cola Report for GDS5093

Date: 2019-12-25 22:00:11 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 51979 rows and 56 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] 51979    56

Density distribution

The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.

library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list), 
    col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
    mc.cores = 4)

plot of chunk density-heatmap

Suggest the best k

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

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

suggest_best_k(res_list)

	The best k	1-PAC	Mean silhouette	Concordance		Optional k
SD:hclust	2	1.000	0.987	0.992	**
SD:kmeans	2	1.000	0.993	0.997	**
CV:hclust	5	1.000	0.973	0.987	**	2
CV:kmeans	2	1.000	1.000	1.000	**
MAD:hclust	5	1.000	0.998	0.981	**	2,4
MAD:kmeans	2	1.000	0.992	0.996	**
MAD:mclust	6	1.000	0.996	0.998	**	2,5
ATC:hclust	5	1.000	0.960	0.984	**	2,4
ATC:kmeans	2	1.000	0.992	0.996	**
ATC:mclust	4	1.000	0.962	0.978	**	2
ATC:NMF	2	1.000	0.986	0.994	**
CV:mclust	6	0.990	0.983	0.988	**	2,3,5
CV:pam	6	0.984	0.961	0.966	**	2,5
SD:mclust	6	0.983	0.971	0.980	**	2,5
SD:pam	6	0.971	0.953	0.967	**	2,5
SD:skmeans	5	0.962	0.936	0.961	**	2,3,4
CV:skmeans	5	0.955	0.873	0.944	**	2,3,4
MAD:pam	6	0.948	0.975	0.970	*	2,4,5
CV:NMF	5	0.945	0.884	0.963	*	2,4
MAD:NMF	5	0.938	0.903	0.944	*	2,4
ATC:pam	6	0.936	0.915	0.954	*	2,3
MAD:skmeans	5	0.931	0.918	0.961	*	2,3,4
SD:NMF	5	0.918	0.800	0.904	*	2,4
ATC:skmeans	5	0.917	0.974	0.970	*	2

**: 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           0.991       0.996          0.495 0.507   0.507
#> CV:NMF      2     1           0.986       0.994          0.495 0.507   0.507
#> MAD:NMF     2     1           0.984       0.994          0.495 0.507   0.507
#> ATC:NMF     2     1           0.986       0.994          0.495 0.507   0.507
#> SD:skmeans  2     1           0.979       0.992          0.497 0.501   0.501
#> CV:skmeans  2     1           0.980       0.993          0.497 0.501   0.501
#> MAD:skmeans 2     1           0.987       0.994          0.498 0.501   0.501
#> ATC:skmeans 2     1           1.000       1.000          0.493 0.507   0.507
#> SD:mclust   2     1           1.000       1.000          0.510 0.491   0.491
#> CV:mclust   2     1           0.998       0.999          0.510 0.491   0.491
#> MAD:mclust  2     1           1.000       1.000          0.510 0.491   0.491
#> ATC:mclust  2     1           0.981       0.990          0.508 0.491   0.491
#> SD:kmeans   2     1           0.993       0.997          0.494 0.507   0.507
#> CV:kmeans   2     1           1.000       1.000          0.493 0.507   0.507
#> MAD:kmeans  2     1           0.992       0.996          0.495 0.507   0.507
#> ATC:kmeans  2     1           0.992       0.996          0.480 0.523   0.523
#> SD:pam      2     1           0.966       0.986          0.484 0.523   0.523
#> CV:pam      2     1           0.970       0.988          0.491 0.514   0.514
#> MAD:pam     2     1           0.992       0.996          0.494 0.507   0.507
#> ATC:pam     2     1           1.000       1.000          0.478 0.523   0.523
#> SD:hclust   2     1           0.987       0.992          0.489 0.507   0.507
#> CV:hclust   2     1           0.994       0.996          0.491 0.507   0.507
#> MAD:hclust  2     1           1.000       1.000          0.493 0.507   0.507
#> ATC:hclust  2     1           0.963       0.986          0.487 0.507   0.507

get_stats(res_list, k = 3)

#>             k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> SD:NMF      3 0.850           0.872       0.944          0.294 0.830   0.675
#> CV:NMF      3 0.786           0.808       0.921          0.302 0.829   0.672
#> MAD:NMF     3 0.782           0.837       0.925          0.337 0.778   0.578
#> ATC:NMF     3 0.628           0.624       0.782          0.258 0.960   0.921
#> SD:skmeans  3 1.000           0.998       0.998          0.218 0.879   0.761
#> CV:skmeans  3 1.000           0.997       0.997          0.219 0.879   0.761
#> MAD:skmeans 3 1.000           0.946       0.974          0.199 0.894   0.790
#> ATC:skmeans 3 0.787           0.910       0.926          0.192 0.909   0.821
#> SD:mclust   3 0.730           0.830       0.811          0.210 1.000   1.000
#> CV:mclust   3 0.906           0.963       0.961          0.240 0.873   0.741
#> MAD:mclust  3 0.778           0.767       0.890          0.210 0.873   0.745
#> ATC:mclust  3 0.631           0.831       0.864          0.267 0.671   0.437
#> SD:kmeans   3 0.702           0.695       0.692          0.276 0.897   0.813
#> CV:kmeans   3 0.663           0.678       0.822          0.284 0.875   0.757
#> MAD:kmeans  3 0.710           0.728       0.804          0.275 0.964   0.932
#> ATC:kmeans  3 0.679           0.664       0.864          0.239 0.908   0.825
#> SD:pam      3 0.713           0.932       0.940          0.269 0.826   0.681
#> CV:pam      3 0.669           0.791       0.802          0.329 0.788   0.596
#> MAD:pam     3 0.739           0.865       0.864          0.271 0.860   0.731
#> ATC:pam     3 1.000           0.992       0.997          0.212 0.873   0.762
#> SD:hclust   3 0.799           0.935       0.926          0.275 0.860   0.723
#> CV:hclust   3 0.827           0.892       0.889          0.251 0.860   0.723
#> MAD:hclust  3 0.827           0.957       0.944          0.262 0.860   0.723
#> ATC:hclust  3 0.899           0.933       0.922          0.170 0.914   0.831

get_stats(res_list, k = 4)

#>             k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> SD:NMF      4 0.945           0.937       0.972         0.1545 0.877   0.677
#> CV:NMF      4 0.927           0.886       0.955         0.1525 0.834   0.582
#> MAD:NMF     4 0.980           0.933       0.974         0.1139 0.817   0.524
#> ATC:NMF     4 0.580           0.785       0.783         0.0948 0.798   0.578
#> SD:skmeans  4 1.000           0.998       0.998         0.1828 0.889   0.719
#> CV:skmeans  4 1.000           0.996       0.995         0.1809 0.889   0.719
#> MAD:skmeans 4 1.000           0.956       0.985         0.1829 0.889   0.726
#> ATC:skmeans 4 0.821           0.958       0.911         0.1215 0.889   0.733
#> SD:mclust   4 0.894           0.944       0.959         0.2038 0.764   0.520
#> CV:mclust   4 0.877           0.871       0.927         0.1868 0.845   0.594
#> MAD:mclust  4 0.889           0.906       0.938         0.2110 0.816   0.551
#> ATC:mclust  4 1.000           0.962       0.978         0.1553 0.884   0.678
#> SD:kmeans   4 0.763           0.905       0.877         0.1351 0.725   0.463
#> CV:kmeans   4 0.786           0.854       0.840         0.1329 0.803   0.535
#> MAD:kmeans  4 0.781           0.843       0.845         0.1269 0.695   0.424
#> ATC:kmeans  4 0.729           0.794       0.808         0.1589 0.801   0.568
#> SD:pam      4 0.817           0.891       0.934         0.1985 0.864   0.655
#> CV:pam      4 0.897           0.918       0.942         0.1522 0.880   0.650
#> MAD:pam     4 0.933           0.937       0.967         0.1988 0.832   0.584
#> ATC:pam     4 0.784           0.822       0.890         0.2758 0.843   0.627
#> SD:hclust   4 0.775           0.933       0.911         0.1256 0.914   0.766
#> CV:hclust   4 0.734           0.510       0.670         0.1276 0.717   0.437
#> MAD:hclust  4 1.000           1.000       1.000         0.1167 0.938   0.832
#> ATC:hclust  4 1.000           0.960       0.984         0.0912 0.960   0.904

get_stats(res_list, k = 5)

