cola Report for GDS3345

Date: 2019-12-25 20:43:55 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 11993 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] 11993    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:skmeans	2	1.000	0.968	0.987	**
SD:NMF	2	1.000	0.944	0.978	**
MAD:kmeans	2	1.000	0.944	0.977	**
MAD:skmeans	3	1.000	0.968	0.983	**	2
MAD:NMF	2	1.000	0.939	0.976	**
ATC:kmeans	2	1.000	0.990	0.995	**
ATC:skmeans	2	1.000	0.973	0.990	**
ATC:NMF	2	1.000	0.951	0.981	**
MAD:pam	2	0.999	0.956	0.981	**
SD:kmeans	2	0.974	0.948	0.974	**
CV:mclust	3	0.958	0.928	0.966	**	2
ATC:pam	5	0.946	0.892	0.933	*	3
SD:pam	2	0.916	0.962	0.982	*
MAD:mclust	3	0.907	0.898	0.951	*	2
SD:mclust	3	0.850	0.898	0.955
CV:kmeans	2	0.742	0.893	0.948
CV:NMF	2	0.722	0.845	0.936
CV:skmeans	2	0.674	0.845	0.931
MAD:hclust	4	0.654	0.840	0.899
CV:hclust	3	0.636	0.828	0.936
SD:hclust	4	0.582	0.742	0.876
ATC:mclust	2	0.542	0.911	0.918
ATC:hclust	3	0.489	0.769	0.806
CV:pam	NA	NA	NA	NA

**: 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 1.000           0.944       0.978         0.4613 0.530   0.530
#> CV:NMF      2 0.722           0.845       0.936         0.5039 0.490   0.490
#> MAD:NMF     2 1.000           0.939       0.976         0.4660 0.530   0.530
#> ATC:NMF     2 1.000           0.951       0.981         0.4307 0.571   0.571
#> SD:skmeans  2 1.000           0.968       0.987         0.4850 0.510   0.510
#> CV:skmeans  2 0.674           0.845       0.931         0.5086 0.490   0.490
#> MAD:skmeans 2 0.916           0.960       0.980         0.4921 0.510   0.510
#> ATC:skmeans 2 1.000           0.973       0.990         0.4856 0.519   0.519
#> SD:mclust   2 0.711           0.864       0.927         0.3853 0.607   0.607
#> CV:mclust   2 0.916           0.911       0.964         0.5030 0.493   0.493
#> MAD:mclust  2 0.984           0.934       0.969         0.3704 0.628   0.628
#> ATC:mclust  2 0.542           0.911       0.918         0.4484 0.542   0.542
#> SD:kmeans   2 0.974           0.948       0.974         0.4498 0.542   0.542
#> CV:kmeans   2 0.742           0.893       0.948         0.4724 0.542   0.542
#> MAD:kmeans  2 1.000           0.944       0.977         0.4578 0.542   0.542
#> ATC:kmeans  2 1.000           0.990       0.995         0.4478 0.556   0.556
#> SD:pam      2 0.916           0.962       0.982         0.4548 0.542   0.542
#> CV:pam      2 0.630           0.902       0.946         0.1156 0.960   0.960
#> MAD:pam     2 0.999           0.956       0.981         0.4649 0.542   0.542
#> ATC:pam     2 0.761           0.872       0.943         0.4812 0.497   0.497
#> SD:hclust   2 0.613           0.863       0.934         0.3125 0.726   0.726
#> CV:hclust   2 0.958           0.952       0.984         0.0582 0.960   0.960
#> MAD:hclust  2 0.759           0.900       0.949         0.3101 0.726   0.726
#> ATC:hclust  2 0.483           0.805       0.903         0.3220 0.754   0.754

get_stats(res_list, k = 3)

#>             k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> SD:NMF      3 0.550           0.684       0.812         0.3717 0.776   0.602
#> CV:NMF      3 0.661           0.776       0.896         0.3101 0.816   0.638
#> MAD:NMF     3 0.545           0.652       0.794         0.3880 0.735   0.538
#> ATC:NMF     3 0.475           0.650       0.795         0.4308 0.750   0.586
#> SD:skmeans  3 0.837           0.917       0.948         0.3783 0.805   0.624
#> CV:skmeans  3 0.364           0.603       0.785         0.3126 0.770   0.566
#> MAD:skmeans 3 1.000           0.968       0.983         0.3604 0.805   0.624
#> ATC:skmeans 3 0.819           0.826       0.907         0.3550 0.806   0.626
#> SD:mclust   3 0.850           0.898       0.955         0.6485 0.634   0.455
#> CV:mclust   3 0.958           0.928       0.966         0.1926 0.874   0.754
#> MAD:mclust  3 0.907           0.898       0.951         0.7235 0.604   0.431
#> ATC:mclust  3 0.414           0.697       0.808         0.2658 0.846   0.726
#> SD:kmeans   3 0.469           0.534       0.667         0.3492 0.771   0.586
#> CV:kmeans   3 0.557           0.664       0.811         0.2159 0.807   0.660
#> MAD:kmeans  3 0.520           0.615       0.723         0.3647 0.791   0.620
#> ATC:kmeans  3 0.488           0.649       0.707         0.3560 1.000   1.000
#> SD:pam      3 0.652           0.772       0.833         0.2366 0.851   0.726
#> CV:pam      3 0.512           0.799       0.913         0.4796 0.961   0.959
#> MAD:pam     3 0.624           0.865       0.901         0.2984 0.868   0.756
#> ATC:pam     3 0.920           0.891       0.950         0.2225 0.909   0.816
#> SD:hclust   3 0.642           0.845       0.933         0.0716 0.990   0.987
#> CV:hclust   3 0.636           0.828       0.936         2.2811 0.887   0.883
#> MAD:hclust  3 0.779           0.886       0.949         0.0567 0.990   0.987
#> ATC:hclust  3 0.489           0.769       0.806         0.6942 0.620   0.506

get_stats(res_list, k = 4)

#>             k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> SD:NMF      4 0.784           0.799       0.909        0.15689 0.770   0.467
#> CV:NMF      4 0.640           0.718       0.853        0.09609 0.881   0.685
#> MAD:NMF     4 0.825           0.852       0.929        0.14081 0.747   0.415
#> ATC:NMF     4 0.477           0.574       0.744        0.17255 0.784   0.499
#> SD:skmeans  4 0.763           0.816       0.892        0.12912 0.892   0.687
#> CV:skmeans  4 0.371           0.435       0.666        0.12172 0.902   0.732
#> MAD:skmeans 4 0.774           0.830       0.907        0.12903 0.875   0.643
#> ATC:skmeans 4 0.642           0.689       0.794        0.12127 0.847   0.585
#> SD:mclust   4 0.682           0.756       0.888        0.03308 0.758   0.507
#> CV:mclust   4 0.805           0.793       0.907        0.00479 0.724   0.496
#> MAD:mclust  4 0.796           0.830       0.926        0.06395 0.766   0.512
#> ATC:mclust  4 0.399           0.366       0.630        0.16197 0.860   0.709
#> SD:kmeans   4 0.517           0.634       0.788        0.16148 0.740   0.411
#> CV:kmeans   4 0.668           0.761       0.864        0.13069 0.865   0.681
#> MAD:kmeans  4 0.608           0.739       0.842        0.14538 0.828   0.564
#> ATC:kmeans  4 0.486           0.593       0.743        0.14822 0.684   0.463
#> SD:pam      4 0.733           0.868       0.927        0.16890 0.901   0.764
#> CV:pam      4 0.439           0.797       0.904        0.20818 0.962   0.958
#> MAD:pam     4 0.796           0.874       0.934        0.12552 0.926   0.821
#> ATC:pam     4 0.795           0.729       0.808        0.12139 0.957   0.894
#> SD:hclust   4 0.582           0.742       0.876        0.83485 0.653   0.515
#> CV:hclust   4 0.466           0.660       0.878        0.58475 0.928   0.915
#> MAD:hclust  4 0.654           0.840       0.899        0.90941 0.647   0.507
#> ATC:hclust  4 0.509           0.716       0.815        0.12586 0.993   0.984

get_stats(res_list, k = 5)

#>             k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> SD:NMF      5 0.743           0.657       0.816         0.0793 0.909   0.676
#> CV:NMF      5 0.644           0.558       0.768         0.0662 0.878   0.623
#> MAD:NMF     5 0.736           0.696       0.831         0.0716 0.922   0.715
#> ATC:NMF     5 0.707           0.647       0.827         0.0870 0.842   0.501
#> SD:skmeans  5 0.671           0.556       0.720         0.0601 0.931   0.727
#> CV:skmeans  5 0.414           0.303       0.587         0.0663 0.930   0.775
#> MAD:skmeans 5 0.677           0.587       0.795         0.0605 0.969   0.873
#> ATC:skmeans 5 0.649           0.576       0.758         0.0657 0.869   0.562
#> SD:mclust   5 0.765           0.781       0.897         0.1070 0.907   0.755
#> CV:mclust   5 0.838           0.783       0.846         0.1384 0.867   0.689
#> MAD:mclust  5 0.792           0.751       0.882         0.0976 0.869   0.655
#> ATC:mclust  5 0.482           0.455       0.692         0.1355 0.792   0.517
#> SD:kmeans   5 0.606           0.619       0.780         0.0764 0.851   0.565
#> CV:kmeans   5 0.673           0.645       0.788         0.0669 0.962   0.884
#> MAD:kmeans  5 0.683           0.709       0.823         0.0691 0.892   0.654
#> ATC:kmeans  5 0.572           0.702       0.780         0.0948 0.878   0.622
#> SD:pam      5 0.739           0.781       0.874         0.0768 0.984   0.952
#> CV:pam      5 0.488           0.840       0.922         0.1742 0.962   0.957
#> MAD:pam     5 0.794           0.796       0.900         0.0610 0.811   0.529
#> ATC:pam     5 0.946           0.892       0.933         0.1015 0.878   0.682
#> SD:hclust   5 0.485           0.584       0.758         0.1257 0.962   0.898
#> CV:hclust   5 0.355           0.659       0.863         0.2545 0.965   0.955
#> MAD:hclust  5 0.525           0.676       0.807         0.1252 0.949   0.858
#> ATC:hclust  5 0.557           0.705       0.801         0.1150 0.937   0.841

get_stats(res_list, k = 6)

#>             k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> SD:NMF      6 0.801           0.777       0.858         0.0403 0.922   0.669
#> CV:NMF      6 0.709           0.665       0.820         0.0462 0.932   0.727
#> MAD:NMF     6 0.796           0.722       0.853         0.0409 0.945   0.756
#> ATC:NMF     6 0.698           0.628       0.812         0.0449 0.885   0.557
#> SD:skmeans  6 0.694           0.591       0.773         0.0430 0.900   0.567
#> CV:skmeans  6 0.492           0.332       0.565         0.0406 0.909   0.680
#> MAD:skmeans 6 0.700           0.592       0.765         0.0404 0.906   0.610
#> ATC:skmeans 6 0.711           0.611       0.796         0.0451 0.936   0.704
#> SD:mclust   6 0.760           0.772       0.884         0.0803 0.841   0.527
#> CV:mclust   6 0.685           0.745       0.799         0.0842 0.951   0.851
#> MAD:mclust  6 0.793           0.760       0.885         0.0803 0.844   0.499
#> ATC:mclust  6 0.691           0.801       0.866         0.0590 0.845   0.501
#> SD:kmeans   6 0.675           0.650       0.790         0.0454 0.959   0.848
#> CV:kmeans   6 0.693           0.533       0.713         0.0572 0.896   0.695
#> MAD:kmeans  6 0.692           0.578       0.759         0.0528 0.952   0.814
#> ATC:kmeans  6 0.739           0.737       0.794         0.0573 1.000   1.000
#> SD:pam      6 0.676           0.632       0.838         0.0668 0.961   0.880
#> CV:pam      6 0.433           0.782       0.907         0.1871 0.963   0.957
#> MAD:pam     6 0.759           0.719       0.850         0.0591 0.928   0.746
#> ATC:pam     6 0.801           0.805       0.899         0.0734 0.945   0.805
#> SD:hclust   6 0.543           0.563       0.745         0.1021 0.902   0.706
#> CV:hclust   6 0.385           0.640       0.838         0.1009 0.999   0.999
#> MAD:hclust  6 0.584           0.693       0.758         0.0956 0.907   0.706
#> ATC:hclust  6 0.619           0.710       0.763         0.1321 0.860   0.588

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)

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 disease.state(p) k
#> SD:NMF      48            0.719 2
#> CV:NMF      45            0.805 2
#> MAD:NMF     48            0.696 2
#> ATC:NMF     49            0.869 2
#> SD:skmeans  49            0.553 2
#> CV:skmeans  46            0.763 2
#> MAD:skmeans 50            0.448 2
#> ATC:skmeans 49            0.553 2
#> SD:mclust   47            0.710 2
#> CV:mclust   48            0.929 2
#> MAD:mclust  48            0.694 2
#> ATC:mclust  50            0.714 2
#> SD:kmeans   49            0.706 2
#> CV:kmeans   50            0.394 2
#> MAD:kmeans  48            0.719 2
#> ATC:kmeans  50            0.878 2
#> SD:pam      50            0.438 2
#> CV:pam      49               NA 2
#> MAD:pam     50            0.438 2
#> ATC:pam     46            0.639 2
#> SD:hclust   47            0.561 2
#> CV:hclust   49               NA 2
#> MAD:hclust  48            0.528 2
#> ATC:hclust  46            0.826 2

test_to_known_factors(res_list, k = 3)

#>              n disease.state(p) k
#> SD:NMF      45            0.625 3
#> CV:NMF      44            0.966 3
#> MAD:NMF     42            0.612 3
#> ATC:NMF     42            0.568 3
#> SD:skmeans  50            0.689 3
#> CV:skmeans  38            0.838 3
#> MAD:skmeans 50            0.689 3
#> ATC:skmeans 48            0.632 3
#> SD:mclust   48            0.750 3
#> CV:mclust   50            0.447 3
#> MAD:mclust  49            0.593 3
#> ATC:mclust  45            0.687 3
#> SD:kmeans   34            0.527 3
#> CV:kmeans   37            0.733 3
#> MAD:kmeans  44            0.823 3
#> ATC:kmeans  45            0.806 3
#> SD:pam      47            0.569 3
#> CV:pam      46               NA 3
#> MAD:pam     49            0.470 3
#> ATC:pam     48            0.953 3
#> SD:hclust   47            0.566 3
#> CV:hclust   47            0.572 3
#> MAD:hclust  48            0.539 3
#> ATC:hclust  47            0.570 3

test_to_known_factors(res_list, k = 4)

#>              n disease.state(p) k
#> SD:NMF      47            0.901 4
#> CV:NMF      44            0.880 4
#> MAD:NMF     48            0.902 4
#> ATC:NMF     38            0.798 4
#> SD:skmeans  48            0.738 4
#> CV:skmeans  24            0.506 4
#> MAD:skmeans 48            0.738 4
#> ATC:skmeans 46            0.931 4
#> SD:mclust   43            0.918 4
#> CV:mclust   44            0.519 4
#> MAD:mclust  45            0.877 4
#> ATC:mclust  19               NA 4
#> SD:kmeans   42            0.928 4
#> CV:kmeans   40            0.519 4
#> MAD:kmeans  45            0.878 4
#> ATC:kmeans  37            0.924 4
#> SD:pam      50            0.602 4
#> CV:pam      46               NA 4
#> MAD:pam     48            0.671 4
#> ATC:pam     41            0.977 4
#> SD:hclust   45            0.417 4
#> CV:hclust   40            0.224 4
#> MAD:hclust  48            0.584 4
#> ATC:hclust  43            0.406 4

test_to_known_factors(res_list, k = 5)

#>              n disease.state(p) k
#> SD:NMF      39           0.7748 5
#> CV:NMF      30           0.4768 5
#> MAD:NMF     39           0.8458 5
#> ATC:NMF     39           0.7052 5
#> SD:skmeans  36           0.8138 5
#> CV:skmeans   9           0.0842 5
#> MAD:skmeans 36           0.8565 5
#> ATC:skmeans 32           0.8479 5
#> SD:mclust   46           0.8550 5
#> CV:mclust   45           0.6888 5
#> MAD:mclust  41           0.7390 5
#> ATC:mclust  24           0.8270 5
#> SD:kmeans   35           0.9431 5
#> CV:kmeans   42           0.7116 5
#> MAD:kmeans  40           0.4737 5
#> ATC:kmeans  44           0.9073 5
#> SD:pam      43           0.7128 5
#> CV:pam      46               NA 5
#> MAD:pam     47           0.6629 5
#> ATC:pam     49           0.8744 5
#> SD:hclust   38           0.6820 5
#> CV:hclust   42           0.1964 5
#> MAD:hclust  45           0.5525 5
#> ATC:hclust  43           0.7721 5

test_to_known_factors(res_list, k = 6)

#>              n disease.state(p) k
#> SD:NMF      42           0.5815 6
#> CV:NMF      40           0.3800 6
#> MAD:NMF     41           0.6382 6
#> ATC:NMF     35           0.7628 6
#> SD:skmeans  39           0.6798 6
#> CV:skmeans  11           0.0601 6
#> MAD:skmeans 35           0.7834 6
#> ATC:skmeans 37           0.7651 6
#> SD:mclust   46           0.7006 6
#> CV:mclust   40           0.5705 6
#> MAD:mclust  45           0.4268 6
#> ATC:mclust  50           0.6564 6
#> SD:kmeans   40           0.8272 6
#> CV:kmeans   30           0.6118 6
#> MAD:kmeans  35           0.8689 6
#> ATC:kmeans  48           0.8439 6
#> SD:pam      37           0.6702 6
#> CV:pam      45               NA 6
#> MAD:pam     41           0.7202 6
#> ATC:pam     49           0.4539 6
#> SD:hclust   35           0.4084 6
#> CV:hclust   39               NA 6
#> MAD:hclust  43           0.4561 6
#> ATC:hclust  45           0.7071 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 11993 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 4.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

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 0.613           0.863       0.934         0.3125 0.726   0.726
#> 3 3 0.642           0.845       0.933         0.0716 0.990   0.987
#> 4 4 0.582           0.742       0.876         0.8349 0.653   0.515
#> 5 5 0.485           0.584       0.758         0.1257 0.962   0.898
#> 6 6 0.543           0.563       0.745         0.1021 0.902   0.706

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] 4

Following shows the table of the partitions (You need to click the show/hide code output link to see it). The membership matrix (columns with name p*) is inferred by clue::cl_consensus() function with the SE method. Basically the value in the membership matrix represents the probability to belong to a certain group. The finall class label for an item is determined with the group with highest probability it belongs to.

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

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
#> GSM317649     1  0.0000      0.930 1.000 0.000
#> GSM317652     1  0.0000      0.930 1.000 0.000
#> GSM317666     1  0.4939      0.875 0.892 0.108
#> GSM317672     1  0.9491      0.471 0.632 0.368
#> GSM317679     1  0.0000      0.930 1.000 0.000
#> GSM317681     1  0.5519      0.860 0.872 0.128
#> GSM317682     1  0.0000      0.930 1.000 0.000
#> GSM317683     2  0.0938      0.907 0.012 0.988
#> GSM317689     1  0.9922      0.243 0.552 0.448
#> GSM317691     1  0.2603      0.914 0.956 0.044
#> GSM317692     1  0.5737      0.831 0.864 0.136
#> GSM317693     1  0.1414      0.925 0.980 0.020
#> GSM317696     1  0.0000      0.930 1.000 0.000
#> GSM317697     1  0.0938      0.927 0.988 0.012
#> GSM317698     1  0.0000      0.930 1.000 0.000
#> GSM317650     2  0.0938      0.907 0.012 0.988
#> GSM317651     1  0.0000      0.930 1.000 0.000
#> GSM317657     1  0.5842      0.848 0.860 0.140
#> GSM317667     2  0.0000      0.901 0.000 1.000
#> GSM317670     1  0.7219      0.783 0.800 0.200
#> GSM317674     1  0.0000      0.930 1.000 0.000
#> GSM317675     1  0.0000      0.930 1.000 0.000
#> GSM317677     1  0.4161      0.890 0.916 0.084
#> GSM317678     2  0.6148      0.782 0.152 0.848
#> GSM317687     1  0.1184      0.927 0.984 0.016
#> GSM317695     1  0.0000      0.930 1.000 0.000
#> GSM317653     1  0.2778      0.914 0.952 0.048
#> GSM317656     1  0.0000      0.930 1.000 0.000
#> GSM317658     1  0.8661      0.647 0.712 0.288
#> GSM317660     1  0.0938      0.926 0.988 0.012
#> GSM317663     1  0.5842      0.848 0.860 0.140
#> GSM317664     1  0.0000      0.930 1.000 0.000
#> GSM317665     1  0.0376      0.929 0.996 0.004
#> GSM317673     1  0.0000      0.930 1.000 0.000
#> GSM317686     2  0.0000      0.901 0.000 1.000
#> GSM317688     1  0.0000      0.930 1.000 0.000
#> GSM317690     2  0.9710      0.239 0.400 0.600
#> GSM317654     1  0.0376      0.929 0.996 0.004
#> GSM317655     1  0.7883      0.738 0.764 0.236
#> GSM317659     1  0.4690      0.880 0.900 0.100
#> GSM317661     2  0.1184      0.906 0.016 0.984
#> GSM317662     2  0.0938      0.907 0.012 0.988
#> GSM317668     1  0.0000      0.930 1.000 0.000
#> GSM317669     1  0.0000      0.930 1.000 0.000
#> GSM317671     1  0.0000      0.930 1.000 0.000
#> GSM317676     1  0.4690      0.880 0.900 0.100
#> GSM317680     1  0.0000      0.930 1.000 0.000
#> GSM317684     1  0.1184      0.927 0.984 0.016
#> GSM317685     1  0.0000      0.930 1.000 0.000
#> GSM317694     1  0.1414      0.925 0.980 0.020

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> GSM317649     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317652     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317666     1  0.3116      0.876 0.892 0.000 0.108
#> GSM317672     1  0.6008      0.430 0.628 0.372 0.000
#> GSM317679     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317681     1  0.3851      0.842 0.860 0.136 0.004
#> GSM317682     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317683     2  0.0000      0.723 0.000 1.000 0.000
#> GSM317689     1  0.7013      0.201 0.548 0.432 0.020
#> GSM317691     1  0.1950      0.911 0.952 0.040 0.008
#> GSM317692     1  0.3851      0.824 0.860 0.136 0.004
#> GSM317693     1  0.1129      0.923 0.976 0.020 0.004
#> GSM317696     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317697     1  0.0747      0.924 0.984 0.016 0.000
#> GSM317698     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317650     2  0.0000      0.723 0.000 1.000 0.000
#> GSM317651     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317657     1  0.4565      0.852 0.860 0.064 0.076
#> GSM317667     3  0.0000      1.000 0.000 0.000 1.000
#> GSM317670     1  0.5744      0.788 0.800 0.128 0.072
#> GSM317674     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317675     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317677     1  0.2625      0.892 0.916 0.000 0.084
#> GSM317678     2  0.3752      0.588 0.144 0.856 0.000
#> GSM317687     1  0.0747      0.926 0.984 0.000 0.016
#> GSM317695     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317653     1  0.2434      0.909 0.940 0.024 0.036
#> GSM317656     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317658     1  0.5497      0.618 0.708 0.292 0.000
#> GSM317660     1  0.1031      0.921 0.976 0.024 0.000
#> GSM317663     1  0.4544      0.853 0.860 0.056 0.084
#> GSM317664     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317665     1  0.0237      0.929 0.996 0.000 0.004
#> GSM317673     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317686     3  0.0000      1.000 0.000 0.000 1.000
#> GSM317688     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317690     2  0.8097      0.228 0.388 0.540 0.072
#> GSM317654     1  0.0237      0.929 0.996 0.000 0.004
#> GSM317655     1  0.6510      0.736 0.756 0.156 0.088
#> GSM317659     1  0.2959      0.882 0.900 0.000 0.100
#> GSM317661     2  0.0237      0.722 0.004 0.996 0.000
#> GSM317662     2  0.0000      0.723 0.000 1.000 0.000
#> GSM317668     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317669     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317671     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317676     1  0.2959      0.882 0.900 0.000 0.100
#> GSM317680     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317684     1  0.0747      0.926 0.984 0.000 0.016
#> GSM317685     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317694     1  0.0892      0.925 0.980 0.000 0.020

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM317649     1  0.0000     0.9359 1.000 0.000 0.000 0.000
#> GSM317652     1  0.0000     0.9359 1.000 0.000 0.000 0.000
#> GSM317666     4  0.0336     0.6383 0.000 0.000 0.008 0.992
#> GSM317672     4  0.7235     0.3036 0.148 0.372 0.000 0.480
#> GSM317679     1  0.0000     0.9359 1.000 0.000 0.000 0.000
#> GSM317681     1  0.4586     0.7268 0.796 0.136 0.000 0.068
#> GSM317682     1  0.0188     0.9347 0.996 0.000 0.000 0.004
#> GSM317683     2  0.0000     0.8150 0.000 1.000 0.000 0.000
#> GSM317689     4  0.6187     0.1822 0.052 0.432 0.000 0.516
#> GSM317691     4  0.5512     0.6119 0.300 0.040 0.000 0.660
#> GSM317692     4  0.7033     0.5066 0.336 0.136 0.000 0.528
#> GSM317693     1  0.5581    -0.1490 0.532 0.020 0.000 0.448
#> GSM317696     1  0.0469     0.9335 0.988 0.000 0.000 0.012
#> GSM317697     1  0.4175     0.6586 0.784 0.016 0.000 0.200
#> GSM317698     1  0.0592     0.9311 0.984 0.000 0.000 0.016
#> GSM317650     2  0.0000     0.8150 0.000 1.000 0.000 0.000
#> GSM317651     1  0.0188     0.9347 0.996 0.000 0.000 0.004
#> GSM317657     4  0.2179     0.6436 0.012 0.064 0.000 0.924
#> GSM317667     3  0.0000     1.0000 0.000 0.000 1.000 0.000
#> GSM317670     4  0.3749     0.6173 0.032 0.128 0.000 0.840
#> GSM317674     1  0.0592     0.9311 0.984 0.000 0.000 0.016
#> GSM317675     1  0.0592     0.9311 0.984 0.000 0.000 0.016
#> GSM317677     4  0.4008     0.6219 0.244 0.000 0.000 0.756
#> GSM317678     2  0.3667     0.6917 0.088 0.856 0.000 0.056
#> GSM317687     4  0.3528     0.6773 0.192 0.000 0.000 0.808
#> GSM317695     1  0.0000     0.9359 1.000 0.000 0.000 0.000
#> GSM317653     1  0.4095     0.7477 0.804 0.024 0.000 0.172
#> GSM317656     1  0.0000     0.9359 1.000 0.000 0.000 0.000
#> GSM317658     4  0.7397     0.4324 0.200 0.292 0.000 0.508
#> GSM317660     1  0.1629     0.9077 0.952 0.024 0.000 0.024
#> GSM317663     4  0.2076     0.6389 0.004 0.056 0.008 0.932
#> GSM317664     1  0.0592     0.9311 0.984 0.000 0.000 0.016
#> GSM317665     1  0.0921     0.9219 0.972 0.000 0.000 0.028
#> GSM317673     1  0.0469     0.9335 0.988 0.000 0.000 0.012
#> GSM317686     3  0.0000     1.0000 0.000 0.000 1.000 0.000
#> GSM317688     1  0.0000     0.9359 1.000 0.000 0.000 0.000
#> GSM317690     2  0.4977     0.0679 0.000 0.540 0.000 0.460
#> GSM317654     1  0.1022     0.9193 0.968 0.000 0.000 0.032
#> GSM317655     4  0.3450     0.5842 0.000 0.156 0.008 0.836
#> GSM317659     4  0.1557     0.6677 0.056 0.000 0.000 0.944
#> GSM317661     2  0.0188     0.8136 0.000 0.996 0.000 0.004
#> GSM317662     2  0.0000     0.8150 0.000 1.000 0.000 0.000
#> GSM317668     4  0.4661     0.5743 0.348 0.000 0.000 0.652
#> GSM317669     1  0.0000     0.9359 1.000 0.000 0.000 0.000
#> GSM317671     1  0.0000     0.9359 1.000 0.000 0.000 0.000
#> GSM317676     4  0.1557     0.6677 0.056 0.000 0.000 0.944
#> GSM317680     1  0.0000     0.9359 1.000 0.000 0.000 0.000
#> GSM317684     4  0.3764     0.6686 0.216 0.000 0.000 0.784
#> GSM317685     1  0.0188     0.9347 0.996 0.000 0.000 0.004
#> GSM317694     4  0.4790     0.5047 0.380 0.000 0.000 0.620

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> GSM317649     1  0.3074     0.6876 0.804 0.000 0.000 0.000 0.196
#> GSM317652     1  0.3177     0.6810 0.792 0.000 0.000 0.000 0.208
#> GSM317666     4  0.1282     0.6411 0.000 0.000 0.004 0.952 0.044
#> GSM317672     4  0.7455     0.2666 0.104 0.332 0.000 0.456 0.108
#> GSM317679     1  0.3534     0.6369 0.744 0.000 0.000 0.000 0.256
#> GSM317681     5  0.6387     0.8310 0.396 0.080 0.000 0.032 0.492
#> GSM317682     1  0.1410     0.6781 0.940 0.000 0.000 0.000 0.060
#> GSM317683     2  0.0000     0.7943 0.000 1.000 0.000 0.000 0.000
#> GSM317689     4  0.6476     0.1702 0.020 0.384 0.000 0.484 0.112
#> GSM317691     4  0.5449     0.4895 0.264 0.000 0.000 0.632 0.104
#> GSM317692     4  0.7270     0.3710 0.292 0.096 0.000 0.504 0.108
#> GSM317693     1  0.5631    -0.2493 0.500 0.000 0.000 0.424 0.076
#> GSM317696     1  0.0693     0.6987 0.980 0.000 0.000 0.008 0.012
#> GSM317697     1  0.4409     0.2909 0.752 0.000 0.000 0.176 0.072
#> GSM317698     1  0.0798     0.7010 0.976 0.000 0.000 0.016 0.008
#> GSM317650     2  0.0000     0.7943 0.000 1.000 0.000 0.000 0.000
#> GSM317651     1  0.1544     0.6705 0.932 0.000 0.000 0.000 0.068
#> GSM317657     4  0.2438     0.6397 0.008 0.040 0.000 0.908 0.044
#> GSM317667     3  0.0000     1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM317670     4  0.4245     0.5857 0.024 0.008 0.000 0.744 0.224
#> GSM317674     1  0.0798     0.7010 0.976 0.000 0.000 0.016 0.008
#> GSM317675     1  0.0798     0.7010 0.976 0.000 0.000 0.016 0.008
#> GSM317677     4  0.4873     0.4967 0.244 0.000 0.000 0.688 0.068
#> GSM317678     2  0.3930     0.6919 0.044 0.824 0.000 0.028 0.104
#> GSM317687     4  0.4170     0.6015 0.192 0.000 0.000 0.760 0.048
#> GSM317695     1  0.3534     0.6369 0.744 0.000 0.000 0.000 0.256
#> GSM317653     5  0.6059     0.8264 0.412 0.000 0.000 0.120 0.468
#> GSM317656     1  0.3074     0.6876 0.804 0.000 0.000 0.000 0.196
#> GSM317658     4  0.7613     0.4015 0.164 0.252 0.000 0.484 0.100
#> GSM317660     1  0.4161    -0.3573 0.608 0.000 0.000 0.000 0.392
#> GSM317663     4  0.2074     0.6392 0.004 0.032 0.004 0.928 0.032
#> GSM317664     1  0.0798     0.7010 0.976 0.000 0.000 0.016 0.008
#> GSM317665     1  0.3724     0.6581 0.788 0.000 0.000 0.028 0.184
#> GSM317673     1  0.0992     0.6979 0.968 0.000 0.000 0.008 0.024
#> GSM317686     3  0.0000     1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM317688     1  0.0404     0.7042 0.988 0.000 0.000 0.000 0.012
#> GSM317690     2  0.6646     0.0721 0.000 0.416 0.000 0.356 0.228
#> GSM317654     1  0.3805     0.6548 0.784 0.000 0.000 0.032 0.184
#> GSM317655     4  0.3817     0.5636 0.000 0.004 0.004 0.740 0.252
#> GSM317659     4  0.2859     0.6342 0.056 0.000 0.000 0.876 0.068
#> GSM317661     2  0.1965     0.7563 0.000 0.904 0.000 0.000 0.096
#> GSM317662     2  0.0000     0.7943 0.000 1.000 0.000 0.000 0.000
#> GSM317668     4  0.5049     0.4127 0.296 0.000 0.000 0.644 0.060
#> GSM317669     1  0.3534     0.6369 0.744 0.000 0.000 0.000 0.256
#> GSM317671     1  0.3534     0.6369 0.744 0.000 0.000 0.000 0.256
#> GSM317676     4  0.2859     0.6342 0.056 0.000 0.000 0.876 0.068
#> GSM317680     1  0.3534     0.6369 0.744 0.000 0.000 0.000 0.256
#> GSM317684     4  0.4364     0.5801 0.216 0.000 0.000 0.736 0.048
#> GSM317685     1  0.1410     0.6781 0.940 0.000 0.000 0.000 0.060
#> GSM317694     4  0.5037     0.3198 0.376 0.000 0.000 0.584 0.040

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5 p6
#> GSM317649     1  0.4739     -0.157 0.516 0.000 0.436 0.000 0.048  0
#> GSM317652     3  0.4756      0.186 0.464 0.000 0.488 0.000 0.048  0
#> GSM317666     4  0.1082      0.626 0.000 0.000 0.004 0.956 0.040  0
#> GSM317672     4  0.7551      0.214 0.088 0.324 0.040 0.404 0.144  0
#> GSM317679     3  0.2793      0.891 0.200 0.000 0.800 0.000 0.000  0
#> GSM317681     5  0.4864      0.698 0.224 0.076 0.000 0.020 0.680  0
#> GSM317682     1  0.2009      0.653 0.908 0.000 0.024 0.000 0.068  0
#> GSM317683     2  0.0000      0.782 0.000 1.000 0.000 0.000 0.000  0
#> GSM317689     4  0.6816      0.144 0.024 0.376 0.040 0.424 0.136  0
#> GSM317691     4  0.5718      0.492 0.276 0.000 0.036 0.584 0.104  0
#> GSM317692     4  0.7357      0.381 0.300 0.092 0.040 0.452 0.116  0
#> GSM317693     1  0.5708     -0.176 0.512 0.000 0.032 0.376 0.080  0
#> GSM317696     1  0.0436      0.688 0.988 0.000 0.004 0.004 0.004  0
#> GSM317697     1  0.4262      0.402 0.760 0.000 0.024 0.148 0.068  0
#> GSM317698     1  0.0603      0.690 0.980 0.000 0.004 0.016 0.000  0
#> GSM317650     2  0.0790      0.784 0.000 0.968 0.032 0.000 0.000  0
#> GSM317651     1  0.2201      0.644 0.896 0.000 0.028 0.000 0.076  0
#> GSM317657     4  0.2860      0.626 0.008 0.040 0.012 0.876 0.064  0
#> GSM317667     6  0.0000      1.000 0.000 0.000 0.000 0.000 0.000  1
#> GSM317670     4  0.4928      0.540 0.012 0.004 0.076 0.668 0.240  0
#> GSM317674     1  0.0603      0.690 0.980 0.000 0.004 0.016 0.000  0
#> GSM317675     1  0.0603      0.690 0.980 0.000 0.004 0.016 0.000  0
#> GSM317677     4  0.4586      0.508 0.240 0.000 0.012 0.688 0.060  0
#> GSM317678     2  0.3662      0.676 0.024 0.816 0.040 0.004 0.116  0
#> GSM317687     4  0.4113      0.594 0.192 0.000 0.008 0.744 0.056  0
#> GSM317695     3  0.2793      0.891 0.200 0.000 0.800 0.000 0.000  0
#> GSM317653     5  0.5009      0.722 0.256 0.000 0.000 0.120 0.624  0
#> GSM317656     1  0.4735     -0.129 0.520 0.000 0.432 0.000 0.048  0
#> GSM317658     4  0.7711      0.355 0.176 0.244 0.040 0.432 0.108  0
#> GSM317660     5  0.5471      0.580 0.336 0.000 0.140 0.000 0.524  0
#> GSM317663     4  0.2307      0.627 0.000 0.032 0.004 0.896 0.068  0
#> GSM317664     1  0.0603      0.690 0.980 0.000 0.004 0.016 0.000  0
#> GSM317665     1  0.5403      0.307 0.600 0.000 0.292 0.028 0.080  0
#> GSM317673     1  0.1080      0.682 0.960 0.000 0.004 0.004 0.032  0
#> GSM317686     6  0.0000      1.000 0.000 0.000 0.000 0.000 0.000  1
#> GSM317688     1  0.0837      0.682 0.972 0.000 0.020 0.004 0.004  0
#> GSM317690     2  0.7130      0.123 0.000 0.412 0.096 0.272 0.220  0
#> GSM317654     1  0.5470      0.304 0.596 0.000 0.292 0.032 0.080  0
#> GSM317655     4  0.4663      0.526 0.000 0.000 0.092 0.664 0.244  0
#> GSM317659     4  0.2822      0.615 0.056 0.000 0.008 0.868 0.068  0
#> GSM317661     2  0.2672      0.742 0.000 0.868 0.080 0.000 0.052  0
#> GSM317662     2  0.0790      0.784 0.000 0.968 0.032 0.000 0.000  0
#> GSM317668     4  0.5414      0.468 0.140 0.000 0.208 0.632 0.020  0
#> GSM317669     3  0.2793      0.891 0.200 0.000 0.800 0.000 0.000  0
#> GSM317671     3  0.2793      0.891 0.200 0.000 0.800 0.000 0.000  0
#> GSM317676     4  0.2822      0.615 0.056 0.000 0.008 0.868 0.068  0
#> GSM317680     3  0.2793      0.891 0.200 0.000 0.800 0.000 0.000  0
#> GSM317684     4  0.4284      0.578 0.216 0.000 0.008 0.720 0.056  0
#> GSM317685     1  0.2009      0.653 0.908 0.000 0.024 0.000 0.068  0
#> GSM317694     4  0.4819      0.404 0.376 0.000 0.008 0.572 0.044  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-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 disease.state(p) k
#> SD:hclust 47            0.561 2
#> SD:hclust 47            0.566 3
#> SD:hclust 45            0.417 4
#> SD:hclust 38            0.682 5
#> SD:hclust 35            0.408 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 11993 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 0.974           0.948       0.974         0.4498 0.542   0.542
#> 3 3 0.469           0.534       0.667         0.3492 0.771   0.586
#> 4 4 0.517           0.634       0.788         0.1615 0.740   0.411
#> 5 5 0.606           0.619       0.780         0.0764 0.851   0.565
#> 6 6 0.675           0.650       0.790         0.0454 0.959   0.848

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
#> GSM317649     1  0.0938      0.980 0.988 0.012
#> GSM317652     1  0.0000      0.988 1.000 0.000
#> GSM317666     2  0.1414      0.949 0.020 0.980
#> GSM317672     2  0.2778      0.930 0.048 0.952
#> GSM317679     1  0.0938      0.980 0.988 0.012
#> GSM317681     2  0.6801      0.788 0.180 0.820
#> GSM317682     1  0.0000      0.988 1.000 0.000
#> GSM317683     2  0.0938      0.953 0.012 0.988
#> GSM317689     2  0.0938      0.953 0.012 0.988
#> GSM317691     1  0.0000      0.988 1.000 0.000
#> GSM317692     1  0.0000      0.988 1.000 0.000
#> GSM317693     1  0.0000      0.988 1.000 0.000
#> GSM317696     1  0.0000      0.988 1.000 0.000
#> GSM317697     1  0.0000      0.988 1.000 0.000
#> GSM317698     1  0.0000      0.988 1.000 0.000
#> GSM317650     2  0.0938      0.953 0.012 0.988
#> GSM317651     1  0.0000      0.988 1.000 0.000
#> GSM317657     2  0.0938      0.953 0.012 0.988
#> GSM317667     2  0.0938      0.953 0.012 0.988
#> GSM317670     2  0.4815      0.879 0.104 0.896
#> GSM317674     1  0.0000      0.988 1.000 0.000
#> GSM317675     1  0.0000      0.988 1.000 0.000
#> GSM317677     1  0.0000      0.988 1.000 0.000
#> GSM317678     2  0.0938      0.953 0.012 0.988
#> GSM317687     1  0.0000      0.988 1.000 0.000
#> GSM317695     1  0.0938      0.980 0.988 0.012
#> GSM317653     1  0.8713      0.553 0.708 0.292
#> GSM317656     1  0.0000      0.988 1.000 0.000
#> GSM317658     2  0.9850      0.300 0.428 0.572
#> GSM317660     1  0.0000      0.988 1.000 0.000
#> GSM317663     2  0.0938      0.953 0.012 0.988
#> GSM317664     1  0.0000      0.988 1.000 0.000
#> GSM317665     1  0.0000      0.988 1.000 0.000
#> GSM317673     1  0.0000      0.988 1.000 0.000
#> GSM317686     2  0.0938      0.953 0.012 0.988
#> GSM317688     1  0.0000      0.988 1.000 0.000
#> GSM317690     2  0.0938      0.953 0.012 0.988
#> GSM317654     1  0.0000      0.988 1.000 0.000
#> GSM317655     2  0.0938      0.953 0.012 0.988
#> GSM317659     1  0.0000      0.988 1.000 0.000
#> GSM317661     2  0.0938      0.953 0.012 0.988
#> GSM317662     2  0.0938      0.953 0.012 0.988
#> GSM317668     1  0.0000      0.988 1.000 0.000
#> GSM317669     1  0.0938      0.980 0.988 0.012
#> GSM317671     1  0.0938      0.980 0.988 0.012
#> GSM317676     1  0.0000      0.988 1.000 0.000
#> GSM317680     1  0.0938      0.980 0.988 0.012
#> GSM317684     1  0.0000      0.988 1.000 0.000
#> GSM317685     1  0.0000      0.988 1.000 0.000
#> GSM317694     1  0.0000      0.988 1.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> GSM317649     1  0.0000     0.6139 1.000 0.000 0.000
#> GSM317652     1  0.2878     0.6301 0.904 0.000 0.096
#> GSM317666     3  0.6062    -0.5815 0.000 0.384 0.616
#> GSM317672     2  0.4921     0.7585 0.020 0.816 0.164
#> GSM317679     1  0.0237     0.6114 0.996 0.000 0.004
#> GSM317681     2  0.6644     0.6910 0.108 0.752 0.140
#> GSM317682     1  0.6154     0.3394 0.592 0.000 0.408
#> GSM317683     2  0.0000     0.8008 0.000 1.000 0.000
#> GSM317689     2  0.3116     0.7888 0.000 0.892 0.108
#> GSM317691     3  0.5760     0.6202 0.328 0.000 0.672
#> GSM317692     3  0.5956     0.6234 0.324 0.004 0.672
#> GSM317693     3  0.5706     0.6284 0.320 0.000 0.680
#> GSM317696     1  0.6192     0.3206 0.580 0.000 0.420
#> GSM317697     3  0.6095     0.4736 0.392 0.000 0.608
#> GSM317698     3  0.6309     0.0287 0.496 0.000 0.504
#> GSM317650     2  0.0000     0.8008 0.000 1.000 0.000
#> GSM317651     1  0.6126     0.3507 0.600 0.000 0.400
#> GSM317657     2  0.6286     0.6798 0.000 0.536 0.464
#> GSM317667     2  0.6154     0.6854 0.000 0.592 0.408
#> GSM317670     2  0.6090     0.7175 0.020 0.716 0.264
#> GSM317674     1  0.6192     0.3206 0.580 0.000 0.420
#> GSM317675     1  0.6192     0.3206 0.580 0.000 0.420
#> GSM317677     3  0.5678     0.6302 0.316 0.000 0.684
#> GSM317678     2  0.0237     0.8000 0.000 0.996 0.004
#> GSM317687     3  0.5529     0.6187 0.296 0.000 0.704
#> GSM317695     1  0.0592     0.6154 0.988 0.000 0.012
#> GSM317653     3  0.9463     0.3562 0.244 0.256 0.500
#> GSM317656     1  0.3412     0.6222 0.876 0.000 0.124
#> GSM317658     2  0.8405    -0.0102 0.084 0.460 0.456
#> GSM317660     1  0.3456     0.6078 0.904 0.036 0.060
#> GSM317663     2  0.6252     0.6947 0.000 0.556 0.444
#> GSM317664     1  0.6192     0.3206 0.580 0.000 0.420
#> GSM317665     1  0.2261     0.6302 0.932 0.000 0.068
#> GSM317673     1  0.6180     0.3311 0.584 0.000 0.416
#> GSM317686     2  0.5650     0.7320 0.000 0.688 0.312
#> GSM317688     1  0.6192     0.3258 0.580 0.000 0.420
#> GSM317690     2  0.1860     0.8002 0.000 0.948 0.052
#> GSM317654     1  0.3038     0.6287 0.896 0.000 0.104
#> GSM317655     2  0.6192     0.7094 0.000 0.580 0.420
#> GSM317659     3  0.5678     0.6302 0.316 0.000 0.684
#> GSM317661     2  0.0000     0.8008 0.000 1.000 0.000
#> GSM317662     2  0.0000     0.8008 0.000 1.000 0.000
#> GSM317668     1  0.4974     0.5428 0.764 0.000 0.236
#> GSM317669     1  0.0000     0.6139 1.000 0.000 0.000
#> GSM317671     1  0.0000     0.6139 1.000 0.000 0.000
#> GSM317676     3  0.1964     0.4187 0.056 0.000 0.944
#> GSM317680     1  0.0000     0.6139 1.000 0.000 0.000
#> GSM317684     3  0.5733     0.6267 0.324 0.000 0.676
#> GSM317685     1  0.6180     0.3311 0.584 0.000 0.416
#> GSM317694     3  0.6305     0.0873 0.484 0.000 0.516

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM317649     3  0.0921     0.7841 0.028 0.000 0.972 0.000
#> GSM317652     3  0.6215     0.6687 0.192 0.000 0.668 0.140
#> GSM317666     4  0.6252     0.6704 0.192 0.128 0.004 0.676
#> GSM317672     2  0.5985     0.5405 0.036 0.660 0.020 0.284
#> GSM317679     3  0.1109     0.7824 0.028 0.000 0.968 0.004
#> GSM317681     2  0.7810     0.3587 0.148 0.524 0.028 0.300
#> GSM317682     1  0.6357     0.5454 0.656 0.000 0.184 0.160
#> GSM317683     2  0.0000     0.7564 0.000 1.000 0.000 0.000
#> GSM317689     2  0.3908     0.6619 0.032 0.844 0.008 0.116
#> GSM317691     1  0.2281     0.7102 0.904 0.000 0.000 0.096
#> GSM317692     1  0.3108     0.6943 0.872 0.000 0.016 0.112
#> GSM317693     1  0.0707     0.7380 0.980 0.000 0.000 0.020
#> GSM317696     1  0.3649     0.6886 0.796 0.000 0.204 0.000
#> GSM317697     1  0.0937     0.7395 0.976 0.000 0.012 0.012
#> GSM317698     1  0.2216     0.7338 0.908 0.000 0.092 0.000
#> GSM317650     2  0.0000     0.7564 0.000 1.000 0.000 0.000
#> GSM317651     1  0.6816     0.4641 0.604 0.000 0.212 0.184
#> GSM317657     4  0.6617     0.7356 0.120 0.280 0.000 0.600
#> GSM317667     4  0.5281     0.6448 0.012 0.300 0.012 0.676
#> GSM317670     2  0.7278     0.2078 0.220 0.576 0.008 0.196
#> GSM317674     1  0.3649     0.6886 0.796 0.000 0.204 0.000
#> GSM317675     1  0.3649     0.6886 0.796 0.000 0.204 0.000
#> GSM317677     1  0.1398     0.7336 0.956 0.000 0.004 0.040
#> GSM317678     2  0.0921     0.7519 0.000 0.972 0.000 0.028
#> GSM317687     1  0.2589     0.6976 0.884 0.000 0.000 0.116
#> GSM317695     3  0.1022     0.7831 0.032 0.000 0.968 0.000
#> GSM317653     1  0.7458     0.3360 0.540 0.124 0.020 0.316
#> GSM317656     3  0.5750     0.2348 0.440 0.000 0.532 0.028
#> GSM317658     1  0.7349    -0.0581 0.488 0.392 0.016 0.104
#> GSM317660     3  0.6133     0.7095 0.084 0.020 0.704 0.192
#> GSM317663     4  0.6426     0.7432 0.108 0.272 0.000 0.620
#> GSM317664     1  0.3649     0.6886 0.796 0.000 0.204 0.000
#> GSM317665     3  0.5889     0.7117 0.116 0.000 0.696 0.188
#> GSM317673     1  0.4361     0.6714 0.772 0.000 0.208 0.020
#> GSM317686     4  0.5093     0.6220 0.000 0.348 0.012 0.640
#> GSM317688     1  0.4919     0.6609 0.752 0.000 0.200 0.048
#> GSM317690     2  0.2216     0.6966 0.000 0.908 0.000 0.092
#> GSM317654     3  0.6978     0.6088 0.208 0.000 0.584 0.208
#> GSM317655     4  0.6430     0.7242 0.092 0.312 0.000 0.596
#> GSM317659     1  0.1940     0.7201 0.924 0.000 0.000 0.076
#> GSM317661     2  0.0000     0.7564 0.000 1.000 0.000 0.000
#> GSM317662     2  0.0000     0.7564 0.000 1.000 0.000 0.000
#> GSM317668     3  0.5724     0.2477 0.424 0.000 0.548 0.028
#> GSM317669     3  0.0921     0.7841 0.028 0.000 0.972 0.000
#> GSM317671     3  0.1109     0.7824 0.028 0.000 0.968 0.004
#> GSM317676     1  0.5028     0.1631 0.596 0.000 0.004 0.400
#> GSM317680     3  0.0921     0.7841 0.028 0.000 0.972 0.000
#> GSM317684     1  0.1118     0.7336 0.964 0.000 0.000 0.036
#> GSM317685     1  0.4399     0.6678 0.768 0.000 0.212 0.020
#> GSM317694     1  0.2469     0.7296 0.892 0.000 0.108 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
#> GSM317649     3  0.0566    0.99250 0.012 0.000 0.984 0.000 0.004
#> GSM317652     5  0.7069    0.31995 0.256 0.000 0.364 0.012 0.368
#> GSM317666     4  0.3078    0.64707 0.056 0.008 0.000 0.872 0.064
#> GSM317672     5  0.6999    0.02998 0.044 0.372 0.000 0.128 0.456
#> GSM317679     3  0.0404    0.99557 0.012 0.000 0.988 0.000 0.000
#> GSM317681     5  0.6088    0.45564 0.052 0.188 0.000 0.104 0.656
#> GSM317682     1  0.5206    0.02859 0.572 0.000 0.040 0.004 0.384
#> GSM317683     2  0.0162    0.82517 0.000 0.996 0.000 0.000 0.004
#> GSM317689     2  0.4295    0.63224 0.004 0.732 0.000 0.236 0.028
#> GSM317691     1  0.4974    0.58583 0.696 0.000 0.000 0.212 0.092
#> GSM317692     1  0.5565    0.51072 0.632 0.000 0.000 0.240 0.128
#> GSM317693     1  0.2770    0.72152 0.880 0.000 0.000 0.044 0.076
#> GSM317696     1  0.1956    0.73914 0.916 0.000 0.076 0.000 0.008
#> GSM317697     1  0.1300    0.73850 0.956 0.000 0.000 0.016 0.028
#> GSM317698     1  0.0566    0.74347 0.984 0.000 0.012 0.000 0.004
#> GSM317650     2  0.0162    0.82517 0.000 0.996 0.000 0.000 0.004
#> GSM317651     5  0.5322    0.32534 0.408 0.000 0.044 0.004 0.544
#> GSM317657     4  0.3716    0.63406 0.048 0.072 0.000 0.844 0.036
#> GSM317667     4  0.6157    0.49129 0.004 0.120 0.012 0.596 0.268
#> GSM317670     2  0.6636    0.03246 0.188 0.420 0.000 0.388 0.004
#> GSM317674     1  0.2069    0.73915 0.912 0.000 0.076 0.000 0.012
#> GSM317675     1  0.2069    0.73915 0.912 0.000 0.076 0.000 0.012
#> GSM317677     1  0.3622    0.69680 0.816 0.000 0.000 0.048 0.136
#> GSM317678     2  0.1117    0.81297 0.000 0.964 0.000 0.016 0.020
#> GSM317687     1  0.5774    0.48924 0.612 0.000 0.000 0.232 0.156
#> GSM317695     3  0.0510    0.99173 0.016 0.000 0.984 0.000 0.000
#> GSM317653     5  0.5283    0.45188 0.112 0.024 0.000 0.144 0.720
#> GSM317656     1  0.4501    0.58777 0.740 0.000 0.212 0.012 0.036
#> GSM317658     1  0.6994    0.26242 0.528 0.268 0.000 0.156 0.048
#> GSM317660     5  0.5458    0.44483 0.040 0.004 0.380 0.008 0.568
#> GSM317663     4  0.2846    0.64832 0.028 0.076 0.000 0.884 0.012
#> GSM317664     1  0.2069    0.73915 0.912 0.000 0.076 0.000 0.012
#> GSM317665     5  0.5489    0.47840 0.064 0.000 0.356 0.004 0.576
#> GSM317673     1  0.2429    0.73223 0.900 0.000 0.076 0.004 0.020
#> GSM317686     4  0.6142    0.47568 0.000 0.148 0.012 0.596 0.244
#> GSM317688     1  0.3386    0.70732 0.856 0.000 0.068 0.012 0.064
#> GSM317690     2  0.2970    0.72990 0.000 0.828 0.000 0.168 0.004
#> GSM317654     5  0.5389    0.55620 0.088 0.000 0.260 0.004 0.648
#> GSM317655     4  0.2921    0.62479 0.020 0.124 0.000 0.856 0.000
#> GSM317659     1  0.5125    0.60384 0.696 0.000 0.000 0.156 0.148
#> GSM317661     2  0.0000    0.82480 0.000 1.000 0.000 0.000 0.000
#> GSM317662     2  0.0000    0.82480 0.000 1.000 0.000 0.000 0.000
#> GSM317668     1  0.5746    0.36648 0.576 0.000 0.348 0.020 0.056
#> GSM317669     3  0.0451    0.98997 0.008 0.000 0.988 0.000 0.004
#> GSM317671     3  0.0404    0.99557 0.012 0.000 0.988 0.000 0.000
#> GSM317676     4  0.6253   -0.00199 0.388 0.000 0.000 0.464 0.148
#> GSM317680     3  0.0404    0.99557 0.012 0.000 0.988 0.000 0.000
#> GSM317684     1  0.3506    0.70085 0.824 0.000 0.000 0.044 0.132
#> GSM317685     1  0.2913    0.73029 0.876 0.000 0.080 0.004 0.040
#> GSM317694     1  0.2932    0.72901 0.864 0.000 0.020 0.004 0.112

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> GSM317649     3  0.0508     0.9802 0.000 0.000 0.984 0.000 0.012 0.004
#> GSM317652     1  0.6653    -0.1354 0.408 0.000 0.128 0.000 0.388 0.076
#> GSM317666     4  0.5047     0.5301 0.028 0.000 0.000 0.692 0.128 0.152
#> GSM317672     5  0.6861     0.4787 0.056 0.156 0.000 0.156 0.572 0.060
#> GSM317679     3  0.0146     0.9924 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM317681     5  0.4880     0.6517 0.040 0.056 0.000 0.104 0.756 0.044
#> GSM317682     1  0.5478    -0.0543 0.504 0.000 0.004 0.004 0.392 0.096
#> GSM317683     2  0.0000     0.7922 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM317689     2  0.5059     0.0727 0.000 0.480 0.000 0.464 0.036 0.020
#> GSM317691     1  0.5619     0.5526 0.608 0.000 0.000 0.244 0.116 0.032
#> GSM317692     1  0.6440     0.3954 0.496 0.000 0.000 0.304 0.140 0.060
#> GSM317693     1  0.4220     0.6941 0.776 0.000 0.000 0.104 0.088 0.032
#> GSM317696     1  0.1116     0.7307 0.960 0.000 0.028 0.004 0.000 0.008
#> GSM317697     1  0.2216     0.7267 0.908 0.000 0.000 0.052 0.016 0.024
#> GSM317698     1  0.0291     0.7346 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM317650     2  0.0000     0.7922 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM317651     5  0.4750     0.5493 0.264 0.000 0.016 0.000 0.664 0.056
#> GSM317657     4  0.2271     0.6689 0.000 0.024 0.000 0.908 0.036 0.032
#> GSM317667     6  0.3243     0.9732 0.000 0.028 0.000 0.156 0.004 0.812
#> GSM317670     4  0.4807     0.4348 0.016 0.224 0.000 0.700 0.032 0.028
#> GSM317674     1  0.1116     0.7324 0.960 0.000 0.028 0.000 0.008 0.004
#> GSM317675     1  0.1332     0.7320 0.952 0.000 0.028 0.000 0.008 0.012
#> GSM317677     1  0.4560     0.6731 0.744 0.000 0.000 0.092 0.132 0.032
#> GSM317678     2  0.1148     0.7744 0.000 0.960 0.000 0.020 0.004 0.016
#> GSM317687     1  0.6203     0.4562 0.536 0.000 0.000 0.256 0.168 0.040
#> GSM317695     3  0.0146     0.9900 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM317653     5  0.1821     0.6666 0.008 0.000 0.000 0.040 0.928 0.024
#> GSM317656     1  0.3775     0.6717 0.816 0.000 0.076 0.000 0.048 0.060
#> GSM317658     1  0.6520     0.4030 0.552 0.128 0.000 0.252 0.036 0.032
#> GSM317660     5  0.3546     0.6933 0.016 0.000 0.196 0.000 0.776 0.012
#> GSM317663     4  0.3007     0.6575 0.000 0.020 0.000 0.860 0.040 0.080
#> GSM317664     1  0.1116     0.7324 0.960 0.000 0.028 0.000 0.008 0.004
#> GSM317665     5  0.3269     0.7052 0.024 0.000 0.184 0.000 0.792 0.000
#> GSM317673     1  0.2245     0.7158 0.908 0.000 0.028 0.004 0.008 0.052
#> GSM317686     6  0.3240     0.9731 0.000 0.040 0.000 0.148 0.000 0.812
#> GSM317688     1  0.3668     0.6816 0.816 0.000 0.020 0.004 0.048 0.112
#> GSM317690     2  0.4627     0.2328 0.000 0.532 0.000 0.436 0.020 0.012
#> GSM317654     5  0.2412     0.7215 0.028 0.000 0.092 0.000 0.880 0.000
#> GSM317655     4  0.3337     0.6176 0.000 0.044 0.000 0.840 0.028 0.088
#> GSM317659     1  0.5538     0.5826 0.636 0.000 0.000 0.184 0.148 0.032
#> GSM317661     2  0.0146     0.7917 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM317662     2  0.0146     0.7917 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM317668     1  0.6569     0.5024 0.604 0.000 0.140 0.040 0.144 0.072
#> GSM317669     3  0.0146     0.9924 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM317671     3  0.0000     0.9930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM317676     4  0.5638     0.3937 0.180 0.000 0.000 0.632 0.148 0.040
#> GSM317680     3  0.0000     0.9930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM317684     1  0.4874     0.6583 0.716 0.000 0.000 0.104 0.144 0.036
#> GSM317685     1  0.2839     0.7113 0.876 0.000 0.032 0.000 0.040 0.052
#> GSM317694     1  0.4105     0.6903 0.780 0.000 0.000 0.068 0.124 0.028

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 disease.state(p) k
#> SD:kmeans 49            0.706 2
#> SD:kmeans 34            0.527 3
#> SD:kmeans 42            0.928 4
#> SD:kmeans 35            0.943 5
#> SD:kmeans 40            0.827 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 11993 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 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-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           0.968       0.987         0.4850 0.510   0.510
#> 3 3 0.837           0.917       0.948         0.3783 0.805   0.624
#> 4 4 0.763           0.816       0.892         0.1291 0.892   0.687
#> 5 5 0.671           0.556       0.720         0.0601 0.931   0.727
#> 6 6 0.694           0.591       0.773         0.0430 0.900   0.567

