.934 2.67e-07       0.00142 2
#> MAD:NMF     50         1            0.934 2.67e-07       0.00142 2
#> ATC:NMF     50         1            0.934 2.67e-07       0.00142 2
#> SD:skmeans  50         1            0.934 2.67e-07       0.00142 2
#> CV:skmeans  50         1            0.934 2.67e-07       0.00142 2
#> MAD:skmeans 50         1            0.934 2.67e-07       0.00142 2
#> ATC:skmeans 50         1            0.934 2.67e-07       0.00142 2
#> SD:mclust   50         1            0.934 2.67e-07       0.00142 2
#> CV:mclust   50         1            0.934 2.67e-07       0.00142 2
#> MAD:mclust  50         1            0.934 2.67e-07       0.00142 2
#> ATC:mclust  50         1            0.934 2.67e-07       0.00142 2
#> SD:kmeans   50         1            0.934 2.67e-07       0.00142 2
#> CV:kmeans   50         1            0.934 2.67e-07       0.00142 2
#> MAD:kmeans  50         1            0.934 2.67e-07       0.00142 2
#> ATC:kmeans  50         1            0.934 2.67e-07       0.00142 2
#> SD:pam      50         1            0.934 2.67e-07       0.00142 2
#> CV:pam      50         1            0.934 2.67e-07       0.00142 2
#> MAD:pam     50         1            0.934 2.67e-07       0.00142 2
#> ATC:pam     50         1            0.934 2.67e-07       0.00142 2
#> SD:hclust   50         1            0.934 2.67e-07       0.00142 2
#> CV:hclust   50         1            0.934 2.67e-07       0.00142 2
#> MAD:hclust  50         1            0.934 2.67e-07       0.00142 2
#> ATC:hclust  50         1            0.934 2.67e-07       0.00142 2

test_to_known_factors(res_list, k = 3)

#>              n tissue(p) disease.state(p) other(p) individual(p) k
#> SD:NMF      49     0.981            0.952 1.63e-11      6.57e-05 3
#> CV:NMF      50     0.939            0.875 8.67e-12      3.79e-05 3
#> MAD:NMF     50     1.000            0.931 1.69e-11      8.93e-05 3
#> ATC:NMF     50     1.000            0.931 1.26e-12      1.60e-05 3
#> SD:skmeans  47     0.847            0.875 1.47e-11      8.15e-05 3
#> CV:skmeans  50     0.939            0.875 8.67e-12      3.79e-05 3
#> MAD:skmeans 50     1.000            0.931 1.69e-11      8.93e-05 3
#> ATC:skmeans 50     0.933            0.869 1.06e-11      4.14e-05 3
#> SD:mclust   50     1.000            0.931 1.26e-12      1.60e-05 3
#> CV:mclust   50     1.000            0.931 1.26e-12      1.60e-05 3
#> MAD:mclust  50     1.000            0.931 1.26e-12      1.60e-05 3
#> ATC:mclust  50     1.000            0.931 1.26e-12      1.60e-05 3
#> SD:kmeans   49     0.870            0.944 1.68e-11      6.67e-05 3
#> CV:kmeans   50     0.776            0.931 1.69e-11      8.93e-05 3
#> MAD:kmeans  46     0.905            0.934 3.31e-11      1.38e-04 3
#> ATC:kmeans  50     0.933            0.869 1.06e-11      4.14e-05 3
#> SD:pam      50     0.937            0.873 9.23e-12      3.89e-05 3
#> CV:pam      50     0.939            0.875 8.67e-12      3.79e-05 3
#> MAD:pam     49     0.981            0.952 1.63e-11      6.57e-05 3
#> ATC:pam     46     1.000            0.871 3.31e-11      6.62e-05 3
#> SD:hclust   49     0.972            0.870 1.68e-11      6.67e-05 3
#> CV:hclust   50     0.776            0.931 1.69e-11      8.93e-05 3
#> MAD:hclust  50     1.000            0.931 1.69e-11      8.93e-05 3
#> ATC:hclust  50     1.000            0.931 1.26e-12      1.60e-05 3

test_to_known_factors(res_list, k = 4)

#>              n tissue(p) disease.state(p) other(p) individual(p) k
#> SD:NMF      49     0.995            0.988 2.28e-17      4.54e-07 4
#> CV:NMF      48     1.000            0.987 7.68e-17      1.01e-06 4
#> MAD:NMF     50     1.000            0.986 6.71e-18      2.02e-07 4
#> ATC:NMF     49     0.995            0.961 2.28e-17      4.54e-07 4
#> SD:skmeans  50     1.000            0.986 6.71e-18      2.02e-07 4
#> CV:skmeans  46     0.957            0.891 2.21e-14      7.92e-06 4
#> MAD:skmeans 49     0.995            0.988 2.28e-17      4.54e-07 4
#> ATC:skmeans 47     0.993            0.986 2.58e-16      7.31e-07 4
#> SD:mclust   48     0.987            0.948 6.57e-16      1.01e-06 4
#> CV:mclust   48     0.974            0.948 1.91e-15      3.99e-06 4
#> MAD:mclust  48     0.985            0.946 7.68e-17      1.01e-06 4
#> ATC:mclust  50     1.000            0.986 6.71e-18      2.02e-07 4
#> SD:kmeans   46     1.000            0.987 8.58e-16      1.62e-06 4
#> CV:kmeans   48     1.000            0.987 4.74e-15      7.28e-06 4
#> MAD:kmeans  47     0.981            0.940 2.58e-16      2.20e-06 4
#> ATC:kmeans  41     0.967            0.954 7.24e-11      1.02e-04 4
#> SD:pam      50     0.977            0.951 1.45e-16      7.83e-07 4
#> CV:pam      49     0.995            0.988 1.32e-14      7.04e-06 4
#> MAD:pam     50     0.977            0.951 1.45e-16      7.83e-07 4
#> ATC:pam     50     0.979            0.866 8.76e-16      7.14e-07 4
#> SD:hclust   49     0.996            0.964 5.65e-16      2.18e-06 4
#> CV:hclust   50     0.528            0.986 4.32e-13      2.04e-04 4
#> MAD:hclust  50     1.000            0.986 8.26e-16      4.62e-06 4
#> ATC:hclust  49     0.998            0.993 2.28e-17      4.54e-07 4

test_to_known_factors(res_list, k = 5)

#>              n tissue(p) disease.state(p) other(p) individual(p) k
#> SD:NMF      49     0.996            0.982 2.33e-20      7.98e-08 5
#> CV:NMF      50     1.000            0.998 3.06e-20      2.01e-07 5
#> MAD:NMF     50     1.000            0.998 3.06e-20      2.01e-07 5
#> ATC:NMF     50     1.000            0.986 6.71e-18      2.02e-07 5
#> SD:skmeans  50     1.000            0.998 3.06e-20      2.01e-07 5
#> CV:skmeans  44     0.970            0.955 1.80e-18      6.18e-07 5
#> MAD:skmeans 49     0.996            0.982 2.33e-20      7.98e-08 5
#> ATC:skmeans 50     1.000            0.998 3.76e-23      2.67e-09 5
#> SD:mclust   50     1.000            0.998 1.59e-16      6.55e-06 5
#> CV:mclust   40     0.592            0.989 1.08e-13      2.01e-05 5
#> MAD:mclust  48     0.992            0.975 8.94e-16      1.54e-06 5
#> ATC:mclust  50     0.987            0.975 6.70e-21      2.57e-08 5
#> SD:kmeans   45     1.000            0.614 2.70e-15      1.17e-07 5
#> CV:kmeans   43     0.999            0.719 1.42e-16      7.38e-07 5
#> MAD:kmeans  45     0.999            0.723 1.15e-19      2.75e-08 5
#> ATC:kmeans  48     0.982            0.532 5.15e-16      6.33e-08 5
#> SD:pam      50     1.000            0.998 3.06e-20      2.01e-07 5
#> CV:pam      50     0.979            0.964 3.20e-17      9.29e-07 5
#> MAD:pam     50     1.000            0.998 3.06e-20      2.01e-07 5
#> ATC:pam     46     0.982            0.560 3.62e-16      1.08e-07 5
#> SD:hclust   49     0.996            0.982 2.33e-20      7.98e-08 5
#> CV:hclust   41     0.554            0.958 3.28e-14      9.32e-06 5
#> MAD:hclust  49     0.996            0.993 2.50e-19      7.39e-07 5
#> ATC:hclust  46     0.922            0.927 2.35e-20      4.18e-08 5

test_to_known_factors(res_list, k = 6)

#>              n tissue(p) disease.state(p) other(p) individual(p) k
#> SD:NMF      50     1.000            0.998 3.06e-20      2.01e-07 6
#> CV:NMF      50     1.000            0.998 3.06e-20      2.01e-07 6
#> MAD:NMF     50     1.000            0.998 3.06e-20      2.01e-07 6
#> ATC:NMF     48     1.000            0.962 7.68e-17      3.25e-07 6
#> SD:skmeans  49     0.996            0.982 2.33e-20      7.98e-08 6
#> CV:skmeans  43     0.860            0.987 2.10e-16      4.86e-06 6
#> MAD:skmeans 49     0.996            0.982 2.33e-20      7.98e-08 6
#> ATC:skmeans 48     1.000            0.863 1.22e-26      7.95e-11 6
#> SD:mclust   48     0.860            0.863 1.85e-13      3.25e-04 6
#> CV:mclust   39     0.691            0.980 4.22e-10      1.80e-03 6
#> MAD:mclust  50     0.994            0.989 5.92e-15      1.19e-04 6
#> ATC:mclust  49     0.692            0.996 8.70e-20      2.73e-06 6
#> SD:kmeans   46     0.998            0.586 7.36e-16      4.18e-08 6
#> CV:kmeans   43     0.999            0.420 5.80e-14      3.43e-06 6
#> MAD:kmeans  44     1.000            0.752 5.57e-19      7.88e-08 6
#> ATC:kmeans  43     0.998            0.998 2.92e-15      1.90e-06 6
#> SD:pam      50     0.991            0.984 4.62e-22      7.12e-08 6
#> CV:pam      50     0.979            0.969 1.52e-20      2.12e-07 6
#> MAD:pam     50     0.991            0.984 4.62e-22      7.12e-08 6
#> ATC:pam     48     0.986            0.666 6.76e-21      5.72e-09 6
#> SD:hclust   48     0.989            0.970 4.44e-20      2.22e-08 6
#> CV:hclust   50     0.549            0.990 7.86e-20      2.17e-06 6
#> MAD:hclust  45     0.703            0.994 1.15e-19      4.58e-07 6
#> ATC:hclust  45     0.970            1.000 1.15e-19      1.17e-07 6

Results for each method

SD:hclust**

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 31632 rows and 50 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 5.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk SD-hclust-collect-plots

The plots are:

The first row: a plot of the ECDF (empirical cumulative distribution function) curves of the consensus matrix for each k and the heatmap of predicted classes for each k.
The second row: heatmaps of the consensus matrix for each k.
The third row: heatmaps of the membership matrix for each k.
The fouth row: heatmaps of the signatures for each 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:

ECDF curves of the consensus matrix for each k;
1-PAC. The PAC score measures the proportion of the ambiguous subgrouping.
Mean silhouette score.
Concordance. The mean probability of fiting the consensus class ids in all partitions.
Area increased. Denote \(A_k\) as the area under the ECDF curve for current k, the area increased is defined as \(A_k - A_{k-1}\).
Rand index. The percent of pairs of samples that are both in a same cluster or both are not in a same cluster in the partition of k and k-1.
Jaccard index. The ratio of pairs of samples are both in a same cluster in the partition of k and k-1 and the pairs of samples are both in a same cluster in the partition k or 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)

plot of chunk SD-hclust-select-partition-number

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         0.4707 0.530   0.530
#> 3 3 1.000           0.958       0.982         0.4316 0.794   0.612
#> 4 4 1.000           0.957       0.983         0.0933 0.941   0.819
#> 5 5 1.000           0.954       0.978         0.0483 0.961   0.852
#> 6 6 0.924           0.893       0.926         0.0239 1.000   1.000

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

All \(k\) with Jaccard index larger than 0.95 are removed because increasing \(k\) does not provide enough extra information. If all \(k\) are removed, it is marked as no subgroup is detected.
For all \(k\) with 1-PAC score larger than 0.9, the maximal \(k\) is taken as the best \(k\), and other \(k\) are marked as optional \(k\).
If it does not fit the second rule. The \(k\) with the maximal vote of the highest 1-PAC score, highest mean silhouette, and highest concordance is taken as the best \(k\).

suggest_best_k(res)

#> [1] 5
#> attr(,"optional")
#> [1] 2 3 4

There is also optional best \(k\) = 2 3 4 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.

k = 2
k = 3
k = 4
k = 5
k = 6

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>           class entropy silhouette p1 p2
#> GSM892342     1       0          1  1  0
#> GSM892345     1       0          1  1  0
#> GSM892349     1       0          1  1  0
#> GSM892353     1       0          1  1  0
#> GSM892355     1       0          1  1  0
#> GSM892361     1       0          1  1  0
#> GSM892365     1       0          1  1  0
#> GSM892369     1       0          1  1  0
#> GSM892373     2       0          1  0  1
#> GSM892377     2       0          1  0  1
#> GSM892381     2       0          1  0  1
#> GSM892383     2       0          1  0  1
#> GSM892387     2       0          1  0  1
#> GSM892344     1       0          1  1  0
#> GSM892347     1       0          1  1  0
#> GSM892351     1       0          1  1  0
#> GSM892357     1       0          1  1  0
#> GSM892359     1       0          1  1  0
#> GSM892363     1       0          1  1  0
#> GSM892367     1       0          1  1  0
#> GSM892371     1       0          1  1  0
#> GSM892375     2       0          1  0  1
#> GSM892379     2       0          1  0  1
#> GSM892385     2       0          1  0  1
#> GSM892389     2       0          1  0  1
#> GSM892341     1       0          1  1  0
#> GSM892346     1       0          1  1  0
#> GSM892350     1       0          1  1  0
#> GSM892354     1       0          1  1  0
#> GSM892356     1       0          1  1  0
#> GSM892362     1       0          1  1  0
#> GSM892366     1       0          1  1  0
#> GSM892370     1       0          1  1  0
#> GSM892374     2       0          1  0  1
#> GSM892378     2       0          1  0  1
#> GSM892382     2       0          1  0  1
#> GSM892384     2       0          1  0  1
#> GSM892388     2       0          1  0  1
#> GSM892343     1       0          1  1  0
#> GSM892348     1       0          1  1  0
#> GSM892352     1       0          1  1  0
#> GSM892358     1       0          1  1  0
#> GSM892360     1       0          1  1  0
#> GSM892364     1       0          1  1  0
#> GSM892368     1       0          1  1  0
#> GSM892372     1       0          1  1  0
#> GSM892376     2       0          1  0  1
#> GSM892380     2       0          1  0  1
#> GSM892386     2       0          1  0  1
#> GSM892390     2       0          1  0  1

show/hide code output

cbind(get_classes(res, k = 3), get_membership(res, k = 3))

#>           class entropy silhouette    p1 p2    p3
#> GSM892342     3  0.0000      0.950 0.000  0 1.000
#> GSM892345     1  0.0424      0.981 0.992  0 0.008
#> GSM892349     3  0.6126      0.337 0.400  0 0.600
#> GSM892353     1  0.0237      0.982 0.996  0 0.004
#> GSM892355     1  0.0000      0.984 1.000  0 0.000
#> GSM892361     1  0.0000      0.984 1.000  0 0.000
#> GSM892365     3  0.0000      0.950 0.000  0 1.000
#> GSM892369     3  0.0424      0.947 0.008  0 0.992
#> GSM892373     2  0.0000      1.000 0.000  1 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000
#> GSM892344     3  0.0000      0.950 0.000  0 1.000
#> GSM892347     1  0.0424      0.981 0.992  0 0.008
#> GSM892351     1  0.4750      0.710 0.784  0 0.216
#> GSM892357     1  0.0000      0.984 1.000  0 0.000
#> GSM892359     1  0.0000      0.984 1.000  0 0.000
#> GSM892363     1  0.0000      0.984 1.000  0 0.000
#> GSM892367     3  0.0000      0.950 0.000  0 1.000
#> GSM892371     3  0.0424      0.947 0.008  0 0.992
#> GSM892375     2  0.0000      1.000 0.000  1 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000
#> GSM892341     3  0.0000      0.950 0.000  0 1.000
#> GSM892346     1  0.0424      0.981 0.992  0 0.008
#> GSM892350     1  0.0424      0.981 0.992  0 0.008
#> GSM892354     1  0.0000      0.984 1.000  0 0.000
#> GSM892356     1  0.0000      0.984 1.000  0 0.000
#> GSM892362     1  0.0000      0.984 1.000  0 0.000
#> GSM892366     3  0.0000      0.950 0.000  0 1.000
#> GSM892370     3  0.0424      0.947 0.008  0 0.992
#> GSM892374     2  0.0000      1.000 0.000  1 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000
#> GSM892343     3  0.4504      0.750 0.196  0 0.804
#> GSM892348     1  0.0424      0.981 0.992  0 0.008
#> GSM892352     3  0.0000      0.950 0.000  0 1.000
#> GSM892358     1  0.0000      0.984 1.000  0 0.000
#> GSM892360     1  0.0000      0.984 1.000  0 0.000
#> GSM892364     1  0.0000      0.984 1.000  0 0.000
#> GSM892368     3  0.0000      0.950 0.000  0 1.000
#> GSM892372     3  0.0000      0.950 0.000  0 1.000
#> GSM892376     2  0.0000      1.000 0.000  1 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000

show/hide code output

cbind(get_classes(res, k = 4), get_membership(res, k = 4))

#>           class entropy silhouette    p1 p2    p3    p4
#> GSM892342     3  0.0000      0.949 0.000  0 1.000 0.000
#> GSM892345     4  0.0000      0.955 0.000  0 0.000 1.000
#> GSM892349     3  0.4877      0.287 0.000  0 0.592 0.408
#> GSM892353     1  0.0188      0.993 0.996  0 0.004 0.000
#> GSM892355     1  0.0000      0.997 1.000  0 0.000 0.000
#> GSM892361     1  0.0000      0.997 1.000  0 0.000 0.000
#> GSM892365     3  0.0000      0.949 0.000  0 1.000 0.000
#> GSM892369     3  0.0336      0.945 0.000  0 0.992 0.008
#> GSM892373     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892344     3  0.0000      0.949 0.000  0 1.000 0.000
#> GSM892347     4  0.0000      0.955 0.000  0 0.000 1.000
#> GSM892351     4  0.3688      0.715 0.000  0 0.208 0.792
#> GSM892357     1  0.0000      0.997 1.000  0 0.000 0.000
#> GSM892359     1  0.0000      0.997 1.000  0 0.000 0.000
#> GSM892363     1  0.0000      0.997 1.000  0 0.000 0.000
#> GSM892367     3  0.0000      0.949 0.000  0 1.000 0.000
#> GSM892371     3  0.0336      0.945 0.000  0 0.992 0.008
#> GSM892375     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892341     3  0.0000      0.949 0.000  0 1.000 0.000
#> GSM892346     4  0.0000      0.955 0.000  0 0.000 1.000
#> GSM892350     4  0.0000      0.955 0.000  0 0.000 1.000
#> GSM892354     1  0.0000      0.997 1.000  0 0.000 0.000
#> GSM892356     1  0.0000      0.997 1.000  0 0.000 0.000
#> GSM892362     1  0.0000      0.997 1.000  0 0.000 0.000
#> GSM892366     3  0.0000      0.949 0.000  0 1.000 0.000
#> GSM892370     3  0.0336      0.945 0.000  0 0.992 0.008
#> GSM892374     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892343     3  0.3895      0.747 0.012  0 0.804 0.184
#> GSM892348     4  0.0000      0.955 0.000  0 0.000 1.000
#> GSM892352     3  0.0000      0.949 0.000  0 1.000 0.000
#> GSM892358     1  0.0000      0.997 1.000  0 0.000 0.000
#> GSM892360     1  0.0000      0.997 1.000  0 0.000 0.000
#> GSM892364     1  0.0817      0.975 0.976  0 0.000 0.024
#> GSM892368     3  0.0000      0.949 0.000  0 1.000 0.000
#> GSM892372     3  0.0000      0.949 0.000  0 1.000 0.000
#> GSM892376     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 5), get_membership(res, k = 5))

#>           class entropy silhouette    p1 p2    p3    p4    p5
#> GSM892342     5  0.1197      0.852 0.000  0 0.048 0.000 0.952
#> GSM892345     4  0.0000      0.951 0.000  0 0.000 1.000 0.000
#> GSM892349     5  0.4192      0.279 0.000  0 0.000 0.404 0.596
#> GSM892353     1  0.0290      0.992 0.992  0 0.000 0.000 0.008
#> GSM892355     1  0.0162      0.995 0.996  0 0.000 0.000 0.004
#> GSM892361     1  0.0000      0.996 1.000  0 0.000 0.000 0.000
#> GSM892365     3  0.0290      0.996 0.000  0 0.992 0.000 0.008
#> GSM892369     3  0.0000      0.993 0.000  0 1.000 0.000 0.000
#> GSM892373     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892344     5  0.1197      0.852 0.000  0 0.048 0.000 0.952
#> GSM892347     4  0.0000      0.951 0.000  0 0.000 1.000 0.000
#> GSM892351     4  0.3210      0.700 0.000  0 0.000 0.788 0.212
#> GSM892357     1  0.0000      0.996 1.000  0 0.000 0.000 0.000
#> GSM892359     1  0.0000      0.996 1.000  0 0.000 0.000 0.000
#> GSM892363     1  0.0000      0.996 1.000  0 0.000 0.000 0.000
#> GSM892367     3  0.0290      0.996 0.000  0 0.992 0.000 0.008
#> GSM892371     3  0.0000      0.993 0.000  0 1.000 0.000 0.000
#> GSM892375     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892341     5  0.1197      0.852 0.000  0 0.048 0.000 0.952
#> GSM892346     4  0.0000      0.951 0.000  0 0.000 1.000 0.000
#> GSM892350     4  0.0162      0.949 0.000  0 0.000 0.996 0.004
#> GSM892354     1  0.0000      0.996 1.000  0 0.000 0.000 0.000
#> GSM892356     1  0.0162      0.995 0.996  0 0.000 0.000 0.004
#> GSM892362     1  0.0000      0.996 1.000  0 0.000 0.000 0.000
#> GSM892366     3  0.0290      0.996 0.000  0 0.992 0.000 0.008
#> GSM892370     3  0.0000      0.993 0.000  0 1.000 0.000 0.000
#> GSM892374     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892343     5  0.4851      0.710 0.008  0 0.084 0.176 0.732
#> GSM892348     4  0.0000      0.951 0.000  0 0.000 1.000 0.000
#> GSM892352     5  0.0290      0.833 0.000  0 0.008 0.000 0.992
#> GSM892358     1  0.0000      0.996 1.000  0 0.000 0.000 0.000
#> GSM892360     1  0.0000      0.996 1.000  0 0.000 0.000 0.000
#> GSM892364     1  0.0865      0.972 0.972  0 0.000 0.024 0.004
#> GSM892368     3  0.0290      0.996 0.000  0 0.992 0.000 0.008
#> GSM892372     3  0.0290      0.996 0.000  0 0.992 0.000 0.008
#> GSM892376     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 6), get_membership(res, k = 6))

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> GSM892342     5  0.1007      0.808 0.000 0.000 0.044 0.000 0.956 0.000
#> GSM892345     4  0.3390      0.807 0.000 0.000 0.000 0.704 0.000 0.296
#> GSM892349     5  0.5743      0.339 0.000 0.000 0.000 0.404 0.428 0.168
#> GSM892353     1  0.2482      0.895 0.848 0.000 0.000 0.000 0.004 0.148
#> GSM892355     1  0.2300      0.900 0.856 0.000 0.000 0.000 0.000 0.144
#> GSM892361     1  0.0260      0.956 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM892365     3  0.0146      0.972 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM892369     3  0.1267      0.955 0.000 0.000 0.940 0.000 0.000 0.060
#> GSM892373     2  0.2048      0.911 0.000 0.880 0.000 0.000 0.000 0.120
#> GSM892377     2  0.1387      0.942 0.000 0.932 0.000 0.000 0.000 0.068
#> GSM892381     2  0.0000      0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892383     2  0.0000      0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892387     2  0.0458      0.967 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM892344     5  0.1007      0.808 0.000 0.000 0.044 0.000 0.956 0.000
#> GSM892347     4  0.3390      0.807 0.000 0.000 0.000 0.704 0.000 0.296
#> GSM892351     4  0.3487      0.452 0.000 0.000 0.000 0.788 0.044 0.168
#> GSM892357     1  0.0260      0.956 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM892359     1  0.0363      0.954 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM892363     1  0.0790      0.953 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM892367     3  0.0146      0.972 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM892371     3  0.1267      0.955 0.000 0.000 0.940 0.000 0.000 0.060
#> GSM892375     2  0.0458      0.966 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM892379     2  0.0146      0.968 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM892385     2  0.1204      0.941 0.000 0.944 0.000 0.000 0.000 0.056
#> GSM892389     2  0.0260      0.967 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM892341     5  0.1007      0.808 0.000 0.000 0.044 0.000 0.956 0.000
#> GSM892346     4  0.3765      0.787 0.000 0.000 0.000 0.596 0.000 0.404
#> GSM892350     4  0.0000      0.666 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM892354     1  0.0260      0.956 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM892356     1  0.2260      0.901 0.860 0.000 0.000 0.000 0.000 0.140
#> GSM892362     1  0.0000      0.956 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892366     3  0.0146      0.972 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM892370     3  0.1267      0.955 0.000 0.000 0.940 0.000 0.000 0.060
#> GSM892374     2  0.2048      0.911 0.000 0.880 0.000 0.000 0.000 0.120
#> GSM892378     2  0.1387      0.942 0.000 0.932 0.000 0.000 0.000 0.068
#> GSM892382     2  0.0000      0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892384     2  0.0000      0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892388     2  0.2135      0.894 0.000 0.872 0.000 0.000 0.000 0.128
#> GSM892343     5  0.4634      0.693 0.000 0.000 0.020 0.160 0.724 0.096
#> GSM892348     4  0.3765      0.787 0.000 0.000 0.000 0.596 0.000 0.404
#> GSM892352     5  0.2454      0.742 0.000 0.000 0.000 0.000 0.840 0.160
#> GSM892358     1  0.0458      0.955 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM892360     1  0.0363      0.954 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM892364     1  0.1686      0.937 0.924 0.000 0.000 0.012 0.000 0.064
#> GSM892368     3  0.0146      0.972 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM892372     3  0.0000      0.972 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM892376     2  0.0458      0.966 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM892380     2  0.0146      0.968 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM892386     2  0.0146      0.968 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM892390     2  0.0260      0.967 0.000 0.992 0.000 0.000 0.000 0.008

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

k = 2
k = 3
k = 4
k = 5
k = 6

consensus_heatmap(res, k = 2)

plot of chunk tab-SD-hclust-consensus-heatmap-1

consensus_heatmap(res, k = 3)

plot of chunk tab-SD-hclust-consensus-heatmap-2

consensus_heatmap(res, k = 4)

plot of chunk tab-SD-hclust-consensus-heatmap-3

consensus_heatmap(res, k = 5)

plot of chunk tab-SD-hclust-consensus-heatmap-4

consensus_heatmap(res, k = 6)

plot of chunk tab-SD-hclust-consensus-heatmap-5

Heatmaps for the membership of samples in all partitions to see how consistent they are:

k = 2
k = 3
k = 4
k = 5
k = 6

membership_heatmap(res, k = 2)

plot of chunk tab-SD-hclust-membership-heatmap-1

membership_heatmap(res, k = 3)

plot of chunk tab-SD-hclust-membership-heatmap-2

membership_heatmap(res, k = 4)

plot of chunk tab-SD-hclust-membership-heatmap-3

membership_heatmap(res, k = 5)

plot of chunk tab-SD-hclust-membership-heatmap-4

membership_heatmap(res, k = 6)

plot of chunk tab-SD-hclust-membership-heatmap-5

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:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2)

plot of chunk tab-SD-hclust-get-signatures-1

get_signatures(res, k = 3)

plot of chunk tab-SD-hclust-get-signatures-2

get_signatures(res, k = 4)

plot of chunk tab-SD-hclust-get-signatures-3

get_signatures(res, k = 5)

plot of chunk tab-SD-hclust-get-signatures-4

get_signatures(res, k = 6)

plot of chunk tab-SD-hclust-get-signatures-5

Signature heatmaps where rows are not scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-SD-hclust-get-signatures-no-scale-1

get_signatures(res, k = 3, scale_rows = FALSE)

plot of chunk tab-SD-hclust-get-signatures-no-scale-2

get_signatures(res, k = 4, scale_rows = FALSE)

plot of chunk tab-SD-hclust-get-signatures-no-scale-3

get_signatures(res, k = 5, scale_rows = FALSE)

plot of chunk tab-SD-hclust-get-signatures-no-scale-4

get_signatures(res, k = 6, scale_rows = FALSE)

plot of chunk tab-SD-hclust-get-signatures-no-scale-5

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk SD-hclust-signature_compare

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.

k = 2
k = 3
k = 4
k = 5
k = 6

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-SD-hclust-dimension-reduction-1

dimension_reduction(res, k = 3, method = "UMAP")

plot of chunk tab-SD-hclust-dimension-reduction-2

dimension_reduction(res, k = 4, method = "UMAP")

plot of chunk tab-SD-hclust-dimension-reduction-3

dimension_reduction(res, k = 5, method = "UMAP")

plot of chunk tab-SD-hclust-dimension-reduction-4

dimension_reduction(res, k = 6, method = "UMAP")

plot of chunk tab-SD-hclust-dimension-reduction-5

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk SD-hclust-collect-classes

test_to_known_factors(res)

#>            n tissue(p) disease.state(p) other(p) individual(p) k
#> SD:hclust 50     1.000            0.934 2.67e-07      1.42e-03 2
#> SD:hclust 49     0.972            0.870 1.68e-11      6.67e-05 3
#> SD:hclust 49     0.996            0.964 5.65e-16      2.18e-06 4
#> SD:hclust 49     0.996            0.982 2.33e-20      7.98e-08 5
#> SD:hclust 48     0.989            0.970 4.44e-20      2.22e-08 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

SD:kmeans**

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 31632 rows and 50 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)

plot of chunk SD-kmeans-collect-plots

The plots are:

The first row: a plot of the ECDF (empirical cumulative distribution function) curves of the consensus matrix for each k and the heatmap of predicted classes for each k.
The second row: heatmaps of the consensus matrix for each k.
The third row: heatmaps of the membership matrix for each k.
The fouth row: heatmaps of the signatures for each 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:

ECDF curves of the consensus matrix for each k;
1-PAC. The PAC score measures the proportion of the ambiguous subgrouping.
Mean silhouette score.
Concordance. The mean probability of fiting the consensus class ids in all partitions.
Area increased. Denote \(A_k\) as the area under the ECDF curve for current k, the area increased is defined as \(A_k - A_{k-1}\).
Rand index. The percent of pairs of samples that are both in a same cluster or both are not in a same cluster in the partition of k and k-1.
Jaccard index. The ratio of pairs of samples are both in a same cluster in the partition of k and k-1 and the pairs of samples are both in a same cluster in the partition k or k-1.

The detailed explanations of these statistics can be found in the cola vignette.

select_partition_number(res)

plot of chunk SD-kmeans-select-partition-number

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         0.4707 0.530   0.530
#> 3 3 0.704           0.906       0.878         0.3438 0.794   0.612
#> 4 4 0.794           0.794       0.824         0.1277 0.939   0.814
#> 5 5 0.693           0.697       0.811         0.0628 0.958   0.850
#> 6 6 0.762           0.693       0.803         0.0584 0.971   0.882

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

All \(k\) with Jaccard index larger than 0.95 are removed because increasing \(k\) does not provide enough extra information. If all \(k\) are removed, it is marked as no subgroup is detected.
For all \(k\) with 1-PAC score larger than 0.9, the maximal \(k\) is taken as the best \(k\), and other \(k\) are marked as optional \(k\).
If it does not fit the second rule. The \(k\) with the maximal vote of the highest 1-PAC score, highest mean silhouette, and highest concordance is taken as the best \(k\).

suggest_best_k(res)

#> [1] 2

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

k = 2
k = 3
k = 4
k = 5
k = 6

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>           class entropy silhouette p1 p2
#> GSM892342     1       0          1  1  0
#> GSM892345     1       0          1  1  0
#> GSM892349     1       0          1  1  0
#> GSM892353     1       0          1  1  0
#> GSM892355     1       0          1  1  0
#> GSM892361     1       0          1  1  0
#> GSM892365     1       0          1  1  0
#> GSM892369     1       0          1  1  0
#> GSM892373     2       0          1  0  1
#> GSM892377     2       0          1  0  1
#> GSM892381     2       0          1  0  1
#> GSM892383     2       0          1  0  1
#> GSM892387     2       0          1  0  1
#> GSM892344     1       0          1  1  0
#> GSM892347     1       0          1  1  0
#> GSM892351     1       0          1  1  0
#> GSM892357     1       0          1  1  0
#> GSM892359     1       0          1  1  0
#> GSM892363     1       0          1  1  0
#> GSM892367     1       0          1  1  0
#> GSM892371     1       0          1  1  0
#> GSM892375     2       0          1  0  1
#> GSM892379     2       0          1  0  1
#> GSM892385     2       0          1  0  1
#> GSM892389     2       0          1  0  1
#> GSM892341     1       0          1  1  0
#> GSM892346     1       0          1  1  0
#> GSM892350     1       0          1  1  0
#> GSM892354     1       0          1  1  0
#> GSM892356     1       0          1  1  0
#> GSM892362     1       0          1  1  0
#> GSM892366     1       0          1  1  0
#> GSM892370     1       0          1  1  0
#> GSM892374     2       0          1  0  1
#> GSM892378     2       0          1  0  1
#> GSM892382     2       0          1  0  1
#> GSM892384     2       0          1  0  1
#> GSM892388     2       0          1  0  1
#> GSM892343     1       0          1  1  0
#> GSM892348     1       0          1  1  0
#> GSM892352     1       0          1  1  0
#> GSM892358     1       0          1  1  0
#> GSM892360     1       0          1  1  0
#> GSM892364     1       0          1  1  0
#> GSM892368     1       0          1  1  0
#> GSM892372     1       0          1  1  0
#> GSM892376     2       0          1  0  1
#> GSM892380     2       0          1  0  1
#> GSM892386     2       0          1  0  1
#> GSM892390     2       0          1  0  1

show/hide code output

cbind(get_classes(res, k = 3), get_membership(res, k = 3))

#>           class entropy silhouette    p1    p2    p3
#> GSM892342     3  0.5327      0.956 0.272 0.000 0.728
#> GSM892345     3  0.6126      0.760 0.400 0.000 0.600
#> GSM892349     3  0.5178      0.944 0.256 0.000 0.744
#> GSM892353     1  0.0000      0.939 1.000 0.000 0.000
#> GSM892355     1  0.0000      0.939 1.000 0.000 0.000
#> GSM892361     1  0.0000      0.939 1.000 0.000 0.000
#> GSM892365     3  0.5327      0.956 0.272 0.000 0.728
#> GSM892369     3  0.5327      0.956 0.272 0.000 0.728
#> GSM892373     2  0.4796      0.867 0.000 0.780 0.220
#> GSM892377     2  0.3879      0.909 0.000 0.848 0.152
#> GSM892381     2  0.0424      0.958 0.000 0.992 0.008
#> GSM892383     2  0.1163      0.956 0.000 0.972 0.028
#> GSM892387     2  0.0424      0.958 0.000 0.992 0.008
#> GSM892344     3  0.5327      0.956 0.272 0.000 0.728
#> GSM892347     3  0.6126      0.760 0.400 0.000 0.600
#> GSM892351     3  0.5178      0.944 0.256 0.000 0.744
#> GSM892357     1  0.0000      0.939 1.000 0.000 0.000
#> GSM892359     1  0.0000      0.939 1.000 0.000 0.000
#> GSM892363     1  0.0000      0.939 1.000 0.000 0.000
#> GSM892367     3  0.5327      0.956 0.272 0.000 0.728
#> GSM892371     3  0.5327      0.956 0.272 0.000 0.728
#> GSM892375     2  0.0592      0.958 0.000 0.988 0.012
#> GSM892379     2  0.1411      0.957 0.000 0.964 0.036
#> GSM892385     2  0.1529      0.956 0.000 0.960 0.040
#> GSM892389     2  0.1031      0.958 0.000 0.976 0.024
#> GSM892341     3  0.5327      0.956 0.272 0.000 0.728
#> GSM892346     1  0.4062      0.700 0.836 0.000 0.164
#> GSM892350     3  0.6126      0.760 0.400 0.000 0.600
#> GSM892354     1  0.0000      0.939 1.000 0.000 0.000
#> GSM892356     1  0.0000      0.939 1.000 0.000 0.000
#> GSM892362     1  0.0000      0.939 1.000 0.000 0.000
#> GSM892366     3  0.5327      0.956 0.272 0.000 0.728
#> GSM892370     3  0.5327      0.956 0.272 0.000 0.728
#> GSM892374     2  0.4796      0.867 0.000 0.780 0.220
#> GSM892378     2  0.3879      0.909 0.000 0.848 0.152
#> GSM892382     2  0.0424      0.958 0.000 0.992 0.008
#> GSM892384     2  0.0424      0.958 0.000 0.992 0.008
#> GSM892388     2  0.3116      0.923 0.000 0.892 0.108
#> GSM892343     3  0.5327      0.956 0.272 0.000 0.728
#> GSM892348     1  0.6111     -0.154 0.604 0.000 0.396
#> GSM892352     3  0.5178      0.944 0.256 0.000 0.744
#> GSM892358     1  0.0000      0.939 1.000 0.000 0.000
#> GSM892360     1  0.0000      0.939 1.000 0.000 0.000
#> GSM892364     1  0.0000      0.939 1.000 0.000 0.000
#> GSM892368     3  0.5327      0.956 0.272 0.000 0.728
#> GSM892372     3  0.5327      0.956 0.272 0.000 0.728
#> GSM892376     2  0.0592      0.958 0.000 0.988 0.012
#> GSM892380     2  0.1163      0.958 0.000 0.972 0.028
#> GSM892386     2  0.0424      0.958 0.000 0.992 0.008
#> GSM892390     2  0.1289      0.958 0.000 0.968 0.032

show/hide code output

cbind(get_classes(res, k = 4), get_membership(res, k = 4))

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM892342     3  0.0469     0.8081 0.000 0.000 0.988 0.012
#> GSM892345     4  0.6915     0.7632 0.108 0.000 0.416 0.476
#> GSM892349     3  0.4941    -0.2668 0.000 0.000 0.564 0.436
#> GSM892353     1  0.3550     0.9621 0.860 0.000 0.096 0.044
#> GSM892355     1  0.3463     0.9643 0.864 0.000 0.096 0.040
#> GSM892361     1  0.2611     0.9830 0.896 0.000 0.096 0.008
#> GSM892365     3  0.0000     0.8084 0.000 0.000 1.000 0.000
#> GSM892369     3  0.2081     0.7725 0.000 0.000 0.916 0.084
#> GSM892373     2  0.4898     0.7086 0.000 0.584 0.000 0.416
#> GSM892377     2  0.5198     0.8015 0.040 0.708 0.000 0.252
#> GSM892381     2  0.1284     0.9021 0.024 0.964 0.000 0.012
#> GSM892383     2  0.2319     0.8957 0.036 0.924 0.000 0.040
#> GSM892387     2  0.1406     0.9040 0.024 0.960 0.000 0.016
#> GSM892344     3  0.0469     0.8081 0.000 0.000 0.988 0.012
#> GSM892347     4  0.6915     0.7632 0.108 0.000 0.416 0.476
#> GSM892351     3  0.4992    -0.4096 0.000 0.000 0.524 0.476
#> GSM892357     1  0.2741     0.9829 0.892 0.000 0.096 0.012
#> GSM892359     1  0.2611     0.9830 0.896 0.000 0.096 0.008
#> GSM892363     1  0.2281     0.9823 0.904 0.000 0.096 0.000
#> GSM892367     3  0.0000     0.8084 0.000 0.000 1.000 0.000
#> GSM892371     3  0.2081     0.7725 0.000 0.000 0.916 0.084
#> GSM892375     2  0.1706     0.9035 0.016 0.948 0.000 0.036
#> GSM892379     2  0.2521     0.8997 0.024 0.912 0.000 0.064
#> GSM892385     2  0.2919     0.8925 0.044 0.896 0.000 0.060
#> GSM892389     2  0.1913     0.9034 0.020 0.940 0.000 0.040
#> GSM892341     3  0.0469     0.8081 0.000 0.000 0.988 0.012
#> GSM892346     4  0.7375     0.4872 0.348 0.000 0.172 0.480
#> GSM892350     4  0.6915     0.7632 0.108 0.000 0.416 0.476
#> GSM892354     1  0.2611     0.9830 0.896 0.000 0.096 0.008
#> GSM892356     1  0.3463     0.9643 0.864 0.000 0.096 0.040
#> GSM892362     1  0.2611     0.9830 0.896 0.000 0.096 0.008
#> GSM892366     3  0.0000     0.8084 0.000 0.000 1.000 0.000
#> GSM892370     3  0.2081     0.7725 0.000 0.000 0.916 0.084
#> GSM892374     2  0.4898     0.7086 0.000 0.584 0.000 0.416
#> GSM892378     2  0.5198     0.8015 0.040 0.708 0.000 0.252
#> GSM892382     2  0.1284     0.9021 0.024 0.964 0.000 0.012
#> GSM892384     2  0.1284     0.9021 0.024 0.964 0.000 0.012
#> GSM892388     2  0.4799     0.8131 0.032 0.744 0.000 0.224
#> GSM892343     3  0.2469     0.7504 0.000 0.000 0.892 0.108
#> GSM892348     4  0.7438     0.7386 0.188 0.000 0.328 0.484
#> GSM892352     3  0.4661     0.0688 0.000 0.000 0.652 0.348
#> GSM892358     1  0.2741     0.9784 0.892 0.000 0.096 0.012
#> GSM892360     1  0.2611     0.9830 0.896 0.000 0.096 0.008
#> GSM892364     1  0.2466     0.9817 0.900 0.000 0.096 0.004
#> GSM892368     3  0.0000     0.8084 0.000 0.000 1.000 0.000
#> GSM892372     3  0.0000     0.8084 0.000 0.000 1.000 0.000
#> GSM892376     2  0.1610     0.9037 0.016 0.952 0.000 0.032
#> GSM892380     2  0.1584     0.9028 0.012 0.952 0.000 0.036
#> GSM892386     2  0.1297     0.9029 0.020 0.964 0.000 0.016
#> GSM892390     2  0.1584     0.9031 0.012 0.952 0.000 0.036

show/hide code output

cbind(get_classes(res, k = 5), get_membership(res, k = 5))

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> GSM892342     3  0.0404     0.7327 0.000 0.000 0.988 0.012 0.000
#> GSM892345     4  0.4744     0.8927 0.056 0.000 0.252 0.692 0.000
#> GSM892349     3  0.4557    -0.4544 0.000 0.000 0.516 0.476 0.008
#> GSM892353     1  0.4536     0.8814 0.780 0.000 0.060 0.028 0.132
#> GSM892355     1  0.4451     0.8833 0.784 0.000 0.060 0.024 0.132
#> GSM892361     1  0.2193     0.9486 0.912 0.000 0.060 0.000 0.028
#> GSM892365     3  0.2648     0.7804 0.000 0.000 0.848 0.000 0.152
#> GSM892369     3  0.4637     0.7474 0.000 0.000 0.728 0.076 0.196
#> GSM892373     5  0.4235     1.0000 0.000 0.424 0.000 0.000 0.576
#> GSM892377     2  0.6103    -0.2892 0.008 0.532 0.000 0.108 0.352
#> GSM892381     2  0.0992     0.7092 0.000 0.968 0.000 0.024 0.008
#> GSM892383     2  0.3244     0.6662 0.008 0.860 0.000 0.084 0.048
#> GSM892387     2  0.2721     0.6933 0.012 0.892 0.000 0.068 0.028
#> GSM892344     3  0.0404     0.7327 0.000 0.000 0.988 0.012 0.000
#> GSM892347     4  0.4744     0.8927 0.056 0.000 0.252 0.692 0.000
#> GSM892351     4  0.4108     0.7749 0.000 0.000 0.308 0.684 0.008
#> GSM892357     1  0.2264     0.9501 0.912 0.000 0.060 0.004 0.024
#> GSM892359     1  0.1410     0.9524 0.940 0.000 0.060 0.000 0.000
#> GSM892363     1  0.1410     0.9524 0.940 0.000 0.060 0.000 0.000
#> GSM892367     3  0.3074     0.7717 0.000 0.000 0.804 0.000 0.196
#> GSM892371     3  0.4637     0.7474 0.000 0.000 0.728 0.076 0.196
#> GSM892375     2  0.3191     0.6587 0.016 0.868 0.000 0.040 0.076
#> GSM892379     2  0.4002     0.6486 0.000 0.796 0.000 0.120 0.084
#> GSM892385     2  0.3926     0.6363 0.008 0.808 0.000 0.132 0.052
#> GSM892389     2  0.3384     0.6868 0.004 0.848 0.000 0.088 0.060
#> GSM892341     3  0.0404     0.7327 0.000 0.000 0.988 0.012 0.000
#> GSM892346     4  0.5535     0.7317 0.188 0.000 0.124 0.676 0.012
#> GSM892350     4  0.4744     0.8927 0.056 0.000 0.252 0.692 0.000
#> GSM892354     1  0.2193     0.9486 0.912 0.000 0.060 0.000 0.028
#> GSM892356     1  0.4314     0.8894 0.796 0.000 0.060 0.024 0.120
#> GSM892362     1  0.1809     0.9507 0.928 0.000 0.060 0.000 0.012
#> GSM892366     3  0.2648     0.7804 0.000 0.000 0.848 0.000 0.152
#> GSM892370     3  0.4637     0.7474 0.000 0.000 0.728 0.076 0.196
#> GSM892374     5  0.4235     1.0000 0.000 0.424 0.000 0.000 0.576
#> GSM892378     2  0.6103    -0.2892 0.008 0.532 0.000 0.108 0.352
#> GSM892382     2  0.0992     0.7092 0.000 0.968 0.000 0.024 0.008
#> GSM892384     2  0.1082     0.7072 0.000 0.964 0.000 0.028 0.008
#> GSM892388     2  0.6277    -0.0681 0.028 0.604 0.000 0.128 0.240
#> GSM892343     3  0.2230     0.6652 0.000 0.000 0.884 0.116 0.000
#> GSM892348     4  0.5196     0.8600 0.100 0.000 0.208 0.688 0.004
#> GSM892352     3  0.4392    -0.1592 0.000 0.000 0.612 0.380 0.008
#> GSM892358     1  0.1571     0.9523 0.936 0.000 0.060 0.004 0.000
#> GSM892360     1  0.1410     0.9524 0.940 0.000 0.060 0.000 0.000
#> GSM892364     1  0.2519     0.9419 0.900 0.000 0.060 0.004 0.036
#> GSM892368     3  0.2648     0.7804 0.000 0.000 0.848 0.000 0.152
#> GSM892372     3  0.2891     0.7774 0.000 0.000 0.824 0.000 0.176
#> GSM892376     2  0.3067     0.6654 0.016 0.876 0.000 0.040 0.068
#> GSM892380     2  0.2992     0.6802 0.000 0.868 0.000 0.068 0.064
#> GSM892386     2  0.1843     0.7055 0.008 0.932 0.000 0.052 0.008
#> GSM892390     2  0.2843     0.6956 0.000 0.876 0.000 0.076 0.048

show/hide code output

cbind(get_classes(res, k = 6), get_membership(res, k = 6))

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> GSM892342     3  0.4224      0.635 0.016 0.000 0.660 0.012 0.312 0.000
#> GSM892345     4  0.2164      0.830 0.032 0.000 0.068 0.900 0.000 0.000
#> GSM892349     4  0.5970      0.510 0.016 0.000 0.128 0.528 0.320 0.008
#> GSM892353     1  0.3725      0.768 0.676 0.000 0.000 0.008 0.000 0.316
#> GSM892355     1  0.3601      0.771 0.684 0.000 0.000 0.004 0.000 0.312
#> GSM892361     1  0.2201      0.888 0.904 0.000 0.000 0.004 0.036 0.056
#> GSM892365     3  0.0458      0.778 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM892369     3  0.4860      0.710 0.016 0.000 0.752 0.096 0.072 0.064
#> GSM892373     5  0.6125      1.000 0.000 0.312 0.000 0.000 0.348 0.340
#> GSM892377     2  0.5190     -0.167 0.000 0.460 0.000 0.000 0.452 0.088
#> GSM892381     2  0.1369      0.704 0.000 0.952 0.000 0.016 0.016 0.016
#> GSM892383     2  0.3583      0.672 0.000 0.820 0.000 0.032 0.108 0.040
#> GSM892387     2  0.3097      0.683 0.000 0.856 0.000 0.036 0.028 0.080
#> GSM892344     3  0.4224      0.635 0.016 0.000 0.660 0.012 0.312 0.000
#> GSM892347     4  0.2164      0.830 0.032 0.000 0.068 0.900 0.000 0.000
#> GSM892351     4  0.3085      0.810 0.016 0.000 0.084 0.860 0.032 0.008
#> GSM892357     1  0.2263      0.888 0.900 0.000 0.000 0.004 0.036 0.060
#> GSM892359     1  0.0146      0.897 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM892363     1  0.0436      0.896 0.988 0.000 0.000 0.004 0.004 0.004
#> GSM892367     3  0.2698      0.762 0.016 0.000 0.880 0.000 0.064 0.040
#> GSM892371     3  0.4860      0.710 0.016 0.000 0.752 0.096 0.072 0.064
#> GSM892375     2  0.2831      0.678 0.000 0.876 0.000 0.028 0.044 0.052
#> GSM892379     2  0.4485      0.645 0.000 0.724 0.000 0.012 0.180 0.084
#> GSM892385     2  0.4252      0.652 0.000 0.772 0.000 0.032 0.116 0.080
#> GSM892389     2  0.3992      0.681 0.000 0.788 0.000 0.020 0.088 0.104
#> GSM892341     3  0.4224      0.635 0.016 0.000 0.660 0.012 0.312 0.000
#> GSM892346     4  0.2936      0.786 0.080 0.000 0.024 0.868 0.004 0.024
#> GSM892350     4  0.2307      0.830 0.032 0.000 0.068 0.896 0.000 0.004
#> GSM892354     1  0.2263      0.888 0.900 0.000 0.000 0.004 0.036 0.060
#> GSM892356     1  0.3489      0.786 0.708 0.000 0.000 0.004 0.000 0.288
#> GSM892362     1  0.1194      0.891 0.956 0.000 0.000 0.004 0.008 0.032
#> GSM892366     3  0.0458      0.778 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM892370     3  0.4860      0.710 0.016 0.000 0.752 0.096 0.072 0.064
#> GSM892374     5  0.6125      1.000 0.000 0.312 0.000 0.000 0.348 0.340
#> GSM892378     2  0.5190     -0.167 0.000 0.460 0.000 0.000 0.452 0.088
#> GSM892382     2  0.1369      0.704 0.000 0.952 0.000 0.016 0.016 0.016
#> GSM892384     2  0.1237      0.703 0.000 0.956 0.000 0.020 0.004 0.020
#> GSM892388     2  0.5723     -0.219 0.000 0.468 0.016 0.008 0.080 0.428
#> GSM892343     3  0.5866      0.501 0.016 0.000 0.524 0.148 0.312 0.000
#> GSM892348     4  0.2897      0.815 0.048 0.000 0.048 0.876 0.004 0.024
#> GSM892352     4  0.6576      0.189 0.016 0.000 0.276 0.364 0.340 0.004
#> GSM892358     1  0.0146      0.897 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM892360     1  0.0146      0.897 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM892364     1  0.2101      0.871 0.892 0.000 0.000 0.004 0.004 0.100
#> GSM892368     3  0.0458      0.778 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM892372     3  0.1718      0.773 0.016 0.000 0.932 0.000 0.044 0.008
#> GSM892376     2  0.2769      0.680 0.000 0.880 0.000 0.032 0.036 0.052
#> GSM892380     2  0.3495      0.668 0.000 0.792 0.000 0.008 0.172 0.028
#> GSM892386     2  0.2231      0.699 0.000 0.908 0.000 0.028 0.016 0.048
#> GSM892390     2  0.3357      0.695 0.000 0.840 0.000 0.024 0.068 0.068

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

k = 2
k = 3
k = 4
k = 5
k = 6

consensus_heatmap(res, k = 2)

plot of chunk tab-SD-kmeans-consensus-heatmap-1

consensus_heatmap(res, k = 3)

plot of chunk tab-SD-kmeans-consensus-heatmap-2

consensus_heatmap(res, k = 4)

plot of chunk tab-SD-kmeans-consensus-heatmap-3

consensus_heatmap(res, k = 5)

plot of chunk tab-SD-kmeans-consensus-heatmap-4

consensus_heatmap(res, k = 6)

plot of chunk tab-SD-kmeans-consensus-heatmap-5

Heatmaps for the membership of samples in all partitions to see how consistent they are:

k = 2
k = 3
k = 4
k = 5
k = 6

membership_heatmap(res, k = 2)

plot of chunk tab-SD-kmeans-membership-heatmap-1

membership_heatmap(res, k = 3)

plot of chunk tab-SD-kmeans-membership-heatmap-2

membership_heatmap(res, k = 4)

plot of chunk tab-SD-kmeans-membership-heatmap-3

membership_heatmap(res, k = 5)

plot of chunk tab-SD-kmeans-membership-heatmap-4

membership_heatmap(res, k = 6)

plot of chunk tab-SD-kmeans-membership-heatmap-5

Signature heatmaps where rows are scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2)

plot of chunk tab-SD-kmeans-get-signatures-1

get_signatures(res, k = 3)

plot of chunk tab-SD-kmeans-get-signatures-2

get_signatures(res, k = 4)

plot of chunk tab-SD-kmeans-get-signatures-3

get_signatures(res, k = 5)

plot of chunk tab-SD-kmeans-get-signatures-4

get_signatures(res, k = 6)

plot of chunk tab-SD-kmeans-get-signatures-5

Signature heatmaps where rows are not scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-SD-kmeans-get-signatures-no-scale-1

get_signatures(res, k = 3, scale_rows = FALSE)

plot of chunk tab-SD-kmeans-get-signatures-no-scale-2

get_signatures(res, k = 4, scale_rows = FALSE)

plot of chunk tab-SD-kmeans-get-signatures-no-scale-3

get_signatures(res, k = 5, scale_rows = FALSE)

plot of chunk tab-SD-kmeans-get-signatures-no-scale-4

get_signatures(res, k = 6, scale_rows = FALSE)

plot of chunk tab-SD-kmeans-get-signatures-no-scale-5

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk SD-kmeans-signature_compare

# 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.

k = 2
k = 3
k = 4
k = 5
k = 6

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-SD-kmeans-dimension-reduction-1

dimension_reduction(res, k = 3, method = "UMAP")

plot of chunk tab-SD-kmeans-dimension-reduction-2

dimension_reduction(res, k = 4, method = "UMAP")

plot of chunk tab-SD-kmeans-dimension-reduction-3

dimension_reduction(res, k = 5, method = "UMAP")

plot of chunk tab-SD-kmeans-dimension-reduction-4

dimension_reduction(res, k = 6, method = "UMAP")

plot of chunk tab-SD-kmeans-dimension-reduction-5

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk SD-kmeans-collect-classes

test_to_known_factors(res)

#>            n tissue(p) disease.state(p) other(p) individual(p) k
#> SD:kmeans 50     1.000            0.934 2.67e-07      1.42e-03 2
#> SD:kmeans 49     0.870            0.944 1.68e-11      6.67e-05 3
#> SD:kmeans 46     1.000            0.987 8.58e-16      1.62e-06 4
#> SD:kmeans 45     1.000            0.614 2.70e-15      1.17e-07 5
#> SD:kmeans 46     0.998            0.586 7.36e-16      4.18e-08 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

SD:skmeans**

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 31632 rows and 50 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 5.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk SD-skmeans-collect-plots

The plots are:

The first row: a plot of the ECDF (empirical cumulative distribution function) curves of the consensus matrix for each k and the heatmap of predicted classes for each k.
The second row: heatmaps of the consensus matrix for each k.
The third row: heatmaps of the membership matrix for each k.
The fouth row: heatmaps of the signatures for each 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:

ECDF curves of the consensus matrix for each k;
1-PAC. The PAC score measures the proportion of the ambiguous subgrouping.
Mean silhouette score.
Concordance. The mean probability of fiting the consensus class ids in all partitions.
Area increased. Denote \(A_k\) as the area under the ECDF curve for current k, the area increased is defined as \(A_k - A_{k-1}\).
Rand index. The percent of pairs of samples that are both in a same cluster or both are not in a same cluster in the partition of k and k-1.
Jaccard index. The ratio of pairs of samples are both in a same cluster in the partition of k and k-1 and the pairs of samples are both in a same cluster in the partition k or k-1.

The detailed explanations of these statistics can be found in the cola vignette.

select_partition_number(res)

plot of chunk SD-skmeans-select-partition-number

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         0.4707 0.530   0.530
#> 3 3 0.950           0.905       0.965         0.4349 0.794   0.612
#> 4 4 1.000           0.985       0.993         0.1030 0.912   0.736
#> 5 5 0.976           0.954       0.970         0.0372 0.958   0.838
#> 6 6 0.962           0.901       0.926         0.0156 1.000   1.000

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

All \(k\) with Jaccard index larger than 0.95 are removed because increasing \(k\) does not provide enough extra information. If all \(k\) are removed, it is marked as no subgroup is detected.
For all \(k\) with 1-PAC score larger than 0.9, the maximal \(k\) is taken as the best \(k\), and other \(k\) are marked as optional \(k\).
If it does not fit the second rule. The \(k\) with the maximal vote of the highest 1-PAC score, highest mean silhouette, and highest concordance is taken as the best \(k\).

suggest_best_k(res)

#> [1] 5
#> attr(,"optional")
#> [1] 2 3 4

There is also optional best \(k\) = 2 3 4 that is worth to check.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

k = 2
k = 3
k = 4
k = 5
k = 6

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>           class entropy silhouette p1 p2
#> GSM892342     1       0          1  1  0
#> GSM892345     1       0          1  1  0
#> GSM892349     1       0          1  1  0
#> GSM892353     1       0          1  1  0
#> GSM892355     1       0          1  1  0
#> GSM892361     1       0          1  1  0
#> GSM892365     1       0          1  1  0
#> GSM892369     1       0          1  1  0
#> GSM892373     2       0          1  0  1
#> GSM892377     2       0          1  0  1
#> GSM892381     2       0          1  0  1
#> GSM892383     2       0          1  0  1
#> GSM892387     2       0          1  0  1
#> GSM892344     1       0          1  1  0
#> GSM892347     1       0          1  1  0
#> GSM892351     1       0          1  1  0
#> GSM892357     1       0          1  1  0
#> GSM892359     1       0          1  1  0
#> GSM892363     1       0          1  1  0
#> GSM892367     1       0          1  1  0
#> GSM892371     1       0          1  1  0
#> GSM892375     2       0          1  0  1
#> GSM892379     2       0          1  0  1
#> GSM892385     2       0          1  0  1
#> GSM892389     2       0          1  0  1
#> GSM892341     1       0          1  1  0
#> GSM892346     1       0          1  1  0
#> GSM892350     1       0          1  1  0
#> GSM892354     1       0          1  1  0
#> GSM892356     1       0          1  1  0
#> GSM892362     1       0          1  1  0
#> GSM892366     1       0          1  1  0
#> GSM892370     1       0          1  1  0
#> GSM892374     2       0          1  0  1
#> GSM892378     2       0          1  0  1
#> GSM892382     2       0          1  0  1
#> GSM892384     2       0          1  0  1
#> GSM892388     2       0          1  0  1
#> GSM892343     1       0          1  1  0
#> GSM892348     1       0          1  1  0
#> GSM892352     1       0          1  1  0
#> GSM892358     1       0          1  1  0
#> GSM892360     1       0          1  1  0
#> GSM892364     1       0          1  1  0
#> GSM892368     1       0          1  1  0
#> GSM892372     1       0          1  1  0
#> GSM892376     2       0          1  0  1
#> GSM892380     2       0          1  0  1
#> GSM892386     2       0          1  0  1
#> GSM892390     2       0          1  0  1

show/hide code output

cbind(get_classes(res, k = 3), get_membership(res, k = 3))

#>           class entropy silhouette    p1 p2    p3
#> GSM892342     3   0.000      0.911 0.000  0 1.000
#> GSM892345     3   0.628      0.186 0.460  0 0.540
#> GSM892349     3   0.000      0.911 0.000  0 1.000
#> GSM892353     1   0.000      0.965 1.000  0 0.000
#> GSM892355     1   0.000      0.965 1.000  0 0.000
#> GSM892361     1   0.000      0.965 1.000  0 0.000
#> GSM892365     3   0.000      0.911 0.000  0 1.000
#> GSM892369     3   0.000      0.911 0.000  0 1.000
#> GSM892373     2   0.000      1.000 0.000  1 0.000
#> GSM892377     2   0.000      1.000 0.000  1 0.000
#> GSM892381     2   0.000      1.000 0.000  1 0.000
#> GSM892383     2   0.000      1.000 0.000  1 0.000
#> GSM892387     2   0.000      1.000 0.000  1 0.000
#> GSM892344     3   0.000      0.911 0.000  0 1.000
#> GSM892347     3   0.628      0.186 0.460  0 0.540
#> GSM892351     3   0.000      0.911 0.000  0 1.000
#> GSM892357     1   0.000      0.965 1.000  0 0.000
#> GSM892359     1   0.000      0.965 1.000  0 0.000
#> GSM892363     1   0.000      0.965 1.000  0 0.000
#> GSM892367     3   0.000      0.911 0.000  0 1.000
#> GSM892371     3   0.000      0.911 0.000  0 1.000
#> GSM892375     2   0.000      1.000 0.000  1 0.000
#> GSM892379     2   0.000      1.000 0.000  1 0.000
#> GSM892385     2   0.000      1.000 0.000  1 0.000
#> GSM892389     2   0.000      1.000 0.000  1 0.000
#> GSM892341     3   0.000      0.911 0.000  0 1.000
#> GSM892346     1   0.440      0.751 0.812  0 0.188
#> GSM892350     3   0.628      0.186 0.460  0 0.540
#> GSM892354     1   0.000      0.965 1.000  0 0.000
#> GSM892356     1   0.000      0.965 1.000  0 0.000
#> GSM892362     1   0.000      0.965 1.000  0 0.000
#> GSM892366     3   0.000      0.911 0.000  0 1.000
#> GSM892370     3   0.000      0.911 0.000  0 1.000
#> GSM892374     2   0.000      1.000 0.000  1 0.000
#> GSM892378     2   0.000      1.000 0.000  1 0.000
#> GSM892382     2   0.000      1.000 0.000  1 0.000
#> GSM892384     2   0.000      1.000 0.000  1 0.000
#> GSM892388     2   0.000      1.000 0.000  1 0.000
#> GSM892343     3   0.000      0.911 0.000  0 1.000
#> GSM892348     1   0.460      0.726 0.796  0 0.204
#> GSM892352     3   0.000      0.911 0.000  0 1.000
#> GSM892358     1   0.000      0.965 1.000  0 0.000
#> GSM892360     1   0.000      0.965 1.000  0 0.000
#> GSM892364     1   0.000      0.965 1.000  0 0.000
#> GSM892368     3   0.000      0.911 0.000  0 1.000
#> GSM892372     3   0.000      0.911 0.000  0 1.000
#> GSM892376     2   0.000      1.000 0.000  1 0.000
#> GSM892380     2   0.000      1.000 0.000  1 0.000
#> GSM892386     2   0.000      1.000 0.000  1 0.000
#> GSM892390     2   0.000      1.000 0.000  1 0.000

show/hide code output

cbind(get_classes(res, k = 4), get_membership(res, k = 4))

#>           class entropy silhouette    p1 p2    p3    p4
#> GSM892342     3  0.0336      0.973 0.000  0 0.992 0.008
#> GSM892345     4  0.0000      0.987 0.000  0 0.000 1.000
#> GSM892349     4  0.0000      0.987 0.000  0 0.000 1.000
#> GSM892353     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892355     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892361     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892365     3  0.0000      0.975 0.000  0 1.000 0.000
#> GSM892369     3  0.0336      0.973 0.000  0 0.992 0.008
#> GSM892373     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892344     3  0.0336      0.973 0.000  0 0.992 0.008
#> GSM892347     4  0.0000      0.987 0.000  0 0.000 1.000
#> GSM892351     4  0.0000      0.987 0.000  0 0.000 1.000
#> GSM892357     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892359     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892363     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892367     3  0.0000      0.975 0.000  0 1.000 0.000
#> GSM892371     3  0.0336      0.973 0.000  0 0.992 0.008
#> GSM892375     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892341     3  0.0336      0.973 0.000  0 0.992 0.008
#> GSM892346     4  0.0336      0.982 0.008  0 0.000 0.992
#> GSM892350     4  0.0000      0.987 0.000  0 0.000 1.000
#> GSM892354     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892356     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892362     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892366     3  0.0000      0.975 0.000  0 1.000 0.000
#> GSM892370     3  0.0336      0.973 0.000  0 0.992 0.008
#> GSM892374     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892343     3  0.3873      0.711 0.000  0 0.772 0.228
#> GSM892348     4  0.0188      0.985 0.004  0 0.000 0.996
#> GSM892352     4  0.1940      0.918 0.000  0 0.076 0.924
#> GSM892358     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892360     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892364     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892368     3  0.0000      0.975 0.000  0 1.000 0.000
#> GSM892372     3  0.0000      0.975 0.000  0 1.000 0.000
#> GSM892376     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 5), get_membership(res, k = 5))

#>           class entropy silhouette    p1 p2    p3    p4    p5
#> GSM892342     5  0.0703      0.875 0.000  0 0.024 0.000 0.976
#> GSM892345     4  0.0162      0.994 0.000  0 0.004 0.996 0.000
#> GSM892349     5  0.4047      0.561 0.000  0 0.004 0.320 0.676
#> GSM892353     1  0.0162      0.997 0.996  0 0.000 0.000 0.004
#> GSM892355     1  0.0162      0.997 0.996  0 0.000 0.000 0.004
#> GSM892361     1  0.0000      0.999 1.000  0 0.000 0.000 0.000
#> GSM892365     3  0.3395      0.835 0.000  0 0.764 0.000 0.236
#> GSM892369     3  0.0000      0.870 0.000  0 1.000 0.000 0.000
#> GSM892373     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892344     5  0.0609      0.875 0.000  0 0.020 0.000 0.980
#> GSM892347     4  0.0162      0.994 0.000  0 0.000 0.996 0.004
#> GSM892351     4  0.0451      0.991 0.000  0 0.004 0.988 0.008
#> GSM892357     1  0.0000      0.999 1.000  0 0.000 0.000 0.000
#> GSM892359     1  0.0000      0.999 1.000  0 0.000 0.000 0.000
#> GSM892363     1  0.0000      0.999 1.000  0 0.000 0.000 0.000
#> GSM892367     3  0.1270      0.878 0.000  0 0.948 0.000 0.052
#> GSM892371     3  0.0000      0.870 0.000  0 1.000 0.000 0.000
#> GSM892375     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892341     5  0.0703      0.875 0.000  0 0.024 0.000 0.976
#> GSM892346     4  0.0162      0.993 0.000  0 0.004 0.996 0.000
#> GSM892350     4  0.0162      0.994 0.000  0 0.000 0.996 0.004
#> GSM892354     1  0.0000      0.999 1.000  0 0.000 0.000 0.000
#> GSM892356     1  0.0162      0.997 0.996  0 0.000 0.000 0.004
#> GSM892362     1  0.0000      0.999 1.000  0 0.000 0.000 0.000
#> GSM892366     3  0.3424      0.831 0.000  0 0.760 0.000 0.240
#> GSM892370     3  0.0000      0.870 0.000  0 1.000 0.000 0.000
#> GSM892374     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892343     5  0.1774      0.873 0.000  0 0.016 0.052 0.932
#> GSM892348     4  0.0162      0.993 0.000  0 0.004 0.996 0.000
#> GSM892352     5  0.2338      0.839 0.000  0 0.004 0.112 0.884
#> GSM892358     1  0.0000      0.999 1.000  0 0.000 0.000 0.000
#> GSM892360     1  0.0000      0.999 1.000  0 0.000 0.000 0.000
#> GSM892364     1  0.0000      0.999 1.000  0 0.000 0.000 0.000
#> GSM892368     3  0.3274      0.845 0.000  0 0.780 0.000 0.220
#> GSM892372     3  0.2605      0.872 0.000  0 0.852 0.000 0.148
#> GSM892376     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 6), get_membership(res, k = 6))

#>           class entropy silhouette    p1    p2    p3    p4    p5 p6
#> GSM892342     5  0.1910      0.787 0.000 0.000 0.108 0.000 0.892 NA
#> GSM892345     4  0.0820      0.949 0.000 0.000 0.000 0.972 0.016 NA
#> GSM892349     5  0.5983      0.248 0.000 0.000 0.004 0.340 0.452 NA
#> GSM892353     1  0.1814      0.930 0.900 0.000 0.000 0.000 0.000 NA
#> GSM892355     1  0.1501      0.947 0.924 0.000 0.000 0.000 0.000 NA
#> GSM892361     1  0.0260      0.979 0.992 0.000 0.000 0.000 0.000 NA
#> GSM892365     3  0.1049      0.777 0.000 0.000 0.960 0.000 0.032 NA
#> GSM892369     3  0.3828      0.696 0.000 0.000 0.560 0.000 0.000 NA
#> GSM892373     2  0.0865      0.974 0.000 0.964 0.000 0.000 0.000 NA
#> GSM892377     2  0.0713      0.978 0.000 0.972 0.000 0.000 0.000 NA
#> GSM892381     2  0.0146      0.990 0.000 0.996 0.000 0.000 0.000 NA
#> GSM892383     2  0.0000      0.990 0.000 1.000 0.000 0.000 0.000 NA
#> GSM892387     2  0.0146      0.990 0.000 0.996 0.000 0.000 0.000 NA
#> GSM892344     5  0.1806      0.790 0.000 0.000 0.088 0.000 0.908 NA
#> GSM892347     4  0.0363      0.949 0.000 0.000 0.000 0.988 0.000 NA
#> GSM892351     4  0.2629      0.882 0.000 0.000 0.000 0.868 0.040 NA
#> GSM892357     1  0.0260      0.979 0.992 0.000 0.000 0.000 0.000 NA
#> GSM892359     1  0.0146      0.979 0.996 0.000 0.000 0.000 0.000 NA
#> GSM892363     1  0.0260      0.980 0.992 0.000 0.000 0.000 0.000 NA
#> GSM892367     3  0.2302      0.781 0.000 0.000 0.872 0.000 0.008 NA
#> GSM892371     3  0.3810      0.701 0.000 0.000 0.572 0.000 0.000 NA
#> GSM892375     2  0.0260      0.990 0.000 0.992 0.000 0.000 0.000 NA
#> GSM892379     2  0.0363      0.988 0.000 0.988 0.000 0.000 0.000 NA
#> GSM892385     2  0.0000      0.990 0.000 1.000 0.000 0.000 0.000 NA
#> GSM892389     2  0.0260      0.990 0.000 0.992 0.000 0.000 0.000 NA
#> GSM892341     5  0.1910      0.785 0.000 0.000 0.108 0.000 0.892 NA
#> GSM892346     4  0.0993      0.939 0.000 0.000 0.000 0.964 0.012 NA
#> GSM892350     4  0.1265      0.940 0.000 0.000 0.000 0.948 0.008 NA
#> GSM892354     1  0.0260      0.979 0.992 0.000 0.000 0.000 0.000 NA
#> GSM892356     1  0.1075      0.964 0.952 0.000 0.000 0.000 0.000 NA
#> GSM892362     1  0.0146      0.980 0.996 0.000 0.000 0.000 0.000 NA
#> GSM892366     3  0.0935      0.779 0.000 0.000 0.964 0.000 0.032 NA
#> GSM892370     3  0.3828      0.696 0.000 0.000 0.560 0.000 0.000 NA
#> GSM892374     2  0.0865      0.974 0.000 0.964 0.000 0.000 0.000 NA
#> GSM892378     2  0.0713      0.978 0.000 0.972 0.000 0.000 0.000 NA
#> GSM892382     2  0.0146      0.990 0.000 0.996 0.000 0.000 0.000 NA
#> GSM892384     2  0.0146      0.990 0.000 0.996 0.000 0.000 0.000 NA
#> GSM892388     2  0.0146      0.990 0.000 0.996 0.000 0.000 0.000 NA
#> GSM892343     5  0.3694      0.755 0.000 0.000 0.044 0.032 0.812 NA
#> GSM892348     4  0.0891      0.940 0.000 0.000 0.000 0.968 0.008 NA
#> GSM892352     5  0.4534      0.654 0.000 0.000 0.008 0.052 0.672 NA
#> GSM892358     1  0.0146      0.979 0.996 0.000 0.000 0.000 0.000 NA
#> GSM892360     1  0.0146      0.979 0.996 0.000 0.000 0.000 0.000 NA
#> GSM892364     1  0.0458      0.978 0.984 0.000 0.000 0.000 0.000 NA
#> GSM892368     3  0.0935      0.781 0.000 0.000 0.964 0.000 0.032 NA
#> GSM892372     3  0.0914      0.787 0.000 0.000 0.968 0.000 0.016 NA
#> GSM892376     2  0.0260      0.990 0.000 0.992 0.000 0.000 0.000 NA
#> GSM892380     2  0.0260      0.990 0.000 0.992 0.000 0.000 0.000 NA
#> GSM892386     2  0.0260      0.990 0.000 0.992 0.000 0.000 0.000 NA
#> GSM892390     2  0.0146      0.990 0.000 0.996 0.000 0.000 0.000 NA

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

k = 2
k = 3
k = 4
k = 5
k = 6

consensus_heatmap(res, k = 2)

plot of chunk tab-SD-skmeans-consensus-heatmap-1

consensus_heatmap(res, k = 3)

plot of chunk tab-SD-skmeans-consensus-heatmap-2

consensus_heatmap(res, k = 4)

plot of chunk tab-SD-skmeans-consensus-heatmap-3

consensus_heatmap(res, k = 5)

plot of chunk tab-SD-skmeans-consensus-heatmap-4

consensus_heatmap(res, k = 6)

plot of chunk tab-SD-skmeans-consensus-heatmap-5

Heatmaps for the membership of samples in all partitions to see how consistent they are:

k = 2
k = 3
k = 4
k = 5
k = 6

membership_heatmap(res, k = 2)

plot of chunk tab-SD-skmeans-membership-heatmap-1

membership_heatmap(res, k = 3)

plot of chunk tab-SD-skmeans-membership-heatmap-2

membership_heatmap(res, k = 4)

plot of chunk tab-SD-skmeans-membership-heatmap-3

membership_heatmap(res, k = 5)

plot of chunk tab-SD-skmeans-membership-heatmap-4

membership_heatmap(res, k = 6)

plot of chunk tab-SD-skmeans-membership-heatmap-5

Signature heatmaps where rows are scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2)

plot of chunk tab-SD-skmeans-get-signatures-1

get_signatures(res, k = 3)

plot of chunk tab-SD-skmeans-get-signatures-2

get_signatures(res, k = 4)

plot of chunk tab-SD-skmeans-get-signatures-3

get_signatures(res, k = 5)

plot of chunk tab-SD-skmeans-get-signatures-4

get_signatures(res, k = 6)

plot of chunk tab-SD-skmeans-get-signatures-5

Signature heatmaps where rows are not scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-SD-skmeans-get-signatures-no-scale-1

get_signatures(res, k = 3, scale_rows = FALSE)

plot of chunk tab-SD-skmeans-get-signatures-no-scale-2

get_signatures(res, k = 4, scale_rows = FALSE)

plot of chunk tab-SD-skmeans-get-signatures-no-scale-3

get_signatures(res, k = 5, scale_rows = FALSE)

plot of chunk tab-SD-skmeans-get-signatures-no-scale-4

get_signatures(res, k = 6, scale_rows = FALSE)

plot of chunk tab-SD-skmeans-get-signatures-no-scale-5

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk SD-skmeans-signature_compare

# 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.

k = 2
k = 3
k = 4
k = 5
k = 6

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-SD-skmeans-dimension-reduction-1

dimension_reduction(res, k = 3, method = "UMAP")

plot of chunk tab-SD-skmeans-dimension-reduction-2

dimension_reduction(res, k = 4, method = "UMAP")

plot of chunk tab-SD-skmeans-dimension-reduction-3

dimension_reduction(res, k = 5, method = "UMAP")

plot of chunk tab-SD-skmeans-dimension-reduction-4

dimension_reduction(res, k = 6, method = "UMAP")

plot of chunk tab-SD-skmeans-dimension-reduction-5

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk SD-skmeans-collect-classes

test_to_known_factors(res)

#>             n tissue(p) disease.state(p) other(p) individual(p) k
#> SD:skmeans 50     1.000            0.934 2.67e-07      1.42e-03 2
#> SD:skmeans 47     0.847            0.875 1.47e-11      8.15e-05 3
#> SD:skmeans 50     1.000            0.986 6.71e-18      2.02e-07 4
#> SD:skmeans 50     1.000            0.998 3.06e-20      2.01e-07 5
#> SD:skmeans 49     0.996            0.982 2.33e-20      7.98e-08 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

SD:pam**

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 31632 rows and 50 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 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)

plot of chunk SD-pam-collect-plots

The plots are:

The first row: a plot of the ECDF (empirical cumulative distribution function) curves of the consensus matrix for each k and the heatmap of predicted classes for each k.
The second row: heatmaps of the consensus matrix for each k.
The third row: heatmaps of the membership matrix for each k.
The fouth row: heatmaps of the signatures for each 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:

ECDF curves of the consensus matrix for each k;
1-PAC. The PAC score measures the proportion of the ambiguous subgrouping.
Mean silhouette score.
Concordance. The mean probability of fiting the consensus class ids in all partitions.
Area increased. Denote \(A_k\) as the area under the ECDF curve for current k, the area increased is defined as \(A_k - A_{k-1}\).
Rand index. The percent of pairs of samples that are both in a same cluster or both are not in a same cluster in the partition of k and k-1.
Jaccard index. The ratio of pairs of samples are both in a same cluster in the partition of k and k-1 and the pairs of samples are both in a same cluster in the partition k or k-1.