#>             k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> SD:NMF      5 0.918           0.800       0.904        0.01898 0.969   0.889
#> CV:NMF      5 0.945           0.884       0.963        0.00267 0.960   0.858
#> MAD:NMF     5 0.938           0.903       0.944        0.01559 0.971   0.894
#> ATC:NMF     5 0.758           0.827       0.882        0.07416 0.920   0.747
#> SD:skmeans  5 0.962           0.936       0.961        0.08569 0.912   0.702
#> CV:skmeans  5 0.955           0.873       0.944        0.08183 0.921   0.730
#> MAD:skmeans 5 0.931           0.918       0.961        0.09185 0.931   0.767
#> ATC:skmeans 5 0.917           0.974       0.970        0.06996 0.973   0.911
#> SD:mclust   5 0.900           0.938       0.947        0.07388 0.943   0.776
#> CV:mclust   5 0.907           0.937       0.920        0.05969 0.953   0.809
#> MAD:mclust  5 0.911           0.934       0.930        0.06381 0.928   0.729
#> ATC:mclust  5 0.783           0.856       0.871        0.06025 0.932   0.741
#> SD:kmeans   5 0.723           0.937       0.902        0.07082 0.964   0.860
#> CV:kmeans   5 0.701           0.916       0.880        0.06729 0.935   0.758
#> MAD:kmeans  5 0.742           0.902       0.869        0.07232 0.953   0.820
#> ATC:kmeans  5 0.687           0.889       0.871        0.08273 0.938   0.781
#> SD:pam      5 1.000           0.992       0.996        0.06228 0.929   0.742
#> CV:pam      5 0.952           0.904       0.965        0.05023 0.903   0.645
#> MAD:pam     5 1.000           0.941       0.979        0.04513 0.934   0.745
#> ATC:pam     5 0.776           0.873       0.892        0.04448 0.911   0.689
#> SD:hclust   5 0.855           0.971       0.968        0.09432 0.938   0.781
#> CV:hclust   5 1.000           0.973       0.987        0.12434 0.850   0.586
#> MAD:hclust  5 1.000           0.998       0.981        0.11278 0.914   0.719
#> ATC:hclust  5 1.000           0.960       0.984        0.13597 0.916   0.779

get_stats(res_list, k = 6)

#>             k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> SD:NMF      6 0.879           0.811       0.883         0.0193 0.973   0.900
#> CV:NMF      6 0.842           0.785       0.881         0.0185 0.974   0.904
#> MAD:NMF     6 0.874           0.836       0.903         0.0195 0.982   0.933
#> ATC:NMF     6 0.742           0.727       0.854         0.0351 0.977   0.917
#> SD:skmeans  6 0.878           0.874       0.899         0.0403 0.982   0.917
#> CV:skmeans  6 0.855           0.630       0.778         0.0499 0.940   0.739
#> MAD:skmeans 6 0.890           0.894       0.913         0.0389 0.947   0.783
#> ATC:skmeans 6 0.949           0.930       0.961         0.0412 0.995   0.981
#> SD:mclust   6 0.983           0.971       0.980         0.0500 0.964   0.820
#> CV:mclust   6 0.990           0.983       0.988         0.0541 0.964   0.820
#> MAD:mclust  6 1.000           0.996       0.998         0.0553 0.949   0.757
#> ATC:mclust  6 0.833           0.899       0.906         0.0506 0.933   0.688
#> SD:kmeans   6 0.870           0.875       0.865         0.0422 1.000   1.000
#> CV:kmeans   6 0.832           0.848       0.841         0.0468 1.000   1.000
#> MAD:kmeans  6 0.815           0.857       0.852         0.0519 1.000   1.000
#> ATC:kmeans  6 0.754           0.817       0.876         0.0507 0.995   0.976
#> SD:pam      6 0.971           0.953       0.967         0.0668 0.945   0.751
#> CV:pam      6 0.984           0.961       0.966         0.0575 0.943   0.735
#> MAD:pam     6 0.948           0.975       0.970         0.0521 0.949   0.764
#> ATC:pam     6 0.936           0.915       0.954         0.0315 0.981   0.912
#> SD:hclust   6 0.956           0.943       0.962         0.0170 0.991   0.959
#> CV:hclust   6 0.987           0.959       0.973         0.0103 0.991   0.959
#> MAD:hclust  6 1.000           0.941       0.983         0.0171 0.995   0.976
#> ATC:hclust  6 1.000           0.987       0.993         0.0152 0.988   0.961

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 infection(p) disease.state(p) individual(p) k
#> SD:NMF      56       0.0181         1.69e-08         0.955 2
#> CV:NMF      56       0.0181         1.69e-08         0.955 2
#> MAD:NMF     55       0.0159         6.02e-09         0.956 2
#> ATC:NMF     56       0.0181         1.69e-08         0.955 2
#> SD:skmeans  55       0.0159         6.02e-09         0.956 2
#> CV:skmeans  55       0.0159         6.02e-09         0.956 2
#> MAD:skmeans 56       0.0136         3.63e-09         0.949 2
#> ATC:skmeans 56       0.0181         1.69e-08         0.955 2
#> SD:mclust   56       0.0036         4.20e-12         0.995 2
#> CV:mclust   56       0.0036         4.20e-12         0.995 2
#> MAD:mclust  56       0.0036         4.20e-12         0.995 2
#> ATC:mclust  56       0.0036         4.20e-12         0.995 2
#> SD:kmeans   56       0.0181         1.69e-08         0.955 2
#> CV:kmeans   56       0.0181         1.69e-08         0.955 2
#> MAD:kmeans  56       0.0181         1.69e-08         0.955 2
#> ATC:kmeans  56       0.0307         2.22e-07         0.937 2
#> SD:pam      54       0.0246         4.58e-08         0.950 2
#> CV:pam      55       0.0211         2.77e-08         0.962 2
#> MAD:pam     56       0.0181         1.69e-08         0.955 2
#> ATC:pam     56       0.0307         2.22e-07         0.937 2
#> SD:hclust   56       0.0181         1.69e-08         0.955 2
#> CV:hclust   56       0.0181         1.69e-08         0.955 2
#> MAD:hclust  56       0.0181         1.69e-08         0.955 2
#> ATC:hclust  54       0.0246         4.58e-08         0.950 2

test_to_known_factors(res_list, k = 3)

#>              n infection(p) disease.state(p) individual(p) k
#> SD:NMF      51     1.47e-02         8.96e-09         0.908 3
#> CV:NMF      51     1.47e-02         8.96e-09         0.908 3
#> MAD:NMF     51     4.81e-03         1.14e-08         0.819 3
#> ATC:NMF     46     4.65e-03         5.67e-10         0.929 3
#> SD:skmeans  56     4.69e-03         2.40e-10         0.902 3
#> CV:skmeans  56     4.69e-03         2.40e-10         0.902 3
#> MAD:skmeans 54     6.64e-03         7.33e-10         0.903 3
#> ATC:skmeans 56     4.69e-03         2.78e-10         0.907 3
#> SD:mclust   56     3.60e-03         4.20e-12         0.995 3
#> CV:mclust   56     4.69e-03         2.85e-11         0.932 3
#> MAD:mclust  48     9.80e-05         1.38e-10         0.911 3
#> ATC:mclust  55     1.57e-05         1.41e-08         0.749 3
#> SD:kmeans   51     8.61e-03         4.89e-11         0.985 3
#> CV:kmeans   51     1.12e-02         2.87e-09         0.897 3
#> MAD:kmeans  51     8.61e-03         4.89e-11         0.985 3
#> ATC:kmeans  45     1.09e-01         4.72e-06         0.908 3
#> SD:pam      56     1.32e-02         4.24e-10         0.807 3
#> CV:pam      51     2.35e-03         2.27e-08         0.663 3
#> MAD:pam     55     1.13e-02         1.36e-10         0.845 3
#> ATC:pam     56     2.38e-02         6.27e-10         0.856 3
#> SD:hclust   56     7.86e-04         1.93e-09         0.944 3
#> CV:hclust   51     1.01e-04         1.43e-11         0.940 3
#> MAD:hclust  56     7.86e-04         1.93e-09         0.944 3
#> ATC:hclust  56     2.38e-02         2.72e-09         0.851 3

test_to_known_factors(res_list, k = 4)