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
#> GSM317649     1  0.0000      0.999 1.000 0.000
#> GSM317652     1  0.0000      0.999 1.000 0.000
#> GSM317666     2  0.0000      0.968 0.000 1.000
#> GSM317672     2  0.0000      0.968 0.000 1.000
#> GSM317679     1  0.0000      0.999 1.000 0.000
#> GSM317681     2  0.0000      0.968 0.000 1.000
#> GSM317682     1  0.0000      0.999 1.000 0.000
#> GSM317683     2  0.0000      0.968 0.000 1.000
#> GSM317689     2  0.0000      0.968 0.000 1.000
#> GSM317691     1  0.1184      0.984 0.984 0.016
#> GSM317692     2  0.0000      0.968 0.000 1.000
#> GSM317693     1  0.0000      0.999 1.000 0.000
#> GSM317696     1  0.0000      0.999 1.000 0.000
#> GSM317697     1  0.0938      0.988 0.988 0.012
#> GSM317698     1  0.0000      0.999 1.000 0.000
#> GSM317650     2  0.0000      0.968 0.000 1.000
#> GSM317651     1  0.0000      0.999 1.000 0.000
#> GSM317657     2  0.0000      0.968 0.000 1.000
#> GSM317667     2  0.0000      0.968 0.000 1.000
#> GSM317670     2  0.0000      0.968 0.000 1.000
#> GSM317674     1  0.0000      0.999 1.000 0.000
#> GSM317675     1  0.0000      0.999 1.000 0.000
#> GSM317677     1  0.0000      0.999 1.000 0.000
#> GSM317678     2  0.0000      0.968 0.000 1.000
#> GSM317687     1  0.0000      0.999 1.000 0.000
#> GSM317695     1  0.0000      0.999 1.000 0.000
#> GSM317653     2  0.6148      0.811 0.152 0.848
#> GSM317656     1  0.0000      0.999 1.000 0.000
#> GSM317658     2  0.0000      0.968 0.000 1.000
#> GSM317660     2  0.9922      0.211 0.448 0.552
#> GSM317663     2  0.0000      0.968 0.000 1.000
#> GSM317664     1  0.0000      0.999 1.000 0.000
#> GSM317665     1  0.0000      0.999 1.000 0.000
#> GSM317673     1  0.0000      0.999 1.000 0.000
#> GSM317686     2  0.0000      0.968 0.000 1.000
#> GSM317688     1  0.0000      0.999 1.000 0.000
#> GSM317690     2  0.0000      0.968 0.000 1.000
#> GSM317654     1  0.0000      0.999 1.000 0.000
#> GSM317655     2  0.0000      0.968 0.000 1.000
#> GSM317659     1  0.0000      0.999 1.000 0.000
#> GSM317661     2  0.0000      0.968 0.000 1.000
#> GSM317662     2  0.0000      0.968 0.000 1.000
#> GSM317668     1  0.0000      0.999 1.000 0.000
#> GSM317669     1  0.0000      0.999 1.000 0.000
#> GSM317671     1  0.0000      0.999 1.000 0.000
#> GSM317676     1  0.0376      0.995 0.996 0.004
#> GSM317680     1  0.0000      0.999 1.000 0.000
#> GSM317684     1  0.0000      0.999 1.000 0.000
#> GSM317685     1  0.0000      0.999 1.000 0.000
#> GSM317694     1  0.0000      0.999 1.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> GSM317649     3  0.0000      0.995 0.000 0.000 1.000
#> GSM317652     3  0.0000      0.995 0.000 0.000 1.000
#> GSM317666     2  0.4555      0.792 0.200 0.800 0.000
#> GSM317672     2  0.0000      0.970 0.000 1.000 0.000
#> GSM317679     3  0.0000      0.995 0.000 0.000 1.000
#> GSM317681     2  0.0000      0.970 0.000 1.000 0.000
#> GSM317682     1  0.4605      0.834 0.796 0.000 0.204
#> GSM317683     2  0.0000      0.970 0.000 1.000 0.000
#> GSM317689     2  0.0000      0.970 0.000 1.000 0.000
#> GSM317691     1  0.0000      0.880 1.000 0.000 0.000
#> GSM317692     2  0.1753      0.936 0.048 0.952 0.000
#> GSM317693     1  0.0000      0.880 1.000 0.000 0.000
#> GSM317696     1  0.4399      0.845 0.812 0.000 0.188
#> GSM317697     1  0.0237      0.880 0.996 0.000 0.004
#> GSM317698     1  0.0237      0.880 0.996 0.000 0.004
#> GSM317650     2  0.0000      0.970 0.000 1.000 0.000
#> GSM317651     1  0.4842      0.815 0.776 0.000 0.224
#> GSM317657     2  0.0000      0.970 0.000 1.000 0.000
#> GSM317667     2  0.0424      0.965 0.008 0.992 0.000
#> GSM317670     2  0.0000      0.970 0.000 1.000 0.000
#> GSM317674     1  0.4346      0.847 0.816 0.000 0.184
#> GSM317675     1  0.4346      0.847 0.816 0.000 0.184
#> GSM317677     1  0.0000      0.880 1.000 0.000 0.000
#> GSM317678     2  0.0000      0.970 0.000 1.000 0.000
#> GSM317687     1  0.0000      0.880 1.000 0.000 0.000
#> GSM317695     3  0.0000      0.995 0.000 0.000 1.000
#> GSM317653     2  0.7772      0.651 0.196 0.672 0.132
#> GSM317656     3  0.0000      0.995 0.000 0.000 1.000
#> GSM317658     2  0.0424      0.965 0.008 0.992 0.000
#> GSM317660     3  0.0000      0.995 0.000 0.000 1.000
#> GSM317663     2  0.0000      0.970 0.000 1.000 0.000
#> GSM317664     1  0.4346      0.847 0.816 0.000 0.184
#> GSM317665     3  0.0000      0.995 0.000 0.000 1.000
#> GSM317673     1  0.4555      0.837 0.800 0.000 0.200
#> GSM317686     2  0.0000      0.970 0.000 1.000 0.000
#> GSM317688     1  0.6111      0.537 0.604 0.000 0.396
#> GSM317690     2  0.0000      0.970 0.000 1.000 0.000
#> GSM317654     3  0.0237      0.991 0.004 0.000 0.996
#> GSM317655     2  0.0000      0.970 0.000 1.000 0.000
#> GSM317659     1  0.0000      0.880 1.000 0.000 0.000
#> GSM317661     2  0.0000      0.970 0.000 1.000 0.000
#> GSM317662     2  0.0000      0.970 0.000 1.000 0.000
#> GSM317668     3  0.1529      0.951 0.040 0.000 0.960
#> GSM317669     3  0.0000      0.995 0.000 0.000 1.000
#> GSM317671     3  0.0000      0.995 0.000 0.000 1.000
#> GSM317676     1  0.0000      0.880 1.000 0.000 0.000
#> GSM317680     3  0.0000      0.995 0.000 0.000 1.000
#> GSM317684     1  0.0000      0.880 1.000 0.000 0.000
#> GSM317685     1  0.4555      0.837 0.800 0.000 0.200
#> GSM317694     1  0.0000      0.880 1.000 0.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM317649     3  0.0000      0.947 0.000 0.000 1.000 0.000
#> GSM317652     3  0.0927      0.945 0.008 0.000 0.976 0.016
#> GSM317666     4  0.1489      0.750 0.004 0.044 0.000 0.952
#> GSM317672     2  0.0592      0.918 0.000 0.984 0.000 0.016
#> GSM317679     3  0.0000      0.947 0.000 0.000 1.000 0.000
#> GSM317681     2  0.1557      0.891 0.000 0.944 0.000 0.056
#> GSM317682     1  0.1854      0.832 0.940 0.000 0.012 0.048
#> GSM317683     2  0.0000      0.927 0.000 1.000 0.000 0.000
#> GSM317689     2  0.0188      0.926 0.000 0.996 0.000 0.004
#> GSM317691     1  0.4967      0.435 0.548 0.000 0.000 0.452
#> GSM317692     2  0.4049      0.682 0.008 0.780 0.000 0.212
#> GSM317693     1  0.3356      0.789 0.824 0.000 0.000 0.176
#> GSM317696     1  0.0188      0.855 0.996 0.000 0.004 0.000
#> GSM317697     1  0.0000      0.855 1.000 0.000 0.000 0.000
#> GSM317698     1  0.0000      0.855 1.000 0.000 0.000 0.000
#> GSM317650     2  0.0000      0.927 0.000 1.000 0.000 0.000
#> GSM317651     1  0.5312      0.635 0.712 0.000 0.236 0.052
#> GSM317657     4  0.4356      0.714 0.000 0.292 0.000 0.708
#> GSM317667     4  0.3311      0.762 0.000 0.172 0.000 0.828
#> GSM317670     2  0.4194      0.635 0.000 0.764 0.008 0.228
#> GSM317674     1  0.0188      0.855 0.996 0.000 0.004 0.000
#> GSM317675     1  0.0188      0.855 0.996 0.000 0.004 0.000
#> GSM317677     1  0.3975      0.745 0.760 0.000 0.000 0.240
#> GSM317678     2  0.0000      0.927 0.000 1.000 0.000 0.000
#> GSM317687     4  0.1940      0.705 0.076 0.000 0.000 0.924
#> GSM317695     3  0.0707      0.941 0.020 0.000 0.980 0.000
#> GSM317653     4  0.4284      0.648 0.000 0.200 0.020 0.780
#> GSM317656     3  0.3688      0.753 0.208 0.000 0.792 0.000
#> GSM317658     2  0.1820      0.893 0.036 0.944 0.000 0.020
#> GSM317660     3  0.1854      0.930 0.000 0.012 0.940 0.048
#> GSM317663     4  0.4500      0.700 0.000 0.316 0.000 0.684
#> GSM317664     1  0.0336      0.854 0.992 0.000 0.008 0.000
#> GSM317665     3  0.1389      0.935 0.000 0.000 0.952 0.048
#> GSM317673     1  0.0657      0.852 0.984 0.000 0.012 0.004
#> GSM317686     4  0.4697      0.646 0.000 0.356 0.000 0.644
#> GSM317688     1  0.3708      0.747 0.832 0.000 0.148 0.020
#> GSM317690     2  0.1557      0.891 0.000 0.944 0.000 0.056
#> GSM317654     3  0.2053      0.923 0.000 0.004 0.924 0.072
#> GSM317655     4  0.4477      0.701 0.000 0.312 0.000 0.688
#> GSM317659     1  0.4992      0.393 0.524 0.000 0.000 0.476
#> GSM317661     2  0.0188      0.926 0.000 0.996 0.000 0.004
#> GSM317662     2  0.0000      0.927 0.000 1.000 0.000 0.000
#> GSM317668     3  0.3032      0.842 0.124 0.000 0.868 0.008
#> GSM317669     3  0.0000      0.947 0.000 0.000 1.000 0.000
#> GSM317671     3  0.0000      0.947 0.000 0.000 1.000 0.000
#> GSM317676     4  0.1474      0.726 0.052 0.000 0.000 0.948
#> GSM317680     3  0.0000      0.947 0.000 0.000 1.000 0.000
#> GSM317684     1  0.4103      0.732 0.744 0.000 0.000 0.256
#> GSM317685     1  0.0779      0.852 0.980 0.000 0.016 0.004
#> GSM317694     1  0.2814      0.813 0.868 0.000 0.000 0.132

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> GSM317649     3  0.0794     0.7711 0.028 0.000 0.972 0.000 0.000
#> GSM317652     3  0.5415     0.7076 0.212 0.000 0.688 0.076 0.024
#> GSM317666     4  0.3724     0.5275 0.000 0.020 0.000 0.776 0.204
#> GSM317672     2  0.1830     0.8066 0.028 0.932 0.000 0.040 0.000
#> GSM317679     3  0.0000     0.7710 0.000 0.000 1.000 0.000 0.000
#> GSM317681     2  0.5726     0.5050 0.188 0.640 0.004 0.168 0.000
#> GSM317682     1  0.4026     0.5428 0.736 0.000 0.000 0.020 0.244
#> GSM317683     2  0.0000     0.8308 0.000 1.000 0.000 0.000 0.000
#> GSM317689     2  0.0703     0.8280 0.000 0.976 0.000 0.024 0.000
#> GSM317691     5  0.4337     0.4802 0.056 0.000 0.000 0.196 0.748
#> GSM317692     2  0.7181     0.3487 0.084 0.552 0.000 0.172 0.192
#> GSM317693     5  0.3690     0.1236 0.224 0.000 0.000 0.012 0.764
#> GSM317696     1  0.4278     0.6982 0.548 0.000 0.000 0.000 0.452
#> GSM317697     5  0.4747    -0.6822 0.488 0.000 0.000 0.016 0.496
#> GSM317698     1  0.4297     0.6912 0.528 0.000 0.000 0.000 0.472
#> GSM317650     2  0.0290     0.8309 0.000 0.992 0.000 0.008 0.000
#> GSM317651     1  0.7140     0.0125 0.564 0.000 0.116 0.120 0.200
#> GSM317657     4  0.4285     0.6728 0.008 0.208 0.000 0.752 0.032
#> GSM317667     4  0.3821     0.6743 0.000 0.216 0.000 0.764 0.020
#> GSM317670     2  0.5467     0.4490 0.040 0.656 0.016 0.276 0.012
#> GSM317674     1  0.4291     0.6997 0.536 0.000 0.000 0.000 0.464
#> GSM317675     1  0.4287     0.7018 0.540 0.000 0.000 0.000 0.460
#> GSM317677     5  0.3003     0.4398 0.092 0.000 0.000 0.044 0.864
#> GSM317678     2  0.0324     0.8298 0.004 0.992 0.000 0.004 0.000
#> GSM317687     5  0.4648    -0.2030 0.012 0.000 0.000 0.464 0.524
#> GSM317695     3  0.1478     0.7482 0.064 0.000 0.936 0.000 0.000
#> GSM317653     4  0.8205     0.0829 0.340 0.108 0.004 0.344 0.204
#> GSM317656     3  0.5729     0.3873 0.352 0.000 0.572 0.016 0.060
#> GSM317658     2  0.4397     0.7214 0.080 0.804 0.000 0.056 0.060
#> GSM317660     3  0.6422     0.5954 0.340 0.008 0.504 0.148 0.000
#> GSM317663     4  0.3700     0.6679 0.000 0.240 0.000 0.752 0.008
#> GSM317664     1  0.4291     0.6997 0.536 0.000 0.000 0.000 0.464
#> GSM317665     3  0.6121     0.6087 0.324 0.000 0.528 0.148 0.000
#> GSM317673     1  0.4219     0.6972 0.584 0.000 0.000 0.000 0.416
#> GSM317686     4  0.3857     0.5891 0.000 0.312 0.000 0.688 0.000
#> GSM317688     1  0.5760     0.4883 0.648 0.000 0.088 0.024 0.240
#> GSM317690     2  0.2707     0.7393 0.008 0.860 0.000 0.132 0.000
#> GSM317654     3  0.7458     0.5191 0.352 0.000 0.420 0.168 0.060
#> GSM317655     4  0.3844     0.6448 0.004 0.256 0.000 0.736 0.004
#> GSM317659     5  0.3586     0.5065 0.020 0.000 0.000 0.188 0.792
#> GSM317661     2  0.0609     0.8294 0.000 0.980 0.000 0.020 0.000
#> GSM317662     2  0.0290     0.8309 0.000 0.992 0.000 0.008 0.000
#> GSM317668     3  0.6039     0.6074 0.156 0.000 0.668 0.052 0.124
#> GSM317669     3  0.0162     0.7715 0.004 0.000 0.996 0.000 0.000
#> GSM317671     3  0.0000     0.7710 0.000 0.000 1.000 0.000 0.000
#> GSM317676     4  0.4650     0.1323 0.012 0.000 0.000 0.520 0.468
#> GSM317680     3  0.0000     0.7710 0.000 0.000 1.000 0.000 0.000
#> GSM317684     5  0.2795     0.4977 0.056 0.000 0.000 0.064 0.880
#> GSM317685     1  0.4801     0.6542 0.584 0.000 0.012 0.008 0.396
#> GSM317694     5  0.3300     0.2004 0.204 0.000 0.000 0.004 0.792

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> GSM317649     3  0.0858     0.7668 0.000 0.000 0.968 0.000 0.028 0.004
#> GSM317652     3  0.6637    -0.2707 0.140 0.000 0.412 0.012 0.396 0.040
#> GSM317666     4  0.2615     0.7277 0.000 0.008 0.000 0.852 0.004 0.136
#> GSM317672     2  0.1995     0.7641 0.000 0.912 0.000 0.000 0.052 0.036
#> GSM317679     3  0.0000     0.7860 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM317681     2  0.5451     0.3518 0.000 0.564 0.008 0.044 0.352 0.032
#> GSM317682     1  0.5531     0.5625 0.632 0.008 0.000 0.016 0.212 0.132
#> GSM317683     2  0.0837     0.7872 0.000 0.972 0.000 0.020 0.004 0.004
#> GSM317689     2  0.1841     0.7782 0.000 0.920 0.000 0.064 0.008 0.008
#> GSM317691     6  0.5340     0.5756 0.144 0.000 0.004 0.064 0.096 0.692
#> GSM317692     2  0.7539     0.2677 0.012 0.420 0.000 0.152 0.172 0.244
#> GSM317693     1  0.5419     0.0553 0.476 0.000 0.000 0.016 0.072 0.436
#> GSM317696     1  0.0820     0.7095 0.972 0.000 0.000 0.000 0.012 0.016
#> GSM317697     1  0.4482     0.5802 0.736 0.000 0.000 0.016 0.096 0.152
#> GSM317698     1  0.0653     0.7069 0.980 0.000 0.000 0.004 0.004 0.012
#> GSM317650     2  0.0891     0.7870 0.000 0.968 0.000 0.024 0.008 0.000
#> GSM317651     5  0.6277     0.5032 0.172 0.000 0.064 0.012 0.600 0.152
#> GSM317657     4  0.2803     0.8644 0.000 0.064 0.000 0.872 0.012 0.052
#> GSM317667     4  0.2169     0.8763 0.000 0.080 0.000 0.900 0.008 0.012
#> GSM317670     2  0.6448     0.2916 0.004 0.500 0.000 0.324 0.092 0.080
#> GSM317674     1  0.0291     0.7085 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM317675     1  0.0146     0.7090 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM317677     6  0.4524     0.2698 0.452 0.000 0.000 0.024 0.004 0.520
#> GSM317678     2  0.0767     0.7825 0.000 0.976 0.000 0.004 0.008 0.012
#> GSM317687     6  0.4203     0.5557 0.016 0.000 0.000 0.288 0.016 0.680
#> GSM317695     3  0.0937     0.7553 0.040 0.000 0.960 0.000 0.000 0.000
#> GSM317653     5  0.5428     0.5032 0.000 0.080 0.000 0.112 0.680 0.128
#> GSM317656     1  0.6474     0.0723 0.480 0.000 0.352 0.016 0.112 0.040
#> GSM317658     2  0.5728     0.6406 0.044 0.692 0.000 0.060 0.096 0.108
#> GSM317660     5  0.4353     0.6226 0.000 0.032 0.288 0.004 0.672 0.004
#> GSM317663     4  0.2476     0.8858 0.000 0.092 0.000 0.880 0.004 0.024
#> GSM317664     1  0.0260     0.7090 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM317665     5  0.4022     0.5485 0.004 0.008 0.360 0.000 0.628 0.000
#> GSM317673     1  0.2883     0.6938 0.864 0.000 0.000 0.008 0.060 0.068
#> GSM317686     4  0.2544     0.8567 0.000 0.140 0.000 0.852 0.004 0.004
#> GSM317688     1  0.6871     0.4795 0.556 0.000 0.076 0.036 0.200 0.132
#> GSM317690     2  0.4090     0.6397 0.000 0.748 0.000 0.192 0.048 0.012
#> GSM317654     5  0.4592     0.6556 0.000 0.000 0.240 0.004 0.680 0.076
#> GSM317655     4  0.3394     0.8429 0.000 0.104 0.000 0.832 0.028 0.036
#> GSM317659     6  0.5220     0.6729 0.156 0.000 0.000 0.152 0.024 0.668
#> GSM317661     2  0.1524     0.7790 0.000 0.932 0.000 0.060 0.008 0.000
#> GSM317662     2  0.0972     0.7867 0.000 0.964 0.000 0.028 0.008 0.000
#> GSM317668     3  0.7673     0.1317 0.196 0.004 0.452 0.032 0.212 0.104
#> GSM317669     3  0.0000     0.7860 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM317671     3  0.0000     0.7860 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM317676     6  0.4262     0.3041 0.004 0.000 0.000 0.424 0.012 0.560
#> GSM317680     3  0.0000     0.7860 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM317684     6  0.4228     0.6111 0.184 0.000 0.000 0.028 0.040 0.748
#> GSM317685     1  0.4303     0.6426 0.752 0.000 0.000 0.012 0.108 0.128
#> GSM317694     1  0.3966    -0.1444 0.552 0.000 0.000 0.004 0.000 0.444

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 disease.state(p) k
#> SD:skmeans 49            0.553 2
#> SD:skmeans 50            0.689 3
#> SD:skmeans 48            0.738 4
#> SD:skmeans 36            0.814 5
#> SD:skmeans 39            0.680 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 11993 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 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-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 0.916           0.962       0.982         0.4548 0.542   0.542
#> 3 3 0.652           0.772       0.833         0.2366 0.851   0.726
#> 4 4 0.733           0.868       0.927         0.1689 0.901   0.764
#> 5 5 0.739           0.781       0.874         0.0768 0.984   0.952
#> 6 6 0.676           0.632       0.838         0.0668 0.961   0.880

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
#> GSM317649     1  0.0000      0.989 1.000 0.000
#> GSM317652     1  0.0000      0.989 1.000 0.000
#> GSM317666     2  0.0672      0.960 0.008 0.992
#> GSM317672     1  0.0000      0.989 1.000 0.000
#> GSM317679     1  0.0376      0.986 0.996 0.004
#> GSM317681     1  0.0000      0.989 1.000 0.000
#> GSM317682     1  0.0000      0.989 1.000 0.000
#> GSM317683     2  0.0000      0.964 0.000 1.000
#> GSM317689     2  0.0000      0.964 0.000 1.000
#> GSM317691     2  0.5519      0.860 0.128 0.872
#> GSM317692     1  0.4939      0.876 0.892 0.108
#> GSM317693     1  0.0000      0.989 1.000 0.000
#> GSM317696     1  0.0000      0.989 1.000 0.000
#> GSM317697     1  0.0000      0.989 1.000 0.000
#> GSM317698     1  0.0000      0.989 1.000 0.000
#> GSM317650     2  0.0000      0.964 0.000 1.000
#> GSM317651     1  0.0000      0.989 1.000 0.000
#> GSM317657     2  0.0000      0.964 0.000 1.000
#> GSM317667     2  0.0000      0.964 0.000 1.000
#> GSM317670     2  0.0000      0.964 0.000 1.000
#> GSM317674     1  0.0000      0.989 1.000 0.000
#> GSM317675     1  0.0000      0.989 1.000 0.000
#> GSM317677     1  0.0000      0.989 1.000 0.000
#> GSM317678     2  0.0672      0.960 0.008 0.992
#> GSM317687     2  0.8081      0.704 0.248 0.752
#> GSM317695     1  0.0000      0.989 1.000 0.000
#> GSM317653     1  0.0000      0.989 1.000 0.000
#> GSM317656     1  0.0000      0.989 1.000 0.000
#> GSM317658     1  0.7528      0.723 0.784 0.216
#> GSM317660     1  0.0672      0.982 0.992 0.008
#> GSM317663     2  0.0000      0.964 0.000 1.000
#> GSM317664     1  0.0000      0.989 1.000 0.000
#> GSM317665     1  0.0000      0.989 1.000 0.000
#> GSM317673     1  0.0000      0.989 1.000 0.000
#> GSM317686     2  0.0000      0.964 0.000 1.000
#> GSM317688     1  0.0000      0.989 1.000 0.000
#> GSM317690     2  0.0000      0.964 0.000 1.000
#> GSM317654     1  0.0000      0.989 1.000 0.000
#> GSM317655     2  0.0000      0.964 0.000 1.000
#> GSM317659     1  0.0000      0.989 1.000 0.000
#> GSM317661     2  0.0000      0.964 0.000 1.000
#> GSM317662     2  0.0000      0.964 0.000 1.000
#> GSM317668     1  0.0000      0.989 1.000 0.000
#> GSM317669     1  0.0000      0.989 1.000 0.000
#> GSM317671     1  0.0000      0.989 1.000 0.000
#> GSM317676     2  0.6801      0.802 0.180 0.820
#> GSM317680     1  0.0000      0.989 1.000 0.000
#> GSM317684     1  0.0000      0.989 1.000 0.000
#> GSM317685     1  0.0000      0.989 1.000 0.000
#> GSM317694     1  0.0000      0.989 1.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> GSM317649     3  0.0237      0.814 0.004 0.000 0.996
#> GSM317652     1  0.6308      0.898 0.508 0.000 0.492
#> GSM317666     2  0.6307      0.828 0.488 0.512 0.000
#> GSM317672     1  0.8646      0.628 0.556 0.124 0.320
#> GSM317679     3  0.2096      0.743 0.052 0.004 0.944
#> GSM317681     1  0.8953      0.327 0.560 0.260 0.180
#> GSM317682     1  0.6307      0.895 0.512 0.000 0.488
#> GSM317683     2  0.0000      0.713 0.000 1.000 0.000
#> GSM317689     2  0.6154      0.829 0.408 0.592 0.000
#> GSM317691     2  0.8708      0.744 0.404 0.488 0.108
#> GSM317692     1  0.6416      0.715 0.616 0.008 0.376
#> GSM317693     1  0.6244      0.840 0.560 0.000 0.440
#> GSM317696     1  0.6308      0.898 0.508 0.000 0.492
#> GSM317697     1  0.6244      0.840 0.560 0.000 0.440
#> GSM317698     1  0.6308      0.898 0.508 0.000 0.492
#> GSM317650     2  0.0000      0.713 0.000 1.000 0.000
#> GSM317651     1  0.6308      0.898 0.508 0.000 0.492
#> GSM317657     2  0.6302      0.829 0.480 0.520 0.000
#> GSM317667     2  0.6244      0.830 0.440 0.560 0.000
#> GSM317670     2  0.6204      0.832 0.424 0.576 0.000
#> GSM317674     1  0.6308      0.898 0.508 0.000 0.492
#> GSM317675     1  0.6308      0.898 0.508 0.000 0.492
#> GSM317677     1  0.6308      0.898 0.508 0.000 0.492
#> GSM317678     2  0.1289      0.709 0.032 0.968 0.000
#> GSM317687     2  0.9356      0.620 0.368 0.460 0.172
#> GSM317695     3  0.0000      0.818 0.000 0.000 1.000
#> GSM317653     1  0.6244      0.840 0.560 0.000 0.440
#> GSM317656     1  0.6308      0.898 0.508 0.000 0.492
#> GSM317658     1  0.9014      0.326 0.560 0.208 0.232
#> GSM317660     3  0.6680     -0.872 0.484 0.008 0.508
#> GSM317663     2  0.6302      0.829 0.480 0.520 0.000
#> GSM317664     1  0.6308      0.898 0.508 0.000 0.492
#> GSM317665     1  0.6308      0.898 0.508 0.000 0.492
#> GSM317673     1  0.6308      0.898 0.508 0.000 0.492
#> GSM317686     2  0.6244      0.830 0.440 0.560 0.000
#> GSM317688     1  0.6307      0.895 0.512 0.000 0.488
#> GSM317690     2  0.6126      0.832 0.400 0.600 0.000
#> GSM317654     1  0.6302      0.887 0.520 0.000 0.480
#> GSM317655     2  0.6291      0.831 0.468 0.532 0.000
#> GSM317659     1  0.6308      0.898 0.508 0.000 0.492
#> GSM317661     2  0.0000      0.713 0.000 1.000 0.000
#> GSM317662     2  0.0000      0.713 0.000 1.000 0.000
#> GSM317668     1  0.6308      0.898 0.508 0.000 0.492
#> GSM317669     3  0.0000      0.818 0.000 0.000 1.000
#> GSM317671     3  0.0000      0.818 0.000 0.000 1.000
#> GSM317676     2  0.9050      0.706 0.376 0.484 0.140
#> GSM317680     3  0.0000      0.818 0.000 0.000 1.000
#> GSM317684     1  0.6267      0.855 0.548 0.000 0.452
#> GSM317685     1  0.6308      0.898 0.508 0.000 0.492
#> GSM317694     1  0.6308      0.898 0.508 0.000 0.492

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM317649     3  0.2704      0.909 0.124 0.000 0.876 0.000
#> GSM317652     1  0.0188      0.931 0.996 0.000 0.004 0.000
#> GSM317666     4  0.0000      0.871 0.000 0.000 0.000 1.000
#> GSM317672     1  0.4888      0.776 0.780 0.124 0.000 0.096
#> GSM317679     3  0.2081      0.831 0.000 0.000 0.916 0.084
#> GSM317681     2  0.6020      0.536 0.220 0.684 0.004 0.092
#> GSM317682     1  0.0188      0.931 0.996 0.000 0.004 0.000
#> GSM317683     2  0.0000      0.903 0.000 1.000 0.000 0.000
#> GSM317689     4  0.2281      0.839 0.000 0.096 0.000 0.904
#> GSM317691     4  0.2814      0.788 0.132 0.000 0.000 0.868
#> GSM317692     1  0.3649      0.793 0.796 0.000 0.000 0.204
#> GSM317693     1  0.2944      0.856 0.868 0.000 0.004 0.128
#> GSM317696     1  0.0188      0.931 0.996 0.000 0.004 0.000
#> GSM317697     1  0.2944      0.856 0.868 0.000 0.004 0.128
#> GSM317698     1  0.0188      0.931 0.996 0.000 0.004 0.000
#> GSM317650     2  0.0000      0.903 0.000 1.000 0.000 0.000
#> GSM317651     1  0.0000      0.931 1.000 0.000 0.000 0.000
#> GSM317657     4  0.0336      0.872 0.000 0.008 0.000 0.992
#> GSM317667     4  0.3354      0.818 0.000 0.044 0.084 0.872
#> GSM317670     4  0.1637      0.863 0.000 0.060 0.000 0.940
#> GSM317674     1  0.0188      0.931 0.996 0.000 0.004 0.000
#> GSM317675     1  0.0000      0.931 1.000 0.000 0.000 0.000
#> GSM317677     1  0.0000      0.931 1.000 0.000 0.000 0.000
#> GSM317678     2  0.0817      0.888 0.000 0.976 0.000 0.024
#> GSM317687     4  0.3837      0.669 0.224 0.000 0.000 0.776
#> GSM317695     3  0.2081      0.955 0.084 0.000 0.916 0.000
#> GSM317653     1  0.2760      0.855 0.872 0.000 0.000 0.128
#> GSM317656     1  0.0188      0.931 0.996 0.000 0.004 0.000
#> GSM317658     1  0.6840      0.511 0.600 0.180 0.000 0.220
#> GSM317660     1  0.3791      0.716 0.796 0.004 0.200 0.000
#> GSM317663     4  0.0336      0.872 0.000 0.008 0.000 0.992
#> GSM317664     1  0.0188      0.931 0.996 0.000 0.004 0.000
#> GSM317665     1  0.0188      0.931 0.996 0.000 0.004 0.000
#> GSM317673     1  0.0188      0.931 0.996 0.000 0.004 0.000
#> GSM317686     4  0.3354      0.818 0.000 0.044 0.084 0.872
#> GSM317688     1  0.0188      0.931 0.996 0.000 0.004 0.000
#> GSM317690     4  0.3172      0.795 0.000 0.160 0.000 0.840
#> GSM317654     1  0.1488      0.914 0.956 0.000 0.012 0.032
#> GSM317655     4  0.0707      0.872 0.000 0.020 0.000 0.980
#> GSM317659     1  0.0000      0.931 1.000 0.000 0.000 0.000
#> GSM317661     2  0.0336      0.900 0.000 0.992 0.000 0.008
#> GSM317662     2  0.0000      0.903 0.000 1.000 0.000 0.000
#> GSM317668     1  0.0188      0.931 0.996 0.000 0.004 0.000
#> GSM317669     3  0.2081      0.955 0.084 0.000 0.916 0.000
#> GSM317671     3  0.2081      0.955 0.084 0.000 0.916 0.000
#> GSM317676     4  0.3219      0.752 0.164 0.000 0.000 0.836
#> GSM317680     3  0.2081      0.955 0.084 0.000 0.916 0.000
#> GSM317684     1  0.2647      0.861 0.880 0.000 0.000 0.120
#> GSM317685     1  0.0000      0.931 1.000 0.000 0.000 0.000
#> GSM317694     1  0.0000      0.931 1.000 0.000 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
#> GSM317649     3  0.1043      0.931 0.040 0.000 0.960 0.000 0.000
#> GSM317652     1  0.0000      0.828 1.000 0.000 0.000 0.000 0.000
#> GSM317666     4  0.1965      0.843 0.000 0.000 0.000 0.904 0.096
#> GSM317672     1  0.5373      0.581 0.632 0.092 0.000 0.276 0.000
#> GSM317679     3  0.0000      0.987 0.000 0.000 1.000 0.000 0.000
#> GSM317681     2  0.5107      0.528 0.108 0.688 0.000 0.204 0.000
#> GSM317682     1  0.0880      0.822 0.968 0.000 0.000 0.032 0.000
#> GSM317683     2  0.0000      0.905 0.000 1.000 0.000 0.000 0.000
#> GSM317689     4  0.4360      0.721 0.000 0.184 0.000 0.752 0.064
#> GSM317691     4  0.1082      0.800 0.028 0.000 0.000 0.964 0.008
#> GSM317692     1  0.4872      0.396 0.540 0.000 0.000 0.436 0.024
#> GSM317693     1  0.4210      0.467 0.588 0.000 0.000 0.412 0.000
#> GSM317696     1  0.0794      0.824 0.972 0.000 0.000 0.028 0.000
#> GSM317697     1  0.4219      0.460 0.584 0.000 0.000 0.416 0.000
#> GSM317698     1  0.0703      0.825 0.976 0.000 0.000 0.024 0.000
#> GSM317650     2  0.0000      0.905 0.000 1.000 0.000 0.000 0.000
#> GSM317651     1  0.1671      0.812 0.924 0.000 0.000 0.076 0.000
#> GSM317657     4  0.2304      0.845 0.000 0.008 0.000 0.892 0.100
#> GSM317667     5  0.0000      1.000 0.000 0.000 0.000 0.000 1.000
#> GSM317670     4  0.2795      0.842 0.000 0.028 0.000 0.872 0.100
#> GSM317674     1  0.0000      0.828 1.000 0.000 0.000 0.000 0.000
#> GSM317675     1  0.0290      0.828 0.992 0.000 0.000 0.008 0.000
#> GSM317677     1  0.1671      0.812 0.924 0.000 0.000 0.076 0.000
#> GSM317678     2  0.0703      0.890 0.000 0.976 0.000 0.024 0.000
#> GSM317687     4  0.1544      0.776 0.068 0.000 0.000 0.932 0.000
#> GSM317695     3  0.0000      0.987 0.000 0.000 1.000 0.000 0.000
#> GSM317653     1  0.4291      0.418 0.536 0.000 0.000 0.464 0.000
#> GSM317656     1  0.0162      0.828 0.996 0.000 0.000 0.004 0.000
#> GSM317658     1  0.6328      0.262 0.448 0.136 0.000 0.412 0.004
#> GSM317660     1  0.3300      0.698 0.792 0.004 0.204 0.000 0.000
#> GSM317663     4  0.2304      0.845 0.000 0.008 0.000 0.892 0.100
#> GSM317664     1  0.0000      0.828 1.000 0.000 0.000 0.000 0.000
#> GSM317665     1  0.0000      0.828 1.000 0.000 0.000 0.000 0.000
#> GSM317673     1  0.0609      0.826 0.980 0.000 0.000 0.020 0.000
#> GSM317686     5  0.0000      1.000 0.000 0.000 0.000 0.000 1.000
#> GSM317688     1  0.0963      0.822 0.964 0.000 0.000 0.036 0.000
#> GSM317690     4  0.5700      0.311 0.000 0.380 0.000 0.532 0.088
#> GSM317654     1  0.2488      0.797 0.872 0.000 0.004 0.124 0.000
#> GSM317655     4  0.2795      0.842 0.000 0.028 0.000 0.872 0.100
#> GSM317659     1  0.1671      0.812 0.924 0.000 0.000 0.076 0.000
#> GSM317661     2  0.0162      0.904 0.000 0.996 0.000 0.004 0.000
#> GSM317662     2  0.0000      0.905 0.000 1.000 0.000 0.000 0.000
#> GSM317668     1  0.0162      0.828 0.996 0.000 0.004 0.000 0.000
#> GSM317669     3  0.0000      0.987 0.000 0.000 1.000 0.000 0.000
#> GSM317671     3  0.0000      0.987 0.000 0.000 1.000 0.000 0.000
#> GSM317676     4  0.1478      0.785 0.064 0.000 0.000 0.936 0.000
#> GSM317680     3  0.0000      0.987 0.000 0.000 1.000 0.000 0.000
#> GSM317684     1  0.4256      0.466 0.564 0.000 0.000 0.436 0.000
#> GSM317685     1  0.1544      0.815 0.932 0.000 0.000 0.068 0.000
#> GSM317694     1  0.1608      0.813 0.928 0.000 0.000 0.072 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
#> GSM317649     3  0.0937     0.9344 0.040 0.000 0.960 0.000 0.000  0
#> GSM317652     1  0.0000     0.6707 1.000 0.000 0.000 0.000 0.000  0
#> GSM317666     4  0.2118     0.7355 0.008 0.000 0.000 0.888 0.104  0
#> GSM317672     1  0.5657     0.4288 0.652 0.100 0.000 0.164 0.084  0
#> GSM317679     3  0.0000     0.9871 0.000 0.000 1.000 0.000 0.000  0
#> GSM317681     2  0.6250     0.4605 0.108 0.592 0.000 0.152 0.148  0
#> GSM317682     1  0.2006     0.6510 0.904 0.000 0.000 0.016 0.080  0
#> GSM317683     2  0.0000     0.8723 0.000 1.000 0.000 0.000 0.000  0
#> GSM317689     4  0.1753     0.7547 0.000 0.084 0.000 0.912 0.004  0
#> GSM317691     4  0.2883     0.6466 0.000 0.000 0.000 0.788 0.212  0
#> GSM317692     1  0.4986     0.3530 0.612 0.000 0.000 0.284 0.104  0
#> GSM317693     1  0.4723     0.4135 0.664 0.000 0.000 0.232 0.104  0
#> GSM317696     1  0.1367     0.6672 0.944 0.000 0.000 0.012 0.044  0
#> GSM317697     1  0.4503     0.4351 0.684 0.000 0.000 0.232 0.084  0
#> GSM317698     1  0.0806     0.6713 0.972 0.000 0.000 0.008 0.020  0
#> GSM317650     2  0.0000     0.8723 0.000 1.000 0.000 0.000 0.000  0
#> GSM317651     1  0.2854     0.4827 0.792 0.000 0.000 0.000 0.208  0
#> GSM317657     4  0.0260     0.7700 0.000 0.008 0.000 0.992 0.000  0
#> GSM317667     6  0.0000     1.0000 0.000 0.000 0.000 0.000 0.000  1
#> GSM317670     4  0.3217     0.6752 0.000 0.008 0.000 0.768 0.224  0
#> GSM317674     1  0.0000     0.6707 1.000 0.000 0.000 0.000 0.000  0
#> GSM317675     1  0.0363     0.6679 0.988 0.000 0.000 0.000 0.012  0
#> GSM317677     1  0.2883     0.4749 0.788 0.000 0.000 0.000 0.212  0
#> GSM317678     2  0.0935     0.8548 0.000 0.964 0.000 0.004 0.032  0
#> GSM317687     4  0.4065     0.5380 0.028 0.000 0.000 0.672 0.300  0
#> GSM317695     3  0.0000     0.9871 0.000 0.000 1.000 0.000 0.000  0
#> GSM317653     5  0.5348     0.5007 0.192 0.000 0.000 0.216 0.592  0
#> GSM317656     1  0.0000     0.6707 1.000 0.000 0.000 0.000 0.000  0
#> GSM317658     1  0.6641     0.1813 0.504 0.144 0.000 0.264 0.088  0
#> GSM317660     1  0.5980    -0.3780 0.460 0.004 0.208 0.000 0.328  0
#> GSM317663     4  0.0260     0.7700 0.000 0.008 0.000 0.992 0.000  0
#> GSM317664     1  0.0000     0.6707 1.000 0.000 0.000 0.000 0.000  0
#> GSM317665     1  0.3482    -0.0597 0.684 0.000 0.000 0.000 0.316  0
#> GSM317673     1  0.0692     0.6718 0.976 0.000 0.000 0.004 0.020  0
#> GSM317686     6  0.0000     1.0000 0.000 0.000 0.000 0.000 0.000  1
#> GSM317688     1  0.1895     0.6561 0.912 0.000 0.000 0.016 0.072  0
#> GSM317690     4  0.3314     0.6744 0.000 0.012 0.000 0.764 0.224  0
#> GSM317654     5  0.4642     0.3763 0.452 0.000 0.000 0.040 0.508  0
#> GSM317655     4  0.3217     0.6752 0.000 0.008 0.000 0.768 0.224  0
#> GSM317659     1  0.2996     0.4508 0.772 0.000 0.000 0.000 0.228  0
#> GSM317661     2  0.2006     0.8154 0.000 0.892 0.000 0.004 0.104  0
#> GSM317662     2  0.0000     0.8723 0.000 1.000 0.000 0.000 0.000  0
#> GSM317668     1  0.2595     0.5676 0.836 0.000 0.004 0.000 0.160  0
#> GSM317669     3  0.0000     0.9871 0.000 0.000 1.000 0.000 0.000  0
#> GSM317671     3  0.0000     0.9871 0.000 0.000 1.000 0.000 0.000  0
#> GSM317676     4  0.3885     0.5878 0.044 0.000 0.000 0.736 0.220  0
#> GSM317680     3  0.0000     0.9871 0.000 0.000 1.000 0.000 0.000  0
#> GSM317684     1  0.5524     0.0791 0.560 0.000 0.000 0.204 0.236  0
#> GSM317685     1  0.2178     0.5857 0.868 0.000 0.000 0.000 0.132  0
#> GSM317694     1  0.2003     0.5962 0.884 0.000 0.000 0.000 0.116  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-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 disease.state(p) k
#> SD:pam 50            0.438 2
#> SD:pam 47            0.569 3
#> SD:pam 50            0.602 4
#> SD:pam 43            0.713 5
#> SD:pam 37            0.670 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 11993 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 3.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

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 0.711           0.864       0.927         0.3853 0.607   0.607
#> 3 3 0.850           0.898       0.955         0.6485 0.634   0.455
#> 4 4 0.682           0.756       0.888         0.0331 0.758   0.507
#> 5 5 0.765           0.781       0.897         0.1070 0.907   0.755
#> 6 6 0.760           0.772       0.884         0.0803 0.841   0.527

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] 3

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
#> GSM317649     1  0.3431      0.919 0.936 0.064
#> GSM317652     1  0.3431      0.919 0.936 0.064
#> GSM317666     1  0.7602      0.705 0.780 0.220
#> GSM317672     1  0.5408      0.898 0.876 0.124
#> GSM317679     1  0.3431      0.919 0.936 0.064
#> GSM317681     1  0.8499      0.679 0.724 0.276
#> GSM317682     1  0.1843      0.932 0.972 0.028
#> GSM317683     2  0.0000      0.850 0.000 1.000
#> GSM317689     2  0.7376      0.702 0.208 0.792
#> GSM317691     1  0.2603      0.927 0.956 0.044
#> GSM317692     1  0.2603      0.927 0.956 0.044
#> GSM317693     1  0.0000      0.936 1.000 0.000
#> GSM317696     1  0.0000      0.936 1.000 0.000
#> GSM317697     1  0.0000      0.936 1.000 0.000
#> GSM317698     1  0.0000      0.936 1.000 0.000
#> GSM317650     2  0.0000      0.850 0.000 1.000
#> GSM317651     1  0.0938      0.936 0.988 0.012
#> GSM317657     2  0.9815      0.425 0.420 0.580
#> GSM317667     2  0.3431      0.838 0.064 0.936
#> GSM317670     2  0.9909      0.356 0.444 0.556
#> GSM317674     1  0.0000      0.936 1.000 0.000
#> GSM317675     1  0.0938      0.935 0.988 0.012
#> GSM317677     1  0.2603      0.927 0.956 0.044
#> GSM317678     2  0.0000      0.850 0.000 1.000
#> GSM317687     1  0.2603      0.927 0.956 0.044
#> GSM317695     1  0.3431      0.919 0.936 0.064
#> GSM317653     1  0.7602      0.731 0.780 0.220
#> GSM317656     1  0.0672      0.936 0.992 0.008
#> GSM317658     1  0.3879      0.904 0.924 0.076
#> GSM317660     1  0.3879      0.915 0.924 0.076
#> GSM317663     2  0.9686      0.479 0.396 0.604
#> GSM317664     1  0.0000      0.936 1.000 0.000
#> GSM317665     1  0.3431      0.919 0.936 0.064
#> GSM317673     1  0.0000      0.936 1.000 0.000
#> GSM317686     2  0.3431      0.838 0.064 0.936
#> GSM317688     1  0.0000      0.936 1.000 0.000
#> GSM317690     2  0.0376      0.850 0.004 0.996
#> GSM317654     1  0.3431      0.919 0.936 0.064
#> GSM317655     2  0.3431      0.838 0.064 0.936
#> GSM317659     1  0.2603      0.927 0.956 0.044
#> GSM317661     2  0.0000      0.850 0.000 1.000
#> GSM317662     2  0.0000      0.850 0.000 1.000
#> GSM317668     1  0.0672      0.936 0.992 0.008
#> GSM317669     1  0.3431      0.919 0.936 0.064
#> GSM317671     1  0.3431      0.919 0.936 0.064
#> GSM317676     1  0.3274      0.917 0.940 0.060
#> GSM317680     1  0.3431      0.919 0.936 0.064
#> GSM317684     1  0.2603      0.927 0.956 0.044
#> GSM317685     1  0.0000      0.936 1.000 0.000
#> GSM317694     1  0.2603      0.927 0.956 0.044

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> GSM317649     3  0.0000      0.926 0.000 0.000 1.000
#> GSM317652     1  0.6062      0.416 0.616 0.000 0.384
#> GSM317666     2  0.0829      0.976 0.004 0.984 0.012
#> GSM317672     2  0.0237      0.978 0.004 0.996 0.000
#> GSM317679     3  0.0000      0.926 0.000 0.000 1.000
#> GSM317681     2  0.0747      0.974 0.000 0.984 0.016
#> GSM317682     1  0.3816      0.812 0.852 0.000 0.148
#> GSM317683     2  0.0000      0.977 0.000 1.000 0.000
#> GSM317689     2  0.0237      0.978 0.004 0.996 0.000
#> GSM317691     1  0.0000      0.929 1.000 0.000 0.000
#> GSM317692     1  0.3851      0.801 0.860 0.136 0.004
#> GSM317693     1  0.0237      0.930 0.996 0.000 0.004
#> GSM317696     1  0.0424      0.931 0.992 0.000 0.008
#> GSM317697     1  0.0424      0.931 0.992 0.000 0.008
#> GSM317698     1  0.0424      0.931 0.992 0.000 0.008
#> GSM317650     2  0.0000      0.977 0.000 1.000 0.000
#> GSM317651     1  0.5254      0.662 0.736 0.000 0.264
#> GSM317657     2  0.0237      0.978 0.004 0.996 0.000
#> GSM317667     2  0.0592      0.975 0.000 0.988 0.012
#> GSM317670     2  0.1753      0.940 0.048 0.952 0.000
#> GSM317674     1  0.0424      0.931 0.992 0.000 0.008
#> GSM317675     1  0.0237      0.930 0.996 0.000 0.004
#> GSM317677     1  0.0000      0.929 1.000 0.000 0.000
#> GSM317678     2  0.0237      0.978 0.004 0.996 0.000
#> GSM317687     1  0.3116      0.833 0.892 0.108 0.000
#> GSM317695     1  0.0592      0.929 0.988 0.000 0.012
#> GSM317653     2  0.1751      0.959 0.028 0.960 0.012
#> GSM317656     1  0.0424      0.931 0.992 0.000 0.008
#> GSM317658     2  0.3983      0.805 0.144 0.852 0.004
#> GSM317660     3  0.0424      0.923 0.000 0.008 0.992
#> GSM317663     2  0.0829      0.976 0.004 0.984 0.012
#> GSM317664     1  0.0424      0.931 0.992 0.000 0.008
#> GSM317665     3  0.0424      0.923 0.008 0.000 0.992
#> GSM317673     1  0.0237      0.930 0.996 0.000 0.004
#> GSM317686     2  0.0592      0.975 0.000 0.988 0.012
#> GSM317688     1  0.0424      0.931 0.992 0.000 0.008
#> GSM317690     2  0.0237      0.978 0.004 0.996 0.000
#> GSM317654     3  0.6192      0.148 0.420 0.000 0.580
#> GSM317655     2  0.0829      0.976 0.004 0.984 0.012
#> GSM317659     1  0.0000      0.929 1.000 0.000 0.000
#> GSM317661     2  0.0000      0.977 0.000 1.000 0.000
#> GSM317662     2  0.0000      0.977 0.000 1.000 0.000
#> GSM317668     1  0.5363      0.621 0.724 0.000 0.276
#> GSM317669     3  0.0000      0.926 0.000 0.000 1.000
#> GSM317671     3  0.0892      0.914 0.020 0.000 0.980
#> GSM317676     2  0.1411      0.957 0.036 0.964 0.000
#> GSM317680     3  0.0000      0.926 0.000 0.000 1.000
#> GSM317684     1  0.0000      0.929 1.000 0.000 0.000
#> GSM317685     1  0.0424      0.931 0.992 0.000 0.008
#> GSM317694     1  0.0000      0.929 1.000 0.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM317649     3  0.0188      0.801 0.004 0.000 0.996 0.000
#> GSM317652     3  0.4624      0.505 0.340 0.000 0.660 0.000
#> GSM317666     4  0.2021      0.947 0.012 0.056 0.000 0.932
#> GSM317672     1  0.3726      0.713 0.788 0.212 0.000 0.000
#> GSM317679     3  0.0188      0.801 0.004 0.000 0.996 0.000
#> GSM317681     3  0.6985      0.465 0.312 0.140 0.548 0.000
#> GSM317682     1  0.3074      0.746 0.848 0.000 0.152 0.000
#> GSM317683     2  0.0000      0.951 0.000 1.000 0.000 0.000
#> GSM317689     2  0.3266      0.700 0.168 0.832 0.000 0.000
#> GSM317691     1  0.1557      0.840 0.944 0.000 0.000 0.056
#> GSM317692     1  0.1557      0.828 0.944 0.056 0.000 0.000
#> GSM317693     1  0.1557      0.840 0.944 0.000 0.000 0.056
#> GSM317696     1  0.0000      0.845 1.000 0.000 0.000 0.000
#> GSM317697     1  0.0000      0.845 1.000 0.000 0.000 0.000
#> GSM317698     1  0.0000      0.845 1.000 0.000 0.000 0.000
#> GSM317650     2  0.0000      0.951 0.000 1.000 0.000 0.000
#> GSM317651     1  0.3688      0.675 0.792 0.000 0.208 0.000
#> GSM317657     1  0.7028      0.387 0.568 0.260 0.000 0.172
#> GSM317667     4  0.1557      0.943 0.000 0.056 0.000 0.944
#> GSM317670     1  0.4972      0.220 0.544 0.456 0.000 0.000
#> GSM317674     1  0.0000      0.845 1.000 0.000 0.000 0.000
#> GSM317675     1  0.0000      0.845 1.000 0.000 0.000 0.000
#> GSM317677     1  0.1557      0.840 0.944 0.000 0.000 0.056
#> GSM317678     2  0.0000      0.951 0.000 1.000 0.000 0.000
#> GSM317687     1  0.2921      0.794 0.860 0.000 0.000 0.140
#> GSM317695     1  0.4331      0.485 0.712 0.000 0.288 0.000
#> GSM317653     1  0.7525     -0.171 0.460 0.056 0.428 0.056
#> GSM317656     1  0.0000      0.845 1.000 0.000 0.000 0.000
#> GSM317658     1  0.4103      0.653 0.744 0.256 0.000 0.000
#> GSM317660     3  0.0336      0.797 0.000 0.008 0.992 0.000
#> GSM317663     4  0.3601      0.879 0.084 0.056 0.000 0.860
#> GSM317664     1  0.0000      0.845 1.000 0.000 0.000 0.000
#> GSM317665     3  0.1118      0.789 0.036 0.000 0.964 0.000
#> GSM317673     1  0.0000      0.845 1.000 0.000 0.000 0.000
#> GSM317686     4  0.1557      0.943 0.000 0.056 0.000 0.944
#> GSM317688     1  0.0000      0.845 1.000 0.000 0.000 0.000
#> GSM317690     2  0.0188      0.947 0.004 0.996 0.000 0.000
#> GSM317654     3  0.4855      0.380 0.400 0.000 0.600 0.000
#> GSM317655     4  0.2751      0.935 0.040 0.056 0.000 0.904
#> GSM317659     1  0.1557      0.840 0.944 0.000 0.000 0.056
#> GSM317661     2  0.0000      0.951 0.000 1.000 0.000 0.000
#> GSM317662     2  0.0000      0.951 0.000 1.000 0.000 0.000
#> GSM317668     1  0.4040      0.609 0.752 0.000 0.248 0.000
#> GSM317669     3  0.0188      0.801 0.004 0.000 0.996 0.000
#> GSM317671     3  0.0817      0.792 0.024 0.000 0.976 0.000
#> GSM317676     1  0.4907      0.373 0.580 0.000 0.000 0.420
#> GSM317680     3  0.0188      0.801 0.004 0.000 0.996 0.000
#> GSM317684     1  0.1557      0.840 0.944 0.000 0.000 0.056
#> GSM317685     1  0.0469      0.844 0.988 0.000 0.012 0.000
#> GSM317694     1  0.1474      0.841 0.948 0.000 0.000 0.052

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> GSM317649     3  0.0404     0.8409 0.012 0.000 0.988 0.000 0.000
#> GSM317652     3  0.3949     0.4558 0.332 0.000 0.668 0.000 0.000
#> GSM317666     4  0.2629     0.7805 0.000 0.004 0.000 0.860 0.136
#> GSM317672     1  0.7141     0.1796 0.440 0.368 0.148 0.044 0.000
#> GSM317679     3  0.0290     0.8423 0.008 0.000 0.992 0.000 0.000
#> GSM317681     3  0.8168     0.0827 0.192 0.148 0.404 0.256 0.000
#> GSM317682     1  0.2719     0.7561 0.852 0.000 0.144 0.000 0.004
#> GSM317683     2  0.0000     0.9910 0.000 1.000 0.000 0.000 0.000
#> GSM317689     2  0.0865     0.9709 0.004 0.972 0.000 0.024 0.000
#> GSM317691     1  0.0510     0.8600 0.984 0.000 0.000 0.016 0.000
#> GSM317692     1  0.1430     0.8448 0.944 0.004 0.000 0.052 0.000
#> GSM317693     1  0.0510     0.8600 0.984 0.000 0.000 0.016 0.000
#> GSM317696     1  0.0000     0.8638 1.000 0.000 0.000 0.000 0.000
#> GSM317697     1  0.0162     0.8630 0.996 0.000 0.000 0.004 0.000
#> GSM317698     1  0.0000     0.8638 1.000 0.000 0.000 0.000 0.000
#> GSM317650     2  0.0000     0.9910 0.000 1.000 0.000 0.000 0.000
#> GSM317651     1  0.3398     0.6853 0.780 0.000 0.216 0.000 0.004
#> GSM317657     4  0.3266     0.6691 0.000 0.200 0.000 0.796 0.004
#> GSM317667     5  0.0162     1.0000 0.000 0.004 0.000 0.000 0.996
#> GSM317670     1  0.6219     0.0655 0.440 0.420 0.000 0.140 0.000
#> GSM317674     1  0.0000     0.8638 1.000 0.000 0.000 0.000 0.000
#> GSM317675     1  0.0000     0.8638 1.000 0.000 0.000 0.000 0.000
#> GSM317677     1  0.3274     0.7346 0.780 0.000 0.000 0.220 0.000
#> GSM317678     2  0.0162     0.9897 0.000 0.996 0.000 0.004 0.000
#> GSM317687     4  0.1608     0.7219 0.072 0.000 0.000 0.928 0.000
#> GSM317695     1  0.3274     0.6636 0.780 0.000 0.220 0.000 0.000
#> GSM317653     4  0.3088     0.6344 0.004 0.000 0.164 0.828 0.004
#> GSM317656     1  0.0000     0.8638 1.000 0.000 0.000 0.000 0.000
#> GSM317658     1  0.3882     0.6862 0.756 0.224 0.000 0.020 0.000
#> GSM317660     3  0.0324     0.8362 0.000 0.000 0.992 0.004 0.004
#> GSM317663     4  0.3732     0.7605 0.000 0.032 0.000 0.792 0.176
#> GSM317664     1  0.0000     0.8638 1.000 0.000 0.000 0.000 0.000
#> GSM317665     3  0.0162     0.8372 0.000 0.000 0.996 0.000 0.004
#> GSM317673     1  0.0000     0.8638 1.000 0.000 0.000 0.000 0.000
#> GSM317686     5  0.0162     1.0000 0.000 0.004 0.000 0.000 0.996
#> GSM317688     1  0.0000     0.8638 1.000 0.000 0.000 0.000 0.000
#> GSM317690     2  0.0566     0.9829 0.004 0.984 0.000 0.012 0.000
#> GSM317654     3  0.2068     0.7741 0.092 0.000 0.904 0.000 0.004
#> GSM317655     4  0.3562     0.7534 0.000 0.016 0.000 0.788 0.196
#> GSM317659     1  0.3508     0.7074 0.748 0.000 0.000 0.252 0.000
#> GSM317661     2  0.0000     0.9910 0.000 1.000 0.000 0.000 0.000
#> GSM317662     2  0.0000     0.9910 0.000 1.000 0.000 0.000 0.000
#> GSM317668     1  0.3913     0.5222 0.676 0.000 0.324 0.000 0.000
#> GSM317669     3  0.0290     0.8423 0.008 0.000 0.992 0.000 0.000
#> GSM317671     3  0.1121     0.8182 0.044 0.000 0.956 0.000 0.000
#> GSM317676     4  0.0404     0.7667 0.012 0.000 0.000 0.988 0.000
#> GSM317680     3  0.0290     0.8423 0.008 0.000 0.992 0.000 0.000
#> GSM317684     1  0.1965     0.8240 0.904 0.000 0.000 0.096 0.000
#> GSM317685     1  0.0000     0.8638 1.000 0.000 0.000 0.000 0.000
#> GSM317694     1  0.0290     0.8625 0.992 0.000 0.000 0.008 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
#> GSM317649     3  0.0363      0.936 0.012 0.000 0.988 0.000 0.000 0.000
#> GSM317652     3  0.4151      0.690 0.176 0.000 0.744 0.004 0.076 0.000
#> GSM317666     4  0.1151      0.698 0.000 0.000 0.000 0.956 0.012 0.032
#> GSM317672     5  0.2952      0.658 0.016 0.068 0.052 0.000 0.864 0.000
#> GSM317679     3  0.0508      0.936 0.012 0.004 0.984 0.000 0.000 0.000
#> GSM317681     5  0.4833      0.574 0.004 0.044 0.232 0.032 0.688 0.000
#> GSM317682     1  0.2558      0.765 0.840 0.000 0.156 0.004 0.000 0.000
#> GSM317683     2  0.0146      0.968 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM317689     5  0.1814      0.645 0.000 0.100 0.000 0.000 0.900 0.000
#> GSM317691     1  0.0603      0.895 0.980 0.000 0.000 0.016 0.004 0.000
#> GSM317692     5  0.4704      0.494 0.236 0.000 0.000 0.100 0.664 0.000
#> GSM317693     1  0.0935      0.884 0.964 0.000 0.000 0.032 0.004 0.000
#> GSM317696     1  0.0000      0.904 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317697     1  0.0291      0.901 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM317698     1  0.0146      0.903 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM317650     2  0.0146      0.968 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM317651     1  0.3421      0.647 0.736 0.000 0.256 0.000 0.008 0.000
#> GSM317657     5  0.3728      0.579 0.000 0.000 0.000 0.344 0.652 0.004
#> GSM317667     6  0.0000      1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM317670     5  0.2159      0.657 0.012 0.072 0.000 0.012 0.904 0.000
#> GSM317674     1  0.0000      0.904 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317675     1  0.0000      0.904 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317677     4  0.3684      0.507 0.332 0.000 0.000 0.664 0.004 0.000
#> GSM317678     2  0.1814      0.881 0.000 0.900 0.000 0.000 0.100 0.000
#> GSM317687     4  0.0725      0.724 0.012 0.000 0.000 0.976 0.012 0.000
#> GSM317695     1  0.4284      0.626 0.728 0.000 0.200 0.008 0.064 0.000
#> GSM317653     5  0.5748      0.365 0.000 0.000 0.176 0.360 0.464 0.000
#> GSM317656     1  0.0000      0.904 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317658     5  0.3189      0.562 0.184 0.020 0.000 0.000 0.796 0.000
#> GSM317660     3  0.0291      0.928 0.000 0.004 0.992 0.000 0.004 0.000
#> GSM317663     5  0.4026      0.570 0.000 0.000 0.000 0.348 0.636 0.016
#> GSM317664     1  0.0000      0.904 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317665     3  0.0937      0.920 0.000 0.000 0.960 0.000 0.040 0.000
#> GSM317673     1  0.0000      0.904 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317686     6  0.0000      1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM317688     1  0.0000      0.904 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317690     5  0.3867     -0.108 0.000 0.488 0.000 0.000 0.512 0.000
#> GSM317654     3  0.2006      0.890 0.016 0.000 0.904 0.000 0.080 0.000
#> GSM317655     5  0.4938      0.538 0.000 0.000 0.000 0.340 0.580 0.080
#> GSM317659     4  0.3109      0.626 0.224 0.000 0.000 0.772 0.004 0.000
#> GSM317661     2  0.0363      0.964 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM317662     2  0.0146      0.968 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM317668     1  0.4535      0.485 0.644 0.000 0.296 0.000 0.060 0.000
#> GSM317669     3  0.0508      0.936 0.012 0.004 0.984 0.000 0.000 0.000
#> GSM317671     3  0.1082      0.914 0.040 0.000 0.956 0.004 0.000 0.000
#> GSM317676     4  0.0363      0.716 0.000 0.000 0.000 0.988 0.012 0.000
#> GSM317680     3  0.0363      0.936 0.012 0.000 0.988 0.000 0.000 0.000
#> GSM317684     1  0.2871      0.707 0.804 0.000 0.000 0.192 0.004 0.000
#> GSM317685     1  0.0000      0.904 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317694     1  0.0603      0.896 0.980 0.000 0.000 0.016 0.004 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 disease.state(p) k
#> SD:mclust 47            0.710 2
#> SD:mclust 48            0.750 3
#> SD:mclust 43            0.918 4
#> SD:mclust 46            0.855 5
#> SD:mclust 46            0.701 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 11993 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 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-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           0.944       0.978         0.4613 0.530   0.530
#> 3 3 0.550           0.684       0.812         0.3717 0.776   0.602
#> 4 4 0.784           0.799       0.909         0.1569 0.770   0.467
#> 5 5 0.743           0.657       0.816         0.0793 0.909   0.676
#> 6 6 0.801           0.777       0.858         0.0403 0.922   0.669

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
#> GSM317649     1  0.0000      0.994 1.000 0.000
#> GSM317652     1  0.0000      0.994 1.000 0.000
#> GSM317666     2  0.0000      0.945 0.000 1.000
#> GSM317672     2  0.2236      0.920 0.036 0.964
#> GSM317679     1  0.0376      0.990 0.996 0.004
#> GSM317681     2  0.0376      0.942 0.004 0.996
#> GSM317682     1  0.0000      0.994 1.000 0.000
#> GSM317683     2  0.0000      0.945 0.000 1.000
#> GSM317689     2  0.0000      0.945 0.000 1.000
#> GSM317691     1  0.0000      0.994 1.000 0.000
#> GSM317692     1  0.6623      0.777 0.828 0.172
#> GSM317693     1  0.0000      0.994 1.000 0.000
#> GSM317696     1  0.0000      0.994 1.000 0.000
#> GSM317697     1  0.0000      0.994 1.000 0.000
#> GSM317698     1  0.0000      0.994 1.000 0.000
#> GSM317650     2  0.0000      0.945 0.000 1.000
#> GSM317651     1  0.0000      0.994 1.000 0.000
#> GSM317657     2  0.0000      0.945 0.000 1.000
#> GSM317667     2  0.0000      0.945 0.000 1.000
#> GSM317670     2  0.2603      0.913 0.044 0.956
#> GSM317674     1  0.0000      0.994 1.000 0.000
#> GSM317675     1  0.0000      0.994 1.000 0.000
#> GSM317677     1  0.0000      0.994 1.000 0.000
#> GSM317678     2  0.0000      0.945 0.000 1.000
#> GSM317687     1  0.0000      0.994 1.000 0.000
#> GSM317695     1  0.0000      0.994 1.000 0.000
#> GSM317653     2  0.9608      0.398 0.384 0.616
#> GSM317656     1  0.0000      0.994 1.000 0.000
#> GSM317658     2  0.9933      0.198 0.452 0.548
#> GSM317660     1  0.0376      0.990 0.996 0.004
#> GSM317663     2  0.0000      0.945 0.000 1.000
#> GSM317664     1  0.0000      0.994 1.000 0.000
#> GSM317665     1  0.0000      0.994 1.000 0.000
#> GSM317673     1  0.0000      0.994 1.000 0.000
#> GSM317686     2  0.0000      0.945 0.000 1.000
#> GSM317688     1  0.0000      0.994 1.000 0.000
#> GSM317690     2  0.0000      0.945 0.000 1.000
#> GSM317654     1  0.0000      0.994 1.000 0.000
#> GSM317655     2  0.0000      0.945 0.000 1.000
#> GSM317659     1  0.0000      0.994 1.000 0.000
#> GSM317661     2  0.0000      0.945 0.000 1.000
#> GSM317662     2  0.0000      0.945 0.000 1.000
#> GSM317668     1  0.0000      0.994 1.000 0.000
#> GSM317669     1  0.0000      0.994 1.000 0.000
#> GSM317671     1  0.0376      0.990 0.996 0.004
#> GSM317676     1  0.0000      0.994 1.000 0.000
#> GSM317680     1  0.0000      0.994 1.000 0.000
#> GSM317684     1  0.0000      0.994 1.000 0.000
#> GSM317685     1  0.0000      0.994 1.000 0.000
#> GSM317694     1  0.0000      0.994 1.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> GSM317649     1  0.0592      0.783 0.988 0.012 0.000
#> GSM317652     1  0.0892      0.795 0.980 0.000 0.020
#> GSM317666     3  0.4504      0.635 0.000 0.196 0.804
#> GSM317672     2  0.3551      0.771 0.132 0.868 0.000
#> GSM317679     1  0.1529      0.763 0.960 0.040 0.000
#> GSM317681     2  0.4452      0.713 0.192 0.808 0.000
#> GSM317682     1  0.0237      0.787 0.996 0.004 0.000
#> GSM317683     2  0.0424      0.841 0.000 0.992 0.008
#> GSM317689     2  0.0592      0.839 0.000 0.988 0.012
#> GSM317691     1  0.6244      0.569 0.560 0.000 0.440
#> GSM317692     1  0.7718      0.663 0.612 0.068 0.320
#> GSM317693     3  0.6079     -0.163 0.388 0.000 0.612
#> GSM317696     1  0.5138      0.793 0.748 0.000 0.252
#> GSM317697     1  0.5465      0.773 0.712 0.000 0.288
#> GSM317698     1  0.5650      0.752 0.688 0.000 0.312
#> GSM317650     2  0.0747      0.843 0.016 0.984 0.000
#> GSM317651     1  0.5058      0.796 0.756 0.000 0.244
#> GSM317657     3  0.5327      0.591 0.000 0.272 0.728
#> GSM317667     3  0.5621      0.576 0.000 0.308 0.692
#> GSM317670     2  0.7226      0.530 0.076 0.688 0.236
#> GSM317674     1  0.5291      0.785 0.732 0.000 0.268
#> GSM317675     1  0.5465      0.773 0.712 0.000 0.288
#> GSM317677     3  0.2711      0.621 0.088 0.000 0.912
#> GSM317678     2  0.0892      0.842 0.020 0.980 0.000
#> GSM317687     3  0.0747      0.654 0.016 0.000 0.984
#> GSM317695     1  0.1643      0.799 0.956 0.000 0.044
#> GSM317653     3  0.6675      0.428 0.012 0.404 0.584
#> GSM317656     1  0.1289      0.798 0.968 0.000 0.032
#> GSM317658     2  0.8562      0.349 0.208 0.608 0.184
#> GSM317660     1  0.5988      0.167 0.632 0.368 0.000
#> GSM317663     3  0.5733      0.560 0.000 0.324 0.676
#> GSM317664     1  0.5138      0.793 0.748 0.000 0.252
#> GSM317665     1  0.1031      0.775 0.976 0.024 0.000
#> GSM317673     1  0.4750      0.800 0.784 0.000 0.216
#> GSM317686     3  0.5926      0.517 0.000 0.356 0.644
#> GSM317688     1  0.3879      0.804 0.848 0.000 0.152
#> GSM317690     2  0.1163      0.828 0.000 0.972 0.028
#> GSM317654     1  0.0592      0.791 0.988 0.000 0.012
#> GSM317655     3  0.5591      0.579 0.000 0.304 0.696
#> GSM317659     3  0.1643      0.646 0.044 0.000 0.956
#> GSM317661     2  0.0000      0.844 0.000 1.000 0.000
#> GSM317662     2  0.0000      0.844 0.000 1.000 0.000
#> GSM317668     1  0.5216      0.789 0.740 0.000 0.260
#> GSM317669     1  0.0747      0.781 0.984 0.016 0.000
#> GSM317671     1  0.0424      0.785 0.992 0.008 0.000
#> GSM317676     3  0.0747      0.654 0.016 0.000 0.984
#> GSM317680     1  0.0592      0.783 0.988 0.012 0.000
#> GSM317684     3  0.5363      0.256 0.276 0.000 0.724
#> GSM317685     1  0.5254      0.787 0.736 0.000 0.264
#> GSM317694     1  0.5882      0.714 0.652 0.000 0.348