The detailed explanations of these statistics can be found in the cola vignette.

select_partition_number(res)

plot of chunk SD-pam-select-partition-number

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         0.4707 0.530   0.530
#> 3 3 0.956           0.969       0.985         0.4258 0.798   0.619
#> 4 4 1.000           0.987       0.994         0.1135 0.912   0.737
#> 5 5 0.968           0.960       0.971         0.0348 0.958   0.840
#> 6 6 1.000           0.970       0.987         0.0173 0.988   0.946

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

All \(k\) with Jaccard index larger than 0.95 are removed because increasing \(k\) does not provide enough extra information. If all \(k\) are removed, it is marked as no subgroup is detected.
For all \(k\) with 1-PAC score larger than 0.9, the maximal \(k\) is taken as the best \(k\), and other \(k\) are marked as optional \(k\).
If it does not fit the second rule. The \(k\) with the maximal vote of the highest 1-PAC score, highest mean silhouette, and highest concordance is taken as the best \(k\).

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.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

k = 2
k = 3
k = 4
k = 5
k = 6

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>           class entropy silhouette p1 p2
#> GSM892342     1       0          1  1  0
#> GSM892345     1       0          1  1  0
#> GSM892349     1       0          1  1  0
#> GSM892353     1       0          1  1  0
#> GSM892355     1       0          1  1  0
#> GSM892361     1       0          1  1  0
#> GSM892365     1       0          1  1  0
#> GSM892369     1       0          1  1  0
#> GSM892373     2       0          1  0  1
#> GSM892377     2       0          1  0  1
#> GSM892381     2       0          1  0  1
#> GSM892383     2       0          1  0  1
#> GSM892387     2       0          1  0  1
#> GSM892344     1       0          1  1  0
#> GSM892347     1       0          1  1  0
#> GSM892351     1       0          1  1  0
#> GSM892357     1       0          1  1  0
#> GSM892359     1       0          1  1  0
#> GSM892363     1       0          1  1  0
#> GSM892367     1       0          1  1  0
#> GSM892371     1       0          1  1  0
#> GSM892375     2       0          1  0  1
#> GSM892379     2       0          1  0  1
#> GSM892385     2       0          1  0  1
#> GSM892389     2       0          1  0  1
#> GSM892341     1       0          1  1  0
#> GSM892346     1       0          1  1  0
#> GSM892350     1       0          1  1  0
#> GSM892354     1       0          1  1  0
#> GSM892356     1       0          1  1  0
#> GSM892362     1       0          1  1  0
#> GSM892366     1       0          1  1  0
#> GSM892370     1       0          1  1  0
#> GSM892374     2       0          1  0  1
#> GSM892378     2       0          1  0  1
#> GSM892382     2       0          1  0  1
#> GSM892384     2       0          1  0  1
#> GSM892388     2       0          1  0  1
#> GSM892343     1       0          1  1  0
#> GSM892348     1       0          1  1  0
#> GSM892352     1       0          1  1  0
#> GSM892358     1       0          1  1  0
#> GSM892360     1       0          1  1  0
#> GSM892364     1       0          1  1  0
#> GSM892368     1       0          1  1  0
#> GSM892372     1       0          1  1  0
#> GSM892376     2       0          1  0  1
#> GSM892380     2       0          1  0  1
#> GSM892386     2       0          1  0  1
#> GSM892390     2       0          1  0  1

show/hide code output

cbind(get_classes(res, k = 3), get_membership(res, k = 3))

#>           class entropy silhouette    p1 p2    p3
#> GSM892342     3  0.0000      0.974 0.000  0 1.000
#> GSM892345     3  0.3116      0.898 0.108  0 0.892
#> GSM892349     3  0.0000      0.974 0.000  0 1.000
#> GSM892353     1  0.0000      0.975 1.000  0 0.000
#> GSM892355     1  0.0000      0.975 1.000  0 0.000
#> GSM892361     1  0.0000      0.975 1.000  0 0.000
#> GSM892365     3  0.0000      0.974 0.000  0 1.000
#> GSM892369     3  0.0000      0.974 0.000  0 1.000
#> GSM892373     2  0.0000      1.000 0.000  1 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000
#> GSM892344     3  0.0000      0.974 0.000  0 1.000
#> GSM892347     3  0.2448      0.926 0.076  0 0.924
#> GSM892351     3  0.1163      0.960 0.028  0 0.972
#> GSM892357     1  0.0000      0.975 1.000  0 0.000
#> GSM892359     1  0.0000      0.975 1.000  0 0.000
#> GSM892363     1  0.0000      0.975 1.000  0 0.000
#> GSM892367     3  0.0000      0.974 0.000  0 1.000
#> GSM892371     3  0.0000      0.974 0.000  0 1.000
#> GSM892375     2  0.0000      1.000 0.000  1 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000
#> GSM892341     3  0.0000      0.974 0.000  0 1.000
#> GSM892346     1  0.5397      0.586 0.720  0 0.280
#> GSM892350     3  0.3116      0.898 0.108  0 0.892
#> GSM892354     1  0.0000      0.975 1.000  0 0.000
#> GSM892356     1  0.0000      0.975 1.000  0 0.000
#> GSM892362     1  0.0000      0.975 1.000  0 0.000
#> GSM892366     3  0.0000      0.974 0.000  0 1.000
#> GSM892370     3  0.0000      0.974 0.000  0 1.000
#> GSM892374     2  0.0000      1.000 0.000  1 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000
#> GSM892343     3  0.0747      0.966 0.016  0 0.984
#> GSM892348     3  0.3412      0.881 0.124  0 0.876
#> GSM892352     3  0.0000      0.974 0.000  0 1.000
#> GSM892358     1  0.0000      0.975 1.000  0 0.000
#> GSM892360     1  0.0000      0.975 1.000  0 0.000
#> GSM892364     1  0.0237      0.972 0.996  0 0.004
#> GSM892368     3  0.0000      0.974 0.000  0 1.000
#> GSM892372     3  0.0000      0.974 0.000  0 1.000
#> GSM892376     2  0.0000      1.000 0.000  1 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000

show/hide code output

cbind(get_classes(res, k = 4), get_membership(res, k = 4))

#>           class entropy silhouette    p1 p2    p3    p4
#> GSM892342     3  0.0000      0.970 0.000  0 1.000 0.000
#> GSM892345     4  0.0000      0.998 0.000  0 0.000 1.000
#> GSM892349     4  0.0000      0.998 0.000  0 0.000 1.000
#> GSM892353     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892355     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892361     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892365     3  0.0000      0.970 0.000  0 1.000 0.000
#> GSM892369     3  0.0000      0.970 0.000  0 1.000 0.000
#> GSM892373     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892344     3  0.3528      0.767 0.000  0 0.808 0.192
#> GSM892347     4  0.0000      0.998 0.000  0 0.000 1.000
#> GSM892351     4  0.0000      0.998 0.000  0 0.000 1.000
#> GSM892357     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892359     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892363     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892367     3  0.0000      0.970 0.000  0 1.000 0.000
#> GSM892371     3  0.2281      0.888 0.000  0 0.904 0.096
#> GSM892375     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892341     3  0.0000      0.970 0.000  0 1.000 0.000
#> GSM892346     4  0.0188      0.995 0.004  0 0.000 0.996
#> GSM892350     4  0.0000      0.998 0.000  0 0.000 1.000
#> GSM892354     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892356     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892362     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892366     3  0.0000      0.970 0.000  0 1.000 0.000
#> GSM892370     3  0.0000      0.970 0.000  0 1.000 0.000
#> GSM892374     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892343     4  0.0000      0.998 0.000  0 0.000 1.000
#> GSM892348     4  0.0000      0.998 0.000  0 0.000 1.000
#> GSM892352     4  0.0336      0.992 0.000  0 0.008 0.992
#> GSM892358     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892360     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892364     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892368     3  0.0000      0.970 0.000  0 1.000 0.000
#> GSM892372     3  0.0000      0.970 0.000  0 1.000 0.000
#> GSM892376     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 5), get_membership(res, k = 5))

#>           class entropy silhouette    p1 p2    p3    p4    p5
#> GSM892342     5  0.0000      0.849 0.000  0 0.000 0.000 1.000
#> GSM892345     4  0.0000      1.000 0.000  0 0.000 1.000 0.000
#> GSM892349     5  0.4060      0.561 0.000  0 0.000 0.360 0.640
#> GSM892353     1  0.2127      0.874 0.892  0 0.000 0.000 0.108
#> GSM892355     1  0.0000      0.990 1.000  0 0.000 0.000 0.000
#> GSM892361     1  0.0000      0.990 1.000  0 0.000 0.000 0.000
#> GSM892365     3  0.2471      0.936 0.000  0 0.864 0.000 0.136
#> GSM892369     3  0.0000      0.913 0.000  0 1.000 0.000 0.000
#> GSM892373     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892344     5  0.1121      0.862 0.000  0 0.000 0.044 0.956
#> GSM892347     4  0.0000      1.000 0.000  0 0.000 1.000 0.000
#> GSM892351     4  0.0000      1.000 0.000  0 0.000 1.000 0.000
#> GSM892357     1  0.0000      0.990 1.000  0 0.000 0.000 0.000
#> GSM892359     1  0.0000      0.990 1.000  0 0.000 0.000 0.000
#> GSM892363     1  0.0000      0.990 1.000  0 0.000 0.000 0.000
#> GSM892367     3  0.1792      0.934 0.000  0 0.916 0.000 0.084
#> GSM892371     3  0.0771      0.902 0.000  0 0.976 0.020 0.004
#> GSM892375     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892341     5  0.0000      0.849 0.000  0 0.000 0.000 1.000
#> GSM892346     4  0.0000      1.000 0.000  0 0.000 1.000 0.000
#> GSM892350     4  0.0000      1.000 0.000  0 0.000 1.000 0.000
#> GSM892354     1  0.0000      0.990 1.000  0 0.000 0.000 0.000
#> GSM892356     1  0.0000      0.990 1.000  0 0.000 0.000 0.000
#> GSM892362     1  0.0000      0.990 1.000  0 0.000 0.000 0.000
#> GSM892366     3  0.2471      0.936 0.000  0 0.864 0.000 0.136
#> GSM892370     3  0.0000      0.913 0.000  0 1.000 0.000 0.000
#> GSM892374     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892343     5  0.2377      0.848 0.000  0 0.000 0.128 0.872
#> GSM892348     4  0.0000      1.000 0.000  0 0.000 1.000 0.000
#> GSM892352     5  0.2605      0.838 0.000  0 0.000 0.148 0.852
#> GSM892358     1  0.0000      0.990 1.000  0 0.000 0.000 0.000
#> GSM892360     1  0.0000      0.990 1.000  0 0.000 0.000 0.000
#> GSM892364     1  0.0000      0.990 1.000  0 0.000 0.000 0.000
#> GSM892368     3  0.2471      0.936 0.000  0 0.864 0.000 0.136
#> GSM892372     3  0.2471      0.936 0.000  0 0.864 0.000 0.136
#> GSM892376     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 6), get_membership(res, k = 6))

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> GSM892342     5  0.0000      0.927 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM892345     4  0.0000      1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM892349     5  0.3330      0.616 0.000 0.000 0.000 0.284 0.716 0.000
#> GSM892353     1  0.1910      0.872 0.892 0.000 0.000 0.000 0.108 0.000
#> GSM892355     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892361     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892365     3  0.0000      0.951 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM892369     6  0.0260      1.000 0.000 0.000 0.008 0.000 0.000 0.992
#> GSM892373     2  0.0260      0.994 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM892377     2  0.0260      0.994 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM892381     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892383     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892387     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892344     5  0.0000      0.927 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM892347     4  0.0000      1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM892351     4  0.0000      1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM892357     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892359     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892363     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892367     3  0.2697      0.766 0.000 0.000 0.812 0.000 0.000 0.188
#> GSM892371     6  0.0260      1.000 0.000 0.000 0.008 0.000 0.000 0.992
#> GSM892375     2  0.0146      0.996 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM892379     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892385     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892389     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892341     5  0.0000      0.927 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM892346     4  0.0000      1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM892350     4  0.0000      1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM892354     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892356     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892362     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892366     3  0.0000      0.951 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM892370     6  0.0260      1.000 0.000 0.000 0.008 0.000 0.000 0.992
#> GSM892374     2  0.0260      0.994 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM892378     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892382     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892384     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892388     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892343     5  0.0000      0.927 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM892348     4  0.0000      1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM892352     5  0.0713      0.912 0.000 0.000 0.000 0.028 0.972 0.000
#> GSM892358     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892360     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892364     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892368     3  0.0000      0.951 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM892372     3  0.0000      0.951 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM892376     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892380     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892386     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892390     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

k = 2
k = 3
k = 4
k = 5
k = 6

consensus_heatmap(res, k = 2)

plot of chunk tab-SD-pam-consensus-heatmap-1

consensus_heatmap(res, k = 3)

plot of chunk tab-SD-pam-consensus-heatmap-2

consensus_heatmap(res, k = 4)

plot of chunk tab-SD-pam-consensus-heatmap-3

consensus_heatmap(res, k = 5)

plot of chunk tab-SD-pam-consensus-heatmap-4

consensus_heatmap(res, k = 6)

plot of chunk tab-SD-pam-consensus-heatmap-5

Heatmaps for the membership of samples in all partitions to see how consistent they are:

k = 2
k = 3
k = 4
k = 5
k = 6

membership_heatmap(res, k = 2)

plot of chunk tab-SD-pam-membership-heatmap-1

membership_heatmap(res, k = 3)

plot of chunk tab-SD-pam-membership-heatmap-2

membership_heatmap(res, k = 4)

plot of chunk tab-SD-pam-membership-heatmap-3

membership_heatmap(res, k = 5)

plot of chunk tab-SD-pam-membership-heatmap-4

membership_heatmap(res, k = 6)

plot of chunk tab-SD-pam-membership-heatmap-5

Signature heatmaps where rows are scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2)

plot of chunk tab-SD-pam-get-signatures-1

get_signatures(res, k = 3)

plot of chunk tab-SD-pam-get-signatures-2

get_signatures(res, k = 4)

plot of chunk tab-SD-pam-get-signatures-3

get_signatures(res, k = 5)

plot of chunk tab-SD-pam-get-signatures-4

get_signatures(res, k = 6)

plot of chunk tab-SD-pam-get-signatures-5

Signature heatmaps where rows are not scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-SD-pam-get-signatures-no-scale-1

get_signatures(res, k = 3, scale_rows = FALSE)

plot of chunk tab-SD-pam-get-signatures-no-scale-2

get_signatures(res, k = 4, scale_rows = FALSE)

plot of chunk tab-SD-pam-get-signatures-no-scale-3

get_signatures(res, k = 5, scale_rows = FALSE)

plot of chunk tab-SD-pam-get-signatures-no-scale-4

get_signatures(res, k = 6, scale_rows = FALSE)

plot of chunk tab-SD-pam-get-signatures-no-scale-5

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk SD-pam-signature_compare

# 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.

k = 2
k = 3
k = 4
k = 5
k = 6

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-SD-pam-dimension-reduction-1

dimension_reduction(res, k = 3, method = "UMAP")

plot of chunk tab-SD-pam-dimension-reduction-2

dimension_reduction(res, k = 4, method = "UMAP")

plot of chunk tab-SD-pam-dimension-reduction-3

dimension_reduction(res, k = 5, method = "UMAP")

plot of chunk tab-SD-pam-dimension-reduction-4

dimension_reduction(res, k = 6, method = "UMAP")

plot of chunk tab-SD-pam-dimension-reduction-5

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk SD-pam-collect-classes

test_to_known_factors(res)

#>         n tissue(p) disease.state(p) other(p) individual(p) k
#> SD:pam 50     1.000            0.934 2.67e-07      1.42e-03 2
#> SD:pam 50     0.937            0.873 9.23e-12      3.89e-05 3
#> SD:pam 50     0.977            0.951 1.45e-16      7.83e-07 4
#> SD:pam 50     1.000            0.998 3.06e-20      2.01e-07 5
#> SD:pam 50     0.991            0.984 4.62e-22      7.12e-08 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

SD:mclust**

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 31632 rows and 50 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 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)

plot of chunk SD-mclust-collect-plots

The plots are:

The first row: a plot of the ECDF (empirical cumulative distribution function) curves of the consensus matrix for each k and the heatmap of predicted classes for each k.
The second row: heatmaps of the consensus matrix for each k.
The third row: heatmaps of the membership matrix for each k.
The fouth row: heatmaps of the signatures for each 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:

ECDF curves of the consensus matrix for each k;
1-PAC. The PAC score measures the proportion of the ambiguous subgrouping.
Mean silhouette score.
Concordance. The mean probability of fiting the consensus class ids in all partitions.
Area increased. Denote \(A_k\) as the area under the ECDF curve for current k, the area increased is defined as \(A_k - A_{k-1}\).
Rand index. The percent of pairs of samples that are both in a same cluster or both are not in a same cluster in the partition of k and k-1.
Jaccard index. The ratio of pairs of samples are both in a same cluster in the partition of k and k-1 and the pairs of samples are both in a same cluster in the partition k or k-1.

The detailed explanations of these statistics can be found in the cola vignette.

select_partition_number(res)

plot of chunk SD-mclust-select-partition-number

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         0.4707 0.530   0.530
#> 3 3 1.000           1.000       1.000         0.4158 0.804   0.630
#> 4 4 0.971           0.919       0.967         0.1192 0.919   0.758
#> 5 5 1.000           0.992       0.996         0.0377 0.958   0.840
#> 6 6 0.980           0.927       0.969         0.0279 0.978   0.903

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

All \(k\) with Jaccard index larger than 0.95 are removed because increasing \(k\) does not provide enough extra information. If all \(k\) are removed, it is marked as no subgroup is detected.
For all \(k\) with 1-PAC score larger than 0.9, the maximal \(k\) is taken as the best \(k\), and other \(k\) are marked as optional \(k\).
If it does not fit the second rule. The \(k\) with the maximal vote of the highest 1-PAC score, highest mean silhouette, and highest concordance is taken as the best \(k\).

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.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

k = 2
k = 3
k = 4
k = 5
k = 6

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>           class entropy silhouette p1 p2
#> GSM892342     1       0          1  1  0
#> GSM892345     1       0          1  1  0
#> GSM892349     1       0          1  1  0
#> GSM892353     1       0          1  1  0
#> GSM892355     1       0          1  1  0
#> GSM892361     1       0          1  1  0
#> GSM892365     1       0          1  1  0
#> GSM892369     1       0          1  1  0
#> GSM892373     2       0          1  0  1
#> GSM892377     2       0          1  0  1
#> GSM892381     2       0          1  0  1
#> GSM892383     2       0          1  0  1
#> GSM892387     2       0          1  0  1
#> GSM892344     1       0          1  1  0
#> GSM892347     1       0          1  1  0
#> GSM892351     1       0          1  1  0
#> GSM892357     1       0          1  1  0
#> GSM892359     1       0          1  1  0
#> GSM892363     1       0          1  1  0
#> GSM892367     1       0          1  1  0
#> GSM892371     1       0          1  1  0
#> GSM892375     2       0          1  0  1
#> GSM892379     2       0          1  0  1
#> GSM892385     2       0          1  0  1
#> GSM892389     2       0          1  0  1
#> GSM892341     1       0          1  1  0
#> GSM892346     1       0          1  1  0
#> GSM892350     1       0          1  1  0
#> GSM892354     1       0          1  1  0
#> GSM892356     1       0          1  1  0
#> GSM892362     1       0          1  1  0
#> GSM892366     1       0          1  1  0
#> GSM892370     1       0          1  1  0
#> GSM892374     2       0          1  0  1
#> GSM892378     2       0          1  0  1
#> GSM892382     2       0          1  0  1
#> GSM892384     2       0          1  0  1
#> GSM892388     2       0          1  0  1
#> GSM892343     1       0          1  1  0
#> GSM892348     1       0          1  1  0
#> GSM892352     1       0          1  1  0
#> GSM892358     1       0          1  1  0
#> GSM892360     1       0          1  1  0
#> GSM892364     1       0          1  1  0
#> GSM892368     1       0          1  1  0
#> GSM892372     1       0          1  1  0
#> GSM892376     2       0          1  0  1
#> GSM892380     2       0          1  0  1
#> GSM892386     2       0          1  0  1
#> GSM892390     2       0          1  0  1

show/hide code output

cbind(get_classes(res, k = 3), get_membership(res, k = 3))

#>           class entropy silhouette p1 p2 p3
#> GSM892342     3       0          1  0  0  1
#> GSM892345     3       0          1  0  0  1
#> GSM892349     3       0          1  0  0  1
#> GSM892353     1       0          1  1  0  0
#> GSM892355     1       0          1  1  0  0
#> GSM892361     1       0          1  1  0  0
#> GSM892365     3       0          1  0  0  1
#> GSM892369     3       0          1  0  0  1
#> GSM892373     2       0          1  0  1  0
#> GSM892377     2       0          1  0  1  0
#> GSM892381     2       0          1  0  1  0
#> GSM892383     2       0          1  0  1  0
#> GSM892387     2       0          1  0  1  0
#> GSM892344     3       0          1  0  0  1
#> GSM892347     3       0          1  0  0  1
#> GSM892351     3       0          1  0  0  1
#> GSM892357     1       0          1  1  0  0
#> GSM892359     1       0          1  1  0  0
#> GSM892363     1       0          1  1  0  0
#> GSM892367     3       0          1  0  0  1
#> GSM892371     3       0          1  0  0  1
#> GSM892375     2       0          1  0  1  0
#> GSM892379     2       0          1  0  1  0
#> GSM892385     2       0          1  0  1  0
#> GSM892389     2       0          1  0  1  0
#> GSM892341     3       0          1  0  0  1
#> GSM892346     3       0          1  0  0  1
#> GSM892350     3       0          1  0  0  1
#> GSM892354     1       0          1  1  0  0
#> GSM892356     1       0          1  1  0  0
#> GSM892362     1       0          1  1  0  0
#> GSM892366     3       0          1  0  0  1
#> GSM892370     3       0          1  0  0  1
#> GSM892374     2       0          1  0  1  0
#> GSM892378     2       0          1  0  1  0
#> GSM892382     2       0          1  0  1  0
#> GSM892384     2       0          1  0  1  0
#> GSM892388     2       0          1  0  1  0
#> GSM892343     3       0          1  0  0  1
#> GSM892348     3       0          1  0  0  1
#> GSM892352     3       0          1  0  0  1
#> GSM892358     1       0          1  1  0  0
#> GSM892360     1       0          1  1  0  0
#> GSM892364     1       0          1  1  0  0
#> GSM892368     3       0          1  0  0  1
#> GSM892372     3       0          1  0  0  1
#> GSM892376     2       0          1  0  1  0
#> GSM892380     2       0          1  0  1  0
#> GSM892386     2       0          1  0  1  0
#> GSM892390     2       0          1  0  1  0

show/hide code output

cbind(get_classes(res, k = 4), get_membership(res, k = 4))

#>           class entropy silhouette p1 p2    p3    p4
#> GSM892342     3  0.0000     0.8782  0  0 1.000 0.000
#> GSM892345     4  0.0000     0.9167  0  0 0.000 1.000
#> GSM892349     4  0.0592     0.9079  0  0 0.016 0.984
#> GSM892353     1  0.0000     1.0000  1  0 0.000 0.000
#> GSM892355     1  0.0000     1.0000  1  0 0.000 0.000
#> GSM892361     1  0.0000     1.0000  1  0 0.000 0.000
#> GSM892365     3  0.0000     0.8782  0  0 1.000 0.000
#> GSM892369     3  0.4564     0.4888  0  0 0.672 0.328
#> GSM892373     2  0.0000     1.0000  0  1 0.000 0.000
#> GSM892377     2  0.0000     1.0000  0  1 0.000 0.000
#> GSM892381     2  0.0000     1.0000  0  1 0.000 0.000
#> GSM892383     2  0.0000     1.0000  0  1 0.000 0.000
#> GSM892387     2  0.0000     1.0000  0  1 0.000 0.000
#> GSM892344     3  0.0469     0.8769  0  0 0.988 0.012
#> GSM892347     4  0.0000     0.9167  0  0 0.000 1.000
#> GSM892351     4  0.0000     0.9167  0  0 0.000 1.000
#> GSM892357     1  0.0000     1.0000  1  0 0.000 0.000
#> GSM892359     1  0.0000     1.0000  1  0 0.000 0.000
#> GSM892363     1  0.0000     1.0000  1  0 0.000 0.000
#> GSM892367     3  0.1022     0.8624  0  0 0.968 0.032
#> GSM892371     3  0.4985     0.0974  0  0 0.532 0.468
#> GSM892375     2  0.0000     1.0000  0  1 0.000 0.000
#> GSM892379     2  0.0000     1.0000  0  1 0.000 0.000
#> GSM892385     2  0.0000     1.0000  0  1 0.000 0.000
#> GSM892389     2  0.0000     1.0000  0  1 0.000 0.000
#> GSM892341     3  0.0188     0.8785  0  0 0.996 0.004
#> GSM892346     4  0.0000     0.9167  0  0 0.000 1.000
#> GSM892350     4  0.0000     0.9167  0  0 0.000 1.000
#> GSM892354     1  0.0000     1.0000  1  0 0.000 0.000
#> GSM892356     1  0.0000     1.0000  1  0 0.000 0.000
#> GSM892362     1  0.0000     1.0000  1  0 0.000 0.000
#> GSM892366     3  0.0188     0.8782  0  0 0.996 0.004
#> GSM892370     4  0.4164     0.6298  0  0 0.264 0.736
#> GSM892374     2  0.0000     1.0000  0  1 0.000 0.000
#> GSM892378     2  0.0000     1.0000  0  1 0.000 0.000
#> GSM892382     2  0.0000     1.0000  0  1 0.000 0.000
#> GSM892384     2  0.0000     1.0000  0  1 0.000 0.000
#> GSM892388     2  0.0000     1.0000  0  1 0.000 0.000
#> GSM892343     3  0.3726     0.7082  0  0 0.788 0.212
#> GSM892348     4  0.0000     0.9167  0  0 0.000 1.000
#> GSM892352     4  0.4304     0.5967  0  0 0.284 0.716
#> GSM892358     1  0.0000     1.0000  1  0 0.000 0.000
#> GSM892360     1  0.0000     1.0000  1  0 0.000 0.000
#> GSM892364     1  0.0000     1.0000  1  0 0.000 0.000
#> GSM892368     3  0.0000     0.8782  0  0 1.000 0.000
#> GSM892372     3  0.0592     0.8744  0  0 0.984 0.016
#> GSM892376     2  0.0000     1.0000  0  1 0.000 0.000
#> GSM892380     2  0.0000     1.0000  0  1 0.000 0.000
#> GSM892386     2  0.0000     1.0000  0  1 0.000 0.000
#> GSM892390     2  0.0000     1.0000  0  1 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 5), get_membership(res, k = 5))

#>           class entropy silhouette p1 p2    p3    p4    p5
#> GSM892342     3  0.0000      0.992  0  0 1.000 0.000 0.000
#> GSM892345     4  0.0000      1.000  0  0 0.000 1.000 0.000
#> GSM892349     5  0.2020      0.890  0  0 0.000 0.100 0.900
#> GSM892353     1  0.0000      1.000  1  0 0.000 0.000 0.000
#> GSM892355     1  0.0000      1.000  1  0 0.000 0.000 0.000
#> GSM892361     1  0.0000      1.000  1  0 0.000 0.000 0.000
#> GSM892365     3  0.0000      0.992  0  0 1.000 0.000 0.000
#> GSM892369     5  0.0609      0.965  0  0 0.020 0.000 0.980
#> GSM892373     2  0.0000      1.000  0  1 0.000 0.000 0.000
#> GSM892377     2  0.0000      1.000  0  1 0.000 0.000 0.000
#> GSM892381     2  0.0000      1.000  0  1 0.000 0.000 0.000
#> GSM892383     2  0.0000      1.000  0  1 0.000 0.000 0.000
#> GSM892387     2  0.0000      1.000  0  1 0.000 0.000 0.000
#> GSM892344     3  0.1410      0.938  0  0 0.940 0.000 0.060
#> GSM892347     4  0.0000      1.000  0  0 0.000 1.000 0.000
#> GSM892351     4  0.0000      1.000  0  0 0.000 1.000 0.000
#> GSM892357     1  0.0000      1.000  1  0 0.000 0.000 0.000
#> GSM892359     1  0.0000      1.000  1  0 0.000 0.000 0.000
#> GSM892363     1  0.0000      1.000  1  0 0.000 0.000 0.000
#> GSM892367     3  0.0000      0.992  0  0 1.000 0.000 0.000
#> GSM892371     5  0.0000      0.973  0  0 0.000 0.000 1.000
#> GSM892375     2  0.0000      1.000  0  1 0.000 0.000 0.000
#> GSM892379     2  0.0000      1.000  0  1 0.000 0.000 0.000
#> GSM892385     2  0.0000      1.000  0  1 0.000 0.000 0.000
#> GSM892389     2  0.0000      1.000  0  1 0.000 0.000 0.000
#> GSM892341     3  0.0000      0.992  0  0 1.000 0.000 0.000
#> GSM892346     4  0.0000      1.000  0  0 0.000 1.000 0.000
#> GSM892350     4  0.0000      1.000  0  0 0.000 1.000 0.000
#> GSM892354     1  0.0000      1.000  1  0 0.000 0.000 0.000
#> GSM892356     1  0.0000      1.000  1  0 0.000 0.000 0.000
#> GSM892362     1  0.0000      1.000  1  0 0.000 0.000 0.000
#> GSM892366     3  0.0000      0.992  0  0 1.000 0.000 0.000
#> GSM892370     5  0.0290      0.972  0  0 0.008 0.000 0.992
#> GSM892374     2  0.0000      1.000  0  1 0.000 0.000 0.000
#> GSM892378     2  0.0000      1.000  0  1 0.000 0.000 0.000
#> GSM892382     2  0.0000      1.000  0  1 0.000 0.000 0.000
#> GSM892384     2  0.0000      1.000  0  1 0.000 0.000 0.000
#> GSM892388     2  0.0000      1.000  0  1 0.000 0.000 0.000
#> GSM892343     5  0.0162      0.973  0  0 0.000 0.004 0.996
#> GSM892348     4  0.0000      1.000  0  0 0.000 1.000 0.000
#> GSM892352     5  0.0000      0.973  0  0 0.000 0.000 1.000
#> GSM892358     1  0.0000      1.000  1  0 0.000 0.000 0.000
#> GSM892360     1  0.0000      1.000  1  0 0.000 0.000 0.000
#> GSM892364     1  0.0000      1.000  1  0 0.000 0.000 0.000
#> GSM892368     3  0.0000      0.992  0  0 1.000 0.000 0.000
#> GSM892372     3  0.0000      0.992  0  0 1.000 0.000 0.000
#> GSM892376     2  0.0000      1.000  0  1 0.000 0.000 0.000
#> GSM892380     2  0.0000      1.000  0  1 0.000 0.000 0.000
#> GSM892386     2  0.0000      1.000  0  1 0.000 0.000 0.000
#> GSM892390     2  0.0000      1.000  0  1 0.000 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 6), get_membership(res, k = 6))

#>           class entropy silhouette    p1 p2    p3    p4    p5    p6
#> GSM892342     3  0.0146      0.963 0.000  0 0.996 0.000 0.004 0.000
#> GSM892345     4  0.0260      0.989 0.000  0 0.000 0.992 0.000 0.008
#> GSM892349     5  0.0972      0.962 0.000  0 0.000 0.028 0.964 0.008
#> GSM892353     6  0.0632      0.657 0.024  0 0.000 0.000 0.000 0.976
#> GSM892355     6  0.3198      0.660 0.260  0 0.000 0.000 0.000 0.740
#> GSM892361     1  0.0000      0.905 1.000  0 0.000 0.000 0.000 0.000
#> GSM892365     3  0.0000      0.964 0.000  0 1.000 0.000 0.000 0.000
#> GSM892369     5  0.0146      0.988 0.000  0 0.004 0.000 0.996 0.000
#> GSM892373     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892344     3  0.2664      0.775 0.000  0 0.816 0.000 0.184 0.000
#> GSM892347     4  0.0000      0.991 0.000  0 0.000 1.000 0.000 0.000
#> GSM892351     4  0.0713      0.974 0.000  0 0.000 0.972 0.000 0.028
#> GSM892357     1  0.0000      0.905 1.000  0 0.000 0.000 0.000 0.000
#> GSM892359     1  0.0937      0.878 0.960  0 0.000 0.000 0.000 0.040
#> GSM892363     1  0.0146      0.904 0.996  0 0.000 0.000 0.000 0.004
#> GSM892367     3  0.0000      0.964 0.000  0 1.000 0.000 0.000 0.000
#> GSM892371     5  0.0000      0.988 0.000  0 0.000 0.000 1.000 0.000
#> GSM892375     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892341     3  0.0458      0.959 0.000  0 0.984 0.000 0.016 0.000
#> GSM892346     4  0.0260      0.989 0.000  0 0.000 0.992 0.000 0.008
#> GSM892350     4  0.0146      0.990 0.000  0 0.000 0.996 0.000 0.004
#> GSM892354     1  0.0363      0.900 0.988  0 0.000 0.000 0.000 0.012
#> GSM892356     1  0.1387      0.840 0.932  0 0.000 0.000 0.000 0.068
#> GSM892362     1  0.0000      0.905 1.000  0 0.000 0.000 0.000 0.000
#> GSM892366     3  0.0000      0.964 0.000  0 1.000 0.000 0.000 0.000
#> GSM892370     5  0.0146      0.988 0.000  0 0.004 0.000 0.996 0.000
#> GSM892374     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892343     5  0.0405      0.984 0.000  0 0.004 0.008 0.988 0.000
#> GSM892348     4  0.0000      0.991 0.000  0 0.000 1.000 0.000 0.000
#> GSM892352     5  0.0000      0.988 0.000  0 0.000 0.000 1.000 0.000
#> GSM892358     6  0.3672      0.500 0.368  0 0.000 0.000 0.000 0.632
#> GSM892360     1  0.0000      0.905 1.000  0 0.000 0.000 0.000 0.000
#> GSM892364     1  0.3854      0.049 0.536  0 0.000 0.000 0.000 0.464
#> GSM892368     3  0.0000      0.964 0.000  0 1.000 0.000 0.000 0.000
#> GSM892372     3  0.0547      0.956 0.000  0 0.980 0.000 0.020 0.000
#> GSM892376     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

k = 2
k = 3
k = 4
k = 5
k = 6

consensus_heatmap(res, k = 2)

plot of chunk tab-SD-mclust-consensus-heatmap-1

consensus_heatmap(res, k = 3)

plot of chunk tab-SD-mclust-consensus-heatmap-2

consensus_heatmap(res, k = 4)

plot of chunk tab-SD-mclust-consensus-heatmap-3

consensus_heatmap(res, k = 5)

plot of chunk tab-SD-mclust-consensus-heatmap-4

consensus_heatmap(res, k = 6)

plot of chunk tab-SD-mclust-consensus-heatmap-5

Heatmaps for the membership of samples in all partitions to see how consistent they are:

k = 2
k = 3
k = 4
k = 5
k = 6

membership_heatmap(res, k = 2)

plot of chunk tab-SD-mclust-membership-heatmap-1

membership_heatmap(res, k = 3)

plot of chunk tab-SD-mclust-membership-heatmap-2

membership_heatmap(res, k = 4)

plot of chunk tab-SD-mclust-membership-heatmap-3

membership_heatmap(res, k = 5)

plot of chunk tab-SD-mclust-membership-heatmap-4

membership_heatmap(res, k = 6)

plot of chunk tab-SD-mclust-membership-heatmap-5

Signature heatmaps where rows are scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2)

plot of chunk tab-SD-mclust-get-signatures-1

get_signatures(res, k = 3)

plot of chunk tab-SD-mclust-get-signatures-2

get_signatures(res, k = 4)

plot of chunk tab-SD-mclust-get-signatures-3

get_signatures(res, k = 5)

plot of chunk tab-SD-mclust-get-signatures-4

get_signatures(res, k = 6)

plot of chunk tab-SD-mclust-get-signatures-5

Signature heatmaps where rows are not scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-SD-mclust-get-signatures-no-scale-1

get_signatures(res, k = 3, scale_rows = FALSE)

plot of chunk tab-SD-mclust-get-signatures-no-scale-2

get_signatures(res, k = 4, scale_rows = FALSE)

plot of chunk tab-SD-mclust-get-signatures-no-scale-3

get_signatures(res, k = 5, scale_rows = FALSE)

plot of chunk tab-SD-mclust-get-signatures-no-scale-4

get_signatures(res, k = 6, scale_rows = FALSE)

plot of chunk tab-SD-mclust-get-signatures-no-scale-5

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk SD-mclust-signature_compare

# 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.

k = 2
k = 3
k = 4
k = 5
k = 6

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-SD-mclust-dimension-reduction-1

dimension_reduction(res, k = 3, method = "UMAP")

plot of chunk tab-SD-mclust-dimension-reduction-2

dimension_reduction(res, k = 4, method = "UMAP")

plot of chunk tab-SD-mclust-dimension-reduction-3

dimension_reduction(res, k = 5, method = "UMAP")

plot of chunk tab-SD-mclust-dimension-reduction-4

dimension_reduction(res, k = 6, method = "UMAP")

plot of chunk tab-SD-mclust-dimension-reduction-5

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk SD-mclust-collect-classes

test_to_known_factors(res)

#>            n tissue(p) disease.state(p) other(p) individual(p) k
#> SD:mclust 50     1.000            0.934 2.67e-07      1.42e-03 2
#> SD:mclust 50     1.000            0.931 1.26e-12      1.60e-05 3
#> SD:mclust 48     0.987            0.948 6.57e-16      1.01e-06 4
#> SD:mclust 50     1.000            0.998 1.59e-16      6.55e-06 5
#> SD:mclust 48     0.860            0.863 1.85e-13      3.25e-04 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.

SD:NMF**

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 31632 rows and 50 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 5.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk SD-NMF-collect-plots

The plots are:

The first row: a plot of the ECDF (empirical cumulative distribution function) curves of the consensus matrix for each k and the heatmap of predicted classes for each k.
The second row: heatmaps of the consensus matrix for each k.
The third row: heatmaps of the membership matrix for each k.
The fouth row: heatmaps of the signatures for each 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:

ECDF curves of the consensus matrix for each k;
1-PAC. The PAC score measures the proportion of the ambiguous subgrouping.
Mean silhouette score.
Concordance. The mean probability of fiting the consensus class ids in all partitions.
Area increased. Denote \(A_k\) as the area under the ECDF curve for current k, the area increased is defined as \(A_k - A_{k-1}\).
Rand index. The percent of pairs of samples that are both in a same cluster or both are not in a same cluster in the partition of k and k-1.
Jaccard index. The ratio of pairs of samples are both in a same cluster in the partition of k and k-1 and the pairs of samples are both in a same cluster in the partition k or k-1.

The detailed explanations of these statistics can be found in the cola vignette.

select_partition_number(res)

plot of chunk SD-NMF-select-partition-number

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         0.4707 0.530   0.530
#> 3 3 0.927           0.922       0.966         0.4345 0.792   0.607
#> 4 4 0.996           0.966       0.979         0.0990 0.909   0.729
#> 5 5 0.951           0.930       0.944         0.0348 0.958   0.838
#> 6 6 0.924           0.926       0.944         0.0139 1.000   1.000

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

All \(k\) with Jaccard index larger than 0.95 are removed because increasing \(k\) does not provide enough extra information. If all \(k\) are removed, it is marked as no subgroup is detected.
For all \(k\) with 1-PAC score larger than 0.9, the maximal \(k\) is taken as the best \(k\), and other \(k\) are marked as optional \(k\).
If it does not fit the second rule. The \(k\) with the maximal vote of the highest 1-PAC score, highest mean silhouette, and highest concordance is taken as the best \(k\).

suggest_best_k(res)

#> [1] 5
#> attr(,"optional")
#> [1] 2 3 4

There is also optional best \(k\) = 2 3 4 that is worth to check.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

k = 2
k = 3
k = 4
k = 5
k = 6

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>           class entropy silhouette p1 p2
#> GSM892342     1       0          1  1  0
#> GSM892345     1       0          1  1  0
#> GSM892349     1       0          1  1  0
#> GSM892353     1       0          1  1  0
#> GSM892355     1       0          1  1  0
#> GSM892361     1       0          1  1  0
#> GSM892365     1       0          1  1  0
#> GSM892369     1       0          1  1  0
#> GSM892373     2       0          1  0  1
#> GSM892377     2       0          1  0  1
#> GSM892381     2       0          1  0  1
#> GSM892383     2       0          1  0  1
#> GSM892387     2       0          1  0  1
#> GSM892344     1       0          1  1  0
#> GSM892347     1       0          1  1  0
#> GSM892351     1       0          1  1  0
#> GSM892357     1       0          1  1  0
#> GSM892359     1       0          1  1  0
#> GSM892363     1       0          1  1  0
#> GSM892367     1       0          1  1  0
#> GSM892371     1       0          1  1  0
#> GSM892375     2       0          1  0  1
#> GSM892379     2       0          1  0  1
#> GSM892385     2       0          1  0  1
#> GSM892389     2       0          1  0  1
#> GSM892341     1       0          1  1  0
#> GSM892346     1       0          1  1  0
#> GSM892350     1       0          1  1  0
#> GSM892354     1       0          1  1  0
#> GSM892356     1       0          1  1  0
#> GSM892362     1       0          1  1  0
#> GSM892366     1       0          1  1  0
#> GSM892370     1       0          1  1  0
#> GSM892374     2       0          1  0  1
#> GSM892378     2       0          1  0  1
#> GSM892382     2       0          1  0  1
#> GSM892384     2       0          1  0  1
#> GSM892388     2       0          1  0  1
#> GSM892343     1       0          1  1  0
#> GSM892348     1       0          1  1  0
#> GSM892352     1       0          1  1  0
#> GSM892358     1       0          1  1  0
#> GSM892360     1       0          1  1  0
#> GSM892364     1       0          1  1  0
#> GSM892368     1       0          1  1  0
#> GSM892372     1       0          1  1  0
#> GSM892376     2       0          1  0  1
#> GSM892380     2       0          1  0  1
#> GSM892386     2       0          1  0  1
#> GSM892390     2       0          1  0  1

show/hide code output

cbind(get_classes(res, k = 3), get_membership(res, k = 3))

#>           class entropy silhouette    p1 p2    p3
#> GSM892342     3   0.000      0.967 0.000  0 1.000
#> GSM892345     1   0.536      0.673 0.724  0 0.276
#> GSM892349     3   0.000      0.967 0.000  0 1.000
#> GSM892353     1   0.000      0.910 1.000  0 0.000
#> GSM892355     1   0.000      0.910 1.000  0 0.000
#> GSM892361     1   0.000      0.910 1.000  0 0.000
#> GSM892365     3   0.000      0.967 0.000  0 1.000
#> GSM892369     3   0.000      0.967 0.000  0 1.000
#> GSM892373     2   0.000      1.000 0.000  1 0.000
#> GSM892377     2   0.000      1.000 0.000  1 0.000
#> GSM892381     2   0.000      1.000 0.000  1 0.000
#> GSM892383     2   0.000      1.000 0.000  1 0.000
#> GSM892387     2   0.000      1.000 0.000  1 0.000
#> GSM892344     3   0.000      0.967 0.000  0 1.000
#> GSM892347     1   0.581      0.575 0.664  0 0.336
#> GSM892351     3   0.593      0.337 0.356  0 0.644
#> GSM892357     1   0.000      0.910 1.000  0 0.000
#> GSM892359     1   0.000      0.910 1.000  0 0.000
#> GSM892363     1   0.000      0.910 1.000  0 0.000
#> GSM892367     3   0.000      0.967 0.000  0 1.000
#> GSM892371     3   0.000      0.967 0.000  0 1.000
#> GSM892375     2   0.000      1.000 0.000  1 0.000
#> GSM892379     2   0.000      1.000 0.000  1 0.000
#> GSM892385     2   0.000      1.000 0.000  1 0.000
#> GSM892389     2   0.000      1.000 0.000  1 0.000
#> GSM892341     3   0.000      0.967 0.000  0 1.000
#> GSM892346     1   0.382      0.812 0.852  0 0.148
#> GSM892350     1   0.590      0.543 0.648  0 0.352
#> GSM892354     1   0.000      0.910 1.000  0 0.000
#> GSM892356     1   0.000      0.910 1.000  0 0.000
#> GSM892362     1   0.000      0.910 1.000  0 0.000
#> GSM892366     3   0.000      0.967 0.000  0 1.000
#> GSM892370     3   0.000      0.967 0.000  0 1.000
#> GSM892374     2   0.000      1.000 0.000  1 0.000
#> GSM892378     2   0.000      1.000 0.000  1 0.000
#> GSM892382     2   0.000      1.000 0.000  1 0.000
#> GSM892384     2   0.000      1.000 0.000  1 0.000
#> GSM892388     2   0.000      1.000 0.000  1 0.000
#> GSM892343     3   0.153      0.927 0.040  0 0.960
#> GSM892348     1   0.475      0.748 0.784  0 0.216
#> GSM892352     3   0.000      0.967 0.000  0 1.000
#> GSM892358     1   0.000      0.910 1.000  0 0.000
#> GSM892360     1   0.000      0.910 1.000  0 0.000
#> GSM892364     1   0.000      0.910 1.000  0 0.000
#> GSM892368     3   0.000      0.967 0.000  0 1.000
#> GSM892372     3   0.000      0.967 0.000  0 1.000
#> GSM892376     2   0.000      1.000 0.000  1 0.000
#> GSM892380     2   0.000      1.000 0.000  1 0.000
#> GSM892386     2   0.000      1.000 0.000  1 0.000
#> GSM892390     2   0.000      1.000 0.000  1 0.000

show/hide code output

cbind(get_classes(res, k = 4), get_membership(res, k = 4))

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM892342     3  0.0376      0.948 0.004 0.000 0.992 0.004
#> GSM892345     4  0.1022      0.966 0.000 0.000 0.032 0.968
#> GSM892349     4  0.2530      0.910 0.000 0.000 0.112 0.888
#> GSM892353     1  0.0188      0.995 0.996 0.000 0.004 0.000
#> GSM892355     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM892361     1  0.0188      0.997 0.996 0.000 0.000 0.004
#> GSM892365     3  0.0188      0.947 0.004 0.000 0.996 0.000
#> GSM892369     3  0.0817      0.945 0.000 0.000 0.976 0.024
#> GSM892373     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892377     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892381     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892383     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892387     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892344     3  0.1489      0.933 0.004 0.000 0.952 0.044
#> GSM892347     4  0.1022      0.966 0.000 0.000 0.032 0.968
#> GSM892351     4  0.1118      0.965 0.000 0.000 0.036 0.964
#> GSM892357     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM892359     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM892363     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM892367     3  0.0188      0.947 0.004 0.000 0.996 0.000
#> GSM892371     3  0.1792      0.913 0.000 0.000 0.932 0.068
#> GSM892375     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892379     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892385     2  0.0188      0.997 0.000 0.996 0.000 0.004
#> GSM892389     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892341     3  0.0779      0.947 0.004 0.000 0.980 0.016
#> GSM892346     4  0.0895      0.959 0.004 0.000 0.020 0.976
#> GSM892350     4  0.1022      0.966 0.000 0.000 0.032 0.968
#> GSM892354     1  0.0188      0.997 0.996 0.000 0.000 0.004
#> GSM892356     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM892362     1  0.0188      0.997 0.996 0.000 0.000 0.004
#> GSM892366     3  0.0188      0.947 0.004 0.000 0.996 0.000
#> GSM892370     3  0.0921      0.943 0.000 0.000 0.972 0.028
#> GSM892374     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892378     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892382     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892384     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892388     2  0.0188      0.997 0.000 0.996 0.000 0.004
#> GSM892343     3  0.4730      0.411 0.000 0.000 0.636 0.364
#> GSM892348     4  0.0817      0.962 0.000 0.000 0.024 0.976
#> GSM892352     4  0.2868      0.883 0.000 0.000 0.136 0.864
#> GSM892358     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM892360     1  0.0188      0.997 0.996 0.000 0.000 0.004
#> GSM892364     1  0.0188      0.997 0.996 0.000 0.000 0.004
#> GSM892368     3  0.0188      0.947 0.004 0.000 0.996 0.000
#> GSM892372     3  0.0524      0.948 0.004 0.000 0.988 0.008
#> GSM892376     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892380     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892386     2  0.0188      0.997 0.000 0.996 0.000 0.004
#> GSM892390     2  0.0188      0.997 0.000 0.996 0.000 0.004

show/hide code output

cbind(get_classes(res, k = 5), get_membership(res, k = 5))

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> GSM892342     5  0.3399      0.773 0.000 0.000 0.168 0.020 0.812
#> GSM892345     4  0.1608      0.937 0.000 0.000 0.000 0.928 0.072
#> GSM892349     5  0.4564      0.447 0.000 0.000 0.016 0.372 0.612
#> GSM892353     1  0.0703      0.977 0.976 0.000 0.000 0.000 0.024
#> GSM892355     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000
#> GSM892361     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000
#> GSM892365     3  0.3336      0.822 0.000 0.000 0.772 0.000 0.228
#> GSM892369     3  0.0671      0.831 0.000 0.000 0.980 0.004 0.016
#> GSM892373     2  0.0609      0.988 0.000 0.980 0.000 0.000 0.020
#> GSM892377     2  0.0404      0.990 0.000 0.988 0.000 0.000 0.012
#> GSM892381     2  0.0162      0.995 0.000 0.996 0.000 0.000 0.004
#> GSM892383     2  0.0162      0.995 0.000 0.996 0.000 0.000 0.004
#> GSM892387     2  0.0162      0.995 0.000 0.996 0.000 0.000 0.004
#> GSM892344     5  0.3432      0.805 0.000 0.000 0.132 0.040 0.828
#> GSM892347     4  0.0703      0.943 0.000 0.000 0.000 0.976 0.024
#> GSM892351     4  0.2286      0.900 0.000 0.000 0.004 0.888 0.108
#> GSM892357     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000
#> GSM892359     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000
#> GSM892363     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000
#> GSM892367     3  0.1638      0.874 0.000 0.000 0.932 0.004 0.064
#> GSM892371     3  0.1877      0.874 0.000 0.000 0.924 0.012 0.064
#> GSM892375     2  0.0000      0.995 0.000 1.000 0.000 0.000 0.000
#> GSM892379     2  0.0162      0.994 0.000 0.996 0.000 0.000 0.004
#> GSM892385     2  0.0162      0.995 0.000 0.996 0.000 0.000 0.004
#> GSM892389     2  0.0000      0.995 0.000 1.000 0.000 0.000 0.000
#> GSM892341     5  0.3454      0.791 0.000 0.000 0.156 0.028 0.816
#> GSM892346     4  0.0566      0.924 0.000 0.000 0.004 0.984 0.012
#> GSM892350     4  0.1478      0.942 0.000 0.000 0.000 0.936 0.064
#> GSM892354     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000
#> GSM892356     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000
#> GSM892362     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000
#> GSM892366     3  0.3508      0.793 0.000 0.000 0.748 0.000 0.252
#> GSM892370     3  0.0162      0.843 0.000 0.000 0.996 0.004 0.000
#> GSM892374     2  0.0609      0.985 0.000 0.980 0.000 0.000 0.020
#> GSM892378     2  0.0000      0.995 0.000 1.000 0.000 0.000 0.000
#> GSM892382     2  0.0162      0.995 0.000 0.996 0.000 0.000 0.004
#> GSM892384     2  0.0162      0.995 0.000 0.996 0.000 0.000 0.004
#> GSM892388     2  0.0510      0.991 0.000 0.984 0.000 0.000 0.016
#> GSM892343     5  0.4364      0.802 0.000 0.000 0.112 0.120 0.768
#> GSM892348     4  0.0000      0.934 0.000 0.000 0.000 1.000 0.000
#> GSM892352     5  0.3852      0.710 0.000 0.000 0.020 0.220 0.760
#> GSM892358     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000
#> GSM892360     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000
#> GSM892364     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000
#> GSM892368     3  0.3010      0.866 0.000 0.000 0.824 0.004 0.172
#> GSM892372     3  0.2930      0.870 0.000 0.000 0.832 0.004 0.164
#> GSM892376     2  0.0162      0.995 0.000 0.996 0.000 0.000 0.004
#> GSM892380     2  0.0000      0.995 0.000 1.000 0.000 0.000 0.000
#> GSM892386     2  0.0000      0.995 0.000 1.000 0.000 0.000 0.000
#> GSM892390     2  0.0000      0.995 0.000 1.000 0.000 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 6), get_membership(res, k = 6))

#>           class entropy silhouette    p1    p2    p3    p4    p5 p6
#> GSM892342     5  0.2163      0.814 0.000 0.000 0.096 0.004 0.892 NA
#> GSM892345     4  0.2178      0.880 0.000 0.000 0.000 0.868 0.132 NA
#> GSM892349     5  0.3684      0.522 0.000 0.000 0.004 0.332 0.664 NA
#> GSM892353     1  0.0363      0.989 0.988 0.000 0.000 0.000 0.012 NA
#> GSM892355     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000 NA
#> GSM892361     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000 NA
#> GSM892365     3  0.1387      0.952 0.000 0.000 0.932 0.000 0.068 NA
#> GSM892369     3  0.1078      0.943 0.000 0.000 0.964 0.012 0.016 NA
#> GSM892373     2  0.2697      0.864 0.000 0.812 0.000 0.000 0.000 NA
#> GSM892377     2  0.2003      0.916 0.000 0.884 0.000 0.000 0.000 NA
#> GSM892381     2  0.0146      0.964 0.000 0.996 0.000 0.000 0.000 NA
#> GSM892383     2  0.0146      0.964 0.000 0.996 0.000 0.000 0.000 NA
#> GSM892387     2  0.0260      0.964 0.000 0.992 0.000 0.000 0.000 NA
#> GSM892344     5  0.2138      0.835 0.000 0.000 0.052 0.036 0.908 NA
#> GSM892347     4  0.1387      0.891 0.000 0.000 0.000 0.932 0.068 NA
#> GSM892351     4  0.3287      0.768 0.000 0.000 0.000 0.768 0.220 NA
#> GSM892357     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000 NA
#> GSM892359     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000 NA
#> GSM892363     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000 NA
#> GSM892367     3  0.0806      0.961 0.000 0.000 0.972 0.000 0.020 NA
#> GSM892371     3  0.0779      0.961 0.000 0.000 0.976 0.008 0.008 NA
#> GSM892375     2  0.0937      0.956 0.000 0.960 0.000 0.000 0.000 NA
#> GSM892379     2  0.0790      0.959 0.000 0.968 0.000 0.000 0.000 NA
#> GSM892385     2  0.0146      0.964 0.000 0.996 0.000 0.000 0.000 NA
#> GSM892389     2  0.0260      0.964 0.000 0.992 0.000 0.000 0.000 NA
#> GSM892341     5  0.2121      0.825 0.000 0.000 0.096 0.012 0.892 NA
#> GSM892346     4  0.1219      0.821 0.000 0.000 0.004 0.948 0.000 NA
#> GSM892350     4  0.2146      0.887 0.000 0.000 0.000 0.880 0.116 NA
#> GSM892354     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000 NA
#> GSM892356     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000 NA
#> GSM892362     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000 NA
#> GSM892366     3  0.1700      0.942 0.000 0.000 0.916 0.000 0.080 NA
#> GSM892370     3  0.0508      0.955 0.000 0.000 0.984 0.004 0.000 NA
#> GSM892374     2  0.2762      0.859 0.000 0.804 0.000 0.000 0.000 NA
#> GSM892378     2  0.1267      0.948 0.000 0.940 0.000 0.000 0.000 NA
#> GSM892382     2  0.0146      0.964 0.000 0.996 0.000 0.000 0.000 NA
#> GSM892384     2  0.0000      0.964 0.000 1.000 0.000 0.000 0.000 NA
#> GSM892388     2  0.1714      0.928 0.000 0.908 0.000 0.000 0.000 NA
#> GSM892343     5  0.3103      0.826 0.000 0.000 0.064 0.100 0.836 NA
#> GSM892348     4  0.0972      0.874 0.000 0.000 0.000 0.964 0.028 NA
#> GSM892352     5  0.3323      0.731 0.000 0.000 0.008 0.204 0.780 NA
#> GSM892358     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000 NA
#> GSM892360     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000 NA
#> GSM892364     1  0.0260      0.993 0.992 0.000 0.000 0.000 0.000 NA
#> GSM892368     3  0.1349      0.957 0.000 0.000 0.940 0.000 0.056 NA
#> GSM892372     3  0.1194      0.963 0.000 0.000 0.956 0.004 0.032 NA
#> GSM892376     2  0.0363      0.964 0.000 0.988 0.000 0.000 0.000 NA
#> GSM892380     2  0.0000      0.964 0.000 1.000 0.000 0.000 0.000 NA
#> GSM892386     2  0.0000      0.964 0.000 1.000 0.000 0.000 0.000 NA
#> GSM892390     2  0.0146      0.964 0.000 0.996 0.000 0.000 0.000 NA

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

k = 2
k = 3
k = 4
k = 5
k = 6

consensus_heatmap(res, k = 2)

plot of chunk tab-SD-NMF-consensus-heatmap-1

consensus_heatmap(res, k = 3)

plot of chunk tab-SD-NMF-consensus-heatmap-2

consensus_heatmap(res, k = 4)

plot of chunk tab-SD-NMF-consensus-heatmap-3

consensus_heatmap(res, k = 5)

plot of chunk tab-SD-NMF-consensus-heatmap-4

consensus_heatmap(res, k = 6)

plot of chunk tab-SD-NMF-consensus-heatmap-5

Heatmaps for the membership of samples in all partitions to see how consistent they are:

k = 2
k = 3
k = 4
k = 5
k = 6

membership_heatmap(res, k = 2)

plot of chunk tab-SD-NMF-membership-heatmap-1

membership_heatmap(res, k = 3)

plot of chunk tab-SD-NMF-membership-heatmap-2

membership_heatmap(res, k = 4)

plot of chunk tab-SD-NMF-membership-heatmap-3

membership_heatmap(res, k = 5)

plot of chunk tab-SD-NMF-membership-heatmap-4

membership_heatmap(res, k = 6)

plot of chunk tab-SD-NMF-membership-heatmap-5

Signature heatmaps where rows are scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2)

plot of chunk tab-SD-NMF-get-signatures-1

get_signatures(res, k = 3)

plot of chunk tab-SD-NMF-get-signatures-2

get_signatures(res, k = 4)

plot of chunk tab-SD-NMF-get-signatures-3

get_signatures(res, k = 5)

plot of chunk tab-SD-NMF-get-signatures-4

get_signatures(res, k = 6)

plot of chunk tab-SD-NMF-get-signatures-5

Signature heatmaps where rows are not scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-SD-NMF-get-signatures-no-scale-1

get_signatures(res, k = 3, scale_rows = FALSE)

plot of chunk tab-SD-NMF-get-signatures-no-scale-2

get_signatures(res, k = 4, scale_rows = FALSE)

plot of chunk tab-SD-NMF-get-signatures-no-scale-3

get_signatures(res, k = 5, scale_rows = FALSE)

plot of chunk tab-SD-NMF-get-signatures-no-scale-4

get_signatures(res, k = 6, scale_rows = FALSE)

plot of chunk tab-SD-NMF-get-signatures-no-scale-5

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk SD-NMF-signature_compare

# 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.

k = 2
k = 3
k = 4
k = 5
k = 6

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-SD-NMF-dimension-reduction-1

dimension_reduction(res, k = 3, method = "UMAP")

plot of chunk tab-SD-NMF-dimension-reduction-2

dimension_reduction(res, k = 4, method = "UMAP")

plot of chunk tab-SD-NMF-dimension-reduction-3

dimension_reduction(res, k = 5, method = "UMAP")

plot of chunk tab-SD-NMF-dimension-reduction-4

dimension_reduction(res, k = 6, method = "UMAP")

plot of chunk tab-SD-NMF-dimension-reduction-5

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk SD-NMF-collect-classes

test_to_known_factors(res)

#>         n tissue(p) disease.state(p) other(p) individual(p) k
#> SD:NMF 50     1.000            0.934 2.67e-07      1.42e-03 2
#> SD:NMF 49     0.981            0.952 1.63e-11      6.57e-05 3
#> SD:NMF 49     0.995            0.988 2.28e-17      4.54e-07 4
#> SD:NMF 49     0.996            0.982 2.33e-20      7.98e-08 5
#> SD:NMF 50     1.000            0.998 3.06e-20      2.01e-07 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

CV:hclust*

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 31632 rows and 50 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#>   Subgroups are detected by 'hclust' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 5.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk CV-hclust-collect-plots

The plots are:

The first row: a plot of the ECDF (empirical cumulative distribution function) curves of the consensus matrix for each k and the heatmap of predicted classes for each k.
The second row: heatmaps of the consensus matrix for each k.
The third row: heatmaps of the membership matrix for each k.
The fouth row: heatmaps of the signatures for each 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:

ECDF curves of the consensus matrix for each k;
1-PAC. The PAC score measures the proportion of the ambiguous subgrouping.
Mean silhouette score.
Concordance. The mean probability of fiting the consensus class ids in all partitions.
Area increased. Denote \(A_k\) as the area under the ECDF curve for current k, the area increased is defined as \(A_k - A_{k-1}\).
Rand index. The percent of pairs of samples that are both in a same cluster or both are not in a same cluster in the partition of k and k-1.
Jaccard index. The ratio of pairs of samples are both in a same cluster in the partition of k and k-1 and the pairs of samples are both in a same cluster in the partition k or k-1.