#>              n infection(p) disease.state(p) individual(p) k
#> SD:NMF      55     2.43e-04         2.81e-11         0.903 4
#> CV:NMF      52     8.33e-04         2.25e-10         0.893 4
#> MAD:NMF     54     5.56e-04         7.17e-11         0.899 4
#> ATC:NMF     54     2.60e-03         1.39e-09         0.853 4
#> SD:skmeans  56     1.11e-04         2.41e-11         0.905 4
#> CV:skmeans  56     1.11e-04         2.41e-11         0.905 4
#> MAD:skmeans 54     1.78e-04         8.70e-11         0.880 4
#> ATC:skmeans 54     1.78e-04         8.70e-11         0.880 4
#> SD:mclust   56     1.11e-04         4.17e-13         0.934 4
#> CV:mclust   55     3.17e-05         4.79e-14         0.806 4
#> MAD:mclust  56     1.11e-04         4.17e-13         0.934 4
#> ATC:mclust  56     4.80e-05         1.44e-12         0.933 4
#> SD:kmeans   56     1.11e-04         4.17e-13         0.934 4
#> CV:kmeans   53     2.26e-04         6.92e-12         0.914 4
#> MAD:kmeans  45     1.51e-03         1.02e-09         0.803 4
#> ATC:kmeans  51     3.63e-04         9.82e-13         0.899 4
#> SD:pam      53     2.37e-03         1.13e-10         0.793 4
#> CV:pam      54     4.02e-03         2.84e-10         0.605 4
#> MAD:pam     55     9.85e-03         5.06e-10         0.657 4
#> ATC:pam     53     6.45e-03         1.27e-10         0.856 4
#> SD:hclust   56     2.53e-03         2.21e-10         0.885 4
#> CV:hclust   25           NA         1.05e-05         0.512 4
#> MAD:hclust  56     1.11e-04         2.78e-11         0.909 4
#> ATC:hclust  54     4.57e-02         1.51e-07         0.938 4

test_to_known_factors(res_list, k = 5)

#>              n infection(p) disease.state(p) individual(p) k
#> SD:NMF      51     4.91e-04         2.54e-09         0.903 5
#> CV:NMF      52     8.33e-04         3.91e-10         0.883 5
#> MAD:NMF     55     1.90e-04         2.25e-10         0.951 5
#> ATC:NMF     53     2.26e-04         9.38e-11         0.826 5
#> SD:skmeans  55     4.18e-04         7.90e-12         0.835 5
#> CV:skmeans  50     1.29e-03         1.08e-10         0.837 5
#> MAD:skmeans 52     8.21e-04         1.18e-11         0.874 5
#> ATC:skmeans 56     3.34e-04         2.11e-10         0.784 5
#> SD:mclust   55     3.22e-05         1.22e-12         0.837 5
#> CV:mclust   56     3.15e-05         6.30e-13         0.853 5
#> MAD:mclust  55     3.22e-05         1.22e-12         0.837 5
#> ATC:mclust  55     3.22e-05         1.22e-12         0.837 5
#> SD:kmeans   56     3.34e-04         2.92e-12         0.862 5
#> CV:kmeans   56     3.34e-04         2.92e-12         0.862 5
#> MAD:kmeans  56     3.34e-04         2.92e-12         0.862 5
#> ATC:kmeans  55     4.18e-04         7.69e-12         0.811 5
#> SD:pam      56     3.34e-04         2.92e-12         0.862 5
#> CV:pam      52     5.10e-04         2.18e-11         0.817 5
#> MAD:pam     54     1.54e-03         2.07e-11         0.842 5
#> ATC:pam     56     3.34e-04         7.23e-13         0.865 5
#> SD:hclust   56     3.34e-04         2.92e-12         0.862 5
#> CV:hclust   56     3.34e-04         2.92e-12         0.862 5
#> MAD:hclust  56     3.34e-04         2.92e-12         0.862 5
#> ATC:hclust  54     2.03e-02         1.75e-09         0.912 5

test_to_known_factors(res_list, k = 6)

#>              n infection(p) disease.state(p) individual(p) k
#> SD:NMF      53     3.05e-04         4.19e-10         0.882 6
#> CV:NMF      47     2.74e-04         8.31e-09         0.704 6
#> MAD:NMF     52     3.87e-04         1.02e-09         0.875 6
#> ATC:NMF     50     4.60e-04         1.38e-09         0.827 6
#> SD:skmeans  54     1.31e-03         2.49e-10         0.774 6
#> CV:skmeans  45     2.48e-02         2.01e-07         0.662 6
#> MAD:skmeans 55     1.06e-03         1.02e-10         0.777 6
#> ATC:skmeans 54     5.24e-04         1.24e-09         0.745 6
#> SD:mclust   56     8.89e-05         3.40e-12         0.778 6
#> CV:mclust   56     8.89e-05         3.40e-12         0.778 6
#> MAD:mclust  56     8.89e-05         3.40e-12         0.778 6
#> ATC:mclust  56     1.06e-04         4.21e-12         0.740 6
#> SD:kmeans   56     3.34e-04         2.92e-12         0.862 6
#> CV:kmeans   56     3.34e-04         2.92e-12         0.862 6
#> MAD:kmeans  56     3.34e-04         2.92e-12         0.862 6
#> ATC:kmeans  52     8.21e-04         1.44e-10         0.778 6
#> SD:pam      55     2.22e-04         1.93e-11         0.772 6
#> CV:pam      56     2.39e-04         1.10e-11         0.786 6
#> MAD:pam     56     4.88e-04         2.57e-11         0.785 6
#> ATC:pam     55     1.06e-03         3.22e-11         0.711 6
#> SD:hclust   54     5.24e-04         2.07e-11         0.813 6
#> CV:hclust   56     8.53e-04         5.02e-11         0.923 6
#> MAD:hclust  54     5.24e-04         2.07e-11         0.813 6
#> ATC:hclust  56     3.00e-02         3.73e-09         0.810 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 51979 rows and 56 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#>   Subgroups are detected by 'hclust' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 2.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk SD-hclust-collect-plots

The plots are:

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

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

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

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

Generally speaking, lower PAC score, higher mean silhouette score or higher concordance corresponds to better partition. Rand index and Jaccard index measure how similar the current partition is compared to partition with k-1. If they are too similar, we won't accept k is better than k-1.

select_partition_number(res)

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

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.987       0.992         0.4894 0.507   0.507
#> 3 3 0.799           0.935       0.926         0.2755 0.860   0.723
#> 4 4 0.775           0.933       0.911         0.1256 0.914   0.766
#> 5 5 0.855           0.971       0.968         0.0943 0.938   0.781
#> 6 6 0.956           0.943       0.962         0.0170 0.991   0.959