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM317649     3  0.0707      0.908 0.020 0.000 0.980 0.000
#> GSM317652     3  0.2676      0.880 0.092 0.012 0.896 0.000
#> GSM317666     4  0.0188      0.828 0.000 0.004 0.000 0.996
#> GSM317672     2  0.0336      0.880 0.000 0.992 0.008 0.000
#> GSM317679     3  0.0707      0.908 0.020 0.000 0.980 0.000
#> GSM317681     3  0.4632      0.566 0.000 0.308 0.688 0.004
#> GSM317682     1  0.5010      0.557 0.700 0.024 0.276 0.000
#> GSM317683     2  0.0336      0.882 0.000 0.992 0.000 0.008
#> GSM317689     2  0.0779      0.877 0.000 0.980 0.004 0.016
#> GSM317691     1  0.0336      0.904 0.992 0.000 0.000 0.008
#> GSM317692     1  0.0469      0.901 0.988 0.012 0.000 0.000
#> GSM317693     1  0.0188      0.905 0.996 0.000 0.000 0.004
#> GSM317696     1  0.0000      0.906 1.000 0.000 0.000 0.000
#> GSM317697     1  0.0000      0.906 1.000 0.000 0.000 0.000
#> GSM317698     1  0.0000      0.906 1.000 0.000 0.000 0.000
#> GSM317650     2  0.0188      0.883 0.000 0.996 0.000 0.004
#> GSM317651     3  0.3448      0.805 0.168 0.004 0.828 0.000
#> GSM317657     4  0.7771      0.112 0.396 0.200 0.004 0.400
#> GSM317667     4  0.0469      0.827 0.000 0.012 0.000 0.988
#> GSM317670     2  0.6161      0.640 0.176 0.716 0.072 0.036
#> GSM317674     1  0.0000      0.906 1.000 0.000 0.000 0.000
#> GSM317675     1  0.0000      0.906 1.000 0.000 0.000 0.000
#> GSM317677     1  0.2281      0.829 0.904 0.000 0.000 0.096
#> GSM317678     2  0.0188      0.882 0.000 0.996 0.004 0.000
#> GSM317687     4  0.4382      0.570 0.296 0.000 0.000 0.704
#> GSM317695     3  0.3583      0.773 0.180 0.000 0.816 0.004
#> GSM317653     4  0.4296      0.738 0.008 0.076 0.084 0.832
#> GSM317656     1  0.4277      0.604 0.720 0.000 0.280 0.000
#> GSM317658     2  0.5929      0.155 0.448 0.520 0.004 0.028
#> GSM317660     3  0.1743      0.888 0.004 0.056 0.940 0.000
#> GSM317663     4  0.0188      0.828 0.000 0.004 0.000 0.996
#> GSM317664     1  0.0188      0.905 0.996 0.000 0.000 0.004
#> GSM317665     3  0.1256      0.900 0.008 0.028 0.964 0.000
#> GSM317673     1  0.0000      0.906 1.000 0.000 0.000 0.000
#> GSM317686     4  0.0707      0.823 0.000 0.020 0.000 0.980
#> GSM317688     1  0.0376      0.904 0.992 0.004 0.004 0.000
#> GSM317690     2  0.1661      0.852 0.000 0.944 0.004 0.052
#> GSM317654     3  0.1820      0.902 0.036 0.020 0.944 0.000
#> GSM317655     4  0.0376      0.828 0.000 0.004 0.004 0.992
#> GSM317659     1  0.4356      0.534 0.708 0.000 0.000 0.292
#> GSM317661     2  0.0779      0.878 0.000 0.980 0.016 0.004
#> GSM317662     2  0.0376      0.883 0.000 0.992 0.004 0.004
#> GSM317668     1  0.5138      0.365 0.600 0.000 0.392 0.008
#> GSM317669     3  0.0336      0.905 0.008 0.000 0.992 0.000
#> GSM317671     3  0.1109      0.904 0.028 0.000 0.968 0.004
#> GSM317676     4  0.2704      0.770 0.124 0.000 0.000 0.876
#> GSM317680     3  0.0469      0.907 0.012 0.000 0.988 0.000
#> GSM317684     1  0.0592      0.897 0.984 0.000 0.000 0.016
#> GSM317685     1  0.0336      0.903 0.992 0.000 0.008 0.000
#> GSM317694     1  0.0000      0.906 1.000 0.000 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
#> GSM317649     3  0.0404     0.6335 0.000 0.000 0.988 0.000 0.012
#> GSM317652     3  0.5341    -0.2521 0.060 0.000 0.564 0.000 0.376
#> GSM317666     4  0.0000     0.8496 0.000 0.000 0.000 1.000 0.000
#> GSM317672     2  0.3160     0.7775 0.000 0.808 0.004 0.000 0.188
#> GSM317679     3  0.0000     0.6402 0.000 0.000 1.000 0.000 0.000
#> GSM317681     5  0.6834     0.4412 0.004 0.048 0.268 0.120 0.560
#> GSM317682     1  0.3039     0.6754 0.808 0.000 0.000 0.000 0.192
#> GSM317683     2  0.0162     0.9105 0.000 0.996 0.000 0.000 0.004
#> GSM317689     2  0.0000     0.9103 0.000 1.000 0.000 0.000 0.000
#> GSM317691     1  0.3452     0.7382 0.756 0.000 0.000 0.000 0.244
#> GSM317692     1  0.0404     0.8773 0.988 0.000 0.000 0.000 0.012
#> GSM317693     1  0.0000     0.8783 1.000 0.000 0.000 0.000 0.000
#> GSM317696     1  0.0162     0.8783 0.996 0.000 0.004 0.000 0.000
#> GSM317697     1  0.0162     0.8787 0.996 0.000 0.000 0.000 0.004
#> GSM317698     1  0.0703     0.8766 0.976 0.000 0.000 0.000 0.024
#> GSM317650     2  0.0162     0.9110 0.000 0.996 0.000 0.000 0.004
#> GSM317651     5  0.6032     0.2280 0.388 0.000 0.120 0.000 0.492
#> GSM317657     4  0.6506     0.5252 0.016 0.152 0.000 0.536 0.296
#> GSM317667     4  0.0794     0.8461 0.000 0.000 0.000 0.972 0.028
#> GSM317670     5  0.6500    -0.2371 0.000 0.404 0.188 0.000 0.408
#> GSM317674     1  0.1956     0.8588 0.916 0.000 0.008 0.000 0.076
#> GSM317675     1  0.0963     0.8740 0.964 0.000 0.000 0.000 0.036
#> GSM317677     1  0.5441     0.6084 0.624 0.000 0.000 0.096 0.280
#> GSM317678     2  0.1792     0.8821 0.000 0.916 0.000 0.000 0.084
#> GSM317687     4  0.3039     0.7269 0.152 0.000 0.000 0.836 0.012
#> GSM317695     3  0.2488     0.6180 0.004 0.000 0.872 0.000 0.124
#> GSM317653     5  0.5015     0.1655 0.000 0.004 0.028 0.392 0.576
#> GSM317656     3  0.6392     0.1208 0.400 0.000 0.432 0.000 0.168
#> GSM317658     2  0.1195     0.8911 0.028 0.960 0.000 0.000 0.012
#> GSM317660     5  0.4291     0.3694 0.000 0.000 0.464 0.000 0.536
#> GSM317663     4  0.0794     0.8488 0.000 0.000 0.000 0.972 0.028
#> GSM317664     1  0.3779     0.7681 0.776 0.000 0.024 0.000 0.200
#> GSM317665     5  0.4305     0.3322 0.000 0.000 0.488 0.000 0.512
#> GSM317673     1  0.0162     0.8779 0.996 0.000 0.000 0.000 0.004
#> GSM317686     4  0.0162     0.8500 0.000 0.004 0.000 0.996 0.000
#> GSM317688     1  0.0510     0.8731 0.984 0.000 0.000 0.000 0.016
#> GSM317690     2  0.0566     0.9059 0.000 0.984 0.000 0.004 0.012
#> GSM317654     5  0.4597     0.4033 0.000 0.000 0.424 0.012 0.564
#> GSM317655     4  0.2773     0.8107 0.000 0.000 0.000 0.836 0.164
#> GSM317659     1  0.6417    -0.0228 0.424 0.000 0.000 0.404 0.172
#> GSM317661     2  0.3835     0.6693 0.000 0.732 0.000 0.008 0.260
#> GSM317662     2  0.0963     0.9060 0.000 0.964 0.000 0.000 0.036
#> GSM317668     3  0.6055     0.2797 0.120 0.000 0.472 0.000 0.408
#> GSM317669     3  0.1043     0.6064 0.000 0.000 0.960 0.000 0.040
#> GSM317671     3  0.2424     0.6149 0.000 0.000 0.868 0.000 0.132
#> GSM317676     4  0.3010     0.7750 0.004 0.000 0.000 0.824 0.172
#> GSM317680     3  0.0000     0.6402 0.000 0.000 1.000 0.000 0.000
#> GSM317684     1  0.0162     0.8785 0.996 0.000 0.000 0.000 0.004
#> GSM317685     1  0.0404     0.8766 0.988 0.000 0.000 0.000 0.012
#> GSM317694     1  0.1965     0.8487 0.904 0.000 0.000 0.000 0.096

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> GSM317649     3  0.2173      0.934 0.004 0.000 0.904 0.028 0.064 0.000
#> GSM317652     5  0.4938      0.626 0.024 0.000 0.216 0.080 0.680 0.000
#> GSM317666     6  0.0146      0.905 0.000 0.000 0.000 0.000 0.004 0.996
#> GSM317672     2  0.2653      0.831 0.000 0.844 0.000 0.012 0.144 0.000
#> GSM317679     3  0.0972      0.964 0.000 0.000 0.964 0.008 0.028 0.000
#> GSM317681     5  0.3804      0.791 0.012 0.036 0.016 0.032 0.836 0.068
#> GSM317682     1  0.1863      0.853 0.920 0.000 0.000 0.044 0.036 0.000
#> GSM317683     2  0.0000      0.943 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM317689     2  0.0458      0.942 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM317691     1  0.3047      0.816 0.832 0.000 0.012 0.144 0.008 0.004
#> GSM317692     1  0.2222      0.840 0.896 0.012 0.000 0.084 0.008 0.000
#> GSM317693     1  0.1204      0.861 0.944 0.000 0.000 0.056 0.000 0.000
#> GSM317696     1  0.0458      0.869 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM317697     1  0.0858      0.868 0.968 0.004 0.000 0.028 0.000 0.000
#> GSM317698     1  0.2275      0.852 0.888 0.000 0.008 0.096 0.008 0.000
#> GSM317650     2  0.0260      0.943 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM317651     5  0.2213      0.809 0.044 0.000 0.004 0.048 0.904 0.000
#> GSM317657     4  0.5916      0.192 0.008 0.120 0.004 0.464 0.004 0.400
#> GSM317667     6  0.0146      0.905 0.000 0.000 0.000 0.000 0.004 0.996
#> GSM317670     4  0.3869      0.489 0.000 0.168 0.060 0.768 0.004 0.000
#> GSM317674     1  0.2917      0.827 0.840 0.000 0.016 0.136 0.008 0.000
#> GSM317675     1  0.2845      0.824 0.836 0.000 0.008 0.148 0.008 0.000
#> GSM317677     1  0.5431      0.429 0.560 0.000 0.016 0.356 0.012 0.056
#> GSM317678     2  0.1092      0.939 0.000 0.960 0.000 0.020 0.020 0.000
#> GSM317687     6  0.3513      0.717 0.104 0.000 0.000 0.072 0.008 0.816
#> GSM317695     3  0.0405      0.958 0.000 0.000 0.988 0.004 0.008 0.000
#> GSM317653     5  0.1556      0.816 0.000 0.000 0.000 0.000 0.920 0.080
#> GSM317656     4  0.7086      0.112 0.300 0.000 0.288 0.344 0.068 0.000
#> GSM317658     2  0.1218      0.927 0.028 0.956 0.000 0.012 0.004 0.000
#> GSM317660     5  0.1777      0.840 0.004 0.000 0.044 0.024 0.928 0.000
#> GSM317663     6  0.2119      0.866 0.000 0.008 0.016 0.060 0.004 0.912
#> GSM317664     1  0.4406      0.709 0.712 0.000 0.056 0.220 0.012 0.000
#> GSM317665     5  0.1838      0.835 0.000 0.000 0.068 0.016 0.916 0.000
#> GSM317673     1  0.1333      0.867 0.944 0.000 0.000 0.048 0.008 0.000
#> GSM317686     6  0.0405      0.901 0.000 0.008 0.000 0.004 0.000 0.988
#> GSM317688     1  0.2009      0.865 0.908 0.000 0.000 0.068 0.024 0.000
#> GSM317690     2  0.1010      0.931 0.000 0.960 0.000 0.036 0.004 0.000
#> GSM317654     5  0.1461      0.841 0.000 0.000 0.044 0.000 0.940 0.016
#> GSM317655     4  0.4346      0.382 0.000 0.004 0.000 0.632 0.028 0.336
#> GSM317659     4  0.6278      0.346 0.252 0.000 0.000 0.460 0.016 0.272
#> GSM317661     5  0.3922      0.495 0.000 0.320 0.000 0.016 0.664 0.000
#> GSM317662     2  0.1531      0.917 0.000 0.928 0.000 0.004 0.068 0.000
#> GSM317668     4  0.3134      0.505 0.016 0.000 0.148 0.824 0.012 0.000
#> GSM317669     3  0.1349      0.954 0.000 0.000 0.940 0.004 0.056 0.000
#> GSM317671     3  0.0260      0.953 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM317676     4  0.3993      0.339 0.000 0.000 0.000 0.592 0.008 0.400
#> GSM317680     3  0.0972      0.964 0.000 0.000 0.964 0.008 0.028 0.000
#> GSM317684     1  0.2195      0.844 0.904 0.000 0.000 0.068 0.012 0.016
#> GSM317685     1  0.1625      0.863 0.928 0.000 0.000 0.060 0.012 0.000
#> GSM317694     1  0.2001      0.860 0.900 0.000 0.004 0.092 0.004 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-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 disease.state(p) k
#> SD:NMF 48            0.719 2
#> SD:NMF 45            0.625 3
#> SD:NMF 47            0.901 4
#> SD:NMF 39            0.775 5
#> SD:NMF 42            0.581 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 11993 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 3.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

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 0.958           0.952       0.984         0.0582 0.960   0.960
#> 3 3 0.636           0.828       0.936         2.2811 0.887   0.883
#> 4 4 0.466           0.660       0.878         0.5847 0.928   0.915
#> 5 5 0.355           0.659       0.863         0.2545 0.965   0.955
#> 6 6 0.385           0.640       0.838         0.1009 0.999   0.999

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] 3

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
#> GSM317649     1  0.0000      0.985 1.000 0.000
#> GSM317652     1  0.0000      0.985 1.000 0.000
#> GSM317666     1  0.5737      0.835 0.864 0.136
#> GSM317672     1  0.0000      0.985 1.000 0.000
#> GSM317679     1  0.0000      0.985 1.000 0.000
#> GSM317681     1  0.0000      0.985 1.000 0.000
#> GSM317682     1  0.0000      0.985 1.000 0.000
#> GSM317683     1  0.1414      0.970 0.980 0.020
#> GSM317689     1  0.0938      0.977 0.988 0.012
#> GSM317691     1  0.0672      0.981 0.992 0.008
#> GSM317692     1  0.0000      0.985 1.000 0.000
#> GSM317693     1  0.0672      0.981 0.992 0.008
#> GSM317696     1  0.0000      0.985 1.000 0.000
#> GSM317697     1  0.0000      0.985 1.000 0.000
#> GSM317698     1  0.0000      0.985 1.000 0.000
#> GSM317650     2  0.5946      0.000 0.144 0.856
#> GSM317651     1  0.0000      0.985 1.000 0.000
#> GSM317657     1  0.0672      0.981 0.992 0.008
#> GSM317667     1  0.5946      0.824 0.856 0.144
#> GSM317670     1  0.0000      0.985 1.000 0.000
#> GSM317674     1  0.0000      0.985 1.000 0.000
#> GSM317675     1  0.0000      0.985 1.000 0.000
#> GSM317677     1  0.0000      0.985 1.000 0.000
#> GSM317678     1  0.1184      0.973 0.984 0.016
#> GSM317687     1  0.0672      0.981 0.992 0.008
#> GSM317695     1  0.0000      0.985 1.000 0.000
#> GSM317653     1  0.0672      0.981 0.992 0.008
#> GSM317656     1  0.0000      0.985 1.000 0.000
#> GSM317658     1  0.0672      0.981 0.992 0.008
#> GSM317660     1  0.0000      0.985 1.000 0.000
#> GSM317663     1  0.3879      0.911 0.924 0.076
#> GSM317664     1  0.0000      0.985 1.000 0.000
#> GSM317665     1  0.0000      0.985 1.000 0.000
#> GSM317673     1  0.0000      0.985 1.000 0.000
#> GSM317686     1  0.5842      0.830 0.860 0.140
#> GSM317688     1  0.0000      0.985 1.000 0.000
#> GSM317690     1  0.0376      0.983 0.996 0.004
#> GSM317654     1  0.0000      0.985 1.000 0.000
#> GSM317655     1  0.0000      0.985 1.000 0.000
#> GSM317659     1  0.0000      0.985 1.000 0.000
#> GSM317661     1  0.1184      0.973 0.984 0.016
#> GSM317662     1  0.1184      0.973 0.984 0.016
#> GSM317668     1  0.0000      0.985 1.000 0.000
#> GSM317669     1  0.0000      0.985 1.000 0.000
#> GSM317671     1  0.0000      0.985 1.000 0.000
#> GSM317676     1  0.0376      0.983 0.996 0.004
#> GSM317680     1  0.0000      0.985 1.000 0.000
#> GSM317684     1  0.0672      0.981 0.992 0.008
#> GSM317685     1  0.0000      0.985 1.000 0.000
#> GSM317694     1  0.0000      0.985 1.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> GSM317649     1  0.1031      0.921 0.976 0.024 0.000
#> GSM317652     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317666     2  0.6252      0.576 0.444 0.556 0.000
#> GSM317672     1  0.1031      0.924 0.976 0.024 0.000
#> GSM317679     1  0.1031      0.921 0.976 0.024 0.000
#> GSM317681     1  0.1643      0.908 0.956 0.044 0.000
#> GSM317682     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317683     1  0.4609      0.770 0.844 0.128 0.028
#> GSM317689     1  0.3587      0.841 0.892 0.088 0.020
#> GSM317691     1  0.0424      0.928 0.992 0.008 0.000
#> GSM317692     1  0.0892      0.923 0.980 0.020 0.000
#> GSM317693     1  0.0424      0.928 0.992 0.008 0.000
#> GSM317696     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317697     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317698     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317650     3  0.0000      0.000 0.000 0.000 1.000
#> GSM317651     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317657     1  0.0892      0.926 0.980 0.020 0.000
#> GSM317667     2  0.2711     -0.125 0.088 0.912 0.000
#> GSM317670     1  0.2537      0.873 0.920 0.080 0.000
#> GSM317674     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317675     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317677     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317678     1  0.4045      0.813 0.872 0.104 0.024
#> GSM317687     1  0.0424      0.928 0.992 0.008 0.000
#> GSM317695     1  0.1031      0.921 0.976 0.024 0.000
#> GSM317653     1  0.3752      0.778 0.856 0.144 0.000
#> GSM317656     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317658     1  0.0424      0.928 0.992 0.008 0.000
#> GSM317660     1  0.2625      0.869 0.916 0.084 0.000
#> GSM317663     1  0.5810      0.224 0.664 0.336 0.000
#> GSM317664     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317665     1  0.1643      0.908 0.956 0.044 0.000
#> GSM317673     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317686     2  0.6008      0.623 0.372 0.628 0.000
#> GSM317688     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317690     1  0.3686      0.797 0.860 0.140 0.000
#> GSM317654     1  0.1643      0.908 0.956 0.044 0.000
#> GSM317655     1  0.2537      0.873 0.920 0.080 0.000
#> GSM317659     1  0.0747      0.926 0.984 0.016 0.000
#> GSM317661     1  0.5903      0.595 0.744 0.232 0.024
#> GSM317662     1  0.6105      0.544 0.724 0.252 0.024
#> GSM317668     1  0.2066      0.892 0.940 0.060 0.000
#> GSM317669     1  0.1643      0.908 0.956 0.044 0.000
#> GSM317671     1  0.1031      0.921 0.976 0.024 0.000
#> GSM317676     1  0.1529      0.913 0.960 0.040 0.000
#> GSM317680     1  0.1031      0.921 0.976 0.024 0.000
#> GSM317684     1  0.0424      0.928 0.992 0.008 0.000
#> GSM317685     1  0.0000      0.930 1.000 0.000 0.000
#> GSM317694     1  0.0000      0.930 1.000 0.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM317649     1  0.1940    0.79550 0.924 0.076 0.000 0.000
#> GSM317652     1  0.0188    0.83646 0.996 0.004 0.000 0.000
#> GSM317666     4  0.4769    0.22399 0.308 0.008 0.000 0.684
#> GSM317672     1  0.2586    0.78251 0.912 0.040 0.000 0.048
#> GSM317679     1  0.1940    0.79550 0.924 0.076 0.000 0.000
#> GSM317681     1  0.2760    0.74017 0.872 0.128 0.000 0.000
#> GSM317682     1  0.0000    0.83742 1.000 0.000 0.000 0.000
#> GSM317683     1  0.6830   -0.17577 0.620 0.188 0.004 0.188
#> GSM317689     1  0.5361    0.44893 0.744 0.108 0.000 0.148
#> GSM317691     1  0.1004    0.83166 0.972 0.004 0.000 0.024
#> GSM317692     1  0.2483    0.77709 0.916 0.032 0.000 0.052
#> GSM317693     1  0.0336    0.83619 0.992 0.000 0.000 0.008
#> GSM317696     1  0.0000    0.83742 1.000 0.000 0.000 0.000
#> GSM317697     1  0.0336    0.83646 0.992 0.000 0.000 0.008
#> GSM317698     1  0.0000    0.83742 1.000 0.000 0.000 0.000
#> GSM317650     3  0.0000    0.00000 0.000 0.000 1.000 0.000
#> GSM317651     1  0.0524    0.83683 0.988 0.004 0.000 0.008
#> GSM317657     1  0.2142    0.80207 0.928 0.016 0.000 0.056
#> GSM317667     4  0.4720    0.00681 0.044 0.188 0.000 0.768
#> GSM317670     1  0.4152    0.60879 0.808 0.032 0.000 0.160
#> GSM317674     1  0.0000    0.83742 1.000 0.000 0.000 0.000
#> GSM317675     1  0.0000    0.83742 1.000 0.000 0.000 0.000
#> GSM317677     1  0.0000    0.83742 1.000 0.000 0.000 0.000
#> GSM317678     1  0.6163    0.16859 0.676 0.160 0.000 0.164
#> GSM317687     1  0.0524    0.83572 0.988 0.004 0.000 0.008
#> GSM317695     1  0.1940    0.79550 0.924 0.076 0.000 0.000
#> GSM317653     1  0.4718    0.61022 0.792 0.092 0.000 0.116
#> GSM317656     1  0.0000    0.83742 1.000 0.000 0.000 0.000
#> GSM317658     1  0.1004    0.83166 0.972 0.004 0.000 0.024
#> GSM317660     1  0.5263   -0.10617 0.544 0.448 0.000 0.008
#> GSM317663     1  0.5755   -0.36562 0.528 0.028 0.000 0.444
#> GSM317664     1  0.0000    0.83742 1.000 0.000 0.000 0.000
#> GSM317665     1  0.2704    0.74394 0.876 0.124 0.000 0.000
#> GSM317673     1  0.0000    0.83742 1.000 0.000 0.000 0.000
#> GSM317686     4  0.3870    0.45281 0.208 0.004 0.000 0.788
#> GSM317688     1  0.0188    0.83706 0.996 0.000 0.000 0.004
#> GSM317690     1  0.5083    0.37742 0.716 0.036 0.000 0.248
#> GSM317654     1  0.2704    0.74394 0.876 0.124 0.000 0.000
#> GSM317655     1  0.4152    0.60879 0.808 0.032 0.000 0.160
#> GSM317659     1  0.1398    0.82144 0.956 0.004 0.000 0.040
#> GSM317661     2  0.7740    0.95527 0.364 0.404 0.000 0.232
#> GSM317662     2  0.7811    0.95495 0.368 0.380 0.000 0.252
#> GSM317668     1  0.3760    0.66249 0.836 0.028 0.000 0.136
#> GSM317669     1  0.2704    0.74394 0.876 0.124 0.000 0.000
#> GSM317671     1  0.1940    0.79550 0.924 0.076 0.000 0.000
#> GSM317676     1  0.3266    0.72856 0.868 0.024 0.000 0.108
#> GSM317680     1  0.1940    0.79550 0.924 0.076 0.000 0.000
#> GSM317684     1  0.0524    0.83572 0.988 0.004 0.000 0.008
#> GSM317685     1  0.0000    0.83742 1.000 0.000 0.000 0.000
#> GSM317694     1  0.0000    0.83742 1.000 0.000 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
#> GSM317649     1  0.3010      0.715 0.824 0.004 0.172 0.000 0.000
#> GSM317652     1  0.0290      0.830 0.992 0.000 0.008 0.000 0.000
#> GSM317666     4  0.4975      0.405 0.272 0.040 0.012 0.676 0.000
#> GSM317672     1  0.3099      0.789 0.880 0.040 0.040 0.040 0.000
#> GSM317679     1  0.3010      0.715 0.824 0.004 0.172 0.000 0.000
#> GSM317681     1  0.3480      0.604 0.752 0.000 0.248 0.000 0.000
#> GSM317682     1  0.0324      0.831 0.992 0.004 0.004 0.000 0.000
#> GSM317683     1  0.6169      0.352 0.600 0.268 0.016 0.112 0.004
#> GSM317689     1  0.5809      0.572 0.692 0.152 0.060 0.096 0.000
#> GSM317691     1  0.0932      0.828 0.972 0.004 0.004 0.020 0.000
#> GSM317692     1  0.2853      0.788 0.892 0.036 0.028 0.044 0.000
#> GSM317693     1  0.0290      0.830 0.992 0.000 0.000 0.008 0.000
#> GSM317696     1  0.0000      0.831 1.000 0.000 0.000 0.000 0.000
#> GSM317697     1  0.0290      0.831 0.992 0.000 0.000 0.008 0.000
#> GSM317698     1  0.0000      0.831 1.000 0.000 0.000 0.000 0.000
#> GSM317650     5  0.0000      0.000 0.000 0.000 0.000 0.000 1.000
#> GSM317651     1  0.0613      0.832 0.984 0.008 0.004 0.004 0.000
#> GSM317657     1  0.2060      0.809 0.924 0.016 0.008 0.052 0.000
#> GSM317667     4  0.3081     -0.037 0.000 0.012 0.156 0.832 0.000
#> GSM317670     1  0.4986      0.652 0.748 0.068 0.036 0.148 0.000
#> GSM317674     1  0.0000      0.831 1.000 0.000 0.000 0.000 0.000
#> GSM317675     1  0.0000      0.831 1.000 0.000 0.000 0.000 0.000
#> GSM317677     1  0.0000      0.831 1.000 0.000 0.000 0.000 0.000
#> GSM317678     1  0.6001      0.472 0.648 0.216 0.040 0.096 0.000
#> GSM317687     1  0.0451      0.830 0.988 0.000 0.004 0.008 0.000
#> GSM317695     1  0.3010      0.715 0.824 0.004 0.172 0.000 0.000
#> GSM317653     1  0.5293      0.565 0.720 0.024 0.120 0.136 0.000
#> GSM317656     1  0.0162      0.831 0.996 0.000 0.004 0.000 0.000
#> GSM317658     1  0.0932      0.828 0.972 0.004 0.004 0.020 0.000
#> GSM317660     3  0.3452      0.000 0.244 0.000 0.756 0.000 0.000
#> GSM317663     1  0.6258     -0.112 0.472 0.072 0.028 0.428 0.000
#> GSM317664     1  0.0000      0.831 1.000 0.000 0.000 0.000 0.000
#> GSM317665     1  0.3452      0.612 0.756 0.000 0.244 0.000 0.000
#> GSM317673     1  0.0451      0.830 0.988 0.004 0.008 0.000 0.000
#> GSM317686     4  0.4190      0.479 0.172 0.060 0.000 0.768 0.000
#> GSM317688     1  0.0290      0.831 0.992 0.000 0.000 0.008 0.000
#> GSM317690     1  0.5812      0.509 0.656 0.080 0.036 0.228 0.000
#> GSM317654     1  0.3452      0.614 0.756 0.000 0.244 0.000 0.000
#> GSM317655     1  0.4986      0.652 0.748 0.068 0.036 0.148 0.000
#> GSM317659     1  0.1285      0.822 0.956 0.004 0.004 0.036 0.000
#> GSM317661     2  0.4534      0.599 0.072 0.796 0.068 0.064 0.000
#> GSM317662     2  0.2238      0.551 0.004 0.912 0.064 0.020 0.000
#> GSM317668     1  0.4223      0.700 0.796 0.060 0.016 0.128 0.000
#> GSM317669     1  0.3480      0.605 0.752 0.000 0.248 0.000 0.000
#> GSM317671     1  0.3010      0.715 0.824 0.004 0.172 0.000 0.000
#> GSM317676     1  0.3265      0.762 0.856 0.040 0.008 0.096 0.000
#> GSM317680     1  0.3010      0.715 0.824 0.004 0.172 0.000 0.000
#> GSM317684     1  0.0451      0.830 0.988 0.000 0.004 0.008 0.000
#> GSM317685     1  0.0000      0.831 1.000 0.000 0.000 0.000 0.000
#> GSM317694     1  0.0000      0.831 1.000 0.000 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
#> GSM317649     1  0.3052     0.7388 0.780 0.000 0.000 0.004 0.216 0.000
#> GSM317652     1  0.0363     0.8312 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM317666     4  0.4999     0.4514 0.244 0.000 0.080 0.660 0.012 0.004
#> GSM317672     1  0.3072     0.7862 0.856 0.000 0.084 0.024 0.036 0.000
#> GSM317679     1  0.3081     0.7363 0.776 0.000 0.000 0.004 0.220 0.000
#> GSM317681     1  0.3653     0.6545 0.692 0.000 0.008 0.000 0.300 0.000
#> GSM317682     1  0.0260     0.8316 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM317683     1  0.5743     0.3831 0.584 0.004 0.292 0.076 0.000 0.044
#> GSM317689     1  0.5884     0.5593 0.628 0.000 0.216 0.064 0.080 0.012
#> GSM317691     1  0.0837     0.8287 0.972 0.000 0.004 0.020 0.004 0.000
#> GSM317692     1  0.2976     0.7811 0.860 0.000 0.088 0.028 0.024 0.000
#> GSM317693     1  0.0260     0.8303 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM317696     1  0.0000     0.8311 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317697     1  0.0291     0.8314 0.992 0.000 0.004 0.004 0.000 0.000
#> GSM317698     1  0.0000     0.8311 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317650     2  0.0000     0.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM317651     1  0.0551     0.8319 0.984 0.000 0.004 0.008 0.004 0.000
#> GSM317657     1  0.2594     0.8026 0.892 0.000 0.048 0.040 0.016 0.004
#> GSM317667     4  0.3048     0.0215 0.000 0.000 0.004 0.824 0.020 0.152
#> GSM317670     1  0.5696     0.6026 0.668 0.000 0.120 0.152 0.032 0.028
#> GSM317674     1  0.0000     0.8311 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317675     1  0.0000     0.8311 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317677     1  0.0000     0.8311 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317678     1  0.5713     0.4957 0.620 0.000 0.264 0.048 0.036 0.032
#> GSM317687     1  0.0405     0.8302 0.988 0.000 0.000 0.008 0.004 0.000
#> GSM317695     1  0.3081     0.7363 0.776 0.000 0.000 0.004 0.220 0.000
#> GSM317653     1  0.5527     0.6105 0.680 0.000 0.024 0.140 0.128 0.028
#> GSM317656     1  0.0260     0.8315 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM317658     1  0.0837     0.8287 0.972 0.000 0.004 0.020 0.004 0.000
#> GSM317660     5  0.2563     0.0000 0.028 0.000 0.008 0.000 0.880 0.084
#> GSM317663     1  0.6128    -0.1781 0.428 0.000 0.124 0.420 0.024 0.004
#> GSM317664     1  0.0000     0.8311 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317665     1  0.3409     0.6600 0.700 0.000 0.000 0.000 0.300 0.000
#> GSM317673     1  0.0603     0.8310 0.980 0.000 0.000 0.004 0.016 0.000
#> GSM317686     4  0.4055     0.4818 0.136 0.000 0.088 0.768 0.000 0.008
#> GSM317688     1  0.0260     0.8315 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM317690     1  0.6069     0.4522 0.588 0.000 0.152 0.220 0.024 0.016
#> GSM317654     1  0.3464     0.6480 0.688 0.000 0.000 0.000 0.312 0.000
#> GSM317655     1  0.5696     0.6026 0.668 0.000 0.120 0.152 0.032 0.028
#> GSM317659     1  0.1699     0.8212 0.936 0.000 0.016 0.032 0.016 0.000
#> GSM317661     3  0.1297     0.0000 0.000 0.000 0.948 0.000 0.012 0.040
#> GSM317662     6  0.3720     0.0000 0.000 0.000 0.236 0.028 0.000 0.736
#> GSM317668     1  0.4828     0.6749 0.732 0.000 0.116 0.120 0.016 0.016
#> GSM317669     1  0.3446     0.6512 0.692 0.000 0.000 0.000 0.308 0.000
#> GSM317671     1  0.3081     0.7363 0.776 0.000 0.000 0.004 0.220 0.000
#> GSM317676     1  0.3737     0.7552 0.816 0.000 0.088 0.072 0.020 0.004
#> GSM317680     1  0.3081     0.7363 0.776 0.000 0.000 0.004 0.220 0.000
#> GSM317684     1  0.0405     0.8302 0.988 0.000 0.000 0.008 0.004 0.000
#> GSM317685     1  0.0000     0.8311 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317694     1  0.0000     0.8311 1.000 0.000 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-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 disease.state(p) k
#> CV:hclust 49               NA 2
#> CV:hclust 47            0.572 3
#> CV:hclust 40            0.224 4
#> CV:hclust 42            0.196 5
#> CV:hclust 39               NA 6

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

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 11993 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 0.742           0.893       0.948         0.4724 0.542   0.542
#> 3 3 0.557           0.664       0.811         0.2159 0.807   0.660
#> 4 4 0.668           0.761       0.864         0.1307 0.865   0.681
#> 5 5 0.673           0.645       0.788         0.0669 0.962   0.884
#> 6 6 0.693           0.533       0.713         0.0572 0.896   0.695

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
#> GSM317649     1  0.6148      0.811 0.848 0.152
#> GSM317652     1  0.0000      0.930 1.000 0.000
#> GSM317666     2  0.1184      0.964 0.016 0.984
#> GSM317672     2  0.0376      0.968 0.004 0.996
#> GSM317679     1  0.8144      0.695 0.748 0.252
#> GSM317681     2  0.0376      0.968 0.004 0.996
#> GSM317682     1  0.0000      0.930 1.000 0.000
#> GSM317683     2  0.0672      0.968 0.008 0.992
#> GSM317689     2  0.0376      0.968 0.004 0.996
#> GSM317691     1  0.0000      0.930 1.000 0.000
#> GSM317692     1  0.4562      0.870 0.904 0.096
#> GSM317693     1  0.0000      0.930 1.000 0.000
#> GSM317696     1  0.0000      0.930 1.000 0.000
#> GSM317697     1  0.0000      0.930 1.000 0.000
#> GSM317698     1  0.0000      0.930 1.000 0.000
#> GSM317650     2  0.0000      0.967 0.000 1.000
#> GSM317651     1  0.0000      0.930 1.000 0.000
#> GSM317657     1  0.8499      0.650 0.724 0.276
#> GSM317667     2  0.0672      0.968 0.008 0.992
#> GSM317670     1  0.4562      0.862 0.904 0.096
#> GSM317674     1  0.0000      0.930 1.000 0.000
#> GSM317675     1  0.0000      0.930 1.000 0.000
#> GSM317677     1  0.0000      0.930 1.000 0.000
#> GSM317678     2  0.0376      0.968 0.004 0.996
#> GSM317687     1  0.0000      0.930 1.000 0.000
#> GSM317695     1  0.0000      0.930 1.000 0.000
#> GSM317653     2  0.1184      0.964 0.016 0.984
#> GSM317656     1  0.0000      0.930 1.000 0.000
#> GSM317658     1  0.0000      0.930 1.000 0.000
#> GSM317660     2  0.0000      0.967 0.000 1.000
#> GSM317663     2  0.0672      0.968 0.008 0.992
#> GSM317664     1  0.0000      0.930 1.000 0.000
#> GSM317665     2  0.7376      0.734 0.208 0.792
#> GSM317673     1  0.0000      0.930 1.000 0.000
#> GSM317686     2  0.0938      0.966 0.012 0.988
#> GSM317688     1  0.0000      0.930 1.000 0.000
#> GSM317690     2  0.0672      0.968 0.008 0.992
#> GSM317654     2  0.7056      0.759 0.192 0.808
#> GSM317655     1  0.9087      0.573 0.676 0.324
#> GSM317659     1  0.0000      0.930 1.000 0.000
#> GSM317661     2  0.0000      0.967 0.000 1.000
#> GSM317662     2  0.0000      0.967 0.000 1.000
#> GSM317668     1  0.0000      0.930 1.000 0.000
#> GSM317669     1  0.9393      0.501 0.644 0.356
#> GSM317671     1  0.8081      0.701 0.752 0.248
#> GSM317676     1  0.3114      0.895 0.944 0.056
#> GSM317680     1  0.8081      0.701 0.752 0.248
#> GSM317684     1  0.0000      0.930 1.000 0.000
#> GSM317685     1  0.0000      0.930 1.000 0.000
#> GSM317694     1  0.0000      0.930 1.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> GSM317649     3  0.6309     0.3149 0.500 0.000 0.500
#> GSM317652     1  0.1163     0.8883 0.972 0.000 0.028
#> GSM317666     2  0.6919     0.6056 0.016 0.536 0.448
#> GSM317672     3  0.3682     0.0084 0.008 0.116 0.876
#> GSM317679     3  0.6244     0.4668 0.440 0.000 0.560
#> GSM317681     3  0.0983     0.2129 0.004 0.016 0.980
#> GSM317682     1  0.0475     0.9040 0.992 0.004 0.004
#> GSM317683     2  0.6095     0.7406 0.000 0.608 0.392
#> GSM317689     2  0.6308     0.7138 0.000 0.508 0.492
#> GSM317691     1  0.0237     0.9045 0.996 0.004 0.000
#> GSM317692     1  0.4960     0.7097 0.832 0.040 0.128
#> GSM317693     1  0.0237     0.9045 0.996 0.004 0.000
#> GSM317696     1  0.0475     0.9040 0.992 0.004 0.004
#> GSM317697     1  0.0237     0.9045 0.996 0.004 0.000
#> GSM317698     1  0.0000     0.9044 1.000 0.000 0.000
#> GSM317650     2  0.4504     0.6245 0.000 0.804 0.196
#> GSM317651     1  0.1411     0.8819 0.964 0.000 0.036
#> GSM317657     1  0.8957     0.1095 0.492 0.376 0.132
#> GSM317667     2  0.6026     0.6995 0.000 0.624 0.376
#> GSM317670     1  0.7507     0.4413 0.644 0.288 0.068
#> GSM317674     1  0.0237     0.9041 0.996 0.000 0.004
#> GSM317675     1  0.0000     0.9044 1.000 0.000 0.000
#> GSM317677     1  0.0000     0.9044 1.000 0.000 0.000
#> GSM317678     2  0.6302     0.7099 0.000 0.520 0.480
#> GSM317687     1  0.0237     0.9045 0.996 0.004 0.000
#> GSM317695     1  0.0592     0.9005 0.988 0.000 0.012
#> GSM317653     3  0.6633    -0.5627 0.008 0.444 0.548
#> GSM317656     1  0.0592     0.9004 0.988 0.000 0.012
#> GSM317658     1  0.0237     0.9045 0.996 0.004 0.000
#> GSM317660     3  0.3551     0.1578 0.000 0.132 0.868
#> GSM317663     2  0.6771     0.6558 0.012 0.548 0.440
#> GSM317664     1  0.0237     0.9041 0.996 0.000 0.004
#> GSM317665     3  0.3784     0.4533 0.132 0.004 0.864
#> GSM317673     1  0.0237     0.9041 0.996 0.000 0.004
#> GSM317686     2  0.6008     0.7082 0.004 0.664 0.332
#> GSM317688     1  0.0237     0.9041 0.996 0.000 0.004
#> GSM317690     2  0.6339     0.7241 0.008 0.632 0.360
#> GSM317654     3  0.3715     0.4492 0.128 0.004 0.868
#> GSM317655     1  0.9147     0.1193 0.496 0.348 0.156
#> GSM317659     1  0.0237     0.9030 0.996 0.000 0.004
#> GSM317661     2  0.5363     0.6893 0.000 0.724 0.276
#> GSM317662     2  0.5327     0.6907 0.000 0.728 0.272
#> GSM317668     1  0.1919     0.8750 0.956 0.020 0.024
#> GSM317669     3  0.5497     0.5364 0.292 0.000 0.708
#> GSM317671     3  0.6267     0.4464 0.452 0.000 0.548
#> GSM317676     1  0.6829     0.5934 0.736 0.168 0.096
#> GSM317680     3  0.6267     0.4464 0.452 0.000 0.548
#> GSM317684     1  0.0237     0.9045 0.996 0.004 0.000
#> GSM317685     1  0.0475     0.9040 0.992 0.004 0.004
#> GSM317694     1  0.0237     0.9041 0.996 0.000 0.004

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM317649     3  0.4374      0.723 0.228 0.008 0.760 0.004
#> GSM317652     1  0.1863      0.929 0.944 0.004 0.040 0.012
#> GSM317666     4  0.1610      0.447 0.000 0.016 0.032 0.952
#> GSM317672     3  0.4630      0.555 0.000 0.036 0.768 0.196
#> GSM317679     3  0.4569      0.727 0.220 0.008 0.760 0.012
#> GSM317681     3  0.1398      0.740 0.000 0.004 0.956 0.040
#> GSM317682     1  0.0000      0.970 1.000 0.000 0.000 0.000
#> GSM317683     2  0.5793      0.675 0.000 0.628 0.048 0.324
#> GSM317689     2  0.7371      0.581 0.000 0.472 0.168 0.360
#> GSM317691     1  0.0336      0.970 0.992 0.000 0.000 0.008
#> GSM317692     1  0.4695      0.713 0.800 0.024 0.028 0.148
#> GSM317693     1  0.0336      0.970 0.992 0.000 0.000 0.008
#> GSM317696     1  0.0000      0.970 1.000 0.000 0.000 0.000
#> GSM317697     1  0.0336      0.970 0.992 0.000 0.000 0.008
#> GSM317698     1  0.0376      0.970 0.992 0.004 0.000 0.004
#> GSM317650     2  0.2399      0.679 0.000 0.920 0.032 0.048
#> GSM317651     1  0.1771      0.934 0.948 0.004 0.036 0.012
#> GSM317657     4  0.6611      0.473 0.336 0.068 0.012 0.584
#> GSM317667     4  0.2032      0.429 0.000 0.036 0.028 0.936
#> GSM317670     4  0.7671      0.449 0.360 0.132 0.020 0.488
#> GSM317674     1  0.0188      0.970 0.996 0.004 0.000 0.000
#> GSM317675     1  0.0376      0.970 0.992 0.004 0.000 0.004
#> GSM317677     1  0.0524      0.969 0.988 0.004 0.000 0.008
#> GSM317678     2  0.7382      0.659 0.000 0.520 0.260 0.220
#> GSM317687     1  0.0336      0.970 0.992 0.000 0.000 0.008
#> GSM317695     1  0.1452      0.934 0.956 0.008 0.036 0.000
#> GSM317653     4  0.4452      0.239 0.000 0.008 0.260 0.732
#> GSM317656     1  0.0188      0.970 0.996 0.004 0.000 0.000
#> GSM317658     1  0.0524      0.968 0.988 0.000 0.004 0.008
#> GSM317660     3  0.3398      0.686 0.000 0.068 0.872 0.060
#> GSM317663     4  0.4082      0.407 0.004 0.052 0.108 0.836
#> GSM317664     1  0.0188      0.970 0.996 0.004 0.000 0.000
#> GSM317665     3  0.1888      0.755 0.016 0.000 0.940 0.044
#> GSM317673     1  0.0000      0.970 1.000 0.000 0.000 0.000
#> GSM317686     4  0.2089      0.432 0.000 0.048 0.020 0.932
#> GSM317688     1  0.0188      0.970 0.996 0.004 0.000 0.000
#> GSM317690     4  0.5749      0.279 0.012 0.188 0.076 0.724
#> GSM317654     3  0.1854      0.752 0.012 0.000 0.940 0.048
#> GSM317655     4  0.7569      0.468 0.324 0.132 0.020 0.524
#> GSM317659     1  0.0779      0.966 0.980 0.004 0.000 0.016
#> GSM317661     2  0.4966      0.768 0.000 0.768 0.076 0.156
#> GSM317662     2  0.4989      0.767 0.000 0.764 0.072 0.164
#> GSM317668     1  0.3699      0.838 0.864 0.048 0.008 0.080
#> GSM317669     3  0.1807      0.762 0.052 0.008 0.940 0.000
#> GSM317671     3  0.4604      0.727 0.224 0.008 0.756 0.012
#> GSM317676     4  0.6667      0.352 0.436 0.056 0.012 0.496
#> GSM317680     3  0.4604      0.727 0.224 0.008 0.756 0.012
#> GSM317684     1  0.0336      0.970 0.992 0.000 0.000 0.008
#> GSM317685     1  0.0000      0.970 1.000 0.000 0.000 0.000
#> GSM317694     1  0.0000      0.970 1.000 0.000 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
#> GSM317649     3  0.5547     0.6888 0.148 0.000 0.644 0.000 0.208
#> GSM317652     1  0.2353     0.8241 0.908 0.000 0.060 0.004 0.028
#> GSM317666     4  0.1854     0.5690 0.000 0.008 0.036 0.936 0.020
#> GSM317672     3  0.6072     0.4060 0.000 0.100 0.680 0.120 0.100
#> GSM317679     3  0.5581     0.6947 0.140 0.000 0.636 0.000 0.224
#> GSM317681     3  0.2149     0.6692 0.000 0.036 0.924 0.012 0.028
#> GSM317682     1  0.0566     0.8799 0.984 0.000 0.000 0.004 0.012
#> GSM317683     2  0.5490     0.6547 0.000 0.688 0.016 0.176 0.120
#> GSM317689     2  0.7375     0.5083 0.000 0.520 0.084 0.176 0.220
#> GSM317691     1  0.0865     0.8778 0.972 0.000 0.000 0.004 0.024
#> GSM317692     1  0.5897     0.3520 0.668 0.012 0.024 0.084 0.212
#> GSM317693     1  0.0865     0.8778 0.972 0.000 0.000 0.004 0.024
#> GSM317696     1  0.0000     0.8833 1.000 0.000 0.000 0.000 0.000
#> GSM317697     1  0.0865     0.8778 0.972 0.000 0.000 0.004 0.024
#> GSM317698     1  0.0290     0.8828 0.992 0.000 0.000 0.000 0.008
#> GSM317650     2  0.3730     0.5263 0.000 0.712 0.000 0.000 0.288
#> GSM317651     1  0.2721     0.8161 0.896 0.000 0.052 0.016 0.036
#> GSM317657     4  0.7542    -0.8374 0.252 0.016 0.016 0.380 0.336
#> GSM317667     4  0.1891     0.5574 0.000 0.032 0.016 0.936 0.016
#> GSM317670     5  0.7984     0.9769 0.240 0.044 0.020 0.296 0.400
#> GSM317674     1  0.0290     0.8820 0.992 0.000 0.000 0.000 0.008
#> GSM317675     1  0.0000     0.8833 1.000 0.000 0.000 0.000 0.000
#> GSM317677     1  0.0865     0.8778 0.972 0.000 0.000 0.004 0.024
#> GSM317678     2  0.6673     0.6461 0.000 0.624 0.136 0.128 0.112
#> GSM317687     1  0.1041     0.8769 0.964 0.000 0.000 0.004 0.032
#> GSM317695     1  0.3710     0.6242 0.784 0.000 0.024 0.000 0.192
#> GSM317653     4  0.5525     0.3495 0.000 0.040 0.296 0.632 0.032
#> GSM317656     1  0.0290     0.8820 0.992 0.000 0.000 0.000 0.008
#> GSM317658     1  0.1205     0.8678 0.956 0.000 0.000 0.004 0.040
#> GSM317660     3  0.4700     0.5020 0.000 0.160 0.752 0.012 0.076
#> GSM317663     4  0.5148     0.4203 0.000 0.032 0.064 0.724 0.180
#> GSM317664     1  0.0290     0.8820 0.992 0.000 0.000 0.000 0.008
#> GSM317665     3  0.1095     0.6827 0.000 0.012 0.968 0.012 0.008
#> GSM317673     1  0.0290     0.8820 0.992 0.000 0.000 0.000 0.008
#> GSM317686     4  0.0579     0.5650 0.000 0.008 0.000 0.984 0.008
#> GSM317688     1  0.0000     0.8833 1.000 0.000 0.000 0.000 0.000
#> GSM317690     4  0.7190    -0.0708 0.004 0.172 0.028 0.420 0.376
#> GSM317654     3  0.1200     0.6812 0.000 0.016 0.964 0.012 0.008
#> GSM317655     5  0.7973     0.9766 0.232 0.044 0.020 0.304 0.400
#> GSM317659     1  0.1525     0.8667 0.948 0.000 0.004 0.012 0.036
#> GSM317661     2  0.2772     0.7050 0.000 0.896 0.032 0.044 0.028
#> GSM317662     2  0.2378     0.7030 0.000 0.908 0.012 0.064 0.016
#> GSM317668     1  0.5673     0.0930 0.608 0.000 0.020 0.060 0.312
#> GSM317669     3  0.3779     0.6955 0.024 0.000 0.776 0.000 0.200
#> GSM317671     3  0.5581     0.6947 0.140 0.000 0.636 0.000 0.224
#> GSM317676     1  0.7218    -0.8079 0.344 0.000 0.016 0.304 0.336
#> GSM317680     3  0.5581     0.6947 0.140 0.000 0.636 0.000 0.224
#> GSM317684     1  0.1041     0.8769 0.964 0.000 0.000 0.004 0.032
#> GSM317685     1  0.0771     0.8799 0.976 0.000 0.000 0.004 0.020
#> GSM317694     1  0.0290     0.8820 0.992 0.000 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
#> GSM317649     3  0.5345     0.1379 0.068 0.004 0.468 0.008 0.452 0.000
#> GSM317652     1  0.3748     0.7913 0.824 0.056 0.012 0.024 0.084 0.000
#> GSM317666     3  0.6768    -0.0449 0.000 0.312 0.380 0.268 0.040 0.000
#> GSM317672     5  0.5639     0.2834 0.000 0.268 0.008 0.144 0.576 0.004
#> GSM317679     3  0.5564     0.1573 0.052 0.008 0.468 0.024 0.448 0.000
#> GSM317681     5  0.2250     0.5694 0.000 0.092 0.020 0.000 0.888 0.000
#> GSM317682     1  0.0632     0.9120 0.976 0.024 0.000 0.000 0.000 0.000
#> GSM317683     2  0.6605     0.5213 0.000 0.468 0.016 0.204 0.020 0.292
#> GSM317689     2  0.6721     0.4839 0.000 0.444 0.000 0.312 0.060 0.184
#> GSM317691     1  0.0551     0.9126 0.984 0.008 0.000 0.004 0.004 0.000
#> GSM317692     1  0.6292     0.0810 0.528 0.180 0.012 0.260 0.020 0.000
#> GSM317693     1  0.0291     0.9144 0.992 0.004 0.000 0.000 0.004 0.000
#> GSM317696     1  0.0000     0.9143 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317697     1  0.0291     0.9144 0.992 0.004 0.000 0.000 0.004 0.000
#> GSM317698     1  0.0000     0.9143 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317650     6  0.0146     0.2789 0.000 0.000 0.000 0.004 0.000 0.996
#> GSM317651     1  0.4134     0.7666 0.804 0.056 0.012 0.056 0.072 0.000
#> GSM317657     4  0.5427     0.5837 0.144 0.108 0.044 0.692 0.004 0.008
#> GSM317667     3  0.5878     0.0742 0.000 0.308 0.492 0.196 0.004 0.000
#> GSM317670     4  0.2896     0.6284 0.140 0.012 0.004 0.840 0.004 0.000
#> GSM317674     1  0.0508     0.9137 0.984 0.004 0.012 0.000 0.000 0.000
#> GSM317675     1  0.0000     0.9143 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317677     1  0.0146     0.9148 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM317678     2  0.7262     0.5071 0.000 0.484 0.028 0.144 0.096 0.248
#> GSM317687     1  0.1155     0.9018 0.956 0.036 0.000 0.004 0.004 0.000
#> GSM317695     1  0.4581     0.1890 0.524 0.004 0.448 0.004 0.020 0.000
#> GSM317653     5  0.6966     0.1210 0.000 0.164 0.336 0.092 0.408 0.000
#> GSM317656     1  0.1026     0.9087 0.968 0.004 0.012 0.008 0.008 0.000
#> GSM317658     1  0.0692     0.9049 0.976 0.000 0.000 0.020 0.004 0.000
#> GSM317660     5  0.4625     0.4660 0.000 0.256 0.036 0.020 0.684 0.004
#> GSM317663     4  0.6822     0.0811 0.000 0.268 0.212 0.464 0.048 0.008
#> GSM317664     1  0.0508     0.9137 0.984 0.004 0.012 0.000 0.000 0.000
#> GSM317665     5  0.0405     0.5492 0.000 0.004 0.008 0.000 0.988 0.000
#> GSM317673     1  0.0405     0.9144 0.988 0.004 0.008 0.000 0.000 0.000
#> GSM317686     3  0.5878     0.0529 0.000 0.308 0.468 0.224 0.000 0.000
#> GSM317688     1  0.0146     0.9147 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM317690     4  0.2865     0.3949 0.000 0.092 0.016 0.868 0.008 0.016
#> GSM317654     5  0.1036     0.5623 0.000 0.024 0.008 0.004 0.964 0.000
#> GSM317655     4  0.2989     0.6237 0.120 0.012 0.004 0.848 0.016 0.000
#> GSM317659     1  0.2107     0.8787 0.920 0.024 0.012 0.036 0.008 0.000
#> GSM317661     2  0.5663    -0.4797 0.000 0.472 0.024 0.028 0.032 0.444
#> GSM317662     6  0.5663    -0.1563 0.000 0.444 0.032 0.028 0.024 0.472
#> GSM317668     4  0.4069     0.4664 0.376 0.000 0.008 0.612 0.004 0.000
#> GSM317669     5  0.4220    -0.2285 0.004 0.008 0.468 0.000 0.520 0.000
#> GSM317671     3  0.5564     0.1573 0.052 0.008 0.468 0.024 0.448 0.000
#> GSM317676     4  0.5009     0.5992 0.232 0.036 0.024 0.684 0.024 0.000
#> GSM317680     3  0.5564     0.1573 0.052 0.008 0.468 0.024 0.448 0.000
#> GSM317684     1  0.1003     0.9066 0.964 0.028 0.000 0.004 0.004 0.000
#> GSM317685     1  0.1074     0.9094 0.960 0.028 0.012 0.000 0.000 0.000
#> GSM317694     1  0.0508     0.9137 0.984 0.004 0.012 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-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 disease.state(p) k
#> CV:kmeans 50            0.394 2
#> CV:kmeans 37            0.733 3
#> CV:kmeans 40            0.519 4
#> CV:kmeans 42            0.712 5
#> CV:kmeans 30            0.612 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 11993 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 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-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 0.674           0.845       0.931         0.5086 0.490   0.490
#> 3 3 0.364           0.603       0.785         0.3126 0.770   0.566
#> 4 4 0.371           0.435       0.666         0.1217 0.902   0.732
#> 5 5 0.414           0.303       0.587         0.0663 0.930   0.775
#> 6 6 0.492           0.332       0.565         0.0406 0.909   0.680

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
#> GSM317649     2  0.9963      0.207 0.464 0.536
#> GSM317652     1  0.5629      0.835 0.868 0.132
#> GSM317666     2  0.0938      0.900 0.012 0.988
#> GSM317672     2  0.0000      0.902 0.000 1.000
#> GSM317679     2  0.5059      0.841 0.112 0.888
#> GSM317681     2  0.0000      0.902 0.000 1.000
#> GSM317682     1  0.2043      0.926 0.968 0.032
#> GSM317683     2  0.0672      0.902 0.008 0.992
#> GSM317689     2  0.1843      0.893 0.028 0.972
#> GSM317691     1  0.0672      0.941 0.992 0.008
#> GSM317692     2  0.9795      0.305 0.416 0.584
#> GSM317693     1  0.0000      0.943 1.000 0.000
#> GSM317696     1  0.0000      0.943 1.000 0.000
#> GSM317697     1  0.0000      0.943 1.000 0.000
#> GSM317698     1  0.0000      0.943 1.000 0.000
#> GSM317650     2  0.0000      0.902 0.000 1.000
#> GSM317651     1  0.9323      0.453 0.652 0.348
#> GSM317657     2  0.9881      0.231 0.436 0.564
#> GSM317667     2  0.0000      0.902 0.000 1.000
#> GSM317670     1  0.8499      0.621 0.724 0.276
#> GSM317674     1  0.0000      0.943 1.000 0.000
#> GSM317675     1  0.0000      0.943 1.000 0.000
#> GSM317677     1  0.0000      0.943 1.000 0.000
#> GSM317678     2  0.0000      0.902 0.000 1.000
#> GSM317687     1  0.4298      0.881 0.912 0.088
#> GSM317695     1  0.0000      0.943 1.000 0.000
#> GSM317653     2  0.0376      0.902 0.004 0.996
#> GSM317656     1  0.1843      0.929 0.972 0.028
#> GSM317658     1  0.1184      0.937 0.984 0.016
#> GSM317660     2  0.0000      0.902 0.000 1.000
#> GSM317663     2  0.0000      0.902 0.000 1.000
#> GSM317664     1  0.0000      0.943 1.000 0.000
#> GSM317665     2  0.2043      0.893 0.032 0.968
#> GSM317673     1  0.0000      0.943 1.000 0.000
#> GSM317686     2  0.0938      0.900 0.012 0.988
#> GSM317688     1  0.0000      0.943 1.000 0.000
#> GSM317690     2  0.0672      0.901 0.008 0.992
#> GSM317654     2  0.0938      0.901 0.012 0.988
#> GSM317655     2  0.7139      0.739 0.196 0.804
#> GSM317659     1  0.1633      0.932 0.976 0.024
#> GSM317661     2  0.0000      0.902 0.000 1.000
#> GSM317662     2  0.0000      0.902 0.000 1.000
#> GSM317668     1  0.0938      0.939 0.988 0.012
#> GSM317669     2  0.4562      0.853 0.096 0.904
#> GSM317671     2  0.6531      0.791 0.168 0.832
#> GSM317676     1  0.8555      0.620 0.720 0.280
#> GSM317680     2  0.7056      0.766 0.192 0.808
#> GSM317684     1  0.0000      0.943 1.000 0.000
#> GSM317685     1  0.0000      0.943 1.000 0.000
#> GSM317694     1  0.0000      0.943 1.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> GSM317649     3  0.3295    0.63951 0.096 0.008 0.896
#> GSM317652     3  0.8734   -0.00949 0.424 0.108 0.468
#> GSM317666     2  0.5414    0.59493 0.016 0.772 0.212
#> GSM317672     2  0.6754    0.22856 0.012 0.556 0.432
#> GSM317679     3  0.2063    0.66712 0.008 0.044 0.948
#> GSM317681     3  0.5621    0.40201 0.000 0.308 0.692
#> GSM317682     1  0.6537    0.69673 0.740 0.064 0.196
#> GSM317683     2  0.4539    0.66748 0.016 0.836 0.148
#> GSM317689     2  0.6737    0.57507 0.040 0.688 0.272
#> GSM317691     1  0.4281    0.81817 0.872 0.072 0.056
#> GSM317692     2  0.9528    0.25330 0.288 0.484 0.228
#> GSM317693     1  0.2187    0.83154 0.948 0.028 0.024
#> GSM317696     1  0.1163    0.83246 0.972 0.000 0.028
#> GSM317697     1  0.1337    0.83107 0.972 0.016 0.012
#> GSM317698     1  0.0237    0.82918 0.996 0.000 0.004
#> GSM317650     2  0.4887    0.61955 0.000 0.772 0.228
#> GSM317651     3  0.9874    0.17906 0.304 0.284 0.412
#> GSM317657     2  0.6304    0.55278 0.192 0.752 0.056
#> GSM317667     2  0.1529    0.66332 0.000 0.960 0.040
#> GSM317670     2  0.8703    0.36341 0.332 0.544 0.124
#> GSM317674     1  0.2165    0.83163 0.936 0.000 0.064
#> GSM317675     1  0.0237    0.82990 0.996 0.000 0.004
#> GSM317677     1  0.0661    0.83083 0.988 0.004 0.008
#> GSM317678     2  0.6252    0.28330 0.000 0.556 0.444
#> GSM317687     1  0.8334    0.54071 0.616 0.248 0.136
#> GSM317695     1  0.6095    0.47926 0.608 0.000 0.392
#> GSM317653     2  0.6627    0.40161 0.020 0.644 0.336
#> GSM317656     1  0.7128    0.58578 0.664 0.052 0.284
#> GSM317658     1  0.5891    0.73747 0.780 0.168 0.052
#> GSM317660     3  0.6274    0.02017 0.000 0.456 0.544
#> GSM317663     2  0.4452    0.64682 0.000 0.808 0.192
#> GSM317664     1  0.2796    0.82421 0.908 0.000 0.092
#> GSM317665     3  0.5360    0.57463 0.012 0.220 0.768
#> GSM317673     1  0.5987    0.73406 0.756 0.036 0.208
#> GSM317686     2  0.0237    0.65777 0.000 0.996 0.004
#> GSM317688     1  0.4015    0.82525 0.876 0.028 0.096
#> GSM317690     2  0.4196    0.67013 0.024 0.864 0.112
#> GSM317654     3  0.6096    0.49827 0.016 0.280 0.704
#> GSM317655     2  0.5780    0.63294 0.080 0.800 0.120
#> GSM317659     1  0.7344    0.64998 0.696 0.204 0.100
#> GSM317661     2  0.4399    0.64120 0.000 0.812 0.188
#> GSM317662     2  0.4062    0.65455 0.000 0.836 0.164
#> GSM317668     1  0.8125    0.58928 0.648 0.176 0.176
#> GSM317669     3  0.1919    0.67324 0.024 0.020 0.956
#> GSM317671     3  0.1905    0.67107 0.016 0.028 0.956
#> GSM317676     2  0.8179    0.29697 0.352 0.564 0.084
#> GSM317680     3  0.1585    0.67110 0.028 0.008 0.964
#> GSM317684     1  0.2434    0.82969 0.940 0.036 0.024
#> GSM317685     1  0.5473    0.78312 0.808 0.052 0.140
#> GSM317694     1  0.2066    0.83344 0.940 0.000 0.060

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM317649     3   0.268     0.6352 0.044 0.012 0.916 0.028
#> GSM317652     4   0.952     0.1758 0.280 0.108 0.284 0.328
#> GSM317666     2   0.787     0.3067 0.028 0.492 0.140 0.340
#> GSM317672     2   0.786     0.3935 0.020 0.524 0.248 0.208
#> GSM317679     3   0.159     0.6672 0.004 0.024 0.956 0.016
#> GSM317681     3   0.677     0.1444 0.000 0.364 0.532 0.104
#> GSM317682     1   0.731     0.5414 0.644 0.056 0.144 0.156
#> GSM317683     2   0.531     0.5253 0.020 0.768 0.060 0.152
#> GSM317689     2   0.709     0.4749 0.032 0.644 0.156 0.168
#> GSM317691     1   0.680     0.5482 0.656 0.036 0.088 0.220
#> GSM317692     2   0.962    -0.0482 0.164 0.360 0.180 0.296
#> GSM317693     1   0.334     0.6733 0.856 0.016 0.000 0.128
#> GSM317696     1   0.300     0.6871 0.892 0.000 0.060 0.048
#> GSM317697     1   0.289     0.6778 0.896 0.020 0.004 0.080
#> GSM317698     1   0.155     0.6780 0.952 0.000 0.008 0.040
#> GSM317650     2   0.568     0.5205 0.000 0.720 0.140 0.140
#> GSM317651     4   0.883     0.2719 0.128 0.148 0.220 0.504
#> GSM317657     2   0.768    -0.0448 0.148 0.432 0.012 0.408
#> GSM317667     2   0.573     0.4567 0.004 0.648 0.040 0.308
#> GSM317670     4   0.876     0.3376 0.268 0.248 0.052 0.432
#> GSM317674     1   0.423     0.6773 0.824 0.000 0.084 0.092
#> GSM317675     1   0.166     0.6783 0.944 0.000 0.004 0.052
#> GSM317677     1   0.307     0.6729 0.848 0.000 0.000 0.152
#> GSM317678     2   0.659     0.4735 0.004 0.608 0.288 0.100
#> GSM317687     1   0.839     0.0790 0.452 0.168 0.044 0.336
#> GSM317695     3   0.599    -0.0210 0.392 0.004 0.568 0.036
#> GSM317653     2   0.785     0.3603 0.024 0.520 0.168 0.288
#> GSM317656     1   0.855     0.2409 0.484 0.068 0.288 0.160
#> GSM317658     1   0.715     0.4999 0.656 0.116 0.056 0.172
#> GSM317660     2   0.747     0.2822 0.000 0.488 0.312 0.200
#> GSM317663     2   0.753     0.4333 0.016 0.564 0.204 0.216
#> GSM317664     1   0.551     0.6130 0.720 0.000 0.196 0.084
#> GSM317665     3   0.769     0.3496 0.012 0.220 0.528 0.240
#> GSM317673     1   0.648     0.6161 0.692 0.024 0.136 0.148
#> GSM317686     2   0.499     0.4430 0.012 0.720 0.012 0.256
#> GSM317688     1   0.633     0.5890 0.680 0.008 0.136 0.176
#> GSM317690     2   0.589     0.4173 0.016 0.692 0.052 0.240
#> GSM317654     3   0.795     0.2338 0.024 0.284 0.508 0.184
#> GSM317655     4   0.689    -0.0370 0.032 0.408 0.044 0.516
#> GSM317659     1   0.729     0.2444 0.500 0.060 0.040 0.400
#> GSM317661     2   0.441     0.5452 0.000 0.812 0.108 0.080
#> GSM317662     2   0.360     0.5451 0.000 0.860 0.084 0.056
#> GSM317668     1   0.816     0.0591 0.444 0.076 0.084 0.396
#> GSM317669     3   0.202     0.6643 0.004 0.028 0.940 0.028
#> GSM317671     3   0.217     0.6629 0.008 0.032 0.936 0.024
#> GSM317676     4   0.748     0.3456 0.176 0.180 0.036 0.608
#> GSM317680     3   0.139     0.6656 0.008 0.016 0.964 0.012
#> GSM317684     1   0.448     0.6358 0.760 0.008 0.008 0.224
#> GSM317685     1   0.716     0.5055 0.616 0.020 0.156 0.208
#> GSM317694     1   0.451     0.6738 0.812 0.004 0.112 0.072