The detailed explanations of these statistics can be found in the cola vignette.

select_partition_number(res)

plot of chunk CV-hclust-select-partition-number

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         0.4707 0.530   0.530
#> 3 3 0.971           0.944       0.969         0.4350 0.794   0.612
#> 4 4 0.982           0.944       0.969         0.0511 0.980   0.940
#> 5 5 0.904           0.782       0.857         0.0615 0.948   0.832
#> 6 6 0.890           0.873       0.871         0.0398 0.947   0.802

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

All \(k\) with Jaccard index larger than 0.95 are removed because increasing \(k\) does not provide enough extra information. If all \(k\) are removed, it is marked as no subgroup is detected.
For all \(k\) with 1-PAC score larger than 0.9, the maximal \(k\) is taken as the best \(k\), and other \(k\) are marked as optional \(k\).
If it does not fit the second rule. The \(k\) with the maximal vote of the highest 1-PAC score, highest mean silhouette, and highest concordance is taken as the best \(k\).

suggest_best_k(res)

#> [1] 5
#> attr(,"optional")
#> [1] 2 3 4

There is also optional best \(k\) = 2 3 4 that is worth to check.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

k = 2
k = 3
k = 4
k = 5
k = 6

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>           class entropy silhouette p1 p2
#> GSM892342     1       0          1  1  0
#> GSM892345     1       0          1  1  0
#> GSM892349     1       0          1  1  0
#> GSM892353     1       0          1  1  0
#> GSM892355     1       0          1  1  0
#> GSM892361     1       0          1  1  0
#> GSM892365     1       0          1  1  0
#> GSM892369     1       0          1  1  0
#> GSM892373     2       0          1  0  1
#> GSM892377     2       0          1  0  1
#> GSM892381     2       0          1  0  1
#> GSM892383     2       0          1  0  1
#> GSM892387     2       0          1  0  1
#> GSM892344     1       0          1  1  0
#> GSM892347     1       0          1  1  0
#> GSM892351     1       0          1  1  0
#> GSM892357     1       0          1  1  0
#> GSM892359     1       0          1  1  0
#> GSM892363     1       0          1  1  0
#> GSM892367     1       0          1  1  0
#> GSM892371     1       0          1  1  0
#> GSM892375     2       0          1  0  1
#> GSM892379     2       0          1  0  1
#> GSM892385     2       0          1  0  1
#> GSM892389     2       0          1  0  1
#> GSM892341     1       0          1  1  0
#> GSM892346     1       0          1  1  0
#> GSM892350     1       0          1  1  0
#> GSM892354     1       0          1  1  0
#> GSM892356     1       0          1  1  0
#> GSM892362     1       0          1  1  0
#> GSM892366     1       0          1  1  0
#> GSM892370     1       0          1  1  0
#> GSM892374     2       0          1  0  1
#> GSM892378     2       0          1  0  1
#> GSM892382     2       0          1  0  1
#> GSM892384     2       0          1  0  1
#> GSM892388     2       0          1  0  1
#> GSM892343     1       0          1  1  0
#> GSM892348     1       0          1  1  0
#> GSM892352     1       0          1  1  0
#> GSM892358     1       0          1  1  0
#> GSM892360     1       0          1  1  0
#> GSM892364     1       0          1  1  0
#> GSM892368     1       0          1  1  0
#> GSM892372     1       0          1  1  0
#> GSM892376     2       0          1  0  1
#> GSM892380     2       0          1  0  1
#> GSM892386     2       0          1  0  1
#> GSM892390     2       0          1  0  1

show/hide code output

cbind(get_classes(res, k = 3), get_membership(res, k = 3))

#>           class entropy silhouette    p1 p2    p3
#> GSM892342     3  0.0000      0.908 0.000  0 1.000
#> GSM892345     3  0.5948      0.569 0.360  0 0.640
#> GSM892349     3  0.2796      0.869 0.092  0 0.908
#> GSM892353     1  0.0000      1.000 1.000  0 0.000
#> GSM892355     1  0.0000      1.000 1.000  0 0.000
#> GSM892361     1  0.0000      1.000 1.000  0 0.000
#> GSM892365     3  0.0000      0.908 0.000  0 1.000
#> GSM892369     3  0.2165      0.891 0.064  0 0.936
#> GSM892373     2  0.0000      1.000 0.000  1 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000
#> GSM892344     3  0.0000      0.908 0.000  0 1.000
#> GSM892347     3  0.5988      0.554 0.368  0 0.632
#> GSM892351     3  0.4555      0.778 0.200  0 0.800
#> GSM892357     1  0.0000      1.000 1.000  0 0.000
#> GSM892359     1  0.0000      1.000 1.000  0 0.000
#> GSM892363     1  0.0000      1.000 1.000  0 0.000
#> GSM892367     3  0.0000      0.908 0.000  0 1.000
#> GSM892371     3  0.2165      0.891 0.064  0 0.936
#> GSM892375     2  0.0000      1.000 0.000  1 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000
#> GSM892341     3  0.0000      0.908 0.000  0 1.000
#> GSM892346     1  0.0000      1.000 1.000  0 0.000
#> GSM892350     3  0.5560      0.667 0.300  0 0.700
#> GSM892354     1  0.0000      1.000 1.000  0 0.000
#> GSM892356     1  0.0000      1.000 1.000  0 0.000
#> GSM892362     1  0.0000      1.000 1.000  0 0.000
#> GSM892366     3  0.0000      0.908 0.000  0 1.000
#> GSM892370     3  0.2165      0.891 0.064  0 0.936
#> GSM892374     2  0.0000      1.000 0.000  1 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000
#> GSM892343     3  0.0892      0.905 0.020  0 0.980
#> GSM892348     1  0.0000      1.000 1.000  0 0.000
#> GSM892352     3  0.0000      0.908 0.000  0 1.000
#> GSM892358     1  0.0000      1.000 1.000  0 0.000
#> GSM892360     1  0.0000      1.000 1.000  0 0.000
#> GSM892364     1  0.0237      0.995 0.996  0 0.004
#> GSM892368     3  0.0000      0.908 0.000  0 1.000
#> GSM892372     3  0.0000      0.908 0.000  0 1.000
#> GSM892376     2  0.0000      1.000 0.000  1 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000

show/hide code output

cbind(get_classes(res, k = 4), get_membership(res, k = 4))

#>           class entropy silhouette    p1 p2    p3    p4
#> GSM892342     3  0.0000      0.907 0.000  0 1.000 0.000
#> GSM892345     3  0.4713      0.585 0.000  0 0.640 0.360
#> GSM892349     3  0.2216      0.862 0.000  0 0.908 0.092
#> GSM892353     1  0.0000      0.999 1.000  0 0.000 0.000
#> GSM892355     1  0.0000      0.999 1.000  0 0.000 0.000
#> GSM892361     1  0.0000      0.999 1.000  0 0.000 0.000
#> GSM892365     3  0.0000      0.907 0.000  0 1.000 0.000
#> GSM892369     3  0.1716      0.886 0.000  0 0.936 0.064
#> GSM892373     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892344     3  0.0000      0.907 0.000  0 1.000 0.000
#> GSM892347     3  0.4746      0.571 0.000  0 0.632 0.368
#> GSM892351     3  0.3610      0.774 0.000  0 0.800 0.200
#> GSM892357     1  0.0000      0.999 1.000  0 0.000 0.000
#> GSM892359     1  0.0000      0.999 1.000  0 0.000 0.000
#> GSM892363     1  0.0000      0.999 1.000  0 0.000 0.000
#> GSM892367     3  0.0000      0.907 0.000  0 1.000 0.000
#> GSM892371     3  0.1716      0.886 0.000  0 0.936 0.064
#> GSM892375     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892341     3  0.0000      0.907 0.000  0 1.000 0.000
#> GSM892346     4  0.0000      1.000 0.000  0 0.000 1.000
#> GSM892350     3  0.4406      0.675 0.000  0 0.700 0.300
#> GSM892354     1  0.0000      0.999 1.000  0 0.000 0.000
#> GSM892356     1  0.0000      0.999 1.000  0 0.000 0.000
#> GSM892362     1  0.0000      0.999 1.000  0 0.000 0.000
#> GSM892366     3  0.0000      0.907 0.000  0 1.000 0.000
#> GSM892370     3  0.1716      0.886 0.000  0 0.936 0.064
#> GSM892374     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892343     3  0.0707      0.903 0.000  0 0.980 0.020
#> GSM892348     4  0.0000      1.000 0.000  0 0.000 1.000
#> GSM892352     3  0.0000      0.907 0.000  0 1.000 0.000
#> GSM892358     1  0.0000      0.999 1.000  0 0.000 0.000
#> GSM892360     1  0.0000      0.999 1.000  0 0.000 0.000
#> GSM892364     1  0.0188      0.994 0.996  0 0.004 0.000
#> GSM892368     3  0.0000      0.907 0.000  0 1.000 0.000
#> GSM892372     3  0.0000      0.907 0.000  0 1.000 0.000
#> GSM892376     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 5), get_membership(res, k = 5))

#>           class entropy silhouette    p1 p2    p3    p4 p5
#> GSM892342     3  0.5534      0.478 0.000  0 0.508 0.068 NA
#> GSM892345     4  0.3857      0.532 0.000  0 0.312 0.688 NA
#> GSM892349     3  0.6127     -0.220 0.000  0 0.456 0.416 NA
#> GSM892353     1  0.0162      0.966 0.996  0 0.000 0.000 NA
#> GSM892355     1  0.0162      0.966 0.996  0 0.000 0.000 NA
#> GSM892361     1  0.1965      0.945 0.904  0 0.000 0.000 NA
#> GSM892365     3  0.0703      0.640 0.000  0 0.976 0.000 NA
#> GSM892369     3  0.3471      0.539 0.000  0 0.836 0.072 NA
#> GSM892373     2  0.0000      1.000 0.000  1 0.000 0.000 NA
#> GSM892377     2  0.0000      1.000 0.000  1 0.000 0.000 NA
#> GSM892381     2  0.0000      1.000 0.000  1 0.000 0.000 NA
#> GSM892383     2  0.0000      1.000 0.000  1 0.000 0.000 NA
#> GSM892387     2  0.0000      1.000 0.000  1 0.000 0.000 NA
#> GSM892344     3  0.5534      0.478 0.000  0 0.508 0.068 NA
#> GSM892347     4  0.3816      0.535 0.000  0 0.304 0.696 NA
#> GSM892351     4  0.4961      0.282 0.000  0 0.448 0.524 NA
#> GSM892357     1  0.1965      0.945 0.904  0 0.000 0.000 NA
#> GSM892359     1  0.1792      0.950 0.916  0 0.000 0.000 NA
#> GSM892363     1  0.0000      0.967 1.000  0 0.000 0.000 NA
#> GSM892367     3  0.0451      0.630 0.000  0 0.988 0.008 NA
#> GSM892371     3  0.3471      0.539 0.000  0 0.836 0.072 NA
#> GSM892375     2  0.0000      1.000 0.000  1 0.000 0.000 NA
#> GSM892379     2  0.0000      1.000 0.000  1 0.000 0.000 NA
#> GSM892385     2  0.0000      1.000 0.000  1 0.000 0.000 NA
#> GSM892389     2  0.0000      1.000 0.000  1 0.000 0.000 NA
#> GSM892341     3  0.5534      0.478 0.000  0 0.508 0.068 NA
#> GSM892346     4  0.4126      0.416 0.000  0 0.000 0.620 NA
#> GSM892350     4  0.4668      0.483 0.000  0 0.352 0.624 NA
#> GSM892354     1  0.1965      0.945 0.904  0 0.000 0.000 NA
#> GSM892356     1  0.0162      0.966 0.996  0 0.000 0.000 NA
#> GSM892362     1  0.1121      0.961 0.956  0 0.000 0.000 NA
#> GSM892366     3  0.0703      0.640 0.000  0 0.976 0.000 NA
#> GSM892370     3  0.3471      0.539 0.000  0 0.836 0.072 NA
#> GSM892374     2  0.0000      1.000 0.000  1 0.000 0.000 NA
#> GSM892378     2  0.0000      1.000 0.000  1 0.000 0.000 NA
#> GSM892382     2  0.0000      1.000 0.000  1 0.000 0.000 NA
#> GSM892384     2  0.0000      1.000 0.000  1 0.000 0.000 NA
#> GSM892388     2  0.0000      1.000 0.000  1 0.000 0.000 NA
#> GSM892343     3  0.5400      0.512 0.000  0 0.632 0.096 NA
#> GSM892348     4  0.4126      0.416 0.000  0 0.000 0.620 NA
#> GSM892352     3  0.6300      0.391 0.000  0 0.424 0.152 NA
#> GSM892358     1  0.0000      0.967 1.000  0 0.000 0.000 NA
#> GSM892360     1  0.0510      0.966 0.984  0 0.000 0.000 NA
#> GSM892364     1  0.0324      0.964 0.992  0 0.004 0.000 NA
#> GSM892368     3  0.0290      0.635 0.000  0 0.992 0.000 NA
#> GSM892372     3  0.0703      0.640 0.000  0 0.976 0.000 NA
#> GSM892376     2  0.0000      1.000 0.000  1 0.000 0.000 NA
#> GSM892380     2  0.0000      1.000 0.000  1 0.000 0.000 NA
#> GSM892386     2  0.0000      1.000 0.000  1 0.000 0.000 NA
#> GSM892390     2  0.0000      1.000 0.000  1 0.000 0.000 NA

show/hide code output

cbind(get_classes(res, k = 6), get_membership(res, k = 6))

#>           class entropy silhouette    p1 p2    p3    p4    p5    p6
#> GSM892342     5  0.5737      0.888 0.000  0 0.236 0.248 0.516 0.000
#> GSM892345     4  0.4215      0.797 0.000  0 0.056 0.700 0.000 0.244
#> GSM892349     4  0.2147      0.657 0.000  0 0.084 0.896 0.020 0.000
#> GSM892353     1  0.0976      0.801 0.968  0 0.000 0.016 0.008 0.008
#> GSM892355     1  0.0976      0.801 0.968  0 0.000 0.016 0.008 0.008
#> GSM892361     1  0.3838      0.677 0.552  0 0.000 0.000 0.448 0.000
#> GSM892365     3  0.2170      0.830 0.000  0 0.888 0.100 0.012 0.000
#> GSM892369     3  0.2764      0.776 0.000  0 0.864 0.100 0.028 0.008
#> GSM892373     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892344     5  0.5737      0.888 0.000  0 0.236 0.248 0.516 0.000
#> GSM892347     4  0.4145      0.788 0.000  0 0.048 0.700 0.000 0.252
#> GSM892351     4  0.2852      0.785 0.000  0 0.064 0.856 0.000 0.080
#> GSM892357     1  0.3833      0.679 0.556  0 0.000 0.000 0.444 0.000
#> GSM892359     1  0.3765      0.700 0.596  0 0.000 0.000 0.404 0.000
#> GSM892363     1  0.0713      0.815 0.972  0 0.000 0.000 0.028 0.000
#> GSM892367     3  0.2003      0.837 0.000  0 0.884 0.116 0.000 0.000
#> GSM892371     3  0.2764      0.776 0.000  0 0.864 0.100 0.028 0.008
#> GSM892375     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892341     5  0.5737      0.888 0.000  0 0.236 0.248 0.516 0.000
#> GSM892346     6  0.0260      1.000 0.000  0 0.000 0.008 0.000 0.992
#> GSM892350     4  0.3885      0.816 0.000  0 0.064 0.756 0.000 0.180
#> GSM892354     1  0.3838      0.677 0.552  0 0.000 0.000 0.448 0.000
#> GSM892356     1  0.0976      0.801 0.968  0 0.000 0.016 0.008 0.008
#> GSM892362     1  0.2854      0.779 0.792  0 0.000 0.000 0.208 0.000
#> GSM892366     3  0.2170      0.830 0.000  0 0.888 0.100 0.012 0.000
#> GSM892370     3  0.2764      0.776 0.000  0 0.864 0.100 0.028 0.008
#> GSM892374     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892343     5  0.6029      0.725 0.000  0 0.260 0.324 0.416 0.000
#> GSM892348     6  0.0260      1.000 0.000  0 0.000 0.008 0.000 0.992
#> GSM892352     5  0.5271      0.759 0.000  0 0.104 0.380 0.516 0.000
#> GSM892358     1  0.0363      0.813 0.988  0 0.000 0.000 0.012 0.000
#> GSM892360     1  0.1327      0.812 0.936  0 0.000 0.000 0.064 0.000
#> GSM892364     1  0.0820      0.811 0.972  0 0.000 0.012 0.016 0.000
#> GSM892368     3  0.2053      0.837 0.000  0 0.888 0.108 0.004 0.000
#> GSM892372     3  0.2170      0.830 0.000  0 0.888 0.100 0.012 0.000
#> GSM892376     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

k = 2
k = 3
k = 4
k = 5
k = 6

consensus_heatmap(res, k = 2)

plot of chunk tab-CV-hclust-consensus-heatmap-1

consensus_heatmap(res, k = 3)

plot of chunk tab-CV-hclust-consensus-heatmap-2

consensus_heatmap(res, k = 4)

plot of chunk tab-CV-hclust-consensus-heatmap-3

consensus_heatmap(res, k = 5)

plot of chunk tab-CV-hclust-consensus-heatmap-4

consensus_heatmap(res, k = 6)

plot of chunk tab-CV-hclust-consensus-heatmap-5

Heatmaps for the membership of samples in all partitions to see how consistent they are:

k = 2
k = 3
k = 4
k = 5
k = 6

membership_heatmap(res, k = 2)

plot of chunk tab-CV-hclust-membership-heatmap-1

membership_heatmap(res, k = 3)

plot of chunk tab-CV-hclust-membership-heatmap-2

membership_heatmap(res, k = 4)

plot of chunk tab-CV-hclust-membership-heatmap-3

membership_heatmap(res, k = 5)

plot of chunk tab-CV-hclust-membership-heatmap-4

membership_heatmap(res, k = 6)

plot of chunk tab-CV-hclust-membership-heatmap-5

Signature heatmaps where rows are scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2)

plot of chunk tab-CV-hclust-get-signatures-1

get_signatures(res, k = 3)

plot of chunk tab-CV-hclust-get-signatures-2

get_signatures(res, k = 4)

plot of chunk tab-CV-hclust-get-signatures-3

get_signatures(res, k = 5)

plot of chunk tab-CV-hclust-get-signatures-4

get_signatures(res, k = 6)

plot of chunk tab-CV-hclust-get-signatures-5

Signature heatmaps where rows are not scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-CV-hclust-get-signatures-no-scale-1

get_signatures(res, k = 3, scale_rows = FALSE)

plot of chunk tab-CV-hclust-get-signatures-no-scale-2

get_signatures(res, k = 4, scale_rows = FALSE)

plot of chunk tab-CV-hclust-get-signatures-no-scale-3

get_signatures(res, k = 5, scale_rows = FALSE)

plot of chunk tab-CV-hclust-get-signatures-no-scale-4

get_signatures(res, k = 6, scale_rows = FALSE)

plot of chunk tab-CV-hclust-get-signatures-no-scale-5

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk CV-hclust-signature_compare

# 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.

k = 2
k = 3
k = 4
k = 5
k = 6

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-CV-hclust-dimension-reduction-1

dimension_reduction(res, k = 3, method = "UMAP")

plot of chunk tab-CV-hclust-dimension-reduction-2

dimension_reduction(res, k = 4, method = "UMAP")

plot of chunk tab-CV-hclust-dimension-reduction-3

dimension_reduction(res, k = 5, method = "UMAP")

plot of chunk tab-CV-hclust-dimension-reduction-4

dimension_reduction(res, k = 6, method = "UMAP")

plot of chunk tab-CV-hclust-dimension-reduction-5

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk CV-hclust-collect-classes

test_to_known_factors(res)

#>            n tissue(p) disease.state(p) other(p) individual(p) k
#> CV:hclust 50     1.000            0.934 2.67e-07      1.42e-03 2
#> CV:hclust 50     0.776            0.931 1.69e-11      8.93e-05 3
#> CV:hclust 50     0.528            0.986 4.32e-13      2.04e-04 4
#> CV:hclust 41     0.554            0.958 3.28e-14      9.32e-06 5
#> CV:hclust 50     0.549            0.990 7.86e-20      2.17e-06 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

CV:kmeans**

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 31632 rows and 50 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)

plot of chunk CV-kmeans-collect-plots

The plots are:

The first row: a plot of the ECDF (empirical cumulative distribution function) curves of the consensus matrix for each k and the heatmap of predicted classes for each k.
The second row: heatmaps of the consensus matrix for each k.
The third row: heatmaps of the membership matrix for each k.
The fouth row: heatmaps of the signatures for each 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:

ECDF curves of the consensus matrix for each k;
1-PAC. The PAC score measures the proportion of the ambiguous subgrouping.
Mean silhouette score.
Concordance. The mean probability of fiting the consensus class ids in all partitions.
Area increased. Denote \(A_k\) as the area under the ECDF curve for current k, the area increased is defined as \(A_k - A_{k-1}\).
Rand index. The percent of pairs of samples that are both in a same cluster or both are not in a same cluster in the partition of k and k-1.
Jaccard index. The ratio of pairs of samples are both in a same cluster in the partition of k and k-1 and the pairs of samples are both in a same cluster in the partition k or k-1.

The detailed explanations of these statistics can be found in the cola vignette.

select_partition_number(res)

plot of chunk CV-kmeans-select-partition-number

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         0.4707 0.530   0.530
#> 3 3 0.707           0.921       0.860         0.3385 0.794   0.612
#> 4 4 0.619           0.866       0.836         0.1225 0.928   0.783
#> 5 5 0.736           0.691       0.822         0.0795 0.974   0.902
#> 6 6 0.715           0.703       0.785         0.0485 0.974   0.892

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

All \(k\) with Jaccard index larger than 0.95 are removed because increasing \(k\) does not provide enough extra information. If all \(k\) are removed, it is marked as no subgroup is detected.
For all \(k\) with 1-PAC score larger than 0.9, the maximal \(k\) is taken as the best \(k\), and other \(k\) are marked as optional \(k\).
If it does not fit the second rule. The \(k\) with the maximal vote of the highest 1-PAC score, highest mean silhouette, and highest concordance is taken as the best \(k\).

suggest_best_k(res)

#> [1] 2

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

k = 2
k = 3
k = 4
k = 5
k = 6

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>           class entropy silhouette p1 p2
#> GSM892342     1       0          1  1  0
#> GSM892345     1       0          1  1  0
#> GSM892349     1       0          1  1  0
#> GSM892353     1       0          1  1  0
#> GSM892355     1       0          1  1  0
#> GSM892361     1       0          1  1  0
#> GSM892365     1       0          1  1  0
#> GSM892369     1       0          1  1  0
#> GSM892373     2       0          1  0  1
#> GSM892377     2       0          1  0  1
#> GSM892381     2       0          1  0  1
#> GSM892383     2       0          1  0  1
#> GSM892387     2       0          1  0  1
#> GSM892344     1       0          1  1  0
#> GSM892347     1       0          1  1  0
#> GSM892351     1       0          1  1  0
#> GSM892357     1       0          1  1  0
#> GSM892359     1       0          1  1  0
#> GSM892363     1       0          1  1  0
#> GSM892367     1       0          1  1  0
#> GSM892371     1       0          1  1  0
#> GSM892375     2       0          1  0  1
#> GSM892379     2       0          1  0  1
#> GSM892385     2       0          1  0  1
#> GSM892389     2       0          1  0  1
#> GSM892341     1       0          1  1  0
#> GSM892346     1       0          1  1  0
#> GSM892350     1       0          1  1  0
#> GSM892354     1       0          1  1  0
#> GSM892356     1       0          1  1  0
#> GSM892362     1       0          1  1  0
#> GSM892366     1       0          1  1  0
#> GSM892370     1       0          1  1  0
#> GSM892374     2       0          1  0  1
#> GSM892378     2       0          1  0  1
#> GSM892382     2       0          1  0  1
#> GSM892384     2       0          1  0  1
#> GSM892388     2       0          1  0  1
#> GSM892343     1       0          1  1  0
#> GSM892348     1       0          1  1  0
#> GSM892352     1       0          1  1  0
#> GSM892358     1       0          1  1  0
#> GSM892360     1       0          1  1  0
#> GSM892364     1       0          1  1  0
#> GSM892368     1       0          1  1  0
#> GSM892372     1       0          1  1  0
#> GSM892376     2       0          1  0  1
#> GSM892380     2       0          1  0  1
#> GSM892386     2       0          1  0  1
#> GSM892390     2       0          1  0  1

show/hide code output

cbind(get_classes(res, k = 3), get_membership(res, k = 3))

#>           class entropy silhouette    p1    p2    p3
#> GSM892342     3  0.0000      0.935 0.000 0.000 1.000
#> GSM892345     3  0.5016      0.547 0.240 0.000 0.760
#> GSM892349     3  0.0424      0.929 0.008 0.000 0.992
#> GSM892353     1  0.5591      0.986 0.696 0.000 0.304
#> GSM892355     1  0.5591      0.986 0.696 0.000 0.304
#> GSM892361     1  0.5591      0.986 0.696 0.000 0.304
#> GSM892365     3  0.0000      0.935 0.000 0.000 1.000
#> GSM892369     3  0.0000      0.935 0.000 0.000 1.000
#> GSM892373     2  0.4452      0.909 0.192 0.808 0.000
#> GSM892377     2  0.4235      0.916 0.176 0.824 0.000
#> GSM892381     2  0.0000      0.945 0.000 1.000 0.000
#> GSM892383     2  0.1411      0.942 0.036 0.964 0.000
#> GSM892387     2  0.1860      0.945 0.052 0.948 0.000
#> GSM892344     3  0.0000      0.935 0.000 0.000 1.000
#> GSM892347     3  0.5016      0.547 0.240 0.000 0.760
#> GSM892351     3  0.0424      0.929 0.008 0.000 0.992
#> GSM892357     1  0.5591      0.986 0.696 0.000 0.304
#> GSM892359     1  0.5591      0.986 0.696 0.000 0.304
#> GSM892363     1  0.5591      0.986 0.696 0.000 0.304
#> GSM892367     3  0.0000      0.935 0.000 0.000 1.000
#> GSM892371     3  0.0000      0.935 0.000 0.000 1.000
#> GSM892375     2  0.3116      0.935 0.108 0.892 0.000
#> GSM892379     2  0.2261      0.945 0.068 0.932 0.000
#> GSM892385     2  0.3340      0.919 0.120 0.880 0.000
#> GSM892389     2  0.2165      0.947 0.064 0.936 0.000
#> GSM892341     3  0.0000      0.935 0.000 0.000 1.000
#> GSM892346     1  0.5529      0.975 0.704 0.000 0.296
#> GSM892350     3  0.5016      0.547 0.240 0.000 0.760
#> GSM892354     1  0.5591      0.986 0.696 0.000 0.304
#> GSM892356     1  0.5591      0.986 0.696 0.000 0.304
#> GSM892362     1  0.5591      0.986 0.696 0.000 0.304
#> GSM892366     3  0.0000      0.935 0.000 0.000 1.000
#> GSM892370     3  0.0000      0.935 0.000 0.000 1.000
#> GSM892374     2  0.4452      0.909 0.192 0.808 0.000
#> GSM892378     2  0.4235      0.916 0.176 0.824 0.000
#> GSM892382     2  0.0000      0.945 0.000 1.000 0.000
#> GSM892384     2  0.0237      0.945 0.004 0.996 0.000
#> GSM892388     2  0.3038      0.924 0.104 0.896 0.000
#> GSM892343     3  0.0000      0.935 0.000 0.000 1.000
#> GSM892348     1  0.6140      0.792 0.596 0.000 0.404
#> GSM892352     3  0.0424      0.929 0.008 0.000 0.992
#> GSM892358     1  0.5591      0.986 0.696 0.000 0.304
#> GSM892360     1  0.5591      0.986 0.696 0.000 0.304
#> GSM892364     1  0.5591      0.986 0.696 0.000 0.304
#> GSM892368     3  0.0000      0.935 0.000 0.000 1.000
#> GSM892372     3  0.0000      0.935 0.000 0.000 1.000
#> GSM892376     2  0.2959      0.937 0.100 0.900 0.000
#> GSM892380     2  0.0000      0.945 0.000 1.000 0.000
#> GSM892386     2  0.1964      0.934 0.056 0.944 0.000
#> GSM892390     2  0.2625      0.931 0.084 0.916 0.000

show/hide code output

cbind(get_classes(res, k = 4), get_membership(res, k = 4))

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM892342     3  0.3763      0.905 0.144 0.000 0.832 0.024
#> GSM892345     4  0.7336      0.764 0.256 0.000 0.216 0.528
#> GSM892349     3  0.4307      0.895 0.144 0.000 0.808 0.048
#> GSM892353     1  0.0188      0.996 0.996 0.000 0.000 0.004
#> GSM892355     1  0.0188      0.996 0.996 0.000 0.000 0.004
#> GSM892361     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM892365     3  0.2973      0.905 0.144 0.000 0.856 0.000
#> GSM892369     3  0.6295      0.677 0.144 0.000 0.660 0.196
#> GSM892373     2  0.4605      0.814 0.000 0.664 0.000 0.336
#> GSM892377     2  0.4807      0.839 0.000 0.728 0.024 0.248
#> GSM892381     2  0.0524      0.891 0.000 0.988 0.008 0.004
#> GSM892383     2  0.2021      0.882 0.000 0.932 0.012 0.056
#> GSM892387     2  0.3307      0.887 0.000 0.868 0.028 0.104
#> GSM892344     3  0.3763      0.905 0.144 0.000 0.832 0.024
#> GSM892347     4  0.7336      0.764 0.256 0.000 0.216 0.528
#> GSM892351     4  0.7083      0.463 0.144 0.000 0.328 0.528
#> GSM892357     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM892359     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM892363     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM892367     3  0.3300      0.902 0.144 0.000 0.848 0.008
#> GSM892371     3  0.6295      0.677 0.144 0.000 0.660 0.196
#> GSM892375     2  0.3910      0.875 0.000 0.820 0.024 0.156
#> GSM892379     2  0.2737      0.894 0.000 0.888 0.008 0.104
#> GSM892385     2  0.4817      0.829 0.000 0.784 0.088 0.128
#> GSM892389     2  0.2924      0.894 0.000 0.884 0.016 0.100
#> GSM892341     3  0.3763      0.905 0.144 0.000 0.832 0.024
#> GSM892346     4  0.5000      0.430 0.496 0.000 0.000 0.504
#> GSM892350     4  0.7336      0.764 0.256 0.000 0.216 0.528
#> GSM892354     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM892356     1  0.0188      0.996 0.996 0.000 0.000 0.004
#> GSM892362     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM892366     3  0.2973      0.905 0.144 0.000 0.856 0.000
#> GSM892370     3  0.6295      0.677 0.144 0.000 0.660 0.196
#> GSM892374     2  0.4605      0.814 0.000 0.664 0.000 0.336
#> GSM892378     2  0.4776      0.840 0.000 0.732 0.024 0.244
#> GSM892382     2  0.0524      0.891 0.000 0.988 0.008 0.004
#> GSM892384     2  0.0927      0.891 0.000 0.976 0.016 0.008
#> GSM892388     2  0.5080      0.830 0.000 0.764 0.092 0.144
#> GSM892343     3  0.4541      0.886 0.144 0.000 0.796 0.060
#> GSM892348     4  0.6229      0.631 0.416 0.000 0.056 0.528
#> GSM892352     3  0.3763      0.905 0.144 0.000 0.832 0.024
#> GSM892358     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM892360     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM892364     1  0.0188      0.996 0.996 0.000 0.000 0.004
#> GSM892368     3  0.2973      0.905 0.144 0.000 0.856 0.000
#> GSM892372     3  0.3300      0.902 0.144 0.000 0.848 0.008
#> GSM892376     2  0.3862      0.876 0.000 0.824 0.024 0.152
#> GSM892380     2  0.0817      0.893 0.000 0.976 0.000 0.024
#> GSM892386     2  0.3168      0.877 0.000 0.884 0.060 0.056
#> GSM892390     2  0.3652      0.867 0.000 0.856 0.052 0.092

show/hide code output

cbind(get_classes(res, k = 5), get_membership(res, k = 5))

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> GSM892342     3  0.2376      0.827 0.052 0.000 0.904 0.044 0.000
#> GSM892345     4  0.4280      0.850 0.088 0.000 0.140 0.772 0.000
#> GSM892349     3  0.3849      0.793 0.052 0.000 0.820 0.116 0.012
#> GSM892353     1  0.1478      0.925 0.936 0.000 0.000 0.000 0.064
#> GSM892355     1  0.1478      0.925 0.936 0.000 0.000 0.000 0.064
#> GSM892361     1  0.1671      0.938 0.924 0.000 0.000 0.000 0.076
#> GSM892365     3  0.2592      0.835 0.052 0.000 0.892 0.000 0.056
#> GSM892369     3  0.6737      0.596 0.052 0.000 0.584 0.208 0.156
#> GSM892373     5  0.4593      1.000 0.000 0.480 0.004 0.004 0.512
#> GSM892377     2  0.5392     -0.542 0.000 0.568 0.024 0.024 0.384
#> GSM892381     2  0.0324      0.619 0.000 0.992 0.004 0.004 0.000
#> GSM892383     2  0.2853      0.572 0.000 0.880 0.004 0.040 0.076
#> GSM892387     2  0.3707      0.470 0.000 0.828 0.016 0.036 0.120
#> GSM892344     3  0.2376      0.827 0.052 0.000 0.904 0.044 0.000
#> GSM892347     4  0.4280      0.850 0.088 0.000 0.140 0.772 0.000
#> GSM892351     4  0.4481      0.782 0.052 0.000 0.176 0.760 0.012
#> GSM892357     1  0.1671      0.938 0.924 0.000 0.000 0.000 0.076
#> GSM892359     1  0.1544      0.940 0.932 0.000 0.000 0.000 0.068
#> GSM892363     1  0.0510      0.939 0.984 0.000 0.000 0.000 0.016
#> GSM892367     3  0.3863      0.799 0.052 0.000 0.796 0.000 0.152
#> GSM892371     3  0.6737      0.596 0.052 0.000 0.584 0.208 0.156
#> GSM892375     2  0.4734      0.143 0.000 0.720 0.020 0.032 0.228
#> GSM892379     2  0.2957      0.533 0.000 0.860 0.008 0.012 0.120
#> GSM892385     2  0.5086      0.402 0.000 0.700 0.000 0.156 0.144
#> GSM892389     2  0.3155      0.563 0.000 0.852 0.008 0.020 0.120
#> GSM892341     3  0.2376      0.827 0.052 0.000 0.904 0.044 0.000
#> GSM892346     4  0.4576      0.688 0.268 0.000 0.000 0.692 0.040
#> GSM892350     4  0.4280      0.850 0.088 0.000 0.140 0.772 0.000
#> GSM892354     1  0.1671      0.938 0.924 0.000 0.000 0.000 0.076
#> GSM892356     1  0.1478      0.925 0.936 0.000 0.000 0.000 0.064
#> GSM892362     1  0.1608      0.939 0.928 0.000 0.000 0.000 0.072
#> GSM892366     3  0.2592      0.835 0.052 0.000 0.892 0.000 0.056
#> GSM892370     3  0.6737      0.596 0.052 0.000 0.584 0.208 0.156
#> GSM892374     5  0.4593      1.000 0.000 0.480 0.004 0.004 0.512
#> GSM892378     2  0.5392     -0.542 0.000 0.568 0.024 0.024 0.384
#> GSM892382     2  0.0324      0.619 0.000 0.992 0.004 0.004 0.000
#> GSM892384     2  0.0833      0.617 0.000 0.976 0.004 0.016 0.004
#> GSM892388     2  0.5032      0.399 0.000 0.704 0.000 0.168 0.128
#> GSM892343     3  0.3555      0.799 0.052 0.000 0.824 0.124 0.000
#> GSM892348     4  0.4288      0.758 0.224 0.000 0.004 0.740 0.032
#> GSM892352     3  0.3308      0.808 0.052 0.000 0.860 0.076 0.012
#> GSM892358     1  0.0162      0.940 0.996 0.000 0.000 0.000 0.004
#> GSM892360     1  0.1197      0.942 0.952 0.000 0.000 0.000 0.048
#> GSM892364     1  0.1410      0.927 0.940 0.000 0.000 0.000 0.060
#> GSM892368     3  0.2592      0.835 0.052 0.000 0.892 0.000 0.056
#> GSM892372     3  0.3359      0.820 0.052 0.000 0.840 0.000 0.108
#> GSM892376     2  0.4676      0.180 0.000 0.728 0.020 0.032 0.220
#> GSM892380     2  0.1106      0.613 0.000 0.964 0.000 0.012 0.024
#> GSM892386     2  0.3281      0.565 0.000 0.848 0.000 0.092 0.060
#> GSM892390     2  0.3682      0.543 0.000 0.820 0.000 0.072 0.108

show/hide code output

cbind(get_classes(res, k = 6), get_membership(res, k = 6))

#>           class entropy silhouette    p1    p2    p3    p4    p5 p6
#> GSM892342     3  0.3411      0.762 0.000 0.000 0.824 0.008 0.100 NA
#> GSM892345     4  0.2510      0.905 0.028 0.000 0.100 0.872 0.000 NA
#> GSM892349     3  0.5392      0.700 0.000 0.000 0.684 0.120 0.116 NA
#> GSM892353     1  0.4049      0.802 0.648 0.000 0.020 0.000 0.000 NA
#> GSM892355     1  0.4049      0.802 0.648 0.000 0.020 0.000 0.000 NA
#> GSM892361     1  0.1401      0.858 0.948 0.000 0.020 0.000 0.028 NA
#> GSM892365     3  0.0000      0.776 0.000 0.000 1.000 0.000 0.000 NA
#> GSM892369     3  0.6128      0.486 0.000 0.000 0.576 0.228 0.064 NA
#> GSM892373     5  0.3717      0.789 0.000 0.384 0.000 0.000 0.616 NA
#> GSM892377     5  0.5699      0.769 0.008 0.436 0.000 0.040 0.472 NA
#> GSM892381     2  0.0790      0.648 0.000 0.968 0.000 0.000 0.000 NA
#> GSM892383     2  0.3092      0.570 0.000 0.836 0.000 0.000 0.060 NA
#> GSM892387     2  0.3934      0.508 0.000 0.796 0.000 0.052 0.116 NA
#> GSM892344     3  0.3503      0.760 0.000 0.000 0.816 0.008 0.108 NA
#> GSM892347     4  0.2510      0.905 0.028 0.000 0.100 0.872 0.000 NA
#> GSM892351     4  0.3252      0.847 0.000 0.000 0.128 0.828 0.032 NA
#> GSM892357     1  0.1401      0.858 0.948 0.000 0.020 0.000 0.028 NA
#> GSM892359     1  0.0692      0.864 0.976 0.000 0.020 0.000 0.004 NA
#> GSM892363     1  0.3043      0.862 0.832 0.000 0.020 0.000 0.008 NA
#> GSM892367     3  0.3150      0.717 0.000 0.000 0.844 0.008 0.060 NA
#> GSM892371     3  0.6128      0.486 0.000 0.000 0.576 0.228 0.064 NA
#> GSM892375     2  0.4826      0.184 0.000 0.676 0.000 0.048 0.244 NA
#> GSM892379     2  0.3465      0.524 0.000 0.820 0.000 0.016 0.120 NA
#> GSM892385     2  0.5109      0.353 0.000 0.572 0.000 0.000 0.100 NA
#> GSM892389     2  0.3526      0.593 0.000 0.828 0.000 0.032 0.092 NA
#> GSM892341     3  0.3411      0.762 0.000 0.000 0.824 0.008 0.100 NA
#> GSM892346     4  0.4462      0.811 0.116 0.000 0.020 0.776 0.040 NA
#> GSM892350     4  0.2764      0.903 0.028 0.000 0.100 0.864 0.008 NA
#> GSM892354     1  0.1515      0.856 0.944 0.000 0.020 0.000 0.028 NA
#> GSM892356     1  0.4034      0.804 0.652 0.000 0.020 0.000 0.000 NA
#> GSM892362     1  0.0692      0.863 0.976 0.000 0.020 0.000 0.004 NA
#> GSM892366     3  0.0000      0.776 0.000 0.000 1.000 0.000 0.000 NA
#> GSM892370     3  0.6128      0.486 0.000 0.000 0.576 0.228 0.064 NA
#> GSM892374     5  0.3717      0.789 0.000 0.384 0.000 0.000 0.616 NA
#> GSM892378     5  0.5699      0.769 0.008 0.436 0.000 0.040 0.472 NA
#> GSM892382     2  0.0790      0.648 0.000 0.968 0.000 0.000 0.000 NA
#> GSM892384     2  0.1124      0.648 0.000 0.956 0.000 0.000 0.008 NA
#> GSM892388     2  0.5331      0.371 0.004 0.588 0.000 0.008 0.092 NA
#> GSM892343     3  0.4990      0.734 0.000 0.000 0.720 0.096 0.116 NA
#> GSM892348     4  0.4308      0.852 0.088 0.000 0.040 0.796 0.032 NA
#> GSM892352     3  0.4882      0.724 0.000 0.000 0.728 0.068 0.124 NA
#> GSM892358     1  0.2633      0.867 0.864 0.000 0.020 0.000 0.004 NA
#> GSM892360     1  0.1889      0.869 0.920 0.000 0.020 0.000 0.004 NA
#> GSM892364     1  0.4071      0.811 0.672 0.000 0.020 0.000 0.004 NA
#> GSM892368     3  0.0000      0.776 0.000 0.000 1.000 0.000 0.000 NA
#> GSM892372     3  0.1821      0.757 0.000 0.000 0.928 0.008 0.024 NA
#> GSM892376     2  0.4743      0.190 0.000 0.684 0.000 0.044 0.240 NA
#> GSM892380     2  0.1341      0.634 0.000 0.948 0.000 0.000 0.028 NA
#> GSM892386     2  0.4497      0.560 0.012 0.768 0.000 0.036 0.064 NA
#> GSM892390     2  0.4075      0.560 0.000 0.760 0.000 0.012 0.060 NA

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

k = 2
k = 3
k = 4
k = 5
k = 6

consensus_heatmap(res, k = 2)

plot of chunk tab-CV-kmeans-consensus-heatmap-1

consensus_heatmap(res, k = 3)

plot of chunk tab-CV-kmeans-consensus-heatmap-2

consensus_heatmap(res, k = 4)

plot of chunk tab-CV-kmeans-consensus-heatmap-3

consensus_heatmap(res, k = 5)

plot of chunk tab-CV-kmeans-consensus-heatmap-4

consensus_heatmap(res, k = 6)

plot of chunk tab-CV-kmeans-consensus-heatmap-5

Heatmaps for the membership of samples in all partitions to see how consistent they are:

k = 2
k = 3
k = 4
k = 5
k = 6

membership_heatmap(res, k = 2)

plot of chunk tab-CV-kmeans-membership-heatmap-1

membership_heatmap(res, k = 3)

plot of chunk tab-CV-kmeans-membership-heatmap-2

membership_heatmap(res, k = 4)

plot of chunk tab-CV-kmeans-membership-heatmap-3

membership_heatmap(res, k = 5)

plot of chunk tab-CV-kmeans-membership-heatmap-4

membership_heatmap(res, k = 6)

plot of chunk tab-CV-kmeans-membership-heatmap-5

Signature heatmaps where rows are scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2)

plot of chunk tab-CV-kmeans-get-signatures-1

get_signatures(res, k = 3)

plot of chunk tab-CV-kmeans-get-signatures-2

get_signatures(res, k = 4)

plot of chunk tab-CV-kmeans-get-signatures-3

get_signatures(res, k = 5)

plot of chunk tab-CV-kmeans-get-signatures-4

get_signatures(res, k = 6)

plot of chunk tab-CV-kmeans-get-signatures-5

Signature heatmaps where rows are not scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-CV-kmeans-get-signatures-no-scale-1

get_signatures(res, k = 3, scale_rows = FALSE)

plot of chunk tab-CV-kmeans-get-signatures-no-scale-2

get_signatures(res, k = 4, scale_rows = FALSE)

plot of chunk tab-CV-kmeans-get-signatures-no-scale-3

get_signatures(res, k = 5, scale_rows = FALSE)

plot of chunk tab-CV-kmeans-get-signatures-no-scale-4

get_signatures(res, k = 6, scale_rows = FALSE)

plot of chunk tab-CV-kmeans-get-signatures-no-scale-5

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk CV-kmeans-signature_compare

# 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.

k = 2
k = 3
k = 4
k = 5
k = 6

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-CV-kmeans-dimension-reduction-1

dimension_reduction(res, k = 3, method = "UMAP")

plot of chunk tab-CV-kmeans-dimension-reduction-2

dimension_reduction(res, k = 4, method = "UMAP")

plot of chunk tab-CV-kmeans-dimension-reduction-3

dimension_reduction(res, k = 5, method = "UMAP")

plot of chunk tab-CV-kmeans-dimension-reduction-4

dimension_reduction(res, k = 6, method = "UMAP")

plot of chunk tab-CV-kmeans-dimension-reduction-5

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk CV-kmeans-collect-classes

test_to_known_factors(res)

#>            n tissue(p) disease.state(p) other(p) individual(p) k
#> CV:kmeans 50     1.000            0.934 2.67e-07      1.42e-03 2
#> CV:kmeans 50     0.776            0.931 1.69e-11      8.93e-05 3
#> CV:kmeans 48     1.000            0.987 4.74e-15      7.28e-06 4
#> CV:kmeans 43     0.999            0.719 1.42e-16      7.38e-07 5
#> CV:kmeans 43     0.999            0.420 5.80e-14      3.43e-06 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

CV:skmeans*

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 31632 rows and 50 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 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)

plot of chunk CV-skmeans-collect-plots

The plots are:

The first row: a plot of the ECDF (empirical cumulative distribution function) curves of the consensus matrix for each k and the heatmap of predicted classes for each k.
The second row: heatmaps of the consensus matrix for each k.
The third row: heatmaps of the membership matrix for each k.
The fouth row: heatmaps of the signatures for each 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:

ECDF curves of the consensus matrix for each k;
1-PAC. The PAC score measures the proportion of the ambiguous subgrouping.
Mean silhouette score.
Concordance. The mean probability of fiting the consensus class ids in all partitions.
Area increased. Denote \(A_k\) as the area under the ECDF curve for current k, the area increased is defined as \(A_k - A_{k-1}\).
Rand index. The percent of pairs of samples that are both in a same cluster or both are not in a same cluster in the partition of k and k-1.
Jaccard index. The ratio of pairs of samples are both in a same cluster in the partition of k and k-1 and the pairs of samples are both in a same cluster in the partition k or k-1.

The detailed explanations of these statistics can be found in the cola vignette.

select_partition_number(res)

plot of chunk CV-skmeans-select-partition-number

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         0.4707 0.530   0.530
#> 3 3 1.000           0.966       0.984         0.4404 0.792   0.607
#> 4 4 0.958           0.894       0.949         0.0974 0.899   0.700
#> 5 5 0.971           0.870       0.924         0.0341 0.985   0.942
#> 6 6 0.914           0.812       0.869         0.0239 0.980   0.918

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

All \(k\) with Jaccard index larger than 0.95 are removed because increasing \(k\) does not provide enough extra information. If all \(k\) are removed, it is marked as no subgroup is detected.
For all \(k\) with 1-PAC score larger than 0.9, the maximal \(k\) is taken as the best \(k\), and other \(k\) are marked as optional \(k\).
If it does not fit the second rule. The \(k\) with the maximal vote of the highest 1-PAC score, highest mean silhouette, and highest concordance is taken as the best \(k\).

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.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

k = 2
k = 3
k = 4
k = 5
k = 6

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>           class entropy silhouette p1 p2
#> GSM892342     1       0          1  1  0
#> GSM892345     1       0          1  1  0
#> GSM892349     1       0          1  1  0
#> GSM892353     1       0          1  1  0
#> GSM892355     1       0          1  1  0
#> GSM892361     1       0          1  1  0
#> GSM892365     1       0          1  1  0
#> GSM892369     1       0          1  1  0
#> GSM892373     2       0          1  0  1
#> GSM892377     2       0          1  0  1
#> GSM892381     2       0          1  0  1
#> GSM892383     2       0          1  0  1
#> GSM892387     2       0          1  0  1
#> GSM892344     1       0          1  1  0
#> GSM892347     1       0          1  1  0
#> GSM892351     1       0          1  1  0
#> GSM892357     1       0          1  1  0
#> GSM892359     1       0          1  1  0
#> GSM892363     1       0          1  1  0
#> GSM892367     1       0          1  1  0
#> GSM892371     1       0          1  1  0
#> GSM892375     2       0          1  0  1
#> GSM892379     2       0          1  0  1
#> GSM892385     2       0          1  0  1
#> GSM892389     2       0          1  0  1
#> GSM892341     1       0          1  1  0
#> GSM892346     1       0          1  1  0
#> GSM892350     1       0          1  1  0
#> GSM892354     1       0          1  1  0
#> GSM892356     1       0          1  1  0
#> GSM892362     1       0          1  1  0
#> GSM892366     1       0          1  1  0
#> GSM892370     1       0          1  1  0
#> GSM892374     2       0          1  0  1
#> GSM892378     2       0          1  0  1
#> GSM892382     2       0          1  0  1
#> GSM892384     2       0          1  0  1
#> GSM892388     2       0          1  0  1
#> GSM892343     1       0          1  1  0
#> GSM892348     1       0          1  1  0
#> GSM892352     1       0          1  1  0
#> GSM892358     1       0          1  1  0
#> GSM892360     1       0          1  1  0
#> GSM892364     1       0          1  1  0
#> GSM892368     1       0          1  1  0
#> GSM892372     1       0          1  1  0
#> GSM892376     2       0          1  0  1
#> GSM892380     2       0          1  0  1
#> GSM892386     2       0          1  0  1
#> GSM892390     2       0          1  0  1

show/hide code output

cbind(get_classes(res, k = 3), get_membership(res, k = 3))

#>           class entropy silhouette    p1 p2    p3
#> GSM892342     3   0.000      1.000 0.000  0 1.000
#> GSM892345     1   0.529      0.680 0.732  0 0.268
#> GSM892349     3   0.000      1.000 0.000  0 1.000
#> GSM892353     1   0.000      0.948 1.000  0 0.000
#> GSM892355     1   0.000      0.948 1.000  0 0.000
#> GSM892361     1   0.000      0.948 1.000  0 0.000
#> GSM892365     3   0.000      1.000 0.000  0 1.000
#> GSM892369     3   0.000      1.000 0.000  0 1.000
#> GSM892373     2   0.000      1.000 0.000  1 0.000
#> GSM892377     2   0.000      1.000 0.000  1 0.000
#> GSM892381     2   0.000      1.000 0.000  1 0.000
#> GSM892383     2   0.000      1.000 0.000  1 0.000
#> GSM892387     2   0.000      1.000 0.000  1 0.000
#> GSM892344     3   0.000      1.000 0.000  0 1.000
#> GSM892347     1   0.529      0.680 0.732  0 0.268
#> GSM892351     3   0.000      1.000 0.000  0 1.000
#> GSM892357     1   0.000      0.948 1.000  0 0.000
#> GSM892359     1   0.000      0.948 1.000  0 0.000
#> GSM892363     1   0.000      0.948 1.000  0 0.000
#> GSM892367     3   0.000      1.000 0.000  0 1.000
#> GSM892371     3   0.000      1.000 0.000  0 1.000
#> GSM892375     2   0.000      1.000 0.000  1 0.000
#> GSM892379     2   0.000      1.000 0.000  1 0.000
#> GSM892385     2   0.000      1.000 0.000  1 0.000
#> GSM892389     2   0.000      1.000 0.000  1 0.000
#> GSM892341     3   0.000      1.000 0.000  0 1.000
#> GSM892346     1   0.000      0.948 1.000  0 0.000
#> GSM892350     1   0.529      0.680 0.732  0 0.268
#> GSM892354     1   0.000      0.948 1.000  0 0.000
#> GSM892356     1   0.000      0.948 1.000  0 0.000
#> GSM892362     1   0.000      0.948 1.000  0 0.000
#> GSM892366     3   0.000      1.000 0.000  0 1.000
#> GSM892370     3   0.000      1.000 0.000  0 1.000
#> GSM892374     2   0.000      1.000 0.000  1 0.000
#> GSM892378     2   0.000      1.000 0.000  1 0.000
#> GSM892382     2   0.000      1.000 0.000  1 0.000
#> GSM892384     2   0.000      1.000 0.000  1 0.000
#> GSM892388     2   0.000      1.000 0.000  1 0.000
#> GSM892343     3   0.000      1.000 0.000  0 1.000
#> GSM892348     1   0.000      0.948 1.000  0 0.000
#> GSM892352     3   0.000      1.000 0.000  0 1.000
#> GSM892358     1   0.000      0.948 1.000  0 0.000
#> GSM892360     1   0.000      0.948 1.000  0 0.000
#> GSM892364     1   0.000      0.948 1.000  0 0.000
#> GSM892368     3   0.000      1.000 0.000  0 1.000
#> GSM892372     3   0.000      1.000 0.000  0 1.000
#> GSM892376     2   0.000      1.000 0.000  1 0.000
#> GSM892380     2   0.000      1.000 0.000  1 0.000
#> GSM892386     2   0.000      1.000 0.000  1 0.000
#> GSM892390     2   0.000      1.000 0.000  1 0.000

show/hide code output

cbind(get_classes(res, k = 4), get_membership(res, k = 4))

#>           class entropy silhouette    p1 p2    p3    p4
#> GSM892342     3  0.1302      0.886 0.000  0 0.956 0.044
#> GSM892345     4  0.0921      0.780 0.028  0 0.000 0.972
#> GSM892349     3  0.4877      0.365 0.000  0 0.592 0.408
#> GSM892353     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892355     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892361     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892365     3  0.0000      0.889 0.000  0 1.000 0.000
#> GSM892369     4  0.4977      0.363 0.000  0 0.460 0.540
#> GSM892373     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892344     3  0.1302      0.886 0.000  0 0.956 0.044
#> GSM892347     4  0.0921      0.781 0.028  0 0.000 0.972
#> GSM892351     4  0.0817      0.763 0.000  0 0.024 0.976
#> GSM892357     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892359     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892363     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892367     3  0.0469      0.883 0.000  0 0.988 0.012
#> GSM892371     4  0.4961      0.385 0.000  0 0.448 0.552
#> GSM892375     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892341     3  0.1302      0.886 0.000  0 0.956 0.044
#> GSM892346     4  0.1716      0.769 0.064  0 0.000 0.936
#> GSM892350     4  0.0817      0.781 0.024  0 0.000 0.976
#> GSM892354     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892356     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892362     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892366     3  0.0000      0.889 0.000  0 1.000 0.000
#> GSM892370     4  0.4977      0.363 0.000  0 0.460 0.540
#> GSM892374     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892343     3  0.3024      0.803 0.000  0 0.852 0.148
#> GSM892348     4  0.1637      0.772 0.060  0 0.000 0.940
#> GSM892352     3  0.3837      0.699 0.000  0 0.776 0.224
#> GSM892358     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892360     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892364     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892368     3  0.0000      0.889 0.000  0 1.000 0.000
#> GSM892372     3  0.0188      0.888 0.000  0 0.996 0.004
#> GSM892376     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 5), get_membership(res, k = 5))

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> GSM892342     5  0.4101      0.653 0.000 0.000 0.372 0.000 0.628
#> GSM892345     4  0.0703      0.971 0.000 0.000 0.024 0.976 0.000
#> GSM892349     5  0.6775      0.426 0.000 0.000 0.348 0.276 0.376
#> GSM892353     1  0.1121      0.973 0.956 0.000 0.044 0.000 0.000
#> GSM892355     1  0.0880      0.981 0.968 0.000 0.032 0.000 0.000
#> GSM892361     1  0.0162      0.988 0.996 0.000 0.004 0.000 0.000
#> GSM892365     5  0.0162      0.482 0.000 0.000 0.004 0.000 0.996
#> GSM892369     3  0.5556      0.984 0.000 0.000 0.524 0.072 0.404
#> GSM892373     2  0.0000      0.998 0.000 1.000 0.000 0.000 0.000
#> GSM892377     2  0.0162      0.998 0.000 0.996 0.004 0.000 0.000
#> GSM892381     2  0.0000      0.998 0.000 1.000 0.000 0.000 0.000
#> GSM892383     2  0.0000      0.998 0.000 1.000 0.000 0.000 0.000
#> GSM892387     2  0.0000      0.998 0.000 1.000 0.000 0.000 0.000
#> GSM892344     5  0.4088      0.653 0.000 0.000 0.368 0.000 0.632
#> GSM892347     4  0.0404      0.974 0.000 0.000 0.012 0.988 0.000
#> GSM892351     4  0.1430      0.943 0.000 0.000 0.052 0.944 0.004
#> GSM892357     1  0.0162      0.988 0.996 0.000 0.004 0.000 0.000
#> GSM892359     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000
#> GSM892363     1  0.0162      0.989 0.996 0.000 0.004 0.000 0.000
#> GSM892367     5  0.3796     -0.378 0.000 0.000 0.300 0.000 0.700
#> GSM892371     3  0.5658      0.984 0.000 0.000 0.512 0.080 0.408
#> GSM892375     2  0.0000      0.998 0.000 1.000 0.000 0.000 0.000
#> GSM892379     2  0.0162      0.998 0.000 0.996 0.004 0.000 0.000
#> GSM892385     2  0.0000      0.998 0.000 1.000 0.000 0.000 0.000
#> GSM892389     2  0.0162      0.998 0.000 0.996 0.004 0.000 0.000
#> GSM892341     5  0.4101      0.653 0.000 0.000 0.372 0.000 0.628
#> GSM892346     4  0.1018      0.963 0.016 0.000 0.016 0.968 0.000
#> GSM892350     4  0.0162      0.974 0.000 0.000 0.004 0.996 0.000
#> GSM892354     1  0.0162      0.988 0.996 0.000 0.004 0.000 0.000
#> GSM892356     1  0.0794      0.982 0.972 0.000 0.028 0.000 0.000
#> GSM892362     1  0.0162      0.988 0.996 0.000 0.004 0.000 0.000
#> GSM892366     5  0.0000      0.479 0.000 0.000 0.000 0.000 1.000
#> GSM892370     3  0.5524      0.983 0.000 0.000 0.516 0.068 0.416
#> GSM892374     2  0.0162      0.998 0.000 0.996 0.004 0.000 0.000
#> GSM892378     2  0.0162      0.998 0.000 0.996 0.004 0.000 0.000
#> GSM892382     2  0.0000      0.998 0.000 1.000 0.000 0.000 0.000
#> GSM892384     2  0.0000      0.998 0.000 1.000 0.000 0.000 0.000
#> GSM892388     2  0.0000      0.998 0.000 1.000 0.000 0.000 0.000
#> GSM892343     5  0.5691      0.607 0.000 0.000 0.400 0.084 0.516
#> GSM892348     4  0.0451      0.973 0.004 0.000 0.008 0.988 0.000
#> GSM892352     5  0.5281      0.625 0.000 0.000 0.400 0.052 0.548
#> GSM892358     1  0.0290      0.988 0.992 0.000 0.008 0.000 0.000
#> GSM892360     1  0.0162      0.989 0.996 0.000 0.004 0.000 0.000
#> GSM892364     1  0.0794      0.983 0.972 0.000 0.028 0.000 0.000
#> GSM892368     5  0.0290      0.469 0.000 0.000 0.008 0.000 0.992
#> GSM892372     5  0.2074      0.291 0.000 0.000 0.104 0.000 0.896
#> GSM892376     2  0.0162      0.998 0.000 0.996 0.004 0.000 0.000
#> GSM892380     2  0.0162      0.998 0.000 0.996 0.004 0.000 0.000
#> GSM892386     2  0.0000      0.998 0.000 1.000 0.000 0.000 0.000
#> GSM892390     2  0.0162      0.998 0.000 0.996 0.004 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 6), get_membership(res, k = 6))

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> GSM892342     3  0.3828    0.05925 0.000 0.000 0.560 0.000 0.440 0.000
#> GSM892345     4  0.0858    0.89632 0.000 0.000 0.000 0.968 0.028 0.004
#> GSM892349     5  0.6413    0.49984 0.000 0.000 0.180 0.296 0.484 0.040
#> GSM892353     1  0.3439    0.86303 0.808 0.000 0.000 0.000 0.120 0.072
#> GSM892355     1  0.2554    0.91079 0.876 0.000 0.000 0.000 0.076 0.048
#> GSM892361     1  0.0777    0.94319 0.972 0.000 0.000 0.000 0.024 0.004
#> GSM892365     3  0.0405    0.58541 0.000 0.000 0.988 0.000 0.008 0.004
#> GSM892369     6  0.3933    0.98230 0.000 0.000 0.248 0.036 0.000 0.716
#> GSM892373     2  0.1572    0.96683 0.000 0.936 0.000 0.000 0.036 0.028
#> GSM892377     2  0.1003    0.97371 0.000 0.964 0.000 0.000 0.016 0.020
#> GSM892381     2  0.0725    0.97726 0.000 0.976 0.000 0.000 0.012 0.012
#> GSM892383     2  0.0914    0.97617 0.000 0.968 0.000 0.000 0.016 0.016
#> GSM892387     2  0.0909    0.97790 0.000 0.968 0.000 0.000 0.020 0.012
#> GSM892344     3  0.3854    0.00777 0.000 0.000 0.536 0.000 0.464 0.000
#> GSM892347     4  0.1088    0.89610 0.000 0.000 0.000 0.960 0.024 0.016
#> GSM892351     4  0.2981    0.79421 0.000 0.000 0.000 0.820 0.160 0.020
#> GSM892357     1  0.0777    0.94319 0.972 0.000 0.000 0.000 0.024 0.004
#> GSM892359     1  0.0520    0.94550 0.984 0.000 0.000 0.000 0.008 0.008
#> GSM892363     1  0.1334    0.94027 0.948 0.000 0.000 0.000 0.020 0.032
#> GSM892367     3  0.3371    0.05566 0.000 0.000 0.708 0.000 0.000 0.292
#> GSM892371     6  0.4306    0.97453 0.000 0.000 0.248 0.044 0.008 0.700
#> GSM892375     2  0.1261    0.97399 0.000 0.952 0.000 0.000 0.024 0.024
#> GSM892379     2  0.0725    0.97777 0.000 0.976 0.000 0.000 0.012 0.012
#> GSM892385     2  0.1003    0.97267 0.000 0.964 0.000 0.000 0.016 0.020
#> GSM892389     2  0.0717    0.97828 0.000 0.976 0.000 0.000 0.016 0.008
#> GSM892341     3  0.3810    0.06891 0.000 0.000 0.572 0.000 0.428 0.000
#> GSM892346     4  0.2816    0.83584 0.036 0.000 0.000 0.876 0.028 0.060
#> GSM892350     4  0.1701    0.87652 0.000 0.000 0.000 0.920 0.072 0.008
#> GSM892354     1  0.0806    0.94354 0.972 0.000 0.000 0.000 0.020 0.008
#> GSM892356     1  0.2119    0.92274 0.904 0.000 0.000 0.000 0.060 0.036
#> GSM892362     1  0.0717    0.94442 0.976 0.000 0.000 0.000 0.016 0.008
#> GSM892366     3  0.0260    0.58402 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM892370     6  0.4049    0.97929 0.000 0.000 0.256 0.032 0.004 0.708
#> GSM892374     2  0.1261    0.96853 0.000 0.952 0.000 0.000 0.024 0.024
#> GSM892378     2  0.1003    0.97273 0.000 0.964 0.000 0.000 0.016 0.020
#> GSM892382     2  0.0909    0.97717 0.000 0.968 0.000 0.000 0.020 0.012
#> GSM892384     2  0.0508    0.97857 0.000 0.984 0.000 0.000 0.012 0.004
#> GSM892388     2  0.1088    0.97381 0.000 0.960 0.000 0.000 0.024 0.016
#> GSM892343     5  0.6286    0.47188 0.000 0.000 0.240 0.112 0.560 0.088
#> GSM892348     4  0.1624    0.88005 0.004 0.000 0.000 0.936 0.020 0.040
#> GSM892352     5  0.5575    0.37705 0.000 0.000 0.344 0.080 0.548 0.028
#> GSM892358     1  0.0820    0.94437 0.972 0.000 0.000 0.000 0.016 0.012
#> GSM892360     1  0.0508    0.94503 0.984 0.000 0.000 0.000 0.004 0.012
#> GSM892364     1  0.2905    0.90124 0.852 0.000 0.000 0.000 0.084 0.064
#> GSM892368     3  0.0146    0.58487 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM892372     3  0.2446    0.50087 0.000 0.000 0.864 0.000 0.012 0.124
#> GSM892376     2  0.0820    0.97679 0.000 0.972 0.000 0.000 0.012 0.016
#> GSM892380     2  0.0622    0.97831 0.000 0.980 0.000 0.000 0.012 0.008
#> GSM892386     2  0.0725    0.97656 0.000 0.976 0.000 0.000 0.012 0.012
#> GSM892390     2  0.1003    0.97352 0.000 0.964 0.000 0.000 0.016 0.020

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

k = 2
k = 3
k = 4
k = 5
k = 6

consensus_heatmap(res, k = 2)

plot of chunk tab-CV-skmeans-consensus-heatmap-1

consensus_heatmap(res, k = 3)

plot of chunk tab-CV-skmeans-consensus-heatmap-2

consensus_heatmap(res, k = 4)

plot of chunk tab-CV-skmeans-consensus-heatmap-3

consensus_heatmap(res, k = 5)

plot of chunk tab-CV-skmeans-consensus-heatmap-4

consensus_heatmap(res, k = 6)

plot of chunk tab-CV-skmeans-consensus-heatmap-5

Heatmaps for the membership of samples in all partitions to see how consistent they are:

k = 2
k = 3
k = 4
k = 5
k = 6

membership_heatmap(res, k = 2)

plot of chunk tab-CV-skmeans-membership-heatmap-1

membership_heatmap(res, k = 3)

plot of chunk tab-CV-skmeans-membership-heatmap-2

membership_heatmap(res, k = 4)

plot of chunk tab-CV-skmeans-membership-heatmap-3

membership_heatmap(res, k = 5)

plot of chunk tab-CV-skmeans-membership-heatmap-4

membership_heatmap(res, k = 6)

plot of chunk tab-CV-skmeans-membership-heatmap-5

Signature heatmaps where rows are scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2)

plot of chunk tab-CV-skmeans-get-signatures-1

get_signatures(res, k = 3)

plot of chunk tab-CV-skmeans-get-signatures-2

get_signatures(res, k = 4)

plot of chunk tab-CV-skmeans-get-signatures-3

get_signatures(res, k = 5)

plot of chunk tab-CV-skmeans-get-signatures-4

get_signatures(res, k = 6)

plot of chunk tab-CV-skmeans-get-signatures-5

Signature heatmaps where rows are not scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-CV-skmeans-get-signatures-no-scale-1

get_signatures(res, k = 3, scale_rows = FALSE)

plot of chunk tab-CV-skmeans-get-signatures-no-scale-2

get_signatures(res, k = 4, scale_rows = FALSE)

plot of chunk tab-CV-skmeans-get-signatures-no-scale-3

get_signatures(res, k = 5, scale_rows = FALSE)

plot of chunk tab-CV-skmeans-get-signatures-no-scale-4

get_signatures(res, k = 6, scale_rows = FALSE)

plot of chunk tab-CV-skmeans-get-signatures-no-scale-5

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk CV-skmeans-signature_compare

# 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.

k = 2
k = 3
k = 4
k = 5
k = 6

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-CV-skmeans-dimension-reduction-1

dimension_reduction(res, k = 3, method = "UMAP")

plot of chunk tab-CV-skmeans-dimension-reduction-2

dimension_reduction(res, k = 4, method = "UMAP")

plot of chunk tab-CV-skmeans-dimension-reduction-3

dimension_reduction(res, k = 5, method = "UMAP")

plot of chunk tab-CV-skmeans-dimension-reduction-4

dimension_reduction(res, k = 6, method = "UMAP")

plot of chunk tab-CV-skmeans-dimension-reduction-5

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk CV-skmeans-collect-classes

test_to_known_factors(res)

#>             n tissue(p) disease.state(p) other(p) individual(p) k
#> CV:skmeans 50     1.000            0.934 2.67e-07      1.42e-03 2
#> CV:skmeans 50     0.939            0.875 8.67e-12      3.79e-05 3
#> CV:skmeans 46     0.957            0.891 2.21e-14      7.92e-06 4
#> CV:skmeans 44     0.970            0.955 1.80e-18      6.18e-07 5
#> CV:skmeans 43     0.860            0.987 2.10e-16      4.86e-06 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

CV:pam**

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 31632 rows and 50 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#>   Subgroups are detected by 'pam' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 6.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk CV-pam-collect-plots

The plots are:

The first row: a plot of the ECDF (empirical cumulative distribution function) curves of the consensus matrix for each k and the heatmap of predicted classes for each k.
The second row: heatmaps of the consensus matrix for each k.
The third row: heatmaps of the membership matrix for each k.
The fouth row: heatmaps of the signatures for each 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:

ECDF curves of the consensus matrix for each k;
1-PAC. The PAC score measures the proportion of the ambiguous subgrouping.
Mean silhouette score.
Concordance. The mean probability of fiting the consensus class ids in all partitions.
Area increased. Denote \(A_k\) as the area under the ECDF curve for current k, the area increased is defined as \(A_k - A_{k-1}\).
Rand index. The percent of pairs of samples that are both in a same cluster or both are not in a same cluster in the partition of k and k-1.
Jaccard index. The ratio of pairs of samples are both in a same cluster in the partition of k and k-1 and the pairs of samples are both in a same cluster in the partition k or k-1.