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

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
#> GSM1253056     1   0.000      1.000 1.000 0.000
#> GSM1253057     1   0.000      1.000 1.000 0.000
#> GSM1253058     1   0.000      1.000 1.000 0.000
#> GSM1253059     1   0.000      1.000 1.000 0.000
#> GSM1253060     1   0.000      1.000 1.000 0.000
#> GSM1253061     1   0.000      1.000 1.000 0.000
#> GSM1253062     1   0.000      1.000 1.000 0.000
#> GSM1253063     1   0.000      1.000 1.000 0.000
#> GSM1253064     1   0.000      1.000 1.000 0.000
#> GSM1253065     1   0.000      1.000 1.000 0.000
#> GSM1253066     1   0.000      1.000 1.000 0.000
#> GSM1253067     1   0.000      1.000 1.000 0.000
#> GSM1253068     1   0.000      1.000 1.000 0.000
#> GSM1253069     1   0.000      1.000 1.000 0.000
#> GSM1253070     1   0.000      1.000 1.000 0.000
#> GSM1253071     1   0.000      1.000 1.000 0.000
#> GSM1253072     1   0.000      1.000 1.000 0.000
#> GSM1253073     1   0.000      1.000 1.000 0.000
#> GSM1253074     1   0.000      1.000 1.000 0.000
#> GSM1253032     1   0.000      1.000 1.000 0.000
#> GSM1253034     2   0.000      0.981 0.000 1.000
#> GSM1253039     2   0.000      0.981 0.000 1.000
#> GSM1253040     2   0.000      0.981 0.000 1.000
#> GSM1253041     2   0.000      0.981 0.000 1.000
#> GSM1253046     1   0.000      1.000 1.000 0.000
#> GSM1253048     2   0.000      0.981 0.000 1.000
#> GSM1253049     2   0.000      0.981 0.000 1.000
#> GSM1253052     2   0.000      0.981 0.000 1.000
#> GSM1253037     2   0.000      0.981 0.000 1.000
#> GSM1253028     2   0.327      0.944 0.060 0.940
#> GSM1253029     2   0.000      0.981 0.000 1.000
#> GSM1253030     2   0.000      0.981 0.000 1.000
#> GSM1253031     2   0.358      0.937 0.068 0.932
#> GSM1253033     1   0.000      1.000 1.000 0.000
#> GSM1253035     2   0.204      0.963 0.032 0.968
#> GSM1253036     2   0.000      0.981 0.000 1.000
#> GSM1253038     2   0.000      0.981 0.000 1.000
#> GSM1253042     2   0.000      0.981 0.000 1.000
#> GSM1253045     2   0.482      0.902 0.104 0.896
#> GSM1253043     2   0.518      0.889 0.116 0.884
#> GSM1253044     2   0.000      0.981 0.000 1.000
#> GSM1253047     1   0.000      1.000 1.000 0.000
#> GSM1253050     2   0.000      0.981 0.000 1.000
#> GSM1253051     2   0.000      0.981 0.000 1.000
#> GSM1253053     2   0.000      0.981 0.000 1.000
#> GSM1253054     1   0.000      1.000 1.000 0.000
#> GSM1253055     2   0.278      0.953 0.048 0.952
#> GSM1253079     1   0.000      1.000 1.000 0.000
#> GSM1253083     1   0.000      1.000 1.000 0.000
#> GSM1253075     1   0.000      1.000 1.000 0.000
#> GSM1253077     1   0.000      1.000 1.000 0.000
#> GSM1253076     1   0.000      1.000 1.000 0.000
#> GSM1253078     1   0.000      1.000 1.000 0.000
#> GSM1253081     1   0.000      1.000 1.000 0.000
#> GSM1253080     1   0.000      1.000 1.000 0.000
#> GSM1253082     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
#> GSM1253056     3   0.525      1.000 0.264 0.000 0.736
#> GSM1253057     1   0.000      0.921 1.000 0.000 0.000
#> GSM1253058     3   0.525      1.000 0.264 0.000 0.736
#> GSM1253059     3   0.525      1.000 0.264 0.000 0.736
#> GSM1253060     3   0.525      1.000 0.264 0.000 0.736
#> GSM1253061     1   0.000      0.921 1.000 0.000 0.000
#> GSM1253062     1   0.000      0.921 1.000 0.000 0.000
#> GSM1253063     3   0.525      1.000 0.264 0.000 0.736
#> GSM1253064     1   0.000      0.921 1.000 0.000 0.000
#> GSM1253065     3   0.525      1.000 0.264 0.000 0.736
#> GSM1253066     1   0.000      0.921 1.000 0.000 0.000
#> GSM1253067     3   0.525      1.000 0.264 0.000 0.736
#> GSM1253068     1   0.000      0.921 1.000 0.000 0.000
#> GSM1253069     1   0.000      0.921 1.000 0.000 0.000
#> GSM1253070     1   0.000      0.921 1.000 0.000 0.000
#> GSM1253071     3   0.525      1.000 0.264 0.000 0.736
#> GSM1253072     1   0.000      0.921 1.000 0.000 0.000
#> GSM1253073     3   0.525      1.000 0.264 0.000 0.736
#> GSM1253074     1   0.000      0.921 1.000 0.000 0.000
#> GSM1253032     1   0.525      0.705 0.736 0.000 0.264
#> GSM1253034     2   0.000      0.983 0.000 1.000 0.000
#> GSM1253039     2   0.000      0.983 0.000 1.000 0.000
#> GSM1253040     2   0.000      0.983 0.000 1.000 0.000
#> GSM1253041     2   0.000      0.983 0.000 1.000 0.000
#> GSM1253046     1   0.525      0.705 0.736 0.000 0.264
#> GSM1253048     2   0.000      0.983 0.000 1.000 0.000
#> GSM1253049     2   0.000      0.983 0.000 1.000 0.000
#> GSM1253052     2   0.000      0.983 0.000 1.000 0.000
#> GSM1253037     2   0.000      0.983 0.000 1.000 0.000
#> GSM1253028     2   0.207      0.951 0.000 0.940 0.060
#> GSM1253029     2   0.000      0.983 0.000 1.000 0.000
#> GSM1253030     2   0.000      0.983 0.000 1.000 0.000
#> GSM1253031     2   0.226      0.946 0.000 0.932 0.068
#> GSM1253033     1   0.525      0.705 0.736 0.000 0.264
#> GSM1253035     2   0.129      0.967 0.000 0.968 0.032
#> GSM1253036     2   0.000      0.983 0.000 1.000 0.000
#> GSM1253038     2   0.000      0.983 0.000 1.000 0.000
#> GSM1253042     2   0.000      0.983 0.000 1.000 0.000
#> GSM1253045     2   0.304      0.918 0.000 0.896 0.104
#> GSM1253043     2   0.327      0.907 0.000 0.884 0.116
#> GSM1253044     2   0.000      0.983 0.000 1.000 0.000
#> GSM1253047     1   0.525      0.705 0.736 0.000 0.264
#> GSM1253050     2   0.000      0.983 0.000 1.000 0.000
#> GSM1253051     2   0.000      0.983 0.000 1.000 0.000
#> GSM1253053     2   0.000      0.983 0.000 1.000 0.000
#> GSM1253054     1   0.525      0.705 0.736 0.000 0.264
#> GSM1253055     2   0.175      0.958 0.000 0.952 0.048
#> GSM1253079     1   0.000      0.921 1.000 0.000 0.000
#> GSM1253083     1   0.000      0.921 1.000 0.000 0.000
#> GSM1253075     1   0.000      0.921 1.000 0.000 0.000
#> GSM1253077     1   0.000      0.921 1.000 0.000 0.000
#> GSM1253076     1   0.000      0.921 1.000 0.000 0.000
#> GSM1253078     1   0.000      0.921 1.000 0.000 0.000
#> GSM1253081     1   0.000      0.921 1.000 0.000 0.000
#> GSM1253080     1   0.000      0.921 1.000 0.000 0.000
#> GSM1253082     1   0.000      0.921 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
#> GSM1253056     4  0.0469      0.996 0.012 0.000 0.000 0.988
#> GSM1253057     1  0.3907      0.920 0.768 0.000 0.000 0.232
#> GSM1253058     4  0.0469      0.996 0.012 0.000 0.000 0.988
#> GSM1253059     4  0.0000      0.987 0.000 0.000 0.000 1.000
#> GSM1253060     4  0.0469      0.996 0.012 0.000 0.000 0.988
#> GSM1253061     1  0.3907      0.920 0.768 0.000 0.000 0.232
#> GSM1253062     1  0.3907      0.920 0.768 0.000 0.000 0.232
#> GSM1253063     4  0.0469      0.996 0.012 0.000 0.000 0.988
#> GSM1253064     1  0.3907      0.920 0.768 0.000 0.000 0.232
#> GSM1253065     4  0.0592      0.992 0.016 0.000 0.000 0.984
#> GSM1253066     1  0.3907      0.920 0.768 0.000 0.000 0.232
#> GSM1253067     4  0.0469      0.996 0.012 0.000 0.000 0.988
#> GSM1253068     1  0.3907      0.920 0.768 0.000 0.000 0.232
#> GSM1253069     1  0.3907      0.920 0.768 0.000 0.000 0.232
#> GSM1253070     1  0.3907      0.920 0.768 0.000 0.000 0.232
#> GSM1253071     4  0.0469      0.996 0.012 0.000 0.000 0.988
#> GSM1253072     1  0.3907      0.920 0.768 0.000 0.000 0.232
#> GSM1253073     4  0.0000      0.987 0.000 0.000 0.000 1.000
#> GSM1253074     1  0.3907      0.920 0.768 0.000 0.000 0.232
#> GSM1253032     1  0.1637      0.687 0.940 0.000 0.060 0.000
#> GSM1253034     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253039     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253040     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253041     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253046     1  0.1637      0.687 0.940 0.000 0.060 0.000
#> GSM1253048     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253049     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253052     3  0.3024      0.952 0.000 0.148 0.852 0.000
#> GSM1253037     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253028     3  0.2149      0.950 0.000 0.088 0.912 0.000
#> GSM1253029     3  0.3024      0.952 0.000 0.148 0.852 0.000
#> GSM1253030     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253031     3  0.2011      0.946 0.000 0.080 0.920 0.000
#> GSM1253033     1  0.2011      0.686 0.920 0.000 0.080 0.000
#> GSM1253035     3  0.2589      0.955 0.000 0.116 0.884 0.000
#> GSM1253036     3  0.3024      0.952 0.000 0.148 0.852 0.000
#> GSM1253038     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253042     3  0.3024      0.952 0.000 0.148 0.852 0.000
#> GSM1253045     3  0.2002      0.920 0.020 0.044 0.936 0.000
#> GSM1253043     3  0.2313      0.914 0.032 0.044 0.924 0.000
#> GSM1253044     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253047     1  0.1637      0.687 0.940 0.000 0.060 0.000
#> GSM1253050     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253051     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253053     3  0.3024      0.952 0.000 0.148 0.852 0.000
#> GSM1253054     1  0.2760      0.682 0.872 0.000 0.128 0.000
#> GSM1253055     3  0.2345      0.953 0.000 0.100 0.900 0.000
#> GSM1253079     1  0.3907      0.920 0.768 0.000 0.000 0.232
#> GSM1253083     1  0.3907      0.920 0.768 0.000 0.000 0.232
#> GSM1253075     1  0.3907      0.920 0.768 0.000 0.000 0.232
#> GSM1253077     1  0.3907      0.920 0.768 0.000 0.000 0.232
#> GSM1253076     1  0.3907      0.920 0.768 0.000 0.000 0.232
#> GSM1253078     1  0.3907      0.920 0.768 0.000 0.000 0.232
#> GSM1253081     1  0.3907      0.920 0.768 0.000 0.000 0.232
#> GSM1253080     1  0.3907      0.920 0.768 0.000 0.000 0.232
#> GSM1253082     1  0.3907      0.920 0.768 0.000 0.000 0.232