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> GSM317649     3   0.332    0.67528 0.040 0.004 0.868 0.020 0.068
#> GSM317652     4   0.921    0.00236 0.228 0.036 0.196 0.276 0.264
#> GSM317666     2   0.846    0.20712 0.012 0.328 0.100 0.272 0.288
#> GSM317672     2   0.822    0.35461 0.020 0.448 0.224 0.092 0.216
#> GSM317679     3   0.288    0.69177 0.008 0.040 0.896 0.020 0.036
#> GSM317681     3   0.759   -0.01316 0.004 0.348 0.424 0.064 0.160
#> GSM317682     1   0.757    0.24077 0.520 0.024 0.112 0.072 0.272
#> GSM317683     2   0.644    0.38152 0.028 0.648 0.032 0.096 0.196
#> GSM317689     2   0.651    0.40248 0.008 0.656 0.092 0.124 0.120
#> GSM317691     1   0.826   -0.08817 0.424 0.040 0.068 0.156 0.312
#> GSM317692     2   0.910    0.09353 0.104 0.336 0.084 0.156 0.320
#> GSM317693     1   0.520    0.38313 0.712 0.004 0.008 0.096 0.180
#> GSM317696     1   0.364    0.52467 0.848 0.000 0.052 0.032 0.068
#> GSM317697     1   0.474    0.41785 0.744 0.000 0.008 0.084 0.164
#> GSM317698     1   0.207    0.51470 0.920 0.000 0.000 0.032 0.048
#> GSM317650     2   0.456    0.44054 0.000 0.792 0.048 0.080 0.080
#> GSM317651     4   0.933    0.09396 0.128 0.088 0.176 0.344 0.264
#> GSM317657     4   0.829   -0.00408 0.088 0.200 0.024 0.436 0.252
#> GSM317667     2   0.699    0.29436 0.000 0.448 0.016 0.312 0.224
#> GSM317670     4   0.726    0.30686 0.148 0.220 0.028 0.564 0.040
#> GSM317674     1   0.439    0.51671 0.812 0.008 0.056 0.040 0.084
#> GSM317675     1   0.234    0.52435 0.916 0.000 0.016 0.032 0.036
#> GSM317677     1   0.424    0.47749 0.788 0.000 0.008 0.132 0.072
#> GSM317678     2   0.665    0.41815 0.016 0.628 0.204 0.060 0.092
#> GSM317687     5   0.820    0.00000 0.292 0.064 0.020 0.232 0.392
#> GSM317695     3   0.544    0.34066 0.280 0.000 0.644 0.016 0.060
#> GSM317653     2   0.819    0.29737 0.012 0.396 0.096 0.180 0.316
#> GSM317656     1   0.880    0.17247 0.436 0.060 0.196 0.116 0.192
#> GSM317658     1   0.825    0.16976 0.520 0.108 0.060 0.172 0.140
#> GSM317660     2   0.789    0.30743 0.004 0.468 0.248 0.116 0.164
#> GSM317663     2   0.816    0.27812 0.004 0.408 0.124 0.284 0.180
#> GSM317664     1   0.610    0.44146 0.664 0.004 0.184 0.048 0.100
#> GSM317665     3   0.770    0.23670 0.008 0.208 0.488 0.072 0.224
#> GSM317673     1   0.713    0.39211 0.616 0.032 0.128 0.072 0.152
#> GSM317686     2   0.654    0.25128 0.000 0.464 0.004 0.356 0.176
#> GSM317688     1   0.748    0.28130 0.540 0.004 0.152 0.112 0.192
#> GSM317690     2   0.669    0.20311 0.008 0.520 0.052 0.356 0.064
#> GSM317654     2   0.843    0.00766 0.024 0.344 0.324 0.076 0.232
#> GSM317655     4   0.491    0.08843 0.004 0.304 0.020 0.660 0.012
#> GSM317659     1   0.769   -0.11880 0.428 0.044 0.024 0.360 0.144
#> GSM317661     2   0.472    0.46131 0.000 0.780 0.064 0.104 0.052
#> GSM317662     2   0.320    0.46813 0.000 0.872 0.032 0.064 0.032
#> GSM317668     4   0.734    0.08196 0.336 0.028 0.052 0.496 0.088
#> GSM317669     3   0.329    0.68378 0.020 0.040 0.876 0.012 0.052
#> GSM317671     3   0.230    0.70164 0.012 0.028 0.924 0.020 0.016
#> GSM317676     4   0.746    0.14193 0.124 0.132 0.024 0.584 0.136
#> GSM317680     3   0.213    0.70372 0.016 0.016 0.928 0.004 0.036
#> GSM317684     1   0.621   -0.00464 0.528 0.000 0.004 0.140 0.328
#> GSM317685     1   0.721    0.21057 0.540 0.032 0.056 0.076 0.296
#> GSM317694     1   0.517    0.49660 0.740 0.000 0.104 0.036 0.120

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> GSM317649     3   0.324    0.66102 0.008 0.016 0.848 0.004 0.104 0.020
#> GSM317652     5   0.949    0.35440 0.212 0.076 0.160 0.140 0.300 0.112
#> GSM317666     4   0.669    0.34621 0.016 0.172 0.080 0.616 0.052 0.064
#> GSM317672     2   0.817    0.25240 0.008 0.452 0.132 0.188 0.100 0.120
#> GSM317679     3   0.337    0.68321 0.004 0.052 0.860 0.036 0.024 0.024
#> GSM317681     2   0.774    0.18553 0.004 0.392 0.332 0.104 0.124 0.044
#> GSM317682     1   0.799    0.26055 0.424 0.064 0.136 0.056 0.292 0.028
#> GSM317683     2   0.699    0.19291 0.032 0.564 0.024 0.224 0.064 0.092
#> GSM317689     2   0.645    0.35205 0.008 0.644 0.060 0.104 0.064 0.120
#> GSM317691     1   0.798    0.32689 0.464 0.016 0.052 0.116 0.212 0.140
#> GSM317692     2   0.948   -0.01390 0.088 0.276 0.108 0.144 0.260 0.124
#> GSM317693     1   0.539    0.51501 0.676 0.000 0.000 0.076 0.164 0.084
#> GSM317696     1   0.392    0.55114 0.808 0.000 0.048 0.016 0.108 0.020
#> GSM317697     1   0.489    0.52544 0.724 0.000 0.004 0.044 0.152 0.076
#> GSM317698     1   0.316    0.55216 0.856 0.004 0.004 0.008 0.056 0.072
#> GSM317650     2   0.502    0.37463 0.000 0.744 0.028 0.076 0.052 0.100
#> GSM317651     5   0.931    0.26879 0.080 0.084 0.128 0.152 0.304 0.252
#> GSM317657     4   0.830    0.00742 0.072 0.140 0.016 0.384 0.100 0.288
#> GSM317667     4   0.516    0.34698 0.000 0.268 0.016 0.644 0.012 0.060
#> GSM317670     6   0.546    0.46010 0.076 0.112 0.016 0.044 0.028 0.724
#> GSM317674     1   0.542    0.48470 0.696 0.000 0.084 0.020 0.152 0.048
#> GSM317675     1   0.279    0.54568 0.876 0.000 0.008 0.004 0.060 0.052
#> GSM317677     1   0.536    0.50496 0.684 0.004 0.008 0.024 0.136 0.144
#> GSM317678     2   0.673    0.34366 0.012 0.612 0.148 0.120 0.048 0.060
#> GSM317687     4   0.884   -0.08146 0.252 0.052 0.056 0.308 0.244 0.088
#> GSM317695     3   0.498    0.41465 0.216 0.008 0.692 0.008 0.064 0.012
#> GSM317653     4   0.739   -0.08725 0.004 0.384 0.052 0.388 0.112 0.060
#> GSM317656     1   0.884   -0.09570 0.340 0.044 0.188 0.080 0.260 0.088
#> GSM317658     1   0.851    0.27734 0.464 0.112 0.056 0.084 0.128 0.156
#> GSM317660     2   0.755    0.29968 0.000 0.508 0.136 0.152 0.140 0.064
#> GSM317663     4   0.696    0.30631 0.008 0.184 0.128 0.572 0.056 0.052
#> GSM317664     1   0.555    0.42140 0.656 0.000 0.176 0.008 0.128 0.032
#> GSM317665     3   0.829   -0.01462 0.008 0.240 0.392 0.136 0.164 0.060
#> GSM317673     1   0.807    0.32846 0.472 0.040 0.120 0.060 0.228 0.080
#> GSM317686     4   0.588    0.34594 0.004 0.264 0.004 0.584 0.024 0.120
#> GSM317688     1   0.801    0.36877 0.496 0.028 0.132 0.064 0.168 0.112
#> GSM317690     6   0.701    0.05345 0.012 0.336 0.024 0.236 0.008 0.384
#> GSM317654     2   0.885    0.06498 0.020 0.312 0.244 0.188 0.164 0.072
#> GSM317655     6   0.458    0.46439 0.004 0.128 0.012 0.076 0.020 0.760
#> GSM317659     1   0.839   -0.06537 0.316 0.020 0.040 0.120 0.188 0.316
#> GSM317661     2   0.458    0.34885 0.000 0.764 0.028 0.132 0.036 0.040
#> GSM317662     2   0.451    0.34868 0.000 0.768 0.020 0.120 0.024 0.068
#> GSM317668     6   0.668    0.22081 0.200 0.028 0.048 0.032 0.088 0.604
#> GSM317669     3   0.302    0.67098 0.000 0.032 0.872 0.024 0.060 0.012
#> GSM317671     3   0.167    0.70896 0.004 0.012 0.944 0.012 0.008 0.020
#> GSM317676     6   0.718    0.24245 0.104 0.032 0.004 0.216 0.116 0.528
#> GSM317680     3   0.191    0.70689 0.004 0.004 0.928 0.020 0.040 0.004
#> GSM317684     1   0.620    0.43053 0.548 0.000 0.008 0.100 0.292 0.052
#> GSM317685     1   0.714    0.31806 0.480 0.020 0.048 0.052 0.332 0.068
#> GSM317694     1   0.607    0.49884 0.644 0.004 0.104 0.024 0.172 0.052

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 disease.state(p) k
#> CV:skmeans 46           0.7626 2
#> CV:skmeans 38           0.8377 3
#> CV:skmeans 24           0.5060 4
#> CV:skmeans  9           0.0842 5
#> CV:skmeans 11           0.0601 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 11993 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.
#>   There is no best k.
#> 
#> 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 0.630           0.902       0.946          0.116 0.960   0.960
#> 3 3 0.512           0.799       0.913          0.480 0.961   0.959
#> 4 4 0.439           0.797       0.904          0.208 0.962   0.958
#> 5 5 0.488           0.840       0.922          0.174 0.962   0.957
#> 6 6 0.433           0.782       0.907          0.187 0.963   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] NA

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
#> GSM317649     1  0.0000      0.947 1.000 0.000
#> GSM317652     1  0.0000      0.947 1.000 0.000
#> GSM317666     1  0.2603      0.936 0.956 0.044
#> GSM317672     1  0.0000      0.947 1.000 0.000
#> GSM317679     1  0.0000      0.947 1.000 0.000
#> GSM317681     1  0.0000      0.947 1.000 0.000
#> GSM317682     1  0.0000      0.947 1.000 0.000
#> GSM317683     1  0.7139      0.826 0.804 0.196
#> GSM317689     1  0.5946      0.874 0.856 0.144
#> GSM317691     1  0.2043      0.943 0.968 0.032
#> GSM317692     1  0.0000      0.947 1.000 0.000
#> GSM317693     1  0.2603      0.939 0.956 0.044
#> GSM317696     1  0.0672      0.946 0.992 0.008
#> GSM317697     1  0.2603      0.939 0.956 0.044
#> GSM317698     1  0.1633      0.944 0.976 0.024
#> GSM317650     2  0.1414      0.000 0.020 0.980
#> GSM317651     1  0.0000      0.947 1.000 0.000
#> GSM317657     1  0.7528      0.817 0.784 0.216
#> GSM317667     1  0.7299      0.820 0.796 0.204
#> GSM317670     1  0.2236      0.941 0.964 0.036
#> GSM317674     1  0.1184      0.944 0.984 0.016
#> GSM317675     1  0.1184      0.944 0.984 0.016
#> GSM317677     1  0.1184      0.944 0.984 0.016
#> GSM317678     1  0.6247      0.865 0.844 0.156
#> GSM317687     1  0.2236      0.942 0.964 0.036
#> GSM317695     1  0.0000      0.947 1.000 0.000
#> GSM317653     1  0.1633      0.943 0.976 0.024
#> GSM317656     1  0.0000      0.947 1.000 0.000
#> GSM317658     1  0.2043      0.941 0.968 0.032
#> GSM317660     1  0.0000      0.947 1.000 0.000
#> GSM317663     1  0.4815      0.896 0.896 0.104
#> GSM317664     1  0.0672      0.946 0.992 0.008
#> GSM317665     1  0.0000      0.947 1.000 0.000
#> GSM317673     1  0.0938      0.947 0.988 0.012
#> GSM317686     1  0.7528      0.817 0.784 0.216
#> GSM317688     1  0.1184      0.944 0.984 0.016
#> GSM317690     1  0.6048      0.871 0.852 0.148
#> GSM317654     1  0.0000      0.947 1.000 0.000
#> GSM317655     1  0.5842      0.884 0.860 0.140
#> GSM317659     1  0.1184      0.944 0.984 0.016
#> GSM317661     1  0.6887      0.834 0.816 0.184
#> GSM317662     1  0.7219      0.822 0.800 0.200
#> GSM317668     1  0.1414      0.945 0.980 0.020
#> GSM317669     1  0.0000      0.947 1.000 0.000
#> GSM317671     1  0.0000      0.947 1.000 0.000
#> GSM317676     1  0.6887      0.841 0.816 0.184
#> GSM317680     1  0.0000      0.947 1.000 0.000
#> GSM317684     1  0.4690      0.909 0.900 0.100
#> GSM317685     1  0.0000      0.947 1.000 0.000
#> GSM317694     1  0.0376      0.947 0.996 0.004

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> GSM317649     1  0.0000     0.8898 1.000 0.000 0.000
#> GSM317652     1  0.0000     0.8898 1.000 0.000 0.000
#> GSM317666     1  0.1753     0.8836 0.952 0.000 0.048
#> GSM317672     1  0.0237     0.8900 0.996 0.004 0.000
#> GSM317679     1  0.0000     0.8898 1.000 0.000 0.000
#> GSM317681     1  0.0000     0.8898 1.000 0.000 0.000
#> GSM317682     1  0.0000     0.8898 1.000 0.000 0.000
#> GSM317683     1  0.4654     0.7116 0.792 0.000 0.208
#> GSM317689     1  0.3816     0.7994 0.852 0.000 0.148
#> GSM317691     1  0.3590     0.8697 0.896 0.076 0.028
#> GSM317692     1  0.0000     0.8898 1.000 0.000 0.000
#> GSM317693     1  0.4165     0.8572 0.876 0.076 0.048
#> GSM317696     1  0.2261     0.8815 0.932 0.068 0.000
#> GSM317697     1  0.4165     0.8572 0.876 0.076 0.048
#> GSM317698     1  0.3325     0.8705 0.904 0.076 0.020
#> GSM317650     2  0.3482     0.0000 0.000 0.872 0.128
#> GSM317651     1  0.0000     0.8898 1.000 0.000 0.000
#> GSM317657     1  0.4796     0.7019 0.780 0.000 0.220
#> GSM317667     3  0.5956     0.0000 0.324 0.004 0.672
#> GSM317670     1  0.3921     0.8605 0.884 0.080 0.036
#> GSM317674     1  0.2866     0.8743 0.916 0.076 0.008
#> GSM317675     1  0.3031     0.8720 0.912 0.076 0.012
#> GSM317677     1  0.3031     0.8720 0.912 0.076 0.012
#> GSM317678     1  0.4062     0.7812 0.836 0.000 0.164
#> GSM317687     1  0.2434     0.8886 0.940 0.036 0.024
#> GSM317695     1  0.0000     0.8898 1.000 0.000 0.000
#> GSM317653     1  0.1031     0.8883 0.976 0.000 0.024
#> GSM317656     1  0.0000     0.8898 1.000 0.000 0.000
#> GSM317658     1  0.2297     0.8839 0.944 0.020 0.036
#> GSM317660     1  0.0000     0.8898 1.000 0.000 0.000
#> GSM317663     1  0.3116     0.8270 0.892 0.000 0.108
#> GSM317664     1  0.2200     0.8845 0.940 0.056 0.004
#> GSM317665     1  0.0892     0.8912 0.980 0.020 0.000
#> GSM317673     1  0.2590     0.8800 0.924 0.072 0.004
#> GSM317686     1  0.4842     0.6946 0.776 0.000 0.224
#> GSM317688     1  0.1585     0.8896 0.964 0.028 0.008
#> GSM317690     1  0.4002     0.7850 0.840 0.000 0.160
#> GSM317654     1  0.0000     0.8898 1.000 0.000 0.000
#> GSM317655     1  0.5426     0.8025 0.820 0.088 0.092
#> GSM317659     1  0.3031     0.8720 0.912 0.076 0.012
#> GSM317661     1  0.6282     0.0778 0.612 0.004 0.384
#> GSM317662     1  0.6313     0.4010 0.676 0.016 0.308
#> GSM317668     1  0.3690     0.8614 0.884 0.100 0.016
#> GSM317669     1  0.0000     0.8898 1.000 0.000 0.000
#> GSM317671     1  0.0000     0.8898 1.000 0.000 0.000
#> GSM317676     1  0.4291     0.7559 0.820 0.000 0.180
#> GSM317680     1  0.0000     0.8898 1.000 0.000 0.000
#> GSM317684     1  0.4075     0.8621 0.880 0.072 0.048
#> GSM317685     1  0.0000     0.8898 1.000 0.000 0.000
#> GSM317694     1  0.0592     0.8909 0.988 0.012 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM317649     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317652     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317666     1  0.1388      0.899 0.960 0.000 0.012 0.028
#> GSM317672     1  0.0188      0.902 0.996 0.000 0.004 0.000
#> GSM317679     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317681     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317682     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317683     1  0.4151      0.772 0.800 0.004 0.016 0.180
#> GSM317689     1  0.3519      0.829 0.852 0.004 0.016 0.128
#> GSM317691     1  0.2714      0.880 0.884 0.000 0.112 0.004
#> GSM317692     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317693     1  0.2773      0.877 0.880 0.000 0.116 0.004
#> GSM317696     1  0.1940      0.893 0.924 0.000 0.076 0.000
#> GSM317697     1  0.2899      0.878 0.880 0.004 0.112 0.004
#> GSM317698     1  0.2593      0.881 0.892 0.000 0.104 0.004
#> GSM317650     2  0.1576      0.000 0.000 0.948 0.004 0.048
#> GSM317651     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317657     1  0.4406      0.764 0.788 0.004 0.024 0.184
#> GSM317667     4  0.3024      0.000 0.148 0.000 0.000 0.852
#> GSM317670     1  0.3441      0.858 0.856 0.024 0.120 0.000
#> GSM317674     1  0.2466      0.884 0.900 0.000 0.096 0.004
#> GSM317675     1  0.2530      0.882 0.896 0.000 0.100 0.004
#> GSM317677     1  0.2530      0.882 0.896 0.000 0.100 0.004
#> GSM317678     1  0.3679      0.819 0.840 0.004 0.016 0.140
#> GSM317687     1  0.1675      0.902 0.948 0.004 0.044 0.004
#> GSM317695     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317653     1  0.0967      0.901 0.976 0.004 0.004 0.016
#> GSM317656     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317658     1  0.1398      0.902 0.956 0.004 0.040 0.000
#> GSM317660     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317663     1  0.2647      0.844 0.880 0.000 0.000 0.120
#> GSM317664     1  0.1792      0.896 0.932 0.000 0.068 0.000
#> GSM317665     1  0.0817      0.903 0.976 0.000 0.024 0.000
#> GSM317673     1  0.2216      0.889 0.908 0.000 0.092 0.000
#> GSM317686     1  0.4448      0.759 0.784 0.004 0.024 0.188
#> GSM317688     1  0.1305      0.902 0.960 0.000 0.036 0.004
#> GSM317690     1  0.3774      0.824 0.844 0.008 0.020 0.128
#> GSM317654     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317655     1  0.4536      0.826 0.812 0.020 0.136 0.032
#> GSM317659     1  0.2530      0.882 0.896 0.000 0.100 0.004
#> GSM317661     1  0.7977     -0.404 0.432 0.008 0.232 0.328
#> GSM317662     3  0.7006      0.000 0.236 0.032 0.632 0.100
#> GSM317668     1  0.3789      0.846 0.836 0.020 0.140 0.004
#> GSM317669     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317671     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317676     1  0.3852      0.787 0.808 0.000 0.012 0.180
#> GSM317680     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317684     1  0.3463      0.872 0.864 0.000 0.096 0.040
#> GSM317685     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317694     1  0.0592      0.903 0.984 0.000 0.016 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
#> GSM317649     1  0.0000      0.932 1.000 0.000 0.000 0.000 0.000
#> GSM317652     1  0.0000      0.932 1.000 0.000 0.000 0.000 0.000
#> GSM317666     1  0.1195      0.931 0.960 0.000 0.000 0.028 0.012
#> GSM317672     1  0.0162      0.932 0.996 0.000 0.004 0.000 0.000
#> GSM317679     1  0.0000      0.932 1.000 0.000 0.000 0.000 0.000
#> GSM317681     1  0.0000      0.932 1.000 0.000 0.000 0.000 0.000
#> GSM317682     1  0.0000      0.932 1.000 0.000 0.000 0.000 0.000
#> GSM317683     1  0.3359      0.857 0.816 0.000 0.000 0.164 0.020
#> GSM317689     1  0.2921      0.886 0.856 0.000 0.000 0.124 0.020
#> GSM317691     1  0.2727      0.912 0.868 0.000 0.116 0.000 0.016
#> GSM317692     1  0.0000      0.932 1.000 0.000 0.000 0.000 0.000
#> GSM317693     1  0.2825      0.908 0.860 0.000 0.124 0.000 0.016
#> GSM317696     1  0.1792      0.925 0.916 0.000 0.084 0.000 0.000
#> GSM317697     1  0.2873      0.909 0.860 0.000 0.120 0.000 0.020
#> GSM317698     1  0.2488      0.911 0.872 0.000 0.124 0.000 0.004
#> GSM317650     2  0.0162      0.000 0.000 0.996 0.000 0.000 0.004
#> GSM317651     1  0.0000      0.932 1.000 0.000 0.000 0.000 0.000
#> GSM317657     1  0.4117      0.846 0.788 0.000 0.028 0.164 0.020
#> GSM317667     4  0.0162      0.000 0.004 0.000 0.000 0.996 0.000
#> GSM317670     1  0.3197      0.891 0.836 0.000 0.140 0.000 0.024
#> GSM317674     1  0.2179      0.917 0.888 0.000 0.112 0.000 0.000
#> GSM317675     1  0.2329      0.912 0.876 0.000 0.124 0.000 0.000
#> GSM317677     1  0.2329      0.912 0.876 0.000 0.124 0.000 0.000
#> GSM317678     1  0.3016      0.882 0.848 0.000 0.000 0.132 0.020
#> GSM317687     1  0.1525      0.933 0.948 0.000 0.036 0.004 0.012
#> GSM317695     1  0.0000      0.932 1.000 0.000 0.000 0.000 0.000
#> GSM317653     1  0.0798      0.932 0.976 0.000 0.000 0.016 0.008
#> GSM317656     1  0.0000      0.932 1.000 0.000 0.000 0.000 0.000
#> GSM317658     1  0.1310      0.933 0.956 0.000 0.024 0.000 0.020
#> GSM317660     1  0.0000      0.932 1.000 0.000 0.000 0.000 0.000
#> GSM317663     1  0.2179      0.899 0.888 0.000 0.000 0.112 0.000
#> GSM317664     1  0.1671      0.927 0.924 0.000 0.076 0.000 0.000
#> GSM317665     1  0.0794      0.933 0.972 0.000 0.028 0.000 0.000
#> GSM317673     1  0.2233      0.919 0.892 0.000 0.104 0.000 0.004
#> GSM317686     1  0.4274      0.834 0.776 0.000 0.032 0.172 0.020
#> GSM317688     1  0.1121      0.932 0.956 0.000 0.044 0.000 0.000
#> GSM317690     1  0.3106      0.887 0.856 0.000 0.008 0.116 0.020
#> GSM317654     1  0.0000      0.932 1.000 0.000 0.000 0.000 0.000
#> GSM317655     1  0.3888      0.870 0.796 0.000 0.168 0.020 0.016
#> GSM317659     1  0.2329      0.912 0.876 0.000 0.124 0.000 0.000
#> GSM317661     3  0.3709      0.000 0.012 0.004 0.808 0.164 0.012
#> GSM317662     5  0.0566      0.000 0.012 0.000 0.000 0.004 0.984
#> GSM317668     1  0.3282      0.874 0.804 0.000 0.188 0.000 0.008
#> GSM317669     1  0.0000      0.932 1.000 0.000 0.000 0.000 0.000
#> GSM317671     1  0.0000      0.932 1.000 0.000 0.000 0.000 0.000
#> GSM317676     1  0.3449      0.859 0.812 0.000 0.024 0.164 0.000
#> GSM317680     1  0.0000      0.932 1.000 0.000 0.000 0.000 0.000
#> GSM317684     1  0.3051      0.906 0.852 0.000 0.120 0.028 0.000
#> GSM317685     1  0.0000      0.932 1.000 0.000 0.000 0.000 0.000
#> GSM317694     1  0.0510      0.933 0.984 0.000 0.016 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
#> GSM317649     1  0.0000      0.896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317652     1  0.0000      0.896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317666     1  0.1363      0.895 0.952 0.012 0.000 0.028 0.004 0.004
#> GSM317672     1  0.0146      0.897 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM317679     1  0.0000      0.896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317681     1  0.0000      0.896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317682     1  0.0000      0.896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317683     1  0.3242      0.834 0.840 0.008 0.016 0.120 0.004 0.012
#> GSM317689     1  0.2869      0.853 0.864 0.008 0.008 0.104 0.004 0.012
#> GSM317691     1  0.2362      0.877 0.860 0.136 0.000 0.000 0.000 0.004
#> GSM317692     1  0.0000      0.896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317693     1  0.2946      0.845 0.808 0.184 0.000 0.000 0.004 0.004
#> GSM317696     1  0.1863      0.887 0.896 0.104 0.000 0.000 0.000 0.000
#> GSM317697     1  0.3053      0.849 0.812 0.172 0.000 0.000 0.004 0.012
#> GSM317698     1  0.2631      0.849 0.820 0.180 0.000 0.000 0.000 0.000
#> GSM317650     2  0.3172      0.000 0.000 0.816 0.036 0.000 0.148 0.000
#> GSM317651     1  0.0000      0.896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317657     1  0.4417      0.807 0.772 0.076 0.016 0.120 0.004 0.012
#> GSM317667     4  0.0000      0.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM317670     1  0.3644      0.836 0.812 0.068 0.004 0.000 0.108 0.008
#> GSM317674     1  0.2178      0.876 0.868 0.132 0.000 0.000 0.000 0.000
#> GSM317675     1  0.2562      0.851 0.828 0.172 0.000 0.000 0.000 0.000
#> GSM317677     1  0.2597      0.850 0.824 0.176 0.000 0.000 0.000 0.000
#> GSM317678     1  0.2923      0.858 0.868 0.012 0.012 0.092 0.004 0.012
#> GSM317687     1  0.1578      0.899 0.936 0.048 0.000 0.004 0.000 0.012
#> GSM317695     1  0.0000      0.896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317653     1  0.0717      0.897 0.976 0.000 0.000 0.016 0.000 0.008
#> GSM317656     1  0.0146      0.896 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM317658     1  0.1218      0.899 0.956 0.028 0.000 0.000 0.004 0.012
#> GSM317660     5  0.3351      0.000 0.288 0.000 0.000 0.000 0.712 0.000
#> GSM317663     1  0.1858      0.873 0.912 0.000 0.012 0.076 0.000 0.000
#> GSM317664     1  0.1863      0.887 0.896 0.104 0.000 0.000 0.000 0.000
#> GSM317665     1  0.0790      0.899 0.968 0.032 0.000 0.000 0.000 0.000
#> GSM317673     1  0.2100      0.885 0.884 0.112 0.000 0.000 0.000 0.004
#> GSM317686     1  0.5434      0.736 0.712 0.096 0.016 0.124 0.040 0.012
#> GSM317688     1  0.1141      0.898 0.948 0.052 0.000 0.000 0.000 0.000
#> GSM317690     1  0.3034      0.856 0.864 0.012 0.008 0.092 0.012 0.012
#> GSM317654     1  0.0000      0.896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317655     1  0.4402      0.790 0.752 0.124 0.004 0.012 0.108 0.000
#> GSM317659     1  0.2597      0.850 0.824 0.176 0.000 0.000 0.000 0.000
#> GSM317661     3  0.0937      0.000 0.000 0.000 0.960 0.040 0.000 0.000
#> GSM317662     6  0.0000      0.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM317668     1  0.4199      0.786 0.748 0.148 0.004 0.000 0.100 0.000
#> GSM317669     1  0.0000      0.896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317671     1  0.0000      0.896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317676     1  0.4129      0.807 0.772 0.092 0.016 0.120 0.000 0.000
#> GSM317680     1  0.0000      0.896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317684     1  0.3268      0.845 0.808 0.164 0.008 0.020 0.000 0.000
#> GSM317685     1  0.0146      0.896 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM317694     1  0.0547      0.899 0.980 0.020 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 disease.state(p) k
#> CV:pam 49               NA 2
#> CV:pam 46               NA 3
#> CV:pam 46               NA 4
#> CV:pam 46               NA 5
#> CV:pam 45               NA 6

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

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 11993 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 3.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

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 0.916           0.911       0.964        0.50301 0.493   0.493
#> 3 3 0.958           0.928       0.966        0.19260 0.874   0.754
#> 4 4 0.805           0.793       0.907        0.00479 0.724   0.496
#> 5 5 0.838           0.783       0.846        0.13840 0.867   0.689
#> 6 6 0.685           0.745       0.799        0.08424 0.951   0.851

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] 3
#> 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
#> GSM317649     2  0.0672     0.9714 0.008 0.992
#> GSM317652     1  0.3879     0.8891 0.924 0.076
#> GSM317666     2  0.0672     0.9714 0.008 0.992
#> GSM317672     2  0.0672     0.9714 0.008 0.992
#> GSM317679     2  0.0672     0.9714 0.008 0.992
#> GSM317681     2  0.0672     0.9714 0.008 0.992
#> GSM317682     1  0.0000     0.9517 1.000 0.000
#> GSM317683     2  0.0000     0.9687 0.000 1.000
#> GSM317689     2  0.0672     0.9714 0.008 0.992
#> GSM317691     1  0.0000     0.9517 1.000 0.000
#> GSM317692     2  0.9850     0.2215 0.428 0.572
#> GSM317693     1  0.0000     0.9517 1.000 0.000
#> GSM317696     1  0.0000     0.9517 1.000 0.000
#> GSM317697     1  0.0000     0.9517 1.000 0.000
#> GSM317698     1  0.0000     0.9517 1.000 0.000
#> GSM317650     2  0.0000     0.9687 0.000 1.000
#> GSM317651     1  1.0000    -0.0123 0.500 0.500
#> GSM317657     2  0.0672     0.9714 0.008 0.992
#> GSM317667     2  0.0000     0.9687 0.000 1.000
#> GSM317670     2  0.0376     0.9676 0.004 0.996
#> GSM317674     1  0.0000     0.9517 1.000 0.000
#> GSM317675     1  0.0000     0.9517 1.000 0.000
#> GSM317677     1  0.0000     0.9517 1.000 0.000
#> GSM317678     2  0.0672     0.9714 0.008 0.992
#> GSM317687     1  0.8555     0.5988 0.720 0.280
#> GSM317695     1  0.5842     0.8206 0.860 0.140
#> GSM317653     2  0.0672     0.9714 0.008 0.992
#> GSM317656     1  0.0000     0.9517 1.000 0.000
#> GSM317658     1  0.0000     0.9517 1.000 0.000
#> GSM317660     2  0.0672     0.9714 0.008 0.992
#> GSM317663     2  0.0672     0.9714 0.008 0.992
#> GSM317664     1  0.0000     0.9517 1.000 0.000
#> GSM317665     2  0.0672     0.9714 0.008 0.992
#> GSM317673     1  0.0000     0.9517 1.000 0.000
#> GSM317686     2  0.0000     0.9687 0.000 1.000
#> GSM317688     1  0.0000     0.9517 1.000 0.000
#> GSM317690     2  0.0000     0.9687 0.000 1.000
#> GSM317654     2  0.0672     0.9714 0.008 0.992
#> GSM317655     2  0.0000     0.9687 0.000 1.000
#> GSM317659     1  0.0000     0.9517 1.000 0.000
#> GSM317661     2  0.0000     0.9687 0.000 1.000
#> GSM317662     2  0.0000     0.9687 0.000 1.000
#> GSM317668     1  0.0376     0.9492 0.996 0.004
#> GSM317669     2  0.0672     0.9714 0.008 0.992
#> GSM317671     2  0.0672     0.9714 0.008 0.992
#> GSM317676     2  0.7376     0.7260 0.208 0.792
#> GSM317680     2  0.0672     0.9714 0.008 0.992
#> GSM317684     1  0.0000     0.9517 1.000 0.000
#> GSM317685     1  0.0938     0.9438 0.988 0.012
#> GSM317694     1  0.0000     0.9517 1.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> GSM317649     3  0.0747      0.957 0.000 0.016 0.984
#> GSM317652     1  0.0848      0.972 0.984 0.008 0.008
#> GSM317666     2  0.0424      0.939 0.000 0.992 0.008
#> GSM317672     2  0.0592      0.937 0.000 0.988 0.012
#> GSM317679     3  0.0892      0.957 0.000 0.020 0.980
#> GSM317681     2  0.2448      0.893 0.000 0.924 0.076
#> GSM317682     1  0.0237      0.979 0.996 0.000 0.004
#> GSM317683     2  0.0424      0.937 0.000 0.992 0.008
#> GSM317689     2  0.0000      0.938 0.000 1.000 0.000
#> GSM317691     1  0.0000      0.980 1.000 0.000 0.000
#> GSM317692     1  0.4796      0.685 0.780 0.220 0.000
#> GSM317693     1  0.0000      0.980 1.000 0.000 0.000
#> GSM317696     1  0.0237      0.979 0.996 0.000 0.004
#> GSM317697     1  0.0000      0.980 1.000 0.000 0.000
#> GSM317698     1  0.0000      0.980 1.000 0.000 0.000
#> GSM317650     2  0.0592      0.935 0.000 0.988 0.012
#> GSM317651     1  0.2496      0.908 0.928 0.068 0.004
#> GSM317657     2  0.0424      0.939 0.000 0.992 0.008
#> GSM317667     2  0.0424      0.939 0.000 0.992 0.008
#> GSM317670     2  0.0848      0.933 0.008 0.984 0.008
#> GSM317674     1  0.0237      0.979 0.996 0.000 0.004
#> GSM317675     1  0.0000      0.980 1.000 0.000 0.000
#> GSM317677     1  0.0000      0.980 1.000 0.000 0.000
#> GSM317678     2  0.0424      0.938 0.000 0.992 0.008
#> GSM317687     1  0.1411      0.946 0.964 0.036 0.000
#> GSM317695     1  0.0661      0.975 0.988 0.004 0.008
#> GSM317653     2  0.0424      0.939 0.000 0.992 0.008
#> GSM317656     1  0.0000      0.980 1.000 0.000 0.000
#> GSM317658     1  0.0000      0.980 1.000 0.000 0.000
#> GSM317660     2  0.2448      0.891 0.000 0.924 0.076
#> GSM317663     2  0.0424      0.939 0.000 0.992 0.008
#> GSM317664     1  0.0237      0.979 0.996 0.000 0.004
#> GSM317665     2  0.5650      0.556 0.000 0.688 0.312
#> GSM317673     1  0.0237      0.979 0.996 0.000 0.004
#> GSM317686     2  0.0424      0.939 0.000 0.992 0.008
#> GSM317688     1  0.0237      0.979 0.996 0.000 0.004
#> GSM317690     2  0.0424      0.937 0.000 0.992 0.008
#> GSM317654     2  0.4178      0.790 0.000 0.828 0.172
#> GSM317655     2  0.0424      0.937 0.000 0.992 0.008
#> GSM317659     1  0.0000      0.980 1.000 0.000 0.000
#> GSM317661     2  0.0592      0.935 0.000 0.988 0.012
#> GSM317662     2  0.0592      0.935 0.000 0.988 0.012
#> GSM317668     1  0.0000      0.980 1.000 0.000 0.000
#> GSM317669     3  0.4002      0.818 0.000 0.160 0.840
#> GSM317671     3  0.0747      0.957 0.000 0.016 0.984
#> GSM317676     2  0.5722      0.511 0.292 0.704 0.004
#> GSM317680     3  0.1031      0.956 0.000 0.024 0.976
#> GSM317684     1  0.0000      0.980 1.000 0.000 0.000
#> GSM317685     1  0.0661      0.975 0.988 0.004 0.008
#> GSM317694     1  0.0237      0.979 0.996 0.000 0.004

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM317649     3  0.0336      0.864 0.008 0.000 0.992 0.000
#> GSM317652     1  0.0469      0.917 0.988 0.000 0.000 0.012
#> GSM317666     4  0.4870      0.782 0.096 0.056 0.036 0.812
#> GSM317672     3  0.5105      0.782 0.060 0.056 0.804 0.080
#> GSM317679     3  0.0336      0.864 0.008 0.000 0.992 0.000
#> GSM317681     3  0.3372      0.854 0.000 0.036 0.868 0.096
#> GSM317682     1  0.0707      0.916 0.980 0.000 0.000 0.020
#> GSM317683     2  0.3900      0.585 0.164 0.816 0.000 0.020
#> GSM317689     1  0.7496     -0.262 0.444 0.444 0.072 0.040
#> GSM317691     1  0.0336      0.916 0.992 0.008 0.000 0.000
#> GSM317692     1  0.0779      0.912 0.980 0.016 0.000 0.004
#> GSM317693     1  0.0336      0.916 0.992 0.008 0.000 0.000
#> GSM317696     1  0.0817      0.915 0.976 0.000 0.000 0.024
#> GSM317697     1  0.0000      0.918 1.000 0.000 0.000 0.000
#> GSM317698     1  0.0000      0.918 1.000 0.000 0.000 0.000
#> GSM317650     2  0.0921      0.667 0.000 0.972 0.000 0.028
#> GSM317651     1  0.0524      0.915 0.988 0.000 0.004 0.008
#> GSM317657     1  0.3647      0.785 0.852 0.108 0.000 0.040
#> GSM317667     4  0.1867      0.852 0.000 0.072 0.000 0.928
#> GSM317670     1  0.5024      0.368 0.632 0.360 0.000 0.008
#> GSM317674     1  0.0817      0.915 0.976 0.000 0.000 0.024
#> GSM317675     1  0.0000      0.918 1.000 0.000 0.000 0.000
#> GSM317677     1  0.0000      0.918 1.000 0.000 0.000 0.000
#> GSM317678     3  0.6840      0.344 0.012 0.392 0.524 0.072
#> GSM317687     1  0.0336      0.916 0.992 0.008 0.000 0.000
#> GSM317695     1  0.0817      0.915 0.976 0.000 0.000 0.024
#> GSM317653     4  0.4779      0.791 0.020 0.048 0.128 0.804
#> GSM317656     1  0.0592      0.917 0.984 0.000 0.000 0.016
#> GSM317658     1  0.0469      0.915 0.988 0.012 0.000 0.000
#> GSM317660     3  0.3533      0.845 0.000 0.056 0.864 0.080
#> GSM317663     1  0.7107      0.481 0.660 0.056 0.168 0.116
#> GSM317664     1  0.0817      0.915 0.976 0.000 0.000 0.024
#> GSM317665     3  0.3134      0.864 0.008 0.012 0.880 0.100
#> GSM317673     1  0.0817      0.915 0.976 0.000 0.000 0.024
#> GSM317686     4  0.1940      0.850 0.000 0.076 0.000 0.924
#> GSM317688     1  0.0707      0.916 0.980 0.000 0.000 0.020
#> GSM317690     2  0.5112      0.333 0.384 0.608 0.000 0.008
#> GSM317654     3  0.3670      0.856 0.008 0.032 0.860 0.100
#> GSM317655     1  0.5138      0.295 0.600 0.392 0.000 0.008
#> GSM317659     1  0.0336      0.916 0.992 0.008 0.000 0.000
#> GSM317661     2  0.1022      0.671 0.000 0.968 0.000 0.032
#> GSM317662     2  0.1022      0.671 0.000 0.968 0.000 0.032
#> GSM317668     1  0.0000      0.918 1.000 0.000 0.000 0.000
#> GSM317669     3  0.1339      0.869 0.008 0.004 0.964 0.024
#> GSM317671     3  0.0336      0.864 0.008 0.000 0.992 0.000
#> GSM317676     1  0.1151      0.905 0.968 0.024 0.000 0.008
#> GSM317680     3  0.0336      0.864 0.008 0.000 0.992 0.000
#> GSM317684     1  0.0336      0.916 0.992 0.008 0.000 0.000
#> GSM317685     1  0.0469      0.917 0.988 0.000 0.000 0.012
#> GSM317694     1  0.0336      0.918 0.992 0.000 0.000 0.008

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> GSM317649     3  0.0000    0.79345 0.000 0.000 1.000 0.000 0.000
#> GSM317652     1  0.1461    0.95156 0.952 0.016 0.004 0.028 0.000
#> GSM317666     4  0.2165    0.62341 0.016 0.056 0.004 0.920 0.004
#> GSM317672     3  0.6972    0.30663 0.012 0.196 0.444 0.344 0.004
#> GSM317679     3  0.0000    0.79345 0.000 0.000 1.000 0.000 0.000
#> GSM317681     3  0.4403    0.75340 0.004 0.032 0.724 0.240 0.000
#> GSM317682     1  0.0486    0.96222 0.988 0.004 0.004 0.004 0.000
#> GSM317683     2  0.5019    0.47744 0.024 0.536 0.000 0.004 0.436
#> GSM317689     2  0.6636    0.54865 0.036 0.572 0.020 0.072 0.300
#> GSM317691     1  0.0613    0.96237 0.984 0.008 0.000 0.004 0.004
#> GSM317692     1  0.4478    0.53788 0.700 0.272 0.000 0.020 0.008
#> GSM317693     1  0.0798    0.96082 0.976 0.016 0.000 0.008 0.000
#> GSM317696     1  0.0613    0.96048 0.984 0.004 0.008 0.004 0.000
#> GSM317697     1  0.0740    0.96179 0.980 0.008 0.000 0.008 0.004
#> GSM317698     1  0.0775    0.96165 0.980 0.008 0.004 0.004 0.004
#> GSM317650     5  0.0290    0.98789 0.000 0.008 0.000 0.000 0.992
#> GSM317651     1  0.2011    0.92476 0.928 0.020 0.008 0.044 0.000
#> GSM317657     2  0.6404    0.37757 0.300 0.568 0.000 0.092 0.040
#> GSM317667     4  0.4851    0.52024 0.000 0.340 0.000 0.624 0.036
#> GSM317670     2  0.6234    0.51769 0.176 0.528 0.000 0.000 0.296
#> GSM317674     1  0.0451    0.96152 0.988 0.000 0.008 0.004 0.000
#> GSM317675     1  0.1029    0.96063 0.972 0.008 0.008 0.008 0.004
#> GSM317677     1  0.0451    0.96237 0.988 0.004 0.000 0.008 0.000
#> GSM317678     2  0.8749    0.11866 0.012 0.340 0.252 0.188 0.208
#> GSM317687     1  0.1211    0.95176 0.960 0.016 0.000 0.024 0.000
#> GSM317695     1  0.1251    0.94464 0.956 0.008 0.036 0.000 0.000
#> GSM317653     4  0.2220    0.62029 0.016 0.052 0.008 0.920 0.004
#> GSM317656     1  0.0324    0.96205 0.992 0.000 0.004 0.004 0.000
#> GSM317658     1  0.0932    0.96078 0.972 0.020 0.000 0.004 0.004
#> GSM317660     3  0.4567    0.75188 0.004 0.044 0.720 0.232 0.000
#> GSM317663     4  0.7666   -0.00838 0.076 0.324 0.140 0.452 0.008
#> GSM317664     1  0.0671    0.95894 0.980 0.004 0.016 0.000 0.000
#> GSM317665     3  0.4288    0.76145 0.004 0.032 0.740 0.224 0.000
#> GSM317673     1  0.0324    0.96258 0.992 0.000 0.004 0.004 0.000
#> GSM317686     4  0.4866    0.52232 0.000 0.344 0.000 0.620 0.036
#> GSM317688     1  0.0486    0.96263 0.988 0.004 0.000 0.004 0.004
#> GSM317690     2  0.5118    0.54719 0.036 0.584 0.000 0.004 0.376
#> GSM317654     3  0.4318    0.76034 0.004 0.032 0.736 0.228 0.000
#> GSM317655     2  0.6063    0.58845 0.096 0.588 0.000 0.020 0.296
#> GSM317659     1  0.0671    0.96069 0.980 0.016 0.000 0.004 0.000
#> GSM317661     5  0.0162    0.98988 0.000 0.004 0.000 0.000 0.996
#> GSM317662     5  0.0000    0.99155 0.000 0.000 0.000 0.000 1.000
#> GSM317668     1  0.0613    0.96157 0.984 0.008 0.000 0.004 0.004
#> GSM317669     3  0.0290    0.79390 0.000 0.000 0.992 0.008 0.000
#> GSM317671     3  0.0000    0.79345 0.000 0.000 1.000 0.000 0.000
#> GSM317676     1  0.3334    0.85374 0.852 0.064 0.000 0.080 0.004
#> GSM317680     3  0.0000    0.79345 0.000 0.000 1.000 0.000 0.000
#> GSM317684     1  0.0798    0.96066 0.976 0.016 0.000 0.008 0.000
#> GSM317685     1  0.1074    0.96062 0.968 0.016 0.004 0.012 0.000
#> GSM317694     1  0.0486    0.96222 0.988 0.004 0.004 0.004 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
#> GSM317649     3  0.3714     0.9909 0.000 0.004 0.656 0.000 0.340 0.000
#> GSM317652     1  0.3192     0.8540 0.828 0.136 0.016 0.000 0.020 0.000
#> GSM317666     5  0.6356     0.0997 0.012 0.176 0.004 0.012 0.504 0.292
#> GSM317672     5  0.2293     0.4585 0.016 0.004 0.004 0.080 0.896 0.000
#> GSM317679     3  0.3578     0.9959 0.000 0.000 0.660 0.000 0.340 0.000
#> GSM317681     5  0.3103     0.2565 0.008 0.000 0.208 0.000 0.784 0.000
#> GSM317682     1  0.2313     0.8550 0.884 0.100 0.004 0.000 0.012 0.000
#> GSM317683     4  0.1293     0.8339 0.000 0.020 0.016 0.956 0.004 0.004
#> GSM317689     4  0.3019     0.7643 0.008 0.020 0.004 0.844 0.124 0.000
#> GSM317691     1  0.1806     0.8575 0.908 0.088 0.000 0.000 0.004 0.000
#> GSM317692     1  0.5549     0.3356 0.552 0.044 0.000 0.348 0.056 0.000
#> GSM317693     1  0.2838     0.8209 0.808 0.188 0.000 0.000 0.000 0.004
#> GSM317696     1  0.2346     0.8457 0.868 0.124 0.000 0.000 0.008 0.000
#> GSM317697     1  0.2100     0.8524 0.884 0.112 0.000 0.000 0.000 0.004
#> GSM317698     1  0.1588     0.8629 0.924 0.072 0.000 0.000 0.000 0.004
#> GSM317650     2  0.6322     0.9846 0.000 0.412 0.316 0.260 0.000 0.012
#> GSM317651     1  0.4577     0.8172 0.752 0.152 0.016 0.008 0.064 0.008
#> GSM317657     4  0.4665     0.6479 0.104 0.060 0.004 0.768 0.052 0.012
#> GSM317667     6  0.0146     0.9825 0.000 0.004 0.000 0.000 0.000 0.996
#> GSM317670     4  0.0924     0.8592 0.008 0.008 0.004 0.972 0.008 0.000
#> GSM317674     1  0.2212     0.8500 0.880 0.112 0.000 0.000 0.008 0.000
#> GSM317675     1  0.1812     0.8631 0.912 0.080 0.000 0.000 0.008 0.000
#> GSM317677     1  0.2100     0.8531 0.884 0.112 0.004 0.000 0.000 0.000
#> GSM317678     5  0.5210     0.0484 0.008 0.028 0.024 0.424 0.516 0.000
#> GSM317687     1  0.3748     0.7760 0.748 0.224 0.016 0.000 0.012 0.000
#> GSM317695     1  0.3354     0.8132 0.796 0.168 0.036 0.000 0.000 0.000
#> GSM317653     5  0.6140     0.1317 0.008 0.176 0.004 0.008 0.524 0.280
#> GSM317656     1  0.2673     0.8436 0.852 0.132 0.004 0.000 0.012 0.000
#> GSM317658     1  0.1779     0.8633 0.920 0.064 0.000 0.000 0.016 0.000
#> GSM317660     5  0.3383     0.2501 0.004 0.004 0.208 0.008 0.776 0.000
#> GSM317663     5  0.5469     0.3954 0.020 0.180 0.000 0.112 0.668 0.020
#> GSM317664     1  0.3053     0.8206 0.812 0.172 0.012 0.000 0.004 0.000
#> GSM317665     5  0.3271     0.2072 0.008 0.000 0.232 0.000 0.760 0.000
#> GSM317673     1  0.2313     0.8547 0.884 0.100 0.004 0.000 0.012 0.000
#> GSM317686     6  0.0405     0.9825 0.000 0.000 0.004 0.008 0.000 0.988
#> GSM317688     1  0.0767     0.8666 0.976 0.012 0.004 0.000 0.008 0.000
#> GSM317690     4  0.0291     0.8587 0.000 0.000 0.000 0.992 0.004 0.004
#> GSM317654     5  0.3161     0.2403 0.008 0.000 0.216 0.000 0.776 0.000
#> GSM317655     4  0.0665     0.8604 0.000 0.008 0.004 0.980 0.008 0.000
#> GSM317659     1  0.2520     0.8345 0.844 0.152 0.000 0.000 0.004 0.000
#> GSM317661     2  0.6326     0.9923 0.000 0.412 0.312 0.264 0.000 0.012
#> GSM317662     2  0.6326     0.9923 0.000 0.412 0.312 0.264 0.000 0.012
#> GSM317668     1  0.1261     0.8674 0.956 0.028 0.004 0.000 0.008 0.004
#> GSM317669     3  0.3592     0.9912 0.000 0.000 0.656 0.000 0.344 0.000
#> GSM317671     3  0.3578     0.9959 0.000 0.000 0.660 0.000 0.340 0.000
#> GSM317676     1  0.5534     0.6889 0.652 0.236 0.020 0.032 0.056 0.004
#> GSM317680     3  0.3578     0.9959 0.000 0.000 0.660 0.000 0.340 0.000
#> GSM317684     1  0.2793     0.8161 0.800 0.200 0.000 0.000 0.000 0.000
#> GSM317685     1  0.2692     0.8601 0.840 0.148 0.000 0.000 0.012 0.000
#> GSM317694     1  0.2302     0.8535 0.872 0.120 0.000 0.000 0.008 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-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 disease.state(p) k
#> CV:mclust 48            0.929 2
#> CV:mclust 50            0.447 3
#> CV:mclust 44            0.519 4
#> CV:mclust 45            0.689 5
#> CV:mclust 40            0.570 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 11993 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 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-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 0.722           0.845       0.936         0.5039 0.490   0.490
#> 3 3 0.661           0.776       0.896         0.3101 0.816   0.638
#> 4 4 0.640           0.718       0.853         0.0961 0.881   0.685
#> 5 5 0.644           0.558       0.768         0.0662 0.878   0.623
#> 6 6 0.709           0.665       0.820         0.0462 0.932   0.727

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
#> GSM317649     2  0.9850      0.333 0.428 0.572
#> GSM317652     1  0.2423      0.930 0.960 0.040
#> GSM317666     2  0.0000      0.887 0.000 1.000
#> GSM317672     2  0.0000      0.887 0.000 1.000
#> GSM317679     2  0.7883      0.686 0.236 0.764
#> GSM317681     2  0.0000      0.887 0.000 1.000
#> GSM317682     1  0.0000      0.969 1.000 0.000
#> GSM317683     2  0.0000      0.887 0.000 1.000
#> GSM317689     2  0.0000      0.887 0.000 1.000
#> GSM317691     1  0.0000      0.969 1.000 0.000
#> GSM317692     2  0.8207      0.656 0.256 0.744
#> GSM317693     1  0.0000      0.969 1.000 0.000
#> GSM317696     1  0.0000      0.969 1.000 0.000
#> GSM317697     1  0.0000      0.969 1.000 0.000
#> GSM317698     1  0.0000      0.969 1.000 0.000
#> GSM317650     2  0.0000      0.887 0.000 1.000
#> GSM317651     1  0.9850      0.106 0.572 0.428
#> GSM317657     2  0.9963      0.188 0.464 0.536
#> GSM317667     2  0.0000      0.887 0.000 1.000
#> GSM317670     1  0.0376      0.965 0.996 0.004
#> GSM317674     1  0.0000      0.969 1.000 0.000
#> GSM317675     1  0.0000      0.969 1.000 0.000
#> GSM317677     1  0.0000      0.969 1.000 0.000
#> GSM317678     2  0.0000      0.887 0.000 1.000
#> GSM317687     1  0.0000      0.969 1.000 0.000
#> GSM317695     1  0.0000      0.969 1.000 0.000
#> GSM317653     2  0.0000      0.887 0.000 1.000
#> GSM317656     1  0.1633      0.947 0.976 0.024
#> GSM317658     1  0.0000      0.969 1.000 0.000
#> GSM317660     2  0.0000      0.887 0.000 1.000
#> GSM317663     2  0.0000      0.887 0.000 1.000
#> GSM317664     1  0.0000      0.969 1.000 0.000
#> GSM317665     2  0.0000      0.887 0.000 1.000
#> GSM317673     1  0.0000      0.969 1.000 0.000
#> GSM317686     2  0.0938      0.881 0.012 0.988
#> GSM317688     1  0.0000      0.969 1.000 0.000
#> GSM317690     2  0.0000      0.887 0.000 1.000
#> GSM317654     2  0.0000      0.887 0.000 1.000
#> GSM317655     2  0.5842      0.787 0.140 0.860
#> GSM317659     1  0.0000      0.969 1.000 0.000
#> GSM317661     2  0.0000      0.887 0.000 1.000
#> GSM317662     2  0.0000      0.887 0.000 1.000
#> GSM317668     1  0.0000      0.969 1.000 0.000
#> GSM317669     2  0.5519      0.800 0.128 0.872
#> GSM317671     2  0.9580      0.447 0.380 0.620
#> GSM317676     1  0.6343      0.778 0.840 0.160
#> GSM317680     2  0.9993      0.165 0.484 0.516
#> GSM317684     1  0.0000      0.969 1.000 0.000
#> GSM317685     1  0.0000      0.969 1.000 0.000
#> GSM317694     1  0.0000      0.969 1.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> GSM317649     3  0.1031      0.846 0.024 0.000 0.976
#> GSM317652     1  0.5201      0.717 0.760 0.004 0.236
#> GSM317666     2  0.0000      0.863 0.000 1.000 0.000
#> GSM317672     3  0.6111      0.298 0.000 0.396 0.604
#> GSM317679     3  0.0237      0.853 0.004 0.000 0.996
#> GSM317681     3  0.1289      0.846 0.000 0.032 0.968
#> GSM317682     1  0.4235      0.788 0.824 0.000 0.176
#> GSM317683     2  0.0747      0.863 0.000 0.984 0.016
#> GSM317689     2  0.4399      0.747 0.000 0.812 0.188
#> GSM317691     1  0.0000      0.893 1.000 0.000 0.000
#> GSM317692     2  0.6482      0.623 0.244 0.716 0.040
#> GSM317693     1  0.1411      0.881 0.964 0.036 0.000
#> GSM317696     1  0.0424      0.894 0.992 0.000 0.008
#> GSM317697     1  0.0424      0.892 0.992 0.008 0.000
#> GSM317698     1  0.0237      0.894 0.996 0.000 0.004
#> GSM317650     2  0.6168      0.293 0.000 0.588 0.412
#> GSM317651     3  0.6051      0.464 0.292 0.012 0.696
#> GSM317657     2  0.2711      0.813 0.088 0.912 0.000
#> GSM317667     2  0.0237      0.863 0.004 0.996 0.000
#> GSM317670     1  0.5948      0.435 0.640 0.360 0.000
#> GSM317674     1  0.0747      0.893 0.984 0.000 0.016
#> GSM317675     1  0.0424      0.894 0.992 0.000 0.008
#> GSM317677     1  0.0000      0.893 1.000 0.000 0.000
#> GSM317678     3  0.5529      0.538 0.000 0.296 0.704
#> GSM317687     1  0.2537      0.854 0.920 0.080 0.000
#> GSM317695     1  0.6235      0.338 0.564 0.000 0.436
#> GSM317653     2  0.2165      0.843 0.000 0.936 0.064
#> GSM317656     1  0.6286      0.259 0.536 0.000 0.464
#> GSM317658     1  0.0747      0.891 0.984 0.016 0.000
#> GSM317660     3  0.4291      0.719 0.000 0.180 0.820
#> GSM317663     2  0.0892      0.862 0.000 0.980 0.020
#> GSM317664     1  0.2356      0.870 0.928 0.000 0.072
#> GSM317665     3  0.0424      0.852 0.000 0.008 0.992
#> GSM317673     1  0.3412      0.833 0.876 0.000 0.124
#> GSM317686     2  0.0424      0.862 0.008 0.992 0.000
#> GSM317688     1  0.0592      0.893 0.988 0.000 0.012
#> GSM317690     2  0.0237      0.863 0.000 0.996 0.004
#> GSM317654     3  0.1289      0.846 0.000 0.032 0.968
#> GSM317655     2  0.0592      0.861 0.012 0.988 0.000
#> GSM317659     1  0.2878      0.843 0.904 0.096 0.000
#> GSM317661     2  0.4346      0.753 0.000 0.816 0.184
#> GSM317662     2  0.3551      0.801 0.000 0.868 0.132
#> GSM317668     1  0.0424      0.894 0.992 0.000 0.008
#> GSM317669     3  0.0000      0.853 0.000 0.000 1.000
#> GSM317671     3  0.0592      0.851 0.012 0.000 0.988
#> GSM317676     2  0.4555      0.694 0.200 0.800 0.000
#> GSM317680     3  0.1529      0.835 0.040 0.000 0.960
#> GSM317684     1  0.0747      0.889 0.984 0.016 0.000
#> GSM317685     1  0.2165      0.874 0.936 0.000 0.064
#> GSM317694     1  0.0892      0.892 0.980 0.000 0.020