The detailed explanations of these statistics can be found in the cola vignette.

select_partition_number(res)

plot of chunk CV-pam-select-partition-number

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         0.4707 0.530   0.530
#> 3 3 0.974           0.953       0.976         0.4381 0.792   0.607
#> 4 4 0.975           0.939       0.972         0.1002 0.899   0.700
#> 5 5 0.999           0.966       0.984         0.0286 0.977   0.910
#> 6 6 1.000           0.966       0.981         0.0297 0.953   0.810

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

All \(k\) with Jaccard index larger than 0.95 are removed because increasing \(k\) does not provide enough extra information. If all \(k\) are removed, it is marked as no subgroup is detected.
For all \(k\) with 1-PAC score larger than 0.9, the maximal \(k\) is taken as the best \(k\), and other \(k\) are marked as optional \(k\).
If it does not fit the second rule. The \(k\) with the maximal vote of the highest 1-PAC score, highest mean silhouette, and highest concordance is taken as the best \(k\).

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.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

k = 2
k = 3
k = 4
k = 5
k = 6

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>           class entropy silhouette p1 p2
#> GSM892342     1       0          1  1  0
#> GSM892345     1       0          1  1  0
#> GSM892349     1       0          1  1  0
#> GSM892353     1       0          1  1  0
#> GSM892355     1       0          1  1  0
#> GSM892361     1       0          1  1  0
#> GSM892365     1       0          1  1  0
#> GSM892369     1       0          1  1  0
#> GSM892373     2       0          1  0  1
#> GSM892377     2       0          1  0  1
#> GSM892381     2       0          1  0  1
#> GSM892383     2       0          1  0  1
#> GSM892387     2       0          1  0  1
#> GSM892344     1       0          1  1  0
#> GSM892347     1       0          1  1  0
#> GSM892351     1       0          1  1  0
#> GSM892357     1       0          1  1  0
#> GSM892359     1       0          1  1  0
#> GSM892363     1       0          1  1  0
#> GSM892367     1       0          1  1  0
#> GSM892371     1       0          1  1  0
#> GSM892375     2       0          1  0  1
#> GSM892379     2       0          1  0  1
#> GSM892385     2       0          1  0  1
#> GSM892389     2       0          1  0  1
#> GSM892341     1       0          1  1  0
#> GSM892346     1       0          1  1  0
#> GSM892350     1       0          1  1  0
#> GSM892354     1       0          1  1  0
#> GSM892356     1       0          1  1  0
#> GSM892362     1       0          1  1  0
#> GSM892366     1       0          1  1  0
#> GSM892370     1       0          1  1  0
#> GSM892374     2       0          1  0  1
#> GSM892378     2       0          1  0  1
#> GSM892382     2       0          1  0  1
#> GSM892384     2       0          1  0  1
#> GSM892388     2       0          1  0  1
#> GSM892343     1       0          1  1  0
#> GSM892348     1       0          1  1  0
#> GSM892352     1       0          1  1  0
#> GSM892358     1       0          1  1  0
#> GSM892360     1       0          1  1  0
#> GSM892364     1       0          1  1  0
#> GSM892368     1       0          1  1  0
#> GSM892372     1       0          1  1  0
#> GSM892376     2       0          1  0  1
#> GSM892380     2       0          1  0  1
#> GSM892386     2       0          1  0  1
#> GSM892390     2       0          1  0  1

show/hide code output

cbind(get_classes(res, k = 3), get_membership(res, k = 3))

#>           class entropy silhouette    p1 p2    p3
#> GSM892342     3  0.0000      1.000 0.000  0 1.000
#> GSM892345     1  0.5760      0.606 0.672  0 0.328
#> GSM892349     3  0.0000      1.000 0.000  0 1.000
#> GSM892353     1  0.1643      0.901 0.956  0 0.044
#> GSM892355     1  0.0000      0.924 1.000  0 0.000
#> GSM892361     1  0.0000      0.924 1.000  0 0.000
#> GSM892365     3  0.0000      1.000 0.000  0 1.000
#> GSM892369     3  0.0000      1.000 0.000  0 1.000
#> GSM892373     2  0.0000      1.000 0.000  1 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000
#> GSM892344     3  0.0000      1.000 0.000  0 1.000
#> GSM892347     1  0.5431      0.676 0.716  0 0.284
#> GSM892351     3  0.0000      1.000 0.000  0 1.000
#> GSM892357     1  0.0000      0.924 1.000  0 0.000
#> GSM892359     1  0.0000      0.924 1.000  0 0.000
#> GSM892363     1  0.0000      0.924 1.000  0 0.000
#> GSM892367     3  0.0000      1.000 0.000  0 1.000
#> GSM892371     3  0.0000      1.000 0.000  0 1.000
#> GSM892375     2  0.0000      1.000 0.000  1 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000
#> GSM892341     3  0.0000      1.000 0.000  0 1.000
#> GSM892346     1  0.0424      0.921 0.992  0 0.008
#> GSM892350     1  0.5650      0.634 0.688  0 0.312
#> GSM892354     1  0.0000      0.924 1.000  0 0.000
#> GSM892356     1  0.0000      0.924 1.000  0 0.000
#> GSM892362     1  0.0000      0.924 1.000  0 0.000
#> GSM892366     3  0.0000      1.000 0.000  0 1.000
#> GSM892370     3  0.0000      1.000 0.000  0 1.000
#> GSM892374     2  0.0000      1.000 0.000  1 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000
#> GSM892343     3  0.0000      1.000 0.000  0 1.000
#> GSM892348     1  0.4605      0.769 0.796  0 0.204
#> GSM892352     3  0.0000      1.000 0.000  0 1.000
#> GSM892358     1  0.0000      0.924 1.000  0 0.000
#> GSM892360     1  0.0000      0.924 1.000  0 0.000
#> GSM892364     1  0.0237      0.923 0.996  0 0.004
#> GSM892368     3  0.0000      1.000 0.000  0 1.000
#> GSM892372     3  0.0000      1.000 0.000  0 1.000
#> GSM892376     2  0.0000      1.000 0.000  1 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000

show/hide code output

cbind(get_classes(res, k = 4), get_membership(res, k = 4))

#>           class entropy silhouette    p1 p2    p3    p4
#> GSM892342     3  0.0000      0.955 0.000  0 1.000 0.000
#> GSM892345     4  0.0000      0.864 0.000  0 0.000 1.000
#> GSM892349     4  0.4543      0.556 0.000  0 0.324 0.676
#> GSM892353     1  0.0188      0.995 0.996  0 0.000 0.004
#> GSM892355     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892361     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892365     3  0.0000      0.955 0.000  0 1.000 0.000
#> GSM892369     3  0.3074      0.831 0.000  0 0.848 0.152
#> GSM892373     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892344     3  0.0921      0.947 0.000  0 0.972 0.028
#> GSM892347     4  0.0000      0.864 0.000  0 0.000 1.000
#> GSM892351     4  0.0000      0.864 0.000  0 0.000 1.000
#> GSM892357     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892359     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892363     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892367     3  0.0000      0.955 0.000  0 1.000 0.000
#> GSM892371     4  0.4817      0.327 0.000  0 0.388 0.612
#> GSM892375     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892341     3  0.0817      0.948 0.000  0 0.976 0.024
#> GSM892346     4  0.1022      0.843 0.032  0 0.000 0.968
#> GSM892350     4  0.0000      0.864 0.000  0 0.000 1.000
#> GSM892354     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892356     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892362     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892366     3  0.0000      0.955 0.000  0 1.000 0.000
#> GSM892370     3  0.2408      0.887 0.000  0 0.896 0.104
#> GSM892374     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892343     4  0.3942      0.683 0.000  0 0.236 0.764
#> GSM892348     4  0.0000      0.864 0.000  0 0.000 1.000
#> GSM892352     3  0.2281      0.890 0.000  0 0.904 0.096
#> GSM892358     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892360     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892364     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892368     3  0.0000      0.955 0.000  0 1.000 0.000
#> GSM892372     3  0.0000      0.955 0.000  0 1.000 0.000
#> GSM892376     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 5), get_membership(res, k = 5))

#>           class entropy silhouette   p1 p2    p3    p4    p5
#> GSM892342     5  0.0000      0.974 0.00  0 0.000 0.000 1.000
#> GSM892345     4  0.0000      0.897 0.00  0 0.000 1.000 0.000
#> GSM892349     4  0.3661      0.659 0.00  0 0.000 0.724 0.276
#> GSM892353     1  0.0000      1.000 1.00  0 0.000 0.000 0.000
#> GSM892355     1  0.0000      1.000 1.00  0 0.000 0.000 0.000
#> GSM892361     1  0.0000      1.000 1.00  0 0.000 0.000 0.000
#> GSM892365     5  0.0000      0.974 0.00  0 0.000 0.000 1.000
#> GSM892369     3  0.0000      1.000 0.00  0 1.000 0.000 0.000
#> GSM892373     2  0.0000      1.000 0.00  1 0.000 0.000 0.000
#> GSM892377     2  0.0000      1.000 0.00  1 0.000 0.000 0.000
#> GSM892381     2  0.0000      1.000 0.00  1 0.000 0.000 0.000
#> GSM892383     2  0.0000      1.000 0.00  1 0.000 0.000 0.000
#> GSM892387     2  0.0000      1.000 0.00  1 0.000 0.000 0.000
#> GSM892344     5  0.0000      0.974 0.00  0 0.000 0.000 1.000
#> GSM892347     4  0.0162      0.895 0.00  0 0.004 0.996 0.000
#> GSM892351     4  0.0000      0.897 0.00  0 0.000 1.000 0.000
#> GSM892357     1  0.0000      1.000 1.00  0 0.000 0.000 0.000
#> GSM892359     1  0.0000      1.000 1.00  0 0.000 0.000 0.000
#> GSM892363     1  0.0000      1.000 1.00  0 0.000 0.000 0.000
#> GSM892367     5  0.1908      0.896 0.00  0 0.092 0.000 0.908
#> GSM892371     3  0.0000      1.000 0.00  0 1.000 0.000 0.000
#> GSM892375     2  0.0000      1.000 0.00  1 0.000 0.000 0.000
#> GSM892379     2  0.0000      1.000 0.00  1 0.000 0.000 0.000
#> GSM892385     2  0.0000      1.000 0.00  1 0.000 0.000 0.000
#> GSM892389     2  0.0000      1.000 0.00  1 0.000 0.000 0.000
#> GSM892341     5  0.0000      0.974 0.00  0 0.000 0.000 1.000
#> GSM892346     4  0.0771      0.880 0.02  0 0.004 0.976 0.000
#> GSM892350     4  0.0000      0.897 0.00  0 0.000 1.000 0.000
#> GSM892354     1  0.0000      1.000 1.00  0 0.000 0.000 0.000
#> GSM892356     1  0.0000      1.000 1.00  0 0.000 0.000 0.000
#> GSM892362     1  0.0000      1.000 1.00  0 0.000 0.000 0.000
#> GSM892366     5  0.0000      0.974 0.00  0 0.000 0.000 1.000
#> GSM892370     3  0.0000      1.000 0.00  0 1.000 0.000 0.000
#> GSM892374     2  0.0000      1.000 0.00  1 0.000 0.000 0.000
#> GSM892378     2  0.0000      1.000 0.00  1 0.000 0.000 0.000
#> GSM892382     2  0.0000      1.000 0.00  1 0.000 0.000 0.000
#> GSM892384     2  0.0000      1.000 0.00  1 0.000 0.000 0.000
#> GSM892388     2  0.0000      1.000 0.00  1 0.000 0.000 0.000
#> GSM892343     4  0.4354      0.668 0.00  0 0.032 0.712 0.256
#> GSM892348     4  0.0000      0.897 0.00  0 0.000 1.000 0.000
#> GSM892352     5  0.1908      0.887 0.00  0 0.000 0.092 0.908
#> GSM892358     1  0.0000      1.000 1.00  0 0.000 0.000 0.000
#> GSM892360     1  0.0000      1.000 1.00  0 0.000 0.000 0.000
#> GSM892364     1  0.0000      1.000 1.00  0 0.000 0.000 0.000
#> GSM892368     5  0.0000      0.974 0.00  0 0.000 0.000 1.000
#> GSM892372     5  0.0162      0.972 0.00  0 0.004 0.000 0.996
#> GSM892376     2  0.0000      1.000 0.00  1 0.000 0.000 0.000
#> GSM892380     2  0.0000      1.000 0.00  1 0.000 0.000 0.000
#> GSM892386     2  0.0000      1.000 0.00  1 0.000 0.000 0.000
#> GSM892390     2  0.0000      1.000 0.00  1 0.000 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 6), get_membership(res, k = 6))

#>           class entropy silhouette    p1 p2    p3    p4    p5    p6
#> GSM892342     5  0.0937      0.870 0.000  0 0.040 0.000 0.960 0.000
#> GSM892345     4  0.0865      0.984 0.000  0 0.000 0.964 0.036 0.000
#> GSM892349     5  0.1633      0.844 0.000  0 0.024 0.044 0.932 0.000
#> GSM892353     5  0.3684      0.509 0.332  0 0.004 0.000 0.664 0.000
#> GSM892355     1  0.0146      0.998 0.996  0 0.004 0.000 0.000 0.000
#> GSM892361     1  0.0000      0.998 1.000  0 0.000 0.000 0.000 0.000
#> GSM892365     3  0.0146      0.983 0.000  0 0.996 0.000 0.004 0.000
#> GSM892369     6  0.0000      1.000 0.000  0 0.000 0.000 0.000 1.000
#> GSM892373     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892344     5  0.0937      0.870 0.000  0 0.040 0.000 0.960 0.000
#> GSM892347     4  0.0865      0.984 0.000  0 0.000 0.964 0.036 0.000
#> GSM892351     4  0.0865      0.984 0.000  0 0.000 0.964 0.036 0.000
#> GSM892357     1  0.0000      0.998 1.000  0 0.000 0.000 0.000 0.000
#> GSM892359     1  0.0146      0.998 0.996  0 0.004 0.000 0.000 0.000
#> GSM892363     1  0.0000      0.998 1.000  0 0.000 0.000 0.000 0.000
#> GSM892367     3  0.1327      0.929 0.000  0 0.936 0.000 0.000 0.064
#> GSM892371     6  0.0000      1.000 0.000  0 0.000 0.000 0.000 1.000
#> GSM892375     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892341     5  0.2597      0.777 0.000  0 0.176 0.000 0.824 0.000
#> GSM892346     4  0.0146      0.968 0.000  0 0.000 0.996 0.004 0.000
#> GSM892350     4  0.0865      0.984 0.000  0 0.000 0.964 0.036 0.000
#> GSM892354     1  0.0000      0.998 1.000  0 0.000 0.000 0.000 0.000
#> GSM892356     1  0.0000      0.998 1.000  0 0.000 0.000 0.000 0.000
#> GSM892362     1  0.0000      0.998 1.000  0 0.000 0.000 0.000 0.000
#> GSM892366     3  0.0146      0.983 0.000  0 0.996 0.000 0.004 0.000
#> GSM892370     6  0.0000      1.000 0.000  0 0.000 0.000 0.000 1.000
#> GSM892374     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892343     5  0.0260      0.869 0.000  0 0.008 0.000 0.992 0.000
#> GSM892348     4  0.0146      0.968 0.000  0 0.000 0.996 0.004 0.000
#> GSM892352     5  0.0146      0.868 0.000  0 0.004 0.000 0.996 0.000
#> GSM892358     1  0.0146      0.998 0.996  0 0.004 0.000 0.000 0.000
#> GSM892360     1  0.0146      0.998 0.996  0 0.004 0.000 0.000 0.000
#> GSM892364     1  0.0146      0.998 0.996  0 0.004 0.000 0.000 0.000
#> GSM892368     3  0.0146      0.983 0.000  0 0.996 0.000 0.004 0.000
#> GSM892372     3  0.0146      0.983 0.000  0 0.996 0.000 0.004 0.000
#> GSM892376     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

k = 2
k = 3
k = 4
k = 5
k = 6

consensus_heatmap(res, k = 2)

plot of chunk tab-CV-pam-consensus-heatmap-1

consensus_heatmap(res, k = 3)

plot of chunk tab-CV-pam-consensus-heatmap-2

consensus_heatmap(res, k = 4)

plot of chunk tab-CV-pam-consensus-heatmap-3

consensus_heatmap(res, k = 5)

plot of chunk tab-CV-pam-consensus-heatmap-4

consensus_heatmap(res, k = 6)

plot of chunk tab-CV-pam-consensus-heatmap-5

Heatmaps for the membership of samples in all partitions to see how consistent they are:

k = 2
k = 3
k = 4
k = 5
k = 6

membership_heatmap(res, k = 2)

plot of chunk tab-CV-pam-membership-heatmap-1

membership_heatmap(res, k = 3)

plot of chunk tab-CV-pam-membership-heatmap-2

membership_heatmap(res, k = 4)

plot of chunk tab-CV-pam-membership-heatmap-3

membership_heatmap(res, k = 5)

plot of chunk tab-CV-pam-membership-heatmap-4

membership_heatmap(res, k = 6)

plot of chunk tab-CV-pam-membership-heatmap-5

Signature heatmaps where rows are scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2)

plot of chunk tab-CV-pam-get-signatures-1

get_signatures(res, k = 3)

plot of chunk tab-CV-pam-get-signatures-2

get_signatures(res, k = 4)

plot of chunk tab-CV-pam-get-signatures-3

get_signatures(res, k = 5)

plot of chunk tab-CV-pam-get-signatures-4

get_signatures(res, k = 6)

plot of chunk tab-CV-pam-get-signatures-5

Signature heatmaps where rows are not scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-CV-pam-get-signatures-no-scale-1

get_signatures(res, k = 3, scale_rows = FALSE)

plot of chunk tab-CV-pam-get-signatures-no-scale-2

get_signatures(res, k = 4, scale_rows = FALSE)

plot of chunk tab-CV-pam-get-signatures-no-scale-3

get_signatures(res, k = 5, scale_rows = FALSE)

plot of chunk tab-CV-pam-get-signatures-no-scale-4

get_signatures(res, k = 6, scale_rows = FALSE)

plot of chunk tab-CV-pam-get-signatures-no-scale-5

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk CV-pam-signature_compare

# 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.

k = 2
k = 3
k = 4
k = 5
k = 6

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-CV-pam-dimension-reduction-1

dimension_reduction(res, k = 3, method = "UMAP")

plot of chunk tab-CV-pam-dimension-reduction-2

dimension_reduction(res, k = 4, method = "UMAP")

plot of chunk tab-CV-pam-dimension-reduction-3

dimension_reduction(res, k = 5, method = "UMAP")

plot of chunk tab-CV-pam-dimension-reduction-4

dimension_reduction(res, k = 6, method = "UMAP")

plot of chunk tab-CV-pam-dimension-reduction-5

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk CV-pam-collect-classes

test_to_known_factors(res)

#>         n tissue(p) disease.state(p) other(p) individual(p) k
#> CV:pam 50     1.000            0.934 2.67e-07      1.42e-03 2
#> CV:pam 50     0.939            0.875 8.67e-12      3.79e-05 3
#> CV:pam 49     0.995            0.988 1.32e-14      7.04e-06 4
#> CV:pam 50     0.979            0.964 3.20e-17      9.29e-07 5
#> CV:pam 50     0.979            0.969 1.52e-20      2.12e-07 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

CV:mclust*

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 31632 rows and 50 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 5.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk CV-mclust-collect-plots

The plots are:

The first row: a plot of the ECDF (empirical cumulative distribution function) curves of the consensus matrix for each k and the heatmap of predicted classes for each k.
The second row: heatmaps of the consensus matrix for each k.
The third row: heatmaps of the membership matrix for each k.
The fouth row: heatmaps of the signatures for each 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:

ECDF curves of the consensus matrix for each k;
1-PAC. The PAC score measures the proportion of the ambiguous subgrouping.
Mean silhouette score.
Concordance. The mean probability of fiting the consensus class ids in all partitions.
Area increased. Denote \(A_k\) as the area under the ECDF curve for current k, the area increased is defined as \(A_k - A_{k-1}\).
Rand index. The percent of pairs of samples that are both in a same cluster or both are not in a same cluster in the partition of k and k-1.
Jaccard index. The ratio of pairs of samples are both in a same cluster in the partition of k and k-1 and the pairs of samples are both in a same cluster in the partition k or k-1.

The detailed explanations of these statistics can be found in the cola vignette.

select_partition_number(res)

plot of chunk CV-mclust-select-partition-number

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         0.4707 0.530   0.530
#> 3 3 1.000           1.000       1.000         0.4158 0.804   0.630
#> 4 4 0.966           0.920       0.966         0.1189 0.918   0.756
#> 5 5 0.907           0.762       0.901         0.0344 0.987   0.948
#> 6 6 0.855           0.679       0.851         0.0342 0.984   0.932

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

All \(k\) with Jaccard index larger than 0.95 are removed because increasing \(k\) does not provide enough extra information. If all \(k\) are removed, it is marked as no subgroup is detected.
For all \(k\) with 1-PAC score larger than 0.9, the maximal \(k\) is taken as the best \(k\), and other \(k\) are marked as optional \(k\).
If it does not fit the second rule. The \(k\) with the maximal vote of the highest 1-PAC score, highest mean silhouette, and highest concordance is taken as the best \(k\).

suggest_best_k(res)

#> [1] 5
#> attr(,"optional")
#> [1] 2 3 4

There is also optional best \(k\) = 2 3 4 that is worth to check.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

k = 2
k = 3
k = 4
k = 5
k = 6

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>           class entropy silhouette p1 p2
#> GSM892342     1       0          1  1  0
#> GSM892345     1       0          1  1  0
#> GSM892349     1       0          1  1  0
#> GSM892353     1       0          1  1  0
#> GSM892355     1       0          1  1  0
#> GSM892361     1       0          1  1  0
#> GSM892365     1       0          1  1  0
#> GSM892369     1       0          1  1  0
#> GSM892373     2       0          1  0  1
#> GSM892377     2       0          1  0  1
#> GSM892381     2       0          1  0  1
#> GSM892383     2       0          1  0  1
#> GSM892387     2       0          1  0  1
#> GSM892344     1       0          1  1  0
#> GSM892347     1       0          1  1  0
#> GSM892351     1       0          1  1  0
#> GSM892357     1       0          1  1  0
#> GSM892359     1       0          1  1  0
#> GSM892363     1       0          1  1  0
#> GSM892367     1       0          1  1  0
#> GSM892371     1       0          1  1  0
#> GSM892375     2       0          1  0  1
#> GSM892379     2       0          1  0  1
#> GSM892385     2       0          1  0  1
#> GSM892389     2       0          1  0  1
#> GSM892341     1       0          1  1  0
#> GSM892346     1       0          1  1  0
#> GSM892350     1       0          1  1  0
#> GSM892354     1       0          1  1  0
#> GSM892356     1       0          1  1  0
#> GSM892362     1       0          1  1  0
#> GSM892366     1       0          1  1  0
#> GSM892370     1       0          1  1  0
#> GSM892374     2       0          1  0  1
#> GSM892378     2       0          1  0  1
#> GSM892382     2       0          1  0  1
#> GSM892384     2       0          1  0  1
#> GSM892388     2       0          1  0  1
#> GSM892343     1       0          1  1  0
#> GSM892348     1       0          1  1  0
#> GSM892352     1       0          1  1  0
#> GSM892358     1       0          1  1  0
#> GSM892360     1       0          1  1  0
#> GSM892364     1       0          1  1  0
#> GSM892368     1       0          1  1  0
#> GSM892372     1       0          1  1  0
#> GSM892376     2       0          1  0  1
#> GSM892380     2       0          1  0  1
#> GSM892386     2       0          1  0  1
#> GSM892390     2       0          1  0  1

show/hide code output

cbind(get_classes(res, k = 3), get_membership(res, k = 3))

#>           class entropy silhouette p1 p2 p3
#> GSM892342     3       0          1  0  0  1
#> GSM892345     3       0          1  0  0  1
#> GSM892349     3       0          1  0  0  1
#> GSM892353     1       0          1  1  0  0
#> GSM892355     1       0          1  1  0  0
#> GSM892361     1       0          1  1  0  0
#> GSM892365     3       0          1  0  0  1
#> GSM892369     3       0          1  0  0  1
#> GSM892373     2       0          1  0  1  0
#> GSM892377     2       0          1  0  1  0
#> GSM892381     2       0          1  0  1  0
#> GSM892383     2       0          1  0  1  0
#> GSM892387     2       0          1  0  1  0
#> GSM892344     3       0          1  0  0  1
#> GSM892347     3       0          1  0  0  1
#> GSM892351     3       0          1  0  0  1
#> GSM892357     1       0          1  1  0  0
#> GSM892359     1       0          1  1  0  0
#> GSM892363     1       0          1  1  0  0
#> GSM892367     3       0          1  0  0  1
#> GSM892371     3       0          1  0  0  1
#> GSM892375     2       0          1  0  1  0
#> GSM892379     2       0          1  0  1  0
#> GSM892385     2       0          1  0  1  0
#> GSM892389     2       0          1  0  1  0
#> GSM892341     3       0          1  0  0  1
#> GSM892346     3       0          1  0  0  1
#> GSM892350     3       0          1  0  0  1
#> GSM892354     1       0          1  1  0  0
#> GSM892356     1       0          1  1  0  0
#> GSM892362     1       0          1  1  0  0
#> GSM892366     3       0          1  0  0  1
#> GSM892370     3       0          1  0  0  1
#> GSM892374     2       0          1  0  1  0
#> GSM892378     2       0          1  0  1  0
#> GSM892382     2       0          1  0  1  0
#> GSM892384     2       0          1  0  1  0
#> GSM892388     2       0          1  0  1  0
#> GSM892343     3       0          1  0  0  1
#> GSM892348     3       0          1  0  0  1
#> GSM892352     3       0          1  0  0  1
#> GSM892358     1       0          1  1  0  0
#> GSM892360     1       0          1  1  0  0
#> GSM892364     1       0          1  1  0  0
#> GSM892368     3       0          1  0  0  1
#> GSM892372     3       0          1  0  0  1
#> GSM892376     2       0          1  0  1  0
#> GSM892380     2       0          1  0  1  0
#> GSM892386     2       0          1  0  1  0
#> GSM892390     2       0          1  0  1  0

show/hide code output

cbind(get_classes(res, k = 4), get_membership(res, k = 4))

#>           class entropy silhouette p1 p2    p3    p4
#> GSM892342     3  0.0000      0.862  0  0 1.000 0.000
#> GSM892345     4  0.0000      0.921  0  0 0.000 1.000
#> GSM892349     4  0.4866      0.143  0  0 0.404 0.596
#> GSM892353     1  0.0000      1.000  1  0 0.000 0.000
#> GSM892355     1  0.0000      1.000  1  0 0.000 0.000
#> GSM892361     1  0.0000      1.000  1  0 0.000 0.000
#> GSM892365     3  0.0921      0.860  0  0 0.972 0.028
#> GSM892369     4  0.2868      0.786  0  0 0.136 0.864
#> GSM892373     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892377     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892381     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892383     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892387     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892344     3  0.0188      0.863  0  0 0.996 0.004
#> GSM892347     4  0.0000      0.921  0  0 0.000 1.000
#> GSM892351     4  0.0000      0.921  0  0 0.000 1.000
#> GSM892357     1  0.0000      1.000  1  0 0.000 0.000
#> GSM892359     1  0.0000      1.000  1  0 0.000 0.000
#> GSM892363     1  0.0000      1.000  1  0 0.000 0.000
#> GSM892367     3  0.2011      0.846  0  0 0.920 0.080
#> GSM892371     4  0.0817      0.909  0  0 0.024 0.976
#> GSM892375     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892379     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892385     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892389     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892341     3  0.0188      0.863  0  0 0.996 0.004
#> GSM892346     4  0.0000      0.921  0  0 0.000 1.000
#> GSM892350     4  0.0000      0.921  0  0 0.000 1.000
#> GSM892354     1  0.0000      1.000  1  0 0.000 0.000
#> GSM892356     1  0.0000      1.000  1  0 0.000 0.000
#> GSM892362     1  0.0000      1.000  1  0 0.000 0.000
#> GSM892366     3  0.2149      0.837  0  0 0.912 0.088
#> GSM892370     4  0.0707      0.912  0  0 0.020 0.980
#> GSM892374     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892378     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892382     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892384     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892388     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892343     3  0.4250      0.630  0  0 0.724 0.276
#> GSM892348     4  0.0000      0.921  0  0 0.000 1.000
#> GSM892352     3  0.4843      0.391  0  0 0.604 0.396
#> GSM892358     1  0.0000      1.000  1  0 0.000 0.000
#> GSM892360     1  0.0000      1.000  1  0 0.000 0.000
#> GSM892364     1  0.0000      1.000  1  0 0.000 0.000
#> GSM892368     3  0.0188      0.863  0  0 0.996 0.004
#> GSM892372     3  0.3942      0.721  0  0 0.764 0.236
#> GSM892376     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892380     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892386     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892390     2  0.0000      1.000  0  1 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 5), get_membership(res, k = 5))

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> GSM892342     3  0.0404      0.862 0.000 0.000 0.988 0.000 0.012
#> GSM892345     4  0.4262     -0.208 0.000 0.000 0.000 0.560 0.440
#> GSM892349     4  0.5703     -0.274 0.000 0.000 0.408 0.508 0.084
#> GSM892353     1  0.0162      0.993 0.996 0.000 0.000 0.000 0.004
#> GSM892355     1  0.0290      0.992 0.992 0.000 0.000 0.000 0.008
#> GSM892361     1  0.0290      0.992 0.992 0.000 0.000 0.000 0.008
#> GSM892365     3  0.0451      0.864 0.000 0.000 0.988 0.004 0.008
#> GSM892369     4  0.0609      0.334 0.000 0.000 0.000 0.980 0.020
#> GSM892373     2  0.2891      0.853 0.000 0.824 0.000 0.000 0.176
#> GSM892377     2  0.0000      0.966 0.000 1.000 0.000 0.000 0.000
#> GSM892381     2  0.0000      0.966 0.000 1.000 0.000 0.000 0.000
#> GSM892383     2  0.0000      0.966 0.000 1.000 0.000 0.000 0.000
#> GSM892387     2  0.0000      0.966 0.000 1.000 0.000 0.000 0.000
#> GSM892344     3  0.1386      0.862 0.000 0.000 0.952 0.016 0.032
#> GSM892347     4  0.4268     -0.218 0.000 0.000 0.000 0.556 0.444
#> GSM892351     4  0.4262     -0.208 0.000 0.000 0.000 0.560 0.440
#> GSM892357     1  0.0290      0.992 0.992 0.000 0.000 0.000 0.008
#> GSM892359     1  0.0000      0.994 1.000 0.000 0.000 0.000 0.000
#> GSM892363     1  0.0000      0.994 1.000 0.000 0.000 0.000 0.000
#> GSM892367     3  0.2694      0.818 0.000 0.000 0.884 0.040 0.076
#> GSM892371     4  0.1121      0.333 0.000 0.000 0.000 0.956 0.044
#> GSM892375     2  0.0000      0.966 0.000 1.000 0.000 0.000 0.000
#> GSM892379     2  0.0000      0.966 0.000 1.000 0.000 0.000 0.000
#> GSM892385     2  0.0000      0.966 0.000 1.000 0.000 0.000 0.000
#> GSM892389     2  0.0000      0.966 0.000 1.000 0.000 0.000 0.000
#> GSM892341     3  0.1281      0.863 0.000 0.000 0.956 0.012 0.032
#> GSM892346     5  0.3452      0.802 0.000 0.000 0.000 0.244 0.756
#> GSM892350     4  0.4273     -0.228 0.000 0.000 0.000 0.552 0.448
#> GSM892354     1  0.0290      0.992 0.992 0.000 0.000 0.000 0.008
#> GSM892356     1  0.0000      0.994 1.000 0.000 0.000 0.000 0.000
#> GSM892362     1  0.0000      0.994 1.000 0.000 0.000 0.000 0.000
#> GSM892366     3  0.0671      0.864 0.000 0.000 0.980 0.004 0.016
#> GSM892370     4  0.0510      0.339 0.000 0.000 0.000 0.984 0.016
#> GSM892374     2  0.2891      0.853 0.000 0.824 0.000 0.000 0.176
#> GSM892378     2  0.0000      0.966 0.000 1.000 0.000 0.000 0.000
#> GSM892382     2  0.0000      0.966 0.000 1.000 0.000 0.000 0.000
#> GSM892384     2  0.0000      0.966 0.000 1.000 0.000 0.000 0.000
#> GSM892388     2  0.2929      0.850 0.000 0.820 0.000 0.000 0.180
#> GSM892343     3  0.5267      0.448 0.000 0.000 0.524 0.428 0.048
#> GSM892348     5  0.3966      0.780 0.000 0.000 0.000 0.336 0.664
#> GSM892352     3  0.4937      0.464 0.000 0.000 0.544 0.428 0.028
#> GSM892358     1  0.0290      0.992 0.992 0.000 0.000 0.000 0.008
#> GSM892360     1  0.0000      0.994 1.000 0.000 0.000 0.000 0.000
#> GSM892364     1  0.1216      0.969 0.960 0.000 0.000 0.020 0.020
#> GSM892368     3  0.0566      0.865 0.000 0.000 0.984 0.004 0.012
#> GSM892372     3  0.2438      0.848 0.000 0.000 0.900 0.060 0.040
#> GSM892376     2  0.2127      0.902 0.000 0.892 0.000 0.000 0.108
#> GSM892380     2  0.0000      0.966 0.000 1.000 0.000 0.000 0.000
#> GSM892386     2  0.0000      0.966 0.000 1.000 0.000 0.000 0.000
#> GSM892390     2  0.0000      0.966 0.000 1.000 0.000 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 6), get_membership(res, k = 6))

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> GSM892342     5  0.0146     0.8699 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM892345     3  0.3851    -0.0729 0.000 0.000 0.540 0.460 0.000 0.000
#> GSM892349     3  0.4453    -0.2003 0.000 0.000 0.592 0.036 0.372 0.000
#> GSM892353     6  0.5147     0.9293 0.436 0.000 0.000 0.084 0.000 0.480
#> GSM892355     1  0.3766     0.1570 0.736 0.000 0.000 0.032 0.000 0.232
#> GSM892361     1  0.1245     0.8153 0.952 0.000 0.000 0.032 0.000 0.016
#> GSM892365     5  0.0000     0.8698 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM892369     3  0.0692     0.4009 0.000 0.000 0.976 0.000 0.004 0.020
#> GSM892373     2  0.3838     0.5373 0.000 0.552 0.000 0.000 0.000 0.448
#> GSM892377     2  0.0146     0.9088 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM892381     2  0.0000     0.9089 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892383     2  0.0146     0.9088 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM892387     2  0.0146     0.9085 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM892344     5  0.0405     0.8688 0.000 0.000 0.000 0.004 0.988 0.008
#> GSM892347     3  0.3851    -0.0683 0.000 0.000 0.540 0.460 0.000 0.000
#> GSM892351     3  0.3838    -0.0496 0.000 0.000 0.552 0.448 0.000 0.000
#> GSM892357     1  0.0914     0.8246 0.968 0.000 0.000 0.016 0.000 0.016
#> GSM892359     1  0.1812     0.7342 0.912 0.000 0.000 0.008 0.000 0.080
#> GSM892363     1  0.0146     0.8315 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM892367     5  0.3224     0.8017 0.000 0.000 0.128 0.036 0.828 0.008
#> GSM892371     3  0.0547     0.4032 0.000 0.000 0.980 0.020 0.000 0.000
#> GSM892375     2  0.0260     0.9077 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM892379     2  0.0000     0.9089 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892385     2  0.0260     0.9076 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM892389     2  0.0260     0.9077 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM892341     5  0.0146     0.8699 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM892346     4  0.2562     0.8212 0.000 0.000 0.172 0.828 0.000 0.000
#> GSM892350     3  0.3854    -0.0820 0.000 0.000 0.536 0.464 0.000 0.000
#> GSM892354     1  0.1245     0.8153 0.952 0.000 0.000 0.032 0.000 0.016
#> GSM892356     1  0.0405     0.8286 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM892362     1  0.0260     0.8288 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM892366     5  0.0520     0.8684 0.000 0.000 0.000 0.008 0.984 0.008
#> GSM892370     3  0.0622     0.3981 0.000 0.000 0.980 0.012 0.000 0.008
#> GSM892374     2  0.3838     0.5373 0.000 0.552 0.000 0.000 0.000 0.448
#> GSM892378     2  0.0363     0.9065 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM892382     2  0.0146     0.9088 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM892384     2  0.0146     0.9088 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM892388     2  0.4702     0.4619 0.000 0.496 0.000 0.044 0.000 0.460
#> GSM892343     5  0.5110     0.5940 0.000 0.000 0.316 0.020 0.604 0.060
#> GSM892348     4  0.3221     0.8030 0.000 0.000 0.264 0.736 0.000 0.000
#> GSM892352     5  0.4415     0.5014 0.000 0.000 0.420 0.004 0.556 0.020
#> GSM892358     6  0.5145     0.9299 0.432 0.000 0.000 0.084 0.000 0.484
#> GSM892360     1  0.0146     0.8300 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM892364     1  0.4152     0.1251 0.664 0.000 0.000 0.032 0.000 0.304
#> GSM892368     5  0.0291     0.8698 0.000 0.000 0.004 0.000 0.992 0.004
#> GSM892372     5  0.3043     0.8101 0.000 0.000 0.140 0.008 0.832 0.020
#> GSM892376     2  0.2730     0.7852 0.000 0.808 0.000 0.000 0.000 0.192
#> GSM892380     2  0.0146     0.9088 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM892386     2  0.0146     0.9088 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM892390     2  0.0547     0.9031 0.000 0.980 0.000 0.000 0.000 0.020

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

k = 2
k = 3
k = 4
k = 5
k = 6

consensus_heatmap(res, k = 2)

plot of chunk tab-CV-mclust-consensus-heatmap-1

consensus_heatmap(res, k = 3)

plot of chunk tab-CV-mclust-consensus-heatmap-2

consensus_heatmap(res, k = 4)

plot of chunk tab-CV-mclust-consensus-heatmap-3

consensus_heatmap(res, k = 5)

plot of chunk tab-CV-mclust-consensus-heatmap-4

consensus_heatmap(res, k = 6)

plot of chunk tab-CV-mclust-consensus-heatmap-5

Heatmaps for the membership of samples in all partitions to see how consistent they are:

k = 2
k = 3
k = 4
k = 5
k = 6

membership_heatmap(res, k = 2)

plot of chunk tab-CV-mclust-membership-heatmap-1

membership_heatmap(res, k = 3)

plot of chunk tab-CV-mclust-membership-heatmap-2

membership_heatmap(res, k = 4)

plot of chunk tab-CV-mclust-membership-heatmap-3

membership_heatmap(res, k = 5)

plot of chunk tab-CV-mclust-membership-heatmap-4

membership_heatmap(res, k = 6)

plot of chunk tab-CV-mclust-membership-heatmap-5

Signature heatmaps where rows are scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2)

plot of chunk tab-CV-mclust-get-signatures-1

get_signatures(res, k = 3)

plot of chunk tab-CV-mclust-get-signatures-2

get_signatures(res, k = 4)

plot of chunk tab-CV-mclust-get-signatures-3

get_signatures(res, k = 5)

plot of chunk tab-CV-mclust-get-signatures-4

get_signatures(res, k = 6)

plot of chunk tab-CV-mclust-get-signatures-5

Signature heatmaps where rows are not scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-CV-mclust-get-signatures-no-scale-1

get_signatures(res, k = 3, scale_rows = FALSE)

plot of chunk tab-CV-mclust-get-signatures-no-scale-2

get_signatures(res, k = 4, scale_rows = FALSE)

plot of chunk tab-CV-mclust-get-signatures-no-scale-3

get_signatures(res, k = 5, scale_rows = FALSE)

plot of chunk tab-CV-mclust-get-signatures-no-scale-4

get_signatures(res, k = 6, scale_rows = FALSE)

plot of chunk tab-CV-mclust-get-signatures-no-scale-5

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk CV-mclust-signature_compare

# 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.

k = 2
k = 3
k = 4
k = 5
k = 6

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-CV-mclust-dimension-reduction-1

dimension_reduction(res, k = 3, method = "UMAP")

plot of chunk tab-CV-mclust-dimension-reduction-2

dimension_reduction(res, k = 4, method = "UMAP")

plot of chunk tab-CV-mclust-dimension-reduction-3

dimension_reduction(res, k = 5, method = "UMAP")

plot of chunk tab-CV-mclust-dimension-reduction-4

dimension_reduction(res, k = 6, method = "UMAP")

plot of chunk tab-CV-mclust-dimension-reduction-5

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk CV-mclust-collect-classes

test_to_known_factors(res)

#>            n tissue(p) disease.state(p) other(p) individual(p) k
#> CV:mclust 50     1.000            0.934 2.67e-07      1.42e-03 2
#> CV:mclust 50     1.000            0.931 1.26e-12      1.60e-05 3
#> CV:mclust 48     0.974            0.948 1.91e-15      3.99e-06 4
#> CV:mclust 40     0.592            0.989 1.08e-13      2.01e-05 5
#> CV:mclust 39     0.691            0.980 4.22e-10      1.80e-03 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

CV:NMF*

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 31632 rows and 50 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 5.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk CV-NMF-collect-plots

The plots are:

The first row: a plot of the ECDF (empirical cumulative distribution function) curves of the consensus matrix for each k and the heatmap of predicted classes for each k.
The second row: heatmaps of the consensus matrix for each k.
The third row: heatmaps of the membership matrix for each k.
The fouth row: heatmaps of the signatures for each 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:

ECDF curves of the consensus matrix for each k;
1-PAC. The PAC score measures the proportion of the ambiguous subgrouping.
Mean silhouette score.
Concordance. The mean probability of fiting the consensus class ids in all partitions.
Area increased. Denote \(A_k\) as the area under the ECDF curve for current k, the area increased is defined as \(A_k - A_{k-1}\).
Rand index. The percent of pairs of samples that are both in a same cluster or both are not in a same cluster in the partition of k and k-1.
Jaccard index. The ratio of pairs of samples are both in a same cluster in the partition of k and k-1 and the pairs of samples are both in a same cluster in the partition k or k-1.

The detailed explanations of these statistics can be found in the cola vignette.

select_partition_number(res)

plot of chunk CV-NMF-select-partition-number

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         0.4707 0.530   0.530
#> 3 3 0.949           0.933       0.969         0.4361 0.792   0.607
#> 4 4 0.985           0.921       0.966         0.0935 0.922   0.762
#> 5 5 0.939           0.915       0.934         0.0389 0.958   0.842
#> 6 6 0.902           0.914       0.934         0.0198 1.000   1.000

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

All \(k\) with Jaccard index larger than 0.95 are removed because increasing \(k\) does not provide enough extra information. If all \(k\) are removed, it is marked as no subgroup is detected.
For all \(k\) with 1-PAC score larger than 0.9, the maximal \(k\) is taken as the best \(k\), and other \(k\) are marked as optional \(k\).
If it does not fit the second rule. The \(k\) with the maximal vote of the highest 1-PAC score, highest mean silhouette, and highest concordance is taken as the best \(k\).

suggest_best_k(res)

#> [1] 5
#> attr(,"optional")
#> [1] 2 3 4

There is also optional best \(k\) = 2 3 4 that is worth to check.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

k = 2
k = 3
k = 4
k = 5
k = 6

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>           class entropy silhouette p1 p2
#> GSM892342     1       0          1  1  0
#> GSM892345     1       0          1  1  0
#> GSM892349     1       0          1  1  0
#> GSM892353     1       0          1  1  0
#> GSM892355     1       0          1  1  0
#> GSM892361     1       0          1  1  0
#> GSM892365     1       0          1  1  0
#> GSM892369     1       0          1  1  0
#> GSM892373     2       0          1  0  1
#> GSM892377     2       0          1  0  1
#> GSM892381     2       0          1  0  1
#> GSM892383     2       0          1  0  1
#> GSM892387     2       0          1  0  1
#> GSM892344     1       0          1  1  0
#> GSM892347     1       0          1  1  0
#> GSM892351     1       0          1  1  0
#> GSM892357     1       0          1  1  0
#> GSM892359     1       0          1  1  0
#> GSM892363     1       0          1  1  0
#> GSM892367     1       0          1  1  0
#> GSM892371     1       0          1  1  0
#> GSM892375     2       0          1  0  1
#> GSM892379     2       0          1  0  1
#> GSM892385     2       0          1  0  1
#> GSM892389     2       0          1  0  1
#> GSM892341     1       0          1  1  0
#> GSM892346     1       0          1  1  0
#> GSM892350     1       0          1  1  0
#> GSM892354     1       0          1  1  0
#> GSM892356     1       0          1  1  0
#> GSM892362     1       0          1  1  0
#> GSM892366     1       0          1  1  0
#> GSM892370     1       0          1  1  0
#> GSM892374     2       0          1  0  1
#> GSM892378     2       0          1  0  1
#> GSM892382     2       0          1  0  1
#> GSM892384     2       0          1  0  1
#> GSM892388     2       0          1  0  1
#> GSM892343     1       0          1  1  0
#> GSM892348     1       0          1  1  0
#> GSM892352     1       0          1  1  0
#> GSM892358     1       0          1  1  0
#> GSM892360     1       0          1  1  0
#> GSM892364     1       0          1  1  0
#> GSM892368     1       0          1  1  0
#> GSM892372     1       0          1  1  0
#> GSM892376     2       0          1  0  1
#> GSM892380     2       0          1  0  1
#> GSM892386     2       0          1  0  1
#> GSM892390     2       0          1  0  1

show/hide code output

cbind(get_classes(res, k = 3), get_membership(res, k = 3))

#>           class entropy silhouette    p1 p2    p3
#> GSM892342     3  0.0000      0.984 0.000  0 1.000
#> GSM892345     1  0.5968      0.524 0.636  0 0.364
#> GSM892349     3  0.0000      0.984 0.000  0 1.000
#> GSM892353     1  0.0892      0.902 0.980  0 0.020
#> GSM892355     1  0.0424      0.907 0.992  0 0.008
#> GSM892361     1  0.0000      0.910 1.000  0 0.000
#> GSM892365     3  0.0000      0.984 0.000  0 1.000
#> GSM892369     3  0.0000      0.984 0.000  0 1.000
#> GSM892373     2  0.0000      1.000 0.000  1 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000
#> GSM892344     3  0.0000      0.984 0.000  0 1.000
#> GSM892347     1  0.5882      0.553 0.652  0 0.348
#> GSM892351     3  0.4346      0.738 0.184  0 0.816
#> GSM892357     1  0.0000      0.910 1.000  0 0.000
#> GSM892359     1  0.0000      0.910 1.000  0 0.000
#> GSM892363     1  0.0000      0.910 1.000  0 0.000
#> GSM892367     3  0.0000      0.984 0.000  0 1.000
#> GSM892371     3  0.0000      0.984 0.000  0 1.000
#> GSM892375     2  0.0000      1.000 0.000  1 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000
#> GSM892341     3  0.0000      0.984 0.000  0 1.000
#> GSM892346     1  0.2261      0.872 0.932  0 0.068
#> GSM892350     1  0.5968      0.524 0.636  0 0.364
#> GSM892354     1  0.0000      0.910 1.000  0 0.000
#> GSM892356     1  0.0000      0.910 1.000  0 0.000
#> GSM892362     1  0.0000      0.910 1.000  0 0.000
#> GSM892366     3  0.0000      0.984 0.000  0 1.000
#> GSM892370     3  0.0000      0.984 0.000  0 1.000
#> GSM892374     2  0.0000      1.000 0.000  1 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000
#> GSM892343     3  0.0747      0.968 0.016  0 0.984
#> GSM892348     1  0.4399      0.770 0.812  0 0.188
#> GSM892352     3  0.0000      0.984 0.000  0 1.000
#> GSM892358     1  0.0000      0.910 1.000  0 0.000
#> GSM892360     1  0.0000      0.910 1.000  0 0.000
#> GSM892364     1  0.0000      0.910 1.000  0 0.000
#> GSM892368     3  0.0000      0.984 0.000  0 1.000
#> GSM892372     3  0.0000      0.984 0.000  0 1.000
#> GSM892376     2  0.0000      1.000 0.000  1 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000

show/hide code output

cbind(get_classes(res, k = 4), get_membership(res, k = 4))

#>           class entropy silhouette    p1 p2    p3    p4
#> GSM892342     3  0.0592     0.9036 0.000  0 0.984 0.016
#> GSM892345     4  0.0817     0.9037 0.000  0 0.024 0.976
#> GSM892349     4  0.4933     0.0899 0.000  0 0.432 0.568
#> GSM892353     1  0.0000     0.9989 1.000  0 0.000 0.000
#> GSM892355     1  0.0000     0.9989 1.000  0 0.000 0.000
#> GSM892361     1  0.0188     0.9959 0.996  0 0.000 0.004
#> GSM892365     3  0.0000     0.8998 0.000  0 1.000 0.000
#> GSM892369     3  0.1637     0.8867 0.000  0 0.940 0.060
#> GSM892373     2  0.0000     1.0000 0.000  1 0.000 0.000
#> GSM892377     2  0.0000     1.0000 0.000  1 0.000 0.000
#> GSM892381     2  0.0000     1.0000 0.000  1 0.000 0.000
#> GSM892383     2  0.0000     1.0000 0.000  1 0.000 0.000
#> GSM892387     2  0.0000     1.0000 0.000  1 0.000 0.000
#> GSM892344     3  0.0921     0.9019 0.000  0 0.972 0.028
#> GSM892347     4  0.0895     0.9037 0.004  0 0.020 0.976
#> GSM892351     4  0.1211     0.8938 0.000  0 0.040 0.960
#> GSM892357     1  0.0000     0.9989 1.000  0 0.000 0.000
#> GSM892359     1  0.0000     0.9989 1.000  0 0.000 0.000
#> GSM892363     1  0.0000     0.9989 1.000  0 0.000 0.000
#> GSM892367     3  0.0188     0.8977 0.000  0 0.996 0.004
#> GSM892371     3  0.3074     0.8112 0.000  0 0.848 0.152
#> GSM892375     2  0.0000     1.0000 0.000  1 0.000 0.000
#> GSM892379     2  0.0000     1.0000 0.000  1 0.000 0.000
#> GSM892385     2  0.0000     1.0000 0.000  1 0.000 0.000
#> GSM892389     2  0.0000     1.0000 0.000  1 0.000 0.000
#> GSM892341     3  0.0592     0.9036 0.000  0 0.984 0.016
#> GSM892346     4  0.0804     0.8939 0.012  0 0.008 0.980
#> GSM892350     4  0.0817     0.9037 0.000  0 0.024 0.976
#> GSM892354     1  0.0000     0.9989 1.000  0 0.000 0.000
#> GSM892356     1  0.0000     0.9989 1.000  0 0.000 0.000
#> GSM892362     1  0.0000     0.9989 1.000  0 0.000 0.000
#> GSM892366     3  0.0336     0.9025 0.000  0 0.992 0.008
#> GSM892370     3  0.1792     0.8835 0.000  0 0.932 0.068
#> GSM892374     2  0.0000     1.0000 0.000  1 0.000 0.000
#> GSM892378     2  0.0000     1.0000 0.000  1 0.000 0.000
#> GSM892382     2  0.0000     1.0000 0.000  1 0.000 0.000
#> GSM892384     2  0.0000     1.0000 0.000  1 0.000 0.000
#> GSM892388     2  0.0000     1.0000 0.000  1 0.000 0.000
#> GSM892343     3  0.4164     0.6520 0.000  0 0.736 0.264
#> GSM892348     4  0.0804     0.9001 0.008  0 0.012 0.980
#> GSM892352     3  0.4981     0.1314 0.000  0 0.536 0.464
#> GSM892358     1  0.0000     0.9989 1.000  0 0.000 0.000
#> GSM892360     1  0.0000     0.9989 1.000  0 0.000 0.000
#> GSM892364     1  0.0336     0.9923 0.992  0 0.000 0.008
#> GSM892368     3  0.0188     0.8977 0.000  0 0.996 0.004
#> GSM892372     3  0.0592     0.9035 0.000  0 0.984 0.016
#> GSM892376     2  0.0000     1.0000 0.000  1 0.000 0.000
#> GSM892380     2  0.0000     1.0000 0.000  1 0.000 0.000
#> GSM892386     2  0.0000     1.0000 0.000  1 0.000 0.000
#> GSM892390     2  0.0000     1.0000 0.000  1 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 5), get_membership(res, k = 5))

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> GSM892342     5  0.2732      0.851 0.000 0.000 0.160 0.000 0.840
#> GSM892345     4  0.2020      0.917 0.000 0.000 0.000 0.900 0.100
#> GSM892349     5  0.3764      0.783 0.000 0.000 0.044 0.156 0.800
#> GSM892353     1  0.0404      0.988 0.988 0.000 0.000 0.000 0.012
#> GSM892355     1  0.0000      0.999 1.000 0.000 0.000 0.000 0.000
#> GSM892361     1  0.0000      0.999 1.000 0.000 0.000 0.000 0.000
#> GSM892365     3  0.4060      0.621 0.000 0.000 0.640 0.000 0.360
#> GSM892369     3  0.0510      0.729 0.000 0.000 0.984 0.016 0.000
#> GSM892373     2  0.1270      0.960 0.000 0.948 0.000 0.000 0.052
#> GSM892377     2  0.0510      0.986 0.000 0.984 0.000 0.000 0.016
#> GSM892381     2  0.0000      0.992 0.000 1.000 0.000 0.000 0.000
#> GSM892383     2  0.0290      0.990 0.000 0.992 0.000 0.000 0.008
#> GSM892387     2  0.0000      0.992 0.000 1.000 0.000 0.000 0.000
#> GSM892344     5  0.2583      0.881 0.000 0.000 0.132 0.004 0.864
#> GSM892347     4  0.1544      0.920 0.000 0.000 0.000 0.932 0.068
#> GSM892351     4  0.3336      0.794 0.000 0.000 0.000 0.772 0.228
#> GSM892357     1  0.0000      0.999 1.000 0.000 0.000 0.000 0.000
#> GSM892359     1  0.0000      0.999 1.000 0.000 0.000 0.000 0.000
#> GSM892363     1  0.0000      0.999 1.000 0.000 0.000 0.000 0.000
#> GSM892367     3  0.1544      0.764 0.000 0.000 0.932 0.000 0.068
#> GSM892371     3  0.2676      0.761 0.000 0.000 0.884 0.036 0.080
#> GSM892375     2  0.0000      0.992 0.000 1.000 0.000 0.000 0.000
#> GSM892379     2  0.0000      0.992 0.000 1.000 0.000 0.000 0.000
#> GSM892385     2  0.0290      0.990 0.000 0.992 0.000 0.000 0.008
#> GSM892389     2  0.0000      0.992 0.000 1.000 0.000 0.000 0.000
#> GSM892341     5  0.2561      0.873 0.000 0.000 0.144 0.000 0.856
#> GSM892346     4  0.0290      0.891 0.000 0.000 0.008 0.992 0.000
#> GSM892350     4  0.2230      0.910 0.000 0.000 0.000 0.884 0.116
#> GSM892354     1  0.0000      0.999 1.000 0.000 0.000 0.000 0.000
#> GSM892356     1  0.0000      0.999 1.000 0.000 0.000 0.000 0.000
#> GSM892362     1  0.0000      0.999 1.000 0.000 0.000 0.000 0.000
#> GSM892366     3  0.4219      0.506 0.000 0.000 0.584 0.000 0.416
#> GSM892370     3  0.1012      0.746 0.000 0.000 0.968 0.012 0.020
#> GSM892374     2  0.1670      0.951 0.000 0.936 0.012 0.000 0.052
#> GSM892378     2  0.0510      0.986 0.000 0.984 0.000 0.000 0.016
#> GSM892382     2  0.0000      0.992 0.000 1.000 0.000 0.000 0.000
#> GSM892384     2  0.0000      0.992 0.000 1.000 0.000 0.000 0.000
#> GSM892388     2  0.0162      0.991 0.000 0.996 0.000 0.000 0.004
#> GSM892343     5  0.3037      0.883 0.000 0.000 0.100 0.040 0.860
#> GSM892348     4  0.0404      0.902 0.000 0.000 0.000 0.988 0.012
#> GSM892352     5  0.3159      0.849 0.000 0.000 0.056 0.088 0.856
#> GSM892358     1  0.0000      0.999 1.000 0.000 0.000 0.000 0.000
#> GSM892360     1  0.0000      0.999 1.000 0.000 0.000 0.000 0.000
#> GSM892364     1  0.0000      0.999 1.000 0.000 0.000 0.000 0.000
#> GSM892368     3  0.3752      0.707 0.000 0.000 0.708 0.000 0.292
#> GSM892372     3  0.3508      0.735 0.000 0.000 0.748 0.000 0.252
#> GSM892376     2  0.0000      0.992 0.000 1.000 0.000 0.000 0.000
#> GSM892380     2  0.0000      0.992 0.000 1.000 0.000 0.000 0.000
#> GSM892386     2  0.0162      0.990 0.000 0.996 0.000 0.000 0.004
#> GSM892390     2  0.0290      0.990 0.000 0.992 0.000 0.000 0.008

show/hide code output

cbind(get_classes(res, k = 6), get_membership(res, k = 6))

#>           class entropy silhouette    p1    p2    p3    p4    p5 p6
#> GSM892342     5  0.1714      0.835 0.000 0.000 0.092 0.000 0.908 NA
#> GSM892345     4  0.2163      0.898 0.000 0.000 0.000 0.892 0.092 NA
#> GSM892349     5  0.3736      0.626 0.000 0.000 0.008 0.268 0.716 NA
#> GSM892353     1  0.0000      0.997 1.000 0.000 0.000 0.000 0.000 NA
#> GSM892355     1  0.0146      0.996 0.996 0.000 0.000 0.000 0.000 NA
#> GSM892361     1  0.0000      0.997 1.000 0.000 0.000 0.000 0.000 NA
#> GSM892365     3  0.2454      0.876 0.000 0.000 0.840 0.000 0.160 NA
#> GSM892369     3  0.0777      0.888 0.000 0.000 0.972 0.000 0.004 NA
#> GSM892373     2  0.2854      0.844 0.000 0.792 0.000 0.000 0.000 NA
#> GSM892377     2  0.2527      0.882 0.000 0.832 0.000 0.000 0.000 NA
#> GSM892381     2  0.0000      0.951 0.000 1.000 0.000 0.000 0.000 NA
#> GSM892383     2  0.0937      0.944 0.000 0.960 0.000 0.000 0.000 NA
#> GSM892387     2  0.0363      0.951 0.000 0.988 0.000 0.000 0.000 NA
#> GSM892344     5  0.1633      0.864 0.000 0.000 0.044 0.024 0.932 NA
#> GSM892347     4  0.1584      0.898 0.000 0.000 0.000 0.928 0.064 NA
#> GSM892351     4  0.3023      0.778 0.000 0.000 0.000 0.784 0.212 NA
#> GSM892357     1  0.0000      0.997 1.000 0.000 0.000 0.000 0.000 NA
#> GSM892359     1  0.0146      0.997 0.996 0.000 0.000 0.000 0.000 NA
#> GSM892363     1  0.0146      0.997 0.996 0.000 0.000 0.000 0.000 NA
#> GSM892367     3  0.0972      0.908 0.000 0.000 0.964 0.000 0.028 NA
#> GSM892371     3  0.0964      0.905 0.000 0.000 0.968 0.012 0.016 NA
#> GSM892375     2  0.1007      0.944 0.000 0.956 0.000 0.000 0.000 NA
#> GSM892379     2  0.0865      0.948 0.000 0.964 0.000 0.000 0.000 NA
#> GSM892385     2  0.1007      0.944 0.000 0.956 0.000 0.000 0.000 NA
#> GSM892389     2  0.0363      0.952 0.000 0.988 0.000 0.000 0.000 NA
#> GSM892341     5  0.1387      0.855 0.000 0.000 0.068 0.000 0.932 NA
#> GSM892346     4  0.2151      0.812 0.000 0.000 0.008 0.904 0.016 NA
#> GSM892350     4  0.2048      0.883 0.000 0.000 0.000 0.880 0.120 NA
#> GSM892354     1  0.0146      0.996 0.996 0.000 0.000 0.000 0.000 NA
#> GSM892356     1  0.0000      0.997 1.000 0.000 0.000 0.000 0.000 NA
#> GSM892362     1  0.0146      0.997 0.996 0.000 0.000 0.000 0.000 NA
#> GSM892366     3  0.3023      0.800 0.000 0.000 0.768 0.000 0.232 NA
#> GSM892370     3  0.0520      0.902 0.000 0.000 0.984 0.000 0.008 NA
#> GSM892374     2  0.3126      0.808 0.000 0.752 0.000 0.000 0.000 NA
#> GSM892378     2  0.2527      0.882 0.000 0.832 0.000 0.000 0.000 NA
#> GSM892382     2  0.0260      0.950 0.000 0.992 0.000 0.000 0.000 NA
#> GSM892384     2  0.0260      0.950 0.000 0.992 0.000 0.000 0.000 NA
#> GSM892388     2  0.0363      0.951 0.000 0.988 0.000 0.000 0.000 NA
#> GSM892343     5  0.2492      0.856 0.000 0.000 0.036 0.068 0.888 NA
#> GSM892348     4  0.1245      0.882 0.000 0.000 0.000 0.952 0.032 NA
#> GSM892352     5  0.2994      0.781 0.000 0.000 0.008 0.164 0.820 NA
#> GSM892358     1  0.0000      0.997 1.000 0.000 0.000 0.000 0.000 NA
#> GSM892360     1  0.0146      0.997 0.996 0.000 0.000 0.000 0.000 NA
#> GSM892364     1  0.0458      0.989 0.984 0.000 0.000 0.000 0.000 NA
#> GSM892368     3  0.2212      0.900 0.000 0.000 0.880 0.000 0.112 NA
#> GSM892372     3  0.2003      0.901 0.000 0.000 0.884 0.000 0.116 NA
#> GSM892376     2  0.0790      0.948 0.000 0.968 0.000 0.000 0.000 NA
#> GSM892380     2  0.0260      0.951 0.000 0.992 0.000 0.000 0.000 NA
#> GSM892386     2  0.0547      0.951 0.000 0.980 0.000 0.000 0.000 NA
#> GSM892390     2  0.0260      0.950 0.000 0.992 0.000 0.000 0.000 NA

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

k = 2
k = 3
k = 4
k = 5
k = 6

consensus_heatmap(res, k = 2)

plot of chunk tab-CV-NMF-consensus-heatmap-1

consensus_heatmap(res, k = 3)

plot of chunk tab-CV-NMF-consensus-heatmap-2

consensus_heatmap(res, k = 4)

plot of chunk tab-CV-NMF-consensus-heatmap-3

consensus_heatmap(res, k = 5)

plot of chunk tab-CV-NMF-consensus-heatmap-4

consensus_heatmap(res, k = 6)

plot of chunk tab-CV-NMF-consensus-heatmap-5

Heatmaps for the membership of samples in all partitions to see how consistent they are:

k = 2
k = 3
k = 4
k = 5
k = 6

membership_heatmap(res, k = 2)

plot of chunk tab-CV-NMF-membership-heatmap-1

membership_heatmap(res, k = 3)

plot of chunk tab-CV-NMF-membership-heatmap-2

membership_heatmap(res, k = 4)

plot of chunk tab-CV-NMF-membership-heatmap-3

membership_heatmap(res, k = 5)

plot of chunk tab-CV-NMF-membership-heatmap-4

membership_heatmap(res, k = 6)

plot of chunk tab-CV-NMF-membership-heatmap-5

Signature heatmaps where rows are scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2)

plot of chunk tab-CV-NMF-get-signatures-1

get_signatures(res, k = 3)

plot of chunk tab-CV-NMF-get-signatures-2

get_signatures(res, k = 4)

plot of chunk tab-CV-NMF-get-signatures-3

get_signatures(res, k = 5)

plot of chunk tab-CV-NMF-get-signatures-4

get_signatures(res, k = 6)

plot of chunk tab-CV-NMF-get-signatures-5

Signature heatmaps where rows are not scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-CV-NMF-get-signatures-no-scale-1

get_signatures(res, k = 3, scale_rows = FALSE)

plot of chunk tab-CV-NMF-get-signatures-no-scale-2

get_signatures(res, k = 4, scale_rows = FALSE)

plot of chunk tab-CV-NMF-get-signatures-no-scale-3

get_signatures(res, k = 5, scale_rows = FALSE)

plot of chunk tab-CV-NMF-get-signatures-no-scale-4

get_signatures(res, k = 6, scale_rows = FALSE)

plot of chunk tab-CV-NMF-get-signatures-no-scale-5

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk CV-NMF-signature_compare

# 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.

k = 2
k = 3
k = 4
k = 5
k = 6

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-CV-NMF-dimension-reduction-1

dimension_reduction(res, k = 3, method = "UMAP")

plot of chunk tab-CV-NMF-dimension-reduction-2

dimension_reduction(res, k = 4, method = "UMAP")

plot of chunk tab-CV-NMF-dimension-reduction-3

dimension_reduction(res, k = 5, method = "UMAP")

plot of chunk tab-CV-NMF-dimension-reduction-4

dimension_reduction(res, k = 6, method = "UMAP")

plot of chunk tab-CV-NMF-dimension-reduction-5

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk CV-NMF-collect-classes

test_to_known_factors(res)

#>         n tissue(p) disease.state(p) other(p) individual(p) k
#> CV:NMF 50     1.000            0.934 2.67e-07      1.42e-03 2
#> CV:NMF 50     0.939            0.875 8.67e-12      3.79e-05 3
#> CV:NMF 48     1.000            0.987 7.68e-17      1.01e-06 4
#> CV:NMF 50     1.000            0.998 3.06e-20      2.01e-07 5
#> CV:NMF 50     1.000            0.998 3.06e-20      2.01e-07 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

MAD:hclust**

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 31632 rows and 50 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 5.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk MAD-hclust-collect-plots

The plots are:

The first row: a plot of the ECDF (empirical cumulative distribution function) curves of the consensus matrix for each k and the heatmap of predicted classes for each k.
The second row: heatmaps of the consensus matrix for each k.
The third row: heatmaps of the membership matrix for each k.
The fouth row: heatmaps of the signatures for each 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:

ECDF curves of the consensus matrix for each k;
1-PAC. The PAC score measures the proportion of the ambiguous subgrouping.
Mean silhouette score.
Concordance. The mean probability of fiting the consensus class ids in all partitions.
Area increased. Denote \(A_k\) as the area under the ECDF curve for current k, the area increased is defined as \(A_k - A_{k-1}\).
Rand index. The percent of pairs of samples that are both in a same cluster or both are not in a same cluster in the partition of k and k-1.
Jaccard index. The ratio of pairs of samples are both in a same cluster in the partition of k and k-1 and the pairs of samples are both in a same cluster in the partition k or k-1.