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4    p5
#> GSM1253056     4  0.2074      0.957 0.104 0.000 0.000 0.896 0.000
#> GSM1253057     1  0.0000      0.994 1.000 0.000 0.000 0.000 0.000
#> GSM1253058     4  0.2074      0.957 0.104 0.000 0.000 0.896 0.000
#> GSM1253059     4  0.0000      0.859 0.000 0.000 0.000 1.000 0.000
#> GSM1253060     4  0.2074      0.957 0.104 0.000 0.000 0.896 0.000
#> GSM1253061     1  0.0000      0.994 1.000 0.000 0.000 0.000 0.000
#> GSM1253062     1  0.0000      0.994 1.000 0.000 0.000 0.000 0.000
#> GSM1253063     4  0.2074      0.957 0.104 0.000 0.000 0.896 0.000
#> GSM1253064     1  0.0703      0.978 0.976 0.000 0.000 0.024 0.000
#> GSM1253065     4  0.2424      0.925 0.132 0.000 0.000 0.868 0.000
#> GSM1253066     1  0.0609      0.982 0.980 0.000 0.000 0.020 0.000
#> GSM1253067     4  0.2074      0.957 0.104 0.000 0.000 0.896 0.000
#> GSM1253068     1  0.0404      0.987 0.988 0.000 0.000 0.012 0.000
#> GSM1253069     1  0.0000      0.994 1.000 0.000 0.000 0.000 0.000
#> GSM1253070     1  0.0000      0.994 1.000 0.000 0.000 0.000 0.000
#> GSM1253071     4  0.2074      0.957 0.104 0.000 0.000 0.896 0.000
#> GSM1253072     1  0.0000      0.994 1.000 0.000 0.000 0.000 0.000
#> GSM1253073     4  0.0000      0.859 0.000 0.000 0.000 1.000 0.000
#> GSM1253074     1  0.0000      0.994 1.000 0.000 0.000 0.000 0.000
#> GSM1253032     5  0.0000      0.979 0.000 0.000 0.000 0.000 1.000
#> GSM1253034     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253039     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253040     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253041     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253046     5  0.0000      0.979 0.000 0.000 0.000 0.000 1.000
#> GSM1253048     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253049     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253052     3  0.2074      0.949 0.000 0.104 0.896 0.000 0.000
#> GSM1253037     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253028     3  0.1121      0.944 0.000 0.044 0.956 0.000 0.000
#> GSM1253029     3  0.2074      0.949 0.000 0.104 0.896 0.000 0.000
#> GSM1253030     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253031     3  0.0963      0.939 0.000 0.036 0.964 0.000 0.000
#> GSM1253033     5  0.0963      0.964 0.000 0.000 0.036 0.000 0.964
#> GSM1253035     3  0.1608      0.951 0.000 0.072 0.928 0.000 0.000
#> GSM1253036     3  0.2074      0.949 0.000 0.104 0.896 0.000 0.000
#> GSM1253038     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253042     3  0.2074      0.949 0.000 0.104 0.896 0.000 0.000
#> GSM1253045     3  0.0963      0.907 0.000 0.000 0.964 0.000 0.036
#> GSM1253043     3  0.1197      0.900 0.000 0.000 0.952 0.000 0.048
#> GSM1253044     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253047     5  0.0000      0.979 0.000 0.000 0.000 0.000 1.000
#> GSM1253050     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253051     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253053     3  0.2074      0.949 0.000 0.104 0.896 0.000 0.000
#> GSM1253054     5  0.1544      0.940 0.000 0.000 0.068 0.000 0.932
#> GSM1253055     3  0.1341      0.949 0.000 0.056 0.944 0.000 0.000
#> GSM1253079     1  0.0000      0.994 1.000 0.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000      0.994 1.000 0.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000      0.994 1.000 0.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      0.994 1.000 0.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      0.994 1.000 0.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      0.994 1.000 0.000 0.000 0.000 0.000
#> GSM1253081     1  0.0609      0.982 0.980 0.000 0.000 0.020 0.000
#> GSM1253080     1  0.0000      0.994 1.000 0.000 0.000 0.000 0.000
#> GSM1253082     1  0.0703      0.978 0.976 0.000 0.000 0.024 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
#> GSM1253056     4  0.1663      0.945 0.088 0.000 0.000 0.912 0.000 0.000
#> GSM1253057     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253058     6  0.5157      0.194 0.088 0.000 0.000 0.404 0.000 0.508
#> GSM1253059     6  0.2631      0.494 0.000 0.000 0.000 0.180 0.000 0.820
#> GSM1253060     4  0.1663      0.945 0.088 0.000 0.000 0.912 0.000 0.000
#> GSM1253061     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253062     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253063     4  0.1663      0.945 0.088 0.000 0.000 0.912 0.000 0.000
#> GSM1253064     1  0.0937      0.961 0.960 0.000 0.000 0.040 0.000 0.000
#> GSM1253065     4  0.2003      0.888 0.116 0.000 0.000 0.884 0.000 0.000
#> GSM1253066     1  0.0865      0.965 0.964 0.000 0.000 0.036 0.000 0.000
#> GSM1253067     4  0.1663      0.945 0.088 0.000 0.000 0.912 0.000 0.000
#> GSM1253068     1  0.0547      0.976 0.980 0.000 0.000 0.020 0.000 0.000
#> GSM1253069     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253070     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253071     4  0.1663      0.945 0.088 0.000 0.000 0.912 0.000 0.000
#> GSM1253072     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253073     4  0.0547      0.712 0.000 0.000 0.000 0.980 0.000 0.020
#> GSM1253074     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253032     5  0.0000      0.943 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1253034     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253039     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253040     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253041     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253046     5  0.0146      0.943 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM1253048     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253049     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253052     3  0.1092      0.961 0.000 0.020 0.960 0.000 0.000 0.020
#> GSM1253037     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253028     3  0.0547      0.956 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM1253029     3  0.1092      0.961 0.000 0.020 0.960 0.000 0.000 0.020
#> GSM1253030     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253031     3  0.0713      0.953 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM1253033     5  0.1556      0.905 0.000 0.000 0.000 0.000 0.920 0.080
#> GSM1253035     3  0.0260      0.961 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM1253036     3  0.1092      0.961 0.000 0.020 0.960 0.000 0.000 0.020
#> GSM1253038     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253042     3  0.1092      0.961 0.000 0.020 0.960 0.000 0.000 0.020
#> GSM1253045     3  0.1572      0.932 0.000 0.000 0.936 0.000 0.036 0.028
#> GSM1253043     3  0.1780      0.923 0.000 0.000 0.924 0.000 0.048 0.028
#> GSM1253044     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253047     5  0.1141      0.934 0.000 0.000 0.000 0.000 0.948 0.052
#> GSM1253050     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253051     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253053     3  0.1092      0.961 0.000 0.020 0.960 0.000 0.000 0.020
#> GSM1253054     5  0.2474      0.888 0.000 0.000 0.040 0.000 0.880 0.080
#> GSM1253055     3  0.0260      0.959 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM1253079     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253081     1  0.0865      0.965 0.964 0.000 0.000 0.036 0.000 0.000
#> GSM1253080     1  0.0000      0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253082     1  0.0937      0.961 0.960 0.000 0.000 0.040 0.000 0.000