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM317649     3  0.0469     0.8175 0.012 0.000 0.988 0.000
#> GSM317652     1  0.8277     0.0198 0.412 0.016 0.292 0.280
#> GSM317666     4  0.1004     0.7781 0.000 0.024 0.004 0.972
#> GSM317672     3  0.6167     0.5652 0.000 0.096 0.648 0.256
#> GSM317679     3  0.0188     0.8205 0.004 0.000 0.996 0.000
#> GSM317681     3  0.2313     0.8147 0.000 0.044 0.924 0.032
#> GSM317682     1  0.3123     0.7605 0.844 0.000 0.156 0.000
#> GSM317683     2  0.2868     0.8657 0.000 0.864 0.000 0.136
#> GSM317689     2  0.3205     0.8704 0.000 0.872 0.024 0.104
#> GSM317691     1  0.0804     0.8515 0.980 0.000 0.008 0.012
#> GSM317692     1  0.8124     0.0923 0.464 0.352 0.036 0.148
#> GSM317693     1  0.1118     0.8433 0.964 0.000 0.000 0.036
#> GSM317696     1  0.0336     0.8507 0.992 0.000 0.008 0.000
#> GSM317697     1  0.0336     0.8503 0.992 0.000 0.000 0.008
#> GSM317698     1  0.0188     0.8506 0.996 0.004 0.000 0.000
#> GSM317650     2  0.2522     0.8591 0.000 0.908 0.016 0.076
#> GSM317651     3  0.6495     0.6875 0.092 0.068 0.716 0.124
#> GSM317657     4  0.6373     0.5127 0.148 0.200 0.000 0.652
#> GSM317667     4  0.1022     0.7763 0.000 0.032 0.000 0.968
#> GSM317670     1  0.6743     0.1372 0.472 0.452 0.008 0.068
#> GSM317674     1  0.0524     0.8512 0.988 0.004 0.008 0.000
#> GSM317675     1  0.0336     0.8512 0.992 0.008 0.000 0.000
#> GSM317677     1  0.0524     0.8515 0.988 0.008 0.000 0.004
#> GSM317678     3  0.6785     0.1023 0.000 0.420 0.484 0.096
#> GSM317687     4  0.4585     0.4882 0.332 0.000 0.000 0.668
#> GSM317695     3  0.4936     0.2735 0.372 0.004 0.624 0.000
#> GSM317653     4  0.2706     0.7216 0.000 0.080 0.020 0.900
#> GSM317656     1  0.4720     0.6974 0.768 0.032 0.196 0.004
#> GSM317658     1  0.2153     0.8370 0.936 0.036 0.008 0.020
#> GSM317660     3  0.4673     0.7571 0.000 0.132 0.792 0.076
#> GSM317663     4  0.1913     0.7696 0.000 0.040 0.020 0.940
#> GSM317664     1  0.2125     0.8319 0.920 0.004 0.076 0.000
#> GSM317665     3  0.2816     0.8103 0.000 0.064 0.900 0.036
#> GSM317673     1  0.1576     0.8441 0.948 0.004 0.048 0.000
#> GSM317686     4  0.0817     0.7738 0.000 0.024 0.000 0.976
#> GSM317688     1  0.0592     0.8513 0.984 0.000 0.016 0.000
#> GSM317690     2  0.2589     0.8060 0.000 0.884 0.000 0.116
#> GSM317654     3  0.3679     0.7974 0.000 0.084 0.856 0.060
#> GSM317655     2  0.4244     0.7148 0.032 0.800 0.000 0.168
#> GSM317659     1  0.3533     0.7917 0.864 0.056 0.000 0.080
#> GSM317661     2  0.4322     0.8096 0.000 0.804 0.044 0.152
#> GSM317662     2  0.3351     0.8627 0.000 0.844 0.008 0.148
#> GSM317668     1  0.4739     0.7205 0.788 0.160 0.008 0.044
#> GSM317669     3  0.0188     0.8203 0.000 0.004 0.996 0.000
#> GSM317671     3  0.0188     0.8205 0.004 0.000 0.996 0.000
#> GSM317676     4  0.6104     0.5973 0.140 0.180 0.000 0.680
#> GSM317680     3  0.0188     0.8205 0.004 0.000 0.996 0.000
#> GSM317684     1  0.1557     0.8344 0.944 0.000 0.000 0.056
#> GSM317685     1  0.3900     0.7333 0.816 0.000 0.020 0.164
#> GSM317694     1  0.0657     0.8512 0.984 0.004 0.012 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
#> GSM317649     3  0.0566     0.7881 0.012 0.004 0.984 0.000 0.000
#> GSM317652     1  0.8110     0.0366 0.424 0.236 0.092 0.240 0.008
#> GSM317666     4  0.0613     0.7062 0.000 0.004 0.004 0.984 0.008
#> GSM317672     3  0.7187     0.0973 0.000 0.340 0.412 0.224 0.024
#> GSM317679     3  0.0404     0.7879 0.012 0.000 0.988 0.000 0.000
#> GSM317681     3  0.3724     0.6424 0.000 0.184 0.788 0.028 0.000
#> GSM317682     1  0.2965     0.8119 0.876 0.028 0.084 0.000 0.012
#> GSM317683     2  0.5574     0.3846 0.000 0.512 0.000 0.072 0.416
#> GSM317689     2  0.5277     0.4131 0.000 0.524 0.008 0.032 0.436
#> GSM317691     1  0.2376     0.8392 0.916 0.024 0.004 0.044 0.012
#> GSM317692     2  0.8664     0.1078 0.232 0.364 0.024 0.112 0.268
#> GSM317693     1  0.0727     0.8637 0.980 0.004 0.000 0.012 0.004
#> GSM317696     1  0.0324     0.8649 0.992 0.004 0.004 0.000 0.000
#> GSM317697     1  0.0854     0.8638 0.976 0.012 0.000 0.004 0.008
#> GSM317698     1  0.0404     0.8636 0.988 0.000 0.000 0.000 0.012
#> GSM317650     2  0.4219     0.4345 0.000 0.584 0.000 0.000 0.416
#> GSM317651     2  0.7722    -0.2331 0.076 0.412 0.392 0.096 0.024
#> GSM317657     4  0.6168    -0.0519 0.044 0.048 0.000 0.512 0.396
#> GSM317667     4  0.0451     0.7049 0.000 0.008 0.000 0.988 0.004
#> GSM317670     5  0.4888     0.5823 0.220 0.004 0.008 0.052 0.716
#> GSM317674     1  0.0162     0.8643 0.996 0.000 0.000 0.000 0.004
#> GSM317675     1  0.0290     0.8642 0.992 0.000 0.000 0.000 0.008
#> GSM317677     1  0.1952     0.8231 0.912 0.000 0.000 0.004 0.084
#> GSM317678     2  0.7229     0.4204 0.000 0.520 0.196 0.060 0.224
#> GSM317687     4  0.4220     0.3518 0.300 0.004 0.000 0.688 0.008
#> GSM317695     3  0.2361     0.6889 0.096 0.000 0.892 0.000 0.012
#> GSM317653     4  0.4283     0.4370 0.000 0.292 0.012 0.692 0.004
#> GSM317656     1  0.3699     0.7576 0.824 0.128 0.036 0.000 0.012
#> GSM317658     1  0.4082     0.7365 0.812 0.040 0.004 0.020 0.124
#> GSM317660     2  0.6501    -0.0294 0.000 0.564 0.288 0.112 0.036
#> GSM317663     4  0.2184     0.6946 0.000 0.020 0.028 0.924 0.028
#> GSM317664     1  0.2573     0.8065 0.880 0.000 0.104 0.000 0.016
#> GSM317665     3  0.5166     0.2788 0.000 0.436 0.528 0.032 0.004
#> GSM317673     1  0.1205     0.8575 0.956 0.000 0.040 0.000 0.004
#> GSM317686     4  0.1928     0.6719 0.004 0.004 0.000 0.920 0.072
#> GSM317688     1  0.0566     0.8660 0.984 0.004 0.000 0.000 0.012
#> GSM317690     5  0.3477     0.4349 0.000 0.056 0.000 0.112 0.832
#> GSM317654     2  0.6108    -0.2738 0.000 0.456 0.432 0.108 0.004
#> GSM317655     5  0.4634     0.5404 0.036 0.064 0.004 0.108 0.788
#> GSM317659     1  0.5840     0.3238 0.624 0.012 0.000 0.112 0.252
#> GSM317661     2  0.5657     0.4300 0.000 0.664 0.024 0.088 0.224
#> GSM317662     2  0.5192     0.4632 0.000 0.668 0.012 0.056 0.264
#> GSM317668     5  0.5342     0.3506 0.412 0.000 0.012 0.032 0.544
#> GSM317669     3  0.0566     0.7840 0.004 0.012 0.984 0.000 0.000
#> GSM317671     3  0.0566     0.7864 0.012 0.000 0.984 0.000 0.004
#> GSM317676     5  0.6024     0.1621 0.088 0.008 0.000 0.432 0.472
#> GSM317680     3  0.0290     0.7878 0.008 0.000 0.992 0.000 0.000
#> GSM317684     1  0.1983     0.8435 0.924 0.008 0.000 0.060 0.008
#> GSM317685     1  0.3340     0.7903 0.856 0.044 0.012 0.088 0.000
#> GSM317694     1  0.0290     0.8645 0.992 0.000 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
#> GSM317649     3  0.0748     0.9089 0.004 0.000 0.976 0.004 0.016 0.000
#> GSM317652     5  0.6710     0.3170 0.300 0.004 0.032 0.148 0.496 0.020
#> GSM317666     4  0.0806     0.7937 0.000 0.000 0.000 0.972 0.008 0.020
#> GSM317672     5  0.7522     0.2206 0.004 0.248 0.224 0.108 0.408 0.008
#> GSM317679     3  0.0146     0.9133 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM317681     3  0.5082     0.4465 0.000 0.080 0.656 0.024 0.240 0.000
#> GSM317682     1  0.3261     0.8109 0.856 0.068 0.036 0.000 0.032 0.008
#> GSM317683     2  0.1151     0.6725 0.000 0.956 0.000 0.012 0.000 0.032
#> GSM317689     2  0.3841     0.6598 0.000 0.812 0.020 0.008 0.068 0.092
#> GSM317691     1  0.2838     0.7969 0.852 0.116 0.004 0.028 0.000 0.000
#> GSM317692     2  0.6308     0.4531 0.184 0.628 0.012 0.052 0.100 0.024
#> GSM317693     1  0.0582     0.8655 0.984 0.004 0.000 0.004 0.004 0.004
#> GSM317696     1  0.0146     0.8645 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM317697     1  0.0436     0.8653 0.988 0.000 0.004 0.004 0.000 0.004
#> GSM317698     1  0.0713     0.8645 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM317650     2  0.5596     0.4984 0.000 0.596 0.000 0.024 0.260 0.120
#> GSM317651     5  0.6029     0.5218 0.040 0.000 0.172 0.088 0.648 0.052
#> GSM317657     4  0.5456     0.1379 0.000 0.128 0.000 0.500 0.000 0.372
#> GSM317667     4  0.0993     0.7919 0.000 0.000 0.000 0.964 0.012 0.024
#> GSM317670     6  0.1781     0.8124 0.060 0.008 0.008 0.000 0.000 0.924
#> GSM317674     1  0.1138     0.8642 0.960 0.000 0.012 0.000 0.004 0.024
#> GSM317675     1  0.0777     0.8650 0.972 0.000 0.004 0.000 0.000 0.024
#> GSM317677     1  0.2631     0.7596 0.820 0.000 0.000 0.000 0.000 0.180
#> GSM317678     2  0.2964     0.6351 0.000 0.856 0.100 0.024 0.020 0.000
#> GSM317687     4  0.3261     0.5975 0.192 0.008 0.000 0.792 0.004 0.004
#> GSM317695     3  0.0777     0.8922 0.024 0.000 0.972 0.000 0.000 0.004
#> GSM317653     5  0.4312     0.1768 0.000 0.012 0.000 0.476 0.508 0.004
#> GSM317656     1  0.4651     0.6559 0.716 0.008 0.016 0.008 0.216 0.036
#> GSM317658     1  0.4180     0.5902 0.692 0.276 0.004 0.020 0.000 0.008
#> GSM317660     5  0.2395     0.5258 0.000 0.016 0.036 0.016 0.908 0.024
#> GSM317663     4  0.2485     0.7754 0.000 0.040 0.032 0.900 0.004 0.024
#> GSM317664     1  0.3134     0.7739 0.808 0.000 0.168 0.000 0.000 0.024
#> GSM317665     5  0.3613     0.5579 0.000 0.004 0.192 0.024 0.776 0.004
#> GSM317673     1  0.2015     0.8536 0.916 0.000 0.056 0.000 0.012 0.016
#> GSM317686     4  0.1549     0.7949 0.000 0.020 0.000 0.936 0.000 0.044
#> GSM317688     1  0.1265     0.8630 0.948 0.000 0.008 0.000 0.000 0.044
#> GSM317690     6  0.2759     0.7619 0.000 0.080 0.004 0.040 0.004 0.872
#> GSM317654     5  0.3809     0.5654 0.000 0.016 0.140 0.044 0.796 0.004
#> GSM317655     6  0.1442     0.8080 0.000 0.004 0.000 0.040 0.012 0.944
#> GSM317659     1  0.6187    -0.0535 0.448 0.000 0.000 0.088 0.060 0.404
#> GSM317661     5  0.6100    -0.1754 0.000 0.384 0.004 0.036 0.476 0.100
#> GSM317662     2  0.5420     0.3267 0.000 0.568 0.004 0.020 0.340 0.068
#> GSM317668     6  0.3020     0.7078 0.176 0.000 0.004 0.004 0.004 0.812
#> GSM317669     3  0.0547     0.9111 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM317671     3  0.0291     0.9141 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM317676     6  0.3838     0.6496 0.020 0.000 0.000 0.240 0.008 0.732
#> GSM317680     3  0.0363     0.9127 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM317684     1  0.1057     0.8634 0.968 0.004 0.004 0.012 0.008 0.004
#> GSM317685     1  0.3723     0.7869 0.824 0.008 0.008 0.076 0.076 0.008
#> GSM317694     1  0.1124     0.8641 0.956 0.000 0.036 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-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 disease.state(p) k
#> CV:NMF 45            0.805 2
#> CV:NMF 44            0.966 3
#> CV:NMF 44            0.880 4
#> CV:NMF 30            0.477 5
#> CV:NMF 40            0.380 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 11993 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 4.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

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 0.759           0.900       0.949         0.3101 0.726   0.726
#> 3 3 0.779           0.886       0.949         0.0567 0.990   0.987
#> 4 4 0.654           0.840       0.899         0.9094 0.647   0.507
#> 5 5 0.525           0.676       0.807         0.1252 0.949   0.858
#> 6 6 0.584           0.693       0.758         0.0956 0.907   0.706

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] 4

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
#> GSM317649     1  0.0000      0.946 1.000 0.000
#> GSM317652     1  0.0000      0.946 1.000 0.000
#> GSM317666     1  0.6148      0.844 0.848 0.152
#> GSM317672     1  0.7299      0.775 0.796 0.204
#> GSM317679     1  0.0000      0.946 1.000 0.000
#> GSM317681     1  0.1184      0.942 0.984 0.016
#> GSM317682     1  0.0000      0.946 1.000 0.000
#> GSM317683     2  0.0000      0.939 0.000 1.000
#> GSM317689     1  0.9635      0.435 0.612 0.388
#> GSM317691     1  0.1414      0.940 0.980 0.020
#> GSM317692     1  0.3879      0.906 0.924 0.076
#> GSM317693     1  0.0938      0.943 0.988 0.012
#> GSM317696     1  0.0000      0.946 1.000 0.000
#> GSM317697     1  0.0376      0.945 0.996 0.004
#> GSM317698     1  0.0000      0.946 1.000 0.000
#> GSM317650     2  0.0000      0.939 0.000 1.000
#> GSM317651     1  0.0000      0.946 1.000 0.000
#> GSM317657     1  0.7139      0.795 0.804 0.196
#> GSM317667     2  0.0000      0.939 0.000 1.000
#> GSM317670     1  0.7299      0.785 0.796 0.204
#> GSM317674     1  0.0000      0.946 1.000 0.000
#> GSM317675     1  0.0000      0.946 1.000 0.000
#> GSM317677     1  0.3114      0.923 0.944 0.056
#> GSM317678     2  0.3584      0.887 0.068 0.932
#> GSM317687     1  0.2778      0.927 0.952 0.048
#> GSM317695     1  0.0000      0.946 1.000 0.000
#> GSM317653     1  0.0938      0.943 0.988 0.012
#> GSM317656     1  0.0000      0.946 1.000 0.000
#> GSM317658     1  0.6148      0.840 0.848 0.152
#> GSM317660     1  0.0672      0.943 0.992 0.008
#> GSM317663     1  0.7139      0.795 0.804 0.196
#> GSM317664     1  0.0000      0.946 1.000 0.000
#> GSM317665     1  0.0000      0.946 1.000 0.000
#> GSM317673     1  0.0000      0.946 1.000 0.000
#> GSM317686     2  0.0000      0.939 0.000 1.000
#> GSM317688     1  0.0000      0.946 1.000 0.000
#> GSM317690     2  0.8955      0.484 0.312 0.688
#> GSM317654     1  0.0000      0.946 1.000 0.000
#> GSM317655     1  0.8081      0.723 0.752 0.248
#> GSM317659     1  0.3114      0.923 0.944 0.056
#> GSM317661     2  0.0000      0.939 0.000 1.000
#> GSM317662     2  0.0000      0.939 0.000 1.000
#> GSM317668     1  0.0376      0.945 0.996 0.004
#> GSM317669     1  0.0000      0.946 1.000 0.000
#> GSM317671     1  0.0000      0.946 1.000 0.000
#> GSM317676     1  0.3274      0.920 0.940 0.060
#> GSM317680     1  0.0000      0.946 1.000 0.000
#> GSM317684     1  0.2236      0.933 0.964 0.036
#> GSM317685     1  0.0000      0.946 1.000 0.000
#> GSM317694     1  0.1633      0.938 0.976 0.024

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> GSM317649     1  0.0000      0.947 1.000 0.000 0.000
#> GSM317652     1  0.0000      0.947 1.000 0.000 0.000
#> GSM317666     1  0.4047      0.850 0.848 0.004 0.148
#> GSM317672     1  0.4784      0.763 0.796 0.200 0.004
#> GSM317679     1  0.0000      0.947 1.000 0.000 0.000
#> GSM317681     1  0.0829      0.943 0.984 0.012 0.004
#> GSM317682     1  0.0000      0.947 1.000 0.000 0.000
#> GSM317683     2  0.0000      0.810 0.000 1.000 0.000
#> GSM317689     1  0.6566      0.411 0.612 0.376 0.012
#> GSM317691     1  0.1015      0.941 0.980 0.012 0.008
#> GSM317692     1  0.2680      0.903 0.924 0.068 0.008
#> GSM317693     1  0.0661      0.944 0.988 0.004 0.008
#> GSM317696     1  0.0000      0.947 1.000 0.000 0.000
#> GSM317697     1  0.0237      0.946 0.996 0.004 0.000
#> GSM317698     1  0.0000      0.947 1.000 0.000 0.000
#> GSM317650     2  0.0000      0.810 0.000 1.000 0.000
#> GSM317651     1  0.0000      0.947 1.000 0.000 0.000
#> GSM317657     1  0.5710      0.800 0.804 0.080 0.116
#> GSM317667     3  0.0000      1.000 0.000 0.000 1.000
#> GSM317670     1  0.4784      0.773 0.796 0.200 0.004
#> GSM317674     1  0.0000      0.947 1.000 0.000 0.000
#> GSM317675     1  0.0000      0.947 1.000 0.000 0.000
#> GSM317677     1  0.1964      0.924 0.944 0.000 0.056
#> GSM317678     2  0.2261      0.740 0.068 0.932 0.000
#> GSM317687     1  0.1753      0.928 0.952 0.000 0.048
#> GSM317695     1  0.0000      0.947 1.000 0.000 0.000
#> GSM317653     1  0.0661      0.944 0.988 0.008 0.004
#> GSM317656     1  0.0000      0.947 1.000 0.000 0.000
#> GSM317658     1  0.4047      0.832 0.848 0.148 0.004
#> GSM317660     1  0.0424      0.944 0.992 0.008 0.000
#> GSM317663     1  0.5710      0.800 0.804 0.080 0.116
#> GSM317664     1  0.0000      0.947 1.000 0.000 0.000
#> GSM317665     1  0.0000      0.947 1.000 0.000 0.000
#> GSM317673     1  0.0000      0.947 1.000 0.000 0.000
#> GSM317686     3  0.0000      1.000 0.000 0.000 1.000
#> GSM317688     1  0.0000      0.947 1.000 0.000 0.000
#> GSM317690     2  0.5873      0.350 0.312 0.684 0.004
#> GSM317654     1  0.0000      0.947 1.000 0.000 0.000
#> GSM317655     1  0.6208      0.721 0.752 0.200 0.048
#> GSM317659     1  0.1964      0.924 0.944 0.000 0.056
#> GSM317661     2  0.0000      0.810 0.000 1.000 0.000
#> GSM317662     2  0.0000      0.810 0.000 1.000 0.000
#> GSM317668     1  0.0237      0.946 0.996 0.004 0.000
#> GSM317669     1  0.0000      0.947 1.000 0.000 0.000
#> GSM317671     1  0.0000      0.947 1.000 0.000 0.000
#> GSM317676     1  0.2066      0.922 0.940 0.000 0.060
#> GSM317680     1  0.0000      0.947 1.000 0.000 0.000
#> GSM317684     1  0.1411      0.934 0.964 0.000 0.036
#> GSM317685     1  0.0000      0.947 1.000 0.000 0.000
#> GSM317694     1  0.1031      0.939 0.976 0.000 0.024

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM317649     3  0.0469      0.956 0.012 0.000 0.988 0.000
#> GSM317652     3  0.0469      0.956 0.012 0.000 0.988 0.000
#> GSM317666     1  0.2081      0.739 0.916 0.000 0.000 0.084
#> GSM317672     1  0.6049      0.693 0.680 0.200 0.120 0.000
#> GSM317679     3  0.0376      0.952 0.004 0.000 0.992 0.004
#> GSM317681     3  0.1970      0.933 0.060 0.008 0.932 0.000
#> GSM317682     3  0.1211      0.954 0.040 0.000 0.960 0.000
#> GSM317683     2  0.0000      0.869 0.000 1.000 0.000 0.000
#> GSM317689     1  0.5673      0.444 0.596 0.372 0.032 0.000
#> GSM317691     1  0.3978      0.758 0.796 0.012 0.192 0.000
#> GSM317692     1  0.5325      0.733 0.728 0.068 0.204 0.000
#> GSM317693     1  0.4560      0.663 0.700 0.004 0.296 0.000
#> GSM317696     3  0.1389      0.951 0.048 0.000 0.952 0.000
#> GSM317697     3  0.4401      0.605 0.272 0.004 0.724 0.000
#> GSM317698     3  0.1557      0.947 0.056 0.000 0.944 0.000
#> GSM317650     2  0.0000      0.869 0.000 1.000 0.000 0.000
#> GSM317651     3  0.0469      0.956 0.012 0.000 0.988 0.000
#> GSM317657     1  0.4036      0.725 0.836 0.076 0.000 0.088
#> GSM317667     4  0.0188      1.000 0.004 0.000 0.000 0.996
#> GSM317670     1  0.4630      0.709 0.768 0.196 0.036 0.000
#> GSM317674     3  0.1557      0.947 0.056 0.000 0.944 0.000
#> GSM317675     3  0.1557      0.947 0.056 0.000 0.944 0.000
#> GSM317677     1  0.3123      0.750 0.844 0.000 0.156 0.000
#> GSM317678     2  0.2111      0.810 0.024 0.932 0.044 0.000
#> GSM317687     1  0.1716      0.783 0.936 0.000 0.064 0.000
#> GSM317695     3  0.0376      0.952 0.004 0.000 0.992 0.004
#> GSM317653     3  0.1743      0.936 0.056 0.004 0.940 0.000
#> GSM317656     3  0.0707      0.957 0.020 0.000 0.980 0.000
#> GSM317658     1  0.5950      0.723 0.696 0.148 0.156 0.000
#> GSM317660     3  0.1305      0.947 0.036 0.004 0.960 0.000
#> GSM317663     1  0.4036      0.725 0.836 0.076 0.000 0.088
#> GSM317664     3  0.1557      0.947 0.056 0.000 0.944 0.000
#> GSM317665     3  0.1118      0.948 0.036 0.000 0.964 0.000
#> GSM317673     3  0.1211      0.954 0.040 0.000 0.960 0.000
#> GSM317686     4  0.0188      1.000 0.004 0.000 0.000 0.996
#> GSM317688     3  0.1557      0.947 0.056 0.000 0.944 0.000
#> GSM317690     2  0.4500      0.403 0.316 0.684 0.000 0.000
#> GSM317654     3  0.1118      0.948 0.036 0.000 0.964 0.000
#> GSM317655     1  0.4406      0.674 0.780 0.192 0.000 0.028
#> GSM317659     1  0.1211      0.776 0.960 0.000 0.040 0.000
#> GSM317661     2  0.0188      0.867 0.004 0.996 0.000 0.000
#> GSM317662     2  0.0000      0.869 0.000 1.000 0.000 0.000
#> GSM317668     1  0.3907      0.750 0.768 0.000 0.232 0.000
#> GSM317669     3  0.0376      0.952 0.004 0.000 0.992 0.004
#> GSM317671     3  0.0376      0.952 0.004 0.000 0.992 0.004
#> GSM317676     1  0.1022      0.773 0.968 0.000 0.032 0.000
#> GSM317680     3  0.0376      0.952 0.004 0.000 0.992 0.004
#> GSM317684     1  0.2589      0.781 0.884 0.000 0.116 0.000
#> GSM317685     3  0.1211      0.954 0.040 0.000 0.960 0.000
#> GSM317694     1  0.4072      0.686 0.748 0.000 0.252 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
#> GSM317649     1   0.179      0.740 0.916 0.000 0.000 0.000 0.084
#> GSM317652     1   0.218      0.729 0.888 0.000 0.000 0.000 0.112
#> GSM317666     4   0.201      0.712 0.000 0.000 0.088 0.908 0.004
#> GSM317672     4   0.703      0.610 0.096 0.188 0.000 0.576 0.140
#> GSM317679     1   0.293      0.676 0.820 0.000 0.000 0.000 0.180
#> GSM317681     5   0.475      0.923 0.352 0.000 0.000 0.028 0.620
#> GSM317682     1   0.239      0.704 0.896 0.000 0.000 0.020 0.084
#> GSM317683     2   0.000      0.841 0.000 1.000 0.000 0.000 0.000
#> GSM317689     4   0.630      0.452 0.008 0.292 0.000 0.548 0.152
#> GSM317691     4   0.516      0.709 0.168 0.000 0.000 0.692 0.140
#> GSM317692     4   0.650      0.675 0.176 0.056 0.000 0.620 0.148
#> GSM317693     4   0.578      0.590 0.272 0.000 0.000 0.596 0.132
#> GSM317696     1   0.140      0.749 0.952 0.000 0.000 0.028 0.020
#> GSM317697     1   0.493      0.353 0.708 0.000 0.000 0.188 0.104
#> GSM317698     1   0.158      0.747 0.944 0.000 0.000 0.028 0.028
#> GSM317650     2   0.000      0.841 0.000 1.000 0.000 0.000 0.000
#> GSM317651     1   0.323      0.518 0.800 0.000 0.000 0.004 0.196
#> GSM317657     4   0.406      0.709 0.000 0.032 0.092 0.820 0.056
#> GSM317667     3   0.000      1.000 0.000 0.000 1.000 0.000 0.000
#> GSM317670     4   0.536      0.667 0.004 0.100 0.000 0.664 0.232
#> GSM317674     1   0.158      0.747 0.944 0.000 0.000 0.028 0.028
#> GSM317675     1   0.158      0.747 0.944 0.000 0.000 0.028 0.028
#> GSM317677     4   0.340      0.699 0.168 0.000 0.000 0.812 0.020
#> GSM317678     2   0.210      0.806 0.012 0.924 0.000 0.016 0.048
#> GSM317687     4   0.188      0.746 0.064 0.000 0.000 0.924 0.012
#> GSM317695     1   0.293      0.676 0.820 0.000 0.000 0.000 0.180
#> GSM317653     5   0.470      0.928 0.360 0.000 0.000 0.024 0.616
#> GSM317656     1   0.191      0.741 0.908 0.000 0.000 0.000 0.092
#> GSM317658     4   0.698      0.652 0.128 0.136 0.000 0.592 0.144
#> GSM317660     5   0.437      0.862 0.416 0.000 0.000 0.004 0.580
#> GSM317663     4   0.406      0.709 0.000 0.032 0.092 0.820 0.056
#> GSM317664     1   0.158      0.747 0.944 0.000 0.000 0.028 0.028
#> GSM317665     1   0.468     -0.291 0.600 0.000 0.000 0.020 0.380
#> GSM317673     1   0.157      0.747 0.944 0.000 0.000 0.020 0.036
#> GSM317686     3   0.000      1.000 0.000 0.000 1.000 0.000 0.000
#> GSM317688     1   0.183      0.742 0.932 0.000 0.000 0.028 0.040
#> GSM317690     2   0.599      0.262 0.000 0.556 0.000 0.304 0.140
#> GSM317654     1   0.468     -0.291 0.600 0.000 0.000 0.020 0.380
#> GSM317655     4   0.462      0.684 0.000 0.052 0.028 0.768 0.152
#> GSM317659     4   0.144      0.739 0.040 0.000 0.000 0.948 0.012
#> GSM317661     2   0.189      0.811 0.000 0.916 0.000 0.004 0.080
#> GSM317662     2   0.000      0.841 0.000 1.000 0.000 0.000 0.000
#> GSM317668     4   0.548      0.688 0.160 0.000 0.000 0.656 0.184
#> GSM317669     1   0.293      0.676 0.820 0.000 0.000 0.000 0.180
#> GSM317671     1   0.293      0.676 0.820 0.000 0.000 0.000 0.180
#> GSM317676     4   0.128      0.737 0.032 0.000 0.000 0.956 0.012
#> GSM317680     1   0.293      0.676 0.820 0.000 0.000 0.000 0.180
#> GSM317684     4   0.256      0.737 0.120 0.000 0.000 0.872 0.008
#> GSM317685     1   0.131      0.747 0.956 0.000 0.000 0.020 0.024
#> GSM317694     4   0.407      0.623 0.264 0.000 0.000 0.720 0.016

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> GSM317649     1  0.4282      0.171 0.560 0.000 0.420 0.000 0.020 0.000
#> GSM317652     1  0.4344      0.396 0.628 0.000 0.336 0.000 0.036 0.000
#> GSM317666     4  0.1556      0.690 0.000 0.000 0.000 0.920 0.000 0.080
#> GSM317672     4  0.7662      0.563 0.108 0.188 0.080 0.492 0.132 0.000
#> GSM317679     3  0.2378      1.000 0.152 0.000 0.848 0.000 0.000 0.000
#> GSM317681     5  0.4075      0.726 0.168 0.000 0.060 0.012 0.760 0.000
#> GSM317682     1  0.2301      0.675 0.884 0.000 0.020 0.000 0.096 0.000
#> GSM317683     2  0.0000      0.834 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM317689     4  0.6579      0.439 0.004 0.260 0.048 0.500 0.188 0.000
#> GSM317691     4  0.5889      0.680 0.208 0.000 0.068 0.612 0.112 0.000
#> GSM317692     4  0.7179      0.638 0.208 0.056 0.084 0.532 0.120 0.000
#> GSM317693     4  0.6268      0.586 0.300 0.000 0.068 0.524 0.108 0.000
#> GSM317696     1  0.0725      0.757 0.976 0.000 0.012 0.000 0.012 0.000
#> GSM317697     1  0.4747      0.437 0.732 0.000 0.052 0.144 0.072 0.000
#> GSM317698     1  0.0458      0.760 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM317650     2  0.0000      0.834 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM317651     1  0.4233      0.213 0.684 0.000 0.048 0.000 0.268 0.000
#> GSM317657     4  0.3948      0.685 0.000 0.004 0.016 0.796 0.104 0.080
#> GSM317667     6  0.0000      1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM317670     4  0.6355      0.642 0.032 0.060 0.108 0.608 0.192 0.000
#> GSM317674     1  0.0458      0.760 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM317675     1  0.0458      0.760 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM317677     4  0.3309      0.677 0.192 0.000 0.016 0.788 0.004 0.000
#> GSM317678     2  0.1929      0.799 0.004 0.924 0.016 0.008 0.048 0.000
#> GSM317687     4  0.1908      0.722 0.096 0.000 0.000 0.900 0.004 0.000
#> GSM317695     3  0.2378      1.000 0.152 0.000 0.848 0.000 0.000 0.000
#> GSM317653     5  0.4140      0.734 0.172 0.000 0.056 0.016 0.756 0.000
#> GSM317656     1  0.4045      0.453 0.664 0.000 0.312 0.000 0.024 0.000
#> GSM317658     4  0.7626      0.609 0.160 0.136 0.080 0.504 0.120 0.000
#> GSM317660     5  0.4494      0.748 0.216 0.000 0.092 0.000 0.692 0.000
#> GSM317663     4  0.3857      0.685 0.000 0.004 0.012 0.800 0.104 0.080
#> GSM317664     1  0.0458      0.760 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM317665     5  0.5498      0.544 0.436 0.000 0.088 0.012 0.464 0.000
#> GSM317673     1  0.0935      0.743 0.964 0.000 0.004 0.000 0.032 0.000
#> GSM317686     6  0.0000      1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM317688     1  0.0935      0.750 0.964 0.000 0.032 0.000 0.004 0.000
#> GSM317690     2  0.6283      0.202 0.000 0.512 0.052 0.304 0.132 0.000
#> GSM317654     5  0.5498      0.544 0.436 0.000 0.088 0.012 0.464 0.000
#> GSM317655     4  0.4333      0.665 0.000 0.008 0.048 0.748 0.180 0.016
#> GSM317659     4  0.1588      0.717 0.072 0.000 0.000 0.924 0.004 0.000
#> GSM317661     2  0.2279      0.796 0.000 0.904 0.024 0.016 0.056 0.000
#> GSM317662     2  0.0000      0.834 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM317668     4  0.6115      0.640 0.096 0.000 0.228 0.584 0.092 0.000
#> GSM317669     3  0.2378      1.000 0.152 0.000 0.848 0.000 0.000 0.000
#> GSM317671     3  0.2378      1.000 0.152 0.000 0.848 0.000 0.000 0.000
#> GSM317676     4  0.1471      0.714 0.064 0.000 0.000 0.932 0.004 0.000
#> GSM317680     3  0.2378      1.000 0.152 0.000 0.848 0.000 0.000 0.000
#> GSM317684     4  0.2520      0.710 0.152 0.000 0.000 0.844 0.004 0.000
#> GSM317685     1  0.1297      0.734 0.948 0.000 0.012 0.000 0.040 0.000
#> GSM317694     4  0.3915      0.620 0.288 0.000 0.016 0.692 0.004 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 disease.state(p) k
#> MAD:hclust 48            0.528 2
#> MAD:hclust 48            0.539 3
#> MAD:hclust 48            0.584 4
#> MAD:hclust 45            0.552 5
#> MAD:hclust 43            0.456 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 11993 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           0.944       0.977         0.4578 0.542   0.542
#> 3 3 0.520           0.615       0.723         0.3647 0.791   0.620
#> 4 4 0.608           0.739       0.842         0.1454 0.828   0.564
#> 5 5 0.683           0.709       0.823         0.0691 0.892   0.654
#> 6 6 0.692           0.578       0.759         0.0528 0.952   0.814

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
#> GSM317649     1  0.0672      0.981 0.992 0.008
#> GSM317652     1  0.0672      0.981 0.992 0.008
#> GSM317666     2  0.0938      0.964 0.012 0.988
#> GSM317672     2  0.0000      0.964 0.000 1.000
#> GSM317679     1  0.0672      0.981 0.992 0.008
#> GSM317681     2  0.0672      0.962 0.008 0.992
#> GSM317682     1  0.0938      0.980 0.988 0.012
#> GSM317683     2  0.0000      0.964 0.000 1.000
#> GSM317689     2  0.0376      0.964 0.004 0.996
#> GSM317691     1  0.0000      0.982 1.000 0.000
#> GSM317692     1  0.1414      0.969 0.980 0.020
#> GSM317693     1  0.0376      0.982 0.996 0.004
#> GSM317696     1  0.0376      0.982 0.996 0.004
#> GSM317697     1  0.0376      0.982 0.996 0.004
#> GSM317698     1  0.0376      0.982 0.996 0.004
#> GSM317650     2  0.0000      0.964 0.000 1.000
#> GSM317651     1  0.0376      0.982 0.996 0.004
#> GSM317657     2  0.0938      0.964 0.012 0.988
#> GSM317667     2  0.0938      0.964 0.012 0.988
#> GSM317670     2  0.0938      0.962 0.012 0.988
#> GSM317674     1  0.0376      0.982 0.996 0.004
#> GSM317675     1  0.0376      0.982 0.996 0.004
#> GSM317677     1  0.0000      0.982 1.000 0.000
#> GSM317678     2  0.0000      0.964 0.000 1.000
#> GSM317687     1  0.0000      0.982 1.000 0.000
#> GSM317695     1  0.0000      0.982 1.000 0.000
#> GSM317653     1  0.9710      0.314 0.600 0.400
#> GSM317656     1  0.0938      0.980 0.988 0.012
#> GSM317658     2  0.9993      0.057 0.484 0.516
#> GSM317660     1  0.0938      0.980 0.988 0.012
#> GSM317663     2  0.0938      0.964 0.012 0.988
#> GSM317664     1  0.0376      0.982 0.996 0.004
#> GSM317665     1  0.0672      0.981 0.992 0.008
#> GSM317673     1  0.0376      0.982 0.996 0.004
#> GSM317686     2  0.0938      0.964 0.012 0.988
#> GSM317688     1  0.0938      0.980 0.988 0.012
#> GSM317690     2  0.0672      0.963 0.008 0.992
#> GSM317654     1  0.0672      0.981 0.992 0.008
#> GSM317655     2  0.0938      0.964 0.012 0.988
#> GSM317659     1  0.0000      0.982 1.000 0.000
#> GSM317661     2  0.0000      0.964 0.000 1.000
#> GSM317662     2  0.0000      0.964 0.000 1.000
#> GSM317668     1  0.0376      0.982 0.996 0.004
#> GSM317669     1  0.0672      0.981 0.992 0.008
#> GSM317671     1  0.0672      0.981 0.992 0.008
#> GSM317676     1  0.0000      0.982 1.000 0.000
#> GSM317680     1  0.0672      0.981 0.992 0.008
#> GSM317684     1  0.0000      0.982 1.000 0.000
#> GSM317685     1  0.0000      0.982 1.000 0.000
#> GSM317694     1  0.0000      0.982 1.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> GSM317649     3   0.661     0.7952 0.432 0.008 0.560
#> GSM317652     3   0.630     0.7257 0.484 0.000 0.516
#> GSM317666     3   0.903    -0.6446 0.132 0.428 0.440
#> GSM317672     2   0.277     0.8303 0.004 0.916 0.080
#> GSM317679     3   0.660     0.7938 0.428 0.008 0.564
#> GSM317681     2   0.337     0.8251 0.024 0.904 0.072
#> GSM317682     1   0.312     0.6190 0.892 0.000 0.108
#> GSM317683     2   0.000     0.8350 0.000 1.000 0.000
#> GSM317689     2   0.226     0.8333 0.000 0.932 0.068
#> GSM317691     1   0.424     0.6417 0.824 0.000 0.176
#> GSM317692     1   0.465     0.6357 0.816 0.008 0.176
#> GSM317693     1   0.394     0.6531 0.844 0.000 0.156
#> GSM317696     1   0.296     0.6218 0.900 0.000 0.100
#> GSM317697     1   0.236     0.6625 0.928 0.000 0.072
#> GSM317698     1   0.000     0.6563 1.000 0.000 0.000
#> GSM317650     2   0.000     0.8350 0.000 1.000 0.000
#> GSM317651     1   0.334     0.6096 0.880 0.000 0.120
#> GSM317657     2   0.742     0.7281 0.040 0.572 0.388
#> GSM317667     2   0.615     0.7521 0.004 0.640 0.356
#> GSM317670     2   0.517     0.8177 0.024 0.804 0.172
#> GSM317674     1   0.296     0.6218 0.900 0.000 0.100
#> GSM317675     1   0.288     0.6243 0.904 0.000 0.096
#> GSM317677     1   0.388     0.6537 0.848 0.000 0.152
#> GSM317678     2   0.000     0.8350 0.000 1.000 0.000
#> GSM317687     1   0.514     0.5695 0.748 0.000 0.252
#> GSM317695     3   0.624     0.7878 0.440 0.000 0.560
#> GSM317653     1   0.971    -0.0412 0.420 0.356 0.224
#> GSM317656     1   0.631    -0.7101 0.508 0.000 0.492
#> GSM317658     2   0.834     0.0664 0.444 0.476 0.080
#> GSM317660     3   0.806     0.7092 0.376 0.072 0.552
#> GSM317663     2   0.630     0.7528 0.004 0.608 0.388
#> GSM317664     1   0.296     0.6218 0.900 0.000 0.100
#> GSM317665     3   0.663     0.7760 0.444 0.008 0.548
#> GSM317673     1   0.304     0.6173 0.896 0.000 0.104
#> GSM317686     2   0.543     0.7808 0.000 0.716 0.284
#> GSM317688     1   0.304     0.6173 0.896 0.000 0.104
#> GSM317690     2   0.245     0.8330 0.000 0.924 0.076
#> GSM317654     3   0.666     0.7361 0.460 0.008 0.532
#> GSM317655     2   0.630     0.7528 0.004 0.608 0.388
#> GSM317659     1   0.406     0.6488 0.836 0.000 0.164
#> GSM317661     2   0.000     0.8350 0.000 1.000 0.000
#> GSM317662     2   0.000     0.8350 0.000 1.000 0.000
#> GSM317668     1   0.571    -0.0905 0.680 0.000 0.320
#> GSM317669     3   0.661     0.7952 0.432 0.008 0.560
#> GSM317671     3   0.660     0.7938 0.428 0.008 0.564
#> GSM317676     1   0.619     0.3872 0.580 0.000 0.420
#> GSM317680     3   0.661     0.7952 0.432 0.008 0.560
#> GSM317684     1   0.394     0.6531 0.844 0.000 0.156
#> GSM317685     1   0.304     0.6173 0.896 0.000 0.104
#> GSM317694     1   0.116     0.6604 0.972 0.000 0.028

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM317649     3  0.0524     0.7986 0.008 0.000 0.988 0.004
#> GSM317652     3  0.5889     0.6964 0.212 0.000 0.688 0.100
#> GSM317666     4  0.4780     0.7102 0.096 0.116 0.000 0.788
#> GSM317672     2  0.3632     0.7731 0.004 0.832 0.008 0.156
#> GSM317679     3  0.0336     0.7981 0.008 0.000 0.992 0.000
#> GSM317681     2  0.5020     0.6771 0.004 0.760 0.052 0.184
#> GSM317682     1  0.4513     0.7767 0.804 0.000 0.076 0.120
#> GSM317683     2  0.0000     0.8796 0.000 1.000 0.000 0.000
#> GSM317689     2  0.1677     0.8536 0.012 0.948 0.000 0.040
#> GSM317691     1  0.2011     0.8190 0.920 0.000 0.000 0.080
#> GSM317692     1  0.2796     0.8021 0.892 0.008 0.004 0.096
#> GSM317693     1  0.0921     0.8456 0.972 0.000 0.000 0.028
#> GSM317696     1  0.2530     0.8556 0.896 0.000 0.100 0.004
#> GSM317697     1  0.0657     0.8548 0.984 0.000 0.012 0.004
#> GSM317698     1  0.1867     0.8617 0.928 0.000 0.072 0.000
#> GSM317650     2  0.0000     0.8796 0.000 1.000 0.000 0.000
#> GSM317651     1  0.5582     0.6961 0.724 0.000 0.108 0.168
#> GSM317657     4  0.5496     0.7173 0.088 0.188 0.000 0.724
#> GSM317667     4  0.4088     0.6597 0.000 0.232 0.004 0.764
#> GSM317670     2  0.5766     0.5366 0.104 0.704 0.000 0.192
#> GSM317674     1  0.2345     0.8559 0.900 0.000 0.100 0.000
#> GSM317675     1  0.2281     0.8573 0.904 0.000 0.096 0.000
#> GSM317677     1  0.1305     0.8436 0.960 0.000 0.004 0.036
#> GSM317678     2  0.0000     0.8796 0.000 1.000 0.000 0.000
#> GSM317687     1  0.3219     0.7298 0.836 0.000 0.000 0.164
#> GSM317695     3  0.0707     0.7956 0.020 0.000 0.980 0.000
#> GSM317653     4  0.8426     0.0995 0.376 0.148 0.052 0.424
#> GSM317656     3  0.5337     0.3636 0.424 0.000 0.564 0.012
#> GSM317658     1  0.5894     0.0796 0.536 0.428 0.000 0.036
#> GSM317660     3  0.5575     0.7406 0.056 0.032 0.756 0.156
#> GSM317663     4  0.5429     0.7146 0.072 0.208 0.000 0.720
#> GSM317664     1  0.2345     0.8559 0.900 0.000 0.100 0.000
#> GSM317665     3  0.5220     0.7512 0.092 0.000 0.752 0.156
#> GSM317673     1  0.2675     0.8541 0.892 0.000 0.100 0.008
#> GSM317686     4  0.4252     0.6467 0.000 0.252 0.004 0.744
#> GSM317688     1  0.2675     0.8541 0.892 0.000 0.100 0.008
#> GSM317690     2  0.2469     0.7906 0.000 0.892 0.000 0.108
#> GSM317654     3  0.5728     0.7283 0.104 0.000 0.708 0.188
#> GSM317655     4  0.5533     0.7083 0.072 0.220 0.000 0.708
#> GSM317659     1  0.2011     0.8181 0.920 0.000 0.000 0.080
#> GSM317661     2  0.0000     0.8796 0.000 1.000 0.000 0.000
#> GSM317662     2  0.0000     0.8796 0.000 1.000 0.000 0.000
#> GSM317668     3  0.5353     0.3217 0.432 0.000 0.556 0.012
#> GSM317669     3  0.0188     0.7960 0.004 0.000 0.996 0.000
#> GSM317671     3  0.0336     0.7981 0.008 0.000 0.992 0.000
#> GSM317676     4  0.4730     0.4631 0.364 0.000 0.000 0.636
#> GSM317680     3  0.0336     0.7981 0.008 0.000 0.992 0.000
#> GSM317684     1  0.1557     0.8341 0.944 0.000 0.000 0.056
#> GSM317685     1  0.2530     0.8543 0.896 0.000 0.100 0.004
#> GSM317694     1  0.2450     0.8622 0.912 0.000 0.072 0.016

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> GSM317649     3  0.0404     0.9800 0.000 0.000 0.988 0.000 0.012
#> GSM317652     5  0.6740     0.4949 0.140 0.000 0.356 0.024 0.480
#> GSM317666     4  0.2342     0.7935 0.020 0.024 0.000 0.916 0.040
#> GSM317672     2  0.5465     0.3877 0.008 0.600 0.008 0.040 0.344
#> GSM317679     3  0.0000     0.9922 0.000 0.000 1.000 0.000 0.000
#> GSM317681     5  0.5849     0.3899 0.008 0.256 0.016 0.080 0.640
#> GSM317682     1  0.4954     0.0891 0.568 0.004 0.016 0.004 0.408
#> GSM317683     2  0.0162     0.8473 0.000 0.996 0.000 0.004 0.000
#> GSM317689     2  0.2416     0.8005 0.000 0.888 0.000 0.100 0.012
#> GSM317691     1  0.4766     0.7032 0.732 0.000 0.000 0.136 0.132
#> GSM317692     1  0.5624     0.6286 0.648 0.004 0.000 0.140 0.208
#> GSM317693     1  0.2825     0.7811 0.860 0.000 0.000 0.016 0.124
#> GSM317696     1  0.0992     0.7993 0.968 0.000 0.024 0.000 0.008
#> GSM317697     1  0.1197     0.7961 0.952 0.000 0.000 0.000 0.048
#> GSM317698     1  0.0290     0.8004 0.992 0.000 0.008 0.000 0.000
#> GSM317650     2  0.0162     0.8473 0.000 0.996 0.000 0.004 0.000
#> GSM317651     5  0.4607     0.4324 0.320 0.000 0.020 0.004 0.656
#> GSM317657     4  0.2635     0.7981 0.016 0.088 0.000 0.888 0.008
#> GSM317667     4  0.4793     0.7250 0.000 0.076 0.000 0.708 0.216
#> GSM317670     2  0.6891     0.3629 0.180 0.524 0.000 0.264 0.032
#> GSM317674     1  0.0992     0.7993 0.968 0.000 0.024 0.000 0.008
#> GSM317675     1  0.0992     0.7993 0.968 0.000 0.024 0.000 0.008
#> GSM317677     1  0.3003     0.7793 0.864 0.000 0.000 0.044 0.092
#> GSM317678     2  0.0404     0.8437 0.000 0.988 0.000 0.000 0.012
#> GSM317687     1  0.5345     0.6467 0.668 0.000 0.000 0.196 0.136
#> GSM317695     3  0.0404     0.9767 0.012 0.000 0.988 0.000 0.000
#> GSM317653     5  0.5406     0.5302 0.056 0.056 0.012 0.136 0.740
#> GSM317656     1  0.5654     0.4913 0.672 0.000 0.212 0.028 0.088
#> GSM317658     1  0.6360     0.3860 0.576 0.300 0.000 0.064 0.060
#> GSM317660     5  0.4908     0.5471 0.004 0.012 0.380 0.008 0.596
#> GSM317663     4  0.2052     0.8037 0.004 0.080 0.000 0.912 0.004
#> GSM317664     1  0.0992     0.7993 0.968 0.000 0.024 0.000 0.008
#> GSM317665     5  0.4757     0.5660 0.024 0.000 0.380 0.000 0.596
#> GSM317673     1  0.1356     0.7957 0.956 0.000 0.028 0.004 0.012
#> GSM317686     4  0.5223     0.7183 0.000 0.108 0.000 0.672 0.220
#> GSM317688     1  0.2772     0.7774 0.896 0.000 0.028 0.032 0.044
#> GSM317690     2  0.2825     0.7718 0.000 0.860 0.000 0.124 0.016
#> GSM317654     5  0.4526     0.6200 0.028 0.000 0.300 0.000 0.672
#> GSM317655     4  0.2623     0.7944 0.004 0.096 0.000 0.884 0.016
#> GSM317659     1  0.3918     0.7503 0.804 0.000 0.000 0.096 0.100
#> GSM317661     2  0.0162     0.8473 0.000 0.996 0.000 0.004 0.000
#> GSM317662     2  0.0162     0.8473 0.000 0.996 0.000 0.004 0.000
#> GSM317668     1  0.6808     0.2803 0.536 0.000 0.284 0.040 0.140
#> GSM317669     3  0.0000     0.9922 0.000 0.000 1.000 0.000 0.000
#> GSM317671     3  0.0000     0.9922 0.000 0.000 1.000 0.000 0.000
#> GSM317676     4  0.5250     0.4723 0.224 0.000 0.000 0.668 0.108
#> GSM317680     3  0.0000     0.9922 0.000 0.000 1.000 0.000 0.000
#> GSM317684     1  0.2879     0.7814 0.868 0.000 0.000 0.032 0.100
#> GSM317685     1  0.1653     0.7961 0.944 0.000 0.028 0.004 0.024
#> GSM317694     1  0.2664     0.7867 0.884 0.000 0.004 0.020 0.092

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> GSM317649     3  0.1015      0.969 0.004 0.000 0.968 0.004 0.012 0.012
#> GSM317652     5  0.6936      0.412 0.284 0.000 0.124 0.004 0.472 0.116
#> GSM317666     4  0.3728      0.392 0.004 0.000 0.000 0.788 0.068 0.140
#> GSM317672     5  0.6959      0.105 0.004 0.320 0.000 0.116 0.444 0.116
#> GSM317679     3  0.0146      0.989 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM317681     5  0.4343      0.620 0.004 0.064 0.000 0.056 0.780 0.096
#> GSM317682     1  0.5610     -0.217 0.440 0.000 0.000 0.000 0.416 0.144
#> GSM317683     2  0.0146      0.861 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM317689     2  0.4844      0.489 0.000 0.620 0.000 0.320 0.020 0.040
#> GSM317691     1  0.7110      0.314 0.456 0.000 0.000 0.184 0.132 0.228
#> GSM317692     6  0.7619     -0.281 0.292 0.000 0.000 0.224 0.180 0.304
#> GSM317693     1  0.4586      0.600 0.692 0.000 0.000 0.004 0.088 0.216
#> GSM317696     1  0.0993      0.698 0.964 0.000 0.000 0.000 0.012 0.024
#> GSM317697     1  0.2380      0.682 0.892 0.000 0.000 0.004 0.036 0.068
#> GSM317698     1  0.0000      0.701 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317650     2  0.0000      0.861 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM317651     5  0.3641      0.650 0.140 0.000 0.000 0.000 0.788 0.072
#> GSM317657     4  0.2665      0.567 0.000 0.024 0.000 0.884 0.032 0.060
#> GSM317667     6  0.4544      0.213 0.000 0.036 0.000 0.416 0.000 0.548
#> GSM317670     4  0.6163      0.155 0.036 0.304 0.004 0.552 0.012 0.092
#> GSM317674     1  0.0146      0.701 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM317675     1  0.0146      0.701 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM317677     1  0.4400      0.608 0.732 0.000 0.000 0.008 0.096 0.164
#> GSM317678     2  0.1434      0.836 0.000 0.940 0.000 0.000 0.012 0.048
#> GSM317687     1  0.7395      0.189 0.392 0.000 0.000 0.244 0.148 0.216
#> GSM317695     3  0.0547      0.973 0.020 0.000 0.980 0.000 0.000 0.000
#> GSM317653     5  0.1180      0.670 0.016 0.000 0.000 0.012 0.960 0.012
#> GSM317656     1  0.4297      0.588 0.784 0.000 0.052 0.004 0.072 0.088
#> GSM317658     1  0.7374      0.277 0.508 0.208 0.000 0.140 0.056 0.088
#> GSM317660     5  0.3403      0.701 0.020 0.004 0.148 0.004 0.816 0.008
#> GSM317663     4  0.1542      0.554 0.000 0.016 0.000 0.944 0.024 0.016
#> GSM317664     1  0.0146      0.701 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM317665     5  0.3210      0.705 0.036 0.000 0.152 0.000 0.812 0.000
#> GSM317673     1  0.1745      0.686 0.924 0.000 0.000 0.000 0.020 0.056
#> GSM317686     6  0.4544      0.213 0.000 0.036 0.000 0.416 0.000 0.548
#> GSM317688     1  0.2988      0.647 0.824 0.000 0.000 0.000 0.024 0.152
#> GSM317690     2  0.4363      0.608 0.000 0.688 0.004 0.264 0.004 0.040
#> GSM317654     5  0.2110      0.708 0.012 0.000 0.084 0.004 0.900 0.000
#> GSM317655     4  0.1743      0.553 0.000 0.028 0.004 0.936 0.008 0.024
#> GSM317659     1  0.6586      0.405 0.548 0.000 0.000 0.160 0.120 0.172
#> GSM317661     2  0.0146      0.860 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM317662     2  0.0000      0.861 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM317668     1  0.7144      0.371 0.564 0.000 0.120 0.076 0.136 0.104
#> GSM317669     3  0.0146      0.989 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM317671     3  0.0146      0.989 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM317676     4  0.6631      0.168 0.172 0.000 0.000 0.540 0.116 0.172
#> GSM317680     3  0.0146      0.989 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM317684     1  0.5273      0.564 0.648 0.000 0.000 0.020 0.124 0.208
#> GSM317685     1  0.1983      0.685 0.908 0.000 0.000 0.000 0.020 0.072
#> GSM317694     1  0.4355      0.610 0.736 0.000 0.000 0.008 0.092 0.164

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 disease.state(p) k
#> MAD:kmeans 48            0.719 2
#> MAD:kmeans 44            0.823 3
#> MAD:kmeans 45            0.878 4
#> MAD:kmeans 40            0.474 5
#> MAD:kmeans 35            0.869 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 11993 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 3.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

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 0.916           0.960       0.980         0.4921 0.510   0.510
#> 3 3 1.000           0.968       0.983         0.3604 0.805   0.624
#> 4 4 0.774           0.830       0.907         0.1290 0.875   0.643
#> 5 5 0.677           0.587       0.795         0.0605 0.969   0.873
#> 6 6 0.700           0.592       0.765         0.0404 0.906   0.610

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] 3
#> 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
#> GSM317649     1  0.0000      0.978 1.000 0.000
#> GSM317652     1  0.0000      0.978 1.000 0.000
#> GSM317666     2  0.0000      0.981 0.000 1.000
#> GSM317672     2  0.0000      0.981 0.000 1.000
#> GSM317679     1  0.7056      0.776 0.808 0.192
#> GSM317681     2  0.0000      0.981 0.000 1.000
#> GSM317682     1  0.0000      0.978 1.000 0.000
#> GSM317683     2  0.0000      0.981 0.000 1.000
#> GSM317689     2  0.0000      0.981 0.000 1.000
#> GSM317691     1  0.4939      0.886 0.892 0.108
#> GSM317692     2  0.0000      0.981 0.000 1.000
#> GSM317693     1  0.0000      0.978 1.000 0.000
#> GSM317696     1  0.0000      0.978 1.000 0.000
#> GSM317697     1  0.0672      0.972 0.992 0.008
#> GSM317698     1  0.0000      0.978 1.000 0.000
#> GSM317650     2  0.0000      0.981 0.000 1.000
#> GSM317651     1  0.0000      0.978 1.000 0.000
#> GSM317657     2  0.0000      0.981 0.000 1.000
#> GSM317667     2  0.0000      0.981 0.000 1.000
#> GSM317670     2  0.0000      0.981 0.000 1.000
#> GSM317674     1  0.0000      0.978 1.000 0.000
#> GSM317675     1  0.0000      0.978 1.000 0.000
#> GSM317677     1  0.0000      0.978 1.000 0.000
#> GSM317678     2  0.0000      0.981 0.000 1.000
#> GSM317687     1  0.3879      0.915 0.924 0.076
#> GSM317695     1  0.0000      0.978 1.000 0.000
#> GSM317653     2  0.7139      0.762 0.196 0.804
#> GSM317656     1  0.0000      0.978 1.000 0.000
#> GSM317658     2  0.0000      0.981 0.000 1.000
#> GSM317660     2  0.6531      0.807 0.168 0.832
#> GSM317663     2  0.0000      0.981 0.000 1.000
#> GSM317664     1  0.0000      0.978 1.000 0.000
#> GSM317665     1  0.0000      0.978 1.000 0.000
#> GSM317673     1  0.0000      0.978 1.000 0.000
#> GSM317686     2  0.0000      0.981 0.000 1.000
#> GSM317688     1  0.0000      0.978 1.000 0.000
#> GSM317690     2  0.0000      0.981 0.000 1.000
#> GSM317654     1  0.0000      0.978 1.000 0.000
#> GSM317655     2  0.0000      0.981 0.000 1.000
#> GSM317659     1  0.0000      0.978 1.000 0.000
#> GSM317661     2  0.0000      0.981 0.000 1.000
#> GSM317662     2  0.0000      0.981 0.000 1.000
#> GSM317668     1  0.0000      0.978 1.000 0.000
#> GSM317669     1  0.0000      0.978 1.000 0.000
#> GSM317671     1  0.6048      0.833 0.852 0.148
#> GSM317676     1  0.4298      0.903 0.912 0.088
#> GSM317680     1  0.0000      0.978 1.000 0.000
#> GSM317684     1  0.0000      0.978 1.000 0.000
#> GSM317685     1  0.0000      0.978 1.000 0.000
#> GSM317694     1  0.0000      0.978 1.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> GSM317649     3  0.0000      0.996 0.000 0.000 1.000
#> GSM317652     3  0.0000      0.996 0.000 0.000 1.000
#> GSM317666     2  0.0892      0.968 0.020 0.980 0.000
#> GSM317672     2  0.0000      0.980 0.000 1.000 0.000
#> GSM317679     3  0.0000      0.996 0.000 0.000 1.000
#> GSM317681     2  0.0000      0.980 0.000 1.000 0.000
#> GSM317682     1  0.1163      0.969 0.972 0.000 0.028
#> GSM317683     2  0.0000      0.980 0.000 1.000 0.000
#> GSM317689     2  0.0000      0.980 0.000 1.000 0.000
#> GSM317691     1  0.0000      0.977 1.000 0.000 0.000
#> GSM317692     2  0.0892      0.966 0.020 0.980 0.000
#> GSM317693     1  0.0000      0.977 1.000 0.000 0.000
#> GSM317696     1  0.0747      0.975 0.984 0.000 0.016
#> GSM317697     1  0.0000      0.977 1.000 0.000 0.000
#> GSM317698     1  0.0237      0.978 0.996 0.000 0.004
#> GSM317650     2  0.0000      0.980 0.000 1.000 0.000
#> GSM317651     1  0.3619      0.857 0.864 0.000 0.136
#> GSM317657     2  0.0424      0.977 0.008 0.992 0.000
#> GSM317667     2  0.0237      0.979 0.004 0.996 0.000
#> GSM317670     2  0.0000      0.980 0.000 1.000 0.000
#> GSM317674     1  0.0592      0.977 0.988 0.000 0.012
#> GSM317675     1  0.0592      0.977 0.988 0.000 0.012
#> GSM317677     1  0.0000      0.977 1.000 0.000 0.000
#> GSM317678     2  0.0000      0.980 0.000 1.000 0.000
#> GSM317687     1  0.0000      0.977 1.000 0.000 0.000
#> GSM317695     3  0.0000      0.996 0.000 0.000 1.000
#> GSM317653     2  0.6301      0.617 0.028 0.712 0.260
#> GSM317656     3  0.0237      0.992 0.004 0.000 0.996
#> GSM317658     2  0.0747      0.969 0.016 0.984 0.000
#> GSM317660     3  0.0000      0.996 0.000 0.000 1.000
#> GSM317663     2  0.0237      0.979 0.004 0.996 0.000
#> GSM317664     1  0.0747      0.975 0.984 0.000 0.016
#> GSM317665     3  0.0000      0.996 0.000 0.000 1.000
#> GSM317673     1  0.1031      0.971 0.976 0.000 0.024
#> GSM317686     2  0.0000      0.980 0.000 1.000 0.000
#> GSM317688     1  0.3752      0.853 0.856 0.000 0.144
#> GSM317690     2  0.0000      0.980 0.000 1.000 0.000
#> GSM317654     3  0.0000      0.996 0.000 0.000 1.000
#> GSM317655     2  0.0000      0.980 0.000 1.000 0.000
#> GSM317659     1  0.0000      0.977 1.000 0.000 0.000
#> GSM317661     2  0.0000      0.980 0.000 1.000 0.000
#> GSM317662     2  0.0000      0.980 0.000 1.000 0.000
#> GSM317668     3  0.1643      0.953 0.044 0.000 0.956
#> GSM317669     3  0.0000      0.996 0.000 0.000 1.000
#> GSM317671     3  0.0000      0.996 0.000 0.000 1.000
#> GSM317676     1  0.0000      0.977 1.000 0.000 0.000
#> GSM317680     3  0.0000      0.996 0.000 0.000 1.000
#> GSM317684     1  0.0000      0.977 1.000 0.000 0.000
#> GSM317685     1  0.1031      0.971 0.976 0.000 0.024
#> GSM317694     1  0.0237      0.978 0.996 0.000 0.004

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM317649     3  0.0000      0.948 0.000 0.000 1.000 0.000
#> GSM317652     3  0.1297      0.940 0.020 0.000 0.964 0.016
#> GSM317666     4  0.1302      0.781 0.000 0.044 0.000 0.956
#> GSM317672     2  0.0336      0.922 0.000 0.992 0.000 0.008
#> GSM317679     3  0.0000      0.948 0.000 0.000 1.000 0.000
#> GSM317681     2  0.1302      0.903 0.000 0.956 0.000 0.044
#> GSM317682     1  0.1545      0.880 0.952 0.000 0.008 0.040
#> GSM317683     2  0.0000      0.926 0.000 1.000 0.000 0.000
#> GSM317689     2  0.0000      0.926 0.000 1.000 0.000 0.000
#> GSM317691     4  0.4713      0.231 0.360 0.000 0.000 0.640
#> GSM317692     2  0.4857      0.573 0.016 0.700 0.000 0.284
#> GSM317693     1  0.2281      0.862 0.904 0.000 0.000 0.096
#> GSM317696     1  0.0000      0.898 1.000 0.000 0.000 0.000
#> GSM317697     1  0.0188      0.897 0.996 0.000 0.000 0.004
#> GSM317698     1  0.0000      0.898 1.000 0.000 0.000 0.000
#> GSM317650     2  0.0000      0.926 0.000 1.000 0.000 0.000
#> GSM317651     1  0.5111      0.688 0.740 0.000 0.204 0.056
#> GSM317657     4  0.3610      0.774 0.000 0.200 0.000 0.800
#> GSM317667     4  0.3486      0.783 0.000 0.188 0.000 0.812
#> GSM317670     2  0.3528      0.722 0.000 0.808 0.000 0.192
#> GSM317674     1  0.0000      0.898 1.000 0.000 0.000 0.000
#> GSM317675     1  0.0000      0.898 1.000 0.000 0.000 0.000
#> GSM317677     1  0.3311      0.809 0.828 0.000 0.000 0.172
#> GSM317678     2  0.0188      0.924 0.000 0.996 0.000 0.004
#> GSM317687     4  0.1118      0.768 0.036 0.000 0.000 0.964
#> GSM317695     3  0.0817      0.941 0.024 0.000 0.976 0.000
#> GSM317653     4  0.4406      0.693 0.000 0.192 0.028 0.780
#> GSM317656     3  0.3726      0.755 0.212 0.000 0.788 0.000
#> GSM317658     2  0.3015      0.829 0.092 0.884 0.000 0.024
#> GSM317660     3  0.1610      0.933 0.000 0.016 0.952 0.032
#> GSM317663     4  0.3942      0.757 0.000 0.236 0.000 0.764
#> GSM317664     1  0.0000      0.898 1.000 0.000 0.000 0.000
#> GSM317665     3  0.0817      0.943 0.000 0.000 0.976 0.024
#> GSM317673     1  0.0336      0.896 0.992 0.000 0.000 0.008
#> GSM317686     4  0.4277      0.714 0.000 0.280 0.000 0.720
#> GSM317688     1  0.2706      0.844 0.900 0.000 0.080 0.020
#> GSM317690     2  0.1211      0.901 0.000 0.960 0.000 0.040
#> GSM317654     3  0.1022      0.941 0.000 0.000 0.968 0.032
#> GSM317655     4  0.4008      0.750 0.000 0.244 0.000 0.756
#> GSM317659     1  0.4999      0.217 0.508 0.000 0.000 0.492
#> GSM317661     2  0.0000      0.926 0.000 1.000 0.000 0.000
#> GSM317662     2  0.0000      0.926 0.000 1.000 0.000 0.000
#> GSM317668     3  0.3718      0.803 0.168 0.000 0.820 0.012
#> GSM317669     3  0.0000      0.948 0.000 0.000 1.000 0.000
#> GSM317671     3  0.0000      0.948 0.000 0.000 1.000 0.000
#> GSM317676     4  0.1118      0.768 0.036 0.000 0.000 0.964
#> GSM317680     3  0.0000      0.948 0.000 0.000 1.000 0.000
#> GSM317684     1  0.3764      0.769 0.784 0.000 0.000 0.216
#> GSM317685     1  0.0336      0.897 0.992 0.000 0.000 0.008
#> GSM317694     1  0.2530      0.853 0.888 0.000 0.000 0.112