The detailed explanations of these statistics can be found in the cola vignette.

select_partition_number(res)

plot of chunk MAD-hclust-select-partition-number

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         0.4707 0.530   0.530
#> 3 3 1.000           0.962       0.981         0.4312 0.794   0.612
#> 4 4 1.000           0.956       0.976         0.0916 0.941   0.819
#> 5 5 0.961           0.914       0.950         0.0457 0.963   0.862
#> 6 6 0.936           0.787       0.871         0.0227 0.993   0.971

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

All \(k\) with Jaccard index larger than 0.95 are removed because increasing \(k\) does not provide enough extra information. If all \(k\) are removed, it is marked as no subgroup is detected.
For all \(k\) with 1-PAC score larger than 0.9, the maximal \(k\) is taken as the best \(k\), and other \(k\) are marked as optional \(k\).
If it does not fit the second rule. The \(k\) with the maximal vote of the highest 1-PAC score, highest mean silhouette, and highest concordance is taken as the best \(k\).

suggest_best_k(res)

#> [1] 5
#> attr(,"optional")
#> [1] 2 3 4

There is also optional best \(k\) = 2 3 4 that is worth to check.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

k = 2
k = 3
k = 4
k = 5
k = 6

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>           class entropy silhouette p1 p2
#> GSM892342     1       0          1  1  0
#> GSM892345     1       0          1  1  0
#> GSM892349     1       0          1  1  0
#> GSM892353     1       0          1  1  0
#> GSM892355     1       0          1  1  0
#> GSM892361     1       0          1  1  0
#> GSM892365     1       0          1  1  0
#> GSM892369     1       0          1  1  0
#> GSM892373     2       0          1  0  1
#> GSM892377     2       0          1  0  1
#> GSM892381     2       0          1  0  1
#> GSM892383     2       0          1  0  1
#> GSM892387     2       0          1  0  1
#> GSM892344     1       0          1  1  0
#> GSM892347     1       0          1  1  0
#> GSM892351     1       0          1  1  0
#> GSM892357     1       0          1  1  0
#> GSM892359     1       0          1  1  0
#> GSM892363     1       0          1  1  0
#> GSM892367     1       0          1  1  0
#> GSM892371     1       0          1  1  0
#> GSM892375     2       0          1  0  1
#> GSM892379     2       0          1  0  1
#> GSM892385     2       0          1  0  1
#> GSM892389     2       0          1  0  1
#> GSM892341     1       0          1  1  0
#> GSM892346     1       0          1  1  0
#> GSM892350     1       0          1  1  0
#> GSM892354     1       0          1  1  0
#> GSM892356     1       0          1  1  0
#> GSM892362     1       0          1  1  0
#> GSM892366     1       0          1  1  0
#> GSM892370     1       0          1  1  0
#> GSM892374     2       0          1  0  1
#> GSM892378     2       0          1  0  1
#> GSM892382     2       0          1  0  1
#> GSM892384     2       0          1  0  1
#> GSM892388     2       0          1  0  1
#> GSM892343     1       0          1  1  0
#> GSM892348     1       0          1  1  0
#> GSM892352     1       0          1  1  0
#> GSM892358     1       0          1  1  0
#> GSM892360     1       0          1  1  0
#> GSM892364     1       0          1  1  0
#> GSM892368     1       0          1  1  0
#> GSM892372     1       0          1  1  0
#> GSM892376     2       0          1  0  1
#> GSM892380     2       0          1  0  1
#> GSM892386     2       0          1  0  1
#> GSM892390     2       0          1  0  1

show/hide code output

cbind(get_classes(res, k = 3), get_membership(res, k = 3))

#>           class entropy silhouette    p1 p2    p3
#> GSM892342     3  0.0000      0.951 0.000  0 1.000
#> GSM892345     1  0.0000      0.981 1.000  0 0.000
#> GSM892349     3  0.4002      0.828 0.160  0 0.840
#> GSM892353     1  0.0424      0.974 0.992  0 0.008
#> GSM892355     1  0.0000      0.981 1.000  0 0.000
#> GSM892361     1  0.0000      0.981 1.000  0 0.000
#> GSM892365     3  0.0000      0.951 0.000  0 1.000
#> GSM892369     3  0.2356      0.922 0.072  0 0.928
#> GSM892373     2  0.0000      1.000 0.000  1 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000
#> GSM892344     3  0.0000      0.951 0.000  0 1.000
#> GSM892347     1  0.0000      0.981 1.000  0 0.000
#> GSM892351     1  0.5560      0.549 0.700  0 0.300
#> GSM892357     1  0.0000      0.981 1.000  0 0.000
#> GSM892359     1  0.0000      0.981 1.000  0 0.000
#> GSM892363     1  0.0000      0.981 1.000  0 0.000
#> GSM892367     3  0.0000      0.951 0.000  0 1.000
#> GSM892371     3  0.2356      0.922 0.072  0 0.928
#> GSM892375     2  0.0000      1.000 0.000  1 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000
#> GSM892341     3  0.0000      0.951 0.000  0 1.000
#> GSM892346     1  0.0000      0.981 1.000  0 0.000
#> GSM892350     1  0.0000      0.981 1.000  0 0.000
#> GSM892354     1  0.0000      0.981 1.000  0 0.000
#> GSM892356     1  0.0000      0.981 1.000  0 0.000
#> GSM892362     1  0.0000      0.981 1.000  0 0.000
#> GSM892366     3  0.0000      0.951 0.000  0 1.000
#> GSM892370     3  0.2356      0.922 0.072  0 0.928
#> GSM892374     2  0.0000      1.000 0.000  1 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000
#> GSM892343     3  0.5016      0.727 0.240  0 0.760
#> GSM892348     1  0.0000      0.981 1.000  0 0.000
#> GSM892352     3  0.0424      0.949 0.008  0 0.992
#> GSM892358     1  0.0000      0.981 1.000  0 0.000
#> GSM892360     1  0.0000      0.981 1.000  0 0.000
#> GSM892364     1  0.0237      0.977 0.996  0 0.004
#> GSM892368     3  0.0000      0.951 0.000  0 1.000
#> GSM892372     3  0.0000      0.951 0.000  0 1.000
#> GSM892376     2  0.0000      1.000 0.000  1 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000

show/hide code output

cbind(get_classes(res, k = 4), get_membership(res, k = 4))

#>           class entropy silhouette    p1 p2    p3    p4
#> GSM892342     3  0.0336      0.946 0.000  0 0.992 0.008
#> GSM892345     4  0.0817      0.932 0.024  0 0.000 0.976
#> GSM892349     3  0.3266      0.815 0.000  0 0.832 0.168
#> GSM892353     1  0.0469      0.983 0.988  0 0.000 0.012
#> GSM892355     1  0.0188      0.987 0.996  0 0.000 0.004
#> GSM892361     1  0.0817      0.980 0.976  0 0.000 0.024
#> GSM892365     3  0.0000      0.948 0.000  0 1.000 0.000
#> GSM892369     3  0.1867      0.917 0.000  0 0.928 0.072
#> GSM892373     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892344     3  0.0336      0.946 0.000  0 0.992 0.008
#> GSM892347     4  0.0817      0.932 0.024  0 0.000 0.976
#> GSM892351     4  0.4908      0.556 0.016  0 0.292 0.692
#> GSM892357     1  0.0707      0.982 0.980  0 0.000 0.020
#> GSM892359     1  0.0000      0.988 1.000  0 0.000 0.000
#> GSM892363     1  0.0000      0.988 1.000  0 0.000 0.000
#> GSM892367     3  0.0000      0.948 0.000  0 1.000 0.000
#> GSM892371     3  0.1867      0.917 0.000  0 0.928 0.072
#> GSM892375     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892341     3  0.0336      0.946 0.000  0 0.992 0.008
#> GSM892346     4  0.0469      0.922 0.012  0 0.000 0.988
#> GSM892350     4  0.0817      0.932 0.024  0 0.000 0.976
#> GSM892354     1  0.0817      0.980 0.976  0 0.000 0.024
#> GSM892356     1  0.0188      0.987 0.996  0 0.000 0.004
#> GSM892362     1  0.0336      0.986 0.992  0 0.000 0.008
#> GSM892366     3  0.0000      0.948 0.000  0 1.000 0.000
#> GSM892370     3  0.1867      0.917 0.000  0 0.928 0.072
#> GSM892374     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892343     3  0.4538      0.733 0.024  0 0.760 0.216
#> GSM892348     4  0.0921      0.931 0.028  0 0.000 0.972
#> GSM892352     3  0.0592      0.944 0.000  0 0.984 0.016
#> GSM892358     1  0.0000      0.988 1.000  0 0.000 0.000
#> GSM892360     1  0.0000      0.988 1.000  0 0.000 0.000
#> GSM892364     1  0.1398      0.954 0.956  0 0.004 0.040
#> GSM892368     3  0.0000      0.948 0.000  0 1.000 0.000
#> GSM892372     3  0.0000      0.948 0.000  0 1.000 0.000
#> GSM892376     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 5), get_membership(res, k = 5))

#>           class entropy silhouette    p1 p2    p3    p4    p5
#> GSM892342     5  0.3876      0.775 0.000  0 0.316 0.000 0.684
#> GSM892345     4  0.0000      0.925 0.000  0 0.000 1.000 0.000
#> GSM892349     5  0.3197      0.567 0.000  0 0.024 0.140 0.836
#> GSM892353     1  0.0404      0.984 0.988  0 0.000 0.000 0.012
#> GSM892355     1  0.0162      0.988 0.996  0 0.000 0.000 0.004
#> GSM892361     1  0.0703      0.981 0.976  0 0.000 0.000 0.024
#> GSM892365     3  0.0162      0.870 0.000  0 0.996 0.000 0.004
#> GSM892369     3  0.2659      0.838 0.000  0 0.888 0.060 0.052
#> GSM892373     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892344     5  0.3876      0.775 0.000  0 0.316 0.000 0.684
#> GSM892347     4  0.0000      0.925 0.000  0 0.000 1.000 0.000
#> GSM892351     4  0.3895      0.619 0.000  0 0.000 0.680 0.320
#> GSM892357     1  0.0609      0.983 0.980  0 0.000 0.000 0.020
#> GSM892359     1  0.0000      0.988 1.000  0 0.000 0.000 0.000
#> GSM892363     1  0.0000      0.988 1.000  0 0.000 0.000 0.000
#> GSM892367     3  0.0162      0.870 0.000  0 0.996 0.000 0.004
#> GSM892371     3  0.2659      0.838 0.000  0 0.888 0.060 0.052
#> GSM892375     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892341     5  0.3876      0.775 0.000  0 0.316 0.000 0.684
#> GSM892346     4  0.1124      0.910 0.004  0 0.000 0.960 0.036
#> GSM892350     4  0.0404      0.920 0.000  0 0.000 0.988 0.012
#> GSM892354     1  0.0703      0.981 0.976  0 0.000 0.000 0.024
#> GSM892356     1  0.0162      0.988 0.996  0 0.000 0.000 0.004
#> GSM892362     1  0.0290      0.987 0.992  0 0.000 0.000 0.008
#> GSM892366     3  0.0162      0.870 0.000  0 0.996 0.000 0.004
#> GSM892370     3  0.2659      0.838 0.000  0 0.888 0.060 0.052
#> GSM892374     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892343     3  0.6855      0.211 0.024  0 0.512 0.192 0.272
#> GSM892348     4  0.0566      0.921 0.004  0 0.000 0.984 0.012
#> GSM892352     5  0.1270      0.704 0.000  0 0.052 0.000 0.948
#> GSM892358     1  0.0000      0.988 1.000  0 0.000 0.000 0.000
#> GSM892360     1  0.0000      0.988 1.000  0 0.000 0.000 0.000
#> GSM892364     1  0.1300      0.957 0.956  0 0.000 0.028 0.016
#> GSM892368     3  0.0162      0.870 0.000  0 0.996 0.000 0.004
#> GSM892372     3  0.0162      0.870 0.000  0 0.996 0.000 0.004
#> GSM892376     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 6), get_membership(res, k = 6))

#>           class entropy silhouette    p1 p2    p3    p4    p5    p6
#> GSM892342     5  0.0000    0.78930 0.000  0 0.000 0.000 1.000 0.000
#> GSM892345     4  0.3695   -0.14715 0.000  0 0.000 0.624 0.000 0.376
#> GSM892349     5  0.4289    0.56648 0.000  0 0.012 0.444 0.540 0.004
#> GSM892353     1  0.2389    0.91090 0.864  0 0.000 0.000 0.008 0.128
#> GSM892355     1  0.1501    0.93998 0.924  0 0.000 0.000 0.000 0.076
#> GSM892361     1  0.0937    0.94661 0.960  0 0.000 0.000 0.000 0.040
#> GSM892365     3  0.5839    0.65430 0.000  0 0.488 0.000 0.236 0.276
#> GSM892369     3  0.0458    0.55654 0.000  0 0.984 0.016 0.000 0.000
#> GSM892373     2  0.0000    1.00000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892377     2  0.0000    1.00000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892381     2  0.0000    1.00000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892383     2  0.0000    1.00000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892387     2  0.0000    1.00000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892344     5  0.0000    0.78930 0.000  0 0.000 0.000 1.000 0.000
#> GSM892347     4  0.3765   -0.31004 0.000  0 0.000 0.596 0.000 0.404
#> GSM892351     4  0.0363    0.14729 0.000  0 0.012 0.988 0.000 0.000
#> GSM892357     1  0.0790    0.94925 0.968  0 0.000 0.000 0.000 0.032
#> GSM892359     1  0.0458    0.95329 0.984  0 0.000 0.000 0.000 0.016
#> GSM892363     1  0.1765    0.93077 0.904  0 0.000 0.000 0.000 0.096
#> GSM892367     3  0.5839    0.65430 0.000  0 0.488 0.000 0.236 0.276
#> GSM892371     3  0.0458    0.55654 0.000  0 0.984 0.016 0.000 0.000
#> GSM892375     2  0.0000    1.00000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892379     2  0.0000    1.00000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892385     2  0.0000    1.00000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892389     2  0.0000    1.00000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892341     5  0.0000    0.78930 0.000  0 0.000 0.000 1.000 0.000
#> GSM892346     6  0.3975    0.86878 0.004  0 0.000 0.452 0.000 0.544
#> GSM892350     4  0.3802    0.11642 0.000  0 0.012 0.676 0.000 0.312
#> GSM892354     1  0.0937    0.94661 0.960  0 0.000 0.000 0.000 0.040
#> GSM892356     1  0.0790    0.95114 0.968  0 0.000 0.000 0.000 0.032
#> GSM892362     1  0.0547    0.95149 0.980  0 0.000 0.000 0.000 0.020
#> GSM892366     3  0.5839    0.65430 0.000  0 0.488 0.000 0.236 0.276
#> GSM892370     3  0.0458    0.55654 0.000  0 0.984 0.016 0.000 0.000
#> GSM892374     2  0.0000    1.00000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892378     2  0.0000    1.00000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892382     2  0.0000    1.00000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892384     2  0.0000    1.00000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892388     2  0.0000    1.00000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892343     3  0.6268   -0.00826 0.016  0 0.584 0.156 0.204 0.040
#> GSM892348     6  0.3995    0.86043 0.004  0 0.000 0.480 0.000 0.516
#> GSM892352     5  0.3446    0.68491 0.000  0 0.000 0.308 0.692 0.000
#> GSM892358     1  0.0146    0.95344 0.996  0 0.000 0.000 0.000 0.004
#> GSM892360     1  0.0458    0.95329 0.984  0 0.000 0.000 0.000 0.016
#> GSM892364     1  0.2664    0.89894 0.848  0 0.000 0.016 0.000 0.136
#> GSM892368     3  0.5839    0.65430 0.000  0 0.488 0.000 0.236 0.276
#> GSM892372     3  0.5839    0.65430 0.000  0 0.488 0.000 0.236 0.276
#> GSM892376     2  0.0000    1.00000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892380     2  0.0000    1.00000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892386     2  0.0000    1.00000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892390     2  0.0000    1.00000 0.000  1 0.000 0.000 0.000 0.000

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

k = 2
k = 3
k = 4
k = 5
k = 6

consensus_heatmap(res, k = 2)

plot of chunk tab-MAD-hclust-consensus-heatmap-1

consensus_heatmap(res, k = 3)

plot of chunk tab-MAD-hclust-consensus-heatmap-2

consensus_heatmap(res, k = 4)

plot of chunk tab-MAD-hclust-consensus-heatmap-3

consensus_heatmap(res, k = 5)

plot of chunk tab-MAD-hclust-consensus-heatmap-4

consensus_heatmap(res, k = 6)

plot of chunk tab-MAD-hclust-consensus-heatmap-5

Heatmaps for the membership of samples in all partitions to see how consistent they are:

k = 2
k = 3
k = 4
k = 5
k = 6

membership_heatmap(res, k = 2)

plot of chunk tab-MAD-hclust-membership-heatmap-1

membership_heatmap(res, k = 3)

plot of chunk tab-MAD-hclust-membership-heatmap-2

membership_heatmap(res, k = 4)

plot of chunk tab-MAD-hclust-membership-heatmap-3

membership_heatmap(res, k = 5)

plot of chunk tab-MAD-hclust-membership-heatmap-4

membership_heatmap(res, k = 6)

plot of chunk tab-MAD-hclust-membership-heatmap-5

Signature heatmaps where rows are scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2)

plot of chunk tab-MAD-hclust-get-signatures-1

get_signatures(res, k = 3)

plot of chunk tab-MAD-hclust-get-signatures-2

get_signatures(res, k = 4)

plot of chunk tab-MAD-hclust-get-signatures-3

get_signatures(res, k = 5)

plot of chunk tab-MAD-hclust-get-signatures-4

get_signatures(res, k = 6)

plot of chunk tab-MAD-hclust-get-signatures-5

Signature heatmaps where rows are not scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-MAD-hclust-get-signatures-no-scale-1

get_signatures(res, k = 3, scale_rows = FALSE)

plot of chunk tab-MAD-hclust-get-signatures-no-scale-2

get_signatures(res, k = 4, scale_rows = FALSE)

plot of chunk tab-MAD-hclust-get-signatures-no-scale-3

get_signatures(res, k = 5, scale_rows = FALSE)

plot of chunk tab-MAD-hclust-get-signatures-no-scale-4

get_signatures(res, k = 6, scale_rows = FALSE)

plot of chunk tab-MAD-hclust-get-signatures-no-scale-5

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk MAD-hclust-signature_compare

# 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.

k = 2
k = 3
k = 4
k = 5
k = 6

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-MAD-hclust-dimension-reduction-1

dimension_reduction(res, k = 3, method = "UMAP")

plot of chunk tab-MAD-hclust-dimension-reduction-2

dimension_reduction(res, k = 4, method = "UMAP")

plot of chunk tab-MAD-hclust-dimension-reduction-3

dimension_reduction(res, k = 5, method = "UMAP")

plot of chunk tab-MAD-hclust-dimension-reduction-4

dimension_reduction(res, k = 6, method = "UMAP")

plot of chunk tab-MAD-hclust-dimension-reduction-5

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk MAD-hclust-collect-classes

test_to_known_factors(res)

#>             n tissue(p) disease.state(p) other(p) individual(p) k
#> MAD:hclust 50     1.000            0.934 2.67e-07      1.42e-03 2
#> MAD:hclust 50     1.000            0.931 1.69e-11      8.93e-05 3
#> MAD:hclust 50     1.000            0.986 8.26e-16      4.62e-06 4
#> MAD:hclust 49     0.996            0.993 2.50e-19      7.39e-07 5
#> MAD:hclust 45     0.703            0.994 1.15e-19      4.58e-07 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

MAD:kmeans**

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 31632 rows and 50 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)

plot of chunk MAD-kmeans-collect-plots

The plots are:

The first row: a plot of the ECDF (empirical cumulative distribution function) curves of the consensus matrix for each k and the heatmap of predicted classes for each k.
The second row: heatmaps of the consensus matrix for each k.
The third row: heatmaps of the membership matrix for each k.
The fouth row: heatmaps of the signatures for each 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:

ECDF curves of the consensus matrix for each k;
1-PAC. The PAC score measures the proportion of the ambiguous subgrouping.
Mean silhouette score.
Concordance. The mean probability of fiting the consensus class ids in all partitions.
Area increased. Denote \(A_k\) as the area under the ECDF curve for current k, the area increased is defined as \(A_k - A_{k-1}\).
Rand index. The percent of pairs of samples that are both in a same cluster or both are not in a same cluster in the partition of k and k-1.
Jaccard index. The ratio of pairs of samples are both in a same cluster in the partition of k and k-1 and the pairs of samples are both in a same cluster in the partition k or k-1.

The detailed explanations of these statistics can be found in the cola vignette.

select_partition_number(res)

plot of chunk MAD-kmeans-select-partition-number

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         0.4707 0.530   0.530
#> 3 3 0.699           0.874       0.856         0.3384 0.794   0.612
#> 4 4 0.635           0.881       0.831         0.1311 0.912   0.736
#> 5 5 0.693           0.756       0.820         0.0692 0.974   0.898
#> 6 6 0.751           0.699       0.804         0.0509 1.000   1.000

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

All \(k\) with Jaccard index larger than 0.95 are removed because increasing \(k\) does not provide enough extra information. If all \(k\) are removed, it is marked as no subgroup is detected.
For all \(k\) with 1-PAC score larger than 0.9, the maximal \(k\) is taken as the best \(k\), and other \(k\) are marked as optional \(k\).
If it does not fit the second rule. The \(k\) with the maximal vote of the highest 1-PAC score, highest mean silhouette, and highest concordance is taken as the best \(k\).

suggest_best_k(res)

#> [1] 2

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

k = 2
k = 3
k = 4
k = 5
k = 6

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>           class entropy silhouette p1 p2
#> GSM892342     1       0          1  1  0
#> GSM892345     1       0          1  1  0
#> GSM892349     1       0          1  1  0
#> GSM892353     1       0          1  1  0
#> GSM892355     1       0          1  1  0
#> GSM892361     1       0          1  1  0
#> GSM892365     1       0          1  1  0
#> GSM892369     1       0          1  1  0
#> GSM892373     2       0          1  0  1
#> GSM892377     2       0          1  0  1
#> GSM892381     2       0          1  0  1
#> GSM892383     2       0          1  0  1
#> GSM892387     2       0          1  0  1
#> GSM892344     1       0          1  1  0
#> GSM892347     1       0          1  1  0
#> GSM892351     1       0          1  1  0
#> GSM892357     1       0          1  1  0
#> GSM892359     1       0          1  1  0
#> GSM892363     1       0          1  1  0
#> GSM892367     1       0          1  1  0
#> GSM892371     1       0          1  1  0
#> GSM892375     2       0          1  0  1
#> GSM892379     2       0          1  0  1
#> GSM892385     2       0          1  0  1
#> GSM892389     2       0          1  0  1
#> GSM892341     1       0          1  1  0
#> GSM892346     1       0          1  1  0
#> GSM892350     1       0          1  1  0
#> GSM892354     1       0          1  1  0
#> GSM892356     1       0          1  1  0
#> GSM892362     1       0          1  1  0
#> GSM892366     1       0          1  1  0
#> GSM892370     1       0          1  1  0
#> GSM892374     2       0          1  0  1
#> GSM892378     2       0          1  0  1
#> GSM892382     2       0          1  0  1
#> GSM892384     2       0          1  0  1
#> GSM892388     2       0          1  0  1
#> GSM892343     1       0          1  1  0
#> GSM892348     1       0          1  1  0
#> GSM892352     1       0          1  1  0
#> GSM892358     1       0          1  1  0
#> GSM892360     1       0          1  1  0
#> GSM892364     1       0          1  1  0
#> GSM892368     1       0          1  1  0
#> GSM892372     1       0          1  1  0
#> GSM892376     2       0          1  0  1
#> GSM892380     2       0          1  0  1
#> GSM892386     2       0          1  0  1
#> GSM892390     2       0          1  0  1

show/hide code output

cbind(get_classes(res, k = 3), get_membership(res, k = 3))

#>           class entropy silhouette    p1    p2    p3
#> GSM892342     3  0.0000      0.884 0.000 0.000 1.000
#> GSM892345     3  0.5859      0.202 0.344 0.000 0.656
#> GSM892349     3  0.0424      0.877 0.008 0.000 0.992
#> GSM892353     1  0.5560      0.980 0.700 0.000 0.300
#> GSM892355     1  0.5560      0.980 0.700 0.000 0.300
#> GSM892361     1  0.5560      0.980 0.700 0.000 0.300
#> GSM892365     3  0.0000      0.884 0.000 0.000 1.000
#> GSM892369     3  0.0000      0.884 0.000 0.000 1.000
#> GSM892373     2  0.4750      0.897 0.216 0.784 0.000
#> GSM892377     2  0.3879      0.933 0.152 0.848 0.000
#> GSM892381     2  0.0000      0.949 0.000 1.000 0.000
#> GSM892383     2  0.1289      0.948 0.032 0.968 0.000
#> GSM892387     2  0.0747      0.949 0.016 0.984 0.000
#> GSM892344     3  0.0000      0.884 0.000 0.000 1.000
#> GSM892347     3  0.5859      0.202 0.344 0.000 0.656
#> GSM892351     3  0.5178      0.479 0.256 0.000 0.744
#> GSM892357     1  0.5560      0.980 0.700 0.000 0.300
#> GSM892359     1  0.5560      0.980 0.700 0.000 0.300
#> GSM892363     1  0.5560      0.980 0.700 0.000 0.300
#> GSM892367     3  0.0000      0.884 0.000 0.000 1.000
#> GSM892371     3  0.0000      0.884 0.000 0.000 1.000
#> GSM892375     2  0.2165      0.941 0.064 0.936 0.000
#> GSM892379     2  0.2878      0.946 0.096 0.904 0.000
#> GSM892385     2  0.3267      0.938 0.116 0.884 0.000
#> GSM892389     2  0.2878      0.943 0.096 0.904 0.000
#> GSM892341     3  0.0000      0.884 0.000 0.000 1.000
#> GSM892346     1  0.5497      0.969 0.708 0.000 0.292
#> GSM892350     3  0.5859      0.202 0.344 0.000 0.656
#> GSM892354     1  0.5560      0.980 0.700 0.000 0.300
#> GSM892356     1  0.5560      0.980 0.700 0.000 0.300
#> GSM892362     1  0.5560      0.980 0.700 0.000 0.300
#> GSM892366     3  0.0000      0.884 0.000 0.000 1.000
#> GSM892370     3  0.0000      0.884 0.000 0.000 1.000
#> GSM892374     2  0.4750      0.897 0.216 0.784 0.000
#> GSM892378     2  0.3879      0.933 0.152 0.848 0.000
#> GSM892382     2  0.0000      0.949 0.000 1.000 0.000
#> GSM892384     2  0.0000      0.949 0.000 1.000 0.000
#> GSM892388     2  0.4235      0.908 0.176 0.824 0.000
#> GSM892343     3  0.0000      0.884 0.000 0.000 1.000
#> GSM892348     1  0.6235      0.683 0.564 0.000 0.436
#> GSM892352     3  0.0424      0.877 0.008 0.000 0.992
#> GSM892358     1  0.5560      0.980 0.700 0.000 0.300
#> GSM892360     1  0.5560      0.980 0.700 0.000 0.300
#> GSM892364     1  0.5560      0.980 0.700 0.000 0.300
#> GSM892368     3  0.0000      0.884 0.000 0.000 1.000
#> GSM892372     3  0.0000      0.884 0.000 0.000 1.000
#> GSM892376     2  0.2066      0.942 0.060 0.940 0.000
#> GSM892380     2  0.1163      0.949 0.028 0.972 0.000
#> GSM892386     2  0.0424      0.948 0.008 0.992 0.000
#> GSM892390     2  0.2625      0.944 0.084 0.916 0.000

show/hide code output

cbind(get_classes(res, k = 4), get_membership(res, k = 4))

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM892342     3  0.2647      0.972 0.120 0.000 0.880 0.000
#> GSM892345     4  0.7457      0.786 0.276 0.000 0.220 0.504
#> GSM892349     4  0.7026      0.475 0.120 0.000 0.404 0.476
#> GSM892353     1  0.0707      0.979 0.980 0.000 0.000 0.020
#> GSM892355     1  0.0707      0.979 0.980 0.000 0.000 0.020
#> GSM892361     1  0.0000      0.996 1.000 0.000 0.000 0.000
#> GSM892365     3  0.2647      0.972 0.120 0.000 0.880 0.000
#> GSM892369     3  0.3907      0.943 0.120 0.000 0.836 0.044
#> GSM892373     2  0.4907      0.756 0.000 0.580 0.000 0.420
#> GSM892377     2  0.4459      0.856 0.000 0.780 0.032 0.188
#> GSM892381     2  0.1833      0.892 0.000 0.944 0.032 0.024
#> GSM892383     2  0.1406      0.893 0.000 0.960 0.024 0.016
#> GSM892387     2  0.2797      0.891 0.000 0.900 0.032 0.068
#> GSM892344     3  0.2647      0.972 0.120 0.000 0.880 0.000
#> GSM892347     4  0.7457      0.786 0.276 0.000 0.220 0.504
#> GSM892351     4  0.7478      0.753 0.240 0.000 0.256 0.504
#> GSM892357     1  0.0000      0.996 1.000 0.000 0.000 0.000
#> GSM892359     1  0.0000      0.996 1.000 0.000 0.000 0.000
#> GSM892363     1  0.0000      0.996 1.000 0.000 0.000 0.000
#> GSM892367     3  0.2647      0.972 0.120 0.000 0.880 0.000
#> GSM892371     3  0.3907      0.943 0.120 0.000 0.836 0.044
#> GSM892375     2  0.4290      0.865 0.000 0.800 0.036 0.164
#> GSM892379     2  0.2699      0.889 0.000 0.904 0.028 0.068
#> GSM892385     2  0.3764      0.872 0.000 0.852 0.076 0.072
#> GSM892389     2  0.2670      0.889 0.000 0.904 0.024 0.072
#> GSM892341     3  0.2647      0.972 0.120 0.000 0.880 0.000
#> GSM892346     4  0.5000      0.386 0.496 0.000 0.000 0.504
#> GSM892350     4  0.7457      0.786 0.276 0.000 0.220 0.504
#> GSM892354     1  0.0000      0.996 1.000 0.000 0.000 0.000
#> GSM892356     1  0.0000      0.996 1.000 0.000 0.000 0.000
#> GSM892362     1  0.0000      0.996 1.000 0.000 0.000 0.000
#> GSM892366     3  0.2647      0.972 0.120 0.000 0.880 0.000
#> GSM892370     3  0.3907      0.943 0.120 0.000 0.836 0.044
#> GSM892374     2  0.4907      0.756 0.000 0.580 0.000 0.420
#> GSM892378     2  0.4459      0.856 0.000 0.780 0.032 0.188
#> GSM892382     2  0.1724      0.892 0.000 0.948 0.032 0.020
#> GSM892384     2  0.1724      0.892 0.000 0.948 0.032 0.020
#> GSM892388     2  0.5358      0.808 0.000 0.700 0.048 0.252
#> GSM892343     3  0.4227      0.921 0.120 0.000 0.820 0.060
#> GSM892348     4  0.6672      0.626 0.408 0.000 0.088 0.504
#> GSM892352     4  0.7026      0.475 0.120 0.000 0.404 0.476
#> GSM892358     1  0.0000      0.996 1.000 0.000 0.000 0.000
#> GSM892360     1  0.0000      0.996 1.000 0.000 0.000 0.000
#> GSM892364     1  0.0000      0.996 1.000 0.000 0.000 0.000
#> GSM892368     3  0.2647      0.972 0.120 0.000 0.880 0.000
#> GSM892372     3  0.2647      0.972 0.120 0.000 0.880 0.000
#> GSM892376     2  0.4197      0.867 0.000 0.808 0.036 0.156
#> GSM892380     2  0.1042      0.894 0.000 0.972 0.008 0.020
#> GSM892386     2  0.1356      0.894 0.000 0.960 0.032 0.008
#> GSM892390     2  0.2521      0.889 0.000 0.912 0.024 0.064

show/hide code output

cbind(get_classes(res, k = 5), get_membership(res, k = 5))

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> GSM892342     3  0.3950      0.838 0.068 0.000 0.796 0.000 0.136
#> GSM892345     4  0.4428      0.856 0.144 0.000 0.096 0.760 0.000
#> GSM892349     4  0.7026      0.610 0.064 0.000 0.212 0.556 0.168
#> GSM892353     1  0.2574      0.919 0.876 0.000 0.000 0.012 0.112
#> GSM892355     1  0.2574      0.919 0.876 0.000 0.000 0.012 0.112
#> GSM892361     1  0.1608      0.938 0.928 0.000 0.000 0.000 0.072
#> GSM892365     3  0.1704      0.886 0.068 0.000 0.928 0.000 0.004
#> GSM892369     3  0.4465      0.852 0.068 0.000 0.800 0.056 0.076
#> GSM892373     5  0.4256      1.000 0.000 0.436 0.000 0.000 0.564
#> GSM892377     2  0.4971      0.397 0.000 0.708 0.000 0.116 0.176
#> GSM892381     2  0.1934      0.663 0.000 0.932 0.008 0.040 0.020
#> GSM892383     2  0.1990      0.664 0.000 0.920 0.008 0.068 0.004
#> GSM892387     2  0.3666      0.580 0.000 0.840 0.020 0.048 0.092
#> GSM892344     3  0.4036      0.836 0.068 0.000 0.788 0.000 0.144
#> GSM892347     4  0.4428      0.856 0.144 0.000 0.096 0.760 0.000
#> GSM892351     4  0.5029      0.842 0.128 0.000 0.112 0.740 0.020
#> GSM892357     1  0.1544      0.940 0.932 0.000 0.000 0.000 0.068
#> GSM892359     1  0.0290      0.950 0.992 0.000 0.000 0.000 0.008
#> GSM892363     1  0.0609      0.951 0.980 0.000 0.000 0.000 0.020
#> GSM892367     3  0.2645      0.883 0.068 0.000 0.888 0.000 0.044
#> GSM892371     3  0.4465      0.852 0.068 0.000 0.800 0.056 0.076
#> GSM892375     2  0.4719      0.345 0.000 0.732 0.012 0.052 0.204
#> GSM892379     2  0.3970      0.614 0.000 0.820 0.016 0.080 0.084
#> GSM892385     2  0.4510      0.581 0.000 0.788 0.032 0.112 0.068
#> GSM892389     2  0.3800      0.621 0.000 0.836 0.028 0.052 0.084
#> GSM892341     3  0.3950      0.838 0.068 0.000 0.796 0.000 0.136
#> GSM892346     4  0.4223      0.739 0.248 0.000 0.000 0.724 0.028
#> GSM892350     4  0.4428      0.856 0.144 0.000 0.096 0.760 0.000
#> GSM892354     1  0.1544      0.940 0.932 0.000 0.000 0.000 0.068
#> GSM892356     1  0.1768      0.940 0.924 0.000 0.000 0.004 0.072
#> GSM892362     1  0.0609      0.948 0.980 0.000 0.000 0.000 0.020
#> GSM892366     3  0.1704      0.886 0.068 0.000 0.928 0.000 0.004
#> GSM892370     3  0.4465      0.852 0.068 0.000 0.800 0.056 0.076
#> GSM892374     5  0.4256      1.000 0.000 0.436 0.000 0.000 0.564
#> GSM892378     2  0.4971      0.397 0.000 0.708 0.000 0.116 0.176
#> GSM892382     2  0.1710      0.664 0.000 0.940 0.004 0.040 0.016
#> GSM892384     2  0.1787      0.662 0.000 0.936 0.004 0.044 0.016
#> GSM892388     2  0.5841     -0.409 0.000 0.560 0.032 0.044 0.364
#> GSM892343     3  0.6278      0.721 0.068 0.000 0.652 0.124 0.156
#> GSM892348     4  0.4285      0.808 0.208 0.000 0.032 0.752 0.008
#> GSM892352     4  0.7095      0.594 0.064 0.000 0.224 0.544 0.168
#> GSM892358     1  0.0671      0.951 0.980 0.000 0.000 0.004 0.016
#> GSM892360     1  0.0290      0.950 0.992 0.000 0.000 0.000 0.008
#> GSM892364     1  0.1410      0.941 0.940 0.000 0.000 0.000 0.060
#> GSM892368     3  0.1704      0.886 0.068 0.000 0.928 0.000 0.004
#> GSM892372     3  0.2491      0.884 0.068 0.000 0.896 0.000 0.036
#> GSM892376     2  0.4574      0.383 0.000 0.748 0.008 0.060 0.184
#> GSM892380     2  0.1597      0.674 0.000 0.940 0.000 0.048 0.012
#> GSM892386     2  0.1843      0.672 0.000 0.932 0.008 0.052 0.008
#> GSM892390     2  0.3656      0.623 0.000 0.844 0.024 0.052 0.080

show/hide code output

cbind(get_classes(res, k = 6), get_membership(res, k = 6))

#>           class entropy silhouette    p1    p2    p3    p4    p5 p6
#> GSM892342     3  0.4002      0.727 0.020 0.000 0.660 0.000 0.000 NA
#> GSM892345     4  0.2647      0.848 0.088 0.000 0.044 0.868 0.000 NA
#> GSM892349     4  0.6375      0.530 0.020 0.000 0.132 0.528 0.028 NA
#> GSM892353     1  0.3885      0.829 0.756 0.000 0.000 0.004 0.048 NA
#> GSM892355     1  0.3791      0.834 0.768 0.000 0.000 0.004 0.048 NA
#> GSM892361     1  0.2390      0.902 0.888 0.000 0.000 0.000 0.056 NA
#> GSM892365     3  0.1408      0.828 0.020 0.000 0.944 0.000 0.000 NA
#> GSM892369     3  0.3921      0.790 0.020 0.000 0.816 0.040 0.092 NA
#> GSM892373     5  0.3464      1.000 0.000 0.312 0.000 0.000 0.688 NA
#> GSM892377     2  0.6405      0.121 0.000 0.504 0.008 0.032 0.296 NA
#> GSM892381     2  0.1053      0.619 0.000 0.964 0.000 0.004 0.012 NA
#> GSM892383     2  0.2923      0.613 0.000 0.856 0.008 0.004 0.024 NA
#> GSM892387     2  0.2854      0.573 0.000 0.872 0.000 0.024 0.068 NA
#> GSM892344     3  0.4064      0.722 0.020 0.000 0.644 0.000 0.000 NA
#> GSM892347     4  0.2647      0.848 0.088 0.000 0.044 0.868 0.000 NA
#> GSM892351     4  0.3818      0.830 0.072 0.000 0.060 0.824 0.028 NA
#> GSM892357     1  0.2390      0.904 0.888 0.000 0.000 0.000 0.056 NA
#> GSM892359     1  0.0603      0.918 0.980 0.000 0.000 0.000 0.016 NA
#> GSM892363     1  0.1168      0.916 0.956 0.000 0.000 0.000 0.028 NA
#> GSM892367     3  0.0951      0.824 0.020 0.000 0.968 0.000 0.004 NA
#> GSM892371     3  0.3921      0.790 0.020 0.000 0.816 0.040 0.092 NA
#> GSM892375     2  0.4256      0.330 0.000 0.728 0.004 0.032 0.220 NA
#> GSM892379     2  0.4680      0.515 0.000 0.684 0.000 0.000 0.132 NA
#> GSM892385     2  0.5609      0.393 0.000 0.600 0.008 0.024 0.088 NA
#> GSM892389     2  0.4733      0.523 0.000 0.688 0.000 0.004 0.120 NA
#> GSM892341     3  0.4002      0.727 0.020 0.000 0.660 0.000 0.000 NA
#> GSM892346     4  0.3476      0.792 0.132 0.000 0.000 0.816 0.024 NA
#> GSM892350     4  0.2647      0.848 0.088 0.000 0.044 0.868 0.000 NA
#> GSM892354     1  0.2451      0.902 0.884 0.000 0.000 0.000 0.056 NA
#> GSM892356     1  0.2201      0.906 0.896 0.000 0.000 0.000 0.028 NA
#> GSM892362     1  0.1074      0.916 0.960 0.000 0.000 0.000 0.028 NA
#> GSM892366     3  0.1408      0.828 0.020 0.000 0.944 0.000 0.000 NA
#> GSM892370     3  0.3921      0.790 0.020 0.000 0.816 0.040 0.092 NA
#> GSM892374     5  0.3464      1.000 0.000 0.312 0.000 0.000 0.688 NA
#> GSM892378     2  0.6405      0.121 0.000 0.504 0.008 0.032 0.296 NA
#> GSM892382     2  0.0692      0.620 0.000 0.976 0.000 0.000 0.004 NA
#> GSM892384     2  0.1074      0.617 0.000 0.960 0.000 0.000 0.012 NA
#> GSM892388     2  0.6845     -0.279 0.000 0.420 0.000 0.068 0.324 NA
#> GSM892343     3  0.5834      0.585 0.020 0.000 0.532 0.132 0.000 NA
#> GSM892348     4  0.2853      0.819 0.124 0.000 0.008 0.852 0.008 NA
#> GSM892352     4  0.6443      0.508 0.020 0.000 0.136 0.512 0.028 NA
#> GSM892358     1  0.0146      0.920 0.996 0.000 0.000 0.000 0.004 NA
#> GSM892360     1  0.0603      0.918 0.980 0.000 0.000 0.000 0.016 NA
#> GSM892364     1  0.2201      0.903 0.900 0.000 0.000 0.000 0.048 NA
#> GSM892368     3  0.1408      0.828 0.020 0.000 0.944 0.000 0.000 NA
#> GSM892372     3  0.0547      0.825 0.020 0.000 0.980 0.000 0.000 NA
#> GSM892376     2  0.4185      0.345 0.000 0.740 0.004 0.028 0.208 NA
#> GSM892380     2  0.2839      0.620 0.000 0.860 0.000 0.004 0.044 NA
#> GSM892386     2  0.1500      0.624 0.000 0.936 0.000 0.000 0.012 NA
#> GSM892390     2  0.4474      0.528 0.000 0.704 0.000 0.000 0.108 NA

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

k = 2
k = 3
k = 4
k = 5
k = 6

consensus_heatmap(res, k = 2)

plot of chunk tab-MAD-kmeans-consensus-heatmap-1

consensus_heatmap(res, k = 3)

plot of chunk tab-MAD-kmeans-consensus-heatmap-2

consensus_heatmap(res, k = 4)

plot of chunk tab-MAD-kmeans-consensus-heatmap-3

consensus_heatmap(res, k = 5)

plot of chunk tab-MAD-kmeans-consensus-heatmap-4

consensus_heatmap(res, k = 6)

plot of chunk tab-MAD-kmeans-consensus-heatmap-5

Heatmaps for the membership of samples in all partitions to see how consistent they are:

k = 2
k = 3
k = 4
k = 5
k = 6

membership_heatmap(res, k = 2)

plot of chunk tab-MAD-kmeans-membership-heatmap-1

membership_heatmap(res, k = 3)

plot of chunk tab-MAD-kmeans-membership-heatmap-2

membership_heatmap(res, k = 4)

plot of chunk tab-MAD-kmeans-membership-heatmap-3

membership_heatmap(res, k = 5)

plot of chunk tab-MAD-kmeans-membership-heatmap-4

membership_heatmap(res, k = 6)

plot of chunk tab-MAD-kmeans-membership-heatmap-5

Signature heatmaps where rows are scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2)

plot of chunk tab-MAD-kmeans-get-signatures-1

get_signatures(res, k = 3)

plot of chunk tab-MAD-kmeans-get-signatures-2

get_signatures(res, k = 4)

plot of chunk tab-MAD-kmeans-get-signatures-3

get_signatures(res, k = 5)

plot of chunk tab-MAD-kmeans-get-signatures-4

get_signatures(res, k = 6)

plot of chunk tab-MAD-kmeans-get-signatures-5

Signature heatmaps where rows are not scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-MAD-kmeans-get-signatures-no-scale-1

get_signatures(res, k = 3, scale_rows = FALSE)

plot of chunk tab-MAD-kmeans-get-signatures-no-scale-2

get_signatures(res, k = 4, scale_rows = FALSE)

plot of chunk tab-MAD-kmeans-get-signatures-no-scale-3

get_signatures(res, k = 5, scale_rows = FALSE)

plot of chunk tab-MAD-kmeans-get-signatures-no-scale-4

get_signatures(res, k = 6, scale_rows = FALSE)

plot of chunk tab-MAD-kmeans-get-signatures-no-scale-5

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk MAD-kmeans-signature_compare

# 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.

k = 2
k = 3
k = 4
k = 5
k = 6

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-MAD-kmeans-dimension-reduction-1

dimension_reduction(res, k = 3, method = "UMAP")

plot of chunk tab-MAD-kmeans-dimension-reduction-2

dimension_reduction(res, k = 4, method = "UMAP")

plot of chunk tab-MAD-kmeans-dimension-reduction-3

dimension_reduction(res, k = 5, method = "UMAP")

plot of chunk tab-MAD-kmeans-dimension-reduction-4

dimension_reduction(res, k = 6, method = "UMAP")

plot of chunk tab-MAD-kmeans-dimension-reduction-5

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk MAD-kmeans-collect-classes

test_to_known_factors(res)

#>             n tissue(p) disease.state(p) other(p) individual(p) k
#> MAD:kmeans 50     1.000            0.934 2.67e-07      1.42e-03 2
#> MAD:kmeans 46     0.905            0.934 3.31e-11      1.38e-04 3
#> MAD:kmeans 47     0.981            0.940 2.58e-16      2.20e-06 4
#> MAD:kmeans 45     0.999            0.723 1.15e-19      2.75e-08 5
#> MAD:kmeans 44     1.000            0.752 5.57e-19      7.88e-08 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

MAD:skmeans**

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 31632 rows and 50 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 5.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk MAD-skmeans-collect-plots

The plots are:

The first row: a plot of the ECDF (empirical cumulative distribution function) curves of the consensus matrix for each k and the heatmap of predicted classes for each k.
The second row: heatmaps of the consensus matrix for each k.
The third row: heatmaps of the membership matrix for each k.
The fouth row: heatmaps of the signatures for each 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:

ECDF curves of the consensus matrix for each k;
1-PAC. The PAC score measures the proportion of the ambiguous subgrouping.
Mean silhouette score.
Concordance. The mean probability of fiting the consensus class ids in all partitions.
Area increased. Denote \(A_k\) as the area under the ECDF curve for current k, the area increased is defined as \(A_k - A_{k-1}\).
Rand index. The percent of pairs of samples that are both in a same cluster or both are not in a same cluster in the partition of k and k-1.
Jaccard index. The ratio of pairs of samples are both in a same cluster in the partition of k and k-1 and the pairs of samples are both in a same cluster in the partition k or k-1.

The detailed explanations of these statistics can be found in the cola vignette.

select_partition_number(res)

plot of chunk MAD-skmeans-select-partition-number

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         0.4707 0.530   0.530
#> 3 3 1.000           0.989       0.995         0.4377 0.794   0.612
#> 4 4 1.000           0.975       0.991         0.1020 0.912   0.736
#> 5 5 0.972           0.948       0.964         0.0361 0.958   0.838
#> 6 6 0.972           0.911       0.917         0.0164 1.000   1.000

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

All \(k\) with Jaccard index larger than 0.95 are removed because increasing \(k\) does not provide enough extra information. If all \(k\) are removed, it is marked as no subgroup is detected.
For all \(k\) with 1-PAC score larger than 0.9, the maximal \(k\) is taken as the best \(k\), and other \(k\) are marked as optional \(k\).
If it does not fit the second rule. The \(k\) with the maximal vote of the highest 1-PAC score, highest mean silhouette, and highest concordance is taken as the best \(k\).

suggest_best_k(res)

#> [1] 5
#> attr(,"optional")
#> [1] 2 3 4

There is also optional best \(k\) = 2 3 4 that is worth to check.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

k = 2
k = 3
k = 4
k = 5
k = 6

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>           class entropy silhouette p1 p2
#> GSM892342     1       0          1  1  0
#> GSM892345     1       0          1  1  0
#> GSM892349     1       0          1  1  0
#> GSM892353     1       0          1  1  0
#> GSM892355     1       0          1  1  0
#> GSM892361     1       0          1  1  0
#> GSM892365     1       0          1  1  0
#> GSM892369     1       0          1  1  0
#> GSM892373     2       0          1  0  1
#> GSM892377     2       0          1  0  1
#> GSM892381     2       0          1  0  1
#> GSM892383     2       0          1  0  1
#> GSM892387     2       0          1  0  1
#> GSM892344     1       0          1  1  0
#> GSM892347     1       0          1  1  0
#> GSM892351     1       0          1  1  0
#> GSM892357     1       0          1  1  0
#> GSM892359     1       0          1  1  0
#> GSM892363     1       0          1  1  0
#> GSM892367     1       0          1  1  0
#> GSM892371     1       0          1  1  0
#> GSM892375     2       0          1  0  1
#> GSM892379     2       0          1  0  1
#> GSM892385     2       0          1  0  1
#> GSM892389     2       0          1  0  1
#> GSM892341     1       0          1  1  0
#> GSM892346     1       0          1  1  0
#> GSM892350     1       0          1  1  0
#> GSM892354     1       0          1  1  0
#> GSM892356     1       0          1  1  0
#> GSM892362     1       0          1  1  0
#> GSM892366     1       0          1  1  0
#> GSM892370     1       0          1  1  0
#> GSM892374     2       0          1  0  1
#> GSM892378     2       0          1  0  1
#> GSM892382     2       0          1  0  1
#> GSM892384     2       0          1  0  1
#> GSM892388     2       0          1  0  1
#> GSM892343     1       0          1  1  0
#> GSM892348     1       0          1  1  0
#> GSM892352     1       0          1  1  0
#> GSM892358     1       0          1  1  0
#> GSM892360     1       0          1  1  0
#> GSM892364     1       0          1  1  0
#> GSM892368     1       0          1  1  0
#> GSM892372     1       0          1  1  0
#> GSM892376     2       0          1  0  1
#> GSM892380     2       0          1  0  1
#> GSM892386     2       0          1  0  1
#> GSM892390     2       0          1  0  1

show/hide code output

cbind(get_classes(res, k = 3), get_membership(res, k = 3))

#>           class entropy silhouette    p1 p2    p3
#> GSM892342     3   0.000      1.000 0.000  0 1.000
#> GSM892345     1   0.000      0.985 1.000  0 0.000
#> GSM892349     3   0.000      1.000 0.000  0 1.000
#> GSM892353     1   0.000      0.985 1.000  0 0.000
#> GSM892355     1   0.000      0.985 1.000  0 0.000
#> GSM892361     1   0.000      0.985 1.000  0 0.000
#> GSM892365     3   0.000      1.000 0.000  0 1.000
#> GSM892369     3   0.000      1.000 0.000  0 1.000
#> GSM892373     2   0.000      1.000 0.000  1 0.000
#> GSM892377     2   0.000      1.000 0.000  1 0.000
#> GSM892381     2   0.000      1.000 0.000  1 0.000
#> GSM892383     2   0.000      1.000 0.000  1 0.000
#> GSM892387     2   0.000      1.000 0.000  1 0.000
#> GSM892344     3   0.000      1.000 0.000  0 1.000
#> GSM892347     1   0.000      0.985 1.000  0 0.000
#> GSM892351     1   0.445      0.770 0.808  0 0.192
#> GSM892357     1   0.000      0.985 1.000  0 0.000
#> GSM892359     1   0.000      0.985 1.000  0 0.000
#> GSM892363     1   0.000      0.985 1.000  0 0.000
#> GSM892367     3   0.000      1.000 0.000  0 1.000
#> GSM892371     3   0.000      1.000 0.000  0 1.000
#> GSM892375     2   0.000      1.000 0.000  1 0.000
#> GSM892379     2   0.000      1.000 0.000  1 0.000
#> GSM892385     2   0.000      1.000 0.000  1 0.000
#> GSM892389     2   0.000      1.000 0.000  1 0.000
#> GSM892341     3   0.000      1.000 0.000  0 1.000
#> GSM892346     1   0.000      0.985 1.000  0 0.000
#> GSM892350     1   0.207      0.931 0.940  0 0.060
#> GSM892354     1   0.000      0.985 1.000  0 0.000
#> GSM892356     1   0.000      0.985 1.000  0 0.000
#> GSM892362     1   0.000      0.985 1.000  0 0.000
#> GSM892366     3   0.000      1.000 0.000  0 1.000
#> GSM892370     3   0.000      1.000 0.000  0 1.000
#> GSM892374     2   0.000      1.000 0.000  1 0.000
#> GSM892378     2   0.000      1.000 0.000  1 0.000
#> GSM892382     2   0.000      1.000 0.000  1 0.000
#> GSM892384     2   0.000      1.000 0.000  1 0.000
#> GSM892388     2   0.000      1.000 0.000  1 0.000
#> GSM892343     3   0.000      1.000 0.000  0 1.000
#> GSM892348     1   0.000      0.985 1.000  0 0.000
#> GSM892352     3   0.000      1.000 0.000  0 1.000
#> GSM892358     1   0.000      0.985 1.000  0 0.000
#> GSM892360     1   0.000      0.985 1.000  0 0.000
#> GSM892364     1   0.000      0.985 1.000  0 0.000
#> GSM892368     3   0.000      1.000 0.000  0 1.000
#> GSM892372     3   0.000      1.000 0.000  0 1.000
#> GSM892376     2   0.000      1.000 0.000  1 0.000
#> GSM892380     2   0.000      1.000 0.000  1 0.000
#> GSM892386     2   0.000      1.000 0.000  1 0.000
#> GSM892390     2   0.000      1.000 0.000  1 0.000

show/hide code output

cbind(get_classes(res, k = 4), get_membership(res, k = 4))

#>           class entropy silhouette    p1 p2    p3    p4
#> GSM892342     3  0.0000      0.957 0.000  0 1.000 0.000
#> GSM892345     4  0.0000      0.999 0.000  0 0.000 1.000
#> GSM892349     4  0.0000      0.999 0.000  0 0.000 1.000
#> GSM892353     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892355     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892361     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892365     3  0.0000      0.957 0.000  0 1.000 0.000
#> GSM892369     3  0.0188      0.956 0.000  0 0.996 0.004
#> GSM892373     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892344     3  0.0469      0.949 0.000  0 0.988 0.012
#> GSM892347     4  0.0000      0.999 0.000  0 0.000 1.000
#> GSM892351     4  0.0000      0.999 0.000  0 0.000 1.000
#> GSM892357     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892359     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892363     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892367     3  0.0000      0.957 0.000  0 1.000 0.000
#> GSM892371     3  0.0188      0.956 0.000  0 0.996 0.004
#> GSM892375     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892341     3  0.0000      0.957 0.000  0 1.000 0.000
#> GSM892346     4  0.0336      0.991 0.008  0 0.000 0.992
#> GSM892350     4  0.0000      0.999 0.000  0 0.000 1.000
#> GSM892354     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892356     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892362     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892366     3  0.0000      0.957 0.000  0 1.000 0.000
#> GSM892370     3  0.0188      0.956 0.000  0 0.996 0.004
#> GSM892374     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892343     3  0.4941      0.235 0.000  0 0.564 0.436
#> GSM892348     4  0.0000      0.999 0.000  0 0.000 1.000
#> GSM892352     4  0.0000      0.999 0.000  0 0.000 1.000
#> GSM892358     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892360     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892364     1  0.0000      1.000 1.000  0 0.000 0.000
#> GSM892368     3  0.0000      0.957 0.000  0 1.000 0.000
#> GSM892372     3  0.0000      0.957 0.000  0 1.000 0.000
#> GSM892376     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 5), get_membership(res, k = 5))

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> GSM892342     5  0.0609      0.807 0.000 0.000 0.020 0.000 0.980
#> GSM892345     4  0.0162      0.996 0.000 0.000 0.000 0.996 0.004
#> GSM892349     5  0.4201      0.441 0.000 0.000 0.000 0.408 0.592
#> GSM892353     1  0.0000      0.999 1.000 0.000 0.000 0.000 0.000
#> GSM892355     1  0.0000      0.999 1.000 0.000 0.000 0.000 0.000
#> GSM892361     1  0.0162      0.997 0.996 0.000 0.000 0.000 0.004
#> GSM892365     3  0.3074      0.896 0.000 0.000 0.804 0.000 0.196
#> GSM892369     3  0.0000      0.879 0.000 0.000 1.000 0.000 0.000
#> GSM892373     2  0.0162      0.998 0.000 0.996 0.000 0.000 0.004
#> GSM892377     2  0.0000      0.998 0.000 1.000 0.000 0.000 0.000
#> GSM892381     2  0.0000      0.998 0.000 1.000 0.000 0.000 0.000
#> GSM892383     2  0.0000      0.998 0.000 1.000 0.000 0.000 0.000
#> GSM892387     2  0.0162      0.998 0.000 0.996 0.000 0.000 0.004
#> GSM892344     5  0.0510      0.808 0.000 0.000 0.016 0.000 0.984
#> GSM892347     4  0.0000      0.996 0.000 0.000 0.000 1.000 0.000
#> GSM892351     4  0.0290      0.994 0.000 0.000 0.000 0.992 0.008
#> GSM892357     1  0.0162      0.997 0.996 0.000 0.000 0.000 0.004
#> GSM892359     1  0.0000      0.999 1.000 0.000 0.000 0.000 0.000
#> GSM892363     1  0.0000      0.999 1.000 0.000 0.000 0.000 0.000
#> GSM892367     3  0.2230      0.906 0.000 0.000 0.884 0.000 0.116
#> GSM892371     3  0.0000      0.879 0.000 0.000 1.000 0.000 0.000
#> GSM892375     2  0.0000      0.998 0.000 1.000 0.000 0.000 0.000
#> GSM892379     2  0.0000      0.998 0.000 1.000 0.000 0.000 0.000
#> GSM892385     2  0.0000      0.998 0.000 1.000 0.000 0.000 0.000
#> GSM892389     2  0.0162      0.998 0.000 0.996 0.000 0.000 0.004
#> GSM892341     5  0.0609      0.807 0.000 0.000 0.020 0.000 0.980
#> GSM892346     4  0.0162      0.993 0.000 0.000 0.000 0.996 0.004
#> GSM892350     4  0.0162      0.996 0.000 0.000 0.000 0.996 0.004
#> GSM892354     1  0.0162      0.997 0.996 0.000 0.000 0.000 0.004
#> GSM892356     1  0.0000      0.999 1.000 0.000 0.000 0.000 0.000
#> GSM892362     1  0.0162      0.997 0.996 0.000 0.000 0.000 0.004
#> GSM892366     3  0.3074      0.896 0.000 0.000 0.804 0.000 0.196
#> GSM892370     3  0.0000      0.879 0.000 0.000 1.000 0.000 0.000
#> GSM892374     2  0.0162      0.998 0.000 0.996 0.000 0.000 0.004
#> GSM892378     2  0.0000      0.998 0.000 1.000 0.000 0.000 0.000
#> GSM892382     2  0.0000      0.998 0.000 1.000 0.000 0.000 0.000
#> GSM892384     2  0.0000      0.998 0.000 1.000 0.000 0.000 0.000
#> GSM892388     2  0.0162      0.998 0.000 0.996 0.000 0.000 0.004
#> GSM892343     5  0.3321      0.783 0.000 0.000 0.032 0.136 0.832
#> GSM892348     4  0.0000      0.996 0.000 0.000 0.000 1.000 0.000
#> GSM892352     5  0.3336      0.721 0.000 0.000 0.000 0.228 0.772
#> GSM892358     1  0.0000      0.999 1.000 0.000 0.000 0.000 0.000
#> GSM892360     1  0.0000      0.999 1.000 0.000 0.000 0.000 0.000
#> GSM892364     1  0.0000      0.999 1.000 0.000 0.000 0.000 0.000
#> GSM892368     3  0.3074      0.896 0.000 0.000 0.804 0.000 0.196
#> GSM892372     3  0.2648      0.906 0.000 0.000 0.848 0.000 0.152
#> GSM892376     2  0.0162      0.998 0.000 0.996 0.000 0.000 0.004
#> GSM892380     2  0.0000      0.998 0.000 1.000 0.000 0.000 0.000
#> GSM892386     2  0.0162      0.998 0.000 0.996 0.000 0.000 0.004
#> GSM892390     2  0.0162      0.998 0.000 0.996 0.000 0.000 0.004

show/hide code output

cbind(get_classes(res, k = 6), get_membership(res, k = 6))

#>           class entropy silhouette    p1    p2    p3    p4    p5 p6
#> GSM892342     5  0.1349      0.803 0.000 0.000 0.056 0.000 0.940 NA
#> GSM892345     4  0.0891      0.949 0.000 0.000 0.000 0.968 0.008 NA
#> GSM892349     5  0.5847      0.428 0.000 0.000 0.000 0.260 0.488 NA
#> GSM892353     1  0.2118      0.922 0.888 0.000 0.000 0.000 0.008 NA
#> GSM892355     1  0.1644      0.942 0.920 0.000 0.000 0.000 0.004 NA
#> GSM892361     1  0.0547      0.970 0.980 0.000 0.000 0.000 0.000 NA
#> GSM892365     3  0.0405      0.827 0.000 0.000 0.988 0.000 0.008 NA
#> GSM892369     3  0.3789      0.715 0.000 0.000 0.584 0.000 0.000 NA
#> GSM892373     2  0.0458      0.991 0.000 0.984 0.000 0.000 0.000 NA
#> GSM892377     2  0.0363      0.992 0.000 0.988 0.000 0.000 0.000 NA
#> GSM892381     2  0.0260      0.992 0.000 0.992 0.000 0.000 0.000 NA
#> GSM892383     2  0.0363      0.994 0.000 0.988 0.000 0.000 0.000 NA
#> GSM892387     2  0.0146      0.994 0.000 0.996 0.000 0.000 0.000 NA
#> GSM892344     5  0.1196      0.805 0.000 0.000 0.040 0.000 0.952 NA
#> GSM892347     4  0.0363      0.950 0.000 0.000 0.000 0.988 0.000 NA
#> GSM892351     4  0.2494      0.881 0.000 0.000 0.000 0.864 0.016 NA
#> GSM892357     1  0.0547      0.970 0.980 0.000 0.000 0.000 0.000 NA
#> GSM892359     1  0.0713      0.968 0.972 0.000 0.000 0.000 0.000 NA
#> GSM892363     1  0.0790      0.967 0.968 0.000 0.000 0.000 0.000 NA
#> GSM892367     3  0.0790      0.830 0.000 0.000 0.968 0.000 0.000 NA
#> GSM892371     3  0.3765      0.722 0.000 0.000 0.596 0.000 0.000 NA
#> GSM892375     2  0.0458      0.993 0.000 0.984 0.000 0.000 0.000 NA
#> GSM892379     2  0.0146      0.994 0.000 0.996 0.000 0.000 0.000 NA
#> GSM892385     2  0.0146      0.993 0.000 0.996 0.000 0.000 0.000 NA
#> GSM892389     2  0.0146      0.994 0.000 0.996 0.000 0.000 0.000 NA
#> GSM892341     5  0.1204      0.804 0.000 0.000 0.056 0.000 0.944 NA
#> GSM892346     4  0.0713      0.940 0.000 0.000 0.000 0.972 0.000 NA
#> GSM892350     4  0.1285      0.940 0.000 0.000 0.000 0.944 0.004 NA
#> GSM892354     1  0.0458      0.970 0.984 0.000 0.000 0.000 0.000 NA
#> GSM892356     1  0.1007      0.969 0.956 0.000 0.000 0.000 0.000 NA
#> GSM892362     1  0.0547      0.971 0.980 0.000 0.000 0.000 0.000 NA
#> GSM892366     3  0.0405      0.827 0.000 0.000 0.988 0.000 0.008 NA
#> GSM892370     3  0.3774      0.720 0.000 0.000 0.592 0.000 0.000 NA
#> GSM892374     2  0.0458      0.991 0.000 0.984 0.000 0.000 0.000 NA
#> GSM892378     2  0.0363      0.992 0.000 0.988 0.000 0.000 0.000 NA
#> GSM892382     2  0.0260      0.992 0.000 0.992 0.000 0.000 0.000 NA
#> GSM892384     2  0.0146      0.993 0.000 0.996 0.000 0.000 0.000 NA
#> GSM892388     2  0.0146      0.993 0.000 0.996 0.000 0.000 0.000 NA
#> GSM892343     5  0.3208      0.758 0.000 0.000 0.008 0.040 0.832 NA
#> GSM892348     4  0.0632      0.942 0.000 0.000 0.000 0.976 0.000 NA
#> GSM892352     5  0.5105      0.630 0.000 0.000 0.004 0.096 0.600 NA
#> GSM892358     1  0.0260      0.972 0.992 0.000 0.000 0.000 0.000 NA
#> GSM892360     1  0.0632      0.969 0.976 0.000 0.000 0.000 0.000 NA
#> GSM892364     1  0.1141      0.965 0.948 0.000 0.000 0.000 0.000 NA
#> GSM892368     3  0.0260      0.828 0.000 0.000 0.992 0.000 0.008 NA
#> GSM892372     3  0.0547      0.831 0.000 0.000 0.980 0.000 0.000 NA
#> GSM892376     2  0.0458      0.992 0.000 0.984 0.000 0.000 0.000 NA
#> GSM892380     2  0.0146      0.994 0.000 0.996 0.000 0.000 0.000 NA
#> GSM892386     2  0.0146      0.993 0.000 0.996 0.000 0.000 0.000 NA
#> GSM892390     2  0.0146      0.993 0.000 0.996 0.000 0.000 0.000 NA

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

k = 2
k = 3
k = 4
k = 5
k = 6

consensus_heatmap(res, k = 2)

plot of chunk tab-MAD-skmeans-consensus-heatmap-1

consensus_heatmap(res, k = 3)

plot of chunk tab-MAD-skmeans-consensus-heatmap-2

consensus_heatmap(res, k = 4)

plot of chunk tab-MAD-skmeans-consensus-heatmap-3

consensus_heatmap(res, k = 5)

plot of chunk tab-MAD-skmeans-consensus-heatmap-4

consensus_heatmap(res, k = 6)

plot of chunk tab-MAD-skmeans-consensus-heatmap-5

Heatmaps for the membership of samples in all partitions to see how consistent they are:

k = 2
k = 3
k = 4
k = 5
k = 6

membership_heatmap(res, k = 2)

plot of chunk tab-MAD-skmeans-membership-heatmap-1

membership_heatmap(res, k = 3)

plot of chunk tab-MAD-skmeans-membership-heatmap-2

membership_heatmap(res, k = 4)

plot of chunk tab-MAD-skmeans-membership-heatmap-3

membership_heatmap(res, k = 5)

plot of chunk tab-MAD-skmeans-membership-heatmap-4

membership_heatmap(res, k = 6)

plot of chunk tab-MAD-skmeans-membership-heatmap-5

Signature heatmaps where rows are scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2)

plot of chunk tab-MAD-skmeans-get-signatures-1

get_signatures(res, k = 3)

plot of chunk tab-MAD-skmeans-get-signatures-2

get_signatures(res, k = 4)

plot of chunk tab-MAD-skmeans-get-signatures-3

get_signatures(res, k = 5)

plot of chunk tab-MAD-skmeans-get-signatures-4

get_signatures(res, k = 6)

plot of chunk tab-MAD-skmeans-get-signatures-5

Signature heatmaps where rows are not scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-MAD-skmeans-get-signatures-no-scale-1

get_signatures(res, k = 3, scale_rows = FALSE)

plot of chunk tab-MAD-skmeans-get-signatures-no-scale-2

get_signatures(res, k = 4, scale_rows = FALSE)

plot of chunk tab-MAD-skmeans-get-signatures-no-scale-3

get_signatures(res, k = 5, scale_rows = FALSE)

plot of chunk tab-MAD-skmeans-get-signatures-no-scale-4

get_signatures(res, k = 6, scale_rows = FALSE)

plot of chunk tab-MAD-skmeans-get-signatures-no-scale-5

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk MAD-skmeans-signature_compare

# 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.

k = 2
k = 3
k = 4
k = 5
k = 6

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-MAD-skmeans-dimension-reduction-1

dimension_reduction(res, k = 3, method = "UMAP")

plot of chunk tab-MAD-skmeans-dimension-reduction-2

dimension_reduction(res, k = 4, method = "UMAP")

plot of chunk tab-MAD-skmeans-dimension-reduction-3

dimension_reduction(res, k = 5, method = "UMAP")

plot of chunk tab-MAD-skmeans-dimension-reduction-4

dimension_reduction(res, k = 6, method = "UMAP")

plot of chunk tab-MAD-skmeans-dimension-reduction-5

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk MAD-skmeans-collect-classes

test_to_known_factors(res)

#>              n tissue(p) disease.state(p) other(p) individual(p) k
#> MAD:skmeans 50     1.000            0.934 2.67e-07      1.42e-03 2
#> MAD:skmeans 50     1.000            0.931 1.69e-11      8.93e-05 3
#> MAD:skmeans 49     0.995            0.988 2.28e-17      4.54e-07 4
#> MAD:skmeans 49     0.996            0.982 2.33e-20      7.98e-08 5
#> MAD:skmeans 49     0.996            0.982 2.33e-20      7.98e-08 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

MAD:pam**

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 31632 rows and 50 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 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)

plot of chunk MAD-pam-collect-plots

The plots are:

The first row: a plot of the ECDF (empirical cumulative distribution function) curves of the consensus matrix for each k and the heatmap of predicted classes for each k.
The second row: heatmaps of the consensus matrix for each k.
The third row: heatmaps of the membership matrix for each k.
The fouth row: heatmaps of the signatures for each 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:

ECDF curves of the consensus matrix for each k;
1-PAC. The PAC score measures the proportion of the ambiguous subgrouping.
Mean silhouette score.
Concordance. The mean probability of fiting the consensus class ids in all partitions.
Area increased. Denote \(A_k\) as the area under the ECDF curve for current k, the area increased is defined as \(A_k - A_{k-1}\).
Rand index. The percent of pairs of samples that are both in a same cluster or both are not in a same cluster in the partition of k and k-1.
Jaccard index. The ratio of pairs of samples are both in a same cluster in the partition of k and k-1 and the pairs of samples are both in a same cluster in the partition k or k-1.