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

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

consensus_heatmap(res, k = 2)

plot of chunk tab-SD-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 infection(p) disease.state(p) individual(p) k
#> SD:hclust 56     0.018077         1.69e-08         0.955 2
#> SD:hclust 56     0.000786         1.93e-09         0.944 3
#> SD:hclust 56     0.002526         2.21e-10         0.885 4
#> SD:hclust 56     0.000334         2.92e-12         0.862 5
#> SD:hclust 54     0.000524         2.07e-11         0.813 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 51979 rows and 56 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#>   Subgroups are detected by 'kmeans' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 2.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk SD-kmeans-collect-plots

The plots are:

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

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

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

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

select_partition_number(res)

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

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.993       0.997         0.4944 0.507   0.507
#> 3 3 0.702           0.695       0.692         0.2759 0.897   0.813
#> 4 4 0.763           0.905       0.877         0.1351 0.725   0.463
#> 5 5 0.723           0.937       0.902         0.0708 0.964   0.860
#> 6 6 0.870           0.875       0.865         0.0422 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
#> GSM1253056     1    0.00      0.994 1.00 0.00
#> GSM1253057     1    0.00      0.994 1.00 0.00
#> GSM1253058     1    0.00      0.994 1.00 0.00
#> GSM1253059     1    0.00      0.994 1.00 0.00
#> GSM1253060     1    0.00      0.994 1.00 0.00
#> GSM1253061     1    0.00      0.994 1.00 0.00
#> GSM1253062     1    0.00      0.994 1.00 0.00
#> GSM1253063     1    0.00      0.994 1.00 0.00
#> GSM1253064     1    0.00      0.994 1.00 0.00
#> GSM1253065     1    0.00      0.994 1.00 0.00
#> GSM1253066     1    0.00      0.994 1.00 0.00
#> GSM1253067     1    0.00      0.994 1.00 0.00
#> GSM1253068     1    0.00      0.994 1.00 0.00
#> GSM1253069     1    0.00      0.994 1.00 0.00
#> GSM1253070     1    0.00      0.994 1.00 0.00
#> GSM1253071     1    0.00      0.994 1.00 0.00
#> GSM1253072     1    0.00      0.994 1.00 0.00
#> GSM1253073     1    0.00      0.994 1.00 0.00
#> GSM1253074     1    0.00      0.994 1.00 0.00
#> GSM1253032     1    0.00      0.994 1.00 0.00
#> GSM1253034     2    0.00      1.000 0.00 1.00
#> GSM1253039     2    0.00      1.000 0.00 1.00
#> GSM1253040     2    0.00      1.000 0.00 1.00
#> GSM1253041     2    0.00      1.000 0.00 1.00
#> GSM1253046     1    0.00      0.994 1.00 0.00
#> GSM1253048     2    0.00      1.000 0.00 1.00
#> GSM1253049     2    0.00      1.000 0.00 1.00
#> GSM1253052     2    0.00      1.000 0.00 1.00
#> GSM1253037     2    0.00      1.000 0.00 1.00
#> GSM1253028     2    0.00      1.000 0.00 1.00
#> GSM1253029     2    0.00      1.000 0.00 1.00
#> GSM1253030     2    0.00      1.000 0.00 1.00
#> GSM1253031     2    0.00      1.000 0.00 1.00
#> GSM1253033     1    0.00      0.994 1.00 0.00
#> GSM1253035     2    0.00      1.000 0.00 1.00
#> GSM1253036     2    0.00      1.000 0.00 1.00
#> GSM1253038     2    0.00      1.000 0.00 1.00
#> GSM1253042     2    0.00      1.000 0.00 1.00
#> GSM1253045     2    0.00      1.000 0.00 1.00
#> GSM1253043     2    0.00      1.000 0.00 1.00
#> GSM1253044     2    0.00      1.000 0.00 1.00
#> GSM1253047     1    0.00      0.994 1.00 0.00
#> GSM1253050     2    0.00      1.000 0.00 1.00
#> GSM1253051     2    0.00      1.000 0.00 1.00
#> GSM1253053     2    0.00      1.000 0.00 1.00
#> GSM1253054     1    0.68      0.780 0.82 0.18
#> GSM1253055     2    0.00      1.000 0.00 1.00
#> GSM1253079     1    0.00      0.994 1.00 0.00
#> GSM1253083     1    0.00      0.994 1.00 0.00
#> GSM1253075     1    0.00      0.994 1.00 0.00
#> GSM1253077     1    0.00      0.994 1.00 0.00
#> GSM1253076     1    0.00      0.994 1.00 0.00
#> GSM1253078     1    0.00      0.994 1.00 0.00
#> GSM1253081     1    0.00      0.994 1.00 0.00
#> GSM1253080     1    0.00      0.994 1.00 0.00
#> GSM1253082     1    0.00      0.994 1.00 0.00