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> GSM317649     3  0.0404    0.69434 0.000 0.000 0.988 0.000 0.012
#> GSM317652     3  0.4822    0.33330 0.032 0.000 0.616 0.000 0.352
#> GSM317666     4  0.1018    0.67801 0.000 0.016 0.000 0.968 0.016
#> GSM317672     2  0.1410    0.83419 0.000 0.940 0.000 0.000 0.060
#> GSM317679     3  0.0000    0.69757 0.000 0.000 1.000 0.000 0.000
#> GSM317681     2  0.4976    0.58666 0.000 0.696 0.004 0.072 0.228
#> GSM317682     1  0.3796    0.44657 0.700 0.000 0.000 0.000 0.300
#> GSM317683     2  0.0000    0.85769 0.000 1.000 0.000 0.000 0.000
#> GSM317689     2  0.0290    0.85573 0.000 0.992 0.000 0.008 0.000
#> GSM317691     4  0.6763    0.01326 0.288 0.000 0.000 0.400 0.312
#> GSM317692     2  0.6691    0.35555 0.016 0.528 0.000 0.240 0.216
#> GSM317693     1  0.4618    0.65208 0.724 0.000 0.000 0.068 0.208
#> GSM317696     1  0.0162    0.75976 0.996 0.000 0.000 0.000 0.004
#> GSM317697     1  0.1671    0.74398 0.924 0.000 0.000 0.000 0.076
#> GSM317698     1  0.0290    0.76015 0.992 0.000 0.000 0.000 0.008
#> GSM317650     2  0.0000    0.85769 0.000 1.000 0.000 0.000 0.000
#> GSM317651     5  0.5177    0.40897 0.232 0.000 0.076 0.008 0.684
#> GSM317657     4  0.2873    0.71688 0.000 0.120 0.000 0.860 0.020
#> GSM317667     4  0.2329    0.71128 0.000 0.124 0.000 0.876 0.000
#> GSM317670     2  0.5709    0.52116 0.004 0.648 0.016 0.252 0.080
#> GSM317674     1  0.0290    0.76052 0.992 0.000 0.000 0.000 0.008
#> GSM317675     1  0.0290    0.76062 0.992 0.000 0.000 0.000 0.008
#> GSM317677     1  0.5681    0.54456 0.608 0.000 0.000 0.124 0.268
#> GSM317678     2  0.0162    0.85666 0.000 0.996 0.000 0.000 0.004
#> GSM317687     4  0.4465    0.46945 0.024 0.000 0.000 0.672 0.304
#> GSM317695     3  0.1704    0.65419 0.068 0.000 0.928 0.000 0.004
#> GSM317653     5  0.5857    0.29970 0.000 0.092 0.016 0.280 0.612
#> GSM317656     3  0.5533    0.29067 0.336 0.000 0.580 0.000 0.084
#> GSM317658     2  0.4773    0.71990 0.096 0.768 0.000 0.028 0.108
#> GSM317660     3  0.4824    0.00891 0.000 0.020 0.512 0.000 0.468
#> GSM317663     4  0.2561    0.71441 0.000 0.144 0.000 0.856 0.000
#> GSM317664     1  0.0451    0.75850 0.988 0.000 0.004 0.000 0.008
#> GSM317665     3  0.4262    0.11304 0.000 0.000 0.560 0.000 0.440
#> GSM317673     1  0.1502    0.74704 0.940 0.000 0.000 0.004 0.056
#> GSM317686     4  0.3143    0.67312 0.000 0.204 0.000 0.796 0.000
#> GSM317688     1  0.4567    0.58850 0.752 0.000 0.080 0.004 0.164
#> GSM317690     2  0.2423    0.80270 0.000 0.896 0.000 0.080 0.024
#> GSM317654     5  0.4787   -0.08496 0.000 0.000 0.432 0.020 0.548
#> GSM317655     4  0.3183    0.70765 0.000 0.156 0.000 0.828 0.016
#> GSM317659     1  0.6822    0.08060 0.344 0.000 0.000 0.340 0.316
#> GSM317661     2  0.0000    0.85769 0.000 1.000 0.000 0.000 0.000
#> GSM317662     2  0.0000    0.85769 0.000 1.000 0.000 0.000 0.000
#> GSM317668     3  0.6606    0.30565 0.212 0.000 0.564 0.024 0.200
#> GSM317669     3  0.0000    0.69757 0.000 0.000 1.000 0.000 0.000
#> GSM317671     3  0.0000    0.69757 0.000 0.000 1.000 0.000 0.000
#> GSM317676     4  0.3766    0.52541 0.004 0.000 0.000 0.728 0.268
#> GSM317680     3  0.0000    0.69757 0.000 0.000 1.000 0.000 0.000
#> GSM317684     1  0.6254    0.43236 0.500 0.000 0.000 0.160 0.340
#> GSM317685     1  0.2612    0.72833 0.868 0.000 0.000 0.008 0.124
#> GSM317694     1  0.4898    0.61077 0.684 0.000 0.000 0.068 0.248

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> GSM317649     3  0.1268     0.8190 0.000 0.000 0.952 0.004 0.036 0.008
#> GSM317652     5  0.6237     0.2808 0.084 0.000 0.412 0.008 0.448 0.048
#> GSM317666     4  0.2288     0.7662 0.000 0.004 0.000 0.876 0.004 0.116
#> GSM317672     2  0.2393     0.7659 0.000 0.892 0.000 0.004 0.064 0.040
#> GSM317679     3  0.0146     0.8489 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM317681     2  0.6060     0.4290 0.000 0.576 0.008 0.088 0.272 0.056
#> GSM317682     1  0.5365     0.4919 0.612 0.008 0.004 0.000 0.260 0.116
#> GSM317683     2  0.0653     0.7894 0.000 0.980 0.000 0.012 0.004 0.004
#> GSM317689     2  0.2076     0.7734 0.000 0.912 0.000 0.060 0.012 0.016
#> GSM317691     6  0.5665     0.5464 0.148 0.000 0.000 0.140 0.064 0.648
#> GSM317692     2  0.7990     0.1675 0.048 0.376 0.000 0.160 0.132 0.284
#> GSM317693     1  0.4941     0.0169 0.492 0.000 0.000 0.000 0.064 0.444
#> GSM317696     1  0.0520     0.7007 0.984 0.000 0.000 0.000 0.008 0.008
#> GSM317697     1  0.4136     0.5478 0.732 0.000 0.000 0.000 0.076 0.192
#> GSM317698     1  0.0891     0.6983 0.968 0.000 0.000 0.000 0.008 0.024
#> GSM317650     2  0.0767     0.7899 0.000 0.976 0.000 0.012 0.004 0.008
#> GSM317651     5  0.5532     0.4961 0.160 0.000 0.028 0.008 0.656 0.148
#> GSM317657     4  0.3133     0.8708 0.000 0.064 0.000 0.852 0.016 0.068
#> GSM317667     4  0.1657     0.8902 0.000 0.056 0.000 0.928 0.000 0.016
#> GSM317670     2  0.6782     0.3590 0.000 0.504 0.016 0.280 0.064 0.136
#> GSM317674     1  0.0603     0.7009 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM317675     1  0.0603     0.6990 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM317677     6  0.4473     0.1752 0.480 0.000 0.000 0.028 0.000 0.492
#> GSM317678     2  0.0725     0.7877 0.000 0.976 0.000 0.000 0.012 0.012
#> GSM317687     6  0.4090     0.3929 0.004 0.000 0.000 0.384 0.008 0.604
#> GSM317695     3  0.1434     0.7964 0.048 0.000 0.940 0.000 0.012 0.000
#> GSM317653     5  0.6274     0.4358 0.000 0.072 0.008 0.180 0.596 0.144
#> GSM317656     1  0.6706    -0.1068 0.408 0.000 0.392 0.016 0.148 0.036
#> GSM317658     2  0.6385     0.6049 0.084 0.636 0.000 0.056 0.092 0.132
#> GSM317660     5  0.4752     0.6182 0.000 0.028 0.268 0.012 0.672 0.020
#> GSM317663     4  0.1686     0.8977 0.000 0.064 0.000 0.924 0.000 0.012
#> GSM317664     1  0.0858     0.6991 0.968 0.000 0.000 0.000 0.004 0.028
#> GSM317665     5  0.3804     0.5804 0.000 0.000 0.336 0.008 0.656 0.000
#> GSM317673     1  0.2058     0.6854 0.908 0.000 0.000 0.000 0.056 0.036
#> GSM317686     4  0.1765     0.8832 0.000 0.096 0.000 0.904 0.000 0.000
#> GSM317688     1  0.5848     0.5334 0.648 0.000 0.092 0.004 0.140 0.116
#> GSM317690     2  0.4153     0.6477 0.000 0.752 0.000 0.184 0.024 0.040
#> GSM317654     5  0.4470     0.6457 0.000 0.000 0.228 0.004 0.696 0.072
#> GSM317655     4  0.3013     0.8621 0.000 0.064 0.000 0.864 0.028 0.044
#> GSM317659     6  0.5655     0.6057 0.212 0.000 0.000 0.168 0.020 0.600
#> GSM317661     2  0.1750     0.7847 0.000 0.932 0.000 0.040 0.016 0.012
#> GSM317662     2  0.0520     0.7894 0.000 0.984 0.000 0.008 0.000 0.008
#> GSM317668     3  0.7685    -0.0149 0.192 0.000 0.420 0.024 0.232 0.132
#> GSM317669     3  0.0260     0.8479 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM317671     3  0.0146     0.8500 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM317676     6  0.4177     0.2152 0.000 0.000 0.000 0.468 0.012 0.520
#> GSM317680     3  0.0000     0.8500 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM317684     6  0.4712     0.4950 0.272 0.000 0.000 0.040 0.024 0.664
#> GSM317685     1  0.3822     0.6200 0.776 0.000 0.000 0.000 0.096 0.128
#> GSM317694     1  0.4002    -0.0096 0.588 0.000 0.000 0.008 0.000 0.404

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 disease.state(p) k
#> MAD:skmeans 50            0.448 2
#> MAD:skmeans 50            0.689 3
#> MAD:skmeans 48            0.738 4
#> MAD:skmeans 36            0.857 5
#> MAD:skmeans 35            0.783 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 11993 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 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-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 0.999           0.956       0.981         0.4649 0.542   0.542
#> 3 3 0.624           0.865       0.901         0.2984 0.868   0.756
#> 4 4 0.796           0.874       0.934         0.1255 0.926   0.821
#> 5 5 0.794           0.796       0.900         0.0610 0.811   0.529
#> 6 6 0.759           0.719       0.850         0.0591 0.928   0.746

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
#> GSM317649     1  0.0000      0.976 1.000 0.000
#> GSM317652     1  0.0000      0.976 1.000 0.000
#> GSM317666     2  0.0000      0.987 0.000 1.000
#> GSM317672     1  0.0376      0.973 0.996 0.004
#> GSM317679     1  0.0000      0.976 1.000 0.000
#> GSM317681     1  0.2043      0.949 0.968 0.032
#> GSM317682     1  0.0000      0.976 1.000 0.000
#> GSM317683     2  0.0000      0.987 0.000 1.000
#> GSM317689     2  0.0000      0.987 0.000 1.000
#> GSM317691     2  0.0000      0.987 0.000 1.000
#> GSM317692     1  0.9044      0.546 0.680 0.320
#> GSM317693     1  0.0000      0.976 1.000 0.000
#> GSM317696     1  0.0000      0.976 1.000 0.000
#> GSM317697     1  0.0000      0.976 1.000 0.000
#> GSM317698     1  0.0000      0.976 1.000 0.000
#> GSM317650     2  0.0000      0.987 0.000 1.000
#> GSM317651     1  0.0000      0.976 1.000 0.000
#> GSM317657     2  0.0000      0.987 0.000 1.000
#> GSM317667     2  0.0000      0.987 0.000 1.000
#> GSM317670     2  0.0000      0.987 0.000 1.000
#> GSM317674     1  0.0000      0.976 1.000 0.000
#> GSM317675     1  0.0000      0.976 1.000 0.000
#> GSM317677     1  0.0000      0.976 1.000 0.000
#> GSM317678     2  0.2423      0.950 0.040 0.960
#> GSM317687     2  0.0000      0.987 0.000 1.000
#> GSM317695     1  0.0000      0.976 1.000 0.000
#> GSM317653     1  0.4161      0.898 0.916 0.084
#> GSM317656     1  0.0000      0.976 1.000 0.000
#> GSM317658     1  0.9000      0.548 0.684 0.316
#> GSM317660     1  0.0000      0.976 1.000 0.000
#> GSM317663     2  0.0000      0.987 0.000 1.000
#> GSM317664     1  0.0000      0.976 1.000 0.000
#> GSM317665     1  0.0000      0.976 1.000 0.000
#> GSM317673     1  0.0000      0.976 1.000 0.000
#> GSM317686     2  0.0000      0.987 0.000 1.000
#> GSM317688     1  0.0000      0.976 1.000 0.000
#> GSM317690     2  0.0000      0.987 0.000 1.000
#> GSM317654     1  0.0000      0.976 1.000 0.000
#> GSM317655     2  0.0000      0.987 0.000 1.000
#> GSM317659     1  0.0000      0.976 1.000 0.000
#> GSM317661     2  0.0000      0.987 0.000 1.000
#> GSM317662     2  0.0000      0.987 0.000 1.000
#> GSM317668     1  0.0000      0.976 1.000 0.000
#> GSM317669     1  0.0000      0.976 1.000 0.000
#> GSM317671     1  0.0000      0.976 1.000 0.000
#> GSM317676     2  0.6343      0.806 0.160 0.840
#> GSM317680     1  0.0000      0.976 1.000 0.000
#> GSM317684     1  0.0000      0.976 1.000 0.000
#> GSM317685     1  0.0000      0.976 1.000 0.000
#> GSM317694     1  0.0000      0.976 1.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> GSM317649     3  0.4235      0.954 0.176 0.000 0.824
#> GSM317652     1  0.0000      0.893 1.000 0.000 0.000
#> GSM317666     2  0.0237      0.908 0.000 0.996 0.004
#> GSM317672     1  0.4811      0.804 0.828 0.148 0.024
#> GSM317679     3  0.4723      0.750 0.016 0.160 0.824
#> GSM317681     1  0.5574      0.775 0.784 0.184 0.032
#> GSM317682     1  0.0000      0.893 1.000 0.000 0.000
#> GSM317683     2  0.4178      0.890 0.000 0.828 0.172
#> GSM317689     2  0.1964      0.915 0.000 0.944 0.056
#> GSM317691     2  0.0237      0.907 0.004 0.996 0.000
#> GSM317692     1  0.5882      0.597 0.652 0.348 0.000
#> GSM317693     1  0.3879      0.814 0.848 0.152 0.000
#> GSM317696     1  0.0000      0.893 1.000 0.000 0.000
#> GSM317697     1  0.3941      0.811 0.844 0.156 0.000
#> GSM317698     1  0.0000      0.893 1.000 0.000 0.000
#> GSM317650     2  0.4178      0.890 0.000 0.828 0.172
#> GSM317651     1  0.0237      0.891 0.996 0.000 0.004
#> GSM317657     2  0.0000      0.909 0.000 1.000 0.000
#> GSM317667     2  0.1411      0.914 0.000 0.964 0.036
#> GSM317670     2  0.3116      0.909 0.000 0.892 0.108
#> GSM317674     1  0.0000      0.893 1.000 0.000 0.000
#> GSM317675     1  0.0000      0.893 1.000 0.000 0.000
#> GSM317677     1  0.0237      0.891 0.996 0.000 0.004
#> GSM317678     2  0.4676      0.887 0.040 0.848 0.112
#> GSM317687     2  0.0237      0.908 0.000 0.996 0.004
#> GSM317695     3  0.4291      0.951 0.180 0.000 0.820
#> GSM317653     1  0.5070      0.754 0.772 0.224 0.004
#> GSM317656     1  0.0000      0.893 1.000 0.000 0.000
#> GSM317658     1  0.6881      0.488 0.592 0.388 0.020
#> GSM317660     1  0.4834      0.685 0.792 0.004 0.204
#> GSM317663     2  0.0000      0.909 0.000 1.000 0.000
#> GSM317664     1  0.0000      0.893 1.000 0.000 0.000
#> GSM317665     1  0.0424      0.888 0.992 0.000 0.008
#> GSM317673     1  0.0000      0.893 1.000 0.000 0.000
#> GSM317686     2  0.2959      0.910 0.000 0.900 0.100
#> GSM317688     1  0.0000      0.893 1.000 0.000 0.000
#> GSM317690     2  0.3941      0.892 0.000 0.844 0.156
#> GSM317654     1  0.6317      0.765 0.772 0.124 0.104
#> GSM317655     2  0.1031      0.914 0.000 0.976 0.024
#> GSM317659     1  0.0475      0.891 0.992 0.004 0.004
#> GSM317661     2  0.4178      0.890 0.000 0.828 0.172
#> GSM317662     2  0.4178      0.890 0.000 0.828 0.172
#> GSM317668     1  0.0000      0.893 1.000 0.000 0.000
#> GSM317669     3  0.4235      0.954 0.176 0.000 0.824
#> GSM317671     3  0.4235      0.954 0.176 0.000 0.824
#> GSM317676     2  0.3193      0.805 0.100 0.896 0.004
#> GSM317680     3  0.4235      0.954 0.176 0.000 0.824
#> GSM317684     1  0.4172      0.810 0.840 0.156 0.004
#> GSM317685     1  0.0237      0.891 0.996 0.000 0.004
#> GSM317694     1  0.0000      0.893 1.000 0.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM317649     3  0.0817      0.990 0.024 0.000 0.976 0.000
#> GSM317652     1  0.0188      0.900 0.996 0.000 0.004 0.000
#> GSM317666     4  0.0000      0.939 0.000 0.000 0.000 1.000
#> GSM317672     1  0.6739      0.462 0.576 0.304 0.000 0.120
#> GSM317679     3  0.0817      0.955 0.000 0.000 0.976 0.024
#> GSM317681     2  0.2611      0.876 0.008 0.896 0.000 0.096
#> GSM317682     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317683     2  0.0000      0.957 0.000 1.000 0.000 0.000
#> GSM317689     4  0.0707      0.936 0.000 0.020 0.000 0.980
#> GSM317691     4  0.0188      0.939 0.004 0.000 0.000 0.996
#> GSM317692     1  0.4697      0.564 0.644 0.000 0.000 0.356
#> GSM317693     1  0.2589      0.842 0.884 0.000 0.000 0.116
#> GSM317696     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317697     1  0.2647      0.840 0.880 0.000 0.000 0.120
#> GSM317698     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317650     2  0.0000      0.957 0.000 1.000 0.000 0.000
#> GSM317651     1  0.0188      0.901 0.996 0.000 0.000 0.004
#> GSM317657     4  0.0188      0.940 0.000 0.004 0.000 0.996
#> GSM317667     4  0.1733      0.923 0.000 0.028 0.024 0.948
#> GSM317670     4  0.2216      0.896 0.000 0.092 0.000 0.908
#> GSM317674     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317675     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317677     1  0.0188      0.901 0.996 0.000 0.000 0.004
#> GSM317678     2  0.1557      0.923 0.000 0.944 0.000 0.056
#> GSM317687     4  0.0000      0.939 0.000 0.000 0.000 1.000
#> GSM317695     3  0.0921      0.986 0.028 0.000 0.972 0.000
#> GSM317653     1  0.3528      0.787 0.808 0.000 0.000 0.192
#> GSM317656     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317658     1  0.7270      0.356 0.504 0.164 0.000 0.332
#> GSM317660     1  0.4643      0.528 0.656 0.000 0.344 0.000
#> GSM317663     4  0.0188      0.940 0.000 0.004 0.000 0.996
#> GSM317664     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317665     1  0.0336      0.899 0.992 0.000 0.008 0.000
#> GSM317673     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317686     4  0.2949      0.884 0.000 0.088 0.024 0.888
#> GSM317688     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317690     4  0.2704      0.866 0.000 0.124 0.000 0.876
#> GSM317654     1  0.4877      0.712 0.752 0.000 0.204 0.044
#> GSM317655     4  0.0336      0.940 0.000 0.008 0.000 0.992
#> GSM317659     1  0.0469      0.898 0.988 0.000 0.000 0.012
#> GSM317661     2  0.0000      0.957 0.000 1.000 0.000 0.000
#> GSM317662     2  0.0000      0.957 0.000 1.000 0.000 0.000
#> GSM317668     1  0.0000      0.902 1.000 0.000 0.000 0.000
#> GSM317669     3  0.0817      0.990 0.024 0.000 0.976 0.000
#> GSM317671     3  0.0817      0.990 0.024 0.000 0.976 0.000
#> GSM317676     4  0.2814      0.783 0.132 0.000 0.000 0.868
#> GSM317680     3  0.0817      0.990 0.024 0.000 0.976 0.000
#> GSM317684     1  0.2704      0.839 0.876 0.000 0.000 0.124
#> GSM317685     1  0.0188      0.901 0.996 0.000 0.000 0.004
#> GSM317694     1  0.0000      0.902 1.000 0.000 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
#> GSM317649     3  0.0000      1.000 0.000 0.000 1.000 0.000 0.000
#> GSM317652     1  0.0162      0.939 0.996 0.000 0.004 0.000 0.000
#> GSM317666     4  0.1270      0.680 0.000 0.000 0.000 0.948 0.052
#> GSM317672     4  0.5938      0.487 0.376 0.112 0.000 0.512 0.000
#> GSM317679     3  0.0000      1.000 0.000 0.000 1.000 0.000 0.000
#> GSM317681     2  0.3461      0.579 0.004 0.772 0.000 0.224 0.000
#> GSM317682     1  0.0000      0.940 1.000 0.000 0.000 0.000 0.000
#> GSM317683     2  0.0000      0.829 0.000 1.000 0.000 0.000 0.000
#> GSM317689     4  0.3622      0.571 0.000 0.136 0.000 0.816 0.048
#> GSM317691     4  0.0404      0.689 0.000 0.000 0.000 0.988 0.012
#> GSM317692     4  0.5016      0.596 0.348 0.000 0.000 0.608 0.044
#> GSM317693     4  0.4201      0.525 0.408 0.000 0.000 0.592 0.000
#> GSM317696     1  0.0000      0.940 1.000 0.000 0.000 0.000 0.000
#> GSM317697     4  0.4201      0.532 0.408 0.000 0.000 0.592 0.000
#> GSM317698     1  0.0000      0.940 1.000 0.000 0.000 0.000 0.000
#> GSM317650     2  0.0000      0.829 0.000 1.000 0.000 0.000 0.000
#> GSM317651     1  0.1331      0.919 0.952 0.000 0.000 0.040 0.008
#> GSM317657     4  0.1484      0.682 0.000 0.008 0.000 0.944 0.048
#> GSM317667     5  0.0290      1.000 0.000 0.000 0.000 0.008 0.992
#> GSM317670     4  0.1893      0.676 0.000 0.024 0.000 0.928 0.048
#> GSM317674     1  0.0000      0.940 1.000 0.000 0.000 0.000 0.000
#> GSM317675     1  0.0000      0.940 1.000 0.000 0.000 0.000 0.000
#> GSM317677     1  0.1484      0.914 0.944 0.000 0.000 0.048 0.008
#> GSM317678     2  0.0000      0.829 0.000 1.000 0.000 0.000 0.000
#> GSM317687     4  0.0290      0.687 0.000 0.000 0.000 0.992 0.008
#> GSM317695     3  0.0000      1.000 0.000 0.000 1.000 0.000 0.000
#> GSM317653     4  0.4183      0.604 0.324 0.000 0.000 0.668 0.008
#> GSM317656     1  0.0000      0.940 1.000 0.000 0.000 0.000 0.000
#> GSM317658     4  0.5325      0.626 0.276 0.088 0.000 0.636 0.000
#> GSM317660     1  0.3999      0.533 0.656 0.000 0.344 0.000 0.000
#> GSM317663     4  0.1484      0.682 0.000 0.008 0.000 0.944 0.048
#> GSM317664     1  0.0000      0.940 1.000 0.000 0.000 0.000 0.000
#> GSM317665     1  0.0000      0.940 1.000 0.000 0.000 0.000 0.000
#> GSM317673     1  0.0000      0.940 1.000 0.000 0.000 0.000 0.000
#> GSM317686     5  0.0290      1.000 0.000 0.000 0.000 0.008 0.992
#> GSM317688     1  0.0162      0.938 0.996 0.000 0.000 0.004 0.000
#> GSM317690     2  0.5407      0.260 0.004 0.524 0.000 0.424 0.048
#> GSM317654     1  0.5869      0.460 0.628 0.000 0.148 0.216 0.008
#> GSM317655     4  0.1893      0.676 0.000 0.024 0.000 0.928 0.048
#> GSM317659     1  0.2077      0.882 0.908 0.000 0.000 0.084 0.008
#> GSM317661     2  0.0000      0.829 0.000 1.000 0.000 0.000 0.000
#> GSM317662     2  0.0000      0.829 0.000 1.000 0.000 0.000 0.000
#> GSM317668     1  0.0000      0.940 1.000 0.000 0.000 0.000 0.000
#> GSM317669     3  0.0000      1.000 0.000 0.000 1.000 0.000 0.000
#> GSM317671     3  0.0000      1.000 0.000 0.000 1.000 0.000 0.000
#> GSM317676     4  0.0290      0.687 0.000 0.000 0.000 0.992 0.008
#> GSM317680     3  0.0000      1.000 0.000 0.000 1.000 0.000 0.000
#> GSM317684     4  0.4298      0.566 0.352 0.000 0.000 0.640 0.008
#> GSM317685     1  0.1251      0.921 0.956 0.000 0.000 0.036 0.008
#> GSM317694     1  0.1251      0.921 0.956 0.000 0.000 0.036 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
#> GSM317649     3  0.0000     1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM317652     1  0.0146     0.9033 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM317666     5  0.4569     0.4969 0.008 0.000 0.000 0.408 0.560 0.024
#> GSM317672     5  0.5166     0.4899 0.384 0.092 0.000 0.000 0.524 0.000
#> GSM317679     3  0.0000     1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM317681     2  0.3565     0.5509 0.000 0.692 0.000 0.004 0.304 0.000
#> GSM317682     1  0.0790     0.8944 0.968 0.000 0.000 0.000 0.032 0.000
#> GSM317683     2  0.0000     0.8941 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM317689     5  0.5472     0.3846 0.000 0.124 0.000 0.412 0.464 0.000
#> GSM317691     5  0.3634     0.5272 0.000 0.000 0.000 0.356 0.644 0.000
#> GSM317692     5  0.4357     0.5604 0.340 0.000 0.000 0.036 0.624 0.000
#> GSM317693     5  0.3717     0.5352 0.384 0.000 0.000 0.000 0.616 0.000
#> GSM317696     1  0.0713     0.8959 0.972 0.000 0.000 0.000 0.028 0.000
#> GSM317697     5  0.3747     0.5313 0.396 0.000 0.000 0.000 0.604 0.000
#> GSM317698     1  0.0260     0.9018 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM317650     2  0.0000     0.8941 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM317651     1  0.1850     0.8718 0.924 0.000 0.000 0.016 0.052 0.008
#> GSM317657     5  0.4242     0.4904 0.000 0.012 0.000 0.412 0.572 0.004
#> GSM317667     6  0.0260     1.0000 0.000 0.000 0.000 0.008 0.000 0.992
#> GSM317670     4  0.0603     0.6781 0.000 0.016 0.000 0.980 0.004 0.000
#> GSM317674     1  0.0000     0.9036 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317675     1  0.0000     0.9036 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317677     1  0.1649     0.8805 0.936 0.000 0.000 0.016 0.040 0.008
#> GSM317678     2  0.0260     0.8906 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM317687     5  0.4101     0.5284 0.008 0.000 0.000 0.352 0.632 0.008
#> GSM317695     3  0.0000     1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM317653     5  0.2745     0.4905 0.112 0.000 0.000 0.020 0.860 0.008
#> GSM317656     1  0.0000     0.9036 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317658     5  0.5748     0.5595 0.296 0.064 0.000 0.064 0.576 0.000
#> GSM317660     1  0.6224    -0.0893 0.368 0.000 0.340 0.004 0.288 0.000
#> GSM317663     5  0.4242     0.4904 0.000 0.012 0.000 0.412 0.572 0.004
#> GSM317664     1  0.0000     0.9036 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317665     1  0.3189     0.6318 0.760 0.000 0.000 0.004 0.236 0.000
#> GSM317673     1  0.0260     0.9018 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM317686     6  0.0260     1.0000 0.000 0.000 0.000 0.008 0.000 0.992
#> GSM317688     1  0.0937     0.8900 0.960 0.000 0.000 0.000 0.040 0.000
#> GSM317690     4  0.0547     0.6752 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM317654     5  0.6089    -0.0537 0.372 0.000 0.156 0.012 0.456 0.004
#> GSM317655     4  0.0603     0.6781 0.000 0.016 0.000 0.980 0.004 0.000
#> GSM317659     1  0.2468     0.8267 0.880 0.000 0.000 0.016 0.096 0.008
#> GSM317661     2  0.2325     0.8313 0.000 0.892 0.000 0.060 0.048 0.000
#> GSM317662     2  0.0000     0.8941 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM317668     4  0.3860    -0.0412 0.472 0.000 0.000 0.528 0.000 0.000
#> GSM317669     3  0.0000     1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM317671     3  0.0000     1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM317676     5  0.4183     0.5190 0.008 0.000 0.000 0.380 0.604 0.008
#> GSM317680     3  0.0000     1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM317684     5  0.4278     0.5495 0.352 0.000 0.000 0.016 0.624 0.008
#> GSM317685     1  0.1410     0.8842 0.944 0.000 0.000 0.008 0.044 0.004
#> GSM317694     1  0.1003     0.8939 0.964 0.000 0.000 0.004 0.028 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-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 disease.state(p) k
#> MAD:pam 50            0.438 2
#> MAD:pam 49            0.470 3
#> MAD:pam 48            0.671 4
#> MAD:pam 47            0.663 5
#> MAD:pam 41            0.720 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 11993 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 3.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

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 0.984           0.934       0.969         0.3704 0.628   0.628
#> 3 3 0.907           0.898       0.951         0.7235 0.604   0.431
#> 4 4 0.796           0.830       0.926         0.0640 0.766   0.512
#> 5 5 0.792           0.751       0.882         0.0976 0.869   0.655
#> 6 6 0.793           0.760       0.885         0.0803 0.844   0.499

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] 3
#> 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
#> GSM317649     1  0.0000      0.977 1.000 0.000
#> GSM317652     1  0.0000      0.977 1.000 0.000
#> GSM317666     1  0.4022      0.905 0.920 0.080
#> GSM317672     1  0.0376      0.976 0.996 0.004
#> GSM317679     1  0.0000      0.977 1.000 0.000
#> GSM317681     1  0.2948      0.934 0.948 0.052
#> GSM317682     1  0.1184      0.969 0.984 0.016
#> GSM317683     2  0.1414      0.949 0.020 0.980
#> GSM317689     2  0.3431      0.919 0.064 0.936
#> GSM317691     1  0.0376      0.976 0.996 0.004
#> GSM317692     1  0.0376      0.976 0.996 0.004
#> GSM317693     1  0.0000      0.977 1.000 0.000
#> GSM317696     1  0.1414      0.966 0.980 0.020
#> GSM317697     1  0.0000      0.977 1.000 0.000
#> GSM317698     1  0.0000      0.977 1.000 0.000
#> GSM317650     2  0.1414      0.949 0.020 0.980
#> GSM317651     1  0.0000      0.977 1.000 0.000
#> GSM317657     2  0.9850      0.277 0.428 0.572
#> GSM317667     2  0.1414      0.949 0.020 0.980
#> GSM317670     1  0.9833      0.180 0.576 0.424
#> GSM317674     1  0.1414      0.966 0.980 0.020
#> GSM317675     1  0.0000      0.977 1.000 0.000
#> GSM317677     1  0.0376      0.976 0.996 0.004
#> GSM317678     2  0.1414      0.949 0.020 0.980
#> GSM317687     1  0.0376      0.976 0.996 0.004
#> GSM317695     1  0.0000      0.977 1.000 0.000
#> GSM317653     1  0.2603      0.941 0.956 0.044
#> GSM317656     1  0.0938      0.971 0.988 0.012
#> GSM317658     1  0.0672      0.974 0.992 0.008
#> GSM317660     1  0.0000      0.977 1.000 0.000
#> GSM317663     2  0.4690      0.886 0.100 0.900
#> GSM317664     1  0.1414      0.966 0.980 0.020
#> GSM317665     1  0.0000      0.977 1.000 0.000
#> GSM317673     1  0.1414      0.966 0.980 0.020
#> GSM317686     2  0.1414      0.949 0.020 0.980
#> GSM317688     1  0.1414      0.966 0.980 0.020
#> GSM317690     2  0.1414      0.949 0.020 0.980
#> GSM317654     1  0.0000      0.977 1.000 0.000
#> GSM317655     2  0.1414      0.949 0.020 0.980
#> GSM317659     1  0.0376      0.976 0.996 0.004
#> GSM317661     2  0.1414      0.949 0.020 0.980
#> GSM317662     2  0.1414      0.949 0.020 0.980
#> GSM317668     1  0.0376      0.976 0.996 0.004
#> GSM317669     1  0.0000      0.977 1.000 0.000
#> GSM317671     1  0.0000      0.977 1.000 0.000
#> GSM317676     1  0.0672      0.974 0.992 0.008
#> GSM317680     1  0.0000      0.977 1.000 0.000
#> GSM317684     1  0.0376      0.976 0.996 0.004
#> GSM317685     1  0.0000      0.977 1.000 0.000
#> GSM317694     1  0.0376      0.976 0.996 0.004

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> GSM317649     3  0.0829      0.970 0.012 0.004 0.984
#> GSM317652     1  0.6516      0.107 0.516 0.004 0.480
#> GSM317666     2  0.1031      0.983 0.000 0.976 0.024
#> GSM317672     2  0.0424      0.984 0.008 0.992 0.000
#> GSM317679     3  0.0829      0.970 0.012 0.004 0.984
#> GSM317681     2  0.1015      0.982 0.008 0.980 0.012
#> GSM317682     1  0.3192      0.822 0.888 0.000 0.112
#> GSM317683     2  0.0237      0.984 0.000 0.996 0.004
#> GSM317689     2  0.0000      0.985 0.000 1.000 0.000
#> GSM317691     1  0.0661      0.906 0.988 0.008 0.004
#> GSM317692     1  0.5760      0.546 0.672 0.328 0.000
#> GSM317693     1  0.0424      0.906 0.992 0.008 0.000
#> GSM317696     1  0.0000      0.907 1.000 0.000 0.000
#> GSM317697     1  0.0475      0.906 0.992 0.004 0.004
#> GSM317698     1  0.0237      0.907 0.996 0.004 0.000
#> GSM317650     2  0.0237      0.984 0.000 0.996 0.004
#> GSM317651     1  0.5553      0.619 0.724 0.004 0.272
#> GSM317657     2  0.0661      0.984 0.008 0.988 0.004
#> GSM317667     2  0.1031      0.983 0.000 0.976 0.024
#> GSM317670     2  0.0237      0.985 0.004 0.996 0.000
#> GSM317674     1  0.0000      0.907 1.000 0.000 0.000
#> GSM317675     1  0.0475      0.906 0.992 0.004 0.004
#> GSM317677     1  0.0424      0.906 0.992 0.008 0.000
#> GSM317678     2  0.0000      0.985 0.000 1.000 0.000
#> GSM317687     1  0.6033      0.518 0.660 0.336 0.004
#> GSM317695     1  0.0237      0.906 0.996 0.000 0.004
#> GSM317653     2  0.2680      0.929 0.008 0.924 0.068
#> GSM317656     1  0.0000      0.907 1.000 0.000 0.000
#> GSM317658     2  0.1129      0.976 0.020 0.976 0.004
#> GSM317660     3  0.0829      0.970 0.012 0.004 0.984
#> GSM317663     2  0.0892      0.983 0.000 0.980 0.020
#> GSM317664     1  0.0000      0.907 1.000 0.000 0.000
#> GSM317665     3  0.0829      0.970 0.012 0.004 0.984
#> GSM317673     1  0.0000      0.907 1.000 0.000 0.000
#> GSM317686     2  0.1031      0.983 0.000 0.976 0.024
#> GSM317688     1  0.0000      0.907 1.000 0.000 0.000
#> GSM317690     2  0.0000      0.985 0.000 1.000 0.000
#> GSM317654     3  0.4968      0.744 0.188 0.012 0.800
#> GSM317655     2  0.0892      0.983 0.000 0.980 0.020
#> GSM317659     1  0.0829      0.904 0.984 0.012 0.004
#> GSM317661     2  0.0237      0.984 0.000 0.996 0.004
#> GSM317662     2  0.0237      0.984 0.000 0.996 0.004
#> GSM317668     1  0.4555      0.717 0.800 0.000 0.200
#> GSM317669     3  0.0829      0.970 0.012 0.004 0.984
#> GSM317671     3  0.0829      0.970 0.012 0.004 0.984
#> GSM317676     2  0.1170      0.978 0.016 0.976 0.008
#> GSM317680     3  0.0829      0.970 0.012 0.004 0.984
#> GSM317684     1  0.0661      0.906 0.988 0.008 0.004
#> GSM317685     1  0.0237      0.907 0.996 0.004 0.000
#> GSM317694     1  0.0237      0.907 0.996 0.004 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM317649     3  0.0000      0.924 0.000 0.000 1.000 0.000
#> GSM317652     3  0.1637      0.875 0.060 0.000 0.940 0.000
#> GSM317666     4  0.0188      1.000 0.000 0.004 0.000 0.996
#> GSM317672     1  0.6310      0.204 0.512 0.428 0.060 0.000
#> GSM317679     3  0.0000      0.924 0.000 0.000 1.000 0.000
#> GSM317681     3  0.4010      0.803 0.064 0.100 0.836 0.000
#> GSM317682     1  0.2530      0.797 0.888 0.000 0.112 0.000
#> GSM317683     2  0.0000      0.994 0.000 1.000 0.000 0.000
#> GSM317689     2  0.0817      0.963 0.024 0.976 0.000 0.000
#> GSM317691     1  0.0188      0.873 0.996 0.000 0.000 0.004
#> GSM317692     1  0.0188      0.873 0.996 0.004 0.000 0.000
#> GSM317693     1  0.0188      0.873 0.996 0.000 0.000 0.004
#> GSM317696     1  0.0000      0.874 1.000 0.000 0.000 0.000
#> GSM317697     1  0.0000      0.874 1.000 0.000 0.000 0.000
#> GSM317698     1  0.0000      0.874 1.000 0.000 0.000 0.000
#> GSM317650     2  0.0000      0.994 0.000 1.000 0.000 0.000
#> GSM317651     1  0.4817      0.328 0.612 0.000 0.388 0.000
#> GSM317657     1  0.5716      0.271 0.552 0.028 0.000 0.420
#> GSM317667     4  0.0188      1.000 0.000 0.004 0.000 0.996
#> GSM317670     1  0.4948      0.279 0.560 0.440 0.000 0.000
#> GSM317674     1  0.0000      0.874 1.000 0.000 0.000 0.000
#> GSM317675     1  0.0000      0.874 1.000 0.000 0.000 0.000
#> GSM317677     1  0.0188      0.873 0.996 0.000 0.000 0.004
#> GSM317678     2  0.0000      0.994 0.000 1.000 0.000 0.000
#> GSM317687     1  0.4193      0.618 0.732 0.000 0.000 0.268
#> GSM317695     1  0.1940      0.829 0.924 0.000 0.076 0.000
#> GSM317653     3  0.5175      0.492 0.328 0.004 0.656 0.012
#> GSM317656     1  0.0000      0.874 1.000 0.000 0.000 0.000
#> GSM317658     1  0.4193      0.622 0.732 0.268 0.000 0.000
#> GSM317660     3  0.0000      0.924 0.000 0.000 1.000 0.000
#> GSM317663     4  0.0188      1.000 0.000 0.004 0.000 0.996
#> GSM317664     1  0.0000      0.874 1.000 0.000 0.000 0.000
#> GSM317665     3  0.0000      0.924 0.000 0.000 1.000 0.000
#> GSM317673     1  0.0000      0.874 1.000 0.000 0.000 0.000
#> GSM317686     4  0.0188      1.000 0.000 0.004 0.000 0.996
#> GSM317688     1  0.0000      0.874 1.000 0.000 0.000 0.000
#> GSM317690     2  0.0000      0.994 0.000 1.000 0.000 0.000
#> GSM317654     3  0.0707      0.913 0.020 0.000 0.980 0.000
#> GSM317655     4  0.0188      1.000 0.000 0.004 0.000 0.996
#> GSM317659     1  0.0188      0.873 0.996 0.000 0.000 0.004
#> GSM317661     2  0.0000      0.994 0.000 1.000 0.000 0.000
#> GSM317662     2  0.0000      0.994 0.000 1.000 0.000 0.000
#> GSM317668     1  0.3610      0.717 0.800 0.000 0.200 0.000
#> GSM317669     3  0.0000      0.924 0.000 0.000 1.000 0.000
#> GSM317671     3  0.0000      0.924 0.000 0.000 1.000 0.000
#> GSM317676     1  0.4564      0.528 0.672 0.000 0.000 0.328
#> GSM317680     3  0.0000      0.924 0.000 0.000 1.000 0.000
#> GSM317684     1  0.0188      0.873 0.996 0.000 0.000 0.004
#> GSM317685     1  0.0000      0.874 1.000 0.000 0.000 0.000
#> GSM317694     1  0.0188      0.873 0.996 0.000 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
#> GSM317649     3  0.0000      0.973 0.000 0.000 1.000 0.000 0.000
#> GSM317652     3  0.0609      0.949 0.020 0.000 0.980 0.000 0.000
#> GSM317666     4  0.0510      0.441 0.000 0.000 0.000 0.984 0.016
#> GSM317672     2  0.6961      0.452 0.216 0.576 0.160 0.020 0.028
#> GSM317679     3  0.0000      0.973 0.000 0.000 1.000 0.000 0.000
#> GSM317681     3  0.3634      0.770 0.000 0.136 0.820 0.040 0.004
#> GSM317682     1  0.2488      0.764 0.872 0.000 0.124 0.000 0.004
#> GSM317683     2  0.0162      0.833 0.000 0.996 0.000 0.000 0.004
#> GSM317689     2  0.1399      0.812 0.000 0.952 0.000 0.020 0.028
#> GSM317691     1  0.0290      0.862 0.992 0.000 0.000 0.000 0.008
#> GSM317692     1  0.1106      0.847 0.964 0.000 0.000 0.024 0.012
#> GSM317693     1  0.0000      0.864 1.000 0.000 0.000 0.000 0.000
#> GSM317696     1  0.0000      0.864 1.000 0.000 0.000 0.000 0.000
#> GSM317697     1  0.0000      0.864 1.000 0.000 0.000 0.000 0.000
#> GSM317698     1  0.0000      0.864 1.000 0.000 0.000 0.000 0.000
#> GSM317650     2  0.0162      0.833 0.000 0.996 0.000 0.000 0.004
#> GSM317651     1  0.4283      0.237 0.544 0.000 0.456 0.000 0.000
#> GSM317657     4  0.2928      0.480 0.004 0.032 0.000 0.872 0.092
#> GSM317667     5  0.4268      1.000 0.000 0.000 0.000 0.444 0.556
#> GSM317670     2  0.5464      0.183 0.424 0.528 0.000 0.020 0.028
#> GSM317674     1  0.0000      0.864 1.000 0.000 0.000 0.000 0.000
#> GSM317675     1  0.0000      0.864 1.000 0.000 0.000 0.000 0.000
#> GSM317677     1  0.4201      0.516 0.592 0.000 0.000 0.000 0.408
#> GSM317678     2  0.0000      0.833 0.000 1.000 0.000 0.000 0.000
#> GSM317687     4  0.5236      0.505 0.048 0.000 0.000 0.544 0.408
#> GSM317695     1  0.0404      0.860 0.988 0.000 0.012 0.000 0.000
#> GSM317653     4  0.6687      0.348 0.000 0.000 0.248 0.420 0.332
#> GSM317656     1  0.0162      0.863 0.996 0.000 0.000 0.000 0.004
#> GSM317658     1  0.5240      0.364 0.616 0.336 0.000 0.020 0.028
#> GSM317660     3  0.0000      0.973 0.000 0.000 1.000 0.000 0.000
#> GSM317663     4  0.0000      0.452 0.000 0.000 0.000 1.000 0.000
#> GSM317664     1  0.0000      0.864 1.000 0.000 0.000 0.000 0.000
#> GSM317665     3  0.0000      0.973 0.000 0.000 1.000 0.000 0.000
#> GSM317673     1  0.0000      0.864 1.000 0.000 0.000 0.000 0.000
#> GSM317686     5  0.4268      1.000 0.000 0.000 0.000 0.444 0.556
#> GSM317688     1  0.0162      0.863 0.996 0.000 0.000 0.000 0.004
#> GSM317690     2  0.0865      0.823 0.000 0.972 0.000 0.004 0.024
#> GSM317654     3  0.0000      0.973 0.000 0.000 1.000 0.000 0.000
#> GSM317655     4  0.0404      0.446 0.000 0.000 0.000 0.988 0.012
#> GSM317659     1  0.4464      0.504 0.584 0.000 0.000 0.008 0.408
#> GSM317661     2  0.0162      0.833 0.000 0.996 0.000 0.000 0.004
#> GSM317662     2  0.0162      0.833 0.000 0.996 0.000 0.000 0.004
#> GSM317668     1  0.3210      0.713 0.788 0.000 0.212 0.000 0.000
#> GSM317669     3  0.0000      0.973 0.000 0.000 1.000 0.000 0.000
#> GSM317671     3  0.0000      0.973 0.000 0.000 1.000 0.000 0.000
#> GSM317676     4  0.5236      0.505 0.048 0.000 0.000 0.544 0.408
#> GSM317680     3  0.0000      0.973 0.000 0.000 1.000 0.000 0.000
#> GSM317684     1  0.4201      0.516 0.592 0.000 0.000 0.000 0.408
#> GSM317685     1  0.0000      0.864 1.000 0.000 0.000 0.000 0.000
#> GSM317694     1  0.3143      0.740 0.796 0.000 0.000 0.000 0.204

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> GSM317649     5  0.0000     0.8539 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM317652     5  0.0508     0.8446 0.012 0.000 0.000 0.000 0.984 0.004
#> GSM317666     4  0.4252     0.6054 0.000 0.000 0.372 0.604 0.000 0.024
#> GSM317672     6  0.2287     0.7056 0.012 0.036 0.000 0.000 0.048 0.904
#> GSM317679     5  0.0000     0.8539 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM317681     5  0.3838     0.2573 0.000 0.000 0.000 0.000 0.552 0.448
#> GSM317682     1  0.2135     0.7950 0.872 0.000 0.000 0.000 0.128 0.000
#> GSM317683     2  0.0000     0.9773 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM317689     6  0.2003     0.7184 0.000 0.116 0.000 0.000 0.000 0.884
#> GSM317691     1  0.4843     0.5380 0.652 0.000 0.232 0.000 0.000 0.116
#> GSM317692     6  0.3587     0.6091 0.140 0.000 0.068 0.000 0.000 0.792
#> GSM317693     1  0.3354     0.7715 0.812 0.000 0.128 0.000 0.000 0.060
#> GSM317696     1  0.0000     0.9140 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317697     1  0.1267     0.8828 0.940 0.000 0.000 0.000 0.000 0.060
#> GSM317698     1  0.0146     0.9124 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM317650     2  0.0000     0.9773 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM317651     5  0.3930     0.2126 0.420 0.000 0.000 0.000 0.576 0.004
#> GSM317657     6  0.4301     0.4128 0.000 0.000 0.240 0.064 0.000 0.696
#> GSM317667     4  0.0000     0.6777 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM317670     6  0.2300     0.7090 0.000 0.144 0.000 0.000 0.000 0.856
#> GSM317674     1  0.0000     0.9140 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317675     1  0.0000     0.9140 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317677     3  0.2442     0.8126 0.144 0.000 0.852 0.000 0.000 0.004
#> GSM317678     2  0.1444     0.9025 0.000 0.928 0.000 0.000 0.000 0.072
#> GSM317687     3  0.0000     0.7919 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM317695     1  0.0260     0.9101 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM317653     5  0.6195     0.2540 0.000 0.000 0.292 0.016 0.476 0.216
#> GSM317656     1  0.0000     0.9140 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317658     6  0.2112     0.6904 0.088 0.016 0.000 0.000 0.000 0.896
#> GSM317660     5  0.0000     0.8539 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM317663     4  0.5648     0.6215 0.000 0.000 0.240 0.536 0.000 0.224
#> GSM317664     1  0.0000     0.9140 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317665     5  0.0146     0.8529 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM317673     1  0.0000     0.9140 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317686     4  0.0000     0.6777 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM317688     1  0.0000     0.9140 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317690     6  0.3862     0.0723 0.000 0.476 0.000 0.000 0.000 0.524
#> GSM317654     5  0.0146     0.8529 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM317655     4  0.5259     0.6902 0.000 0.000 0.240 0.600 0.000 0.160
#> GSM317659     3  0.1588     0.8382 0.072 0.000 0.924 0.000 0.000 0.004
#> GSM317661     2  0.0000     0.9773 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM317662     2  0.0000     0.9773 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM317668     1  0.3023     0.7131 0.784 0.000 0.000 0.000 0.212 0.004
#> GSM317669     5  0.0000     0.8539 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM317671     5  0.0000     0.8539 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM317676     3  0.0458     0.7796 0.000 0.000 0.984 0.016 0.000 0.000
#> GSM317680     5  0.0000     0.8539 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM317684     3  0.2668     0.7859 0.168 0.000 0.828 0.000 0.000 0.004
#> GSM317685     1  0.0000     0.9140 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317694     1  0.2793     0.7347 0.800 0.000 0.200 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 disease.state(p) k
#> MAD:mclust 48            0.694 2
#> MAD:mclust 49            0.593 3
#> MAD:mclust 45            0.877 4
#> MAD:mclust 41            0.739 5
#> MAD:mclust 45            0.427 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 11993 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 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-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           0.939       0.976         0.4660 0.530   0.530
#> 3 3 0.545           0.652       0.794         0.3880 0.735   0.538
#> 4 4 0.825           0.852       0.929         0.1408 0.747   0.415
#> 5 5 0.736           0.696       0.831         0.0716 0.922   0.715
#> 6 6 0.796           0.722       0.853         0.0409 0.945   0.756

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
#> GSM317649     1  0.0000      0.986 1.000 0.000
#> GSM317652     1  0.0000      0.986 1.000 0.000
#> GSM317666     2  0.0000      0.954 0.000 1.000
#> GSM317672     2  0.0938      0.946 0.012 0.988
#> GSM317679     1  0.1633      0.964 0.976 0.024
#> GSM317681     2  0.0000      0.954 0.000 1.000
#> GSM317682     1  0.0000      0.986 1.000 0.000
#> GSM317683     2  0.0000      0.954 0.000 1.000
#> GSM317689     2  0.0000      0.954 0.000 1.000
#> GSM317691     1  0.0000      0.986 1.000 0.000
#> GSM317692     1  0.9248      0.457 0.660 0.340
#> GSM317693     1  0.0000      0.986 1.000 0.000
#> GSM317696     1  0.0000      0.986 1.000 0.000
#> GSM317697     1  0.0000      0.986 1.000 0.000
#> GSM317698     1  0.0000      0.986 1.000 0.000
#> GSM317650     2  0.0000      0.954 0.000 1.000
#> GSM317651     1  0.0000      0.986 1.000 0.000
#> GSM317657     2  0.0000      0.954 0.000 1.000
#> GSM317667     2  0.0000      0.954 0.000 1.000
#> GSM317670     2  0.1633      0.936 0.024 0.976
#> GSM317674     1  0.0000      0.986 1.000 0.000
#> GSM317675     1  0.0000      0.986 1.000 0.000
#> GSM317677     1  0.0000      0.986 1.000 0.000
#> GSM317678     2  0.0000      0.954 0.000 1.000
#> GSM317687     1  0.0000      0.986 1.000 0.000
#> GSM317695     1  0.0000      0.986 1.000 0.000
#> GSM317653     2  0.8555      0.613 0.280 0.720
#> GSM317656     1  0.0000      0.986 1.000 0.000
#> GSM317658     2  0.9909      0.195 0.444 0.556
#> GSM317660     1  0.2948      0.935 0.948 0.052
#> GSM317663     2  0.0000      0.954 0.000 1.000
#> GSM317664     1  0.0000      0.986 1.000 0.000
#> GSM317665     1  0.0000      0.986 1.000 0.000
#> GSM317673     1  0.0000      0.986 1.000 0.000
#> GSM317686     2  0.0000      0.954 0.000 1.000
#> GSM317688     1  0.0000      0.986 1.000 0.000
#> GSM317690     2  0.0000      0.954 0.000 1.000
#> GSM317654     1  0.0000      0.986 1.000 0.000
#> GSM317655     2  0.0000      0.954 0.000 1.000
#> GSM317659     1  0.0000      0.986 1.000 0.000
#> GSM317661     2  0.0000      0.954 0.000 1.000
#> GSM317662     2  0.0000      0.954 0.000 1.000
#> GSM317668     1  0.0000      0.986 1.000 0.000
#> GSM317669     1  0.0000      0.986 1.000 0.000
#> GSM317671     1  0.0672      0.979 0.992 0.008
#> GSM317676     1  0.0000      0.986 1.000 0.000
#> GSM317680     1  0.0000      0.986 1.000 0.000
#> GSM317684     1  0.0000      0.986 1.000 0.000
#> GSM317685     1  0.0000      0.986 1.000 0.000
#> GSM317694     1  0.0000      0.986 1.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> GSM317649     1  0.0424      0.778 0.992 0.008 0.000
#> GSM317652     1  0.0892      0.787 0.980 0.000 0.020
#> GSM317666     3  0.5058      0.594 0.000 0.244 0.756
#> GSM317672     2  0.3267      0.722 0.116 0.884 0.000
#> GSM317679     1  0.2356      0.723 0.928 0.072 0.000
#> GSM317681     2  0.4121      0.686 0.168 0.832 0.000
#> GSM317682     1  0.0424      0.778 0.992 0.008 0.000
#> GSM317683     2  0.0000      0.766 0.000 1.000 0.000
#> GSM317689     2  0.0424      0.762 0.000 0.992 0.008
#> GSM317691     3  0.4121      0.539 0.168 0.000 0.832
#> GSM317692     1  0.9191      0.287 0.428 0.148 0.424
#> GSM317693     3  0.3941      0.562 0.156 0.000 0.844
#> GSM317696     1  0.5560      0.765 0.700 0.000 0.300
#> GSM317697     1  0.5810      0.739 0.664 0.000 0.336
#> GSM317698     1  0.5835      0.735 0.660 0.000 0.340
#> GSM317650     2  0.0592      0.766 0.012 0.988 0.000
#> GSM317651     1  0.5291      0.776 0.732 0.000 0.268
#> GSM317657     3  0.5465      0.564 0.000 0.288 0.712
#> GSM317667     3  0.5785      0.516 0.000 0.332 0.668
#> GSM317670     2  0.6357      0.461 0.020 0.684 0.296
#> GSM317674     1  0.5706      0.752 0.680 0.000 0.320
#> GSM317675     1  0.5760      0.746 0.672 0.000 0.328
#> GSM317677     3  0.2261      0.672 0.068 0.000 0.932
#> GSM317678     2  0.0892      0.765 0.020 0.980 0.000
#> GSM317687     3  0.0237      0.690 0.004 0.000 0.996
#> GSM317695     1  0.1031      0.788 0.976 0.000 0.024
#> GSM317653     2  0.6955     -0.276 0.016 0.496 0.488
#> GSM317656     1  0.1031      0.788 0.976 0.000 0.024
#> GSM317658     2  0.9020      0.261 0.220 0.560 0.220
#> GSM317660     2  0.6308      0.274 0.492 0.508 0.000
#> GSM317663     3  0.6126      0.427 0.000 0.400 0.600
#> GSM317664     1  0.5497      0.768 0.708 0.000 0.292
#> GSM317665     1  0.0424      0.778 0.992 0.008 0.000
#> GSM317673     1  0.4974      0.784 0.764 0.000 0.236
#> GSM317686     3  0.6286      0.291 0.000 0.464 0.536
#> GSM317688     1  0.4605      0.788 0.796 0.000 0.204
#> GSM317690     2  0.0892      0.755 0.000 0.980 0.020
#> GSM317654     1  0.0892      0.779 0.980 0.000 0.020
#> GSM317655     3  0.5988      0.478 0.000 0.368 0.632
#> GSM317659     3  0.0747      0.689 0.016 0.000 0.984
#> GSM317661     2  0.0000      0.766 0.000 1.000 0.000
#> GSM317662     2  0.0000      0.766 0.000 1.000 0.000
#> GSM317668     1  0.5465      0.770 0.712 0.000 0.288
#> GSM317669     1  0.0424      0.778 0.992 0.008 0.000
#> GSM317671     1  0.0892      0.773 0.980 0.020 0.000
#> GSM317676     3  0.0237      0.690 0.004 0.000 0.996
#> GSM317680     1  0.0424      0.778 0.992 0.008 0.000
#> GSM317684     3  0.3482      0.607 0.128 0.000 0.872
#> GSM317685     1  0.5678      0.755 0.684 0.000 0.316
#> GSM317694     1  0.6204      0.623 0.576 0.000 0.424

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM317649     3  0.0592      0.931 0.016 0.000 0.984 0.000
#> GSM317652     3  0.2281      0.901 0.096 0.000 0.904 0.000
#> GSM317666     4  0.0000      0.924 0.000 0.000 0.000 1.000
#> GSM317672     2  0.0336      0.888 0.000 0.992 0.008 0.000
#> GSM317679     3  0.0592      0.931 0.016 0.000 0.984 0.000
#> GSM317681     3  0.3718      0.808 0.000 0.168 0.820 0.012
#> GSM317682     1  0.5453      0.449 0.648 0.032 0.320 0.000
#> GSM317683     2  0.0188      0.891 0.000 0.996 0.000 0.004
#> GSM317689     2  0.0469      0.888 0.000 0.988 0.000 0.012
#> GSM317691     1  0.0336      0.914 0.992 0.000 0.000 0.008
#> GSM317692     1  0.1807      0.882 0.940 0.052 0.000 0.008
#> GSM317693     1  0.0592      0.910 0.984 0.000 0.000 0.016
#> GSM317696     1  0.0000      0.915 1.000 0.000 0.000 0.000
#> GSM317697     1  0.0188      0.915 0.996 0.000 0.000 0.004
#> GSM317698     1  0.0188      0.915 0.996 0.000 0.000 0.004
#> GSM317650     2  0.0000      0.891 0.000 1.000 0.000 0.000
#> GSM317651     3  0.2921      0.861 0.140 0.000 0.860 0.000
#> GSM317657     4  0.5994      0.614 0.152 0.156 0.000 0.692
#> GSM317667     4  0.0376      0.924 0.000 0.004 0.004 0.992
#> GSM317670     2  0.5769      0.677 0.180 0.736 0.048 0.036
#> GSM317674     1  0.0000      0.915 1.000 0.000 0.000 0.000
#> GSM317675     1  0.0000      0.915 1.000 0.000 0.000 0.000
#> GSM317677     1  0.1211      0.897 0.960 0.000 0.000 0.040
#> GSM317678     2  0.0000      0.891 0.000 1.000 0.000 0.000
#> GSM317687     4  0.1557      0.898 0.056 0.000 0.000 0.944
#> GSM317695     3  0.2647      0.863 0.120 0.000 0.880 0.000
#> GSM317653     4  0.3679      0.831 0.000 0.084 0.060 0.856
#> GSM317656     1  0.4454      0.575 0.692 0.000 0.308 0.000
#> GSM317658     2  0.5581      0.181 0.448 0.532 0.000 0.020
#> GSM317660     3  0.1716      0.911 0.000 0.064 0.936 0.000
#> GSM317663     4  0.0188      0.924 0.000 0.000 0.004 0.996
#> GSM317664     1  0.0188      0.914 0.996 0.000 0.004 0.000
#> GSM317665     3  0.1389      0.919 0.000 0.048 0.952 0.000
#> GSM317673     1  0.0000      0.915 1.000 0.000 0.000 0.000
#> GSM317686     4  0.0336      0.924 0.000 0.008 0.000 0.992
#> GSM317688     1  0.0000      0.915 1.000 0.000 0.000 0.000
#> GSM317690     2  0.1557      0.856 0.000 0.944 0.000 0.056
#> GSM317654     3  0.1820      0.923 0.036 0.020 0.944 0.000
#> GSM317655     4  0.0188      0.924 0.000 0.004 0.000 0.996
#> GSM317659     1  0.4193      0.627 0.732 0.000 0.000 0.268
#> GSM317661     2  0.0524      0.890 0.000 0.988 0.008 0.004
#> GSM317662     2  0.0188      0.891 0.000 0.996 0.000 0.004
#> GSM317668     1  0.4222      0.648 0.728 0.000 0.272 0.000
#> GSM317669     3  0.0336      0.930 0.008 0.000 0.992 0.000
#> GSM317671     3  0.0707      0.930 0.020 0.000 0.980 0.000
#> GSM317676     4  0.1389      0.905 0.048 0.000 0.000 0.952
#> GSM317680     3  0.0000      0.927 0.000 0.000 1.000 0.000
#> GSM317684     1  0.1637      0.883 0.940 0.000 0.000 0.060
#> GSM317685     1  0.0000      0.915 1.000 0.000 0.000 0.000
#> GSM317694     1  0.0188      0.915 0.996 0.000 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
#> GSM317649     3  0.2280   0.681417 0.000 0.000 0.880 0.000 0.120
#> GSM317652     3  0.5151  -0.000488 0.044 0.000 0.560 0.000 0.396
#> GSM317666     4  0.0404   0.880315 0.000 0.000 0.000 0.988 0.012
#> GSM317672     2  0.3336   0.710576 0.000 0.772 0.000 0.000 0.228
#> GSM317679     3  0.2230   0.683614 0.000 0.000 0.884 0.000 0.116
#> GSM317681     5  0.5612   0.519340 0.000 0.032 0.120 0.152 0.696
#> GSM317682     1  0.3837   0.448391 0.692 0.000 0.000 0.000 0.308
#> GSM317683     2  0.0000   0.880084 0.000 1.000 0.000 0.000 0.000
#> GSM317689     2  0.0000   0.880084 0.000 1.000 0.000 0.000 0.000
#> GSM317691     1  0.3767   0.787081 0.800 0.000 0.008 0.024 0.168
#> GSM317692     1  0.0771   0.865583 0.976 0.004 0.000 0.000 0.020
#> GSM317693     1  0.0000   0.870973 1.000 0.000 0.000 0.000 0.000
#> GSM317696     1  0.0451   0.871420 0.988 0.000 0.004 0.000 0.008
#> GSM317697     1  0.0404   0.871889 0.988 0.000 0.000 0.000 0.012
#> GSM317698     1  0.1270   0.867249 0.948 0.000 0.000 0.000 0.052
#> GSM317650     2  0.0000   0.880084 0.000 1.000 0.000 0.000 0.000
#> GSM317651     5  0.5713   0.185260 0.416 0.000 0.084 0.000 0.500
#> GSM317657     4  0.5421   0.709545 0.024 0.104 0.004 0.716 0.152
#> GSM317667     4  0.1908   0.858545 0.000 0.000 0.000 0.908 0.092
#> GSM317670     2  0.6910   0.428685 0.008 0.532 0.144 0.028 0.288
#> GSM317674     1  0.2249   0.851578 0.896 0.000 0.008 0.000 0.096
#> GSM317675     1  0.1638   0.863930 0.932 0.000 0.004 0.000 0.064
#> GSM317677     1  0.5708   0.647049 0.640 0.000 0.016 0.092 0.252
#> GSM317678     2  0.1671   0.858116 0.000 0.924 0.000 0.000 0.076
#> GSM317687     4  0.2915   0.792398 0.116 0.000 0.000 0.860 0.024
#> GSM317695     3  0.0000   0.668589 0.000 0.000 1.000 0.000 0.000
#> GSM317653     5  0.4350   0.126051 0.000 0.004 0.000 0.408 0.588
#> GSM317656     3  0.5365   0.399401 0.204 0.000 0.664 0.000 0.132
#> GSM317658     2  0.1282   0.857511 0.044 0.952 0.000 0.000 0.004
#> GSM317660     5  0.4276   0.400994 0.000 0.004 0.380 0.000 0.616
#> GSM317663     4  0.1544   0.869762 0.000 0.000 0.000 0.932 0.068
#> GSM317664     1  0.4272   0.756584 0.752 0.000 0.052 0.000 0.196
#> GSM317665     5  0.4249   0.301833 0.000 0.000 0.432 0.000 0.568
#> GSM317673     1  0.0290   0.870885 0.992 0.000 0.000 0.000 0.008
#> GSM317686     4  0.0671   0.880367 0.000 0.004 0.000 0.980 0.016
#> GSM317688     1  0.0404   0.868380 0.988 0.000 0.000 0.000 0.012
#> GSM317690     2  0.0880   0.872190 0.000 0.968 0.000 0.000 0.032
#> GSM317654     5  0.4425   0.492210 0.000 0.000 0.296 0.024 0.680
#> GSM317655     4  0.2377   0.860212 0.000 0.000 0.000 0.872 0.128
#> GSM317659     1  0.5938   0.252077 0.512 0.000 0.000 0.376 0.112
#> GSM317661     2  0.2848   0.801807 0.000 0.840 0.000 0.004 0.156
#> GSM317662     2  0.0963   0.875489 0.000 0.964 0.000 0.000 0.036
#> GSM317668     3  0.6596   0.292968 0.164 0.000 0.524 0.016 0.296
#> GSM317669     3  0.2561   0.659016 0.000 0.000 0.856 0.000 0.144
#> GSM317671     3  0.0703   0.658432 0.000 0.000 0.976 0.000 0.024
#> GSM317676     4  0.1952   0.853976 0.004 0.000 0.000 0.912 0.084
#> GSM317680     3  0.2230   0.683614 0.000 0.000 0.884 0.000 0.116
#> GSM317684     1  0.0671   0.867861 0.980 0.000 0.000 0.004 0.016
#> GSM317685     1  0.0703   0.865842 0.976 0.000 0.000 0.000 0.024
#> GSM317694     1  0.2136   0.853973 0.904 0.000 0.008 0.000 0.088