The detailed explanations of these statistics can be found in the cola vignette.

select_partition_number(res)

plot of chunk MAD-pam-select-partition-number

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         0.4707 0.530   0.530
#> 3 3 0.952           0.959       0.981         0.4362 0.794   0.612
#> 4 4 1.000           0.991       0.995         0.1049 0.900   0.704
#> 5 5 1.000           0.966       0.980         0.0372 0.958   0.840
#> 6 6 1.000           0.979       0.991         0.0162 0.988   0.946

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

All \(k\) with Jaccard index larger than 0.95 are removed because increasing \(k\) does not provide enough extra information. If all \(k\) are removed, it is marked as no subgroup is detected.
For all \(k\) with 1-PAC score larger than 0.9, the maximal \(k\) is taken as the best \(k\), and other \(k\) are marked as optional \(k\).
If it does not fit the second rule. The \(k\) with the maximal vote of the highest 1-PAC score, highest mean silhouette, and highest concordance is taken as the best \(k\).

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.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

k = 2
k = 3
k = 4
k = 5
k = 6

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>           class entropy silhouette p1 p2
#> GSM892342     1       0          1  1  0
#> GSM892345     1       0          1  1  0
#> GSM892349     1       0          1  1  0
#> GSM892353     1       0          1  1  0
#> GSM892355     1       0          1  1  0
#> GSM892361     1       0          1  1  0
#> GSM892365     1       0          1  1  0
#> GSM892369     1       0          1  1  0
#> GSM892373     2       0          1  0  1
#> GSM892377     2       0          1  0  1
#> GSM892381     2       0          1  0  1
#> GSM892383     2       0          1  0  1
#> GSM892387     2       0          1  0  1
#> GSM892344     1       0          1  1  0
#> GSM892347     1       0          1  1  0
#> GSM892351     1       0          1  1  0
#> GSM892357     1       0          1  1  0
#> GSM892359     1       0          1  1  0
#> GSM892363     1       0          1  1  0
#> GSM892367     1       0          1  1  0
#> GSM892371     1       0          1  1  0
#> GSM892375     2       0          1  0  1
#> GSM892379     2       0          1  0  1
#> GSM892385     2       0          1  0  1
#> GSM892389     2       0          1  0  1
#> GSM892341     1       0          1  1  0
#> GSM892346     1       0          1  1  0
#> GSM892350     1       0          1  1  0
#> GSM892354     1       0          1  1  0
#> GSM892356     1       0          1  1  0
#> GSM892362     1       0          1  1  0
#> GSM892366     1       0          1  1  0
#> GSM892370     1       0          1  1  0
#> GSM892374     2       0          1  0  1
#> GSM892378     2       0          1  0  1
#> GSM892382     2       0          1  0  1
#> GSM892384     2       0          1  0  1
#> GSM892388     2       0          1  0  1
#> GSM892343     1       0          1  1  0
#> GSM892348     1       0          1  1  0
#> GSM892352     1       0          1  1  0
#> GSM892358     1       0          1  1  0
#> GSM892360     1       0          1  1  0
#> GSM892364     1       0          1  1  0
#> GSM892368     1       0          1  1  0
#> GSM892372     1       0          1  1  0
#> GSM892376     2       0          1  0  1
#> GSM892380     2       0          1  0  1
#> GSM892386     2       0          1  0  1
#> GSM892390     2       0          1  0  1

show/hide code output

cbind(get_classes(res, k = 3), get_membership(res, k = 3))

#>           class entropy silhouette    p1 p2    p3
#> GSM892342     3  0.0000      0.989 0.000  0 1.000
#> GSM892345     1  0.3412      0.868 0.876  0 0.124
#> GSM892349     3  0.0000      0.989 0.000  0 1.000
#> GSM892353     1  0.0237      0.948 0.996  0 0.004
#> GSM892355     1  0.0000      0.950 1.000  0 0.000
#> GSM892361     1  0.0000      0.950 1.000  0 0.000
#> GSM892365     3  0.0000      0.989 0.000  0 1.000
#> GSM892369     3  0.0000      0.989 0.000  0 1.000
#> GSM892373     2  0.0000      1.000 0.000  1 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000
#> GSM892344     3  0.0000      0.989 0.000  0 1.000
#> GSM892347     1  0.3412      0.868 0.876  0 0.124
#> GSM892351     1  0.6062      0.431 0.616  0 0.384
#> GSM892357     1  0.0000      0.950 1.000  0 0.000
#> GSM892359     1  0.0000      0.950 1.000  0 0.000
#> GSM892363     1  0.0000      0.950 1.000  0 0.000
#> GSM892367     3  0.0000      0.989 0.000  0 1.000
#> GSM892371     3  0.0000      0.989 0.000  0 1.000
#> GSM892375     2  0.0000      1.000 0.000  1 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000
#> GSM892341     3  0.0000      0.989 0.000  0 1.000
#> GSM892346     1  0.0000      0.950 1.000  0 0.000
#> GSM892350     1  0.3551      0.860 0.868  0 0.132
#> GSM892354     1  0.0000      0.950 1.000  0 0.000
#> GSM892356     1  0.0000      0.950 1.000  0 0.000
#> GSM892362     1  0.0000      0.950 1.000  0 0.000
#> GSM892366     3  0.0000      0.989 0.000  0 1.000
#> GSM892370     3  0.0000      0.989 0.000  0 1.000
#> GSM892374     2  0.0000      1.000 0.000  1 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000
#> GSM892343     3  0.3551      0.833 0.132  0 0.868
#> GSM892348     1  0.2165      0.913 0.936  0 0.064
#> GSM892352     3  0.0000      0.989 0.000  0 1.000
#> GSM892358     1  0.0000      0.950 1.000  0 0.000
#> GSM892360     1  0.0000      0.950 1.000  0 0.000
#> GSM892364     1  0.0000      0.950 1.000  0 0.000
#> GSM892368     3  0.0000      0.989 0.000  0 1.000
#> GSM892372     3  0.0000      0.989 0.000  0 1.000
#> GSM892376     2  0.0000      1.000 0.000  1 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000

show/hide code output

cbind(get_classes(res, k = 4), get_membership(res, k = 4))

#>           class entropy silhouette   p1 p2    p3    p4
#> GSM892342     3  0.0000      0.987 0.00  0 1.000 0.000
#> GSM892345     4  0.0000      0.987 0.00  0 0.000 1.000
#> GSM892349     4  0.0000      0.987 0.00  0 0.000 1.000
#> GSM892353     1  0.0000      1.000 1.00  0 0.000 0.000
#> GSM892355     1  0.0000      1.000 1.00  0 0.000 0.000
#> GSM892361     1  0.0000      1.000 1.00  0 0.000 0.000
#> GSM892365     3  0.0000      0.987 0.00  0 1.000 0.000
#> GSM892369     3  0.0000      0.987 0.00  0 1.000 0.000
#> GSM892373     2  0.0000      1.000 0.00  1 0.000 0.000
#> GSM892377     2  0.0000      1.000 0.00  1 0.000 0.000
#> GSM892381     2  0.0000      1.000 0.00  1 0.000 0.000
#> GSM892383     2  0.0000      1.000 0.00  1 0.000 0.000
#> GSM892387     2  0.0000      1.000 0.00  1 0.000 0.000
#> GSM892344     3  0.2530      0.874 0.00  0 0.888 0.112
#> GSM892347     4  0.0000      0.987 0.00  0 0.000 1.000
#> GSM892351     4  0.0000      0.987 0.00  0 0.000 1.000
#> GSM892357     1  0.0000      1.000 1.00  0 0.000 0.000
#> GSM892359     1  0.0000      1.000 1.00  0 0.000 0.000
#> GSM892363     1  0.0000      1.000 1.00  0 0.000 0.000
#> GSM892367     3  0.0000      0.987 0.00  0 1.000 0.000
#> GSM892371     3  0.0469      0.978 0.00  0 0.988 0.012
#> GSM892375     2  0.0000      1.000 0.00  1 0.000 0.000
#> GSM892379     2  0.0000      1.000 0.00  1 0.000 0.000
#> GSM892385     2  0.0000      1.000 0.00  1 0.000 0.000
#> GSM892389     2  0.0000      1.000 0.00  1 0.000 0.000
#> GSM892341     3  0.0000      0.987 0.00  0 1.000 0.000
#> GSM892346     4  0.1637      0.935 0.06  0 0.000 0.940
#> GSM892350     4  0.0000      0.987 0.00  0 0.000 1.000
#> GSM892354     1  0.0000      1.000 1.00  0 0.000 0.000
#> GSM892356     1  0.0000      1.000 1.00  0 0.000 0.000
#> GSM892362     1  0.0000      1.000 1.00  0 0.000 0.000
#> GSM892366     3  0.0000      0.987 0.00  0 1.000 0.000
#> GSM892370     3  0.0000      0.987 0.00  0 1.000 0.000
#> GSM892374     2  0.0000      1.000 0.00  1 0.000 0.000
#> GSM892378     2  0.0000      1.000 0.00  1 0.000 0.000
#> GSM892382     2  0.0000      1.000 0.00  1 0.000 0.000
#> GSM892384     2  0.0000      1.000 0.00  1 0.000 0.000
#> GSM892388     2  0.0000      1.000 0.00  1 0.000 0.000
#> GSM892343     4  0.1302      0.950 0.00  0 0.044 0.956
#> GSM892348     4  0.0000      0.987 0.00  0 0.000 1.000
#> GSM892352     4  0.0000      0.987 0.00  0 0.000 1.000
#> GSM892358     1  0.0000      1.000 1.00  0 0.000 0.000
#> GSM892360     1  0.0000      1.000 1.00  0 0.000 0.000
#> GSM892364     1  0.0000      1.000 1.00  0 0.000 0.000
#> GSM892368     3  0.0000      0.987 0.00  0 1.000 0.000
#> GSM892372     3  0.0000      0.987 0.00  0 1.000 0.000
#> GSM892376     2  0.0000      1.000 0.00  1 0.000 0.000
#> GSM892380     2  0.0000      1.000 0.00  1 0.000 0.000
#> GSM892386     2  0.0000      1.000 0.00  1 0.000 0.000
#> GSM892390     2  0.0000      1.000 0.00  1 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 5), get_membership(res, k = 5))

#>           class entropy silhouette    p1 p2    p3    p4    p5
#> GSM892342     5  0.1608      0.916 0.000  0 0.072 0.000 0.928
#> GSM892345     4  0.0000      0.994 0.000  0 0.000 1.000 0.000
#> GSM892349     5  0.3177      0.785 0.000  0 0.000 0.208 0.792
#> GSM892353     1  0.3636      0.615 0.728  0 0.000 0.000 0.272
#> GSM892355     1  0.0000      0.974 1.000  0 0.000 0.000 0.000
#> GSM892361     1  0.0000      0.974 1.000  0 0.000 0.000 0.000
#> GSM892365     3  0.0162      0.969 0.000  0 0.996 0.000 0.004
#> GSM892369     3  0.1608      0.949 0.000  0 0.928 0.000 0.072
#> GSM892373     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892344     5  0.1310      0.924 0.000  0 0.024 0.020 0.956
#> GSM892347     4  0.0000      0.994 0.000  0 0.000 1.000 0.000
#> GSM892351     4  0.0000      0.994 0.000  0 0.000 1.000 0.000
#> GSM892357     1  0.0000      0.974 1.000  0 0.000 0.000 0.000
#> GSM892359     1  0.0000      0.974 1.000  0 0.000 0.000 0.000
#> GSM892363     1  0.0000      0.974 1.000  0 0.000 0.000 0.000
#> GSM892367     3  0.0162      0.969 0.000  0 0.996 0.000 0.004
#> GSM892371     3  0.1608      0.949 0.000  0 0.928 0.000 0.072
#> GSM892375     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892341     5  0.1608      0.916 0.000  0 0.072 0.000 0.928
#> GSM892346     4  0.0609      0.972 0.020  0 0.000 0.980 0.000
#> GSM892350     4  0.0000      0.994 0.000  0 0.000 1.000 0.000
#> GSM892354     1  0.0000      0.974 1.000  0 0.000 0.000 0.000
#> GSM892356     1  0.0000      0.974 1.000  0 0.000 0.000 0.000
#> GSM892362     1  0.0000      0.974 1.000  0 0.000 0.000 0.000
#> GSM892366     3  0.0162      0.969 0.000  0 0.996 0.000 0.004
#> GSM892370     3  0.1608      0.949 0.000  0 0.928 0.000 0.072
#> GSM892374     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892343     5  0.0510      0.912 0.000  0 0.000 0.016 0.984
#> GSM892348     4  0.0000      0.994 0.000  0 0.000 1.000 0.000
#> GSM892352     5  0.1792      0.905 0.000  0 0.000 0.084 0.916
#> GSM892358     1  0.0000      0.974 1.000  0 0.000 0.000 0.000
#> GSM892360     1  0.0000      0.974 1.000  0 0.000 0.000 0.000
#> GSM892364     1  0.0000      0.974 1.000  0 0.000 0.000 0.000
#> GSM892368     3  0.0162      0.969 0.000  0 0.996 0.000 0.004
#> GSM892372     3  0.0162      0.969 0.000  0 0.996 0.000 0.004
#> GSM892376     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 6), get_membership(res, k = 6))

#>           class entropy silhouette    p1 p2 p3    p4    p5 p6
#> GSM892342     5  0.0000      0.963 0.000  0  0 0.000 1.000  0
#> GSM892345     4  0.0000      1.000 0.000  0  0 1.000 0.000  0
#> GSM892349     5  0.2340      0.822 0.000  0  0 0.148 0.852  0
#> GSM892353     1  0.3266      0.621 0.728  0  0 0.000 0.272  0
#> GSM892355     1  0.0000      0.973 1.000  0  0 0.000 0.000  0
#> GSM892361     1  0.0000      0.973 1.000  0  0 0.000 0.000  0
#> GSM892365     3  0.0000      1.000 0.000  0  1 0.000 0.000  0
#> GSM892369     6  0.0000      1.000 0.000  0  0 0.000 0.000  1
#> GSM892373     2  0.0000      1.000 0.000  1  0 0.000 0.000  0
#> GSM892377     2  0.0000      1.000 0.000  1  0 0.000 0.000  0
#> GSM892381     2  0.0000      1.000 0.000  1  0 0.000 0.000  0
#> GSM892383     2  0.0000      1.000 0.000  1  0 0.000 0.000  0
#> GSM892387     2  0.0000      1.000 0.000  1  0 0.000 0.000  0
#> GSM892344     5  0.0000      0.963 0.000  0  0 0.000 1.000  0
#> GSM892347     4  0.0000      1.000 0.000  0  0 1.000 0.000  0
#> GSM892351     4  0.0000      1.000 0.000  0  0 1.000 0.000  0
#> GSM892357     1  0.0000      0.973 1.000  0  0 0.000 0.000  0
#> GSM892359     1  0.0000      0.973 1.000  0  0 0.000 0.000  0
#> GSM892363     1  0.0000      0.973 1.000  0  0 0.000 0.000  0
#> GSM892367     3  0.0000      1.000 0.000  0  1 0.000 0.000  0
#> GSM892371     6  0.0000      1.000 0.000  0  0 0.000 0.000  1
#> GSM892375     2  0.0000      1.000 0.000  1  0 0.000 0.000  0
#> GSM892379     2  0.0000      1.000 0.000  1  0 0.000 0.000  0
#> GSM892385     2  0.0000      1.000 0.000  1  0 0.000 0.000  0
#> GSM892389     2  0.0000      1.000 0.000  1  0 0.000 0.000  0
#> GSM892341     5  0.0000      0.963 0.000  0  0 0.000 1.000  0
#> GSM892346     4  0.0000      1.000 0.000  0  0 1.000 0.000  0
#> GSM892350     4  0.0000      1.000 0.000  0  0 1.000 0.000  0
#> GSM892354     1  0.0000      0.973 1.000  0  0 0.000 0.000  0
#> GSM892356     1  0.0000      0.973 1.000  0  0 0.000 0.000  0
#> GSM892362     1  0.0000      0.973 1.000  0  0 0.000 0.000  0
#> GSM892366     3  0.0000      1.000 0.000  0  1 0.000 0.000  0
#> GSM892370     6  0.0000      1.000 0.000  0  0 0.000 0.000  1
#> GSM892374     2  0.0000      1.000 0.000  1  0 0.000 0.000  0
#> GSM892378     2  0.0000      1.000 0.000  1  0 0.000 0.000  0
#> GSM892382     2  0.0000      1.000 0.000  1  0 0.000 0.000  0
#> GSM892384     2  0.0000      1.000 0.000  1  0 0.000 0.000  0
#> GSM892388     2  0.0000      1.000 0.000  1  0 0.000 0.000  0
#> GSM892343     5  0.0000      0.963 0.000  0  0 0.000 1.000  0
#> GSM892348     4  0.0000      1.000 0.000  0  0 1.000 0.000  0
#> GSM892352     5  0.0363      0.957 0.000  0  0 0.012 0.988  0
#> GSM892358     1  0.0000      0.973 1.000  0  0 0.000 0.000  0
#> GSM892360     1  0.0000      0.973 1.000  0  0 0.000 0.000  0
#> GSM892364     1  0.0000      0.973 1.000  0  0 0.000 0.000  0
#> GSM892368     3  0.0000      1.000 0.000  0  1 0.000 0.000  0
#> GSM892372     3  0.0000      1.000 0.000  0  1 0.000 0.000  0
#> GSM892376     2  0.0000      1.000 0.000  1  0 0.000 0.000  0
#> GSM892380     2  0.0000      1.000 0.000  1  0 0.000 0.000  0
#> GSM892386     2  0.0000      1.000 0.000  1  0 0.000 0.000  0
#> GSM892390     2  0.0000      1.000 0.000  1  0 0.000 0.000  0

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

k = 2
k = 3
k = 4
k = 5
k = 6

consensus_heatmap(res, k = 2)

plot of chunk tab-MAD-pam-consensus-heatmap-1

consensus_heatmap(res, k = 3)

plot of chunk tab-MAD-pam-consensus-heatmap-2

consensus_heatmap(res, k = 4)

plot of chunk tab-MAD-pam-consensus-heatmap-3

consensus_heatmap(res, k = 5)

plot of chunk tab-MAD-pam-consensus-heatmap-4

consensus_heatmap(res, k = 6)

plot of chunk tab-MAD-pam-consensus-heatmap-5

Heatmaps for the membership of samples in all partitions to see how consistent they are:

k = 2
k = 3
k = 4
k = 5
k = 6

membership_heatmap(res, k = 2)

plot of chunk tab-MAD-pam-membership-heatmap-1

membership_heatmap(res, k = 3)

plot of chunk tab-MAD-pam-membership-heatmap-2

membership_heatmap(res, k = 4)

plot of chunk tab-MAD-pam-membership-heatmap-3

membership_heatmap(res, k = 5)

plot of chunk tab-MAD-pam-membership-heatmap-4

membership_heatmap(res, k = 6)

plot of chunk tab-MAD-pam-membership-heatmap-5

Signature heatmaps where rows are scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2)

plot of chunk tab-MAD-pam-get-signatures-1

get_signatures(res, k = 3)

plot of chunk tab-MAD-pam-get-signatures-2

get_signatures(res, k = 4)

plot of chunk tab-MAD-pam-get-signatures-3

get_signatures(res, k = 5)

plot of chunk tab-MAD-pam-get-signatures-4

get_signatures(res, k = 6)

plot of chunk tab-MAD-pam-get-signatures-5

Signature heatmaps where rows are not scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-MAD-pam-get-signatures-no-scale-1

get_signatures(res, k = 3, scale_rows = FALSE)

plot of chunk tab-MAD-pam-get-signatures-no-scale-2

get_signatures(res, k = 4, scale_rows = FALSE)

plot of chunk tab-MAD-pam-get-signatures-no-scale-3

get_signatures(res, k = 5, scale_rows = FALSE)

plot of chunk tab-MAD-pam-get-signatures-no-scale-4

get_signatures(res, k = 6, scale_rows = FALSE)

plot of chunk tab-MAD-pam-get-signatures-no-scale-5

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk MAD-pam-signature_compare

# 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.

k = 2
k = 3
k = 4
k = 5
k = 6

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-MAD-pam-dimension-reduction-1

dimension_reduction(res, k = 3, method = "UMAP")

plot of chunk tab-MAD-pam-dimension-reduction-2

dimension_reduction(res, k = 4, method = "UMAP")

plot of chunk tab-MAD-pam-dimension-reduction-3

dimension_reduction(res, k = 5, method = "UMAP")

plot of chunk tab-MAD-pam-dimension-reduction-4

dimension_reduction(res, k = 6, method = "UMAP")

plot of chunk tab-MAD-pam-dimension-reduction-5

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk MAD-pam-collect-classes

test_to_known_factors(res)

#>          n tissue(p) disease.state(p) other(p) individual(p) k
#> MAD:pam 50     1.000            0.934 2.67e-07      1.42e-03 2
#> MAD:pam 49     0.981            0.952 1.63e-11      6.57e-05 3
#> MAD:pam 50     0.977            0.951 1.45e-16      7.83e-07 4
#> MAD:pam 50     1.000            0.998 3.06e-20      2.01e-07 5
#> MAD:pam 50     0.991            0.984 4.62e-22      7.12e-08 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

MAD:mclust**

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 31632 rows and 50 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 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)

plot of chunk MAD-mclust-collect-plots

The plots are:

The first row: a plot of the ECDF (empirical cumulative distribution function) curves of the consensus matrix for each k and the heatmap of predicted classes for each k.
The second row: heatmaps of the consensus matrix for each k.
The third row: heatmaps of the membership matrix for each k.
The fouth row: heatmaps of the signatures for each 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:

ECDF curves of the consensus matrix for each k;
1-PAC. The PAC score measures the proportion of the ambiguous subgrouping.
Mean silhouette score.
Concordance. The mean probability of fiting the consensus class ids in all partitions.
Area increased. Denote \(A_k\) as the area under the ECDF curve for current k, the area increased is defined as \(A_k - A_{k-1}\).
Rand index. The percent of pairs of samples that are both in a same cluster or both are not in a same cluster in the partition of k and k-1.
Jaccard index. The ratio of pairs of samples are both in a same cluster in the partition of k and k-1 and the pairs of samples are both in a same cluster in the partition k or k-1.

The detailed explanations of these statistics can be found in the cola vignette.

select_partition_number(res)

plot of chunk MAD-mclust-select-partition-number

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         0.4707 0.530   0.530
#> 3 3 1.000           1.000       1.000         0.4158 0.804   0.630
#> 4 4 0.959           0.920       0.966         0.1176 0.922   0.765
#> 5 5 1.000           0.944       0.980         0.0395 0.965   0.864
#> 6 6 0.993           0.984       0.989         0.0272 0.969   0.866

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

All \(k\) with Jaccard index larger than 0.95 are removed because increasing \(k\) does not provide enough extra information. If all \(k\) are removed, it is marked as no subgroup is detected.
For all \(k\) with 1-PAC score larger than 0.9, the maximal \(k\) is taken as the best \(k\), and other \(k\) are marked as optional \(k\).
If it does not fit the second rule. The \(k\) with the maximal vote of the highest 1-PAC score, highest mean silhouette, and highest concordance is taken as the best \(k\).

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.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

k = 2
k = 3
k = 4
k = 5
k = 6

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>           class entropy silhouette p1 p2
#> GSM892342     1       0          1  1  0
#> GSM892345     1       0          1  1  0
#> GSM892349     1       0          1  1  0
#> GSM892353     1       0          1  1  0
#> GSM892355     1       0          1  1  0
#> GSM892361     1       0          1  1  0
#> GSM892365     1       0          1  1  0
#> GSM892369     1       0          1  1  0
#> GSM892373     2       0          1  0  1
#> GSM892377     2       0          1  0  1
#> GSM892381     2       0          1  0  1
#> GSM892383     2       0          1  0  1
#> GSM892387     2       0          1  0  1
#> GSM892344     1       0          1  1  0
#> GSM892347     1       0          1  1  0
#> GSM892351     1       0          1  1  0
#> GSM892357     1       0          1  1  0
#> GSM892359     1       0          1  1  0
#> GSM892363     1       0          1  1  0
#> GSM892367     1       0          1  1  0
#> GSM892371     1       0          1  1  0
#> GSM892375     2       0          1  0  1
#> GSM892379     2       0          1  0  1
#> GSM892385     2       0          1  0  1
#> GSM892389     2       0          1  0  1
#> GSM892341     1       0          1  1  0
#> GSM892346     1       0          1  1  0
#> GSM892350     1       0          1  1  0
#> GSM892354     1       0          1  1  0
#> GSM892356     1       0          1  1  0
#> GSM892362     1       0          1  1  0
#> GSM892366     1       0          1  1  0
#> GSM892370     1       0          1  1  0
#> GSM892374     2       0          1  0  1
#> GSM892378     2       0          1  0  1
#> GSM892382     2       0          1  0  1
#> GSM892384     2       0          1  0  1
#> GSM892388     2       0          1  0  1
#> GSM892343     1       0          1  1  0
#> GSM892348     1       0          1  1  0
#> GSM892352     1       0          1  1  0
#> GSM892358     1       0          1  1  0
#> GSM892360     1       0          1  1  0
#> GSM892364     1       0          1  1  0
#> GSM892368     1       0          1  1  0
#> GSM892372     1       0          1  1  0
#> GSM892376     2       0          1  0  1
#> GSM892380     2       0          1  0  1
#> GSM892386     2       0          1  0  1
#> GSM892390     2       0          1  0  1

show/hide code output

cbind(get_classes(res, k = 3), get_membership(res, k = 3))

#>           class entropy silhouette p1 p2 p3
#> GSM892342     3       0          1  0  0  1
#> GSM892345     3       0          1  0  0  1
#> GSM892349     3       0          1  0  0  1
#> GSM892353     1       0          1  1  0  0
#> GSM892355     1       0          1  1  0  0
#> GSM892361     1       0          1  1  0  0
#> GSM892365     3       0          1  0  0  1
#> GSM892369     3       0          1  0  0  1
#> GSM892373     2       0          1  0  1  0
#> GSM892377     2       0          1  0  1  0
#> GSM892381     2       0          1  0  1  0
#> GSM892383     2       0          1  0  1  0
#> GSM892387     2       0          1  0  1  0
#> GSM892344     3       0          1  0  0  1
#> GSM892347     3       0          1  0  0  1
#> GSM892351     3       0          1  0  0  1
#> GSM892357     1       0          1  1  0  0
#> GSM892359     1       0          1  1  0  0
#> GSM892363     1       0          1  1  0  0
#> GSM892367     3       0          1  0  0  1
#> GSM892371     3       0          1  0  0  1
#> GSM892375     2       0          1  0  1  0
#> GSM892379     2       0          1  0  1  0
#> GSM892385     2       0          1  0  1  0
#> GSM892389     2       0          1  0  1  0
#> GSM892341     3       0          1  0  0  1
#> GSM892346     3       0          1  0  0  1
#> GSM892350     3       0          1  0  0  1
#> GSM892354     1       0          1  1  0  0
#> GSM892356     1       0          1  1  0  0
#> GSM892362     1       0          1  1  0  0
#> GSM892366     3       0          1  0  0  1
#> GSM892370     3       0          1  0  0  1
#> GSM892374     2       0          1  0  1  0
#> GSM892378     2       0          1  0  1  0
#> GSM892382     2       0          1  0  1  0
#> GSM892384     2       0          1  0  1  0
#> GSM892388     2       0          1  0  1  0
#> GSM892343     3       0          1  0  0  1
#> GSM892348     3       0          1  0  0  1
#> GSM892352     3       0          1  0  0  1
#> GSM892358     1       0          1  1  0  0
#> GSM892360     1       0          1  1  0  0
#> GSM892364     1       0          1  1  0  0
#> GSM892368     3       0          1  0  0  1
#> GSM892372     3       0          1  0  0  1
#> GSM892376     2       0          1  0  1  0
#> GSM892380     2       0          1  0  1  0
#> GSM892386     2       0          1  0  1  0
#> GSM892390     2       0          1  0  1  0

show/hide code output

cbind(get_classes(res, k = 4), get_membership(res, k = 4))

#>           class entropy silhouette p1 p2    p3    p4
#> GSM892342     3  0.0000      0.873  0  0 1.000 0.000
#> GSM892345     4  0.0000      0.922  0  0 0.000 1.000
#> GSM892349     4  0.2868      0.802  0  0 0.136 0.864
#> GSM892353     1  0.0000      1.000  1  0 0.000 0.000
#> GSM892355     1  0.0000      1.000  1  0 0.000 0.000
#> GSM892361     1  0.0000      1.000  1  0 0.000 0.000
#> GSM892365     3  0.0921      0.865  0  0 0.972 0.028
#> GSM892369     3  0.3837      0.710  0  0 0.776 0.224
#> GSM892373     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892377     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892381     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892383     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892387     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892344     3  0.0000      0.873  0  0 1.000 0.000
#> GSM892347     4  0.0000      0.922  0  0 0.000 1.000
#> GSM892351     4  0.0000      0.922  0  0 0.000 1.000
#> GSM892357     1  0.0000      1.000  1  0 0.000 0.000
#> GSM892359     1  0.0000      1.000  1  0 0.000 0.000
#> GSM892363     1  0.0000      1.000  1  0 0.000 0.000
#> GSM892367     3  0.0469      0.869  0  0 0.988 0.012
#> GSM892371     3  0.4008      0.674  0  0 0.756 0.244
#> GSM892375     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892379     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892385     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892389     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892341     3  0.0000      0.873  0  0 1.000 0.000
#> GSM892346     4  0.0000      0.922  0  0 0.000 1.000
#> GSM892350     4  0.0000      0.922  0  0 0.000 1.000
#> GSM892354     1  0.0000      1.000  1  0 0.000 0.000
#> GSM892356     1  0.0000      1.000  1  0 0.000 0.000
#> GSM892362     1  0.0000      1.000  1  0 0.000 0.000
#> GSM892366     3  0.0188      0.873  0  0 0.996 0.004
#> GSM892370     3  0.4941      0.268  0  0 0.564 0.436
#> GSM892374     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892378     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892382     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892384     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892388     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892343     3  0.4193      0.605  0  0 0.732 0.268
#> GSM892348     4  0.0000      0.922  0  0 0.000 1.000
#> GSM892352     4  0.4564      0.441  0  0 0.328 0.672
#> GSM892358     1  0.0000      1.000  1  0 0.000 0.000
#> GSM892360     1  0.0000      1.000  1  0 0.000 0.000
#> GSM892364     1  0.0000      1.000  1  0 0.000 0.000
#> GSM892368     3  0.0000      0.873  0  0 1.000 0.000
#> GSM892372     3  0.0592      0.870  0  0 0.984 0.016
#> GSM892376     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892380     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892386     2  0.0000      1.000  0  1 0.000 0.000
#> GSM892390     2  0.0000      1.000  0  1 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 5), get_membership(res, k = 5))

#>           class entropy silhouette    p1 p2    p3    p4    p5
#> GSM892342     3  0.0000      0.935 0.000  0 1.000 0.000 0.000
#> GSM892345     4  0.0000      0.914 0.000  0 0.000 1.000 0.000
#> GSM892349     4  0.4306      0.029 0.000  0 0.000 0.508 0.492
#> GSM892353     1  0.0000      0.999 1.000  0 0.000 0.000 0.000
#> GSM892355     1  0.0000      0.999 1.000  0 0.000 0.000 0.000
#> GSM892361     1  0.0000      0.999 1.000  0 0.000 0.000 0.000
#> GSM892365     3  0.0000      0.935 0.000  0 1.000 0.000 0.000
#> GSM892369     5  0.0000      0.987 0.000  0 0.000 0.000 1.000
#> GSM892373     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892344     3  0.4249      0.244 0.000  0 0.568 0.000 0.432
#> GSM892347     4  0.0000      0.914 0.000  0 0.000 1.000 0.000
#> GSM892351     4  0.0000      0.914 0.000  0 0.000 1.000 0.000
#> GSM892357     1  0.0000      0.999 1.000  0 0.000 0.000 0.000
#> GSM892359     1  0.0000      0.999 1.000  0 0.000 0.000 0.000
#> GSM892363     1  0.0000      0.999 1.000  0 0.000 0.000 0.000
#> GSM892367     3  0.0162      0.932 0.000  0 0.996 0.004 0.000
#> GSM892371     5  0.0162      0.987 0.000  0 0.000 0.004 0.996
#> GSM892375     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892341     3  0.0000      0.935 0.000  0 1.000 0.000 0.000
#> GSM892346     4  0.0000      0.914 0.000  0 0.000 1.000 0.000
#> GSM892350     4  0.0000      0.914 0.000  0 0.000 1.000 0.000
#> GSM892354     1  0.0000      0.999 1.000  0 0.000 0.000 0.000
#> GSM892356     1  0.0000      0.999 1.000  0 0.000 0.000 0.000
#> GSM892362     1  0.0000      0.999 1.000  0 0.000 0.000 0.000
#> GSM892366     3  0.0000      0.935 0.000  0 1.000 0.000 0.000
#> GSM892370     5  0.0510      0.980 0.000  0 0.000 0.016 0.984
#> GSM892374     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892343     5  0.0794      0.971 0.000  0 0.000 0.028 0.972
#> GSM892348     4  0.0000      0.914 0.000  0 0.000 1.000 0.000
#> GSM892352     5  0.0000      0.987 0.000  0 0.000 0.000 1.000
#> GSM892358     1  0.0162      0.996 0.996  0 0.000 0.000 0.004
#> GSM892360     1  0.0000      0.999 1.000  0 0.000 0.000 0.000
#> GSM892364     1  0.0162      0.996 0.996  0 0.000 0.000 0.004
#> GSM892368     3  0.0000      0.935 0.000  0 1.000 0.000 0.000
#> GSM892372     3  0.0162      0.932 0.000  0 0.996 0.004 0.000
#> GSM892376     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 6), get_membership(res, k = 6))

#>           class entropy silhouette    p1 p2    p3    p4    p5    p6
#> GSM892342     3  0.0000      0.983 0.000  0 1.000 0.000 0.000 0.000
#> GSM892345     4  0.0000      0.998 0.000  0 0.000 1.000 0.000 0.000
#> GSM892349     5  0.1082      0.955 0.000  0 0.000 0.040 0.956 0.004
#> GSM892353     6  0.0865      0.929 0.036  0 0.000 0.000 0.000 0.964
#> GSM892355     6  0.1663      0.950 0.088  0 0.000 0.000 0.000 0.912
#> GSM892361     1  0.0000      0.987 1.000  0 0.000 0.000 0.000 0.000
#> GSM892365     3  0.0000      0.983 0.000  0 1.000 0.000 0.000 0.000
#> GSM892369     5  0.0000      0.984 0.000  0 0.000 0.000 1.000 0.000
#> GSM892373     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892344     3  0.1863      0.878 0.000  0 0.896 0.000 0.104 0.000
#> GSM892347     4  0.0000      0.998 0.000  0 0.000 1.000 0.000 0.000
#> GSM892351     4  0.0000      0.998 0.000  0 0.000 1.000 0.000 0.000
#> GSM892357     1  0.0000      0.987 1.000  0 0.000 0.000 0.000 0.000
#> GSM892359     1  0.0260      0.983 0.992  0 0.000 0.000 0.000 0.008
#> GSM892363     1  0.0000      0.987 1.000  0 0.000 0.000 0.000 0.000
#> GSM892367     3  0.0146      0.980 0.000  0 0.996 0.004 0.000 0.000
#> GSM892371     5  0.0000      0.984 0.000  0 0.000 0.000 1.000 0.000
#> GSM892375     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892341     3  0.0000      0.983 0.000  0 1.000 0.000 0.000 0.000
#> GSM892346     4  0.0260      0.993 0.000  0 0.000 0.992 0.000 0.008
#> GSM892350     4  0.0000      0.998 0.000  0 0.000 1.000 0.000 0.000
#> GSM892354     1  0.0146      0.985 0.996  0 0.000 0.000 0.000 0.004
#> GSM892356     1  0.0000      0.987 1.000  0 0.000 0.000 0.000 0.000
#> GSM892362     1  0.0000      0.987 1.000  0 0.000 0.000 0.000 0.000
#> GSM892366     3  0.0000      0.983 0.000  0 1.000 0.000 0.000 0.000
#> GSM892370     5  0.0363      0.980 0.000  0 0.000 0.012 0.988 0.000
#> GSM892374     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892343     5  0.0458      0.978 0.000  0 0.000 0.016 0.984 0.000
#> GSM892348     4  0.0146      0.996 0.000  0 0.000 0.996 0.000 0.004
#> GSM892352     5  0.0000      0.984 0.000  0 0.000 0.000 1.000 0.000
#> GSM892358     6  0.2003      0.935 0.116  0 0.000 0.000 0.000 0.884
#> GSM892360     1  0.0000      0.987 1.000  0 0.000 0.000 0.000 0.000
#> GSM892364     1  0.1663      0.910 0.912  0 0.000 0.000 0.000 0.088
#> GSM892368     3  0.0000      0.983 0.000  0 1.000 0.000 0.000 0.000
#> GSM892372     3  0.0000      0.983 0.000  0 1.000 0.000 0.000 0.000
#> GSM892376     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000 0.000 0.000 0.000

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

k = 2
k = 3
k = 4
k = 5
k = 6

consensus_heatmap(res, k = 2)

plot of chunk tab-MAD-mclust-consensus-heatmap-1

consensus_heatmap(res, k = 3)

plot of chunk tab-MAD-mclust-consensus-heatmap-2

consensus_heatmap(res, k = 4)

plot of chunk tab-MAD-mclust-consensus-heatmap-3

consensus_heatmap(res, k = 5)

plot of chunk tab-MAD-mclust-consensus-heatmap-4

consensus_heatmap(res, k = 6)

plot of chunk tab-MAD-mclust-consensus-heatmap-5

Heatmaps for the membership of samples in all partitions to see how consistent they are:

k = 2
k = 3
k = 4
k = 5
k = 6

membership_heatmap(res, k = 2)

plot of chunk tab-MAD-mclust-membership-heatmap-1

membership_heatmap(res, k = 3)

plot of chunk tab-MAD-mclust-membership-heatmap-2

membership_heatmap(res, k = 4)

plot of chunk tab-MAD-mclust-membership-heatmap-3

membership_heatmap(res, k = 5)

plot of chunk tab-MAD-mclust-membership-heatmap-4

membership_heatmap(res, k = 6)

plot of chunk tab-MAD-mclust-membership-heatmap-5

Signature heatmaps where rows are scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2)

plot of chunk tab-MAD-mclust-get-signatures-1

get_signatures(res, k = 3)

plot of chunk tab-MAD-mclust-get-signatures-2

get_signatures(res, k = 4)

plot of chunk tab-MAD-mclust-get-signatures-3

get_signatures(res, k = 5)

plot of chunk tab-MAD-mclust-get-signatures-4

get_signatures(res, k = 6)

plot of chunk tab-MAD-mclust-get-signatures-5

Signature heatmaps where rows are not scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-MAD-mclust-get-signatures-no-scale-1

get_signatures(res, k = 3, scale_rows = FALSE)

plot of chunk tab-MAD-mclust-get-signatures-no-scale-2

get_signatures(res, k = 4, scale_rows = FALSE)

plot of chunk tab-MAD-mclust-get-signatures-no-scale-3

get_signatures(res, k = 5, scale_rows = FALSE)

plot of chunk tab-MAD-mclust-get-signatures-no-scale-4

get_signatures(res, k = 6, scale_rows = FALSE)

plot of chunk tab-MAD-mclust-get-signatures-no-scale-5

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk MAD-mclust-signature_compare

# 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.

k = 2
k = 3
k = 4
k = 5
k = 6

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-MAD-mclust-dimension-reduction-1

dimension_reduction(res, k = 3, method = "UMAP")

plot of chunk tab-MAD-mclust-dimension-reduction-2

dimension_reduction(res, k = 4, method = "UMAP")

plot of chunk tab-MAD-mclust-dimension-reduction-3

dimension_reduction(res, k = 5, method = "UMAP")

plot of chunk tab-MAD-mclust-dimension-reduction-4

dimension_reduction(res, k = 6, method = "UMAP")

plot of chunk tab-MAD-mclust-dimension-reduction-5

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk MAD-mclust-collect-classes

test_to_known_factors(res)

#>             n tissue(p) disease.state(p) other(p) individual(p) k
#> MAD:mclust 50     1.000            0.934 2.67e-07      1.42e-03 2
#> MAD:mclust 50     1.000            0.931 1.26e-12      1.60e-05 3
#> MAD:mclust 48     0.985            0.946 7.68e-17      1.01e-06 4
#> MAD:mclust 48     0.992            0.975 8.94e-16      1.54e-06 5
#> MAD:mclust 50     0.994            0.989 5.92e-15      1.19e-04 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.

MAD:NMF**

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 31632 rows and 50 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 5.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk MAD-NMF-collect-plots

The plots are:

The first row: a plot of the ECDF (empirical cumulative distribution function) curves of the consensus matrix for each k and the heatmap of predicted classes for each k.
The second row: heatmaps of the consensus matrix for each k.
The third row: heatmaps of the membership matrix for each k.
The fouth row: heatmaps of the signatures for each 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:

ECDF curves of the consensus matrix for each k;
1-PAC. The PAC score measures the proportion of the ambiguous subgrouping.
Mean silhouette score.
Concordance. The mean probability of fiting the consensus class ids in all partitions.
Area increased. Denote \(A_k\) as the area under the ECDF curve for current k, the area increased is defined as \(A_k - A_{k-1}\).
Rand index. The percent of pairs of samples that are both in a same cluster or both are not in a same cluster in the partition of k and k-1.
Jaccard index. The ratio of pairs of samples are both in a same cluster in the partition of k and k-1 and the pairs of samples are both in a same cluster in the partition k or k-1.

The detailed explanations of these statistics can be found in the cola vignette.

select_partition_number(res)

plot of chunk MAD-NMF-select-partition-number

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         0.4707 0.530   0.530
#> 3 3 0.966           0.972       0.974         0.4151 0.794   0.612
#> 4 4 1.000           0.975       0.981         0.1144 0.912   0.736
#> 5 5 0.960           0.944       0.952         0.0360 0.958   0.838
#> 6 6 0.973           0.934       0.951         0.0107 1.000   1.000

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

All \(k\) with Jaccard index larger than 0.95 are removed because increasing \(k\) does not provide enough extra information. If all \(k\) are removed, it is marked as no subgroup is detected.
For all \(k\) with 1-PAC score larger than 0.9, the maximal \(k\) is taken as the best \(k\), and other \(k\) are marked as optional \(k\).
If it does not fit the second rule. The \(k\) with the maximal vote of the highest 1-PAC score, highest mean silhouette, and highest concordance is taken as the best \(k\).

suggest_best_k(res)

#> [1] 5
#> attr(,"optional")
#> [1] 2 3 4

There is also optional best \(k\) = 2 3 4 that is worth to check.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

k = 2
k = 3
k = 4
k = 5
k = 6

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>           class entropy silhouette p1 p2
#> GSM892342     1       0          1  1  0
#> GSM892345     1       0          1  1  0
#> GSM892349     1       0          1  1  0
#> GSM892353     1       0          1  1  0
#> GSM892355     1       0          1  1  0
#> GSM892361     1       0          1  1  0
#> GSM892365     1       0          1  1  0
#> GSM892369     1       0          1  1  0
#> GSM892373     2       0          1  0  1
#> GSM892377     2       0          1  0  1
#> GSM892381     2       0          1  0  1
#> GSM892383     2       0          1  0  1
#> GSM892387     2       0          1  0  1
#> GSM892344     1       0          1  1  0
#> GSM892347     1       0          1  1  0
#> GSM892351     1       0          1  1  0
#> GSM892357     1       0          1  1  0
#> GSM892359     1       0          1  1  0
#> GSM892363     1       0          1  1  0
#> GSM892367     1       0          1  1  0
#> GSM892371     1       0          1  1  0
#> GSM892375     2       0          1  0  1
#> GSM892379     2       0          1  0  1
#> GSM892385     2       0          1  0  1
#> GSM892389     2       0          1  0  1
#> GSM892341     1       0          1  1  0
#> GSM892346     1       0          1  1  0
#> GSM892350     1       0          1  1  0
#> GSM892354     1       0          1  1  0
#> GSM892356     1       0          1  1  0
#> GSM892362     1       0          1  1  0
#> GSM892366     1       0          1  1  0
#> GSM892370     1       0          1  1  0
#> GSM892374     2       0          1  0  1
#> GSM892378     2       0          1  0  1
#> GSM892382     2       0          1  0  1
#> GSM892384     2       0          1  0  1
#> GSM892388     2       0          1  0  1
#> GSM892343     1       0          1  1  0
#> GSM892348     1       0          1  1  0
#> GSM892352     1       0          1  1  0
#> GSM892358     1       0          1  1  0
#> GSM892360     1       0          1  1  0
#> GSM892364     1       0          1  1  0
#> GSM892368     1       0          1  1  0
#> GSM892372     1       0          1  1  0
#> GSM892376     2       0          1  0  1
#> GSM892380     2       0          1  0  1
#> GSM892386     2       0          1  0  1
#> GSM892390     2       0          1  0  1

show/hide code output

cbind(get_classes(res, k = 3), get_membership(res, k = 3))

#>           class entropy silhouette    p1    p2    p3
#> GSM892342     3  0.1529      0.959 0.040 0.000 0.960
#> GSM892345     1  0.0237      0.985 0.996 0.000 0.004
#> GSM892349     3  0.4555      0.834 0.200 0.000 0.800
#> GSM892353     1  0.0000      0.988 1.000 0.000 0.000
#> GSM892355     1  0.0000      0.988 1.000 0.000 0.000
#> GSM892361     1  0.0000      0.988 1.000 0.000 0.000
#> GSM892365     3  0.1529      0.959 0.040 0.000 0.960
#> GSM892369     3  0.1753      0.959 0.048 0.000 0.952
#> GSM892373     2  0.0000      0.997 0.000 1.000 0.000
#> GSM892377     2  0.0000      0.997 0.000 1.000 0.000
#> GSM892381     2  0.0000      0.997 0.000 1.000 0.000
#> GSM892383     2  0.0000      0.997 0.000 1.000 0.000
#> GSM892387     2  0.0747      0.989 0.000 0.984 0.016
#> GSM892344     3  0.2165      0.951 0.064 0.000 0.936
#> GSM892347     1  0.0592      0.979 0.988 0.000 0.012
#> GSM892351     1  0.3116      0.873 0.892 0.000 0.108
#> GSM892357     1  0.0000      0.988 1.000 0.000 0.000
#> GSM892359     1  0.0000      0.988 1.000 0.000 0.000
#> GSM892363     1  0.0000      0.988 1.000 0.000 0.000
#> GSM892367     3  0.1529      0.959 0.040 0.000 0.960
#> GSM892371     3  0.1753      0.959 0.048 0.000 0.952
#> GSM892375     2  0.0424      0.994 0.000 0.992 0.008
#> GSM892379     2  0.0000      0.997 0.000 1.000 0.000
#> GSM892385     2  0.0424      0.994 0.000 0.992 0.008
#> GSM892389     2  0.0000      0.997 0.000 1.000 0.000
#> GSM892341     3  0.1860      0.958 0.052 0.000 0.948
#> GSM892346     1  0.0000      0.988 1.000 0.000 0.000
#> GSM892350     1  0.2066      0.931 0.940 0.000 0.060
#> GSM892354     1  0.0000      0.988 1.000 0.000 0.000
#> GSM892356     1  0.0000      0.988 1.000 0.000 0.000
#> GSM892362     1  0.0000      0.988 1.000 0.000 0.000
#> GSM892366     3  0.1529      0.959 0.040 0.000 0.960
#> GSM892370     3  0.1643      0.959 0.044 0.000 0.956
#> GSM892374     2  0.0000      0.997 0.000 1.000 0.000
#> GSM892378     2  0.0000      0.997 0.000 1.000 0.000
#> GSM892382     2  0.0000      0.997 0.000 1.000 0.000
#> GSM892384     2  0.0000      0.997 0.000 1.000 0.000
#> GSM892388     2  0.0592      0.992 0.000 0.988 0.012
#> GSM892343     3  0.4291      0.857 0.180 0.000 0.820
#> GSM892348     1  0.0000      0.988 1.000 0.000 0.000
#> GSM892352     3  0.4399      0.849 0.188 0.000 0.812
#> GSM892358     1  0.0000      0.988 1.000 0.000 0.000
#> GSM892360     1  0.0000      0.988 1.000 0.000 0.000
#> GSM892364     1  0.0000      0.988 1.000 0.000 0.000
#> GSM892368     3  0.1529      0.959 0.040 0.000 0.960
#> GSM892372     3  0.1529      0.959 0.040 0.000 0.960
#> GSM892376     2  0.0000      0.997 0.000 1.000 0.000
#> GSM892380     2  0.0747      0.989 0.000 0.984 0.016
#> GSM892386     2  0.0237      0.996 0.000 0.996 0.004
#> GSM892390     2  0.0424      0.994 0.000 0.992 0.008

show/hide code output

cbind(get_classes(res, k = 4), get_membership(res, k = 4))

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM892342     3  0.0895      0.956 0.004 0.000 0.976 0.020
#> GSM892345     4  0.1724      0.979 0.020 0.000 0.032 0.948
#> GSM892349     4  0.2125      0.943 0.004 0.000 0.076 0.920
#> GSM892353     1  0.0336      0.990 0.992 0.000 0.000 0.008
#> GSM892355     1  0.0000      0.997 1.000 0.000 0.000 0.000
#> GSM892361     1  0.0336      0.993 0.992 0.000 0.000 0.008
#> GSM892365     3  0.0000      0.962 0.000 0.000 1.000 0.000
#> GSM892369     3  0.0336      0.960 0.000 0.000 0.992 0.008
#> GSM892373     2  0.0188      0.997 0.000 0.996 0.000 0.004
#> GSM892377     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892381     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892383     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892387     2  0.0336      0.994 0.000 0.992 0.000 0.008
#> GSM892344     3  0.1042      0.954 0.008 0.000 0.972 0.020
#> GSM892347     4  0.1724      0.979 0.020 0.000 0.032 0.948
#> GSM892351     4  0.1610      0.978 0.016 0.000 0.032 0.952
#> GSM892357     1  0.0000      0.997 1.000 0.000 0.000 0.000
#> GSM892359     1  0.0000      0.997 1.000 0.000 0.000 0.000
#> GSM892363     1  0.0000      0.997 1.000 0.000 0.000 0.000
#> GSM892367     3  0.0000      0.962 0.000 0.000 1.000 0.000
#> GSM892371     3  0.0469      0.960 0.000 0.000 0.988 0.012
#> GSM892375     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892379     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892385     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892389     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892341     3  0.0895      0.956 0.004 0.000 0.976 0.020
#> GSM892346     4  0.1510      0.965 0.028 0.000 0.016 0.956
#> GSM892350     4  0.1724      0.979 0.020 0.000 0.032 0.948
#> GSM892354     1  0.0188      0.996 0.996 0.000 0.000 0.004
#> GSM892356     1  0.0000      0.997 1.000 0.000 0.000 0.000
#> GSM892362     1  0.0188      0.996 0.996 0.000 0.000 0.004
#> GSM892366     3  0.0000      0.962 0.000 0.000 1.000 0.000
#> GSM892370     3  0.0592      0.957 0.000 0.000 0.984 0.016
#> GSM892374     2  0.0188      0.997 0.000 0.996 0.000 0.004
#> GSM892378     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892382     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892384     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892388     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892343     3  0.4844      0.547 0.012 0.000 0.688 0.300
#> GSM892348     4  0.1624      0.977 0.020 0.000 0.028 0.952
#> GSM892352     4  0.2053      0.947 0.004 0.000 0.072 0.924
#> GSM892358     1  0.0000      0.997 1.000 0.000 0.000 0.000
#> GSM892360     1  0.0188      0.996 0.996 0.000 0.000 0.004
#> GSM892364     1  0.0188      0.996 0.996 0.000 0.000 0.004
#> GSM892368     3  0.0000      0.962 0.000 0.000 1.000 0.000
#> GSM892372     3  0.0000      0.962 0.000 0.000 1.000 0.000
#> GSM892376     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892380     2  0.0336      0.994 0.000 0.992 0.000 0.008
#> GSM892386     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM892390     2  0.0000      0.999 0.000 1.000 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 5), get_membership(res, k = 5))

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> GSM892342     5  0.3715      0.747 0.000 0.000 0.260 0.004 0.736
#> GSM892345     4  0.1851      0.910 0.000 0.000 0.000 0.912 0.088
#> GSM892349     5  0.4206      0.616 0.000 0.000 0.016 0.288 0.696
#> GSM892353     1  0.1043      0.963 0.960 0.000 0.000 0.000 0.040
#> GSM892355     1  0.0162      0.993 0.996 0.000 0.000 0.000 0.004
#> GSM892361     1  0.0162      0.993 0.996 0.000 0.000 0.004 0.000
#> GSM892365     3  0.0794      0.962 0.000 0.000 0.972 0.000 0.028
#> GSM892369     3  0.1300      0.948 0.000 0.000 0.956 0.016 0.028
#> GSM892373     2  0.0794      0.984 0.000 0.972 0.000 0.000 0.028
#> GSM892377     2  0.0510      0.990 0.000 0.984 0.000 0.000 0.016
#> GSM892381     2  0.0000      0.994 0.000 1.000 0.000 0.000 0.000
#> GSM892383     2  0.0162      0.994 0.000 0.996 0.000 0.000 0.004
#> GSM892387     2  0.0290      0.992 0.000 0.992 0.000 0.000 0.008
#> GSM892344     5  0.3803      0.808 0.000 0.000 0.140 0.056 0.804
#> GSM892347     4  0.1043      0.919 0.000 0.000 0.000 0.960 0.040
#> GSM892351     4  0.2966      0.803 0.000 0.000 0.000 0.816 0.184
#> GSM892357     1  0.0000      0.995 1.000 0.000 0.000 0.000 0.000
#> GSM892359     1  0.0000      0.995 1.000 0.000 0.000 0.000 0.000
#> GSM892363     1  0.0000      0.995 1.000 0.000 0.000 0.000 0.000
#> GSM892367     3  0.0162      0.966 0.000 0.000 0.996 0.000 0.004
#> GSM892371     3  0.0898      0.958 0.000 0.000 0.972 0.008 0.020
#> GSM892375     2  0.0404      0.991 0.000 0.988 0.000 0.000 0.012
#> GSM892379     2  0.0162      0.994 0.000 0.996 0.000 0.000 0.004
#> GSM892385     2  0.0162      0.994 0.000 0.996 0.000 0.000 0.004
#> GSM892389     2  0.0162      0.994 0.000 0.996 0.000 0.000 0.004
#> GSM892341     5  0.4169      0.782 0.000 0.000 0.240 0.028 0.732
#> GSM892346     4  0.1197      0.866 0.000 0.000 0.000 0.952 0.048
#> GSM892350     4  0.1608      0.917 0.000 0.000 0.000 0.928 0.072
#> GSM892354     1  0.0000      0.995 1.000 0.000 0.000 0.000 0.000
#> GSM892356     1  0.0162      0.994 0.996 0.000 0.000 0.000 0.004
#> GSM892362     1  0.0162      0.994 0.996 0.000 0.000 0.000 0.004
#> GSM892366     3  0.1043      0.954 0.000 0.000 0.960 0.000 0.040
#> GSM892370     3  0.0992      0.956 0.000 0.000 0.968 0.008 0.024
#> GSM892374     2  0.0794      0.984 0.000 0.972 0.000 0.000 0.028
#> GSM892378     2  0.0290      0.992 0.000 0.992 0.000 0.000 0.008
#> GSM892382     2  0.0000      0.994 0.000 1.000 0.000 0.000 0.000
#> GSM892384     2  0.0000      0.994 0.000 1.000 0.000 0.000 0.000
#> GSM892388     2  0.0510      0.989 0.000 0.984 0.000 0.000 0.016
#> GSM892343     5  0.5344      0.784 0.000 0.000 0.168 0.160 0.672
#> GSM892348     4  0.0290      0.908 0.000 0.000 0.000 0.992 0.008
#> GSM892352     5  0.3929      0.714 0.000 0.000 0.028 0.208 0.764
#> GSM892358     1  0.0000      0.995 1.000 0.000 0.000 0.000 0.000
#> GSM892360     1  0.0000      0.995 1.000 0.000 0.000 0.000 0.000
#> GSM892364     1  0.0162      0.994 0.996 0.000 0.000 0.000 0.004
#> GSM892368     3  0.0880      0.960 0.000 0.000 0.968 0.000 0.032
#> GSM892372     3  0.0404      0.966 0.000 0.000 0.988 0.000 0.012
#> GSM892376     2  0.0290      0.993 0.000 0.992 0.000 0.000 0.008
#> GSM892380     2  0.0000      0.994 0.000 1.000 0.000 0.000 0.000
#> GSM892386     2  0.0000      0.994 0.000 1.000 0.000 0.000 0.000
#> GSM892390     2  0.0000      0.994 0.000 1.000 0.000 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 6), get_membership(res, k = 6))

#>           class entropy silhouette    p1    p2    p3    p4    p5 p6
#> GSM892342     5  0.1901      0.788 0.000 0.000 0.076 0.004 0.912 NA
#> GSM892345     4  0.1970      0.904 0.000 0.000 0.000 0.912 0.060 NA
#> GSM892349     5  0.3728      0.568 0.000 0.000 0.000 0.344 0.652 NA
#> GSM892353     1  0.1555      0.933 0.932 0.000 0.004 0.000 0.060 NA
#> GSM892355     1  0.0146      0.991 0.996 0.000 0.000 0.000 0.000 NA
#> GSM892361     1  0.0146      0.991 0.996 0.000 0.000 0.000 0.000 NA
#> GSM892365     3  0.0937      0.970 0.000 0.000 0.960 0.000 0.040 NA
#> GSM892369     3  0.0891      0.960 0.000 0.000 0.968 0.008 0.000 NA
#> GSM892373     2  0.1714      0.940 0.000 0.908 0.000 0.000 0.000 NA
#> GSM892377     2  0.1007      0.971 0.000 0.956 0.000 0.000 0.000 NA
#> GSM892381     2  0.0260      0.980 0.000 0.992 0.000 0.000 0.000 NA
#> GSM892383     2  0.0260      0.979 0.000 0.992 0.000 0.000 0.000 NA
#> GSM892387     2  0.0363      0.979 0.000 0.988 0.000 0.000 0.000 NA
#> GSM892344     5  0.1901      0.807 0.000 0.000 0.028 0.040 0.924 NA
#> GSM892347     4  0.0806      0.906 0.000 0.000 0.000 0.972 0.020 NA
#> GSM892351     4  0.2730      0.785 0.000 0.000 0.000 0.836 0.152 NA
#> GSM892357     1  0.0000      0.993 1.000 0.000 0.000 0.000 0.000 NA
#> GSM892359     1  0.0000      0.993 1.000 0.000 0.000 0.000 0.000 NA
#> GSM892363     1  0.0000      0.993 1.000 0.000 0.000 0.000 0.000 NA
#> GSM892367     3  0.0508      0.973 0.000 0.000 0.984 0.000 0.012 NA
#> GSM892371     3  0.0622      0.966 0.000 0.000 0.980 0.008 0.000 NA
#> GSM892375     2  0.0937      0.973 0.000 0.960 0.000 0.000 0.000 NA
#> GSM892379     2  0.0713      0.976 0.000 0.972 0.000 0.000 0.000 NA
#> GSM892385     2  0.0458      0.979 0.000 0.984 0.000 0.000 0.000 NA
#> GSM892389     2  0.0260      0.980 0.000 0.992 0.000 0.000 0.000 NA
#> GSM892341     5  0.2006      0.801 0.000 0.000 0.080 0.016 0.904 NA
#> GSM892346     4  0.2135      0.830 0.000 0.000 0.000 0.872 0.000 NA
#> GSM892350     4  0.1398      0.904 0.000 0.000 0.000 0.940 0.052 NA
#> GSM892354     1  0.0146      0.991 0.996 0.000 0.000 0.000 0.000 NA
#> GSM892356     1  0.0000      0.993 1.000 0.000 0.000 0.000 0.000 NA
#> GSM892362     1  0.0000      0.993 1.000 0.000 0.000 0.000 0.000 NA
#> GSM892366     3  0.1075      0.964 0.000 0.000 0.952 0.000 0.048 NA
#> GSM892370     3  0.0508      0.968 0.000 0.000 0.984 0.004 0.000 NA
#> GSM892374     2  0.1908      0.934 0.000 0.900 0.000 0.000 0.004 NA
#> GSM892378     2  0.0458      0.979 0.000 0.984 0.000 0.000 0.000 NA
#> GSM892382     2  0.0146      0.980 0.000 0.996 0.000 0.000 0.000 NA
#> GSM892384     2  0.0260      0.980 0.000 0.992 0.000 0.000 0.000 NA
#> GSM892388     2  0.1387      0.955 0.000 0.932 0.000 0.000 0.000 NA
#> GSM892343     5  0.3584      0.796 0.004 0.000 0.060 0.104 0.820 NA
#> GSM892348     4  0.1196      0.896 0.000 0.000 0.000 0.952 0.008 NA
#> GSM892352     5  0.4058      0.618 0.000 0.000 0.004 0.320 0.660 NA
#> GSM892358     1  0.0000      0.993 1.000 0.000 0.000 0.000 0.000 NA
#> GSM892360     1  0.0000      0.993 1.000 0.000 0.000 0.000 0.000 NA
#> GSM892364     1  0.0260      0.988 0.992 0.000 0.000 0.000 0.000 NA
#> GSM892368     3  0.0865      0.972 0.000 0.000 0.964 0.000 0.036 NA
#> GSM892372     3  0.0713      0.973 0.000 0.000 0.972 0.000 0.028 NA
#> GSM892376     2  0.0363      0.979 0.000 0.988 0.000 0.000 0.000 NA
#> GSM892380     2  0.0146      0.979 0.000 0.996 0.000 0.000 0.000 NA
#> GSM892386     2  0.0363      0.979 0.000 0.988 0.000 0.000 0.000 NA
#> GSM892390     2  0.0000      0.980 0.000 1.000 0.000 0.000 0.000 NA

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

k = 2
k = 3
k = 4
k = 5
k = 6

consensus_heatmap(res, k = 2)

plot of chunk tab-MAD-NMF-consensus-heatmap-1

consensus_heatmap(res, k = 3)

plot of chunk tab-MAD-NMF-consensus-heatmap-2

consensus_heatmap(res, k = 4)

plot of chunk tab-MAD-NMF-consensus-heatmap-3

consensus_heatmap(res, k = 5)

plot of chunk tab-MAD-NMF-consensus-heatmap-4

consensus_heatmap(res, k = 6)

plot of chunk tab-MAD-NMF-consensus-heatmap-5

Heatmaps for the membership of samples in all partitions to see how consistent they are:

k = 2
k = 3
k = 4
k = 5
k = 6

membership_heatmap(res, k = 2)

plot of chunk tab-MAD-NMF-membership-heatmap-1

membership_heatmap(res, k = 3)

plot of chunk tab-MAD-NMF-membership-heatmap-2

membership_heatmap(res, k = 4)

plot of chunk tab-MAD-NMF-membership-heatmap-3

membership_heatmap(res, k = 5)

plot of chunk tab-MAD-NMF-membership-heatmap-4

membership_heatmap(res, k = 6)

plot of chunk tab-MAD-NMF-membership-heatmap-5

Signature heatmaps where rows are scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2)

plot of chunk tab-MAD-NMF-get-signatures-1

get_signatures(res, k = 3)

plot of chunk tab-MAD-NMF-get-signatures-2

get_signatures(res, k = 4)

plot of chunk tab-MAD-NMF-get-signatures-3

get_signatures(res, k = 5)

plot of chunk tab-MAD-NMF-get-signatures-4

get_signatures(res, k = 6)

plot of chunk tab-MAD-NMF-get-signatures-5

Signature heatmaps where rows are not scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-MAD-NMF-get-signatures-no-scale-1

get_signatures(res, k = 3, scale_rows = FALSE)

plot of chunk tab-MAD-NMF-get-signatures-no-scale-2

get_signatures(res, k = 4, scale_rows = FALSE)

plot of chunk tab-MAD-NMF-get-signatures-no-scale-3

get_signatures(res, k = 5, scale_rows = FALSE)

plot of chunk tab-MAD-NMF-get-signatures-no-scale-4

get_signatures(res, k = 6, scale_rows = FALSE)

plot of chunk tab-MAD-NMF-get-signatures-no-scale-5

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk MAD-NMF-signature_compare

# 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.

k = 2
k = 3
k = 4
k = 5
k = 6

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-MAD-NMF-dimension-reduction-1

dimension_reduction(res, k = 3, method = "UMAP")

plot of chunk tab-MAD-NMF-dimension-reduction-2

dimension_reduction(res, k = 4, method = "UMAP")

plot of chunk tab-MAD-NMF-dimension-reduction-3

dimension_reduction(res, k = 5, method = "UMAP")

plot of chunk tab-MAD-NMF-dimension-reduction-4

dimension_reduction(res, k = 6, method = "UMAP")

plot of chunk tab-MAD-NMF-dimension-reduction-5

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk MAD-NMF-collect-classes

test_to_known_factors(res)

#>          n tissue(p) disease.state(p) other(p) individual(p) k
#> MAD:NMF 50         1            0.934 2.67e-07      1.42e-03 2
#> MAD:NMF 50         1            0.931 1.69e-11      8.93e-05 3
#> MAD:NMF 50         1            0.986 6.71e-18      2.02e-07 4
#> MAD:NMF 50         1            0.998 3.06e-20      2.01e-07 5
#> MAD:NMF 50         1            0.998 3.06e-20      2.01e-07 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

ATC:hclust*

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 31632 rows and 50 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 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)

plot of chunk ATC-hclust-collect-plots

The plots are:

The first row: a plot of the ECDF (empirical cumulative distribution function) curves of the consensus matrix for each k and the heatmap of predicted classes for each k.
The second row: heatmaps of the consensus matrix for each k.
The third row: heatmaps of the membership matrix for each k.
The fouth row: heatmaps of the signatures for each 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:

ECDF curves of the consensus matrix for each k;
1-PAC. The PAC score measures the proportion of the ambiguous subgrouping.
Mean silhouette score.
Concordance. The mean probability of fiting the consensus class ids in all partitions.
Area increased. Denote \(A_k\) as the area under the ECDF curve for current k, the area increased is defined as \(A_k - A_{k-1}\).
Rand index. The percent of pairs of samples that are both in a same cluster or both are not in a same cluster in the partition of k and k-1.
Jaccard index. The ratio of pairs of samples are both in a same cluster in the partition of k and k-1 and the pairs of samples are both in a same cluster in the partition k or k-1.