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3
#> GSM1253056     1  0.6204     0.6640 0.576 0.000 0.424
#> GSM1253057     1  0.0000     0.8349 1.000 0.000 0.000
#> GSM1253058     1  0.6204     0.6640 0.576 0.000 0.424
#> GSM1253059     1  0.6204     0.6640 0.576 0.000 0.424
#> GSM1253060     1  0.6204     0.6640 0.576 0.000 0.424
#> GSM1253061     1  0.0000     0.8349 1.000 0.000 0.000
#> GSM1253062     1  0.0000     0.8349 1.000 0.000 0.000
#> GSM1253063     1  0.6204     0.6640 0.576 0.000 0.424
#> GSM1253064     1  0.0000     0.8349 1.000 0.000 0.000
#> GSM1253065     1  0.6204     0.6640 0.576 0.000 0.424
#> GSM1253066     1  0.0000     0.8349 1.000 0.000 0.000
#> GSM1253067     1  0.6204     0.6640 0.576 0.000 0.424
#> GSM1253068     1  0.0000     0.8349 1.000 0.000 0.000
#> GSM1253069     1  0.0000     0.8349 1.000 0.000 0.000
#> GSM1253070     1  0.0592     0.8302 0.988 0.000 0.012
#> GSM1253071     1  0.6204     0.6640 0.576 0.000 0.424
#> GSM1253072     1  0.0000     0.8349 1.000 0.000 0.000
#> GSM1253073     1  0.6204     0.6640 0.576 0.000 0.424
#> GSM1253074     1  0.0000     0.8349 1.000 0.000 0.000
#> GSM1253032     2  0.9633    -0.0170 0.368 0.424 0.208
#> GSM1253034     2  0.6204     0.7559 0.000 0.576 0.424
#> GSM1253039     2  0.6204     0.7559 0.000 0.576 0.424
#> GSM1253040     2  0.6204     0.7559 0.000 0.576 0.424
#> GSM1253041     2  0.6204     0.7559 0.000 0.576 0.424
#> GSM1253046     1  0.9606     0.1188 0.440 0.352 0.208
#> GSM1253048     2  0.6204     0.7559 0.000 0.576 0.424
#> GSM1253049     2  0.6204     0.7559 0.000 0.576 0.424
#> GSM1253052     2  0.1860     0.7342 0.000 0.948 0.052
#> GSM1253037     2  0.6204     0.7559 0.000 0.576 0.424
#> GSM1253028     2  0.1643     0.7041 0.000 0.956 0.044
#> GSM1253029     2  0.4121     0.7473 0.000 0.832 0.168
#> GSM1253030     2  0.6204     0.7559 0.000 0.576 0.424
#> GSM1253031     2  0.1643     0.7041 0.000 0.956 0.044
#> GSM1253033     1  0.9606     0.1188 0.440 0.352 0.208
#> GSM1253035     2  0.0000     0.7196 0.000 1.000 0.000
#> GSM1253036     2  0.1860     0.7342 0.000 0.948 0.052
#> GSM1253038     2  0.6204     0.7559 0.000 0.576 0.424
#> GSM1253042     2  0.3116     0.7419 0.000 0.892 0.108
#> GSM1253045     2  0.3879     0.6455 0.000 0.848 0.152
#> GSM1253043     2  0.3879     0.6455 0.000 0.848 0.152
#> GSM1253044     2  0.6204     0.7559 0.000 0.576 0.424
#> GSM1253047     2  0.9633    -0.0170 0.368 0.424 0.208
#> GSM1253050     2  0.6204     0.7559 0.000 0.576 0.424
#> GSM1253051     2  0.6204     0.7559 0.000 0.576 0.424
#> GSM1253053     2  0.1860     0.7342 0.000 0.948 0.052
#> GSM1253054     2  0.9614     0.0112 0.356 0.436 0.208
#> GSM1253055     2  0.1643     0.7041 0.000 0.956 0.044
#> GSM1253079     1  0.0000     0.8349 1.000 0.000 0.000
#> GSM1253083     1  0.0000     0.8349 1.000 0.000 0.000
#> GSM1253075     1  0.0000     0.8349 1.000 0.000 0.000
#> GSM1253077     1  0.0000     0.8349 1.000 0.000 0.000
#> GSM1253076     1  0.0000     0.8349 1.000 0.000 0.000
#> GSM1253078     1  0.0000     0.8349 1.000 0.000 0.000
#> GSM1253081     1  0.0000     0.8349 1.000 0.000 0.000
#> GSM1253080     1  0.0000     0.8349 1.000 0.000 0.000
#> GSM1253082     1  0.0000     0.8349 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
#> GSM1253056     4  0.4277      0.994 0.280 0.000 0.000 0.720
#> GSM1253057     1  0.0188      0.997 0.996 0.000 0.004 0.000
#> GSM1253058     4  0.5010      0.982 0.276 0.000 0.024 0.700
#> GSM1253059     4  0.5010      0.982 0.276 0.000 0.024 0.700
#> GSM1253060     4  0.4277      0.994 0.280 0.000 0.000 0.720
#> GSM1253061     1  0.0000      0.996 1.000 0.000 0.000 0.000
#> GSM1253062     1  0.0188      0.997 0.996 0.000 0.004 0.000
#> GSM1253063     4  0.4277      0.994 0.280 0.000 0.000 0.720
#> GSM1253064     1  0.0000      0.996 1.000 0.000 0.000 0.000
#> GSM1253065     4  0.4277      0.994 0.280 0.000 0.000 0.720
#> GSM1253066     1  0.0000      0.996 1.000 0.000 0.000 0.000
#> GSM1253067     4  0.4250      0.993 0.276 0.000 0.000 0.724
#> GSM1253068     1  0.0000      0.996 1.000 0.000 0.000 0.000
#> GSM1253069     1  0.0188      0.997 0.996 0.000 0.004 0.000
#> GSM1253070     1  0.0188      0.997 0.996 0.000 0.004 0.000
#> GSM1253071     4  0.4277      0.994 0.280 0.000 0.000 0.720
#> GSM1253072     1  0.0000      0.996 1.000 0.000 0.000 0.000
#> GSM1253073     4  0.4250      0.993 0.276 0.000 0.000 0.724
#> GSM1253074     1  0.0188      0.997 0.996 0.000 0.004 0.000
#> GSM1253032     3  0.4898      0.662 0.024 0.000 0.716 0.260
#> GSM1253034     2  0.0336      0.992 0.000 0.992 0.000 0.008
#> GSM1253039     2  0.0592      0.991 0.000 0.984 0.000 0.016
#> GSM1253040     2  0.0469      0.991 0.000 0.988 0.000 0.012
#> GSM1253041     2  0.0000      0.993 0.000 1.000 0.000 0.000
#> GSM1253046     3  0.6194      0.611 0.096 0.000 0.644 0.260
#> GSM1253048     2  0.0188      0.992 0.000 0.996 0.000 0.004
#> GSM1253049     2  0.0469      0.991 0.000 0.988 0.000 0.012
#> GSM1253052     3  0.4356      0.683 0.000 0.292 0.708 0.000
#> GSM1253037     2  0.0469      0.991 0.000 0.988 0.000 0.012
#> GSM1253028     3  0.3400      0.748 0.000 0.180 0.820 0.000
#> GSM1253029     3  0.4761      0.571 0.000 0.372 0.628 0.000
#> GSM1253030     2  0.0336      0.992 0.000 0.992 0.000 0.008
#> GSM1253031     3  0.3400      0.748 0.000 0.180 0.820 0.000
#> GSM1253033     3  0.6164      0.612 0.092 0.000 0.644 0.264
#> GSM1253035     3  0.3726      0.735 0.000 0.212 0.788 0.000
#> GSM1253036     3  0.4356      0.683 0.000 0.292 0.708 0.000
#> GSM1253038     2  0.0469      0.991 0.000 0.988 0.000 0.012
#> GSM1253042     3  0.4564      0.642 0.000 0.328 0.672 0.000
#> GSM1253045     3  0.0817      0.737 0.000 0.024 0.976 0.000
#> GSM1253043     3  0.0817      0.737 0.000 0.024 0.976 0.000
#> GSM1253044     2  0.0188      0.992 0.000 0.996 0.000 0.004
#> GSM1253047     3  0.5416      0.648 0.048 0.000 0.692 0.260
#> GSM1253050     2  0.0000      0.993 0.000 1.000 0.000 0.000
#> GSM1253051     2  0.0336      0.992 0.000 0.992 0.000 0.008
#> GSM1253053     3  0.4356      0.683 0.000 0.292 0.708 0.000
#> GSM1253054     3  0.4868      0.665 0.024 0.000 0.720 0.256
#> GSM1253055     3  0.3400      0.748 0.000 0.180 0.820 0.000
#> GSM1253079     1  0.0188      0.997 0.996 0.000 0.004 0.000
#> GSM1253083     1  0.0188      0.997 0.996 0.000 0.004 0.000
#> GSM1253075     1  0.0188      0.997 0.996 0.000 0.004 0.000
#> GSM1253077     1  0.0188      0.997 0.996 0.000 0.004 0.000
#> GSM1253076     1  0.0188      0.997 0.996 0.000 0.004 0.000
#> GSM1253078     1  0.0188      0.997 0.996 0.000 0.004 0.000
#> GSM1253081     1  0.0000      0.996 1.000 0.000 0.000 0.000
#> GSM1253080     1  0.0188      0.997 0.996 0.000 0.004 0.000
#> GSM1253082     1  0.0188      0.991 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