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> GSM317649     3  0.0909     0.9667 0.000 0.000 0.968 0.000 0.020 0.012
#> GSM317652     5  0.5521     0.5554 0.032 0.000 0.264 0.000 0.608 0.096
#> GSM317666     4  0.0632     0.7675 0.000 0.000 0.000 0.976 0.000 0.024
#> GSM317672     2  0.2933     0.7359 0.000 0.796 0.000 0.000 0.200 0.004
#> GSM317679     3  0.0146     0.9853 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM317681     5  0.4156     0.7577 0.004 0.016 0.032 0.120 0.796 0.032
#> GSM317682     1  0.2437     0.8070 0.888 0.004 0.000 0.000 0.072 0.036
#> GSM317683     2  0.0000     0.8659 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM317689     2  0.1297     0.8585 0.000 0.948 0.000 0.000 0.012 0.040
#> GSM317691     1  0.3172     0.7723 0.816 0.000 0.000 0.036 0.000 0.148
#> GSM317692     1  0.2359     0.8236 0.904 0.024 0.000 0.004 0.016 0.052
#> GSM317693     1  0.0935     0.8507 0.964 0.000 0.000 0.004 0.000 0.032
#> GSM317696     1  0.0146     0.8563 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM317697     1  0.0603     0.8558 0.980 0.004 0.000 0.000 0.000 0.016
#> GSM317698     1  0.2257     0.8311 0.876 0.000 0.000 0.000 0.008 0.116
#> GSM317650     2  0.0363     0.8666 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM317651     5  0.2344     0.8153 0.048 0.000 0.004 0.000 0.896 0.052
#> GSM317657     4  0.5337     0.3544 0.004 0.100 0.004 0.576 0.000 0.316
#> GSM317667     4  0.1462     0.7552 0.000 0.000 0.000 0.936 0.056 0.008
#> GSM317670     6  0.3124     0.4413 0.000 0.164 0.012 0.004 0.004 0.816
#> GSM317674     1  0.3340     0.7620 0.784 0.000 0.004 0.000 0.016 0.196
#> GSM317675     1  0.2714     0.8131 0.848 0.000 0.004 0.000 0.012 0.136
#> GSM317677     1  0.5420     0.1711 0.476 0.000 0.000 0.080 0.012 0.432
#> GSM317678     2  0.0363     0.8678 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM317687     4  0.2321     0.7207 0.052 0.000 0.000 0.900 0.008 0.040
#> GSM317695     3  0.0000     0.9856 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM317653     5  0.1531     0.8231 0.000 0.000 0.000 0.068 0.928 0.004
#> GSM317656     6  0.7145     0.1905 0.160 0.000 0.292 0.000 0.128 0.420
#> GSM317658     2  0.1152     0.8418 0.044 0.952 0.000 0.000 0.004 0.000
#> GSM317660     5  0.2065     0.8423 0.000 0.004 0.052 0.000 0.912 0.032
#> GSM317663     4  0.1434     0.7663 0.000 0.000 0.008 0.948 0.024 0.020
#> GSM317664     1  0.4260     0.6556 0.692 0.000 0.024 0.000 0.016 0.268
#> GSM317665     5  0.2540     0.8282 0.004 0.000 0.104 0.000 0.872 0.020
#> GSM317673     1  0.1588     0.8547 0.924 0.000 0.000 0.000 0.004 0.072
#> GSM317686     4  0.0777     0.7677 0.000 0.004 0.000 0.972 0.000 0.024
#> GSM317688     1  0.1333     0.8570 0.944 0.000 0.000 0.000 0.008 0.048
#> GSM317690     2  0.1152     0.8550 0.000 0.952 0.000 0.000 0.004 0.044
#> GSM317654     5  0.1989     0.8456 0.000 0.000 0.052 0.028 0.916 0.004
#> GSM317655     6  0.4653    -0.0695 0.000 0.000 0.000 0.360 0.052 0.588
#> GSM317659     6  0.6144     0.1261 0.252 0.000 0.000 0.332 0.004 0.412
#> GSM317661     2  0.4705     0.1150 0.000 0.484 0.000 0.000 0.472 0.044
#> GSM317662     2  0.1644     0.8463 0.000 0.920 0.000 0.000 0.076 0.004
#> GSM317668     6  0.2917     0.4934 0.032 0.000 0.072 0.000 0.028 0.868
#> GSM317669     3  0.0458     0.9805 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM317671     3  0.0260     0.9827 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM317676     4  0.3991     0.1454 0.000 0.000 0.000 0.524 0.004 0.472
#> GSM317680     3  0.0260     0.9849 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM317684     1  0.2263     0.8234 0.900 0.000 0.000 0.036 0.004 0.060
#> GSM317685     1  0.0937     0.8539 0.960 0.000 0.000 0.000 0.000 0.040
#> GSM317694     1  0.1818     0.8528 0.920 0.000 0.004 0.004 0.004 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-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 disease.state(p) k
#> MAD:NMF 48            0.696 2
#> MAD:NMF 42            0.612 3
#> MAD:NMF 48            0.902 4
#> MAD:NMF 39            0.846 5
#> MAD:NMF 41            0.638 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 11993 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 3.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

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 0.483           0.805       0.903          0.322 0.754   0.754
#> 3 3 0.489           0.769       0.806          0.694 0.620   0.506
#> 4 4 0.509           0.716       0.815          0.126 0.993   0.984
#> 5 5 0.557           0.705       0.801          0.115 0.937   0.841
#> 6 6 0.619           0.710       0.763          0.132 0.860   0.588

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] 3

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
#> GSM317649     1   0.000      0.880 1.000 0.000
#> GSM317652     1   0.000      0.880 1.000 0.000
#> GSM317666     1   0.866      0.686 0.712 0.288
#> GSM317672     1   0.969      0.505 0.604 0.396
#> GSM317679     1   0.000      0.880 1.000 0.000
#> GSM317681     1   0.973      0.493 0.596 0.404
#> GSM317682     1   0.634      0.802 0.840 0.160
#> GSM317683     2   0.000      0.922 0.000 1.000
#> GSM317689     1   0.971      0.497 0.600 0.400
#> GSM317691     1   0.000      0.880 1.000 0.000
#> GSM317692     1   0.866      0.653 0.712 0.288
#> GSM317693     1   0.000      0.880 1.000 0.000
#> GSM317696     1   0.000      0.880 1.000 0.000
#> GSM317697     1   0.000      0.880 1.000 0.000
#> GSM317698     1   0.000      0.880 1.000 0.000
#> GSM317650     2   0.000      0.922 0.000 1.000
#> GSM317651     1   0.634      0.802 0.840 0.160
#> GSM317657     1   0.866      0.686 0.712 0.288
#> GSM317667     2   0.000      0.922 0.000 1.000
#> GSM317670     1   0.494      0.822 0.892 0.108
#> GSM317674     1   0.000      0.880 1.000 0.000
#> GSM317675     1   0.000      0.880 1.000 0.000
#> GSM317677     1   0.000      0.880 1.000 0.000
#> GSM317678     2   0.952      0.184 0.372 0.628
#> GSM317687     1   0.000      0.880 1.000 0.000
#> GSM317695     1   0.000      0.880 1.000 0.000
#> GSM317653     1   0.973      0.493 0.596 0.404
#> GSM317656     1   0.000      0.880 1.000 0.000
#> GSM317658     1   0.760      0.754 0.780 0.220
#> GSM317660     1   0.653      0.797 0.832 0.168
#> GSM317663     1   0.866      0.686 0.712 0.288
#> GSM317664     1   0.000      0.880 1.000 0.000
#> GSM317665     1   0.634      0.802 0.840 0.160
#> GSM317673     1   0.000      0.880 1.000 0.000
#> GSM317686     2   0.000      0.922 0.000 1.000
#> GSM317688     1   0.000      0.880 1.000 0.000
#> GSM317690     1   0.881      0.671 0.700 0.300
#> GSM317654     1   0.634      0.802 0.840 0.160
#> GSM317655     1   0.866      0.686 0.712 0.288
#> GSM317659     1   0.000      0.880 1.000 0.000
#> GSM317661     2   0.000      0.922 0.000 1.000
#> GSM317662     2   0.000      0.922 0.000 1.000
#> GSM317668     1   0.000      0.880 1.000 0.000
#> GSM317669     1   0.000      0.880 1.000 0.000
#> GSM317671     1   0.000      0.880 1.000 0.000
#> GSM317676     1   0.000      0.880 1.000 0.000
#> GSM317680     1   0.000      0.880 1.000 0.000
#> GSM317684     1   0.000      0.880 1.000 0.000
#> GSM317685     1   0.000      0.880 1.000 0.000
#> GSM317694     1   0.000      0.880 1.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> GSM317649     1  0.0000      0.920 1.000 0.000 0.000
#> GSM317652     1  0.0237      0.918 0.996 0.004 0.000
#> GSM317666     2  0.3359      0.696 0.084 0.900 0.016
#> GSM317672     2  0.5710      0.663 0.080 0.804 0.116
#> GSM317679     1  0.0000      0.920 1.000 0.000 0.000
#> GSM317681     2  0.4768      0.642 0.052 0.848 0.100
#> GSM317682     2  0.6126      0.523 0.400 0.600 0.000
#> GSM317683     3  0.4399      0.899 0.000 0.188 0.812
#> GSM317689     2  0.5695      0.660 0.076 0.804 0.120
#> GSM317691     1  0.3619      0.840 0.864 0.136 0.000
#> GSM317692     2  0.7199      0.662 0.180 0.712 0.108
#> GSM317693     1  0.3551      0.844 0.868 0.132 0.000
#> GSM317696     1  0.0000      0.920 1.000 0.000 0.000
#> GSM317697     1  0.3551      0.844 0.868 0.132 0.000
#> GSM317698     1  0.0000      0.920 1.000 0.000 0.000
#> GSM317650     3  0.4399      0.899 0.000 0.188 0.812
#> GSM317651     2  0.6126      0.523 0.400 0.600 0.000
#> GSM317657     2  0.3359      0.696 0.084 0.900 0.016
#> GSM317667     3  0.1753      0.818 0.000 0.048 0.952
#> GSM317670     2  0.6225      0.313 0.432 0.568 0.000
#> GSM317674     1  0.0000      0.920 1.000 0.000 0.000
#> GSM317675     1  0.0000      0.920 1.000 0.000 0.000
#> GSM317677     1  0.2878      0.872 0.904 0.096 0.000
#> GSM317678     2  0.7580      0.206 0.056 0.604 0.340
#> GSM317687     1  0.4931      0.673 0.768 0.232 0.000
#> GSM317695     1  0.0000      0.920 1.000 0.000 0.000
#> GSM317653     2  0.4768      0.642 0.052 0.848 0.100
#> GSM317656     1  0.0000      0.920 1.000 0.000 0.000
#> GSM317658     2  0.6168      0.442 0.412 0.588 0.000
#> GSM317660     2  0.5948      0.577 0.360 0.640 0.000
#> GSM317663     2  0.3359      0.696 0.084 0.900 0.016
#> GSM317664     1  0.0000      0.920 1.000 0.000 0.000
#> GSM317665     2  0.6126      0.523 0.400 0.600 0.000
#> GSM317673     1  0.0000      0.920 1.000 0.000 0.000
#> GSM317686     3  0.1753      0.818 0.000 0.048 0.952
#> GSM317688     1  0.0000      0.920 1.000 0.000 0.000
#> GSM317690     2  0.3765      0.690 0.084 0.888 0.028
#> GSM317654     2  0.6126      0.523 0.400 0.600 0.000
#> GSM317655     2  0.3359      0.696 0.084 0.900 0.016
#> GSM317659     1  0.3038      0.867 0.896 0.104 0.000
#> GSM317661     3  0.4399      0.899 0.000 0.188 0.812
#> GSM317662     3  0.4399      0.899 0.000 0.188 0.812
#> GSM317668     1  0.4399      0.754 0.812 0.188 0.000
#> GSM317669     1  0.0000      0.920 1.000 0.000 0.000
#> GSM317671     1  0.0000      0.920 1.000 0.000 0.000
#> GSM317676     1  0.4931      0.673 0.768 0.232 0.000
#> GSM317680     1  0.0000      0.920 1.000 0.000 0.000
#> GSM317684     1  0.3038      0.867 0.896 0.104 0.000
#> GSM317685     1  0.0000      0.920 1.000 0.000 0.000
#> GSM317694     1  0.2878      0.872 0.904 0.096 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM317649     1  0.0000      0.852 1.000 0.000 0.000 0.000
#> GSM317652     1  0.0188      0.852 0.996 0.000 0.000 0.004
#> GSM317666     4  0.2469      0.622 0.000 0.000 0.108 0.892
#> GSM317672     4  0.2859      0.620 0.008 0.112 0.000 0.880
#> GSM317679     1  0.1211      0.836 0.960 0.000 0.040 0.000
#> GSM317681     4  0.5399      0.595 0.052 0.140 0.036 0.772
#> GSM317682     4  0.7018      0.465 0.368 0.024 0.068 0.540
#> GSM317683     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM317689     4  0.2773      0.617 0.004 0.116 0.000 0.880
#> GSM317691     1  0.5585      0.706 0.712 0.000 0.084 0.204
#> GSM317692     4  0.4549      0.618 0.100 0.096 0.000 0.804
#> GSM317693     1  0.5448      0.717 0.724 0.000 0.080 0.196
#> GSM317696     1  0.0000      0.852 1.000 0.000 0.000 0.000
#> GSM317697     1  0.5448      0.717 0.724 0.000 0.080 0.196
#> GSM317698     1  0.0921      0.847 0.972 0.000 0.028 0.000
#> GSM317650     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM317651     4  0.7018      0.465 0.368 0.024 0.068 0.540
#> GSM317657     4  0.2469      0.622 0.000 0.000 0.108 0.892
#> GSM317667     3  0.4868      1.000 0.000 0.304 0.684 0.012
#> GSM317670     4  0.7249      0.226 0.348 0.000 0.156 0.496
#> GSM317674     1  0.0188      0.852 0.996 0.000 0.004 0.000
#> GSM317675     1  0.0000      0.852 1.000 0.000 0.000 0.000
#> GSM317677     1  0.5208      0.740 0.748 0.000 0.080 0.172
#> GSM317678     4  0.4819      0.286 0.004 0.344 0.000 0.652
#> GSM317687     1  0.6383      0.523 0.612 0.000 0.096 0.292
#> GSM317695     1  0.1211      0.836 0.960 0.000 0.040 0.000
#> GSM317653     4  0.5399      0.595 0.052 0.140 0.036 0.772
#> GSM317656     1  0.0000      0.852 1.000 0.000 0.000 0.000
#> GSM317658     4  0.6462      0.383 0.332 0.000 0.088 0.580
#> GSM317660     4  0.7519      0.532 0.280 0.032 0.120 0.568
#> GSM317663     4  0.2469      0.622 0.000 0.000 0.108 0.892
#> GSM317664     1  0.0000      0.852 1.000 0.000 0.000 0.000
#> GSM317665     4  0.7018      0.465 0.368 0.024 0.068 0.540
#> GSM317673     1  0.0921      0.847 0.972 0.000 0.028 0.000
#> GSM317686     3  0.4868      1.000 0.000 0.304 0.684 0.012
#> GSM317688     1  0.0817      0.850 0.976 0.000 0.024 0.000
#> GSM317690     4  0.3695      0.600 0.000 0.016 0.156 0.828
#> GSM317654     4  0.7018      0.465 0.368 0.024 0.068 0.540
#> GSM317655     4  0.2469      0.622 0.000 0.000 0.108 0.892
#> GSM317659     1  0.5292      0.738 0.744 0.000 0.088 0.168
#> GSM317661     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM317662     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM317668     1  0.4222      0.652 0.728 0.000 0.000 0.272
#> GSM317669     1  0.1211      0.836 0.960 0.000 0.040 0.000
#> GSM317671     1  0.1211      0.836 0.960 0.000 0.040 0.000
#> GSM317676     1  0.6383      0.523 0.612 0.000 0.096 0.292
#> GSM317680     1  0.1211      0.836 0.960 0.000 0.040 0.000
#> GSM317684     1  0.5292      0.738 0.744 0.000 0.088 0.168
#> GSM317685     1  0.0000      0.852 1.000 0.000 0.000 0.000
#> GSM317694     1  0.3636      0.772 0.820 0.000 0.008 0.172

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> GSM317649     1  0.0000      0.782 1.000 0.000 0.000 0.000 0.000
#> GSM317652     1  0.0880      0.778 0.968 0.000 0.032 0.000 0.000
#> GSM317666     4  0.0162      0.715 0.000 0.000 0.000 0.996 0.004
#> GSM317672     4  0.4098      0.652 0.000 0.064 0.156 0.780 0.000
#> GSM317679     1  0.1792      0.744 0.916 0.000 0.000 0.000 0.084
#> GSM317681     3  0.4337      0.490 0.000 0.052 0.744 0.204 0.000
#> GSM317682     3  0.3305      0.792 0.224 0.000 0.776 0.000 0.000
#> GSM317683     2  0.0000      0.998 0.000 1.000 0.000 0.000 0.000
#> GSM317689     4  0.4159      0.651 0.000 0.068 0.156 0.776 0.000
#> GSM317691     1  0.6151      0.610 0.604 0.000 0.176 0.208 0.012
#> GSM317692     4  0.5634      0.607 0.092 0.052 0.152 0.704 0.000
#> GSM317693     1  0.6097      0.619 0.612 0.000 0.176 0.200 0.012
#> GSM317696     1  0.0000      0.782 1.000 0.000 0.000 0.000 0.000
#> GSM317697     1  0.6097      0.619 0.612 0.000 0.176 0.200 0.012
#> GSM317698     1  0.0963      0.777 0.964 0.000 0.036 0.000 0.000
#> GSM317650     2  0.0000      0.998 0.000 1.000 0.000 0.000 0.000
#> GSM317651     3  0.3305      0.792 0.224 0.000 0.776 0.000 0.000
#> GSM317657     4  0.0162      0.715 0.000 0.000 0.000 0.996 0.004
#> GSM317667     5  0.3109      1.000 0.000 0.200 0.000 0.000 0.800
#> GSM317670     4  0.7371      0.179 0.312 0.000 0.100 0.480 0.108
#> GSM317674     1  0.0162      0.782 0.996 0.000 0.004 0.000 0.000
#> GSM317675     1  0.0000      0.782 1.000 0.000 0.000 0.000 0.000
#> GSM317677     1  0.5949      0.641 0.632 0.000 0.180 0.176 0.012
#> GSM317678     4  0.6088      0.336 0.000 0.296 0.156 0.548 0.000
#> GSM317687     1  0.6680      0.425 0.496 0.000 0.184 0.308 0.012
#> GSM317695     1  0.1792      0.744 0.916 0.000 0.000 0.000 0.084
#> GSM317653     3  0.4337      0.490 0.000 0.052 0.744 0.204 0.000
#> GSM317656     1  0.0000      0.782 1.000 0.000 0.000 0.000 0.000
#> GSM317658     4  0.7500      0.316 0.256 0.000 0.136 0.500 0.108
#> GSM317660     3  0.2377      0.729 0.128 0.000 0.872 0.000 0.000
#> GSM317663     4  0.0162      0.715 0.000 0.000 0.000 0.996 0.004
#> GSM317664     1  0.0000      0.782 1.000 0.000 0.000 0.000 0.000
#> GSM317665     3  0.3305      0.792 0.224 0.000 0.776 0.000 0.000
#> GSM317673     1  0.0963      0.777 0.964 0.000 0.036 0.000 0.000
#> GSM317686     5  0.3109      1.000 0.000 0.200 0.000 0.000 0.800
#> GSM317688     1  0.2127      0.753 0.892 0.000 0.108 0.000 0.000
#> GSM317690     4  0.4121      0.605 0.000 0.016 0.072 0.808 0.104
#> GSM317654     3  0.3305      0.792 0.224 0.000 0.776 0.000 0.000
#> GSM317655     4  0.0162      0.715 0.000 0.000 0.000 0.996 0.004
#> GSM317659     1  0.5980      0.638 0.628 0.000 0.184 0.176 0.012
#> GSM317661     2  0.0162      0.994 0.000 0.996 0.004 0.000 0.000
#> GSM317662     2  0.0000      0.998 0.000 1.000 0.000 0.000 0.000
#> GSM317668     1  0.4397      0.612 0.696 0.000 0.028 0.276 0.000
#> GSM317669     1  0.1792      0.744 0.916 0.000 0.000 0.000 0.084
#> GSM317671     1  0.1792      0.744 0.916 0.000 0.000 0.000 0.084
#> GSM317676     1  0.6680      0.425 0.496 0.000 0.184 0.308 0.012
#> GSM317680     1  0.1792      0.744 0.916 0.000 0.000 0.000 0.084
#> GSM317684     1  0.5980      0.638 0.628 0.000 0.184 0.176 0.012
#> GSM317685     1  0.0000      0.782 1.000 0.000 0.000 0.000 0.000
#> GSM317694     1  0.4683      0.688 0.732 0.000 0.092 0.176 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
#> GSM317649     3  0.0000     0.7946 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM317652     3  0.1092     0.7833 0.020 0.000 0.960 0.000 0.020 0.000
#> GSM317666     4  0.2562     0.7066 0.172 0.000 0.000 0.828 0.000 0.000
#> GSM317672     4  0.3661     0.6512 0.020 0.012 0.000 0.768 0.200 0.000
#> GSM317679     3  0.3877     0.7200 0.136 0.000 0.792 0.008 0.056 0.008
#> GSM317681     5  0.2762     0.5300 0.000 0.000 0.000 0.196 0.804 0.000
#> GSM317682     5  0.4566     0.7914 0.140 0.000 0.160 0.000 0.700 0.000
#> GSM317683     2  0.0000     0.9980 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM317689     4  0.3666     0.6506 0.016 0.016 0.000 0.768 0.200 0.000
#> GSM317691     1  0.4917     0.8087 0.656 0.000 0.228 0.112 0.004 0.000
#> GSM317692     4  0.5705     0.5681 0.120 0.000 0.052 0.628 0.200 0.000
#> GSM317693     1  0.5128     0.8026 0.636 0.000 0.240 0.116 0.008 0.000
#> GSM317696     3  0.1387     0.7923 0.068 0.000 0.932 0.000 0.000 0.000
#> GSM317697     1  0.5128     0.8026 0.636 0.000 0.240 0.116 0.008 0.000
#> GSM317698     3  0.2176     0.7727 0.080 0.000 0.896 0.000 0.024 0.000
#> GSM317650     2  0.0000     0.9980 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM317651     5  0.4566     0.7914 0.140 0.000 0.160 0.000 0.700 0.000
#> GSM317657     4  0.2562     0.7066 0.172 0.000 0.000 0.828 0.000 0.000
#> GSM317667     6  0.2527     1.0000 0.000 0.168 0.000 0.000 0.000 0.832
#> GSM317670     1  0.7138     0.1946 0.416 0.000 0.064 0.340 0.020 0.160
#> GSM317674     3  0.1531     0.7911 0.068 0.000 0.928 0.000 0.004 0.000
#> GSM317675     3  0.1387     0.7923 0.068 0.000 0.932 0.000 0.000 0.000
#> GSM317677     1  0.3302     0.8206 0.760 0.000 0.232 0.004 0.004 0.000
#> GSM317678     4  0.5671     0.4780 0.004 0.244 0.000 0.552 0.200 0.000
#> GSM317687     1  0.3254     0.7390 0.816 0.000 0.136 0.048 0.000 0.000
#> GSM317695     3  0.3877     0.7200 0.136 0.000 0.792 0.008 0.056 0.008
#> GSM317653     5  0.2762     0.5300 0.000 0.000 0.000 0.196 0.804 0.000
#> GSM317656     3  0.0000     0.7946 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM317658     4  0.6278     0.0445 0.364 0.000 0.008 0.452 0.016 0.160
#> GSM317660     5  0.2762     0.6915 0.196 0.000 0.000 0.000 0.804 0.000
#> GSM317663     4  0.2562     0.7066 0.172 0.000 0.000 0.828 0.000 0.000
#> GSM317664     3  0.1387     0.7923 0.068 0.000 0.932 0.000 0.000 0.000
#> GSM317665     5  0.4566     0.7914 0.140 0.000 0.160 0.000 0.700 0.000
#> GSM317673     3  0.2176     0.7727 0.080 0.000 0.896 0.000 0.024 0.000
#> GSM317686     6  0.2527     1.0000 0.000 0.168 0.000 0.000 0.000 0.832
#> GSM317688     3  0.4924     0.3866 0.268 0.000 0.636 0.004 0.092 0.000
#> GSM317690     4  0.4172     0.5650 0.032 0.016 0.000 0.772 0.020 0.160
#> GSM317654     5  0.4566     0.7914 0.140 0.000 0.160 0.000 0.700 0.000
#> GSM317655     4  0.2562     0.7066 0.172 0.000 0.000 0.828 0.000 0.000
#> GSM317659     1  0.2969     0.8209 0.776 0.000 0.224 0.000 0.000 0.000
#> GSM317661     2  0.0146     0.9941 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM317662     2  0.0000     0.9980 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM317668     3  0.5595    -0.3295 0.392 0.000 0.464 0.144 0.000 0.000
#> GSM317669     3  0.3877     0.7200 0.136 0.000 0.792 0.008 0.056 0.008
#> GSM317671     3  0.3877     0.7200 0.136 0.000 0.792 0.008 0.056 0.008
#> GSM317676     1  0.3254     0.7390 0.816 0.000 0.136 0.048 0.000 0.000
#> GSM317680     3  0.3877     0.7200 0.136 0.000 0.792 0.008 0.056 0.008
#> GSM317684     1  0.2969     0.8209 0.776 0.000 0.224 0.000 0.000 0.000
#> GSM317685     3  0.1387     0.7923 0.068 0.000 0.932 0.000 0.000 0.000
#> GSM317694     1  0.3728     0.7128 0.652 0.000 0.344 0.004 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 disease.state(p) k
#> ATC:hclust 46            0.826 2
#> ATC:hclust 47            0.570 3
#> ATC:hclust 43            0.406 4
#> ATC:hclust 43            0.772 5
#> ATC:hclust 45            0.707 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 11993 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           0.990       0.995         0.4478 0.556   0.556
#> 3 3 0.488           0.649       0.707         0.3560 1.000   1.000
#> 4 4 0.486           0.593       0.743         0.1482 0.684   0.463
#> 5 5 0.572           0.702       0.780         0.0948 0.878   0.622
#> 6 6 0.739           0.737       0.794         0.0573 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
#> GSM317649     1   0.000      0.993 1.000 0.000
#> GSM317652     1   0.000      0.993 1.000 0.000
#> GSM317666     2   0.000      1.000 0.000 1.000
#> GSM317672     2   0.000      1.000 0.000 1.000
#> GSM317679     1   0.000      0.993 1.000 0.000
#> GSM317681     2   0.000      1.000 0.000 1.000
#> GSM317682     1   0.000      0.993 1.000 0.000
#> GSM317683     2   0.000      1.000 0.000 1.000
#> GSM317689     2   0.000      1.000 0.000 1.000
#> GSM317691     1   0.000      0.993 1.000 0.000
#> GSM317692     1   0.775      0.705 0.772 0.228
#> GSM317693     1   0.000      0.993 1.000 0.000
#> GSM317696     1   0.000      0.993 1.000 0.000
#> GSM317697     1   0.000      0.993 1.000 0.000
#> GSM317698     1   0.000      0.993 1.000 0.000
#> GSM317650     2   0.000      1.000 0.000 1.000
#> GSM317651     1   0.000      0.993 1.000 0.000
#> GSM317657     2   0.000      1.000 0.000 1.000
#> GSM317667     2   0.000      1.000 0.000 1.000
#> GSM317670     1   0.000      0.993 1.000 0.000
#> GSM317674     1   0.000      0.993 1.000 0.000
#> GSM317675     1   0.000      0.993 1.000 0.000
#> GSM317677     1   0.000      0.993 1.000 0.000
#> GSM317678     2   0.000      1.000 0.000 1.000
#> GSM317687     1   0.000      0.993 1.000 0.000
#> GSM317695     1   0.000      0.993 1.000 0.000
#> GSM317653     2   0.000      1.000 0.000 1.000
#> GSM317656     1   0.000      0.993 1.000 0.000
#> GSM317658     1   0.000      0.993 1.000 0.000
#> GSM317660     1   0.000      0.993 1.000 0.000
#> GSM317663     2   0.000      1.000 0.000 1.000
#> GSM317664     1   0.000      0.993 1.000 0.000
#> GSM317665     1   0.000      0.993 1.000 0.000
#> GSM317673     1   0.000      0.993 1.000 0.000
#> GSM317686     2   0.000      1.000 0.000 1.000
#> GSM317688     1   0.000      0.993 1.000 0.000
#> GSM317690     2   0.000      1.000 0.000 1.000
#> GSM317654     1   0.000      0.993 1.000 0.000
#> GSM317655     2   0.000      1.000 0.000 1.000
#> GSM317659     1   0.000      0.993 1.000 0.000
#> GSM317661     2   0.000      1.000 0.000 1.000
#> GSM317662     2   0.000      1.000 0.000 1.000
#> GSM317668     1   0.000      0.993 1.000 0.000
#> GSM317669     1   0.000      0.993 1.000 0.000
#> GSM317671     1   0.000      0.993 1.000 0.000
#> GSM317676     1   0.000      0.993 1.000 0.000
#> GSM317680     1   0.000      0.993 1.000 0.000
#> GSM317684     1   0.000      0.993 1.000 0.000
#> GSM317685     1   0.000      0.993 1.000 0.000
#> GSM317694     1   0.000      0.993 1.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2 p3
#> GSM317649     1   0.553      0.582 0.704 0.000 NA
#> GSM317652     1   0.254      0.707 0.920 0.000 NA
#> GSM317666     2   0.412      0.702 0.000 0.832 NA
#> GSM317672     2   0.558      0.570 0.024 0.772 NA
#> GSM317679     1   0.553      0.582 0.704 0.000 NA
#> GSM317681     2   0.525      0.763 0.000 0.736 NA
#> GSM317682     1   0.496      0.707 0.792 0.008 NA
#> GSM317683     2   0.601      0.755 0.000 0.628 NA
#> GSM317689     2   0.000      0.743 0.000 1.000 NA
#> GSM317691     1   0.897      0.559 0.564 0.240 NA
#> GSM317692     1   0.979      0.321 0.384 0.380 NA
#> GSM317693     1   0.897      0.559 0.564 0.240 NA
#> GSM317696     1   0.000      0.728 1.000 0.000 NA
#> GSM317697     1   0.865      0.589 0.600 0.204 NA
#> GSM317698     1   0.271      0.728 0.912 0.000 NA
#> GSM317650     2   0.601      0.755 0.000 0.628 NA
#> GSM317651     1   0.571      0.698 0.768 0.028 NA
#> GSM317657     2   0.543      0.584 0.000 0.716 NA
#> GSM317667     2   0.629      0.744 0.000 0.532 NA
#> GSM317670     1   0.955      0.384 0.436 0.368 NA
#> GSM317674     1   0.000      0.728 1.000 0.000 NA
#> GSM317675     1   0.000      0.728 1.000 0.000 NA
#> GSM317677     1   0.750      0.648 0.696 0.140 NA
#> GSM317678     2   0.502      0.770 0.000 0.760 NA
#> GSM317687     1   0.956      0.383 0.432 0.372 NA
#> GSM317695     1   0.543      0.587 0.716 0.000 NA
#> GSM317653     2   0.493      0.624 0.000 0.768 NA
#> GSM317656     1   0.236      0.709 0.928 0.000 NA
#> GSM317658     1   0.955      0.384 0.436 0.368 NA
#> GSM317660     1   0.754      0.659 0.640 0.068 NA
#> GSM317663     2   0.400      0.703 0.000 0.840 NA
#> GSM317664     1   0.000      0.728 1.000 0.000 NA
#> GSM317665     1   0.645      0.688 0.684 0.024 NA
#> GSM317673     1   0.271      0.728 0.912 0.000 NA
#> GSM317686     2   0.629      0.744 0.000 0.532 NA
#> GSM317688     1   0.175      0.730 0.952 0.000 NA
#> GSM317690     2   0.271      0.765 0.000 0.912 NA
#> GSM317654     1   0.637      0.693 0.704 0.028 NA
#> GSM317655     2   0.355      0.717 0.000 0.868 NA
#> GSM317659     1   0.897      0.559 0.564 0.240 NA
#> GSM317661     2   0.601      0.755 0.000 0.628 NA
#> GSM317662     2   0.601      0.755 0.000 0.628 NA
#> GSM317668     1   0.000      0.728 1.000 0.000 NA
#> GSM317669     1   0.553      0.582 0.704 0.000 NA
#> GSM317671     1   0.553      0.582 0.704 0.000 NA
#> GSM317676     1   0.958      0.377 0.428 0.372 NA
#> GSM317680     1   0.553      0.582 0.704 0.000 NA
#> GSM317684     1   0.826      0.618 0.636 0.168 NA
#> GSM317685     1   0.000      0.728 1.000 0.000 NA
#> GSM317694     1   0.000      0.728 1.000 0.000 NA

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM317649     3  0.4522     0.9923 0.320 0.000 0.680 0.000
#> GSM317652     1  0.3649     0.4913 0.796 0.000 0.204 0.000
#> GSM317666     4  0.2965     0.5817 0.000 0.072 0.036 0.892
#> GSM317672     4  0.8202     0.3716 0.056 0.176 0.228 0.540
#> GSM317679     3  0.4522     0.9923 0.320 0.000 0.680 0.000
#> GSM317681     2  0.7955     0.0791 0.008 0.432 0.224 0.336
#> GSM317682     1  0.5522     0.5472 0.716 0.000 0.204 0.080
#> GSM317683     2  0.0000     0.7767 0.000 1.000 0.000 0.000
#> GSM317689     4  0.5473     0.4118 0.000 0.324 0.032 0.644
#> GSM317691     1  0.5487     0.1773 0.580 0.000 0.020 0.400
#> GSM317692     4  0.5604     0.5890 0.160 0.000 0.116 0.724
#> GSM317693     1  0.4642     0.5489 0.740 0.000 0.020 0.240
#> GSM317696     1  0.2973     0.5762 0.856 0.000 0.144 0.000
#> GSM317697     1  0.4284     0.6027 0.780 0.000 0.020 0.200
#> GSM317698     1  0.1042     0.6464 0.972 0.000 0.008 0.020
#> GSM317650     2  0.0000     0.7767 0.000 1.000 0.000 0.000
#> GSM317651     1  0.6194     0.5278 0.668 0.000 0.200 0.132
#> GSM317657     4  0.1743     0.6051 0.004 0.056 0.000 0.940
#> GSM317667     2  0.5321     0.6651 0.000 0.748 0.112 0.140
#> GSM317670     4  0.4313     0.5861 0.260 0.000 0.004 0.736
#> GSM317674     1  0.2973     0.5762 0.856 0.000 0.144 0.000
#> GSM317675     1  0.2973     0.5762 0.856 0.000 0.144 0.000
#> GSM317677     1  0.3351     0.6302 0.844 0.000 0.008 0.148
#> GSM317678     2  0.5579     0.4370 0.000 0.688 0.060 0.252
#> GSM317687     4  0.5428     0.3952 0.380 0.000 0.020 0.600
#> GSM317695     3  0.4624     0.9611 0.340 0.000 0.660 0.000
#> GSM317653     4  0.8291     0.3359 0.052 0.200 0.224 0.524
#> GSM317656     1  0.3486     0.5091 0.812 0.000 0.188 0.000
#> GSM317658     4  0.4908     0.5580 0.292 0.000 0.016 0.692
#> GSM317660     1  0.8096     0.3390 0.512 0.052 0.308 0.128
#> GSM317663     4  0.2965     0.5817 0.000 0.072 0.036 0.892
#> GSM317664     1  0.2973     0.5762 0.856 0.000 0.144 0.000
#> GSM317665     1  0.6592     0.4503 0.600 0.000 0.284 0.116
#> GSM317673     1  0.0376     0.6461 0.992 0.000 0.004 0.004
#> GSM317686     2  0.5321     0.6651 0.000 0.748 0.112 0.140
#> GSM317688     1  0.0469     0.6435 0.988 0.000 0.012 0.000
#> GSM317690     4  0.5582     0.2677 0.000 0.400 0.024 0.576
#> GSM317654     1  0.6394     0.4940 0.636 0.000 0.244 0.120
#> GSM317655     4  0.3243     0.5669 0.000 0.088 0.036 0.876
#> GSM317659     1  0.4675     0.5468 0.736 0.000 0.020 0.244
#> GSM317661     2  0.0000     0.7767 0.000 1.000 0.000 0.000
#> GSM317662     2  0.0336     0.7756 0.000 0.992 0.008 0.000
#> GSM317668     1  0.2973     0.5762 0.856 0.000 0.144 0.000
#> GSM317669     3  0.4522     0.9923 0.320 0.000 0.680 0.000
#> GSM317671     3  0.4522     0.9923 0.320 0.000 0.680 0.000
#> GSM317676     4  0.4837     0.4646 0.348 0.000 0.004 0.648
#> GSM317680     3  0.4522     0.9923 0.320 0.000 0.680 0.000
#> GSM317684     1  0.4079     0.6199 0.800 0.000 0.020 0.180
#> GSM317685     1  0.2973     0.5762 0.856 0.000 0.144 0.000
#> GSM317694     1  0.3324     0.5834 0.852 0.000 0.136 0.012

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> GSM317649     3  0.2439      0.998 0.120 0.000 0.876 0.004 0.000
#> GSM317652     1  0.3171      0.752 0.816 0.000 0.176 0.008 0.000
#> GSM317666     4  0.2359      0.646 0.000 0.060 0.000 0.904 0.036
#> GSM317672     5  0.2746      0.656 0.008 0.000 0.008 0.112 0.872
#> GSM317679     3  0.2280      0.999 0.120 0.000 0.880 0.000 0.000
#> GSM317681     5  0.3459      0.589 0.000 0.052 0.000 0.116 0.832
#> GSM317682     5  0.3838      0.737 0.280 0.000 0.004 0.000 0.716
#> GSM317683     2  0.2497      0.796 0.000 0.880 0.004 0.004 0.112
#> GSM317689     4  0.5976      0.429 0.000 0.228 0.012 0.620 0.140
#> GSM317691     1  0.5484      0.392 0.640 0.000 0.000 0.240 0.120
#> GSM317692     5  0.5100      0.450 0.056 0.000 0.004 0.288 0.652
#> GSM317693     1  0.4871      0.573 0.732 0.000 0.004 0.144 0.120
#> GSM317696     1  0.2773      0.763 0.836 0.000 0.164 0.000 0.000
#> GSM317697     1  0.4557      0.604 0.760 0.000 0.004 0.132 0.104
#> GSM317698     1  0.0579      0.762 0.984 0.000 0.008 0.000 0.008
#> GSM317650     2  0.2497      0.796 0.000 0.880 0.004 0.004 0.112
#> GSM317651     5  0.3508      0.757 0.252 0.000 0.000 0.000 0.748
#> GSM317657     4  0.2409      0.665 0.020 0.012 0.000 0.908 0.060
#> GSM317667     2  0.5252      0.622 0.000 0.724 0.096 0.152 0.028
#> GSM317670     4  0.4675      0.627 0.196 0.000 0.008 0.736 0.060
#> GSM317674     1  0.2732      0.764 0.840 0.000 0.160 0.000 0.000
#> GSM317675     1  0.2773      0.763 0.836 0.000 0.164 0.000 0.000
#> GSM317677     1  0.2727      0.686 0.868 0.000 0.000 0.116 0.016
#> GSM317678     2  0.6575      0.359 0.000 0.484 0.012 0.152 0.352
#> GSM317687     4  0.6076      0.473 0.320 0.000 0.000 0.536 0.144
#> GSM317695     3  0.2280      0.999 0.120 0.000 0.880 0.000 0.000
#> GSM317653     5  0.2136      0.675 0.008 0.000 0.000 0.088 0.904
#> GSM317656     1  0.3381      0.747 0.808 0.000 0.176 0.016 0.000
#> GSM317658     4  0.5807      0.542 0.300 0.000 0.012 0.600 0.088
#> GSM317660     5  0.3612      0.765 0.172 0.000 0.028 0.000 0.800
#> GSM317663     4  0.2209      0.646 0.000 0.056 0.000 0.912 0.032
#> GSM317664     1  0.2773      0.763 0.836 0.000 0.164 0.000 0.000
#> GSM317665     5  0.4113      0.763 0.232 0.000 0.028 0.000 0.740
#> GSM317673     1  0.2104      0.768 0.916 0.000 0.060 0.000 0.024
#> GSM317686     2  0.5252      0.622 0.000 0.724 0.096 0.152 0.028
#> GSM317688     1  0.3135      0.762 0.868 0.000 0.088 0.020 0.024
#> GSM317690     4  0.5818      0.408 0.000 0.264 0.012 0.620 0.104
#> GSM317654     5  0.3878      0.763 0.236 0.000 0.016 0.000 0.748
#> GSM317655     4  0.2209      0.646 0.000 0.056 0.000 0.912 0.032
#> GSM317659     1  0.4835      0.560 0.724 0.000 0.000 0.156 0.120
#> GSM317661     2  0.2338      0.796 0.000 0.884 0.000 0.004 0.112
#> GSM317662     2  0.2722      0.794 0.000 0.868 0.008 0.004 0.120
#> GSM317668     1  0.3211      0.758 0.824 0.000 0.164 0.008 0.004
#> GSM317669     3  0.2439      0.998 0.120 0.000 0.876 0.004 0.000
#> GSM317671     3  0.2280      0.999 0.120 0.000 0.880 0.000 0.000
#> GSM317676     4  0.5905      0.513 0.292 0.000 0.000 0.572 0.136
#> GSM317680     3  0.2280      0.999 0.120 0.000 0.880 0.000 0.000
#> GSM317684     1  0.4458      0.609 0.760 0.000 0.000 0.120 0.120
#> GSM317685     1  0.2773      0.763 0.836 0.000 0.164 0.000 0.000
#> GSM317694     1  0.3204      0.763 0.860 0.000 0.100 0.024 0.016

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5 p6
#> GSM317649     3  0.0777      0.996 0.024 0.000 0.972 0.000 0.000 NA
#> GSM317652     1  0.3483      0.753 0.820 0.000 0.120 0.000 0.020 NA
#> GSM317666     4  0.1010      0.712 0.000 0.000 0.000 0.960 0.004 NA
#> GSM317672     5  0.4429      0.748 0.000 0.016 0.000 0.080 0.736 NA
#> GSM317679     3  0.0547      0.995 0.020 0.000 0.980 0.000 0.000 NA
#> GSM317681     5  0.4260      0.776 0.000 0.036 0.000 0.072 0.772 NA
#> GSM317682     5  0.1918      0.837 0.088 0.000 0.000 0.000 0.904 NA
#> GSM317683     2  0.0000      0.783 0.000 1.000 0.000 0.000 0.000 NA
#> GSM317689     4  0.4952      0.611 0.000 0.084 0.000 0.688 0.028 NA
#> GSM317691     1  0.5892      0.491 0.572 0.000 0.000 0.068 0.076 NA
#> GSM317692     5  0.5476      0.574 0.008 0.000 0.000 0.136 0.580 NA
#> GSM317693     1  0.5016      0.575 0.636 0.000 0.000 0.016 0.072 NA
#> GSM317696     1  0.2092      0.775 0.876 0.000 0.124 0.000 0.000 NA
#> GSM317697     1  0.4707      0.605 0.672 0.000 0.000 0.012 0.064 NA
#> GSM317698     1  0.0363      0.773 0.988 0.000 0.000 0.000 0.012 NA
#> GSM317650     2  0.0000      0.783 0.000 1.000 0.000 0.000 0.000 NA
#> GSM317651     5  0.1858      0.838 0.076 0.000 0.000 0.000 0.912 NA
#> GSM317657     4  0.1686      0.729 0.008 0.004 0.000 0.932 0.004 NA
#> GSM317667     2  0.5924      0.582 0.000 0.496 0.016 0.088 0.016 NA
#> GSM317670     4  0.5019      0.687 0.068 0.000 0.004 0.664 0.020 NA
#> GSM317674     1  0.2003      0.778 0.884 0.000 0.116 0.000 0.000 NA
#> GSM317675     1  0.2092      0.775 0.876 0.000 0.124 0.000 0.000 NA
#> GSM317677     1  0.3608      0.655 0.736 0.000 0.000 0.004 0.012 NA
#> GSM317678     2  0.6282      0.386 0.000 0.580 0.000 0.108 0.116 NA
#> GSM317687     4  0.6624      0.520 0.140 0.000 0.000 0.488 0.080 NA
#> GSM317695     3  0.0632      0.996 0.024 0.000 0.976 0.000 0.000 NA
#> GSM317653     5  0.3075      0.809 0.000 0.016 0.000 0.040 0.852 NA
#> GSM317656     1  0.2972      0.760 0.836 0.000 0.128 0.000 0.000 NA
#> GSM317658     4  0.6448      0.564 0.196 0.000 0.004 0.476 0.028 NA
#> GSM317660     5  0.1219      0.845 0.048 0.000 0.004 0.000 0.948 NA
#> GSM317663     4  0.0146      0.712 0.000 0.004 0.000 0.996 0.000 NA
#> GSM317664     1  0.2092      0.775 0.876 0.000 0.124 0.000 0.000 NA
#> GSM317665     5  0.1531      0.845 0.068 0.000 0.004 0.000 0.928 NA
#> GSM317673     1  0.1801      0.771 0.924 0.000 0.016 0.000 0.056 NA
#> GSM317686     2  0.5924      0.582 0.000 0.496 0.016 0.088 0.016 NA
#> GSM317688     1  0.3526      0.730 0.828 0.000 0.028 0.000 0.056 NA
#> GSM317690     4  0.4805      0.637 0.000 0.096 0.004 0.716 0.020 NA
#> GSM317654     5  0.1728      0.841 0.064 0.000 0.004 0.000 0.924 NA
#> GSM317655     4  0.0260      0.711 0.000 0.008 0.000 0.992 0.000 NA
#> GSM317659     1  0.5294      0.557 0.612 0.000 0.000 0.028 0.072 NA
#> GSM317661     2  0.0000      0.783 0.000 1.000 0.000 0.000 0.000 NA
#> GSM317662     2  0.0508      0.781 0.000 0.984 0.000 0.000 0.004 NA
#> GSM317668     1  0.2667      0.771 0.852 0.000 0.128 0.000 0.000 NA
#> GSM317669     3  0.0777      0.996 0.024 0.000 0.972 0.000 0.000 NA
#> GSM317671     3  0.0547      0.995 0.020 0.000 0.980 0.000 0.000 NA
#> GSM317676     4  0.6162      0.550 0.128 0.000 0.000 0.532 0.048 NA
#> GSM317680     3  0.0632      0.996 0.024 0.000 0.976 0.000 0.000 NA
#> GSM317684     1  0.5015      0.575 0.628 0.000 0.000 0.012 0.076 NA
#> GSM317685     1  0.2445      0.775 0.868 0.000 0.120 0.000 0.004 NA
#> GSM317694     1  0.3370      0.765 0.828 0.000 0.072 0.000 0.008 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-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 disease.state(p) k
#> ATC:kmeans 50            0.878 2
#> ATC:kmeans 45            0.806 3
#> ATC:kmeans 37            0.924 4
#> ATC:kmeans 44            0.907 5
#> ATC:kmeans 48            0.844 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 11993 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 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-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           0.973       0.990         0.4856 0.519   0.519
#> 3 3 0.819           0.826       0.907         0.3550 0.806   0.626
#> 4 4 0.642           0.689       0.794         0.1213 0.847   0.585
#> 5 5 0.649           0.576       0.758         0.0657 0.869   0.562
#> 6 6 0.711           0.611       0.796         0.0451 0.936   0.704

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
#> GSM317649     1  0.0000      0.984 1.000 0.000
#> GSM317652     1  0.0000      0.984 1.000 0.000
#> GSM317666     2  0.0000      1.000 0.000 1.000
#> GSM317672     2  0.0000      1.000 0.000 1.000
#> GSM317679     1  0.0000      0.984 1.000 0.000
#> GSM317681     2  0.0000      1.000 0.000 1.000
#> GSM317682     1  0.0000      0.984 1.000 0.000
#> GSM317683     2  0.0000      1.000 0.000 1.000
#> GSM317689     2  0.0000      1.000 0.000 1.000
#> GSM317691     1  0.0000      0.984 1.000 0.000
#> GSM317692     2  0.0000      1.000 0.000 1.000
#> GSM317693     1  0.0000      0.984 1.000 0.000
#> GSM317696     1  0.0000      0.984 1.000 0.000
#> GSM317697     1  0.0000      0.984 1.000 0.000
#> GSM317698     1  0.0000      0.984 1.000 0.000
#> GSM317650     2  0.0000      1.000 0.000 1.000
#> GSM317651     1  0.0000      0.984 1.000 0.000
#> GSM317657     2  0.0000      1.000 0.000 1.000
#> GSM317667     2  0.0000      1.000 0.000 1.000
#> GSM317670     2  0.0000      1.000 0.000 1.000
#> GSM317674     1  0.0000      0.984 1.000 0.000
#> GSM317675     1  0.0000      0.984 1.000 0.000
#> GSM317677     1  0.0000      0.984 1.000 0.000
#> GSM317678     2  0.0000      1.000 0.000 1.000
#> GSM317687     1  0.0938      0.973 0.988 0.012
#> GSM317695     1  0.0000      0.984 1.000 0.000
#> GSM317653     2  0.0000      1.000 0.000 1.000
#> GSM317656     1  0.0000      0.984 1.000 0.000
#> GSM317658     2  0.0000      1.000 0.000 1.000
#> GSM317660     1  0.9954      0.148 0.540 0.460
#> GSM317663     2  0.0000      1.000 0.000 1.000
#> GSM317664     1  0.0000      0.984 1.000 0.000
#> GSM317665     1  0.0000      0.984 1.000 0.000
#> GSM317673     1  0.0000      0.984 1.000 0.000
#> GSM317686     2  0.0000      1.000 0.000 1.000
#> GSM317688     1  0.0000      0.984 1.000 0.000
#> GSM317690     2  0.0000      1.000 0.000 1.000
#> GSM317654     1  0.0000      0.984 1.000 0.000
#> GSM317655     2  0.0000      1.000 0.000 1.000
#> GSM317659     1  0.0000      0.984 1.000 0.000
#> GSM317661     2  0.0000      1.000 0.000 1.000
#> GSM317662     2  0.0000      1.000 0.000 1.000
#> GSM317668     1  0.0000      0.984 1.000 0.000
#> GSM317669     1  0.0000      0.984 1.000 0.000
#> GSM317671     1  0.0000      0.984 1.000 0.000
#> GSM317676     1  0.0376      0.981 0.996 0.004
#> GSM317680     1  0.0000      0.984 1.000 0.000
#> GSM317684     1  0.0000      0.984 1.000 0.000
#> GSM317685     1  0.0000      0.984 1.000 0.000
#> GSM317694     1  0.0000      0.984 1.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> GSM317649     3  0.0424     0.8995 0.008 0.000 0.992
#> GSM317652     3  0.0424     0.8995 0.008 0.000 0.992
#> GSM317666     2  0.1753     0.9631 0.048 0.952 0.000
#> GSM317672     2  0.0237     0.9801 0.000 0.996 0.004
#> GSM317679     3  0.0424     0.8995 0.008 0.000 0.992
#> GSM317681     2  0.0424     0.9786 0.000 0.992 0.008
#> GSM317682     3  0.6154    -0.0665 0.408 0.000 0.592
#> GSM317683     2  0.0000     0.9813 0.000 1.000 0.000
#> GSM317689     2  0.0000     0.9813 0.000 1.000 0.000
#> GSM317691     1  0.0000     0.7526 1.000 0.000 0.000
#> GSM317692     2  0.0000     0.9813 0.000 1.000 0.000
#> GSM317693     1  0.1529     0.7763 0.960 0.000 0.040
#> GSM317696     1  0.5926     0.6845 0.644 0.000 0.356
#> GSM317697     1  0.2066     0.7783 0.940 0.000 0.060
#> GSM317698     1  0.5138     0.7454 0.748 0.000 0.252
#> GSM317650     2  0.0000     0.9813 0.000 1.000 0.000
#> GSM317651     1  0.5926     0.6735 0.644 0.000 0.356
#> GSM317657     2  0.2066     0.9564 0.060 0.940 0.000
#> GSM317667     2  0.0000     0.9813 0.000 1.000 0.000
#> GSM317670     2  0.3340     0.9056 0.120 0.880 0.000
#> GSM317674     1  0.5926     0.6845 0.644 0.000 0.356
#> GSM317675     1  0.5926     0.6845 0.644 0.000 0.356
#> GSM317677     1  0.1529     0.7763 0.960 0.000 0.040
#> GSM317678     2  0.0000     0.9813 0.000 1.000 0.000
#> GSM317687     1  0.0000     0.7526 1.000 0.000 0.000
#> GSM317695     3  0.0424     0.8995 0.008 0.000 0.992
#> GSM317653     2  0.0424     0.9786 0.000 0.992 0.008
#> GSM317656     3  0.0424     0.8995 0.008 0.000 0.992
#> GSM317658     2  0.2356     0.9328 0.072 0.928 0.000
#> GSM317660     3  0.0424     0.8867 0.000 0.008 0.992
#> GSM317663     2  0.1529     0.9665 0.040 0.960 0.000
#> GSM317664     1  0.5926     0.6845 0.644 0.000 0.356
#> GSM317665     3  0.0000     0.8942 0.000 0.000 1.000
#> GSM317673     1  0.5926     0.6845 0.644 0.000 0.356
#> GSM317686     2  0.0000     0.9813 0.000 1.000 0.000
#> GSM317688     3  0.2537     0.8231 0.080 0.000 0.920
#> GSM317690     2  0.0000     0.9813 0.000 1.000 0.000
#> GSM317654     3  0.0000     0.8942 0.000 0.000 1.000
#> GSM317655     2  0.1529     0.9665 0.040 0.960 0.000
#> GSM317659     1  0.1411     0.7745 0.964 0.000 0.036
#> GSM317661     2  0.0000     0.9813 0.000 1.000 0.000
#> GSM317662     2  0.0000     0.9813 0.000 1.000 0.000
#> GSM317668     3  0.6244    -0.1819 0.440 0.000 0.560
#> GSM317669     3  0.0424     0.8995 0.008 0.000 0.992
#> GSM317671     3  0.0424     0.8995 0.008 0.000 0.992
#> GSM317676     1  0.0000     0.7526 1.000 0.000 0.000
#> GSM317680     3  0.0424     0.8995 0.008 0.000 0.992
#> GSM317684     1  0.1643     0.7772 0.956 0.000 0.044
#> GSM317685     1  0.5926     0.6845 0.644 0.000 0.356
#> GSM317694     1  0.4654     0.7596 0.792 0.000 0.208

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM317649     3  0.0921      0.839 0.028 0.000 0.972 0.000
#> GSM317652     3  0.2589      0.755 0.116 0.000 0.884 0.000
#> GSM317666     4  0.4978      0.719 0.004 0.384 0.000 0.612
#> GSM317672     2  0.2345      0.775 0.000 0.900 0.000 0.100
#> GSM317679     3  0.0921      0.839 0.028 0.000 0.972 0.000
#> GSM317681     2  0.3444      0.690 0.000 0.816 0.000 0.184
#> GSM317682     1  0.6693      0.537 0.624 0.028 0.064 0.284
#> GSM317683     2  0.0000      0.837 0.000 1.000 0.000 0.000
#> GSM317689     2  0.0000      0.837 0.000 1.000 0.000 0.000
#> GSM317691     1  0.4989     -0.113 0.528 0.000 0.000 0.472
#> GSM317692     2  0.1557      0.814 0.000 0.944 0.000 0.056
#> GSM317693     1  0.2149      0.663 0.912 0.000 0.000 0.088
#> GSM317696     1  0.4103      0.733 0.744 0.000 0.256 0.000
#> GSM317697     1  0.2670      0.722 0.904 0.000 0.072 0.024
#> GSM317698     1  0.3831      0.741 0.792 0.000 0.204 0.004
#> GSM317650     2  0.0000      0.837 0.000 1.000 0.000 0.000
#> GSM317651     1  0.6380      0.544 0.632 0.016 0.060 0.292
#> GSM317657     4  0.4978      0.719 0.004 0.384 0.000 0.612
#> GSM317667     2  0.3610      0.638 0.000 0.800 0.000 0.200
#> GSM317670     4  0.5214      0.706 0.004 0.364 0.008 0.624
#> GSM317674     1  0.4103      0.733 0.744 0.000 0.256 0.000
#> GSM317675     1  0.4103      0.733 0.744 0.000 0.256 0.000
#> GSM317677     1  0.1824      0.674 0.936 0.000 0.004 0.060
#> GSM317678     2  0.0000      0.837 0.000 1.000 0.000 0.000
#> GSM317687     4  0.4522      0.497 0.320 0.000 0.000 0.680
#> GSM317695     3  0.0921      0.839 0.028 0.000 0.972 0.000
#> GSM317653     2  0.4188      0.614 0.000 0.752 0.004 0.244
#> GSM317656     3  0.3024      0.711 0.148 0.000 0.852 0.000
#> GSM317658     2  0.4764      0.556 0.032 0.748 0.000 0.220
#> GSM317660     3  0.6669      0.574 0.004 0.108 0.604 0.284
#> GSM317663     4  0.4817      0.715 0.000 0.388 0.000 0.612
#> GSM317664     1  0.4103      0.733 0.744 0.000 0.256 0.000
#> GSM317665     3  0.4799      0.655 0.004 0.008 0.704 0.284
#> GSM317673     1  0.4072      0.734 0.748 0.000 0.252 0.000
#> GSM317686     2  0.3569      0.644 0.000 0.804 0.000 0.196
#> GSM317688     1  0.5080      0.518 0.576 0.000 0.420 0.004
#> GSM317690     2  0.3219      0.691 0.000 0.836 0.000 0.164
#> GSM317654     3  0.4483      0.661 0.004 0.000 0.712 0.284
#> GSM317655     4  0.4830      0.709 0.000 0.392 0.000 0.608
#> GSM317659     1  0.3400      0.555 0.820 0.000 0.000 0.180
#> GSM317661     2  0.0000      0.837 0.000 1.000 0.000 0.000
#> GSM317662     2  0.0000      0.837 0.000 1.000 0.000 0.000
#> GSM317668     1  0.4989      0.402 0.528 0.000 0.472 0.000
#> GSM317669     3  0.0921      0.839 0.028 0.000 0.972 0.000
#> GSM317671     3  0.0921      0.839 0.028 0.000 0.972 0.000
#> GSM317676     4  0.4522      0.497 0.320 0.000 0.000 0.680
#> GSM317680     3  0.0921      0.839 0.028 0.000 0.972 0.000
#> GSM317684     1  0.2401      0.652 0.904 0.000 0.004 0.092
#> GSM317685     1  0.4103      0.733 0.744 0.000 0.256 0.000
#> GSM317694     1  0.4079      0.739 0.800 0.000 0.180 0.020

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> GSM317649     3  0.3266     0.9263 0.200 0.000 0.796 0.000 0.004
#> GSM317652     3  0.5896     0.3926 0.448 0.000 0.452 0.000 0.100
#> GSM317666     4  0.7040     0.3433 0.000 0.244 0.080 0.552 0.124
#> GSM317672     2  0.1952     0.7752 0.000 0.912 0.004 0.000 0.084
#> GSM317679     3  0.3109     0.9274 0.200 0.000 0.800 0.000 0.000
#> GSM317681     2  0.3980     0.4988 0.000 0.708 0.008 0.000 0.284
#> GSM317682     5  0.3333     0.6930 0.208 0.004 0.000 0.000 0.788
#> GSM317683     2  0.0000     0.8230 0.000 1.000 0.000 0.000 0.000
#> GSM317689     2  0.0324     0.8209 0.000 0.992 0.004 0.000 0.004
#> GSM317691     4  0.5197     0.1573 0.296 0.000 0.040 0.648 0.016
#> GSM317692     2  0.3205     0.7665 0.000 0.864 0.008 0.072 0.056
#> GSM317693     1  0.5821     0.1875 0.524 0.000 0.052 0.404 0.020
#> GSM317696     1  0.0609     0.7546 0.980 0.000 0.020 0.000 0.000
#> GSM317697     1  0.4383     0.6153 0.792 0.000 0.108 0.080 0.020
#> GSM317698     1  0.0579     0.7487 0.984 0.000 0.008 0.008 0.000
#> GSM317650     2  0.0000     0.8230 0.000 1.000 0.000 0.000 0.000
#> GSM317651     5  0.3927     0.7441 0.124 0.004 0.020 0.032 0.820
#> GSM317657     4  0.7251     0.3207 0.000 0.264 0.084 0.520 0.132
#> GSM317667     2  0.5387     0.5556 0.000 0.680 0.020 0.228 0.072
#> GSM317670     4  0.8461     0.3157 0.008 0.172 0.260 0.388 0.172
#> GSM317674     1  0.0609     0.7546 0.980 0.000 0.020 0.000 0.000
#> GSM317675     1  0.0609     0.7546 0.980 0.000 0.020 0.000 0.000
#> GSM317677     1  0.4505     0.3373 0.604 0.000 0.012 0.384 0.000
#> GSM317678     2  0.0000     0.8230 0.000 1.000 0.000 0.000 0.000
#> GSM317687     4  0.0510     0.4497 0.016 0.000 0.000 0.984 0.000
#> GSM317695     3  0.3143     0.9240 0.204 0.000 0.796 0.000 0.000
#> GSM317653     5  0.4504     0.1890 0.000 0.428 0.008 0.000 0.564
#> GSM317656     1  0.4561    -0.4397 0.504 0.000 0.488 0.000 0.008
#> GSM317658     2  0.7639     0.4096 0.056 0.572 0.156 0.060 0.156
#> GSM317660     5  0.3578     0.7722 0.000 0.048 0.132 0.000 0.820
#> GSM317663     4  0.7413     0.2547 0.000 0.312 0.084 0.472 0.132
#> GSM317664     1  0.0609     0.7546 0.980 0.000 0.020 0.000 0.000
#> GSM317665     5  0.3003     0.7579 0.000 0.000 0.188 0.000 0.812
#> GSM317673     1  0.1168     0.7463 0.960 0.000 0.008 0.000 0.032
#> GSM317686     2  0.5387     0.5633 0.000 0.684 0.020 0.220 0.076
#> GSM317688     1  0.4250     0.5522 0.784 0.000 0.128 0.004 0.084
#> GSM317690     2  0.4979     0.6535 0.000 0.756 0.052 0.060 0.132
#> GSM317654     5  0.3003     0.7578 0.000 0.000 0.188 0.000 0.812
#> GSM317655     4  0.7380     0.2743 0.000 0.300 0.084 0.484 0.132
#> GSM317659     4  0.4814    -0.0734 0.412 0.000 0.016 0.568 0.004
#> GSM317661     2  0.0000     0.8230 0.000 1.000 0.000 0.000 0.000
#> GSM317662     2  0.0000     0.8230 0.000 1.000 0.000 0.000 0.000
#> GSM317668     1  0.4337     0.3000 0.696 0.000 0.284 0.004 0.016
#> GSM317669     3  0.3266     0.9263 0.200 0.000 0.796 0.000 0.004
#> GSM317671     3  0.3109     0.9274 0.200 0.000 0.800 0.000 0.000
#> GSM317676     4  0.0798     0.4544 0.008 0.000 0.016 0.976 0.000
#> GSM317680     3  0.3109     0.9274 0.200 0.000 0.800 0.000 0.000
#> GSM317684     4  0.4889    -0.2153 0.476 0.000 0.016 0.504 0.004
#> GSM317685     1  0.0898     0.7527 0.972 0.000 0.020 0.000 0.008
#> GSM317694     1  0.2953     0.6893 0.844 0.000 0.012 0.144 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
#> GSM317649     3  0.0363    0.83306 0.012 0.000 0.988 0.000 0.000 0.000
#> GSM317652     3  0.5749    0.02658 0.404 0.000 0.476 0.004 0.104 0.012
#> GSM317666     4  0.3272    0.69502 0.000 0.124 0.000 0.824 0.004 0.048
#> GSM317672     2  0.1375    0.78315 0.000 0.952 0.004 0.008 0.028 0.008
#> GSM317679     3  0.0363    0.83306 0.012 0.000 0.988 0.000 0.000 0.000
#> GSM317681     2  0.3061    0.67433 0.000 0.816 0.004 0.004 0.168 0.008
#> GSM317682     5  0.3977    0.58872 0.240 0.008 0.000 0.004 0.728 0.020
#> GSM317683     2  0.0260    0.80272 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM317689     2  0.1204    0.78237 0.000 0.944 0.000 0.056 0.000 0.000
#> GSM317691     6  0.3331    0.65873 0.096 0.000 0.004 0.056 0.008 0.836
#> GSM317692     2  0.4178    0.69635 0.000 0.796 0.008 0.084 0.068 0.044
#> GSM317693     6  0.4830    0.33751 0.416 0.000 0.000 0.020 0.024 0.540
#> GSM317696     1  0.2191    0.79448 0.876 0.000 0.120 0.000 0.004 0.000
#> GSM317697     1  0.4607    0.28691 0.688 0.000 0.000 0.048 0.020 0.244
#> GSM317698     1  0.1829    0.76871 0.920 0.000 0.064 0.000 0.004 0.012
#> GSM317650     2  0.0260    0.80272 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM317651     5  0.1856    0.75703 0.048 0.000 0.000 0.000 0.920 0.032
#> GSM317657     4  0.2301    0.72059 0.000 0.096 0.000 0.884 0.000 0.020
#> GSM317667     2  0.3810    0.27319 0.000 0.572 0.000 0.428 0.000 0.000
#> GSM317670     4  0.6393    0.46085 0.072 0.032 0.028 0.612 0.032 0.224
#> GSM317674     1  0.2048    0.79484 0.880 0.000 0.120 0.000 0.000 0.000
#> GSM317675     1  0.2048    0.79484 0.880 0.000 0.120 0.000 0.000 0.000
#> GSM317677     1  0.4222   -0.16311 0.516 0.000 0.000 0.004 0.008 0.472
#> GSM317678     2  0.0363    0.79948 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM317687     6  0.3565    0.53942 0.000 0.000 0.000 0.304 0.004 0.692
#> GSM317695     3  0.0458    0.83096 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM317653     5  0.4208    0.08660 0.000 0.452 0.008 0.000 0.536 0.004
#> GSM317656     3  0.4400    0.00485 0.456 0.000 0.524 0.008 0.000 0.012
#> GSM317658     4  0.8100    0.31043 0.124 0.220 0.004 0.376 0.040 0.236
#> GSM317660     5  0.1649    0.77970 0.000 0.032 0.036 0.000 0.932 0.000
#> GSM317663     4  0.2191    0.72707 0.000 0.120 0.000 0.876 0.000 0.004
#> GSM317664     1  0.2048    0.79484 0.880 0.000 0.120 0.000 0.000 0.000
#> GSM317665     5  0.1644    0.77938 0.000 0.004 0.076 0.000 0.920 0.000
#> GSM317673     1  0.2807    0.77802 0.868 0.000 0.088 0.000 0.028 0.016
#> GSM317686     2  0.3789    0.30093 0.000 0.584 0.000 0.416 0.000 0.000
#> GSM317688     1  0.5752    0.59144 0.640 0.000 0.204 0.012 0.100 0.044
#> GSM317690     2  0.5992    0.12487 0.016 0.524 0.004 0.360 0.024 0.072
#> GSM317654     5  0.1610    0.77486 0.000 0.000 0.084 0.000 0.916 0.000
#> GSM317655     4  0.2482    0.71468 0.000 0.148 0.000 0.848 0.000 0.004
#> GSM317659     6  0.4315    0.66352 0.224 0.000 0.000 0.048 0.012 0.716
#> GSM317661     2  0.0260    0.80272 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM317662     2  0.0260    0.80272 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM317668     1  0.5421    0.35953 0.564 0.000 0.344 0.012 0.008 0.072
#> GSM317669     3  0.0363    0.83306 0.012 0.000 0.988 0.000 0.000 0.000
#> GSM317671     3  0.0363    0.83306 0.012 0.000 0.988 0.000 0.000 0.000
#> GSM317676     6  0.3955    0.43123 0.000 0.000 0.000 0.384 0.008 0.608
#> GSM317680     3  0.0363    0.83306 0.012 0.000 0.988 0.000 0.000 0.000
#> GSM317684     6  0.3650    0.62374 0.272 0.000 0.000 0.004 0.008 0.716
#> GSM317685     1  0.2798    0.79145 0.856 0.000 0.120 0.004 0.008 0.012
#> GSM317694     1  0.4474    0.64580 0.704 0.000 0.108 0.000 0.000 0.188