The detailed explanations of these statistics can be found in the cola vignette.

select_partition_number(res)

plot of chunk ATC-hclust-select-partition-number

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         0.4707 0.530   0.530
#> 3 3 0.846           0.908       0.950         0.3783 0.804   0.630
#> 4 4 0.815           0.874       0.929         0.0799 0.974   0.922
#> 5 5 0.863           0.796       0.866         0.0717 0.922   0.745
#> 6 6 0.918           0.833       0.914         0.0588 0.949   0.780

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

All \(k\) with Jaccard index larger than 0.95 are removed because increasing \(k\) does not provide enough extra information. If all \(k\) are removed, it is marked as no subgroup is detected.
For all \(k\) with 1-PAC score larger than 0.9, the maximal \(k\) is taken as the best \(k\), and other \(k\) are marked as optional \(k\).
If it does not fit the second rule. The \(k\) with the maximal vote of the highest 1-PAC score, highest mean silhouette, and highest concordance is taken as the best \(k\).

suggest_best_k(res)

#> [1] 6
#> attr(,"optional")
#> [1] 2

There is also optional best \(k\) = 2 that is worth to check.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

k = 2
k = 3
k = 4
k = 5
k = 6

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>           class entropy silhouette p1 p2
#> GSM892342     1       0          1  1  0
#> GSM892345     1       0          1  1  0
#> GSM892349     1       0          1  1  0
#> GSM892353     1       0          1  1  0
#> GSM892355     1       0          1  1  0
#> GSM892361     1       0          1  1  0
#> GSM892365     1       0          1  1  0
#> GSM892369     1       0          1  1  0
#> GSM892373     2       0          1  0  1
#> GSM892377     2       0          1  0  1
#> GSM892381     2       0          1  0  1
#> GSM892383     2       0          1  0  1
#> GSM892387     2       0          1  0  1
#> GSM892344     1       0          1  1  0
#> GSM892347     1       0          1  1  0
#> GSM892351     1       0          1  1  0
#> GSM892357     1       0          1  1  0
#> GSM892359     1       0          1  1  0
#> GSM892363     1       0          1  1  0
#> GSM892367     1       0          1  1  0
#> GSM892371     1       0          1  1  0
#> GSM892375     2       0          1  0  1
#> GSM892379     2       0          1  0  1
#> GSM892385     2       0          1  0  1
#> GSM892389     2       0          1  0  1
#> GSM892341     1       0          1  1  0
#> GSM892346     1       0          1  1  0
#> GSM892350     1       0          1  1  0
#> GSM892354     1       0          1  1  0
#> GSM892356     1       0          1  1  0
#> GSM892362     1       0          1  1  0
#> GSM892366     1       0          1  1  0
#> GSM892370     1       0          1  1  0
#> GSM892374     2       0          1  0  1
#> GSM892378     2       0          1  0  1
#> GSM892382     2       0          1  0  1
#> GSM892384     2       0          1  0  1
#> GSM892388     2       0          1  0  1
#> GSM892343     1       0          1  1  0
#> GSM892348     1       0          1  1  0
#> GSM892352     1       0          1  1  0
#> GSM892358     1       0          1  1  0
#> GSM892360     1       0          1  1  0
#> GSM892364     1       0          1  1  0
#> GSM892368     1       0          1  1  0
#> GSM892372     1       0          1  1  0
#> GSM892376     2       0          1  0  1
#> GSM892380     2       0          1  0  1
#> GSM892386     2       0          1  0  1
#> GSM892390     2       0          1  0  1

show/hide code output

cbind(get_classes(res, k = 3), get_membership(res, k = 3))

#>           class entropy silhouette    p1 p2    p3
#> GSM892342     3   0.597      0.601 0.364  0 0.636
#> GSM892345     1   0.288      0.886 0.904  0 0.096
#> GSM892349     1   0.304      0.877 0.896  0 0.104
#> GSM892353     1   0.000      0.954 1.000  0 0.000
#> GSM892355     1   0.000      0.954 1.000  0 0.000
#> GSM892361     1   0.000      0.954 1.000  0 0.000
#> GSM892365     3   0.000      0.816 0.000  0 1.000
#> GSM892369     3   0.304      0.822 0.104  0 0.896
#> GSM892373     2   0.000      1.000 0.000  1 0.000
#> GSM892377     2   0.000      1.000 0.000  1 0.000
#> GSM892381     2   0.000      1.000 0.000  1 0.000
#> GSM892383     2   0.000      1.000 0.000  1 0.000
#> GSM892387     2   0.000      1.000 0.000  1 0.000
#> GSM892344     3   0.599      0.596 0.368  0 0.632
#> GSM892347     1   0.196      0.918 0.944  0 0.056
#> GSM892351     1   0.288      0.886 0.904  0 0.096
#> GSM892357     1   0.000      0.954 1.000  0 0.000
#> GSM892359     1   0.000      0.954 1.000  0 0.000
#> GSM892363     1   0.000      0.954 1.000  0 0.000
#> GSM892367     3   0.000      0.816 0.000  0 1.000
#> GSM892371     3   0.304      0.822 0.104  0 0.896
#> GSM892375     2   0.000      1.000 0.000  1 0.000
#> GSM892379     2   0.000      1.000 0.000  1 0.000
#> GSM892385     2   0.000      1.000 0.000  1 0.000
#> GSM892389     2   0.000      1.000 0.000  1 0.000
#> GSM892341     3   0.597      0.601 0.364  0 0.636
#> GSM892346     1   0.000      0.954 1.000  0 0.000
#> GSM892350     1   0.288      0.886 0.904  0 0.096
#> GSM892354     1   0.000      0.954 1.000  0 0.000
#> GSM892356     1   0.000      0.954 1.000  0 0.000
#> GSM892362     1   0.000      0.954 1.000  0 0.000
#> GSM892366     3   0.000      0.816 0.000  0 1.000
#> GSM892370     3   0.304      0.822 0.104  0 0.896
#> GSM892374     2   0.000      1.000 0.000  1 0.000
#> GSM892378     2   0.000      1.000 0.000  1 0.000
#> GSM892382     2   0.000      1.000 0.000  1 0.000
#> GSM892384     2   0.000      1.000 0.000  1 0.000
#> GSM892388     2   0.000      1.000 0.000  1 0.000
#> GSM892343     3   0.599      0.596 0.368  0 0.632
#> GSM892348     1   0.000      0.954 1.000  0 0.000
#> GSM892352     1   0.510      0.627 0.752  0 0.248
#> GSM892358     1   0.000      0.954 1.000  0 0.000
#> GSM892360     1   0.000      0.954 1.000  0 0.000
#> GSM892364     1   0.000      0.954 1.000  0 0.000
#> GSM892368     3   0.000      0.816 0.000  0 1.000
#> GSM892372     3   0.103      0.821 0.024  0 0.976
#> GSM892376     2   0.000      1.000 0.000  1 0.000
#> GSM892380     2   0.000      1.000 0.000  1 0.000
#> GSM892386     2   0.000      1.000 0.000  1 0.000
#> GSM892390     2   0.000      1.000 0.000  1 0.000

show/hide code output

cbind(get_classes(res, k = 4), get_membership(res, k = 4))

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM892342     4   0.289      0.996 0.124 0.000 0.004 0.872
#> GSM892345     1   0.401      0.666 0.756 0.000 0.000 0.244
#> GSM892349     1   0.422      0.625 0.728 0.000 0.000 0.272
#> GSM892353     1   0.000      0.896 1.000 0.000 0.000 0.000
#> GSM892355     1   0.000      0.896 1.000 0.000 0.000 0.000
#> GSM892361     1   0.000      0.896 1.000 0.000 0.000 0.000
#> GSM892365     3   0.000      0.820 0.000 0.000 1.000 0.000
#> GSM892369     3   0.445      0.716 0.000 0.000 0.692 0.308
#> GSM892373     2   0.270      0.896 0.000 0.876 0.000 0.124
#> GSM892377     2   0.000      0.981 0.000 1.000 0.000 0.000
#> GSM892381     2   0.000      0.981 0.000 1.000 0.000 0.000
#> GSM892383     2   0.000      0.981 0.000 1.000 0.000 0.000
#> GSM892387     2   0.000      0.981 0.000 1.000 0.000 0.000
#> GSM892344     4   0.270      0.996 0.124 0.000 0.000 0.876
#> GSM892347     1   0.228      0.823 0.904 0.000 0.000 0.096
#> GSM892351     1   0.416      0.639 0.736 0.000 0.000 0.264
#> GSM892357     1   0.000      0.896 1.000 0.000 0.000 0.000
#> GSM892359     1   0.000      0.896 1.000 0.000 0.000 0.000
#> GSM892363     1   0.000      0.896 1.000 0.000 0.000 0.000
#> GSM892367     3   0.000      0.820 0.000 0.000 1.000 0.000
#> GSM892371     3   0.445      0.716 0.000 0.000 0.692 0.308
#> GSM892375     2   0.000      0.981 0.000 1.000 0.000 0.000
#> GSM892379     2   0.000      0.981 0.000 1.000 0.000 0.000
#> GSM892385     2   0.000      0.981 0.000 1.000 0.000 0.000
#> GSM892389     2   0.000      0.981 0.000 1.000 0.000 0.000
#> GSM892341     4   0.289      0.996 0.124 0.000 0.004 0.872
#> GSM892346     1   0.000      0.896 1.000 0.000 0.000 0.000
#> GSM892350     1   0.416      0.639 0.736 0.000 0.000 0.264
#> GSM892354     1   0.000      0.896 1.000 0.000 0.000 0.000
#> GSM892356     1   0.000      0.896 1.000 0.000 0.000 0.000
#> GSM892362     1   0.000      0.896 1.000 0.000 0.000 0.000
#> GSM892366     3   0.000      0.820 0.000 0.000 1.000 0.000
#> GSM892370     3   0.445      0.716 0.000 0.000 0.692 0.308
#> GSM892374     2   0.270      0.896 0.000 0.876 0.000 0.124
#> GSM892378     2   0.000      0.981 0.000 1.000 0.000 0.000
#> GSM892382     2   0.000      0.981 0.000 1.000 0.000 0.000
#> GSM892384     2   0.000      0.981 0.000 1.000 0.000 0.000
#> GSM892388     2   0.270      0.896 0.000 0.876 0.000 0.124
#> GSM892343     4   0.270      0.996 0.124 0.000 0.000 0.876
#> GSM892348     1   0.000      0.896 1.000 0.000 0.000 0.000
#> GSM892352     1   0.497      0.151 0.548 0.000 0.000 0.452
#> GSM892358     1   0.000      0.896 1.000 0.000 0.000 0.000
#> GSM892360     1   0.000      0.896 1.000 0.000 0.000 0.000
#> GSM892364     1   0.000      0.896 1.000 0.000 0.000 0.000
#> GSM892368     3   0.000      0.820 0.000 0.000 1.000 0.000
#> GSM892372     3   0.327      0.790 0.000 0.000 0.832 0.168
#> GSM892376     2   0.000      0.981 0.000 1.000 0.000 0.000
#> GSM892380     2   0.000      0.981 0.000 1.000 0.000 0.000
#> GSM892386     2   0.000      0.981 0.000 1.000 0.000 0.000
#> GSM892390     2   0.000      0.981 0.000 1.000 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 5), get_membership(res, k = 5))

#>           class entropy silhouette    p1  p2    p3    p4    p5
#> GSM892342     5  0.0162      0.996 0.000 0.0 0.004 0.000 0.996
#> GSM892345     4  0.0963      0.610 0.036 0.0 0.000 0.964 0.000
#> GSM892349     4  0.0290      0.628 0.000 0.0 0.000 0.992 0.008
#> GSM892353     1  0.4182      1.000 0.600 0.0 0.000 0.400 0.000
#> GSM892355     1  0.4182      1.000 0.600 0.0 0.000 0.400 0.000
#> GSM892361     1  0.4182      1.000 0.600 0.0 0.000 0.400 0.000
#> GSM892365     3  0.0000      0.826 0.000 0.0 1.000 0.000 0.000
#> GSM892369     3  0.3969      0.730 0.000 0.0 0.692 0.004 0.304
#> GSM892373     2  0.4182      0.581 0.400 0.6 0.000 0.000 0.000
#> GSM892377     2  0.0000      0.934 0.000 1.0 0.000 0.000 0.000
#> GSM892381     2  0.0000      0.934 0.000 1.0 0.000 0.000 0.000
#> GSM892383     2  0.0000      0.934 0.000 1.0 0.000 0.000 0.000
#> GSM892387     2  0.0000      0.934 0.000 1.0 0.000 0.000 0.000
#> GSM892344     5  0.0162      0.996 0.000 0.0 0.000 0.004 0.996
#> GSM892347     4  0.3508      0.207 0.252 0.0 0.000 0.748 0.000
#> GSM892351     4  0.0000      0.630 0.000 0.0 0.000 1.000 0.000
#> GSM892357     1  0.4182      1.000 0.600 0.0 0.000 0.400 0.000
#> GSM892359     1  0.4182      1.000 0.600 0.0 0.000 0.400 0.000
#> GSM892363     1  0.4182      1.000 0.600 0.0 0.000 0.400 0.000
#> GSM892367     3  0.0000      0.826 0.000 0.0 1.000 0.000 0.000
#> GSM892371     3  0.3969      0.730 0.000 0.0 0.692 0.004 0.304
#> GSM892375     2  0.0000      0.934 0.000 1.0 0.000 0.000 0.000
#> GSM892379     2  0.0000      0.934 0.000 1.0 0.000 0.000 0.000
#> GSM892385     2  0.0000      0.934 0.000 1.0 0.000 0.000 0.000
#> GSM892389     2  0.0000      0.934 0.000 1.0 0.000 0.000 0.000
#> GSM892341     5  0.0162      0.996 0.000 0.0 0.004 0.000 0.996
#> GSM892346     4  0.4425     -0.600 0.452 0.0 0.000 0.544 0.004
#> GSM892350     4  0.0000      0.630 0.000 0.0 0.000 1.000 0.000
#> GSM892354     1  0.4182      1.000 0.600 0.0 0.000 0.400 0.000
#> GSM892356     1  0.4182      1.000 0.600 0.0 0.000 0.400 0.000
#> GSM892362     1  0.4182      1.000 0.600 0.0 0.000 0.400 0.000
#> GSM892366     3  0.0000      0.826 0.000 0.0 1.000 0.000 0.000
#> GSM892370     3  0.3969      0.730 0.000 0.0 0.692 0.004 0.304
#> GSM892374     2  0.4182      0.581 0.400 0.6 0.000 0.000 0.000
#> GSM892378     2  0.0000      0.934 0.000 1.0 0.000 0.000 0.000
#> GSM892382     2  0.0000      0.934 0.000 1.0 0.000 0.000 0.000
#> GSM892384     2  0.0000      0.934 0.000 1.0 0.000 0.000 0.000
#> GSM892388     2  0.4182      0.581 0.400 0.6 0.000 0.000 0.000
#> GSM892343     5  0.0162      0.996 0.000 0.0 0.000 0.004 0.996
#> GSM892348     4  0.4425     -0.600 0.452 0.0 0.000 0.544 0.004
#> GSM892352     4  0.3534      0.250 0.000 0.0 0.000 0.744 0.256
#> GSM892358     1  0.4182      1.000 0.600 0.0 0.000 0.400 0.000
#> GSM892360     1  0.4182      1.000 0.600 0.0 0.000 0.400 0.000
#> GSM892364     1  0.4182      1.000 0.600 0.0 0.000 0.400 0.000
#> GSM892368     3  0.0000      0.826 0.000 0.0 1.000 0.000 0.000
#> GSM892372     3  0.2813      0.799 0.000 0.0 0.832 0.000 0.168
#> GSM892376     2  0.0000      0.934 0.000 1.0 0.000 0.000 0.000
#> GSM892380     2  0.0000      0.934 0.000 1.0 0.000 0.000 0.000
#> GSM892386     2  0.0000      0.934 0.000 1.0 0.000 0.000 0.000
#> GSM892390     2  0.0000      0.934 0.000 1.0 0.000 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 6), get_membership(res, k = 6))

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> GSM892342     5  0.0405      0.992 0.000 0.000 0.004 0.000 0.988 0.008
#> GSM892345     4  0.1408      0.833 0.020 0.000 0.000 0.944 0.000 0.036
#> GSM892349     4  0.0405      0.851 0.004 0.000 0.000 0.988 0.000 0.008
#> GSM892353     1  0.0000      1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892355     1  0.0000      1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892361     1  0.0000      1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892365     3  0.0000      0.827 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM892369     3  0.3446      0.732 0.000 0.000 0.692 0.000 0.308 0.000
#> GSM892373     6  0.3868      0.256 0.000 0.492 0.000 0.000 0.000 0.508
#> GSM892377     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892381     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892383     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892387     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892344     5  0.0260      0.992 0.000 0.000 0.000 0.000 0.992 0.008
#> GSM892347     4  0.4060      0.590 0.032 0.000 0.000 0.684 0.000 0.284
#> GSM892351     4  0.0146      0.853 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM892357     1  0.0000      1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892359     1  0.0000      1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892363     1  0.0000      1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892367     3  0.0000      0.827 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM892371     3  0.3446      0.732 0.000 0.000 0.692 0.000 0.308 0.000
#> GSM892375     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892379     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892385     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892389     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892341     5  0.0146      0.992 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM892346     6  0.4705     -0.479 0.044 0.000 0.000 0.472 0.000 0.484
#> GSM892350     4  0.0146      0.853 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM892354     1  0.0000      1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892356     1  0.0000      1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892362     1  0.0000      1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892366     3  0.0000      0.827 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM892370     3  0.3446      0.732 0.000 0.000 0.692 0.000 0.308 0.000
#> GSM892374     6  0.3868      0.256 0.000 0.492 0.000 0.000 0.000 0.508
#> GSM892378     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892382     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892384     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892388     6  0.3868      0.256 0.000 0.492 0.000 0.000 0.000 0.508
#> GSM892343     5  0.0000      0.992 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM892348     6  0.4705     -0.479 0.044 0.000 0.000 0.472 0.000 0.484
#> GSM892352     4  0.3373      0.586 0.000 0.000 0.000 0.744 0.248 0.008
#> GSM892358     1  0.0000      1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892360     1  0.0000      1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892364     1  0.0000      1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892368     3  0.0000      0.827 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM892372     3  0.2527      0.800 0.000 0.000 0.832 0.000 0.168 0.000
#> GSM892376     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892380     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892386     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892390     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

k = 2
k = 3
k = 4
k = 5
k = 6

consensus_heatmap(res, k = 2)

plot of chunk tab-ATC-hclust-consensus-heatmap-1

consensus_heatmap(res, k = 3)

plot of chunk tab-ATC-hclust-consensus-heatmap-2

consensus_heatmap(res, k = 4)

plot of chunk tab-ATC-hclust-consensus-heatmap-3

consensus_heatmap(res, k = 5)

plot of chunk tab-ATC-hclust-consensus-heatmap-4

consensus_heatmap(res, k = 6)

plot of chunk tab-ATC-hclust-consensus-heatmap-5

Heatmaps for the membership of samples in all partitions to see how consistent they are:

k = 2
k = 3
k = 4
k = 5
k = 6

membership_heatmap(res, k = 2)

plot of chunk tab-ATC-hclust-membership-heatmap-1

membership_heatmap(res, k = 3)

plot of chunk tab-ATC-hclust-membership-heatmap-2

membership_heatmap(res, k = 4)

plot of chunk tab-ATC-hclust-membership-heatmap-3

membership_heatmap(res, k = 5)

plot of chunk tab-ATC-hclust-membership-heatmap-4

membership_heatmap(res, k = 6)

plot of chunk tab-ATC-hclust-membership-heatmap-5

Signature heatmaps where rows are scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2)

plot of chunk tab-ATC-hclust-get-signatures-1

get_signatures(res, k = 3)

plot of chunk tab-ATC-hclust-get-signatures-2

get_signatures(res, k = 4)

plot of chunk tab-ATC-hclust-get-signatures-3

get_signatures(res, k = 5)

plot of chunk tab-ATC-hclust-get-signatures-4

get_signatures(res, k = 6)

plot of chunk tab-ATC-hclust-get-signatures-5

Signature heatmaps where rows are not scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-ATC-hclust-get-signatures-no-scale-1

get_signatures(res, k = 3, scale_rows = FALSE)

plot of chunk tab-ATC-hclust-get-signatures-no-scale-2

get_signatures(res, k = 4, scale_rows = FALSE)

plot of chunk tab-ATC-hclust-get-signatures-no-scale-3

get_signatures(res, k = 5, scale_rows = FALSE)

plot of chunk tab-ATC-hclust-get-signatures-no-scale-4

get_signatures(res, k = 6, scale_rows = FALSE)

plot of chunk tab-ATC-hclust-get-signatures-no-scale-5

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk ATC-hclust-signature_compare

# 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.

k = 2
k = 3
k = 4
k = 5
k = 6

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-ATC-hclust-dimension-reduction-1

dimension_reduction(res, k = 3, method = "UMAP")

plot of chunk tab-ATC-hclust-dimension-reduction-2

dimension_reduction(res, k = 4, method = "UMAP")

plot of chunk tab-ATC-hclust-dimension-reduction-3

dimension_reduction(res, k = 5, method = "UMAP")

plot of chunk tab-ATC-hclust-dimension-reduction-4

dimension_reduction(res, k = 6, method = "UMAP")

plot of chunk tab-ATC-hclust-dimension-reduction-5

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk ATC-hclust-collect-classes

test_to_known_factors(res)

#>             n tissue(p) disease.state(p) other(p) individual(p) k
#> ATC:hclust 50     1.000            0.934 2.67e-07      1.42e-03 2
#> ATC:hclust 50     1.000            0.931 1.26e-12      1.60e-05 3
#> ATC:hclust 49     0.998            0.993 2.28e-17      4.54e-07 4
#> ATC:hclust 46     0.922            0.927 2.35e-20      4.18e-08 5
#> ATC:hclust 45     0.970            1.000 1.15e-19      1.17e-07 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

ATC:kmeans**

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 31632 rows and 50 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)

plot of chunk ATC-kmeans-collect-plots

The plots are:

The first row: a plot of the ECDF (empirical cumulative distribution function) curves of the consensus matrix for each k and the heatmap of predicted classes for each k.
The second row: heatmaps of the consensus matrix for each k.
The third row: heatmaps of the membership matrix for each k.
The fouth row: heatmaps of the signatures for each 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:

ECDF curves of the consensus matrix for each k;
1-PAC. The PAC score measures the proportion of the ambiguous subgrouping.
Mean silhouette score.
Concordance. The mean probability of fiting the consensus class ids in all partitions.
Area increased. Denote \(A_k\) as the area under the ECDF curve for current k, the area increased is defined as \(A_k - A_{k-1}\).
Rand index. The percent of pairs of samples that are both in a same cluster or both are not in a same cluster in the partition of k and k-1.
Jaccard index. The ratio of pairs of samples are both in a same cluster in the partition of k and k-1 and the pairs of samples are both in a same cluster in the partition k or k-1.

The detailed explanations of these statistics can be found in the cola vignette.

select_partition_number(res)

plot of chunk ATC-kmeans-select-partition-number

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         0.4707 0.530   0.530
#> 3 3 0.775           0.952       0.907         0.3034 0.811   0.644
#> 4 4 0.645           0.532       0.805         0.1402 0.984   0.952
#> 5 5 0.764           0.840       0.823         0.0741 0.878   0.633
#> 6 6 0.747           0.771       0.777         0.0570 0.962   0.832

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

All \(k\) with Jaccard index larger than 0.95 are removed because increasing \(k\) does not provide enough extra information. If all \(k\) are removed, it is marked as no subgroup is detected.
For all \(k\) with 1-PAC score larger than 0.9, the maximal \(k\) is taken as the best \(k\), and other \(k\) are marked as optional \(k\).
If it does not fit the second rule. The \(k\) with the maximal vote of the highest 1-PAC score, highest mean silhouette, and highest concordance is taken as the best \(k\).

suggest_best_k(res)

#> [1] 2

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

k = 2
k = 3
k = 4
k = 5
k = 6

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>           class entropy silhouette p1 p2
#> GSM892342     1       0          1  1  0
#> GSM892345     1       0          1  1  0
#> GSM892349     1       0          1  1  0
#> GSM892353     1       0          1  1  0
#> GSM892355     1       0          1  1  0
#> GSM892361     1       0          1  1  0
#> GSM892365     1       0          1  1  0
#> GSM892369     1       0          1  1  0
#> GSM892373     2       0          1  0  1
#> GSM892377     2       0          1  0  1
#> GSM892381     2       0          1  0  1
#> GSM892383     2       0          1  0  1
#> GSM892387     2       0          1  0  1
#> GSM892344     1       0          1  1  0
#> GSM892347     1       0          1  1  0
#> GSM892351     1       0          1  1  0
#> GSM892357     1       0          1  1  0
#> GSM892359     1       0          1  1  0
#> GSM892363     1       0          1  1  0
#> GSM892367     1       0          1  1  0
#> GSM892371     1       0          1  1  0
#> GSM892375     2       0          1  0  1
#> GSM892379     2       0          1  0  1
#> GSM892385     2       0          1  0  1
#> GSM892389     2       0          1  0  1
#> GSM892341     1       0          1  1  0
#> GSM892346     1       0          1  1  0
#> GSM892350     1       0          1  1  0
#> GSM892354     1       0          1  1  0
#> GSM892356     1       0          1  1  0
#> GSM892362     1       0          1  1  0
#> GSM892366     1       0          1  1  0
#> GSM892370     1       0          1  1  0
#> GSM892374     2       0          1  0  1
#> GSM892378     2       0          1  0  1
#> GSM892382     2       0          1  0  1
#> GSM892384     2       0          1  0  1
#> GSM892388     2       0          1  0  1
#> GSM892343     1       0          1  1  0
#> GSM892348     1       0          1  1  0
#> GSM892352     1       0          1  1  0
#> GSM892358     1       0          1  1  0
#> GSM892360     1       0          1  1  0
#> GSM892364     1       0          1  1  0
#> GSM892368     1       0          1  1  0
#> GSM892372     1       0          1  1  0
#> GSM892376     2       0          1  0  1
#> GSM892380     2       0          1  0  1
#> GSM892386     2       0          1  0  1
#> GSM892390     2       0          1  0  1

show/hide code output

cbind(get_classes(res, k = 3), get_membership(res, k = 3))

#>           class entropy silhouette    p1    p2    p3
#> GSM892342     3   0.562      0.990 0.308 0.000 0.692
#> GSM892345     1   0.000      0.981 1.000 0.000 0.000
#> GSM892349     1   0.116      0.948 0.972 0.000 0.028
#> GSM892353     1   0.000      0.981 1.000 0.000 0.000
#> GSM892355     1   0.000      0.981 1.000 0.000 0.000
#> GSM892361     1   0.000      0.981 1.000 0.000 0.000
#> GSM892365     3   0.562      0.990 0.308 0.000 0.692
#> GSM892369     3   0.562      0.990 0.308 0.000 0.692
#> GSM892373     2   0.562      0.761 0.000 0.692 0.308
#> GSM892377     2   0.000      0.958 0.000 1.000 0.000
#> GSM892381     2   0.000      0.958 0.000 1.000 0.000
#> GSM892383     2   0.000      0.958 0.000 1.000 0.000
#> GSM892387     2   0.000      0.958 0.000 1.000 0.000
#> GSM892344     3   0.601      0.894 0.372 0.000 0.628
#> GSM892347     1   0.000      0.981 1.000 0.000 0.000
#> GSM892351     1   0.000      0.981 1.000 0.000 0.000
#> GSM892357     1   0.000      0.981 1.000 0.000 0.000
#> GSM892359     1   0.000      0.981 1.000 0.000 0.000
#> GSM892363     1   0.000      0.981 1.000 0.000 0.000
#> GSM892367     3   0.562      0.990 0.308 0.000 0.692
#> GSM892371     3   0.562      0.990 0.308 0.000 0.692
#> GSM892375     2   0.000      0.958 0.000 1.000 0.000
#> GSM892379     2   0.000      0.958 0.000 1.000 0.000
#> GSM892385     2   0.000      0.958 0.000 1.000 0.000
#> GSM892389     2   0.000      0.958 0.000 1.000 0.000
#> GSM892341     3   0.562      0.990 0.308 0.000 0.692
#> GSM892346     1   0.000      0.981 1.000 0.000 0.000
#> GSM892350     1   0.000      0.981 1.000 0.000 0.000
#> GSM892354     1   0.000      0.981 1.000 0.000 0.000
#> GSM892356     1   0.000      0.981 1.000 0.000 0.000
#> GSM892362     1   0.000      0.981 1.000 0.000 0.000
#> GSM892366     3   0.562      0.990 0.308 0.000 0.692
#> GSM892370     3   0.562      0.990 0.308 0.000 0.692
#> GSM892374     2   0.562      0.761 0.000 0.692 0.308
#> GSM892378     2   0.000      0.958 0.000 1.000 0.000
#> GSM892382     2   0.000      0.958 0.000 1.000 0.000
#> GSM892384     2   0.000      0.958 0.000 1.000 0.000
#> GSM892388     2   0.562      0.761 0.000 0.692 0.308
#> GSM892343     1   0.450      0.609 0.804 0.000 0.196
#> GSM892348     1   0.000      0.981 1.000 0.000 0.000
#> GSM892352     1   0.116      0.948 0.972 0.000 0.028
#> GSM892358     1   0.000      0.981 1.000 0.000 0.000
#> GSM892360     1   0.000      0.981 1.000 0.000 0.000
#> GSM892364     1   0.000      0.981 1.000 0.000 0.000
#> GSM892368     3   0.562      0.990 0.308 0.000 0.692
#> GSM892372     3   0.562      0.990 0.308 0.000 0.692
#> GSM892376     2   0.000      0.958 0.000 1.000 0.000
#> GSM892380     2   0.000      0.958 0.000 1.000 0.000
#> GSM892386     2   0.000      0.958 0.000 1.000 0.000
#> GSM892390     2   0.000      0.958 0.000 1.000 0.000

show/hide code output

cbind(get_classes(res, k = 4), get_membership(res, k = 4))

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM892342     3  0.5160      0.911 0.136 0.000 0.760 0.104
#> GSM892345     1  0.4916     -0.706 0.576 0.000 0.000 0.424
#> GSM892349     1  0.5168     -0.972 0.504 0.000 0.004 0.492
#> GSM892353     1  0.0592      0.575 0.984 0.000 0.000 0.016
#> GSM892355     1  0.0000      0.596 1.000 0.000 0.000 0.000
#> GSM892361     1  0.0000      0.596 1.000 0.000 0.000 0.000
#> GSM892365     3  0.2868      0.931 0.136 0.000 0.864 0.000
#> GSM892369     3  0.4514      0.930 0.136 0.000 0.800 0.064
#> GSM892373     2  0.5000      0.596 0.000 0.504 0.000 0.496
#> GSM892377     2  0.2408      0.889 0.000 0.896 0.104 0.000
#> GSM892381     2  0.1022      0.899 0.000 0.968 0.032 0.000
#> GSM892383     2  0.0817      0.900 0.000 0.976 0.024 0.000
#> GSM892387     2  0.0921      0.901 0.000 0.972 0.028 0.000
#> GSM892344     3  0.6980      0.636 0.164 0.000 0.572 0.264
#> GSM892347     1  0.4916     -0.706 0.576 0.000 0.000 0.424
#> GSM892351     1  0.4989     -0.886 0.528 0.000 0.000 0.472
#> GSM892357     1  0.0000      0.596 1.000 0.000 0.000 0.000
#> GSM892359     1  0.0000      0.596 1.000 0.000 0.000 0.000
#> GSM892363     1  0.0000      0.596 1.000 0.000 0.000 0.000
#> GSM892367     3  0.2868      0.931 0.136 0.000 0.864 0.000
#> GSM892371     3  0.4514      0.930 0.136 0.000 0.800 0.064
#> GSM892375     2  0.1118      0.898 0.000 0.964 0.036 0.000
#> GSM892379     2  0.2216      0.890 0.000 0.908 0.092 0.000
#> GSM892385     2  0.1302      0.900 0.000 0.956 0.044 0.000
#> GSM892389     2  0.2081      0.892 0.000 0.916 0.084 0.000
#> GSM892341     3  0.5160      0.911 0.136 0.000 0.760 0.104
#> GSM892346     1  0.4877     -0.661 0.592 0.000 0.000 0.408
#> GSM892350     1  0.4916     -0.706 0.576 0.000 0.000 0.424
#> GSM892354     1  0.0000      0.596 1.000 0.000 0.000 0.000
#> GSM892356     1  0.0000      0.596 1.000 0.000 0.000 0.000
#> GSM892362     1  0.0000      0.596 1.000 0.000 0.000 0.000
#> GSM892366     3  0.2868      0.931 0.136 0.000 0.864 0.000
#> GSM892370     3  0.4514      0.930 0.136 0.000 0.800 0.064
#> GSM892374     2  0.5000      0.596 0.000 0.504 0.000 0.496
#> GSM892378     2  0.2345      0.889 0.000 0.900 0.100 0.000
#> GSM892382     2  0.1022      0.899 0.000 0.968 0.032 0.000
#> GSM892384     2  0.0592      0.900 0.000 0.984 0.016 0.000
#> GSM892388     2  0.5000      0.596 0.000 0.504 0.000 0.496
#> GSM892343     1  0.7824     -0.325 0.404 0.000 0.328 0.268
#> GSM892348     1  0.4916     -0.706 0.576 0.000 0.000 0.424
#> GSM892352     4  0.5168      0.000 0.496 0.000 0.004 0.500
#> GSM892358     1  0.0000      0.596 1.000 0.000 0.000 0.000
#> GSM892360     1  0.0000      0.596 1.000 0.000 0.000 0.000
#> GSM892364     1  0.0000      0.596 1.000 0.000 0.000 0.000
#> GSM892368     3  0.2868      0.931 0.136 0.000 0.864 0.000
#> GSM892372     3  0.2868      0.931 0.136 0.000 0.864 0.000
#> GSM892376     2  0.1022      0.899 0.000 0.968 0.032 0.000
#> GSM892380     2  0.1716      0.897 0.000 0.936 0.064 0.000
#> GSM892386     2  0.0707      0.900 0.000 0.980 0.020 0.000
#> GSM892390     2  0.2081      0.892 0.000 0.916 0.084 0.000

show/hide code output

cbind(get_classes(res, k = 5), get_membership(res, k = 5))

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> GSM892342     3  0.6353      0.698 0.008 0.000 0.556 0.180 0.256
#> GSM892345     4  0.2179      0.823 0.100 0.000 0.000 0.896 0.004
#> GSM892349     4  0.1082      0.789 0.000 0.000 0.008 0.964 0.028
#> GSM892353     1  0.4763      0.880 0.632 0.000 0.000 0.336 0.032
#> GSM892355     1  0.4475      0.967 0.692 0.000 0.000 0.276 0.032
#> GSM892361     1  0.3814      0.976 0.720 0.000 0.000 0.276 0.004
#> GSM892365     3  0.1928      0.853 0.004 0.000 0.920 0.072 0.004
#> GSM892369     3  0.3900      0.851 0.008 0.000 0.816 0.108 0.068
#> GSM892373     5  0.3913      0.990 0.000 0.324 0.000 0.000 0.676
#> GSM892377     2  0.3993      0.784 0.216 0.756 0.028 0.000 0.000
#> GSM892381     2  0.0912      0.851 0.012 0.972 0.016 0.000 0.000
#> GSM892383     2  0.2580      0.845 0.064 0.892 0.044 0.000 0.000
#> GSM892387     2  0.0451      0.855 0.004 0.988 0.008 0.000 0.000
#> GSM892344     3  0.6952      0.465 0.008 0.000 0.408 0.328 0.256
#> GSM892347     4  0.2179      0.823 0.100 0.000 0.000 0.896 0.004
#> GSM892351     4  0.0992      0.809 0.024 0.000 0.000 0.968 0.008
#> GSM892357     1  0.4229      0.969 0.704 0.000 0.000 0.276 0.020
#> GSM892359     1  0.3661      0.977 0.724 0.000 0.000 0.276 0.000
#> GSM892363     1  0.4138      0.974 0.708 0.000 0.000 0.276 0.016
#> GSM892367     3  0.1608      0.854 0.000 0.000 0.928 0.072 0.000
#> GSM892371     3  0.3900      0.851 0.008 0.000 0.816 0.108 0.068
#> GSM892375     2  0.0693      0.851 0.012 0.980 0.008 0.000 0.000
#> GSM892379     2  0.3395      0.783 0.236 0.764 0.000 0.000 0.000
#> GSM892385     2  0.3003      0.842 0.092 0.864 0.044 0.000 0.000
#> GSM892389     2  0.3282      0.802 0.188 0.804 0.008 0.000 0.000
#> GSM892341     3  0.6353      0.698 0.008 0.000 0.556 0.180 0.256
#> GSM892346     4  0.2389      0.805 0.116 0.000 0.000 0.880 0.004
#> GSM892350     4  0.2020      0.823 0.100 0.000 0.000 0.900 0.000
#> GSM892354     1  0.4229      0.969 0.704 0.000 0.000 0.276 0.020
#> GSM892356     1  0.3661      0.977 0.724 0.000 0.000 0.276 0.000
#> GSM892362     1  0.4138      0.974 0.708 0.000 0.000 0.276 0.016
#> GSM892366     3  0.1928      0.853 0.004 0.000 0.920 0.072 0.004
#> GSM892370     3  0.3900      0.851 0.008 0.000 0.816 0.108 0.068
#> GSM892374     5  0.3913      0.990 0.000 0.324 0.000 0.000 0.676
#> GSM892378     2  0.3424      0.781 0.240 0.760 0.000 0.000 0.000
#> GSM892382     2  0.0912      0.851 0.012 0.972 0.016 0.000 0.000
#> GSM892384     2  0.0290      0.855 0.000 0.992 0.008 0.000 0.000
#> GSM892388     5  0.4812      0.980 0.012 0.324 0.012 0.004 0.648
#> GSM892343     4  0.6808     -0.144 0.008 0.000 0.268 0.468 0.256
#> GSM892348     4  0.2233      0.820 0.104 0.000 0.000 0.892 0.004
#> GSM892352     4  0.1082      0.789 0.000 0.000 0.008 0.964 0.028
#> GSM892358     1  0.3661      0.977 0.724 0.000 0.000 0.276 0.000
#> GSM892360     1  0.3661      0.977 0.724 0.000 0.000 0.276 0.000
#> GSM892364     1  0.4138      0.974 0.708 0.000 0.000 0.276 0.016
#> GSM892368     3  0.1608      0.854 0.000 0.000 0.928 0.072 0.000
#> GSM892372     3  0.2006      0.854 0.000 0.000 0.916 0.072 0.012
#> GSM892376     2  0.0579      0.852 0.008 0.984 0.008 0.000 0.000
#> GSM892380     2  0.3146      0.832 0.128 0.844 0.028 0.000 0.000
#> GSM892386     2  0.0290      0.854 0.000 0.992 0.008 0.000 0.000
#> GSM892390     2  0.3282      0.802 0.188 0.804 0.008 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 6), get_membership(res, k = 6))

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> GSM892342     5  0.5422     0.1256 0.024 0.000 0.316 0.080 0.580 0.000
#> GSM892345     4  0.2597     0.9196 0.176 0.000 0.000 0.824 0.000 0.000
#> GSM892349     4  0.4287     0.8571 0.108 0.000 0.000 0.768 0.028 0.096
#> GSM892353     1  0.3610     0.8378 0.792 0.000 0.000 0.052 0.004 0.152
#> GSM892355     1  0.2340     0.8939 0.852 0.000 0.000 0.000 0.000 0.148
#> GSM892361     1  0.1141     0.9456 0.948 0.000 0.000 0.000 0.000 0.052
#> GSM892365     3  0.1088     0.8936 0.024 0.000 0.960 0.000 0.000 0.016
#> GSM892369     3  0.4416     0.8530 0.024 0.000 0.776 0.016 0.096 0.088
#> GSM892373     5  0.6049     0.0991 0.000 0.332 0.000 0.000 0.404 0.264
#> GSM892377     2  0.1606     0.7628 0.000 0.932 0.004 0.056 0.000 0.008
#> GSM892381     2  0.3850     0.8343 0.000 0.652 0.004 0.004 0.000 0.340
#> GSM892383     2  0.4134     0.8348 0.000 0.708 0.000 0.052 0.000 0.240
#> GSM892387     2  0.4009     0.8379 0.000 0.684 0.000 0.028 0.000 0.288
#> GSM892344     5  0.5858     0.2254 0.028 0.000 0.228 0.164 0.580 0.000
#> GSM892347     4  0.2597     0.9196 0.176 0.000 0.000 0.824 0.000 0.000
#> GSM892351     4  0.3915     0.8865 0.128 0.000 0.000 0.776 0.004 0.092
#> GSM892357     1  0.1387     0.9365 0.932 0.000 0.000 0.000 0.000 0.068
#> GSM892359     1  0.0000     0.9481 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892363     1  0.0937     0.9436 0.960 0.000 0.000 0.000 0.000 0.040
#> GSM892367     3  0.0632     0.8961 0.024 0.000 0.976 0.000 0.000 0.000
#> GSM892371     3  0.4416     0.8530 0.024 0.000 0.776 0.016 0.096 0.088
#> GSM892375     2  0.3758     0.8356 0.000 0.668 0.000 0.008 0.000 0.324
#> GSM892379     2  0.1003     0.7583 0.000 0.964 0.004 0.028 0.000 0.004
#> GSM892385     2  0.3894     0.8328 0.000 0.740 0.004 0.036 0.000 0.220
#> GSM892389     2  0.0984     0.7663 0.000 0.968 0.012 0.012 0.000 0.008
#> GSM892341     5  0.5422     0.1256 0.024 0.000 0.316 0.080 0.580 0.000
#> GSM892346     4  0.2838     0.9112 0.188 0.000 0.000 0.808 0.000 0.004
#> GSM892350     4  0.3695     0.9153 0.176 0.000 0.000 0.776 0.004 0.044
#> GSM892354     1  0.1444     0.9369 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM892356     1  0.0000     0.9481 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892362     1  0.1327     0.9431 0.936 0.000 0.000 0.000 0.000 0.064
#> GSM892366     3  0.1088     0.8936 0.024 0.000 0.960 0.000 0.000 0.016
#> GSM892370     3  0.4416     0.8530 0.024 0.000 0.776 0.016 0.096 0.088
#> GSM892374     5  0.6049     0.0991 0.000 0.332 0.000 0.000 0.404 0.264
#> GSM892378     2  0.0713     0.7602 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM892382     2  0.3850     0.8343 0.000 0.652 0.004 0.004 0.000 0.340
#> GSM892384     2  0.4042     0.8376 0.000 0.664 0.004 0.016 0.000 0.316
#> GSM892388     5  0.6410     0.0961 0.000 0.332 0.004 0.008 0.384 0.272
#> GSM892343     5  0.6283     0.2458 0.088 0.000 0.160 0.172 0.580 0.000
#> GSM892348     4  0.2631     0.9180 0.180 0.000 0.000 0.820 0.000 0.000
#> GSM892352     4  0.4315     0.8527 0.104 0.000 0.000 0.768 0.032 0.096
#> GSM892358     1  0.0547     0.9467 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM892360     1  0.0000     0.9481 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892364     1  0.0937     0.9436 0.960 0.000 0.000 0.000 0.000 0.040
#> GSM892368     3  0.0632     0.8961 0.024 0.000 0.976 0.000 0.000 0.000
#> GSM892372     3  0.2209     0.8896 0.024 0.000 0.900 0.000 0.004 0.072
#> GSM892376     2  0.3784     0.8359 0.000 0.680 0.000 0.012 0.000 0.308
#> GSM892380     2  0.3254     0.8129 0.000 0.820 0.000 0.056 0.000 0.124
#> GSM892386     2  0.3816     0.8373 0.000 0.688 0.000 0.016 0.000 0.296
#> GSM892390     2  0.1078     0.7667 0.000 0.964 0.012 0.016 0.000 0.008

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

k = 2
k = 3
k = 4
k = 5
k = 6

consensus_heatmap(res, k = 2)

plot of chunk tab-ATC-kmeans-consensus-heatmap-1

consensus_heatmap(res, k = 3)

plot of chunk tab-ATC-kmeans-consensus-heatmap-2

consensus_heatmap(res, k = 4)

plot of chunk tab-ATC-kmeans-consensus-heatmap-3

consensus_heatmap(res, k = 5)

plot of chunk tab-ATC-kmeans-consensus-heatmap-4

consensus_heatmap(res, k = 6)

plot of chunk tab-ATC-kmeans-consensus-heatmap-5

Heatmaps for the membership of samples in all partitions to see how consistent they are:

k = 2
k = 3
k = 4
k = 5
k = 6

membership_heatmap(res, k = 2)

plot of chunk tab-ATC-kmeans-membership-heatmap-1

membership_heatmap(res, k = 3)

plot of chunk tab-ATC-kmeans-membership-heatmap-2

membership_heatmap(res, k = 4)

plot of chunk tab-ATC-kmeans-membership-heatmap-3

membership_heatmap(res, k = 5)

plot of chunk tab-ATC-kmeans-membership-heatmap-4

membership_heatmap(res, k = 6)

plot of chunk tab-ATC-kmeans-membership-heatmap-5

Signature heatmaps where rows are scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2)

plot of chunk tab-ATC-kmeans-get-signatures-1

get_signatures(res, k = 3)

plot of chunk tab-ATC-kmeans-get-signatures-2

get_signatures(res, k = 4)

plot of chunk tab-ATC-kmeans-get-signatures-3

get_signatures(res, k = 5)

plot of chunk tab-ATC-kmeans-get-signatures-4

get_signatures(res, k = 6)

plot of chunk tab-ATC-kmeans-get-signatures-5

Signature heatmaps where rows are not scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-ATC-kmeans-get-signatures-no-scale-1

get_signatures(res, k = 3, scale_rows = FALSE)

plot of chunk tab-ATC-kmeans-get-signatures-no-scale-2

get_signatures(res, k = 4, scale_rows = FALSE)

plot of chunk tab-ATC-kmeans-get-signatures-no-scale-3

get_signatures(res, k = 5, scale_rows = FALSE)

plot of chunk tab-ATC-kmeans-get-signatures-no-scale-4

get_signatures(res, k = 6, scale_rows = FALSE)

plot of chunk tab-ATC-kmeans-get-signatures-no-scale-5

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk ATC-kmeans-signature_compare

# 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.

k = 2
k = 3
k = 4
k = 5
k = 6

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-ATC-kmeans-dimension-reduction-1

dimension_reduction(res, k = 3, method = "UMAP")

plot of chunk tab-ATC-kmeans-dimension-reduction-2

dimension_reduction(res, k = 4, method = "UMAP")

plot of chunk tab-ATC-kmeans-dimension-reduction-3

dimension_reduction(res, k = 5, method = "UMAP")

plot of chunk tab-ATC-kmeans-dimension-reduction-4

dimension_reduction(res, k = 6, method = "UMAP")

plot of chunk tab-ATC-kmeans-dimension-reduction-5

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk ATC-kmeans-collect-classes

test_to_known_factors(res)

#>             n tissue(p) disease.state(p) other(p) individual(p) k
#> ATC:kmeans 50     1.000            0.934 2.67e-07      1.42e-03 2
#> ATC:kmeans 50     0.933            0.869 1.06e-11      4.14e-05 3
#> ATC:kmeans 41     0.967            0.954 7.24e-11      1.02e-04 4
#> ATC:kmeans 48     0.982            0.532 5.15e-16      6.33e-08 5
#> ATC:kmeans 43     0.998            0.998 2.92e-15      1.90e-06 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

ATC:skmeans**

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 31632 rows and 50 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 5.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk ATC-skmeans-collect-plots

The plots are:

The first row: a plot of the ECDF (empirical cumulative distribution function) curves of the consensus matrix for each k and the heatmap of predicted classes for each k.
The second row: heatmaps of the consensus matrix for each k.
The third row: heatmaps of the membership matrix for each k.
The fouth row: heatmaps of the signatures for each 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:

ECDF curves of the consensus matrix for each k;
1-PAC. The PAC score measures the proportion of the ambiguous subgrouping.
Mean silhouette score.
Concordance. The mean probability of fiting the consensus class ids in all partitions.
Area increased. Denote \(A_k\) as the area under the ECDF curve for current k, the area increased is defined as \(A_k - A_{k-1}\).
Rand index. The percent of pairs of samples that are both in a same cluster or both are not in a same cluster in the partition of k and k-1.
Jaccard index. The ratio of pairs of samples are both in a same cluster in the partition of k and k-1 and the pairs of samples are both in a same cluster in the partition k or k-1.

The detailed explanations of these statistics can be found in the cola vignette.

select_partition_number(res)

plot of chunk ATC-skmeans-select-partition-number

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         0.4707 0.530   0.530
#> 3 3 1.000           0.984       0.994         0.3946 0.811   0.644
#> 4 4 1.000           0.890       0.956         0.1358 0.882   0.670
#> 5 5 1.000           0.990       0.993         0.0341 0.971   0.888
#> 6 6 0.982           0.930       0.946         0.0143 0.990   0.957

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

All \(k\) with Jaccard index larger than 0.95 are removed because increasing \(k\) does not provide enough extra information. If all \(k\) are removed, it is marked as no subgroup is detected.
For all \(k\) with 1-PAC score larger than 0.9, the maximal \(k\) is taken as the best \(k\), and other \(k\) are marked as optional \(k\).
If it does not fit the second rule. The \(k\) with the maximal vote of the highest 1-PAC score, highest mean silhouette, and highest concordance is taken as the best \(k\).

suggest_best_k(res)

#> [1] 5
#> attr(,"optional")
#> [1] 2 3 4

There is also optional best \(k\) = 2 3 4 that is worth to check.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

k = 2
k = 3
k = 4
k = 5
k = 6

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>           class entropy silhouette p1 p2
#> GSM892342     1       0          1  1  0
#> GSM892345     1       0          1  1  0
#> GSM892349     1       0          1  1  0
#> GSM892353     1       0          1  1  0
#> GSM892355     1       0          1  1  0
#> GSM892361     1       0          1  1  0
#> GSM892365     1       0          1  1  0
#> GSM892369     1       0          1  1  0
#> GSM892373     2       0          1  0  1
#> GSM892377     2       0          1  0  1
#> GSM892381     2       0          1  0  1
#> GSM892383     2       0          1  0  1
#> GSM892387     2       0          1  0  1
#> GSM892344     1       0          1  1  0
#> GSM892347     1       0          1  1  0
#> GSM892351     1       0          1  1  0
#> GSM892357     1       0          1  1  0
#> GSM892359     1       0          1  1  0
#> GSM892363     1       0          1  1  0
#> GSM892367     1       0          1  1  0
#> GSM892371     1       0          1  1  0
#> GSM892375     2       0          1  0  1
#> GSM892379     2       0          1  0  1
#> GSM892385     2       0          1  0  1
#> GSM892389     2       0          1  0  1
#> GSM892341     1       0          1  1  0
#> GSM892346     1       0          1  1  0
#> GSM892350     1       0          1  1  0
#> GSM892354     1       0          1  1  0
#> GSM892356     1       0          1  1  0
#> GSM892362     1       0          1  1  0
#> GSM892366     1       0          1  1  0
#> GSM892370     1       0          1  1  0
#> GSM892374     2       0          1  0  1
#> GSM892378     2       0          1  0  1
#> GSM892382     2       0          1  0  1
#> GSM892384     2       0          1  0  1
#> GSM892388     2       0          1  0  1
#> GSM892343     1       0          1  1  0
#> GSM892348     1       0          1  1  0
#> GSM892352     1       0          1  1  0
#> GSM892358     1       0          1  1  0
#> GSM892360     1       0          1  1  0
#> GSM892364     1       0          1  1  0
#> GSM892368     1       0          1  1  0
#> GSM892372     1       0          1  1  0
#> GSM892376     2       0          1  0  1
#> GSM892380     2       0          1  0  1
#> GSM892386     2       0          1  0  1
#> GSM892390     2       0          1  0  1

show/hide code output

cbind(get_classes(res, k = 3), get_membership(res, k = 3))

#>           class entropy silhouette    p1 p2    p3
#> GSM892342     3  0.0000      0.968 0.000  0 1.000
#> GSM892345     1  0.0000      0.999 1.000  0 0.000
#> GSM892349     1  0.0000      0.999 1.000  0 0.000
#> GSM892353     1  0.0000      0.999 1.000  0 0.000
#> GSM892355     1  0.0000      0.999 1.000  0 0.000
#> GSM892361     1  0.0000      0.999 1.000  0 0.000
#> GSM892365     3  0.0000      0.968 0.000  0 1.000
#> GSM892369     3  0.0000      0.968 0.000  0 1.000
#> GSM892373     2  0.0000      1.000 0.000  1 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000
#> GSM892344     3  0.5591      0.562 0.304  0 0.696
#> GSM892347     1  0.0000      0.999 1.000  0 0.000
#> GSM892351     1  0.0000      0.999 1.000  0 0.000
#> GSM892357     1  0.0000      0.999 1.000  0 0.000
#> GSM892359     1  0.0000      0.999 1.000  0 0.000
#> GSM892363     1  0.0000      0.999 1.000  0 0.000
#> GSM892367     3  0.0000      0.968 0.000  0 1.000
#> GSM892371     3  0.0000      0.968 0.000  0 1.000
#> GSM892375     2  0.0000      1.000 0.000  1 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000
#> GSM892341     3  0.0000      0.968 0.000  0 1.000
#> GSM892346     1  0.0000      0.999 1.000  0 0.000
#> GSM892350     1  0.0000      0.999 1.000  0 0.000
#> GSM892354     1  0.0000      0.999 1.000  0 0.000
#> GSM892356     1  0.0000      0.999 1.000  0 0.000
#> GSM892362     1  0.0000      0.999 1.000  0 0.000
#> GSM892366     3  0.0000      0.968 0.000  0 1.000
#> GSM892370     3  0.0000      0.968 0.000  0 1.000
#> GSM892374     2  0.0000      1.000 0.000  1 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000
#> GSM892343     1  0.0592      0.987 0.988  0 0.012
#> GSM892348     1  0.0000      0.999 1.000  0 0.000
#> GSM892352     1  0.0000      0.999 1.000  0 0.000
#> GSM892358     1  0.0000      0.999 1.000  0 0.000
#> GSM892360     1  0.0000      0.999 1.000  0 0.000
#> GSM892364     1  0.0000      0.999 1.000  0 0.000
#> GSM892368     3  0.0000      0.968 0.000  0 1.000
#> GSM892372     3  0.0000      0.968 0.000  0 1.000
#> GSM892376     2  0.0000      1.000 0.000  1 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000

show/hide code output

cbind(get_classes(res, k = 4), get_membership(res, k = 4))

#>           class entropy silhouette    p1 p2    p3    p4
#> GSM892342     3  0.5000      0.945 0.000  0 0.500 0.500
#> GSM892345     4  0.5925      0.787 0.036  0 0.452 0.512
#> GSM892349     4  0.5268      0.782 0.008  0 0.452 0.540
#> GSM892353     1  0.0817      0.973 0.976  0 0.000 0.024
#> GSM892355     1  0.0000      0.998 1.000  0 0.000 0.000
#> GSM892361     1  0.0000      0.998 1.000  0 0.000 0.000
#> GSM892365     3  0.4967      0.993 0.000  0 0.548 0.452
#> GSM892369     3  0.4967      0.993 0.000  0 0.548 0.452
#> GSM892373     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892344     4  0.0707      0.140 0.000  0 0.020 0.980
#> GSM892347     4  0.5925      0.787 0.036  0 0.452 0.512
#> GSM892351     4  0.5383      0.783 0.012  0 0.452 0.536
#> GSM892357     1  0.0000      0.998 1.000  0 0.000 0.000
#> GSM892359     1  0.0000      0.998 1.000  0 0.000 0.000
#> GSM892363     1  0.0000      0.998 1.000  0 0.000 0.000
#> GSM892367     3  0.4967      0.993 0.000  0 0.548 0.452
#> GSM892371     3  0.4967      0.993 0.000  0 0.548 0.452
#> GSM892375     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892341     4  0.5000     -0.956 0.000  0 0.500 0.500
#> GSM892346     4  0.6332      0.774 0.060  0 0.452 0.488
#> GSM892350     4  0.5925      0.787 0.036  0 0.452 0.512
#> GSM892354     1  0.0000      0.998 1.000  0 0.000 0.000
#> GSM892356     1  0.0000      0.998 1.000  0 0.000 0.000
#> GSM892362     1  0.0000      0.998 1.000  0 0.000 0.000
#> GSM892366     3  0.4967      0.993 0.000  0 0.548 0.452
#> GSM892370     3  0.4967      0.993 0.000  0 0.548 0.452
#> GSM892374     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892343     4  0.0000      0.194 0.000  0 0.000 1.000
#> GSM892348     4  0.6071      0.784 0.044  0 0.452 0.504
#> GSM892352     4  0.4967      0.777 0.000  0 0.452 0.548
#> GSM892358     1  0.0000      0.998 1.000  0 0.000 0.000
#> GSM892360     1  0.0000      0.998 1.000  0 0.000 0.000
#> GSM892364     1  0.0000      0.998 1.000  0 0.000 0.000
#> GSM892368     3  0.4967      0.993 0.000  0 0.548 0.452
#> GSM892372     3  0.4967      0.993 0.000  0 0.548 0.452
#> GSM892376     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 5), get_membership(res, k = 5))

#>           class entropy silhouette    p1 p2    p3    p4    p5
#> GSM892342     5  0.0000      1.000 0.000  0 0.000 0.000 1.000
#> GSM892345     4  0.0000      0.994 0.000  0 0.000 1.000 0.000
#> GSM892349     4  0.0404      0.987 0.000  0 0.000 0.988 0.012
#> GSM892353     1  0.0000      1.000 1.000  0 0.000 0.000 0.000
#> GSM892355     1  0.0000      1.000 1.000  0 0.000 0.000 0.000
#> GSM892361     1  0.0000      1.000 1.000  0 0.000 0.000 0.000
#> GSM892365     3  0.0000      0.954 0.000  0 1.000 0.000 0.000
#> GSM892369     3  0.1965      0.931 0.000  0 0.904 0.000 0.096
#> GSM892373     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892344     5  0.0000      1.000 0.000  0 0.000 0.000 1.000
#> GSM892347     4  0.0000      0.994 0.000  0 0.000 1.000 0.000
#> GSM892351     4  0.0000      0.994 0.000  0 0.000 1.000 0.000
#> GSM892357     1  0.0000      1.000 1.000  0 0.000 0.000 0.000
#> GSM892359     1  0.0000      1.000 1.000  0 0.000 0.000 0.000
#> GSM892363     1  0.0000      1.000 1.000  0 0.000 0.000 0.000
#> GSM892367     3  0.0290      0.957 0.000  0 0.992 0.000 0.008
#> GSM892371     3  0.1965      0.931 0.000  0 0.904 0.000 0.096
#> GSM892375     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892341     5  0.0000      1.000 0.000  0 0.000 0.000 1.000
#> GSM892346     4  0.0162      0.991 0.004  0 0.000 0.996 0.000
#> GSM892350     4  0.0000      0.994 0.000  0 0.000 1.000 0.000
#> GSM892354     1  0.0000      1.000 1.000  0 0.000 0.000 0.000
#> GSM892356     1  0.0000      1.000 1.000  0 0.000 0.000 0.000
#> GSM892362     1  0.0000      1.000 1.000  0 0.000 0.000 0.000
#> GSM892366     3  0.0000      0.954 0.000  0 1.000 0.000 0.000
#> GSM892370     3  0.1965      0.931 0.000  0 0.904 0.000 0.096
#> GSM892374     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892343     5  0.0000      1.000 0.000  0 0.000 0.000 1.000
#> GSM892348     4  0.0000      0.994 0.000  0 0.000 1.000 0.000
#> GSM892352     4  0.0794      0.974 0.000  0 0.000 0.972 0.028
#> GSM892358     1  0.0000      1.000 1.000  0 0.000 0.000 0.000
#> GSM892360     1  0.0000      1.000 1.000  0 0.000 0.000 0.000
#> GSM892364     1  0.0000      1.000 1.000  0 0.000 0.000 0.000
#> GSM892368     3  0.0290      0.957 0.000  0 0.992 0.000 0.008
#> GSM892372     3  0.0510      0.957 0.000  0 0.984 0.000 0.016
#> GSM892376     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 6), get_membership(res, k = 6))

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> GSM892342     5  0.0000      1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM892345     4  0.0000      0.933 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM892349     4  0.3068      0.867 0.000 0.000 0.008 0.840 0.032 0.120
#> GSM892353     1  0.0603      0.981 0.980 0.000 0.000 0.000 0.016 0.004
#> GSM892355     1  0.0146      0.996 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM892361     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892365     6  0.2762      0.993 0.000 0.000 0.196 0.000 0.000 0.804
#> GSM892369     3  0.0458      0.685 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM892373     2  0.0146      0.997 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM892377     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892381     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892383     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892387     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892344     5  0.0000      1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM892347     4  0.0363      0.932 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM892351     4  0.1075      0.925 0.000 0.000 0.000 0.952 0.000 0.048
#> GSM892357     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892359     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892363     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892367     3  0.3684      0.430 0.000 0.000 0.628 0.000 0.000 0.372
#> GSM892371     3  0.0458      0.685 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM892375     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892379     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892385     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892389     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892341     5  0.0000      1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM892346     4  0.0777      0.928 0.004 0.000 0.000 0.972 0.000 0.024
#> GSM892350     4  0.0547      0.931 0.000 0.000 0.000 0.980 0.000 0.020
#> GSM892354     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892356     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892362     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892366     6  0.2793      0.993 0.000 0.000 0.200 0.000 0.000 0.800
#> GSM892370     3  0.0458      0.685 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM892374     2  0.0146      0.997 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM892378     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892382     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892384     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892388     2  0.0146      0.997 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM892343     5  0.0000      1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM892348     4  0.0632      0.929 0.000 0.000 0.000 0.976 0.000 0.024
#> GSM892352     4  0.4585      0.770 0.000 0.000 0.016 0.724 0.096 0.164
#> GSM892358     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892360     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM892364     1  0.0146      0.996 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM892368     3  0.3782      0.329 0.000 0.000 0.588 0.000 0.000 0.412
#> GSM892372     3  0.3426      0.560 0.000 0.000 0.720 0.000 0.004 0.276
#> GSM892376     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892380     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892386     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM892390     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000 0.000

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

k = 2
k = 3
k = 4
k = 5
k = 6

consensus_heatmap(res, k = 2)

plot of chunk tab-ATC-skmeans-consensus-heatmap-1

consensus_heatmap(res, k = 3)

plot of chunk tab-ATC-skmeans-consensus-heatmap-2

consensus_heatmap(res, k = 4)

plot of chunk tab-ATC-skmeans-consensus-heatmap-3

consensus_heatmap(res, k = 5)

plot of chunk tab-ATC-skmeans-consensus-heatmap-4

consensus_heatmap(res, k = 6)

plot of chunk tab-ATC-skmeans-consensus-heatmap-5

Heatmaps for the membership of samples in all partitions to see how consistent they are:

k = 2
k = 3
k = 4
k = 5
k = 6

membership_heatmap(res, k = 2)

plot of chunk tab-ATC-skmeans-membership-heatmap-1

membership_heatmap(res, k = 3)

plot of chunk tab-ATC-skmeans-membership-heatmap-2

membership_heatmap(res, k = 4)

plot of chunk tab-ATC-skmeans-membership-heatmap-3

membership_heatmap(res, k = 5)

plot of chunk tab-ATC-skmeans-membership-heatmap-4

membership_heatmap(res, k = 6)

plot of chunk tab-ATC-skmeans-membership-heatmap-5

Signature heatmaps where rows are scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2)

plot of chunk tab-ATC-skmeans-get-signatures-1

get_signatures(res, k = 3)

plot of chunk tab-ATC-skmeans-get-signatures-2

get_signatures(res, k = 4)

plot of chunk tab-ATC-skmeans-get-signatures-3

get_signatures(res, k = 5)

plot of chunk tab-ATC-skmeans-get-signatures-4

get_signatures(res, k = 6)

plot of chunk tab-ATC-skmeans-get-signatures-5

Signature heatmaps where rows are not scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-ATC-skmeans-get-signatures-no-scale-1

get_signatures(res, k = 3, scale_rows = FALSE)

plot of chunk tab-ATC-skmeans-get-signatures-no-scale-2

get_signatures(res, k = 4, scale_rows = FALSE)

plot of chunk tab-ATC-skmeans-get-signatures-no-scale-3

get_signatures(res, k = 5, scale_rows = FALSE)

plot of chunk tab-ATC-skmeans-get-signatures-no-scale-4

get_signatures(res, k = 6, scale_rows = FALSE)

plot of chunk tab-ATC-skmeans-get-signatures-no-scale-5

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk ATC-skmeans-signature_compare

# 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.

k = 2
k = 3
k = 4
k = 5
k = 6

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-ATC-skmeans-dimension-reduction-1

dimension_reduction(res, k = 3, method = "UMAP")

plot of chunk tab-ATC-skmeans-dimension-reduction-2

dimension_reduction(res, k = 4, method = "UMAP")

plot of chunk tab-ATC-skmeans-dimension-reduction-3

dimension_reduction(res, k = 5, method = "UMAP")

plot of chunk tab-ATC-skmeans-dimension-reduction-4

dimension_reduction(res, k = 6, method = "UMAP")

plot of chunk tab-ATC-skmeans-dimension-reduction-5

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk ATC-skmeans-collect-classes

test_to_known_factors(res)

#>              n tissue(p) disease.state(p) other(p) individual(p) k
#> ATC:skmeans 50     1.000            0.934 2.67e-07      1.42e-03 2
#> ATC:skmeans 50     0.933            0.869 1.06e-11      4.14e-05 3
#> ATC:skmeans 47     0.993            0.986 2.58e-16      7.31e-07 4
#> ATC:skmeans 50     1.000            0.998 3.76e-23      2.67e-09 5
#> ATC:skmeans 48     1.000            0.863 1.22e-26      7.95e-11 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

ATC:pam**

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 31632 rows and 50 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)

plot of chunk ATC-pam-collect-plots

The plots are:

The first row: a plot of the ECDF (empirical cumulative distribution function) curves of the consensus matrix for each k and the heatmap of predicted classes for each k.
The second row: heatmaps of the consensus matrix for each k.
The third row: heatmaps of the membership matrix for each k.
The fouth row: heatmaps of the signatures for each 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:

ECDF curves of the consensus matrix for each k;
1-PAC. The PAC score measures the proportion of the ambiguous subgrouping.
Mean silhouette score.
Concordance. The mean probability of fiting the consensus class ids in all partitions.
Area increased. Denote \(A_k\) as the area under the ECDF curve for current k, the area increased is defined as \(A_k - A_{k-1}\).
Rand index. The percent of pairs of samples that are both in a same cluster or both are not in a same cluster in the partition of k and k-1.
Jaccard index. The ratio of pairs of samples are both in a same cluster in the partition of k and k-1 and the pairs of samples are both in a same cluster in the partition k or k-1.

The detailed explanations of these statistics can be found in the cola vignette.

select_partition_number(res)

plot of chunk ATC-pam-select-partition-number

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         0.4707 0.530   0.530
#> 3 3 0.974           0.913       0.968         0.4091 0.811   0.644
#> 4 4 1.000           0.986       0.994         0.1247 0.900   0.714
#> 5 5 0.926           0.880       0.909         0.0446 0.945   0.792
#> 6 6 0.969           0.937       0.968         0.0397 0.971   0.869

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

All \(k\) with Jaccard index larger than 0.95 are removed because increasing \(k\) does not provide enough extra information. If all \(k\) are removed, it is marked as no subgroup is detected.
For all \(k\) with 1-PAC score larger than 0.9, the maximal \(k\) is taken as the best \(k\), and other \(k\) are marked as optional \(k\).
If it does not fit the second rule. The \(k\) with the maximal vote of the highest 1-PAC score, highest mean silhouette, and highest concordance is taken as the best \(k\).