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 disease.state(p) k
#> ATC:skmeans 49            0.553 2
#> ATC:skmeans 48            0.632 3
#> ATC:skmeans 46            0.931 4
#> ATC:skmeans 32            0.848 5
#> ATC:skmeans 37            0.765 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 11993 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 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-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 0.761           0.872       0.943         0.4812 0.497   0.497
#> 3 3 0.920           0.891       0.950         0.2225 0.909   0.816
#> 4 4 0.795           0.729       0.808         0.1214 0.957   0.894
#> 5 5 0.946           0.892       0.933         0.1015 0.878   0.682
#> 6 6 0.801           0.805       0.899         0.0734 0.945   0.805

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] 3

There is also optional best \(k\) = 3 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
#> GSM317649     1   0.000      1.000 1.000 0.000
#> GSM317652     1   0.000      1.000 1.000 0.000
#> GSM317666     2   0.000      0.856 0.000 1.000
#> GSM317672     2   0.999      0.201 0.480 0.520
#> GSM317679     1   0.000      1.000 1.000 0.000
#> GSM317681     2   0.730      0.726 0.204 0.796
#> GSM317682     1   0.000      1.000 1.000 0.000
#> GSM317683     2   0.000      0.856 0.000 1.000
#> GSM317689     2   0.000      0.856 0.000 1.000
#> GSM317691     2   1.000      0.176 0.496 0.504
#> GSM317692     2   0.634      0.766 0.160 0.840
#> GSM317693     1   0.000      1.000 1.000 0.000
#> GSM317696     1   0.000      1.000 1.000 0.000
#> GSM317697     1   0.000      1.000 1.000 0.000
#> GSM317698     1   0.000      1.000 1.000 0.000
#> GSM317650     2   0.000      0.856 0.000 1.000
#> GSM317651     1   0.000      1.000 1.000 0.000
#> GSM317657     2   0.000      0.856 0.000 1.000
#> GSM317667     2   0.000      0.856 0.000 1.000
#> GSM317670     2   0.697      0.737 0.188 0.812
#> GSM317674     1   0.000      1.000 1.000 0.000
#> GSM317675     1   0.000      1.000 1.000 0.000
#> GSM317677     1   0.000      1.000 1.000 0.000
#> GSM317678     2   0.000      0.856 0.000 1.000
#> GSM317687     2   1.000      0.176 0.496 0.504
#> GSM317695     1   0.000      1.000 1.000 0.000
#> GSM317653     2   0.722      0.731 0.200 0.800
#> GSM317656     1   0.000      1.000 1.000 0.000
#> GSM317658     2   0.563      0.791 0.132 0.868
#> GSM317660     1   0.000      1.000 1.000 0.000
#> GSM317663     2   0.000      0.856 0.000 1.000
#> GSM317664     1   0.000      1.000 1.000 0.000
#> GSM317665     1   0.000      1.000 1.000 0.000
#> GSM317673     1   0.000      1.000 1.000 0.000
#> GSM317686     2   0.000      0.856 0.000 1.000
#> GSM317688     1   0.000      1.000 1.000 0.000
#> GSM317690     2   0.000      0.856 0.000 1.000
#> GSM317654     1   0.000      1.000 1.000 0.000
#> GSM317655     2   0.000      0.856 0.000 1.000
#> GSM317659     1   0.000      1.000 1.000 0.000
#> GSM317661     2   0.000      0.856 0.000 1.000
#> GSM317662     2   0.000      0.856 0.000 1.000
#> GSM317668     1   0.000      1.000 1.000 0.000
#> GSM317669     1   0.000      1.000 1.000 0.000
#> GSM317671     1   0.000      1.000 1.000 0.000
#> GSM317676     2   1.000      0.176 0.496 0.504
#> GSM317680     1   0.000      1.000 1.000 0.000
#> GSM317684     1   0.000      1.000 1.000 0.000
#> GSM317685     1   0.000      1.000 1.000 0.000
#> GSM317694     1   0.000      1.000 1.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> GSM317649     1  0.0000      0.999 1.000 0.000 0.000
#> GSM317652     1  0.0000      0.999 1.000 0.000 0.000
#> GSM317666     2  0.5859      0.892 0.000 0.656 0.344
#> GSM317672     3  0.1964      0.585 0.000 0.056 0.944
#> GSM317679     1  0.0000      0.999 1.000 0.000 0.000
#> GSM317681     3  0.0000      0.655 0.000 0.000 1.000
#> GSM317682     1  0.0000      0.999 1.000 0.000 0.000
#> GSM317683     3  0.5859      0.742 0.000 0.344 0.656
#> GSM317689     2  0.5859      0.892 0.000 0.656 0.344
#> GSM317691     2  0.5859      0.892 0.000 0.656 0.344
#> GSM317692     2  0.9047      0.662 0.148 0.508 0.344
#> GSM317693     1  0.0592      0.987 0.988 0.000 0.012
#> GSM317696     1  0.0000      0.999 1.000 0.000 0.000
#> GSM317697     1  0.0000      0.999 1.000 0.000 0.000
#> GSM317698     1  0.0000      0.999 1.000 0.000 0.000
#> GSM317650     3  0.5859      0.742 0.000 0.344 0.656
#> GSM317651     1  0.0237      0.995 0.996 0.000 0.004
#> GSM317657     2  0.5859      0.892 0.000 0.656 0.344
#> GSM317667     2  0.1964      0.361 0.000 0.944 0.056
#> GSM317670     2  0.5859      0.892 0.000 0.656 0.344
#> GSM317674     1  0.0000      0.999 1.000 0.000 0.000
#> GSM317675     1  0.0000      0.999 1.000 0.000 0.000
#> GSM317677     1  0.0000      0.999 1.000 0.000 0.000
#> GSM317678     3  0.0000      0.655 0.000 0.000 1.000
#> GSM317687     2  0.5859      0.892 0.000 0.656 0.344
#> GSM317695     1  0.0000      0.999 1.000 0.000 0.000
#> GSM317653     3  0.1753      0.599 0.000 0.048 0.952
#> GSM317656     1  0.0000      0.999 1.000 0.000 0.000
#> GSM317658     2  0.7023      0.854 0.032 0.624 0.344
#> GSM317660     1  0.0592      0.987 0.988 0.000 0.012
#> GSM317663     2  0.5859      0.892 0.000 0.656 0.344
#> GSM317664     1  0.0000      0.999 1.000 0.000 0.000
#> GSM317665     1  0.0000      0.999 1.000 0.000 0.000
#> GSM317673     1  0.0000      0.999 1.000 0.000 0.000
#> GSM317686     2  0.1964      0.361 0.000 0.944 0.056
#> GSM317688     1  0.0000      0.999 1.000 0.000 0.000
#> GSM317690     2  0.5859      0.892 0.000 0.656 0.344
#> GSM317654     1  0.0000      0.999 1.000 0.000 0.000
#> GSM317655     2  0.5859      0.892 0.000 0.656 0.344
#> GSM317659     1  0.0237      0.995 0.996 0.000 0.004
#> GSM317661     3  0.5859      0.742 0.000 0.344 0.656
#> GSM317662     3  0.5859      0.742 0.000 0.344 0.656
#> GSM317668     1  0.0000      0.999 1.000 0.000 0.000
#> GSM317669     1  0.0000      0.999 1.000 0.000 0.000
#> GSM317671     1  0.0000      0.999 1.000 0.000 0.000
#> GSM317676     2  0.5859      0.892 0.000 0.656 0.344
#> GSM317680     1  0.0000      0.999 1.000 0.000 0.000
#> GSM317684     1  0.0000      0.999 1.000 0.000 0.000
#> GSM317685     1  0.0000      0.999 1.000 0.000 0.000
#> GSM317694     1  0.0000      0.999 1.000 0.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM317649     1  0.0707      0.515 0.980 0.000 0.020 0.000
#> GSM317652     1  0.4830      0.838 0.608 0.000 0.392 0.000
#> GSM317666     4  0.0000      0.917 0.000 0.000 0.000 1.000
#> GSM317672     2  0.5820      0.768 0.000 0.696 0.204 0.100
#> GSM317679     1  0.0000      0.497 1.000 0.000 0.000 0.000
#> GSM317681     2  0.5628      0.791 0.000 0.724 0.144 0.132
#> GSM317682     1  0.4967      0.815 0.548 0.000 0.452 0.000
#> GSM317683     2  0.0000      0.804 0.000 1.000 0.000 0.000
#> GSM317689     4  0.0376      0.914 0.000 0.004 0.004 0.992
#> GSM317691     4  0.1867      0.872 0.000 0.000 0.072 0.928
#> GSM317692     4  0.4746      0.482 0.000 0.000 0.368 0.632
#> GSM317693     1  0.4981      0.809 0.536 0.000 0.464 0.000
#> GSM317696     1  0.4830      0.838 0.608 0.000 0.392 0.000
#> GSM317697     1  0.4967      0.815 0.548 0.000 0.452 0.000
#> GSM317698     1  0.4830      0.838 0.608 0.000 0.392 0.000
#> GSM317650     2  0.0000      0.804 0.000 1.000 0.000 0.000
#> GSM317651     1  0.5147      0.807 0.536 0.000 0.460 0.004
#> GSM317657     4  0.0000      0.917 0.000 0.000 0.000 1.000
#> GSM317667     3  0.7870      0.109 0.000 0.304 0.392 0.304
#> GSM317670     4  0.0000      0.917 0.000 0.000 0.000 1.000
#> GSM317674     1  0.4830      0.838 0.608 0.000 0.392 0.000
#> GSM317675     1  0.4830      0.838 0.608 0.000 0.392 0.000
#> GSM317677     1  0.4981      0.809 0.536 0.000 0.464 0.000
#> GSM317678     2  0.5628      0.791 0.000 0.724 0.144 0.132
#> GSM317687     4  0.1867      0.872 0.000 0.000 0.072 0.928
#> GSM317695     1  0.0000      0.497 1.000 0.000 0.000 0.000
#> GSM317653     2  0.5750      0.765 0.000 0.696 0.216 0.088
#> GSM317656     1  0.4830      0.838 0.608 0.000 0.392 0.000
#> GSM317658     4  0.3649      0.755 0.000 0.000 0.204 0.796
#> GSM317660     3  0.5004     -0.721 0.392 0.000 0.604 0.004
#> GSM317663     4  0.0000      0.917 0.000 0.000 0.000 1.000
#> GSM317664     1  0.4830      0.838 0.608 0.000 0.392 0.000
#> GSM317665     1  0.4985      0.806 0.532 0.000 0.468 0.000
#> GSM317673     1  0.4830      0.838 0.608 0.000 0.392 0.000
#> GSM317686     3  0.7870      0.109 0.000 0.304 0.392 0.304
#> GSM317688     1  0.4830      0.838 0.608 0.000 0.392 0.000
#> GSM317690     4  0.0000      0.917 0.000 0.000 0.000 1.000
#> GSM317654     1  0.4981      0.809 0.536 0.000 0.464 0.000
#> GSM317655     4  0.0000      0.917 0.000 0.000 0.000 1.000
#> GSM317659     1  0.4981      0.809 0.536 0.000 0.464 0.000
#> GSM317661     2  0.0000      0.804 0.000 1.000 0.000 0.000
#> GSM317662     2  0.1557      0.768 0.000 0.944 0.056 0.000
#> GSM317668     1  0.4830      0.838 0.608 0.000 0.392 0.000
#> GSM317669     1  0.0000      0.497 1.000 0.000 0.000 0.000
#> GSM317671     1  0.0000      0.497 1.000 0.000 0.000 0.000
#> GSM317676     4  0.0469      0.911 0.000 0.000 0.012 0.988
#> GSM317680     1  0.0000      0.497 1.000 0.000 0.000 0.000
#> GSM317684     1  0.4981      0.809 0.536 0.000 0.464 0.000
#> GSM317685     1  0.4830      0.838 0.608 0.000 0.392 0.000
#> GSM317694     1  0.4830      0.838 0.608 0.000 0.392 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
#> GSM317649     3  0.2516      0.738 0.140 0.000 0.860 0.000 0.000
#> GSM317652     1  0.1671      0.956 0.924 0.000 0.076 0.000 0.000
#> GSM317666     4  0.0000      0.907 0.000 0.000 0.000 1.000 0.000
#> GSM317672     2  0.0000      0.823 0.000 1.000 0.000 0.000 0.000
#> GSM317679     3  0.0000      0.949 0.000 0.000 1.000 0.000 0.000
#> GSM317681     2  0.0000      0.823 0.000 1.000 0.000 0.000 0.000
#> GSM317682     1  0.1341      0.952 0.944 0.000 0.056 0.000 0.000
#> GSM317683     2  0.3177      0.797 0.000 0.792 0.000 0.000 0.208
#> GSM317689     4  0.1270      0.892 0.000 0.052 0.000 0.948 0.000
#> GSM317691     4  0.1671      0.885 0.076 0.000 0.000 0.924 0.000
#> GSM317692     4  0.5902      0.485 0.192 0.208 0.000 0.600 0.000
#> GSM317693     1  0.0000      0.933 1.000 0.000 0.000 0.000 0.000
#> GSM317696     1  0.1671      0.956 0.924 0.000 0.076 0.000 0.000
#> GSM317697     1  0.1341      0.952 0.944 0.000 0.056 0.000 0.000
#> GSM317698     1  0.1671      0.956 0.924 0.000 0.076 0.000 0.000
#> GSM317650     2  0.3177      0.797 0.000 0.792 0.000 0.000 0.208
#> GSM317651     1  0.0000      0.933 1.000 0.000 0.000 0.000 0.000
#> GSM317657     4  0.0000      0.907 0.000 0.000 0.000 1.000 0.000
#> GSM317667     5  0.0000      1.000 0.000 0.000 0.000 0.000 1.000
#> GSM317670     4  0.0000      0.907 0.000 0.000 0.000 1.000 0.000
#> GSM317674     1  0.1671      0.956 0.924 0.000 0.076 0.000 0.000
#> GSM317675     1  0.1671      0.956 0.924 0.000 0.076 0.000 0.000
#> GSM317677     1  0.0000      0.933 1.000 0.000 0.000 0.000 0.000
#> GSM317678     2  0.0000      0.823 0.000 1.000 0.000 0.000 0.000
#> GSM317687     4  0.1671      0.885 0.076 0.000 0.000 0.924 0.000
#> GSM317695     3  0.0000      0.949 0.000 0.000 1.000 0.000 0.000
#> GSM317653     2  0.0703      0.805 0.024 0.976 0.000 0.000 0.000
#> GSM317656     1  0.1671      0.956 0.924 0.000 0.076 0.000 0.000
#> GSM317658     4  0.3883      0.739 0.036 0.184 0.000 0.780 0.000
#> GSM317660     1  0.3177      0.703 0.792 0.208 0.000 0.000 0.000
#> GSM317663     4  0.0000      0.907 0.000 0.000 0.000 1.000 0.000
#> GSM317664     1  0.1671      0.956 0.924 0.000 0.076 0.000 0.000
#> GSM317665     1  0.0000      0.933 1.000 0.000 0.000 0.000 0.000
#> GSM317673     1  0.1671      0.956 0.924 0.000 0.076 0.000 0.000
#> GSM317686     5  0.0000      1.000 0.000 0.000 0.000 0.000 1.000
#> GSM317688     1  0.1671      0.956 0.924 0.000 0.076 0.000 0.000
#> GSM317690     4  0.1121      0.895 0.000 0.044 0.000 0.956 0.000
#> GSM317654     1  0.0000      0.933 1.000 0.000 0.000 0.000 0.000
#> GSM317655     4  0.0000      0.907 0.000 0.000 0.000 1.000 0.000
#> GSM317659     1  0.0000      0.933 1.000 0.000 0.000 0.000 0.000
#> GSM317661     2  0.3177      0.797 0.000 0.792 0.000 0.000 0.208
#> GSM317662     2  0.4015      0.634 0.000 0.652 0.000 0.000 0.348
#> GSM317668     1  0.1671      0.956 0.924 0.000 0.076 0.000 0.000
#> GSM317669     3  0.0000      0.949 0.000 0.000 1.000 0.000 0.000
#> GSM317671     3  0.0000      0.949 0.000 0.000 1.000 0.000 0.000
#> GSM317676     4  0.1341      0.893 0.056 0.000 0.000 0.944 0.000
#> GSM317680     3  0.0000      0.949 0.000 0.000 1.000 0.000 0.000
#> GSM317684     1  0.0000      0.933 1.000 0.000 0.000 0.000 0.000
#> GSM317685     1  0.1671      0.956 0.924 0.000 0.076 0.000 0.000
#> GSM317694     1  0.1671      0.956 0.924 0.000 0.076 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
#> GSM317649     3  0.2823      0.682 0.204 0.000 0.796 0.000 0.000 0.000
#> GSM317652     1  0.0000      0.900 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317666     4  0.0000      0.820 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM317672     2  0.2070      0.827 0.000 0.892 0.008 0.000 0.100 0.000
#> GSM317679     3  0.0458      0.940 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM317681     2  0.2070      0.827 0.000 0.892 0.008 0.000 0.100 0.000
#> GSM317682     1  0.1918      0.838 0.904 0.000 0.008 0.000 0.088 0.000
#> GSM317683     2  0.1556      0.846 0.000 0.920 0.000 0.000 0.000 0.080
#> GSM317689     4  0.1765      0.791 0.000 0.096 0.000 0.904 0.000 0.000
#> GSM317691     4  0.3634      0.668 0.000 0.000 0.008 0.696 0.296 0.000
#> GSM317692     4  0.7105      0.262 0.152 0.080 0.016 0.456 0.296 0.000
#> GSM317693     1  0.3634      0.628 0.696 0.000 0.008 0.000 0.296 0.000
#> GSM317696     1  0.0000      0.900 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317697     1  0.2070      0.831 0.892 0.000 0.008 0.000 0.100 0.000
#> GSM317698     1  0.0000      0.900 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317650     2  0.1556      0.846 0.000 0.920 0.000 0.000 0.000 0.080
#> GSM317651     1  0.3547      0.579 0.668 0.000 0.000 0.000 0.332 0.000
#> GSM317657     4  0.0000      0.820 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM317667     6  0.0000      1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM317670     4  0.0000      0.820 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM317674     1  0.0000      0.900 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317675     1  0.0000      0.900 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317677     1  0.0622      0.890 0.980 0.000 0.008 0.000 0.012 0.000
#> GSM317678     2  0.2070      0.827 0.000 0.892 0.008 0.000 0.100 0.000
#> GSM317687     4  0.3634      0.668 0.000 0.000 0.008 0.696 0.296 0.000
#> GSM317695     3  0.0458      0.940 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM317653     5  0.2212      0.632 0.000 0.112 0.008 0.000 0.880 0.000
#> GSM317656     1  0.0000      0.900 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317658     4  0.4688      0.703 0.024 0.076 0.016 0.748 0.136 0.000
#> GSM317660     5  0.3708      0.662 0.112 0.080 0.008 0.000 0.800 0.000
#> GSM317663     4  0.0000      0.820 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM317664     1  0.0000      0.900 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317665     5  0.3050      0.640 0.236 0.000 0.000 0.000 0.764 0.000
#> GSM317673     1  0.0000      0.900 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317686     6  0.0000      1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM317688     1  0.0000      0.900 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317690     4  0.1765      0.791 0.000 0.096 0.000 0.904 0.000 0.000
#> GSM317654     5  0.1957      0.679 0.112 0.000 0.000 0.000 0.888 0.000
#> GSM317655     4  0.0000      0.820 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM317659     1  0.3634      0.628 0.696 0.000 0.008 0.000 0.296 0.000
#> GSM317661     2  0.1556      0.846 0.000 0.920 0.000 0.000 0.000 0.080
#> GSM317662     2  0.3101      0.679 0.000 0.756 0.000 0.000 0.000 0.244
#> GSM317668     1  0.0000      0.900 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317669     3  0.0458      0.940 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM317671     3  0.0458      0.940 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM317676     4  0.2854      0.727 0.000 0.000 0.000 0.792 0.208 0.000
#> GSM317680     3  0.0458      0.940 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM317684     1  0.3634      0.628 0.696 0.000 0.008 0.000 0.296 0.000
#> GSM317685     1  0.0000      0.900 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317694     1  0.0000      0.900 1.000 0.000 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-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 disease.state(p) k
#> ATC:pam 46            0.639 2
#> ATC:pam 48            0.953 3
#> ATC:pam 41            0.977 4
#> ATC:pam 49            0.874 5
#> ATC:pam 49            0.454 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 11993 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 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-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 0.542           0.911       0.918          0.448 0.542   0.542
#> 3 3 0.414           0.697       0.808          0.266 0.846   0.726
#> 4 4 0.399           0.366       0.630          0.162 0.860   0.709
#> 5 5 0.482           0.455       0.692          0.136 0.792   0.517
#> 6 6 0.691           0.801       0.866          0.059 0.845   0.501

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
#> GSM317649     1  0.3879      0.908 0.924 0.076
#> GSM317652     1  0.0000      0.881 1.000 0.000
#> GSM317666     2  0.1414      0.964 0.020 0.980
#> GSM317672     2  0.4431      0.907 0.092 0.908
#> GSM317679     1  0.7299      0.882 0.796 0.204
#> GSM317681     2  0.2423      0.947 0.040 0.960
#> GSM317682     1  0.6343      0.902 0.840 0.160
#> GSM317683     2  0.0000      0.973 0.000 1.000
#> GSM317689     2  0.0000      0.973 0.000 1.000
#> GSM317691     1  0.7219      0.885 0.800 0.200
#> GSM317692     1  0.8443      0.791 0.728 0.272
#> GSM317693     1  0.5519      0.910 0.872 0.128
#> GSM317696     1  0.0000      0.881 1.000 0.000
#> GSM317697     1  0.4161      0.910 0.916 0.084
#> GSM317698     1  0.0000      0.881 1.000 0.000
#> GSM317650     2  0.0000      0.973 0.000 1.000
#> GSM317651     1  0.6148      0.905 0.848 0.152
#> GSM317657     2  0.2236      0.953 0.036 0.964
#> GSM317667     2  0.0000      0.973 0.000 1.000
#> GSM317670     2  0.4815      0.875 0.104 0.896
#> GSM317674     1  0.0000      0.881 1.000 0.000
#> GSM317675     1  0.0000      0.881 1.000 0.000
#> GSM317677     1  0.6048      0.906 0.852 0.148
#> GSM317678     2  0.0000      0.973 0.000 1.000
#> GSM317687     1  0.7219      0.885 0.800 0.200
#> GSM317695     1  0.7219      0.885 0.800 0.200
#> GSM317653     2  0.3879      0.924 0.076 0.924
#> GSM317656     1  0.3584      0.906 0.932 0.068
#> GSM317658     1  0.8443      0.809 0.728 0.272
#> GSM317660     1  0.7528      0.859 0.784 0.216
#> GSM317663     2  0.0672      0.970 0.008 0.992
#> GSM317664     1  0.0000      0.881 1.000 0.000
#> GSM317665     1  0.2948      0.903 0.948 0.052
#> GSM317673     1  0.0000      0.881 1.000 0.000
#> GSM317686     2  0.0000      0.973 0.000 1.000
#> GSM317688     1  0.1633      0.892 0.976 0.024
#> GSM317690     2  0.0000      0.973 0.000 1.000
#> GSM317654     1  0.3431      0.905 0.936 0.064
#> GSM317655     2  0.0000      0.973 0.000 1.000
#> GSM317659     1  0.6247      0.903 0.844 0.156
#> GSM317661     2  0.0000      0.973 0.000 1.000
#> GSM317662     2  0.0000      0.973 0.000 1.000
#> GSM317668     1  0.5519      0.910 0.872 0.128
#> GSM317669     1  0.3584      0.906 0.932 0.068
#> GSM317671     1  0.7299      0.882 0.796 0.204
#> GSM317676     1  0.7528      0.873 0.784 0.216
#> GSM317680     1  0.7139      0.887 0.804 0.196
#> GSM317684     1  0.5629      0.910 0.868 0.132
#> GSM317685     1  0.0000      0.881 1.000 0.000
#> GSM317694     1  0.5519      0.910 0.872 0.128

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> GSM317649     1  0.4475      0.814 0.840 0.144 0.016
#> GSM317652     1  0.0000      0.866 1.000 0.000 0.000
#> GSM317666     2  0.5760      0.563 0.000 0.672 0.328
#> GSM317672     2  0.9615      0.512 0.220 0.456 0.324
#> GSM317679     1  0.5414      0.797 0.772 0.212 0.016
#> GSM317681     3  0.7956     -0.285 0.060 0.424 0.516
#> GSM317682     1  0.6968      0.700 0.732 0.120 0.148
#> GSM317683     3  0.0000      0.755 0.000 0.000 1.000
#> GSM317689     2  0.7295      0.563 0.036 0.584 0.380
#> GSM317691     1  0.4654      0.800 0.792 0.208 0.000
#> GSM317692     2  0.9659      0.459 0.340 0.440 0.220
#> GSM317693     1  0.3816      0.823 0.852 0.148 0.000
#> GSM317696     1  0.0000      0.866 1.000 0.000 0.000
#> GSM317697     1  0.2261      0.855 0.932 0.068 0.000
#> GSM317698     1  0.0237      0.865 0.996 0.004 0.000
#> GSM317650     3  0.0000      0.755 0.000 0.000 1.000
#> GSM317651     1  0.3713      0.838 0.892 0.076 0.032
#> GSM317657     2  0.6172      0.589 0.012 0.680 0.308
#> GSM317667     3  0.3752      0.668 0.000 0.144 0.856
#> GSM317670     2  0.7901      0.607 0.080 0.608 0.312
#> GSM317674     1  0.0000      0.866 1.000 0.000 0.000
#> GSM317675     1  0.0000      0.866 1.000 0.000 0.000
#> GSM317677     1  0.4887      0.788 0.772 0.228 0.000
#> GSM317678     3  0.5733      0.174 0.000 0.324 0.676
#> GSM317687     1  0.6047      0.676 0.680 0.312 0.008
#> GSM317695     1  0.4702      0.804 0.788 0.212 0.000
#> GSM317653     2  0.9573      0.518 0.212 0.460 0.328
#> GSM317656     1  0.3686      0.822 0.860 0.140 0.000
#> GSM317658     2  0.9553      0.534 0.244 0.484 0.272
#> GSM317660     1  0.8170      0.493 0.624 0.120 0.256
#> GSM317663     2  0.5760      0.563 0.000 0.672 0.328
#> GSM317664     1  0.0237      0.865 0.996 0.004 0.000
#> GSM317665     1  0.6393      0.736 0.768 0.112 0.120
#> GSM317673     1  0.0000      0.866 1.000 0.000 0.000
#> GSM317686     3  0.3686      0.671 0.000 0.140 0.860
#> GSM317688     1  0.0000      0.866 1.000 0.000 0.000
#> GSM317690     2  0.7083      0.538 0.028 0.592 0.380
#> GSM317654     1  0.2550      0.854 0.932 0.056 0.012
#> GSM317655     2  0.5785      0.556 0.000 0.668 0.332
#> GSM317659     1  0.4887      0.788 0.772 0.228 0.000
#> GSM317661     3  0.0000      0.755 0.000 0.000 1.000
#> GSM317662     3  0.0000      0.755 0.000 0.000 1.000
#> GSM317668     1  0.2796      0.853 0.908 0.092 0.000
#> GSM317669     1  0.4615      0.813 0.836 0.144 0.020
#> GSM317671     1  0.4702      0.804 0.788 0.212 0.000
#> GSM317676     2  0.8985      0.299 0.300 0.540 0.160
#> GSM317680     1  0.4702      0.804 0.788 0.212 0.000
#> GSM317684     1  0.4605      0.802 0.796 0.204 0.000
#> GSM317685     1  0.0000      0.866 1.000 0.000 0.000
#> GSM317694     1  0.2625      0.854 0.916 0.084 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM317649     1  0.4610     0.6179 0.744 0.020 0.236 0.000
#> GSM317652     1  0.0188     0.7051 0.996 0.000 0.004 0.000
#> GSM317666     4  0.5350     0.1964 0.008 0.060 0.188 0.744
#> GSM317672     2  0.7819     0.2363 0.344 0.508 0.044 0.104
#> GSM317679     1  0.5273     0.4427 0.536 0.008 0.456 0.000
#> GSM317681     2  0.8066     0.2063 0.232 0.568 0.116 0.084
#> GSM317682     1  0.5231     0.3788 0.604 0.384 0.000 0.012
#> GSM317683     2  0.4998     0.1413 0.000 0.512 0.488 0.000
#> GSM317689     4  0.9676    -0.1713 0.224 0.192 0.200 0.384
#> GSM317691     1  0.5097     0.4488 0.568 0.004 0.000 0.428
#> GSM317692     1  0.7848    -0.1334 0.460 0.404 0.060 0.076
#> GSM317693     1  0.4252     0.6233 0.744 0.004 0.000 0.252
#> GSM317696     1  0.0817     0.7043 0.976 0.000 0.024 0.000
#> GSM317697     1  0.4088     0.6327 0.764 0.004 0.000 0.232
#> GSM317698     1  0.0657     0.7035 0.984 0.004 0.000 0.012
#> GSM317650     2  0.4998     0.1413 0.000 0.512 0.488 0.000
#> GSM317651     1  0.4955     0.5336 0.708 0.268 0.000 0.024
#> GSM317657     4  0.5474     0.1944 0.012 0.060 0.188 0.740
#> GSM317667     3  0.6055     0.2340 0.000 0.044 0.520 0.436
#> GSM317670     3  0.7410     0.0830 0.048 0.060 0.504 0.388
#> GSM317674     1  0.0592     0.7051 0.984 0.000 0.016 0.000
#> GSM317675     1  0.1118     0.7021 0.964 0.000 0.036 0.000
#> GSM317677     1  0.5080     0.4647 0.576 0.004 0.000 0.420
#> GSM317678     2  0.5397     0.0276 0.000 0.716 0.220 0.064
#> GSM317687     4  0.4961    -0.3073 0.448 0.000 0.000 0.552
#> GSM317695     1  0.4972     0.4470 0.544 0.000 0.456 0.000
#> GSM317653     2  0.7646     0.2153 0.364 0.500 0.032 0.104
#> GSM317656     1  0.3688     0.6405 0.792 0.000 0.208 0.000
#> GSM317658     3  0.8655     0.0096 0.164 0.060 0.396 0.380
#> GSM317660     2  0.5942     0.0343 0.412 0.548 0.000 0.040
#> GSM317663     4  0.5030     0.1913 0.000 0.060 0.188 0.752
#> GSM317664     1  0.1389     0.6992 0.952 0.000 0.048 0.000
#> GSM317665     1  0.5093     0.4459 0.640 0.348 0.000 0.012
#> GSM317673     1  0.0657     0.7035 0.984 0.004 0.000 0.012
#> GSM317686     3  0.6875     0.2653 0.000 0.112 0.520 0.368
#> GSM317688     1  0.0524     0.7047 0.988 0.008 0.000 0.004
#> GSM317690     4  0.7685    -0.2543 0.016 0.144 0.360 0.480
#> GSM317654     1  0.4609     0.5830 0.752 0.224 0.000 0.024
#> GSM317655     4  0.5109     0.1768 0.000 0.060 0.196 0.744
#> GSM317659     1  0.5097     0.4523 0.568 0.004 0.000 0.428
#> GSM317661     2  0.4998     0.1413 0.000 0.512 0.488 0.000
#> GSM317662     2  0.4998     0.1413 0.000 0.512 0.488 0.000
#> GSM317668     1  0.3837     0.6455 0.776 0.000 0.224 0.000
#> GSM317669     1  0.4599     0.6277 0.760 0.028 0.212 0.000
#> GSM317671     1  0.4972     0.4470 0.544 0.000 0.456 0.000
#> GSM317676     4  0.2814     0.0827 0.132 0.000 0.000 0.868
#> GSM317680     1  0.4955     0.4604 0.556 0.000 0.444 0.000
#> GSM317684     1  0.4741     0.5698 0.668 0.004 0.000 0.328
#> GSM317685     1  0.0469     0.7053 0.988 0.000 0.012 0.000
#> GSM317694     1  0.3726     0.6458 0.788 0.000 0.000 0.212

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> GSM317649     1  0.4147     -0.130 0.676 0.000 0.316 0.000 0.008
#> GSM317652     1  0.0510      0.505 0.984 0.000 0.000 0.000 0.016
#> GSM317666     4  0.0162      0.567 0.000 0.000 0.004 0.996 0.000
#> GSM317672     5  0.6256      0.655 0.268 0.000 0.032 0.104 0.596
#> GSM317679     3  0.4138      0.996 0.384 0.000 0.616 0.000 0.000
#> GSM317681     5  0.5201      0.596 0.036 0.032 0.032 0.148 0.752
#> GSM317682     5  0.2629      0.730 0.136 0.000 0.004 0.000 0.860
#> GSM317683     2  0.2732      0.912 0.000 0.840 0.000 0.160 0.000
#> GSM317689     4  0.7581      0.268 0.236 0.080 0.056 0.556 0.072
#> GSM317691     1  0.9570      0.242 0.356 0.160 0.184 0.164 0.136
#> GSM317692     5  0.7113      0.427 0.324 0.000 0.040 0.164 0.472
#> GSM317693     1  0.8192      0.349 0.492 0.160 0.184 0.024 0.140
#> GSM317696     1  0.0404      0.486 0.988 0.000 0.012 0.000 0.000
#> GSM317697     1  0.6525      0.417 0.640 0.156 0.128 0.004 0.072
#> GSM317698     1  0.1845      0.510 0.928 0.000 0.016 0.000 0.056
#> GSM317650     2  0.2732      0.912 0.000 0.840 0.000 0.160 0.000
#> GSM317651     5  0.4045      0.696 0.148 0.000 0.056 0.004 0.792
#> GSM317657     4  0.0000      0.568 0.000 0.000 0.000 1.000 0.000
#> GSM317667     4  0.5673      0.315 0.000 0.128 0.188 0.668 0.016
#> GSM317670     4  0.5014      0.373 0.008 0.000 0.412 0.560 0.020
#> GSM317674     1  0.0404      0.504 0.988 0.000 0.000 0.000 0.012
#> GSM317675     1  0.0510      0.481 0.984 0.000 0.016 0.000 0.000
#> GSM317677     1  0.9780      0.169 0.308 0.160 0.184 0.192 0.156
#> GSM317678     2  0.6519      0.576 0.000 0.552 0.032 0.300 0.116
#> GSM317687     4  0.9473      0.163 0.160 0.160 0.184 0.372 0.124
#> GSM317695     3  0.4150      0.991 0.388 0.000 0.612 0.000 0.000
#> GSM317653     5  0.4240      0.671 0.048 0.004 0.032 0.104 0.812
#> GSM317656     1  0.4108     -0.101 0.684 0.000 0.308 0.000 0.008
#> GSM317658     4  0.6198      0.402 0.068 0.000 0.344 0.552 0.036
#> GSM317660     5  0.2660      0.723 0.128 0.000 0.008 0.000 0.864
#> GSM317663     4  0.0000      0.568 0.000 0.000 0.000 1.000 0.000
#> GSM317664     1  0.0963      0.457 0.964 0.000 0.036 0.000 0.000
#> GSM317665     5  0.3093      0.735 0.168 0.000 0.008 0.000 0.824
#> GSM317673     1  0.1571      0.510 0.936 0.000 0.004 0.000 0.060
#> GSM317686     4  0.5673      0.315 0.000 0.128 0.188 0.668 0.016
#> GSM317688     1  0.2795      0.476 0.880 0.000 0.056 0.000 0.064
#> GSM317690     4  0.5218      0.375 0.000 0.072 0.296 0.632 0.000
#> GSM317654     5  0.5477      0.342 0.396 0.000 0.056 0.004 0.544
#> GSM317655     4  0.0000      0.568 0.000 0.000 0.000 1.000 0.000
#> GSM317659     1  0.9842      0.101 0.280 0.160 0.184 0.220 0.156
#> GSM317661     2  0.2732      0.912 0.000 0.840 0.000 0.160 0.000
#> GSM317662     2  0.2732      0.912 0.000 0.840 0.000 0.160 0.000
#> GSM317668     1  0.4564     -0.303 0.612 0.000 0.372 0.000 0.016
#> GSM317669     1  0.4380     -0.111 0.676 0.000 0.304 0.000 0.020
#> GSM317671     3  0.4138      0.996 0.384 0.000 0.616 0.000 0.000
#> GSM317676     4  0.7733      0.355 0.084 0.160 0.156 0.560 0.040
#> GSM317680     1  0.4307     -0.674 0.504 0.000 0.496 0.000 0.000
#> GSM317684     1  0.8748      0.327 0.448 0.160 0.184 0.052 0.156
#> GSM317685     1  0.0566      0.502 0.984 0.000 0.004 0.000 0.012
#> GSM317694     1  0.5319      0.431 0.752 0.036 0.072 0.020 0.120

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> GSM317649     3  0.1615      0.775 0.000 0.000 0.928 0.004 0.064 0.004
#> GSM317652     3  0.2738      0.794 0.176 0.000 0.820 0.000 0.004 0.000
#> GSM317666     4  0.5056      0.621 0.148 0.000 0.000 0.632 0.000 0.220
#> GSM317672     5  0.1644      0.894 0.000 0.004 0.076 0.000 0.920 0.000
#> GSM317679     3  0.3403      0.675 0.000 0.000 0.768 0.212 0.000 0.020
#> GSM317681     5  0.0291      0.892 0.000 0.004 0.004 0.000 0.992 0.000
#> GSM317682     5  0.1297      0.905 0.012 0.000 0.040 0.000 0.948 0.000
#> GSM317683     2  0.0000      0.971 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM317689     4  0.3966      0.685 0.000 0.032 0.056 0.792 0.120 0.000
#> GSM317691     1  0.2442      0.796 0.884 0.000 0.000 0.048 0.000 0.068
#> GSM317692     5  0.2318      0.876 0.044 0.000 0.064 0.000 0.892 0.000
#> GSM317693     1  0.3798      0.731 0.788 0.000 0.068 0.008 0.136 0.000
#> GSM317696     3  0.2597      0.793 0.176 0.000 0.824 0.000 0.000 0.000
#> GSM317697     1  0.4315      0.698 0.744 0.000 0.144 0.008 0.104 0.000
#> GSM317698     3  0.3860      0.729 0.236 0.000 0.728 0.000 0.036 0.000
#> GSM317650     2  0.0000      0.971 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM317651     5  0.2094      0.870 0.080 0.000 0.020 0.000 0.900 0.000
#> GSM317657     4  0.3287      0.772 0.012 0.000 0.000 0.768 0.000 0.220
#> GSM317667     6  0.0914      1.000 0.000 0.016 0.000 0.016 0.000 0.968
#> GSM317670     4  0.0146      0.743 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM317674     3  0.2597      0.793 0.176 0.000 0.824 0.000 0.000 0.000
#> GSM317675     3  0.2738      0.792 0.176 0.000 0.820 0.000 0.004 0.000
#> GSM317677     1  0.0000      0.811 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317678     2  0.1663      0.882 0.000 0.912 0.000 0.000 0.088 0.000
#> GSM317687     1  0.2212      0.783 0.880 0.000 0.000 0.008 0.000 0.112
#> GSM317695     3  0.3514      0.676 0.004 0.000 0.768 0.208 0.000 0.020
#> GSM317653     5  0.0291      0.892 0.000 0.004 0.004 0.000 0.992 0.000
#> GSM317656     3  0.1387      0.776 0.000 0.000 0.932 0.000 0.068 0.000
#> GSM317658     4  0.1429      0.755 0.004 0.000 0.004 0.940 0.052 0.000
#> GSM317660     5  0.1367      0.906 0.012 0.000 0.044 0.000 0.944 0.000
#> GSM317663     4  0.3287      0.772 0.012 0.000 0.000 0.768 0.000 0.220
#> GSM317664     3  0.2562      0.795 0.172 0.000 0.828 0.000 0.000 0.000
#> GSM317665     5  0.1686      0.905 0.012 0.000 0.064 0.000 0.924 0.000
#> GSM317673     3  0.4002      0.768 0.188 0.000 0.744 0.000 0.068 0.000
#> GSM317686     6  0.0914      1.000 0.000 0.016 0.000 0.016 0.000 0.968
#> GSM317688     3  0.3960      0.775 0.176 0.000 0.752 0.000 0.072 0.000
#> GSM317690     4  0.1498      0.763 0.000 0.032 0.000 0.940 0.028 0.000
#> GSM317654     5  0.3767      0.740 0.132 0.000 0.088 0.000 0.780 0.000
#> GSM317655     4  0.3287      0.772 0.012 0.000 0.000 0.768 0.000 0.220
#> GSM317659     1  0.0000      0.811 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM317661     2  0.0000      0.971 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM317662     2  0.0000      0.971 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM317668     3  0.4595      0.760 0.096 0.000 0.740 0.140 0.020 0.004
#> GSM317669     3  0.1615      0.775 0.000 0.000 0.928 0.004 0.064 0.004
#> GSM317671     3  0.3403      0.675 0.000 0.000 0.768 0.212 0.000 0.020
#> GSM317676     1  0.3245      0.715 0.800 0.000 0.000 0.028 0.000 0.172
#> GSM317680     3  0.3194      0.709 0.004 0.000 0.808 0.168 0.000 0.020
#> GSM317684     1  0.0146      0.811 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM317685     3  0.2946      0.793 0.176 0.000 0.812 0.000 0.012 0.000
#> GSM317694     1  0.3582      0.506 0.732 0.000 0.252 0.000 0.016 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 disease.state(p) k
#> ATC:mclust 50            0.714 2
#> ATC:mclust 45            0.687 3
#> ATC:mclust 19               NA 4
#> ATC:mclust 24            0.827 5
#> ATC:mclust 50            0.656 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 11993 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           0.951       0.981         0.4307 0.571   0.571
#> 3 3 0.475           0.650       0.795         0.4308 0.750   0.586
#> 4 4 0.477           0.574       0.744         0.1726 0.784   0.499
#> 5 5 0.707           0.647       0.827         0.0870 0.842   0.501
#> 6 6 0.698           0.628       0.812         0.0449 0.885   0.557

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
#> GSM317649     1  0.0000      0.983 1.000 0.000
#> GSM317652     1  0.0000      0.983 1.000 0.000
#> GSM317666     2  0.0000      0.972 0.000 1.000
#> GSM317672     1  0.9977      0.054 0.528 0.472
#> GSM317679     1  0.0000      0.983 1.000 0.000
#> GSM317681     2  0.0000      0.972 0.000 1.000
#> GSM317682     1  0.0000      0.983 1.000 0.000
#> GSM317683     2  0.0000      0.972 0.000 1.000
#> GSM317689     2  0.0000      0.972 0.000 1.000
#> GSM317691     1  0.0000      0.983 1.000 0.000
#> GSM317692     1  0.3584      0.912 0.932 0.068
#> GSM317693     1  0.0000      0.983 1.000 0.000
#> GSM317696     1  0.0000      0.983 1.000 0.000
#> GSM317697     1  0.0000      0.983 1.000 0.000
#> GSM317698     1  0.0000      0.983 1.000 0.000
#> GSM317650     2  0.0000      0.972 0.000 1.000
#> GSM317651     1  0.0000      0.983 1.000 0.000
#> GSM317657     2  0.5294      0.857 0.120 0.880
#> GSM317667     2  0.0000      0.972 0.000 1.000
#> GSM317670     1  0.0000      0.983 1.000 0.000
#> GSM317674     1  0.0000      0.983 1.000 0.000
#> GSM317675     1  0.0000      0.983 1.000 0.000
#> GSM317677     1  0.0000      0.983 1.000 0.000
#> GSM317678     2  0.0000      0.972 0.000 1.000
#> GSM317687     1  0.0000      0.983 1.000 0.000
#> GSM317695     1  0.0000      0.983 1.000 0.000
#> GSM317653     2  0.8267      0.652 0.260 0.740
#> GSM317656     1  0.0000      0.983 1.000 0.000
#> GSM317658     1  0.0376      0.980 0.996 0.004
#> GSM317660     1  0.0000      0.983 1.000 0.000
#> GSM317663     2  0.0376      0.969 0.004 0.996
#> GSM317664     1  0.0000      0.983 1.000 0.000
#> GSM317665     1  0.0000      0.983 1.000 0.000
#> GSM317673     1  0.0000      0.983 1.000 0.000
#> GSM317686     2  0.0000      0.972 0.000 1.000
#> GSM317688     1  0.0000      0.983 1.000 0.000
#> GSM317690     2  0.0000      0.972 0.000 1.000
#> GSM317654     1  0.0000      0.983 1.000 0.000
#> GSM317655     2  0.0000      0.972 0.000 1.000
#> GSM317659     1  0.0000      0.983 1.000 0.000
#> GSM317661     2  0.0000      0.972 0.000 1.000
#> GSM317662     2  0.0000      0.972 0.000 1.000
#> GSM317668     1  0.0000      0.983 1.000 0.000
#> GSM317669     1  0.0000      0.983 1.000 0.000
#> GSM317671     1  0.0000      0.983 1.000 0.000
#> GSM317676     1  0.0000      0.983 1.000 0.000
#> GSM317680     1  0.0000      0.983 1.000 0.000
#> GSM317684     1  0.0000      0.983 1.000 0.000
#> GSM317685     1  0.0000      0.983 1.000 0.000
#> GSM317694     1  0.0000      0.983 1.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> GSM317649     1  0.3644      0.736 0.872 0.124 0.004
#> GSM317652     1  0.1411      0.772 0.964 0.036 0.000
#> GSM317666     3  0.2796      0.509 0.000 0.092 0.908
#> GSM317672     2  0.6225      0.139 0.432 0.568 0.000
#> GSM317679     1  0.4589      0.701 0.820 0.172 0.008
#> GSM317681     2  0.3267      0.681 0.116 0.884 0.000
#> GSM317682     1  0.5216      0.601 0.740 0.260 0.000
#> GSM317683     2  0.3619      0.774 0.000 0.864 0.136
#> GSM317689     2  0.4504      0.754 0.000 0.804 0.196
#> GSM317691     3  0.6062      0.529 0.384 0.000 0.616
#> GSM317692     1  0.6854      0.634 0.740 0.124 0.136
#> GSM317693     1  0.6062      0.257 0.616 0.000 0.384
#> GSM317696     1  0.3116      0.764 0.892 0.000 0.108
#> GSM317697     1  0.4235      0.718 0.824 0.000 0.176
#> GSM317698     1  0.4178      0.722 0.828 0.000 0.172
#> GSM317650     2  0.1964      0.768 0.000 0.944 0.056
#> GSM317651     1  0.2537      0.758 0.920 0.080 0.000
#> GSM317657     3  0.1620      0.595 0.012 0.024 0.964
#> GSM317667     2  0.5835      0.657 0.000 0.660 0.340
#> GSM317670     3  0.5650      0.639 0.312 0.000 0.688
#> GSM317674     1  0.3619      0.751 0.864 0.000 0.136
#> GSM317675     1  0.3941      0.736 0.844 0.000 0.156
#> GSM317677     3  0.5497      0.673 0.292 0.000 0.708
#> GSM317678     2  0.1525      0.735 0.032 0.964 0.004
#> GSM317687     3  0.4702      0.714 0.212 0.000 0.788
#> GSM317695     1  0.3340      0.761 0.880 0.000 0.120
#> GSM317653     2  0.5327      0.498 0.272 0.728 0.000
#> GSM317656     1  0.1031      0.780 0.976 0.000 0.024
#> GSM317658     1  0.4749      0.721 0.816 0.012 0.172
#> GSM317660     1  0.5859      0.449 0.656 0.344 0.000
#> GSM317663     3  0.3412      0.462 0.000 0.124 0.876
#> GSM317664     1  0.3551      0.753 0.868 0.000 0.132
#> GSM317665     1  0.5216      0.601 0.740 0.260 0.000
#> GSM317673     1  0.1031      0.780 0.976 0.000 0.024
#> GSM317686     2  0.5810      0.661 0.000 0.664 0.336
#> GSM317688     1  0.0661      0.778 0.988 0.008 0.004
#> GSM317690     2  0.5363      0.710 0.000 0.724 0.276
#> GSM317654     1  0.3193      0.750 0.896 0.100 0.004
#> GSM317655     3  0.3412      0.461 0.000 0.124 0.876
#> GSM317659     3  0.5431      0.680 0.284 0.000 0.716
#> GSM317661     2  0.3116      0.777 0.000 0.892 0.108
#> GSM317662     2  0.3412      0.776 0.000 0.876 0.124
#> GSM317668     1  0.4605      0.684 0.796 0.000 0.204
#> GSM317669     1  0.3752      0.720 0.856 0.144 0.000
#> GSM317671     1  0.2400      0.773 0.932 0.004 0.064
#> GSM317676     3  0.4555      0.715 0.200 0.000 0.800
#> GSM317680     1  0.2955      0.760 0.912 0.080 0.008
#> GSM317684     3  0.6225      0.407 0.432 0.000 0.568
#> GSM317685     1  0.3116      0.764 0.892 0.000 0.108
#> GSM317694     1  0.6274     -0.059 0.544 0.000 0.456

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> GSM317649     3  0.3668     0.7244 0.188 0.004 0.808 0.000
#> GSM317652     1  0.3853     0.6134 0.820 0.020 0.160 0.000
#> GSM317666     4  0.0844     0.6155 0.004 0.004 0.012 0.980
#> GSM317672     2  0.7248     0.3388 0.184 0.532 0.284 0.000
#> GSM317679     3  0.3950     0.7356 0.184 0.004 0.804 0.008
#> GSM317681     2  0.7632     0.3690 0.132 0.504 0.344 0.020
#> GSM317682     1  0.6350     0.4617 0.612 0.092 0.296 0.000
#> GSM317683     2  0.1557     0.7267 0.000 0.944 0.000 0.056
#> GSM317689     2  0.2345     0.7134 0.000 0.900 0.000 0.100
#> GSM317691     4  0.5558     0.5155 0.432 0.000 0.020 0.548
#> GSM317692     1  0.3619     0.6631 0.860 0.004 0.036 0.100
#> GSM317693     1  0.2973     0.5937 0.856 0.000 0.000 0.144
#> GSM317696     1  0.1661     0.6898 0.944 0.000 0.052 0.004
#> GSM317697     1  0.2124     0.6791 0.924 0.000 0.008 0.068
#> GSM317698     1  0.1302     0.6987 0.956 0.000 0.000 0.044
#> GSM317650     2  0.0921     0.7285 0.000 0.972 0.000 0.028
#> GSM317651     1  0.5110     0.5419 0.688 0.012 0.292 0.008
#> GSM317657     4  0.3903     0.7005 0.156 0.008 0.012 0.824
#> GSM317667     2  0.6134     0.4712 0.000 0.508 0.048 0.444
#> GSM317670     3  0.7381     0.6425 0.228 0.088 0.620 0.064
#> GSM317674     1  0.0804     0.7060 0.980 0.000 0.008 0.012
#> GSM317675     1  0.1059     0.7016 0.972 0.000 0.012 0.016
#> GSM317677     4  0.5257     0.5082 0.444 0.000 0.008 0.548
#> GSM317678     2  0.0336     0.7211 0.000 0.992 0.008 0.000
#> GSM317687     4  0.4008     0.7122 0.244 0.000 0.000 0.756
#> GSM317695     3  0.5331     0.7021 0.332 0.000 0.644 0.024
#> GSM317653     1  0.9045     0.1000 0.384 0.268 0.284 0.064
#> GSM317656     3  0.4776     0.6660 0.376 0.000 0.624 0.000
#> GSM317658     2  0.9651    -0.0426 0.284 0.360 0.196 0.160
#> GSM317660     3  0.7852    -0.1708 0.332 0.276 0.392 0.000
#> GSM317663     4  0.1739     0.6041 0.008 0.024 0.016 0.952
#> GSM317664     1  0.2124     0.6637 0.924 0.000 0.068 0.008
#> GSM317665     1  0.7449     0.2552 0.464 0.180 0.356 0.000
#> GSM317673     1  0.1118     0.7029 0.964 0.000 0.036 0.000
#> GSM317686     2  0.6108     0.4973 0.000 0.528 0.048 0.424
#> GSM317688     1  0.2011     0.6860 0.920 0.000 0.080 0.000
#> GSM317690     2  0.5477     0.6256 0.000 0.728 0.092 0.180
#> GSM317654     1  0.5972     0.4838 0.632 0.064 0.304 0.000
#> GSM317655     4  0.0844     0.6137 0.004 0.012 0.004 0.980
#> GSM317659     4  0.4925     0.5342 0.428 0.000 0.000 0.572
#> GSM317661     2  0.3037     0.7216 0.000 0.888 0.076 0.036
#> GSM317662     2  0.2124     0.7299 0.000 0.932 0.028 0.040
#> GSM317668     3  0.6324     0.6336 0.340 0.000 0.584 0.076
#> GSM317669     3  0.3577     0.6944 0.156 0.012 0.832 0.000
#> GSM317671     3  0.5297     0.7201 0.292 0.000 0.676 0.032
#> GSM317676     4  0.4353     0.7176 0.232 0.000 0.012 0.756
#> GSM317680     3  0.3636     0.7287 0.172 0.000 0.820 0.008
#> GSM317684     1  0.4500     0.2473 0.684 0.000 0.000 0.316
#> GSM317685     1  0.1022     0.7038 0.968 0.000 0.032 0.000
#> GSM317694     1  0.4456     0.2866 0.716 0.000 0.004 0.280

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> GSM317649     3  0.2966     0.5857 0.000 0.000 0.816 0.000 0.184
#> GSM317652     5  0.6281     0.2820 0.388 0.000 0.152 0.000 0.460
#> GSM317666     4  0.1704     0.7939 0.000 0.004 0.000 0.928 0.068
#> GSM317672     5  0.5498     0.3387 0.080 0.340 0.000 0.000 0.580
#> GSM317679     3  0.1908     0.6517 0.000 0.000 0.908 0.000 0.092
#> GSM317681     5  0.0854     0.6894 0.000 0.012 0.004 0.008 0.976
#> GSM317682     1  0.4171     0.1944 0.604 0.000 0.000 0.000 0.396
#> GSM317683     2  0.0000     0.8652 0.000 1.000 0.000 0.000 0.000
#> GSM317689     2  0.0000     0.8652 0.000 1.000 0.000 0.000 0.000
#> GSM317691     1  0.6580     0.3162 0.484 0.000 0.172 0.336 0.008
#> GSM317692     1  0.1836     0.8041 0.932 0.000 0.000 0.036 0.032
#> GSM317693     1  0.1043     0.8126 0.960 0.000 0.000 0.040 0.000
#> GSM317696     1  0.0290     0.8135 0.992 0.000 0.000 0.000 0.008
#> GSM317697     1  0.1043     0.8113 0.960 0.000 0.000 0.040 0.000
#> GSM317698     1  0.0000     0.8151 1.000 0.000 0.000 0.000 0.000
#> GSM317650     2  0.0000     0.8652 0.000 1.000 0.000 0.000 0.000
#> GSM317651     1  0.4546     0.0595 0.532 0.000 0.000 0.008 0.460
#> GSM317657     4  0.4422     0.6497 0.028 0.008 0.188 0.764 0.012
#> GSM317667     4  0.5690     0.5455 0.000 0.224 0.000 0.624 0.152
#> GSM317670     3  0.6494     0.3217 0.028 0.296 0.576 0.088 0.012
#> GSM317674     1  0.0000     0.8151 1.000 0.000 0.000 0.000 0.000
#> GSM317675     1  0.0000     0.8151 1.000 0.000 0.000 0.000 0.000
#> GSM317677     1  0.4583     0.6465 0.704 0.000 0.036 0.256 0.004
#> GSM317678     2  0.1671     0.8343 0.000 0.924 0.000 0.000 0.076
#> GSM317687     4  0.1329     0.7913 0.032 0.000 0.008 0.956 0.004
#> GSM317695     3  0.0290     0.6533 0.000 0.000 0.992 0.008 0.000
#> GSM317653     5  0.2757     0.6736 0.032 0.008 0.000 0.072 0.888
#> GSM317656     3  0.4517     0.1640 0.436 0.000 0.556 0.000 0.008
#> GSM317658     2  0.4507     0.4879 0.292 0.684 0.000 0.012 0.012
#> GSM317660     5  0.3489     0.7056 0.036 0.000 0.144 0.000 0.820
#> GSM317663     4  0.2728     0.7897 0.000 0.004 0.068 0.888 0.040
#> GSM317664     1  0.1399     0.8062 0.952 0.000 0.020 0.028 0.000
#> GSM317665     5  0.3732     0.6834 0.032 0.000 0.176 0.000 0.792
#> GSM317673     1  0.0771     0.8104 0.976 0.000 0.000 0.004 0.020
#> GSM317686     4  0.5920     0.4819 0.000 0.272 0.000 0.580 0.148
#> GSM317688     1  0.0703     0.8077 0.976 0.000 0.000 0.000 0.024
#> GSM317690     2  0.0290     0.8617 0.000 0.992 0.000 0.000 0.008
#> GSM317654     5  0.3934     0.7061 0.076 0.000 0.124 0.000 0.800
#> GSM317655     4  0.0992     0.8039 0.000 0.008 0.000 0.968 0.024
#> GSM317659     1  0.4288     0.5026 0.612 0.000 0.004 0.384 0.000
#> GSM317661     2  0.3796     0.6079 0.000 0.700 0.000 0.000 0.300
#> GSM317662     2  0.1908     0.8316 0.000 0.908 0.000 0.000 0.092
#> GSM317668     3  0.6046     0.2952 0.332 0.000 0.552 0.108 0.008
#> GSM317669     3  0.3796     0.4169 0.000 0.000 0.700 0.000 0.300
#> GSM317671     3  0.0510     0.6585 0.000 0.000 0.984 0.000 0.016
#> GSM317676     4  0.1750     0.7791 0.036 0.000 0.028 0.936 0.000
#> GSM317680     3  0.2230     0.6416 0.000 0.000 0.884 0.000 0.116
#> GSM317684     1  0.3424     0.6842 0.760 0.000 0.000 0.240 0.000
#> GSM317685     1  0.0771     0.8104 0.976 0.000 0.000 0.004 0.020
#> GSM317694     1  0.3991     0.7131 0.780 0.000 0.048 0.172 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
#> GSM317649     3  0.2583     0.8173 0.032 0.000 0.896 0.008 0.044 0.020
#> GSM317652     1  0.6927     0.1261 0.436 0.000 0.248 0.012 0.264 0.040
#> GSM317666     6  0.3950     0.1806 0.000 0.000 0.000 0.432 0.004 0.564
#> GSM317672     5  0.4667     0.5674 0.036 0.280 0.000 0.004 0.664 0.016
#> GSM317679     3  0.0862     0.8563 0.000 0.000 0.972 0.016 0.008 0.004
#> GSM317681     5  0.1080     0.8080 0.000 0.004 0.000 0.004 0.960 0.032
#> GSM317682     1  0.4631     0.4926 0.644 0.008 0.000 0.020 0.312 0.016
#> GSM317683     2  0.0260     0.8756 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM317689     2  0.2925     0.7789 0.000 0.832 0.000 0.148 0.016 0.004
#> GSM317691     4  0.4454     0.4464 0.232 0.000 0.048 0.704 0.000 0.016
#> GSM317692     1  0.6439     0.3482 0.516 0.016 0.004 0.292 0.152 0.020
#> GSM317693     1  0.3488     0.6744 0.764 0.000 0.000 0.216 0.004 0.016
#> GSM317696     1  0.1223     0.7866 0.960 0.000 0.012 0.016 0.004 0.008
#> GSM317697     1  0.2762     0.7567 0.864 0.012 0.000 0.108 0.004 0.012
#> GSM317698     1  0.0260     0.7848 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM317650     2  0.0508     0.8762 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM317651     5  0.3593     0.6734 0.164 0.000 0.000 0.044 0.788 0.004
#> GSM317657     4  0.2195     0.5064 0.004 0.004 0.056 0.908 0.000 0.028
#> GSM317667     6  0.2984     0.7110 0.000 0.064 0.000 0.064 0.012 0.860
#> GSM317670     4  0.7015     0.0251 0.016 0.364 0.132 0.428 0.008 0.052
#> GSM317674     1  0.1414     0.7791 0.952 0.000 0.020 0.012 0.004 0.012
#> GSM317675     1  0.1364     0.7773 0.952 0.000 0.020 0.016 0.000 0.012
#> GSM317677     1  0.3688     0.6914 0.768 0.000 0.008 0.196 0.000 0.028
#> GSM317678     2  0.1693     0.8655 0.000 0.932 0.000 0.004 0.044 0.020
#> GSM317687     4  0.4178     0.2132 0.020 0.000 0.012 0.684 0.000 0.284
#> GSM317695     3  0.0692     0.8555 0.000 0.000 0.976 0.020 0.000 0.004
#> GSM317653     5  0.0777     0.8079 0.000 0.000 0.000 0.004 0.972 0.024
#> GSM317656     3  0.6255     0.2692 0.360 0.000 0.504 0.040 0.024 0.072
#> GSM317658     2  0.2946     0.7072 0.176 0.812 0.000 0.000 0.000 0.012
#> GSM317660     5  0.1350     0.8083 0.008 0.000 0.020 0.000 0.952 0.020
#> GSM317663     4  0.5355    -0.2306 0.000 0.000 0.092 0.456 0.004 0.448
#> GSM317664     1  0.1944     0.7680 0.924 0.000 0.036 0.024 0.000 0.016
#> GSM317665     5  0.2169     0.7825 0.008 0.000 0.080 0.000 0.900 0.012
#> GSM317673     1  0.1894     0.7817 0.928 0.004 0.000 0.040 0.016 0.012
#> GSM317686     6  0.3039     0.7049 0.000 0.084 0.000 0.056 0.008 0.852
#> GSM317688     1  0.4273     0.6918 0.800 0.000 0.040 0.060 0.028 0.072
#> GSM317690     2  0.2113     0.8524 0.000 0.912 0.008 0.032 0.000 0.048
#> GSM317654     5  0.1458     0.8098 0.016 0.000 0.016 0.000 0.948 0.020
#> GSM317655     4  0.2573     0.4577 0.000 0.000 0.008 0.856 0.004 0.132
#> GSM317659     4  0.3564     0.4234 0.264 0.000 0.000 0.724 0.000 0.012
#> GSM317661     5  0.5371     0.3008 0.000 0.360 0.000 0.000 0.520 0.120
#> GSM317662     2  0.2563     0.8351 0.000 0.876 0.000 0.000 0.052 0.072
#> GSM317668     4  0.6610     0.3312 0.152 0.000 0.204 0.560 0.016 0.068
#> GSM317669     3  0.1757     0.8306 0.000 0.000 0.916 0.000 0.076 0.008
#> GSM317671     3  0.0547     0.8573 0.000 0.000 0.980 0.020 0.000 0.000
#> GSM317676     4  0.1910     0.4790 0.000 0.000 0.000 0.892 0.000 0.108
#> GSM317680     3  0.1251     0.8562 0.000 0.000 0.956 0.012 0.024 0.008
#> GSM317684     1  0.3954     0.4565 0.620 0.000 0.004 0.372 0.004 0.000
#> GSM317685     1  0.1707     0.7829 0.928 0.000 0.004 0.056 0.012 0.000
#> GSM317694     1  0.2540     0.7667 0.872 0.000 0.020 0.104 0.000 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 disease.state(p) k
#> ATC:NMF 49            0.869 2
#> ATC:NMF 42            0.568 3
#> ATC:NMF 38            0.798 4
#> ATC:NMF 39            0.705 5
#> ATC:NMF 35            0.763 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