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.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

k = 2
k = 3
k = 4
k = 5
k = 6

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>           class entropy silhouette p1 p2
#> GSM892342     1       0          1  1  0
#> GSM892345     1       0          1  1  0
#> GSM892349     1       0          1  1  0
#> GSM892353     1       0          1  1  0
#> GSM892355     1       0          1  1  0
#> GSM892361     1       0          1  1  0
#> GSM892365     1       0          1  1  0
#> GSM892369     1       0          1  1  0
#> GSM892373     2       0          1  0  1
#> GSM892377     2       0          1  0  1
#> GSM892381     2       0          1  0  1
#> GSM892383     2       0          1  0  1
#> GSM892387     2       0          1  0  1
#> GSM892344     1       0          1  1  0
#> GSM892347     1       0          1  1  0
#> GSM892351     1       0          1  1  0
#> GSM892357     1       0          1  1  0
#> GSM892359     1       0          1  1  0
#> GSM892363     1       0          1  1  0
#> GSM892367     1       0          1  1  0
#> GSM892371     1       0          1  1  0
#> GSM892375     2       0          1  0  1
#> GSM892379     2       0          1  0  1
#> GSM892385     2       0          1  0  1
#> GSM892389     2       0          1  0  1
#> GSM892341     1       0          1  1  0
#> GSM892346     1       0          1  1  0
#> GSM892350     1       0          1  1  0
#> GSM892354     1       0          1  1  0
#> GSM892356     1       0          1  1  0
#> GSM892362     1       0          1  1  0
#> GSM892366     1       0          1  1  0
#> GSM892370     1       0          1  1  0
#> GSM892374     2       0          1  0  1
#> GSM892378     2       0          1  0  1
#> GSM892382     2       0          1  0  1
#> GSM892384     2       0          1  0  1
#> GSM892388     2       0          1  0  1
#> GSM892343     1       0          1  1  0
#> GSM892348     1       0          1  1  0
#> GSM892352     1       0          1  1  0
#> GSM892358     1       0          1  1  0
#> GSM892360     1       0          1  1  0
#> GSM892364     1       0          1  1  0
#> GSM892368     1       0          1  1  0
#> GSM892372     1       0          1  1  0
#> GSM892376     2       0          1  0  1
#> GSM892380     2       0          1  0  1
#> GSM892386     2       0          1  0  1
#> GSM892390     2       0          1  0  1

show/hide code output

cbind(get_classes(res, k = 3), get_membership(res, k = 3))

#>           class entropy silhouette    p1 p2    p3
#> GSM892342     3   0.000     0.9607 0.000  0 1.000
#> GSM892345     1   0.000     0.9320 1.000  0 0.000
#> GSM892349     1   0.604     0.3948 0.620  0 0.380
#> GSM892353     1   0.000     0.9320 1.000  0 0.000
#> GSM892355     1   0.000     0.9320 1.000  0 0.000
#> GSM892361     1   0.000     0.9320 1.000  0 0.000
#> GSM892365     3   0.000     0.9607 0.000  0 1.000
#> GSM892369     3   0.000     0.9607 0.000  0 1.000
#> GSM892373     2   0.000     1.0000 0.000  1 0.000
#> GSM892377     2   0.000     1.0000 0.000  1 0.000
#> GSM892381     2   0.000     1.0000 0.000  1 0.000
#> GSM892383     2   0.000     1.0000 0.000  1 0.000
#> GSM892387     2   0.000     1.0000 0.000  1 0.000
#> GSM892344     3   0.588     0.3873 0.348  0 0.652
#> GSM892347     1   0.000     0.9320 1.000  0 0.000
#> GSM892351     1   0.000     0.9320 1.000  0 0.000
#> GSM892357     1   0.000     0.9320 1.000  0 0.000
#> GSM892359     1   0.000     0.9320 1.000  0 0.000
#> GSM892363     1   0.000     0.9320 1.000  0 0.000
#> GSM892367     3   0.000     0.9607 0.000  0 1.000
#> GSM892371     3   0.000     0.9607 0.000  0 1.000
#> GSM892375     2   0.000     1.0000 0.000  1 0.000
#> GSM892379     2   0.000     1.0000 0.000  1 0.000
#> GSM892385     2   0.000     1.0000 0.000  1 0.000
#> GSM892389     2   0.000     1.0000 0.000  1 0.000
#> GSM892341     3   0.000     0.9607 0.000  0 1.000
#> GSM892346     1   0.000     0.9320 1.000  0 0.000
#> GSM892350     1   0.000     0.9320 1.000  0 0.000
#> GSM892354     1   0.000     0.9320 1.000  0 0.000
#> GSM892356     1   0.000     0.9320 1.000  0 0.000
#> GSM892362     1   0.000     0.9320 1.000  0 0.000
#> GSM892366     3   0.000     0.9607 0.000  0 1.000
#> GSM892370     3   0.000     0.9607 0.000  0 1.000
#> GSM892374     2   0.000     1.0000 0.000  1 0.000
#> GSM892378     2   0.000     1.0000 0.000  1 0.000
#> GSM892382     2   0.000     1.0000 0.000  1 0.000
#> GSM892384     2   0.000     1.0000 0.000  1 0.000
#> GSM892388     2   0.000     1.0000 0.000  1 0.000
#> GSM892343     1   0.630     0.0864 0.516  0 0.484
#> GSM892348     1   0.000     0.9320 1.000  0 0.000
#> GSM892352     1   0.606     0.3855 0.616  0 0.384
#> GSM892358     1   0.000     0.9320 1.000  0 0.000
#> GSM892360     1   0.000     0.9320 1.000  0 0.000
#> GSM892364     1   0.000     0.9320 1.000  0 0.000
#> GSM892368     3   0.000     0.9607 0.000  0 1.000
#> GSM892372     3   0.000     0.9607 0.000  0 1.000
#> GSM892376     2   0.000     1.0000 0.000  1 0.000
#> GSM892380     2   0.000     1.0000 0.000  1 0.000
#> GSM892386     2   0.000     1.0000 0.000  1 0.000
#> GSM892390     2   0.000     1.0000 0.000  1 0.000

show/hide code output

cbind(get_classes(res, k = 4), get_membership(res, k = 4))

#>           class entropy silhouette    p1 p2    p3    p4
#> GSM892342     3   0.000      1.000 0.000  0 1.000 0.000
#> GSM892345     4   0.000      0.992 0.000  0 0.000 1.000
#> GSM892349     4   0.000      0.992 0.000  0 0.000 1.000
#> GSM892353     1   0.000      0.979 1.000  0 0.000 0.000
#> GSM892355     1   0.000      0.979 1.000  0 0.000 0.000
#> GSM892361     1   0.000      0.979 1.000  0 0.000 0.000
#> GSM892365     3   0.000      1.000 0.000  0 1.000 0.000
#> GSM892369     3   0.000      1.000 0.000  0 1.000 0.000
#> GSM892373     2   0.000      1.000 0.000  1 0.000 0.000
#> GSM892377     2   0.000      1.000 0.000  1 0.000 0.000
#> GSM892381     2   0.000      1.000 0.000  1 0.000 0.000
#> GSM892383     2   0.000      1.000 0.000  1 0.000 0.000
#> GSM892387     2   0.000      1.000 0.000  1 0.000 0.000
#> GSM892344     4   0.189      0.934 0.008  0 0.056 0.936
#> GSM892347     4   0.000      0.992 0.000  0 0.000 1.000
#> GSM892351     4   0.000      0.992 0.000  0 0.000 1.000
#> GSM892357     1   0.000      0.979 1.000  0 0.000 0.000
#> GSM892359     1   0.000      0.979 1.000  0 0.000 0.000
#> GSM892363     1   0.000      0.979 1.000  0 0.000 0.000
#> GSM892367     3   0.000      1.000 0.000  0 1.000 0.000
#> GSM892371     3   0.000      1.000 0.000  0 1.000 0.000
#> GSM892375     2   0.000      1.000 0.000  1 0.000 0.000
#> GSM892379     2   0.000      1.000 0.000  1 0.000 0.000
#> GSM892385     2   0.000      1.000 0.000  1 0.000 0.000
#> GSM892389     2   0.000      1.000 0.000  1 0.000 0.000
#> GSM892341     3   0.000      1.000 0.000  0 1.000 0.000
#> GSM892346     4   0.000      0.992 0.000  0 0.000 1.000
#> GSM892350     4   0.000      0.992 0.000  0 0.000 1.000
#> GSM892354     1   0.000      0.979 1.000  0 0.000 0.000
#> GSM892356     1   0.000      0.979 1.000  0 0.000 0.000
#> GSM892362     1   0.000      0.979 1.000  0 0.000 0.000
#> GSM892366     3   0.000      1.000 0.000  0 1.000 0.000
#> GSM892370     3   0.000      1.000 0.000  0 1.000 0.000
#> GSM892374     2   0.000      1.000 0.000  1 0.000 0.000
#> GSM892378     2   0.000      1.000 0.000  1 0.000 0.000
#> GSM892382     2   0.000      1.000 0.000  1 0.000 0.000
#> GSM892384     2   0.000      1.000 0.000  1 0.000 0.000
#> GSM892388     2   0.000      1.000 0.000  1 0.000 0.000
#> GSM892343     1   0.511      0.678 0.740  0 0.056 0.204
#> GSM892348     4   0.000      0.992 0.000  0 0.000 1.000
#> GSM892352     4   0.000      0.992 0.000  0 0.000 1.000
#> GSM892358     1   0.000      0.979 1.000  0 0.000 0.000
#> GSM892360     1   0.000      0.979 1.000  0 0.000 0.000
#> GSM892364     1   0.000      0.979 1.000  0 0.000 0.000
#> GSM892368     3   0.000      1.000 0.000  0 1.000 0.000
#> GSM892372     3   0.000      1.000 0.000  0 1.000 0.000
#> GSM892376     2   0.000      1.000 0.000  1 0.000 0.000
#> GSM892380     2   0.000      1.000 0.000  1 0.000 0.000
#> GSM892386     2   0.000      1.000 0.000  1 0.000 0.000
#> GSM892390     2   0.000      1.000 0.000  1 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 5), get_membership(res, k = 5))

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> GSM892342     3   0.000      0.497 0.000 0.000 1.000 0.000 0.000
#> GSM892345     4   0.000      0.905 0.000 0.000 0.000 1.000 0.000
#> GSM892349     4   0.000      0.905 0.000 0.000 0.000 1.000 0.000
#> GSM892353     1   0.622      0.626 0.520 0.164 0.316 0.000 0.000
#> GSM892355     1   0.430      0.972 0.520 0.480 0.000 0.000 0.000
#> GSM892361     1   0.430      0.972 0.520 0.480 0.000 0.000 0.000
#> GSM892365     3   0.430      0.820 0.000 0.000 0.520 0.000 0.480
#> GSM892369     3   0.430      0.821 0.000 0.000 0.524 0.000 0.476
#> GSM892373     5   0.430      1.000 0.480 0.000 0.000 0.000 0.520
#> GSM892377     2   0.430      1.000 0.480 0.520 0.000 0.000 0.000
#> GSM892381     2   0.430      1.000 0.480 0.520 0.000 0.000 0.000
#> GSM892383     2   0.430      1.000 0.480 0.520 0.000 0.000 0.000
#> GSM892387     2   0.430      1.000 0.480 0.520 0.000 0.000 0.000
#> GSM892344     4   0.456      0.485 0.008 0.000 0.496 0.496 0.000
#> GSM892347     4   0.000      0.905 0.000 0.000 0.000 1.000 0.000
#> GSM892351     4   0.000      0.905 0.000 0.000 0.000 1.000 0.000
#> GSM892357     1   0.430      0.972 0.520 0.480 0.000 0.000 0.000
#> GSM892359     1   0.430      0.972 0.520 0.480 0.000 0.000 0.000
#> GSM892363     1   0.430      0.972 0.520 0.480 0.000 0.000 0.000
#> GSM892367     3   0.430      0.821 0.000 0.000 0.524 0.000 0.476
#> GSM892371     3   0.430      0.821 0.000 0.000 0.524 0.000 0.476
#> GSM892375     2   0.430      1.000 0.480 0.520 0.000 0.000 0.000
#> GSM892379     2   0.430      1.000 0.480 0.520 0.000 0.000 0.000
#> GSM892385     2   0.430      1.000 0.480 0.520 0.000 0.000 0.000
#> GSM892389     2   0.430      1.000 0.480 0.520 0.000 0.000 0.000
#> GSM892341     3   0.000      0.497 0.000 0.000 1.000 0.000 0.000
#> GSM892346     4   0.000      0.905 0.000 0.000 0.000 1.000 0.000
#> GSM892350     4   0.000      0.905 0.000 0.000 0.000 1.000 0.000
#> GSM892354     1   0.430      0.972 0.520 0.480 0.000 0.000 0.000
#> GSM892356     1   0.430      0.972 0.520 0.480 0.000 0.000 0.000
#> GSM892362     1   0.430      0.972 0.520 0.480 0.000 0.000 0.000
#> GSM892366     3   0.430      0.820 0.000 0.000 0.520 0.000 0.480
#> GSM892370     3   0.430      0.821 0.000 0.000 0.524 0.000 0.476
#> GSM892374     5   0.430      1.000 0.480 0.000 0.000 0.000 0.520
#> GSM892378     2   0.430      1.000 0.480 0.520 0.000 0.000 0.000
#> GSM892382     2   0.430      1.000 0.480 0.520 0.000 0.000 0.000
#> GSM892384     2   0.430      1.000 0.480 0.520 0.000 0.000 0.000
#> GSM892388     5   0.430      1.000 0.480 0.000 0.000 0.000 0.520
#> GSM892343     3   0.517     -0.385 0.464 0.000 0.496 0.040 0.000
#> GSM892348     4   0.000      0.905 0.000 0.000 0.000 1.000 0.000
#> GSM892352     4   0.391      0.677 0.000 0.000 0.324 0.676 0.000
#> GSM892358     1   0.430      0.972 0.520 0.480 0.000 0.000 0.000
#> GSM892360     1   0.430      0.972 0.520 0.480 0.000 0.000 0.000
#> GSM892364     1   0.430      0.972 0.520 0.480 0.000 0.000 0.000
#> GSM892368     3   0.430      0.820 0.000 0.000 0.520 0.000 0.480
#> GSM892372     3   0.430      0.821 0.000 0.000 0.524 0.000 0.476
#> GSM892376     2   0.430      1.000 0.480 0.520 0.000 0.000 0.000
#> GSM892380     2   0.430      1.000 0.480 0.520 0.000 0.000 0.000
#> GSM892386     2   0.430      1.000 0.480 0.520 0.000 0.000 0.000
#> GSM892390     2   0.430      1.000 0.480 0.520 0.000 0.000 0.000

show/hide code output

cbind(get_classes(res, k = 6), get_membership(res, k = 6))

#>           class entropy silhouette    p1 p2    p3    p4    p5 p6
#> GSM892342     5   0.000      1.000 0.000  0 0.000 0.000 1.000  0
#> GSM892345     4   0.000      0.932 0.000  0 0.000 1.000 0.000  0
#> GSM892349     4   0.000      0.932 0.000  0 0.000 1.000 0.000  0
#> GSM892353     1   0.374      0.355 0.608  0 0.000 0.000 0.392  0
#> GSM892355     1   0.000      0.962 1.000  0 0.000 0.000 0.000  0
#> GSM892361     1   0.000      0.962 1.000  0 0.000 0.000 0.000  0
#> GSM892365     3   0.000      0.880 0.000  0 1.000 0.000 0.000  0
#> GSM892369     3   0.253      0.908 0.000  0 0.832 0.000 0.168  0
#> GSM892373     6   0.000      1.000 0.000  0 0.000 0.000 0.000  1
#> GSM892377     2   0.000      1.000 0.000  1 0.000 0.000 0.000  0
#> GSM892381     2   0.000      1.000 0.000  1 0.000 0.000 0.000  0
#> GSM892383     2   0.000      1.000 0.000  1 0.000 0.000 0.000  0
#> GSM892387     2   0.000      1.000 0.000  1 0.000 0.000 0.000  0
#> GSM892344     5   0.000      1.000 0.000  0 0.000 0.000 1.000  0
#> GSM892347     4   0.000      0.932 0.000  0 0.000 1.000 0.000  0
#> GSM892351     4   0.000      0.932 0.000  0 0.000 1.000 0.000  0
#> GSM892357     1   0.000      0.962 1.000  0 0.000 0.000 0.000  0
#> GSM892359     1   0.000      0.962 1.000  0 0.000 0.000 0.000  0
#> GSM892363     1   0.000      0.962 1.000  0 0.000 0.000 0.000  0
#> GSM892367     3   0.186      0.907 0.000  0 0.896 0.000 0.104  0
#> GSM892371     3   0.253      0.908 0.000  0 0.832 0.000 0.168  0
#> GSM892375     2   0.000      1.000 0.000  1 0.000 0.000 0.000  0
#> GSM892379     2   0.000      1.000 0.000  1 0.000 0.000 0.000  0
#> GSM892385     2   0.000      1.000 0.000  1 0.000 0.000 0.000  0
#> GSM892389     2   0.000      1.000 0.000  1 0.000 0.000 0.000  0
#> GSM892341     5   0.000      1.000 0.000  0 0.000 0.000 1.000  0
#> GSM892346     4   0.000      0.932 0.000  0 0.000 1.000 0.000  0
#> GSM892350     4   0.000      0.932 0.000  0 0.000 1.000 0.000  0
#> GSM892354     1   0.000      0.962 1.000  0 0.000 0.000 0.000  0
#> GSM892356     1   0.000      0.962 1.000  0 0.000 0.000 0.000  0
#> GSM892362     1   0.000      0.962 1.000  0 0.000 0.000 0.000  0
#> GSM892366     3   0.000      0.880 0.000  0 1.000 0.000 0.000  0
#> GSM892370     3   0.253      0.908 0.000  0 0.832 0.000 0.168  0
#> GSM892374     6   0.000      1.000 0.000  0 0.000 0.000 0.000  1
#> GSM892378     2   0.000      1.000 0.000  1 0.000 0.000 0.000  0
#> GSM892382     2   0.000      1.000 0.000  1 0.000 0.000 0.000  0
#> GSM892384     2   0.000      1.000 0.000  1 0.000 0.000 0.000  0
#> GSM892388     6   0.000      1.000 0.000  0 0.000 0.000 0.000  1
#> GSM892343     5   0.000      1.000 0.000  0 0.000 0.000 1.000  0
#> GSM892348     4   0.000      0.932 0.000  0 0.000 1.000 0.000  0
#> GSM892352     4   0.382      0.230 0.000  0 0.000 0.564 0.436  0
#> GSM892358     1   0.000      0.962 1.000  0 0.000 0.000 0.000  0
#> GSM892360     1   0.000      0.962 1.000  0 0.000 0.000 0.000  0
#> GSM892364     1   0.000      0.962 1.000  0 0.000 0.000 0.000  0
#> GSM892368     3   0.000      0.880 0.000  0 1.000 0.000 0.000  0
#> GSM892372     3   0.253      0.908 0.000  0 0.832 0.000 0.168  0
#> GSM892376     2   0.000      1.000 0.000  1 0.000 0.000 0.000  0
#> GSM892380     2   0.000      1.000 0.000  1 0.000 0.000 0.000  0
#> GSM892386     2   0.000      1.000 0.000  1 0.000 0.000 0.000  0
#> GSM892390     2   0.000      1.000 0.000  1 0.000 0.000 0.000  0

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

k = 2
k = 3
k = 4
k = 5
k = 6

consensus_heatmap(res, k = 2)

plot of chunk tab-ATC-pam-consensus-heatmap-1

consensus_heatmap(res, k = 3)

plot of chunk tab-ATC-pam-consensus-heatmap-2

consensus_heatmap(res, k = 4)

plot of chunk tab-ATC-pam-consensus-heatmap-3

consensus_heatmap(res, k = 5)

plot of chunk tab-ATC-pam-consensus-heatmap-4

consensus_heatmap(res, k = 6)

plot of chunk tab-ATC-pam-consensus-heatmap-5

Heatmaps for the membership of samples in all partitions to see how consistent they are:

k = 2
k = 3
k = 4
k = 5
k = 6

membership_heatmap(res, k = 2)

plot of chunk tab-ATC-pam-membership-heatmap-1

membership_heatmap(res, k = 3)

plot of chunk tab-ATC-pam-membership-heatmap-2

membership_heatmap(res, k = 4)

plot of chunk tab-ATC-pam-membership-heatmap-3

membership_heatmap(res, k = 5)

plot of chunk tab-ATC-pam-membership-heatmap-4

membership_heatmap(res, k = 6)

plot of chunk tab-ATC-pam-membership-heatmap-5

Signature heatmaps where rows are scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2)

plot of chunk tab-ATC-pam-get-signatures-1

get_signatures(res, k = 3)

plot of chunk tab-ATC-pam-get-signatures-2

get_signatures(res, k = 4)

plot of chunk tab-ATC-pam-get-signatures-3

get_signatures(res, k = 5)

plot of chunk tab-ATC-pam-get-signatures-4

get_signatures(res, k = 6)

plot of chunk tab-ATC-pam-get-signatures-5

Signature heatmaps where rows are not scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-ATC-pam-get-signatures-no-scale-1

get_signatures(res, k = 3, scale_rows = FALSE)

plot of chunk tab-ATC-pam-get-signatures-no-scale-2

get_signatures(res, k = 4, scale_rows = FALSE)

plot of chunk tab-ATC-pam-get-signatures-no-scale-3

get_signatures(res, k = 5, scale_rows = FALSE)

plot of chunk tab-ATC-pam-get-signatures-no-scale-4

get_signatures(res, k = 6, scale_rows = FALSE)

plot of chunk tab-ATC-pam-get-signatures-no-scale-5

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk ATC-pam-signature_compare

# 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.

k = 2
k = 3
k = 4
k = 5
k = 6

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-ATC-pam-dimension-reduction-1

dimension_reduction(res, k = 3, method = "UMAP")

plot of chunk tab-ATC-pam-dimension-reduction-2

dimension_reduction(res, k = 4, method = "UMAP")

plot of chunk tab-ATC-pam-dimension-reduction-3

dimension_reduction(res, k = 5, method = "UMAP")

plot of chunk tab-ATC-pam-dimension-reduction-4

dimension_reduction(res, k = 6, method = "UMAP")

plot of chunk tab-ATC-pam-dimension-reduction-5

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk ATC-pam-collect-classes

test_to_known_factors(res)

#>          n tissue(p) disease.state(p) other(p) individual(p) k
#> ATC:pam 50     1.000            0.934 2.67e-07      1.42e-03 2
#> ATC:pam 46     1.000            0.871 3.31e-11      6.62e-05 3
#> ATC:pam 50     0.979            0.866 8.76e-16      7.14e-07 4
#> ATC:pam 46     0.982            0.560 3.62e-16      1.08e-07 5
#> ATC:pam 48     0.986            0.666 6.76e-21      5.72e-09 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

ATC:mclust**

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 31632 rows and 50 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 5.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

collect_plots() function collects all the plots made from res for all k (number of partitions) into one single page to provide an easy and fast comparison between different k.

collect_plots(res)

plot of chunk ATC-mclust-collect-plots

The plots are:

The first row: a plot of the ECDF (empirical cumulative distribution function) curves of the consensus matrix for each k and the heatmap of predicted classes for each k.
The second row: heatmaps of the consensus matrix for each k.
The third row: heatmaps of the membership matrix for each k.
The fouth row: heatmaps of the signatures for each 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:

ECDF curves of the consensus matrix for each k;
1-PAC. The PAC score measures the proportion of the ambiguous subgrouping.
Mean silhouette score.
Concordance. The mean probability of fiting the consensus class ids in all partitions.
Area increased. Denote \(A_k\) as the area under the ECDF curve for current k, the area increased is defined as \(A_k - A_{k-1}\).
Rand index. The percent of pairs of samples that are both in a same cluster or both are not in a same cluster in the partition of k and k-1.
Jaccard index. The ratio of pairs of samples are both in a same cluster in the partition of k and k-1 and the pairs of samples are both in a same cluster in the partition k or k-1.

The detailed explanations of these statistics can be found in the cola vignette.

select_partition_number(res)

plot of chunk ATC-mclust-select-partition-number

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         0.4707 0.530   0.530
#> 3 3 1.000           1.000       1.000         0.4159 0.804   0.630
#> 4 4 1.000           1.000       1.000         0.1174 0.922   0.765
#> 5 5 1.000           0.995       0.995         0.0381 0.971   0.888
#> 6 6 0.989           0.950       0.956         0.0268 0.990   0.957

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

All \(k\) with Jaccard index larger than 0.95 are removed because increasing \(k\) does not provide enough extra information. If all \(k\) are removed, it is marked as no subgroup is detected.
For all \(k\) with 1-PAC score larger than 0.9, the maximal \(k\) is taken as the best \(k\), and other \(k\) are marked as optional \(k\).
If it does not fit the second rule. The \(k\) with the maximal vote of the highest 1-PAC score, highest mean silhouette, and highest concordance is taken as the best \(k\).

suggest_best_k(res)

#> [1] 5
#> attr(,"optional")
#> [1] 2 3 4

There is also optional best \(k\) = 2 3 4 that is worth to check.

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

k = 2
k = 3
k = 4
k = 5
k = 6

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>           class entropy silhouette p1 p2
#> GSM892342     1       0          1  1  0
#> GSM892345     1       0          1  1  0
#> GSM892349     1       0          1  1  0
#> GSM892353     1       0          1  1  0
#> GSM892355     1       0          1  1  0
#> GSM892361     1       0          1  1  0
#> GSM892365     1       0          1  1  0
#> GSM892369     1       0          1  1  0
#> GSM892373     2       0          1  0  1
#> GSM892377     2       0          1  0  1
#> GSM892381     2       0          1  0  1
#> GSM892383     2       0          1  0  1
#> GSM892387     2       0          1  0  1
#> GSM892344     1       0          1  1  0
#> GSM892347     1       0          1  1  0
#> GSM892351     1       0          1  1  0
#> GSM892357     1       0          1  1  0
#> GSM892359     1       0          1  1  0
#> GSM892363     1       0          1  1  0
#> GSM892367     1       0          1  1  0
#> GSM892371     1       0          1  1  0
#> GSM892375     2       0          1  0  1
#> GSM892379     2       0          1  0  1
#> GSM892385     2       0          1  0  1
#> GSM892389     2       0          1  0  1
#> GSM892341     1       0          1  1  0
#> GSM892346     1       0          1  1  0
#> GSM892350     1       0          1  1  0
#> GSM892354     1       0          1  1  0
#> GSM892356     1       0          1  1  0
#> GSM892362     1       0          1  1  0
#> GSM892366     1       0          1  1  0
#> GSM892370     1       0          1  1  0
#> GSM892374     2       0          1  0  1
#> GSM892378     2       0          1  0  1
#> GSM892382     2       0          1  0  1
#> GSM892384     2       0          1  0  1
#> GSM892388     2       0          1  0  1
#> GSM892343     1       0          1  1  0
#> GSM892348     1       0          1  1  0
#> GSM892352     1       0          1  1  0
#> GSM892358     1       0          1  1  0
#> GSM892360     1       0          1  1  0
#> GSM892364     1       0          1  1  0
#> GSM892368     1       0          1  1  0
#> GSM892372     1       0          1  1  0
#> GSM892376     2       0          1  0  1
#> GSM892380     2       0          1  0  1
#> GSM892386     2       0          1  0  1
#> GSM892390     2       0          1  0  1

show/hide code output

cbind(get_classes(res, k = 3), get_membership(res, k = 3))

#>           class entropy silhouette    p1 p2    p3
#> GSM892342     3  0.0000      1.000 0.000  0 1.000
#> GSM892345     3  0.0000      1.000 0.000  0 1.000
#> GSM892349     3  0.0000      1.000 0.000  0 1.000
#> GSM892353     1  0.0000      1.000 1.000  0 0.000
#> GSM892355     1  0.0000      1.000 1.000  0 0.000
#> GSM892361     1  0.0000      1.000 1.000  0 0.000
#> GSM892365     3  0.0000      1.000 0.000  0 1.000
#> GSM892369     3  0.0000      1.000 0.000  0 1.000
#> GSM892373     2  0.0000      1.000 0.000  1 0.000
#> GSM892377     2  0.0000      1.000 0.000  1 0.000
#> GSM892381     2  0.0000      1.000 0.000  1 0.000
#> GSM892383     2  0.0000      1.000 0.000  1 0.000
#> GSM892387     2  0.0000      1.000 0.000  1 0.000
#> GSM892344     3  0.0000      1.000 0.000  0 1.000
#> GSM892347     3  0.0000      1.000 0.000  0 1.000
#> GSM892351     3  0.0000      1.000 0.000  0 1.000
#> GSM892357     1  0.0000      1.000 1.000  0 0.000
#> GSM892359     1  0.0000      1.000 1.000  0 0.000
#> GSM892363     1  0.0000      1.000 1.000  0 0.000
#> GSM892367     3  0.0000      1.000 0.000  0 1.000
#> GSM892371     3  0.0000      1.000 0.000  0 1.000
#> GSM892375     2  0.0000      1.000 0.000  1 0.000
#> GSM892379     2  0.0000      1.000 0.000  1 0.000
#> GSM892385     2  0.0000      1.000 0.000  1 0.000
#> GSM892389     2  0.0000      1.000 0.000  1 0.000
#> GSM892341     3  0.0000      1.000 0.000  0 1.000
#> GSM892346     3  0.0424      0.992 0.008  0 0.992
#> GSM892350     3  0.0000      1.000 0.000  0 1.000
#> GSM892354     1  0.0000      1.000 1.000  0 0.000
#> GSM892356     1  0.0000      1.000 1.000  0 0.000
#> GSM892362     1  0.0000      1.000 1.000  0 0.000
#> GSM892366     3  0.0000      1.000 0.000  0 1.000
#> GSM892370     3  0.0000      1.000 0.000  0 1.000
#> GSM892374     2  0.0000      1.000 0.000  1 0.000
#> GSM892378     2  0.0000      1.000 0.000  1 0.000
#> GSM892382     2  0.0000      1.000 0.000  1 0.000
#> GSM892384     2  0.0000      1.000 0.000  1 0.000
#> GSM892388     2  0.0000      1.000 0.000  1 0.000
#> GSM892343     3  0.0000      1.000 0.000  0 1.000
#> GSM892348     3  0.0000      1.000 0.000  0 1.000
#> GSM892352     3  0.0000      1.000 0.000  0 1.000
#> GSM892358     1  0.0000      1.000 1.000  0 0.000
#> GSM892360     1  0.0000      1.000 1.000  0 0.000
#> GSM892364     1  0.0000      1.000 1.000  0 0.000
#> GSM892368     3  0.0000      1.000 0.000  0 1.000
#> GSM892372     3  0.0000      1.000 0.000  0 1.000
#> GSM892376     2  0.0000      1.000 0.000  1 0.000
#> GSM892380     2  0.0000      1.000 0.000  1 0.000
#> GSM892386     2  0.0000      1.000 0.000  1 0.000
#> GSM892390     2  0.0000      1.000 0.000  1 0.000

show/hide code output

cbind(get_classes(res, k = 4), get_membership(res, k = 4))

#>           class entropy silhouette p1 p2 p3 p4
#> GSM892342     3       0          1  0  0  1  0
#> GSM892345     4       0          1  0  0  0  1
#> GSM892349     4       0          1  0  0  0  1
#> GSM892353     1       0          1  1  0  0  0
#> GSM892355     1       0          1  1  0  0  0
#> GSM892361     1       0          1  1  0  0  0
#> GSM892365     3       0          1  0  0  1  0
#> GSM892369     3       0          1  0  0  1  0
#> GSM892373     2       0          1  0  1  0  0
#> GSM892377     2       0          1  0  1  0  0
#> GSM892381     2       0          1  0  1  0  0
#> GSM892383     2       0          1  0  1  0  0
#> GSM892387     2       0          1  0  1  0  0
#> GSM892344     3       0          1  0  0  1  0
#> GSM892347     4       0          1  0  0  0  1
#> GSM892351     4       0          1  0  0  0  1
#> GSM892357     1       0          1  1  0  0  0
#> GSM892359     1       0          1  1  0  0  0
#> GSM892363     1       0          1  1  0  0  0
#> GSM892367     3       0          1  0  0  1  0
#> GSM892371     3       0          1  0  0  1  0
#> GSM892375     2       0          1  0  1  0  0
#> GSM892379     2       0          1  0  1  0  0
#> GSM892385     2       0          1  0  1  0  0
#> GSM892389     2       0          1  0  1  0  0
#> GSM892341     3       0          1  0  0  1  0
#> GSM892346     4       0          1  0  0  0  1
#> GSM892350     4       0          1  0  0  0  1
#> GSM892354     1       0          1  1  0  0  0
#> GSM892356     1       0          1  1  0  0  0
#> GSM892362     1       0          1  1  0  0  0
#> GSM892366     3       0          1  0  0  1  0
#> GSM892370     3       0          1  0  0  1  0
#> GSM892374     2       0          1  0  1  0  0
#> GSM892378     2       0          1  0  1  0  0
#> GSM892382     2       0          1  0  1  0  0
#> GSM892384     2       0          1  0  1  0  0
#> GSM892388     2       0          1  0  1  0  0
#> GSM892343     3       0          1  0  0  1  0
#> GSM892348     4       0          1  0  0  0  1
#> GSM892352     4       0          1  0  0  0  1
#> GSM892358     1       0          1  1  0  0  0
#> GSM892360     1       0          1  1  0  0  0
#> GSM892364     1       0          1  1  0  0  0
#> GSM892368     3       0          1  0  0  1  0
#> GSM892372     3       0          1  0  0  1  0
#> GSM892376     2       0          1  0  1  0  0
#> GSM892380     2       0          1  0  1  0  0
#> GSM892386     2       0          1  0  1  0  0
#> GSM892390     2       0          1  0  1  0  0

show/hide code output

cbind(get_classes(res, k = 5), get_membership(res, k = 5))

#>           class entropy silhouette p1    p2    p3 p4    p5
#> GSM892342     5  0.0290      0.997  0 0.000 0.008  0 0.992
#> GSM892345     4  0.0000      1.000  0 0.000 0.000  1 0.000
#> GSM892349     4  0.0000      1.000  0 0.000 0.000  1 0.000
#> GSM892353     1  0.0000      1.000  1 0.000 0.000  0 0.000
#> GSM892355     1  0.0000      1.000  1 0.000 0.000  0 0.000
#> GSM892361     1  0.0000      1.000  1 0.000 0.000  0 0.000
#> GSM892365     3  0.0609      0.985  0 0.000 0.980  0 0.020
#> GSM892369     5  0.0290      0.997  0 0.000 0.008  0 0.992
#> GSM892373     2  0.0510      0.987  0 0.984 0.016  0 0.000
#> GSM892377     2  0.0000      0.997  0 1.000 0.000  0 0.000
#> GSM892381     2  0.0000      0.997  0 1.000 0.000  0 0.000
#> GSM892383     2  0.0000      0.997  0 1.000 0.000  0 0.000
#> GSM892387     2  0.0000      0.997  0 1.000 0.000  0 0.000
#> GSM892344     5  0.0000      0.993  0 0.000 0.000  0 1.000
#> GSM892347     4  0.0000      1.000  0 0.000 0.000  1 0.000
#> GSM892351     4  0.0000      1.000  0 0.000 0.000  1 0.000
#> GSM892357     1  0.0000      1.000  1 0.000 0.000  0 0.000
#> GSM892359     1  0.0000      1.000  1 0.000 0.000  0 0.000
#> GSM892363     1  0.0000      1.000  1 0.000 0.000  0 0.000
#> GSM892367     3  0.0609      0.985  0 0.000 0.980  0 0.020
#> GSM892371     5  0.0290      0.997  0 0.000 0.008  0 0.992
#> GSM892375     2  0.0000      0.997  0 1.000 0.000  0 0.000
#> GSM892379     2  0.0000      0.997  0 1.000 0.000  0 0.000
#> GSM892385     2  0.0000      0.997  0 1.000 0.000  0 0.000
#> GSM892389     2  0.0000      0.997  0 1.000 0.000  0 0.000
#> GSM892341     5  0.0290      0.997  0 0.000 0.008  0 0.992
#> GSM892346     4  0.0000      1.000  0 0.000 0.000  1 0.000
#> GSM892350     4  0.0000      1.000  0 0.000 0.000  1 0.000
#> GSM892354     1  0.0000      1.000  1 0.000 0.000  0 0.000
#> GSM892356     1  0.0000      1.000  1 0.000 0.000  0 0.000
#> GSM892362     1  0.0000      1.000  1 0.000 0.000  0 0.000
#> GSM892366     3  0.0609      0.985  0 0.000 0.980  0 0.020
#> GSM892370     5  0.0290      0.997  0 0.000 0.008  0 0.992
#> GSM892374     2  0.0510      0.987  0 0.984 0.016  0 0.000
#> GSM892378     2  0.0000      0.997  0 1.000 0.000  0 0.000
#> GSM892382     2  0.0000      0.997  0 1.000 0.000  0 0.000
#> GSM892384     2  0.0000      0.997  0 1.000 0.000  0 0.000
#> GSM892388     2  0.0609      0.984  0 0.980 0.020  0 0.000
#> GSM892343     5  0.0000      0.993  0 0.000 0.000  0 1.000
#> GSM892348     4  0.0000      1.000  0 0.000 0.000  1 0.000
#> GSM892352     4  0.0000      1.000  0 0.000 0.000  1 0.000
#> GSM892358     1  0.0000      1.000  1 0.000 0.000  0 0.000
#> GSM892360     1  0.0000      1.000  1 0.000 0.000  0 0.000
#> GSM892364     1  0.0000      1.000  1 0.000 0.000  0 0.000
#> GSM892368     3  0.0609      0.985  0 0.000 0.980  0 0.020
#> GSM892372     3  0.1671      0.939  0 0.000 0.924  0 0.076
#> GSM892376     2  0.0000      0.997  0 1.000 0.000  0 0.000
#> GSM892380     2  0.0000      0.997  0 1.000 0.000  0 0.000
#> GSM892386     2  0.0000      0.997  0 1.000 0.000  0 0.000
#> GSM892390     2  0.0000      0.997  0 1.000 0.000  0 0.000

show/hide code output

cbind(get_classes(res, k = 6), get_membership(res, k = 6))

#>           class entropy silhouette p1    p2    p3    p4    p5    p6
#> GSM892342     5   0.385      0.993  0 0.000 0.000 0.000 0.544 0.456
#> GSM892345     4   0.385      1.000  0 0.000 0.000 0.544 0.456 0.000
#> GSM892349     4   0.385      1.000  0 0.000 0.000 0.544 0.456 0.000
#> GSM892353     1   0.000      1.000  1 0.000 0.000 0.000 0.000 0.000
#> GSM892355     1   0.000      1.000  1 0.000 0.000 0.000 0.000 0.000
#> GSM892361     1   0.000      1.000  1 0.000 0.000 0.000 0.000 0.000
#> GSM892365     3   0.000      1.000  0 0.000 1.000 0.000 0.000 0.000
#> GSM892369     5   0.416      0.988  0 0.000 0.012 0.000 0.544 0.444
#> GSM892373     2   0.374      0.567  0 0.608 0.000 0.392 0.000 0.000
#> GSM892377     2   0.000      0.930  0 1.000 0.000 0.000 0.000 0.000
#> GSM892381     2   0.000      0.930  0 1.000 0.000 0.000 0.000 0.000
#> GSM892383     2   0.000      0.930  0 1.000 0.000 0.000 0.000 0.000
#> GSM892387     2   0.000      0.930  0 1.000 0.000 0.000 0.000 0.000
#> GSM892344     5   0.385      0.992  0 0.000 0.000 0.000 0.536 0.464
#> GSM892347     4   0.385      1.000  0 0.000 0.000 0.544 0.456 0.000
#> GSM892351     4   0.385      1.000  0 0.000 0.000 0.544 0.456 0.000
#> GSM892357     1   0.000      1.000  1 0.000 0.000 0.000 0.000 0.000
#> GSM892359     1   0.000      1.000  1 0.000 0.000 0.000 0.000 0.000
#> GSM892363     1   0.000      1.000  1 0.000 0.000 0.000 0.000 0.000
#> GSM892367     3   0.000      1.000  0 0.000 1.000 0.000 0.000 0.000
#> GSM892371     5   0.385      0.993  0 0.000 0.000 0.000 0.544 0.456
#> GSM892375     2   0.000      0.930  0 1.000 0.000 0.000 0.000 0.000
#> GSM892379     2   0.000      0.930  0 1.000 0.000 0.000 0.000 0.000
#> GSM892385     2   0.000      0.930  0 1.000 0.000 0.000 0.000 0.000
#> GSM892389     2   0.000      0.930  0 1.000 0.000 0.000 0.000 0.000
#> GSM892341     5   0.385      0.993  0 0.000 0.000 0.000 0.544 0.456
#> GSM892346     6   0.408      1.000  0 0.000 0.000 0.008 0.456 0.536
#> GSM892350     4   0.385      1.000  0 0.000 0.000 0.544 0.456 0.000
#> GSM892354     1   0.000      1.000  1 0.000 0.000 0.000 0.000 0.000
#> GSM892356     1   0.000      1.000  1 0.000 0.000 0.000 0.000 0.000
#> GSM892362     1   0.000      1.000  1 0.000 0.000 0.000 0.000 0.000
#> GSM892366     3   0.000      1.000  0 0.000 1.000 0.000 0.000 0.000
#> GSM892370     5   0.416      0.988  0 0.000 0.012 0.000 0.544 0.444
#> GSM892374     2   0.374      0.567  0 0.608 0.000 0.392 0.000 0.000
#> GSM892378     2   0.000      0.930  0 1.000 0.000 0.000 0.000 0.000
#> GSM892382     2   0.000      0.930  0 1.000 0.000 0.000 0.000 0.000
#> GSM892384     2   0.000      0.930  0 1.000 0.000 0.000 0.000 0.000
#> GSM892388     2   0.385      0.477  0 0.544 0.000 0.456 0.000 0.000
#> GSM892343     5   0.385      0.992  0 0.000 0.000 0.000 0.536 0.464
#> GSM892348     6   0.408      1.000  0 0.000 0.000 0.008 0.456 0.536
#> GSM892352     4   0.385      1.000  0 0.000 0.000 0.544 0.456 0.000
#> GSM892358     1   0.000      1.000  1 0.000 0.000 0.000 0.000 0.000
#> GSM892360     1   0.000      1.000  1 0.000 0.000 0.000 0.000 0.000
#> GSM892364     1   0.000      1.000  1 0.000 0.000 0.000 0.000 0.000
#> GSM892368     3   0.000      1.000  0 0.000 1.000 0.000 0.000 0.000
#> GSM892372     3   0.000      1.000  0 0.000 1.000 0.000 0.000 0.000
#> GSM892376     2   0.000      0.930  0 1.000 0.000 0.000 0.000 0.000
#> GSM892380     2   0.000      0.930  0 1.000 0.000 0.000 0.000 0.000
#> GSM892386     2   0.000      0.930  0 1.000 0.000 0.000 0.000 0.000
#> GSM892390     2   0.000      0.930  0 1.000 0.000 0.000 0.000 0.000

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

k = 2
k = 3
k = 4
k = 5
k = 6

consensus_heatmap(res, k = 2)

plot of chunk tab-ATC-mclust-consensus-heatmap-1

consensus_heatmap(res, k = 3)

plot of chunk tab-ATC-mclust-consensus-heatmap-2

consensus_heatmap(res, k = 4)

plot of chunk tab-ATC-mclust-consensus-heatmap-3

consensus_heatmap(res, k = 5)

plot of chunk tab-ATC-mclust-consensus-heatmap-4

consensus_heatmap(res, k = 6)

plot of chunk tab-ATC-mclust-consensus-heatmap-5

Heatmaps for the membership of samples in all partitions to see how consistent they are:

k = 2
k = 3
k = 4
k = 5
k = 6

membership_heatmap(res, k = 2)

plot of chunk tab-ATC-mclust-membership-heatmap-1

membership_heatmap(res, k = 3)

plot of chunk tab-ATC-mclust-membership-heatmap-2

membership_heatmap(res, k = 4)

plot of chunk tab-ATC-mclust-membership-heatmap-3

membership_heatmap(res, k = 5)

plot of chunk tab-ATC-mclust-membership-heatmap-4

membership_heatmap(res, k = 6)

plot of chunk tab-ATC-mclust-membership-heatmap-5

Signature heatmaps where rows are scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2)

plot of chunk tab-ATC-mclust-get-signatures-1

get_signatures(res, k = 3)

plot of chunk tab-ATC-mclust-get-signatures-2

get_signatures(res, k = 4)

plot of chunk tab-ATC-mclust-get-signatures-3

get_signatures(res, k = 5)

plot of chunk tab-ATC-mclust-get-signatures-4

get_signatures(res, k = 6)

plot of chunk tab-ATC-mclust-get-signatures-5

Signature heatmaps where rows are not scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-ATC-mclust-get-signatures-no-scale-1

get_signatures(res, k = 3, scale_rows = FALSE)

plot of chunk tab-ATC-mclust-get-signatures-no-scale-2

get_signatures(res, k = 4, scale_rows = FALSE)

plot of chunk tab-ATC-mclust-get-signatures-no-scale-3

get_signatures(res, k = 5, scale_rows = FALSE)

plot of chunk tab-ATC-mclust-get-signatures-no-scale-4

get_signatures(res, k = 6, scale_rows = FALSE)

plot of chunk tab-ATC-mclust-get-signatures-no-scale-5

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk ATC-mclust-signature_compare

# 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.

k = 2
k = 3
k = 4
k = 5
k = 6

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-ATC-mclust-dimension-reduction-1

dimension_reduction(res, k = 3, method = "UMAP")

plot of chunk tab-ATC-mclust-dimension-reduction-2

dimension_reduction(res, k = 4, method = "UMAP")

plot of chunk tab-ATC-mclust-dimension-reduction-3

dimension_reduction(res, k = 5, method = "UMAP")

plot of chunk tab-ATC-mclust-dimension-reduction-4

dimension_reduction(res, k = 6, method = "UMAP")

plot of chunk tab-ATC-mclust-dimension-reduction-5

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk ATC-mclust-collect-classes

test_to_known_factors(res)

#>             n tissue(p) disease.state(p) other(p) individual(p) k
#> ATC:mclust 50     1.000            0.934 2.67e-07      1.42e-03 2
#> ATC:mclust 50     1.000            0.931 1.26e-12      1.60e-05 3
#> ATC:mclust 50     1.000            0.986 6.71e-18      2.02e-07 4
#> ATC:mclust 50     0.987            0.975 6.70e-21      2.57e-08 5
#> ATC:mclust 49     0.692            0.996 8.70e-20      2.73e-06 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

ATC:NMF**

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 31632 rows and 50 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)

plot of chunk ATC-NMF-collect-plots

The plots are:

The first row: a plot of the ECDF (empirical cumulative distribution function) curves of the consensus matrix for each k and the heatmap of predicted classes for each k.
The second row: heatmaps of the consensus matrix for each k.
The third row: heatmaps of the membership matrix for each k.
The fouth row: heatmaps of the signatures for each 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:

ECDF curves of the consensus matrix for each k;
1-PAC. The PAC score measures the proportion of the ambiguous subgrouping.
Mean silhouette score.
Concordance. The mean probability of fiting the consensus class ids in all partitions.
Area increased. Denote \(A_k\) as the area under the ECDF curve for current k, the area increased is defined as \(A_k - A_{k-1}\).
Rand index. The percent of pairs of samples that are both in a same cluster or both are not in a same cluster in the partition of k and k-1.
Jaccard index. The ratio of pairs of samples are both in a same cluster in the partition of k and k-1 and the pairs of samples are both in a same cluster in the partition k or k-1.

The detailed explanations of these statistics can be found in the cola vignette.

select_partition_number(res)

plot of chunk ATC-NMF-select-partition-number

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         0.4707 0.530   0.530
#> 3 3 0.809           0.964       0.927         0.3206 0.804   0.630
#> 4 4 0.869           0.883       0.867         0.1320 0.919   0.758
#> 5 5 0.846           0.904       0.897         0.0439 0.984   0.941
#> 6 6 0.807           0.860       0.887         0.0263 1.000   1.000

suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:

All \(k\) with Jaccard index larger than 0.95 are removed because increasing \(k\) does not provide enough extra information. If all \(k\) are removed, it is marked as no subgroup is detected.
For all \(k\) with 1-PAC score larger than 0.9, the maximal \(k\) is taken as the best \(k\), and other \(k\) are marked as optional \(k\).
If it does not fit the second rule. The \(k\) with the maximal vote of the highest 1-PAC score, highest mean silhouette, and highest concordance is taken as the best \(k\).

suggest_best_k(res)

#> [1] 2

In get_classes() function, the entropy is calculated from the membership matrix and the silhouette score is calculated from the consensus matrix.

k = 2
k = 3
k = 4
k = 5
k = 6

show/hide code output

cbind(get_classes(res, k = 2), get_membership(res, k = 2))

#>           class entropy silhouette p1 p2
#> GSM892342     1       0          1  1  0
#> GSM892345     1       0          1  1  0
#> GSM892349     1       0          1  1  0
#> GSM892353     1       0          1  1  0
#> GSM892355     1       0          1  1  0
#> GSM892361     1       0          1  1  0
#> GSM892365     1       0          1  1  0
#> GSM892369     1       0          1  1  0
#> GSM892373     2       0          1  0  1
#> GSM892377     2       0          1  0  1
#> GSM892381     2       0          1  0  1
#> GSM892383     2       0          1  0  1
#> GSM892387     2       0          1  0  1
#> GSM892344     1       0          1  1  0
#> GSM892347     1       0          1  1  0
#> GSM892351     1       0          1  1  0
#> GSM892357     1       0          1  1  0
#> GSM892359     1       0          1  1  0
#> GSM892363     1       0          1  1  0
#> GSM892367     1       0          1  1  0
#> GSM892371     1       0          1  1  0
#> GSM892375     2       0          1  0  1
#> GSM892379     2       0          1  0  1
#> GSM892385     2       0          1  0  1
#> GSM892389     2       0          1  0  1
#> GSM892341     1       0          1  1  0
#> GSM892346     1       0          1  1  0
#> GSM892350     1       0          1  1  0
#> GSM892354     1       0          1  1  0
#> GSM892356     1       0          1  1  0
#> GSM892362     1       0          1  1  0
#> GSM892366     1       0          1  1  0
#> GSM892370     1       0          1  1  0
#> GSM892374     2       0          1  0  1
#> GSM892378     2       0          1  0  1
#> GSM892382     2       0          1  0  1
#> GSM892384     2       0          1  0  1
#> GSM892388     2       0          1  0  1
#> GSM892343     1       0          1  1  0
#> GSM892348     1       0          1  1  0
#> GSM892352     1       0          1  1  0
#> GSM892358     1       0          1  1  0
#> GSM892360     1       0          1  1  0
#> GSM892364     1       0          1  1  0
#> GSM892368     1       0          1  1  0
#> GSM892372     1       0          1  1  0
#> GSM892376     2       0          1  0  1
#> GSM892380     2       0          1  0  1
#> GSM892386     2       0          1  0  1
#> GSM892390     2       0          1  0  1

show/hide code output

cbind(get_classes(res, k = 3), get_membership(res, k = 3))

#>           class entropy silhouette    p1    p2    p3
#> GSM892342     3  0.0000      0.964 0.000 0.000 1.000
#> GSM892345     1  0.5016      0.985 0.760 0.000 0.240
#> GSM892349     1  0.5363      0.940 0.724 0.000 0.276
#> GSM892353     1  0.5016      0.985 0.760 0.000 0.240
#> GSM892355     1  0.5016      0.985 0.760 0.000 0.240
#> GSM892361     1  0.5016      0.985 0.760 0.000 0.240
#> GSM892365     3  0.0000      0.964 0.000 0.000 1.000
#> GSM892369     3  0.0000      0.964 0.000 0.000 1.000
#> GSM892373     2  0.0237      0.988 0.004 0.996 0.000
#> GSM892377     2  0.0237      0.988 0.004 0.996 0.000
#> GSM892381     2  0.0000      0.988 0.000 1.000 0.000
#> GSM892383     2  0.1031      0.981 0.024 0.976 0.000
#> GSM892387     2  0.3619      0.901 0.136 0.864 0.000
#> GSM892344     3  0.2448      0.876 0.076 0.000 0.924
#> GSM892347     1  0.5016      0.985 0.760 0.000 0.240
#> GSM892351     1  0.5016      0.985 0.760 0.000 0.240
#> GSM892357     1  0.5016      0.985 0.760 0.000 0.240
#> GSM892359     1  0.5016      0.985 0.760 0.000 0.240
#> GSM892363     1  0.5016      0.985 0.760 0.000 0.240
#> GSM892367     3  0.0000      0.964 0.000 0.000 1.000
#> GSM892371     3  0.0000      0.964 0.000 0.000 1.000
#> GSM892375     2  0.0592      0.985 0.012 0.988 0.000
#> GSM892379     2  0.0237      0.988 0.004 0.996 0.000
#> GSM892385     2  0.0237      0.988 0.004 0.996 0.000
#> GSM892389     2  0.0592      0.986 0.012 0.988 0.000
#> GSM892341     3  0.0000      0.964 0.000 0.000 1.000
#> GSM892346     1  0.5016      0.985 0.760 0.000 0.240
#> GSM892350     1  0.5016      0.985 0.760 0.000 0.240
#> GSM892354     1  0.5016      0.985 0.760 0.000 0.240
#> GSM892356     1  0.5016      0.985 0.760 0.000 0.240
#> GSM892362     1  0.5016      0.985 0.760 0.000 0.240
#> GSM892366     3  0.0000      0.964 0.000 0.000 1.000
#> GSM892370     3  0.0000      0.964 0.000 0.000 1.000
#> GSM892374     2  0.0237      0.988 0.004 0.996 0.000
#> GSM892378     2  0.0424      0.988 0.008 0.992 0.000
#> GSM892382     2  0.0000      0.988 0.000 1.000 0.000
#> GSM892384     2  0.0592      0.986 0.012 0.988 0.000
#> GSM892388     2  0.0237      0.988 0.004 0.996 0.000
#> GSM892343     3  0.4702      0.618 0.212 0.000 0.788
#> GSM892348     1  0.5016      0.985 0.760 0.000 0.240
#> GSM892352     1  0.6140      0.714 0.596 0.000 0.404
#> GSM892358     1  0.5016      0.985 0.760 0.000 0.240
#> GSM892360     1  0.5016      0.985 0.760 0.000 0.240
#> GSM892364     1  0.5016      0.985 0.760 0.000 0.240
#> GSM892368     3  0.0000      0.964 0.000 0.000 1.000
#> GSM892372     3  0.0000      0.964 0.000 0.000 1.000
#> GSM892376     2  0.0000      0.988 0.000 1.000 0.000
#> GSM892380     2  0.1753      0.967 0.048 0.952 0.000
#> GSM892386     2  0.0000      0.988 0.000 1.000 0.000
#> GSM892390     2  0.0424      0.987 0.008 0.992 0.000

show/hide code output

cbind(get_classes(res, k = 4), get_membership(res, k = 4))

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM892342     3  0.1489      0.939 0.004 0.000 0.952 0.044
#> GSM892345     4  0.2546      0.761 0.008 0.000 0.092 0.900
#> GSM892349     4  0.3768      0.710 0.008 0.000 0.184 0.808
#> GSM892353     1  0.6235      0.929 0.524 0.000 0.056 0.420
#> GSM892355     1  0.5982      0.962 0.524 0.000 0.040 0.436
#> GSM892361     1  0.5781      0.908 0.492 0.000 0.028 0.480
#> GSM892365     3  0.0188      0.960 0.000 0.000 0.996 0.004
#> GSM892369     3  0.0000      0.960 0.000 0.000 1.000 0.000
#> GSM892373     2  0.1398      0.971 0.040 0.956 0.000 0.004
#> GSM892377     2  0.0188      0.988 0.000 0.996 0.000 0.004
#> GSM892381     2  0.0376      0.987 0.004 0.992 0.000 0.004
#> GSM892383     2  0.0188      0.988 0.000 0.996 0.000 0.004
#> GSM892387     2  0.1256      0.978 0.028 0.964 0.000 0.008
#> GSM892344     3  0.2861      0.876 0.016 0.000 0.888 0.096
#> GSM892347     4  0.2197      0.761 0.004 0.000 0.080 0.916
#> GSM892351     4  0.3217      0.757 0.012 0.000 0.128 0.860
#> GSM892357     1  0.5894      0.964 0.536 0.000 0.036 0.428
#> GSM892359     1  0.5821      0.965 0.536 0.000 0.032 0.432
#> GSM892363     1  0.5838      0.961 0.524 0.000 0.032 0.444
#> GSM892367     3  0.0000      0.960 0.000 0.000 1.000 0.000
#> GSM892371     3  0.0000      0.960 0.000 0.000 1.000 0.000
#> GSM892375     2  0.0376      0.988 0.004 0.992 0.000 0.004
#> GSM892379     2  0.0376      0.987 0.004 0.992 0.000 0.004
#> GSM892385     2  0.0524      0.987 0.008 0.988 0.000 0.004
#> GSM892389     2  0.0376      0.987 0.004 0.992 0.000 0.004
#> GSM892341     3  0.0895      0.953 0.004 0.000 0.976 0.020
#> GSM892346     4  0.3959      0.594 0.092 0.000 0.068 0.840
#> GSM892350     4  0.2197      0.761 0.004 0.000 0.080 0.916
#> GSM892354     1  0.5808      0.959 0.544 0.000 0.032 0.424
#> GSM892356     1  0.5833      0.964 0.528 0.000 0.032 0.440
#> GSM892362     4  0.5862     -0.921 0.484 0.000 0.032 0.484
#> GSM892366     3  0.0000      0.960 0.000 0.000 1.000 0.000
#> GSM892370     3  0.0592      0.956 0.000 0.000 0.984 0.016
#> GSM892374     2  0.2002      0.959 0.044 0.936 0.000 0.020
#> GSM892378     2  0.0524      0.987 0.008 0.988 0.000 0.004
#> GSM892382     2  0.0188      0.988 0.004 0.996 0.000 0.000
#> GSM892384     2  0.0779      0.985 0.016 0.980 0.000 0.004
#> GSM892388     2  0.1297      0.977 0.016 0.964 0.000 0.020
#> GSM892343     3  0.4370      0.733 0.044 0.000 0.800 0.156
#> GSM892348     4  0.3198      0.701 0.040 0.000 0.080 0.880
#> GSM892352     4  0.4163      0.686 0.020 0.000 0.188 0.792
#> GSM892358     1  0.5888      0.961 0.540 0.000 0.036 0.424
#> GSM892360     1  0.5853      0.944 0.508 0.000 0.032 0.460
#> GSM892364     1  0.5982      0.962 0.524 0.000 0.040 0.436
#> GSM892368     3  0.0000      0.960 0.000 0.000 1.000 0.000
#> GSM892372     3  0.0000      0.960 0.000 0.000 1.000 0.000
#> GSM892376     2  0.0524      0.988 0.008 0.988 0.000 0.004
#> GSM892380     2  0.0524      0.987 0.008 0.988 0.000 0.004
#> GSM892386     2  0.0376      0.988 0.004 0.992 0.000 0.004
#> GSM892390     2  0.0657      0.987 0.012 0.984 0.000 0.004

show/hide code output

cbind(get_classes(res, k = 5), get_membership(res, k = 5))

#>           class entropy silhouette    p1    p2    p3    p4 p5
#> GSM892342     3  0.5560      0.724 0.060 0.000 0.716 0.132 NA
#> GSM892345     4  0.4250      0.887 0.252 0.000 0.028 0.720 NA
#> GSM892349     4  0.5813      0.831 0.200 0.000 0.116 0.660 NA
#> GSM892353     1  0.3863      0.784 0.836 0.000 0.040 0.072 NA
#> GSM892355     1  0.0867      0.953 0.976 0.000 0.008 0.008 NA
#> GSM892361     1  0.1251      0.945 0.956 0.000 0.000 0.036 NA
#> GSM892365     3  0.1041      0.879 0.004 0.000 0.964 0.000 NA
#> GSM892369     3  0.2131      0.859 0.008 0.000 0.920 0.016 NA
#> GSM892373     2  0.1851      0.950 0.000 0.912 0.000 0.000 NA
#> GSM892377     2  0.0963      0.974 0.000 0.964 0.000 0.000 NA
#> GSM892381     2  0.0609      0.976 0.000 0.980 0.000 0.000 NA
#> GSM892383     2  0.1121      0.968 0.000 0.956 0.000 0.000 NA
#> GSM892387     2  0.0880      0.973 0.000 0.968 0.000 0.000 NA
#> GSM892344     3  0.6836      0.510 0.164 0.000 0.596 0.160 NA
#> GSM892347     4  0.4245      0.883 0.236 0.000 0.020 0.736 NA
#> GSM892351     4  0.5228      0.877 0.244 0.000 0.060 0.680 NA
#> GSM892357     1  0.0404      0.960 0.988 0.000 0.000 0.012 NA
#> GSM892359     1  0.1012      0.955 0.968 0.000 0.000 0.020 NA
#> GSM892363     1  0.0451      0.961 0.988 0.000 0.000 0.008 NA
#> GSM892367     3  0.0794      0.873 0.000 0.000 0.972 0.000 NA
#> GSM892371     3  0.1869      0.870 0.012 0.000 0.936 0.016 NA
#> GSM892375     2  0.0794      0.976 0.000 0.972 0.000 0.000 NA
#> GSM892379     2  0.0510      0.975 0.000 0.984 0.000 0.000 NA
#> GSM892385     2  0.1478      0.962 0.000 0.936 0.000 0.000 NA
#> GSM892389     2  0.0609      0.976 0.000 0.980 0.000 0.000 NA
#> GSM892341     3  0.3905      0.820 0.032 0.000 0.832 0.072 NA
#> GSM892346     4  0.5331      0.748 0.344 0.000 0.008 0.600 NA
#> GSM892350     4  0.4181      0.887 0.244 0.000 0.020 0.732 NA
#> GSM892354     1  0.0807      0.958 0.976 0.000 0.000 0.012 NA
#> GSM892356     1  0.0162      0.962 0.996 0.000 0.000 0.004 NA
#> GSM892362     1  0.0703      0.957 0.976 0.000 0.000 0.024 NA
#> GSM892366     3  0.0671      0.880 0.004 0.000 0.980 0.000 NA
#> GSM892370     3  0.1200      0.877 0.016 0.000 0.964 0.012 NA
#> GSM892374     2  0.1732      0.951 0.000 0.920 0.000 0.000 NA
#> GSM892378     2  0.0609      0.977 0.000 0.980 0.000 0.000 NA
#> GSM892382     2  0.0290      0.975 0.000 0.992 0.000 0.000 NA
#> GSM892384     2  0.0671      0.976 0.000 0.980 0.000 0.004 NA
#> GSM892388     2  0.1764      0.957 0.000 0.928 0.000 0.008 NA
#> GSM892343     3  0.5324      0.642 0.204 0.000 0.696 0.080 NA
#> GSM892348     4  0.4564      0.864 0.272 0.000 0.008 0.696 NA
#> GSM892352     4  0.6182      0.766 0.164 0.000 0.152 0.644 NA
#> GSM892358     1  0.0566      0.953 0.984 0.000 0.000 0.012 NA
#> GSM892360     1  0.0798      0.957 0.976 0.000 0.000 0.016 NA
#> GSM892364     1  0.0290      0.961 0.992 0.000 0.000 0.008 NA
#> GSM892368     3  0.0671      0.880 0.004 0.000 0.980 0.000 NA
#> GSM892372     3  0.0324      0.879 0.004 0.000 0.992 0.000 NA
#> GSM892376     2  0.0880      0.974 0.000 0.968 0.000 0.000 NA
#> GSM892380     2  0.0510      0.975 0.000 0.984 0.000 0.000 NA
#> GSM892386     2  0.0880      0.974 0.000 0.968 0.000 0.000 NA
#> GSM892390     2  0.0880      0.974 0.000 0.968 0.000 0.000 NA

show/hide code output

cbind(get_classes(res, k = 6), get_membership(res, k = 6))

#>           class entropy silhouette    p1    p2    p3    p4 p5    p6
#> GSM892342     3  0.6071      0.501 0.040 0.000 0.500 0.112 NA 0.348
#> GSM892345     4  0.3000      0.883 0.124 0.000 0.032 0.840 NA 0.004
#> GSM892349     4  0.5417      0.782 0.112 0.000 0.100 0.684 NA 0.104
#> GSM892353     1  0.3911      0.769 0.796 0.000 0.032 0.036 NA 0.132
#> GSM892355     1  0.0964      0.959 0.968 0.000 0.004 0.016 NA 0.012
#> GSM892361     1  0.0790      0.955 0.968 0.000 0.000 0.032 NA 0.000
#> GSM892365     3  0.1296      0.797 0.000 0.000 0.948 0.004 NA 0.044
#> GSM892369     3  0.3919      0.754 0.012 0.000 0.816 0.080 NA 0.056
#> GSM892373     2  0.2450      0.907 0.000 0.868 0.000 0.000 NA 0.016
#> GSM892377     2  0.1075      0.958 0.000 0.952 0.000 0.000 NA 0.000
#> GSM892381     2  0.0858      0.962 0.000 0.968 0.000 0.000 NA 0.004
#> GSM892383     2  0.1285      0.955 0.000 0.944 0.000 0.000 NA 0.004
#> GSM892387     2  0.0713      0.963 0.000 0.972 0.000 0.000 NA 0.000
#> GSM892344     3  0.7437      0.106 0.128 0.000 0.344 0.248 NA 0.280
#> GSM892347     4  0.2764      0.876 0.100 0.000 0.028 0.864 NA 0.008
#> GSM892351     4  0.3718      0.874 0.124 0.000 0.052 0.804 NA 0.020
#> GSM892357     1  0.0748      0.962 0.976 0.000 0.000 0.016 NA 0.004
#> GSM892359     1  0.0603      0.960 0.980 0.000 0.000 0.000 NA 0.004
#> GSM892363     1  0.0291      0.963 0.992 0.000 0.000 0.000 NA 0.004
#> GSM892367     3  0.1053      0.789 0.000 0.000 0.964 0.004 NA 0.020
#> GSM892371     3  0.2450      0.786 0.008 0.000 0.896 0.068 NA 0.016
#> GSM892375     2  0.1010      0.963 0.000 0.960 0.000 0.000 NA 0.004
#> GSM892379     2  0.0260      0.963 0.000 0.992 0.000 0.000 NA 0.000
#> GSM892385     2  0.1387      0.951 0.000 0.932 0.000 0.000 NA 0.000
#> GSM892389     2  0.0632      0.963 0.000 0.976 0.000 0.000 NA 0.000
#> GSM892341     3  0.5096      0.671 0.028 0.000 0.700 0.096 NA 0.168
#> GSM892346     4  0.4988      0.809 0.180 0.000 0.012 0.712 NA 0.056
#> GSM892350     4  0.2554      0.877 0.092 0.000 0.028 0.876 NA 0.004
#> GSM892354     1  0.0881      0.961 0.972 0.000 0.000 0.008 NA 0.012
#> GSM892356     1  0.0291      0.963 0.992 0.000 0.000 0.004 NA 0.000
#> GSM892362     1  0.0547      0.961 0.980 0.000 0.000 0.020 NA 0.000
#> GSM892366     3  0.1007      0.797 0.000 0.000 0.956 0.000 NA 0.044
#> GSM892370     3  0.2344      0.786 0.008 0.000 0.896 0.068 NA 0.028
#> GSM892374     2  0.2494      0.902 0.000 0.864 0.000 0.000 NA 0.016
#> GSM892378     2  0.0972      0.962 0.000 0.964 0.000 0.000 NA 0.008
#> GSM892382     2  0.0858      0.962 0.000 0.968 0.000 0.000 NA 0.004
#> GSM892384     2  0.0713      0.963 0.000 0.972 0.000 0.000 NA 0.000
#> GSM892388     2  0.2755      0.889 0.000 0.844 0.000 0.004 NA 0.012
#> GSM892343     3  0.7272      0.290 0.164 0.000 0.468 0.264 NA 0.072
#> GSM892348     4  0.3686      0.870 0.152 0.000 0.024 0.800 NA 0.012
#> GSM892352     4  0.6046      0.701 0.088 0.000 0.128 0.624 NA 0.156
#> GSM892358     1  0.0603      0.959 0.980 0.000 0.000 0.004 NA 0.000
#> GSM892360     1  0.0551      0.963 0.984 0.000 0.000 0.004 NA 0.004
#> GSM892364     1  0.1007      0.960 0.968 0.000 0.004 0.016 NA 0.008
#> GSM892368     3  0.0291      0.796 0.000 0.000 0.992 0.004 NA 0.004
#> GSM892372     3  0.0622      0.798 0.000 0.000 0.980 0.012 NA 0.008
#> GSM892376     2  0.0632      0.964 0.000 0.976 0.000 0.000 NA 0.000
#> GSM892380     2  0.0547      0.964 0.000 0.980 0.000 0.000 NA 0.000
#> GSM892386     2  0.1049      0.961 0.000 0.960 0.000 0.000 NA 0.008
#> GSM892390     2  0.0692      0.963 0.000 0.976 0.000 0.000 NA 0.004

Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.

k = 2
k = 3
k = 4
k = 5
k = 6

consensus_heatmap(res, k = 2)

plot of chunk tab-ATC-NMF-consensus-heatmap-1

consensus_heatmap(res, k = 3)

plot of chunk tab-ATC-NMF-consensus-heatmap-2

consensus_heatmap(res, k = 4)

plot of chunk tab-ATC-NMF-consensus-heatmap-3

consensus_heatmap(res, k = 5)

plot of chunk tab-ATC-NMF-consensus-heatmap-4

consensus_heatmap(res, k = 6)

plot of chunk tab-ATC-NMF-consensus-heatmap-5

Heatmaps for the membership of samples in all partitions to see how consistent they are:

k = 2
k = 3
k = 4
k = 5
k = 6

membership_heatmap(res, k = 2)

plot of chunk tab-ATC-NMF-membership-heatmap-1

membership_heatmap(res, k = 3)

plot of chunk tab-ATC-NMF-membership-heatmap-2

membership_heatmap(res, k = 4)

plot of chunk tab-ATC-NMF-membership-heatmap-3

membership_heatmap(res, k = 5)

plot of chunk tab-ATC-NMF-membership-heatmap-4

membership_heatmap(res, k = 6)

plot of chunk tab-ATC-NMF-membership-heatmap-5

Signature heatmaps where rows are scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2)

plot of chunk tab-ATC-NMF-get-signatures-1

get_signatures(res, k = 3)

plot of chunk tab-ATC-NMF-get-signatures-2

get_signatures(res, k = 4)

plot of chunk tab-ATC-NMF-get-signatures-3

get_signatures(res, k = 5)

plot of chunk tab-ATC-NMF-get-signatures-4

get_signatures(res, k = 6)

plot of chunk tab-ATC-NMF-get-signatures-5

Signature heatmaps where rows are not scaled:

k = 2
k = 3
k = 4
k = 5
k = 6

get_signatures(res, k = 2, scale_rows = FALSE)

plot of chunk tab-ATC-NMF-get-signatures-no-scale-1

get_signatures(res, k = 3, scale_rows = FALSE)

plot of chunk tab-ATC-NMF-get-signatures-no-scale-2

get_signatures(res, k = 4, scale_rows = FALSE)

plot of chunk tab-ATC-NMF-get-signatures-no-scale-3

get_signatures(res, k = 5, scale_rows = FALSE)

plot of chunk tab-ATC-NMF-get-signatures-no-scale-4

get_signatures(res, k = 6, scale_rows = FALSE)

plot of chunk tab-ATC-NMF-get-signatures-no-scale-5

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk ATC-NMF-signature_compare

# 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.

k = 2
k = 3
k = 4
k = 5
k = 6

dimension_reduction(res, k = 2, method = "UMAP")

plot of chunk tab-ATC-NMF-dimension-reduction-1

dimension_reduction(res, k = 3, method = "UMAP")

plot of chunk tab-ATC-NMF-dimension-reduction-2

dimension_reduction(res, k = 4, method = "UMAP")

plot of chunk tab-ATC-NMF-dimension-reduction-3

dimension_reduction(res, k = 5, method = "UMAP")

plot of chunk tab-ATC-NMF-dimension-reduction-4

dimension_reduction(res, k = 6, method = "UMAP")

plot of chunk tab-ATC-NMF-dimension-reduction-5

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk ATC-NMF-collect-classes

test_to_known_factors(res)

#>          n tissue(p) disease.state(p) other(p) individual(p) k
#> ATC:NMF 50     1.000            0.934 2.67e-07      1.42e-03 2
#> ATC:NMF 50     1.000            0.931 1.26e-12      1.60e-05 3
#> ATC:NMF 49     0.995            0.961 2.28e-17      4.54e-07 4
#> ATC:NMF 50     1.000            0.986 6.71e-18      2.02e-07 5
#> ATC:NMF 48     1.000            0.962 7.68e-17      3.25e-07 6

If matrix rows can be associated to genes, consider to use functional_enrichment(res, ...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.

Session info

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