#> GSM1253056     4  0.2424      0.975 0.132 0.000 0.000 0.868 0.000
#> GSM1253057     1  0.0000      0.931 1.000 0.000 0.000 0.000 0.000
#> GSM1253058     4  0.4624      0.929 0.132 0.000 0.016 0.768 0.084
#> GSM1253059     4  0.4718      0.927 0.132 0.000 0.020 0.764 0.084
#> GSM1253060     4  0.2424      0.975 0.132 0.000 0.000 0.868 0.000
#> GSM1253061     1  0.2848      0.906 0.868 0.000 0.028 0.000 0.104
#> GSM1253062     1  0.0162      0.931 0.996 0.000 0.000 0.000 0.004
#> GSM1253063     4  0.2424      0.975 0.132 0.000 0.000 0.868 0.000
#> GSM1253064     1  0.3497      0.895 0.836 0.000 0.048 0.004 0.112
#> GSM1253065     4  0.3297      0.958 0.132 0.000 0.020 0.840 0.008
#> GSM1253066     1  0.3497      0.895 0.836 0.000 0.048 0.004 0.112
#> GSM1253067     4  0.2583      0.975 0.132 0.000 0.000 0.864 0.004
#> GSM1253068     1  0.3497      0.895 0.836 0.000 0.048 0.004 0.112
#> GSM1253069     1  0.0000      0.931 1.000 0.000 0.000 0.000 0.000
#> GSM1253070     1  0.2848      0.906 0.868 0.000 0.028 0.000 0.104
#> GSM1253071     4  0.2424      0.975 0.132 0.000 0.000 0.868 0.000
#> GSM1253072     1  0.3497      0.895 0.836 0.000 0.048 0.004 0.112
#> GSM1253073     4  0.2583      0.975 0.132 0.000 0.000 0.864 0.004
#> GSM1253074     1  0.0000      0.931 1.000 0.000 0.000 0.000 0.000
#> GSM1253032     5  0.3210      0.986 0.000 0.000 0.212 0.000 0.788
#> GSM1253034     2  0.1282      0.967 0.000 0.952 0.000 0.044 0.004
#> GSM1253039     2  0.1981      0.963 0.000 0.920 0.000 0.064 0.016
#> GSM1253040     2  0.1364      0.971 0.000 0.952 0.000 0.036 0.012
#> GSM1253041     2  0.0000      0.974 0.000 1.000 0.000 0.000 0.000
#> GSM1253046     5  0.3421      0.985 0.008 0.000 0.204 0.000 0.788
#> GSM1253048     2  0.0162      0.974 0.000 0.996 0.000 0.004 0.000
#> GSM1253049     2  0.1012      0.971 0.000 0.968 0.000 0.020 0.012
#> GSM1253052     3  0.2825      0.911 0.000 0.124 0.860 0.016 0.000
#> GSM1253037     2  0.1012      0.971 0.000 0.968 0.000 0.020 0.012
#> GSM1253028     3  0.2325      0.904 0.000 0.068 0.904 0.028 0.000
#> GSM1253029     3  0.2920      0.903 0.000 0.132 0.852 0.016 0.000
#> GSM1253030     2  0.1357      0.966 0.000 0.948 0.000 0.048 0.004
#> GSM1253031     3  0.2325      0.904 0.000 0.068 0.904 0.028 0.000
#> GSM1253033     5  0.3421      0.985 0.008 0.000 0.204 0.000 0.788
#> GSM1253035     3  0.2020      0.917 0.000 0.100 0.900 0.000 0.000
#> GSM1253036     3  0.2921      0.911 0.000 0.124 0.856 0.020 0.000
#> GSM1253038     2  0.1281      0.971 0.000 0.956 0.000 0.032 0.012
#> GSM1253042     3  0.2825      0.911 0.000 0.124 0.860 0.016 0.000
#> GSM1253045     3  0.2719      0.805 0.000 0.000 0.884 0.048 0.068
#> GSM1253043     3  0.2569      0.811 0.000 0.000 0.892 0.040 0.068
#> GSM1253044     2  0.0162      0.974 0.000 0.996 0.000 0.004 0.000
#> GSM1253047     5  0.3487      0.986 0.000 0.000 0.212 0.008 0.780
#> GSM1253050     2  0.0162      0.975 0.000 0.996 0.000 0.004 0.000
#> GSM1253051     2  0.1282      0.967 0.000 0.952 0.000 0.044 0.004
#> GSM1253053     3  0.2825      0.911 0.000 0.124 0.860 0.016 0.000
#> GSM1253054     5  0.3877      0.978 0.000 0.000 0.212 0.024 0.764
#> GSM1253055     3  0.1704      0.907 0.000 0.068 0.928 0.004 0.000
#> GSM1253079     1  0.0000      0.931 1.000 0.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000      0.931 1.000 0.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000      0.931 1.000 0.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      0.931 1.000 0.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      0.931 1.000 0.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      0.931 1.000 0.000 0.000 0.000 0.000
#> GSM1253081     1  0.3497      0.895 0.836 0.000 0.048 0.004 0.112
#> GSM1253080     1  0.0000      0.931 1.000 0.000 0.000 0.000 0.000
#> GSM1253082     1  0.3497      0.895 0.836 0.000 0.048 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
#> GSM1253056     4  0.1714      0.944 0.092 0.000 0.000 0.908 0.000 NA
#> GSM1253057     1  0.3988      0.828 0.660 0.000 0.004 0.000 0.012 NA
#> GSM1253058     4  0.5371      0.839 0.092 0.000 0.016 0.692 0.040 NA
#> GSM1253059     4  0.5578      0.825 0.092 0.000 0.020 0.672 0.040 NA
#> GSM1253060     4  0.1714      0.944 0.092 0.000 0.000 0.908 0.000 NA
#> GSM1253061     1  0.1411      0.781 0.936 0.000 0.000 0.000 0.004 NA
#> GSM1253062     1  0.3724      0.837 0.716 0.000 0.004 0.000 0.012 NA
#> GSM1253063     4  0.1714      0.944 0.092 0.000 0.000 0.908 0.000 NA
#> GSM1253064     1  0.1313      0.763 0.952 0.000 0.004 0.016 0.000 NA
#> GSM1253065     4  0.2701      0.918 0.104 0.000 0.004 0.864 0.000 NA
#> GSM1253066     1  0.1218      0.765 0.956 0.000 0.004 0.012 0.000 NA
#> GSM1253067     4  0.2306      0.940 0.092 0.000 0.004 0.888 0.000 NA
#> GSM1253068     1  0.1218      0.765 0.956 0.000 0.004 0.012 0.000 NA
#> GSM1253069     1  0.3699      0.828 0.660 0.000 0.000 0.000 0.004 NA
#> GSM1253070     1  0.1349      0.781 0.940 0.000 0.000 0.000 0.004 NA
#> GSM1253071     4  0.1714      0.944 0.092 0.000 0.000 0.908 0.000 NA
#> GSM1253072     1  0.1218      0.765 0.956 0.000 0.004 0.012 0.000 NA
#> GSM1253073     4  0.2518      0.939 0.092 0.000 0.016 0.880 0.000 NA
#> GSM1253074     1  0.3699      0.828 0.660 0.000 0.000 0.000 0.004 NA
#> GSM1253032     5  0.1204      0.989 0.000 0.000 0.056 0.000 0.944 NA
#> GSM1253034     2  0.3027      0.879 0.000 0.824 0.000 0.028 0.000 NA
#> GSM1253039     2  0.3672      0.878 0.000 0.776 0.000 0.056 0.000 NA
#> GSM1253040     2  0.2237      0.909 0.000 0.896 0.000 0.036 0.000 NA
#> GSM1253041     2  0.0146      0.920 0.000 0.996 0.000 0.004 0.000 NA
#> GSM1253046     5  0.1204      0.989 0.000 0.000 0.056 0.000 0.944 NA
#> GSM1253048     2  0.0806      0.918 0.000 0.972 0.000 0.008 0.000 NA
#> GSM1253049     2  0.1333      0.916 0.000 0.944 0.000 0.008 0.000 NA
#> GSM1253052     3  0.3927      0.884 0.000 0.072 0.756 0.000 0.000 NA
#> GSM1253037     2  0.1333      0.916 0.000 0.944 0.000 0.008 0.000 NA
#> GSM1253028     3  0.1929      0.886 0.000 0.048 0.924 0.004 0.008 NA
#> GSM1253029     3  0.3927      0.884 0.000 0.072 0.756 0.000 0.000 NA
#> GSM1253030     2  0.3422      0.871 0.000 0.792 0.000 0.040 0.000 NA
#> GSM1253031     3  0.2143      0.886 0.000 0.048 0.916 0.012 0.008 NA
#> GSM1253033     5  0.2058      0.975 0.000 0.000 0.056 0.000 0.908 NA
#> GSM1253035     3  0.2733      0.901 0.000 0.056 0.864 0.000 0.000 NA
#> GSM1253036     3  0.1895      0.897 0.000 0.072 0.912 0.000 0.000 NA
#> GSM1253038     2  0.1921      0.913 0.000 0.916 0.000 0.032 0.000 NA
#> GSM1253042     3  0.3927      0.884 0.000 0.072 0.756 0.000 0.000 NA
#> GSM1253045     3  0.2434      0.839 0.000 0.000 0.896 0.016 0.056 NA
#> GSM1253043     3  0.2366      0.841 0.000 0.000 0.900 0.020 0.056 NA
#> GSM1253044     2  0.0891      0.917 0.000 0.968 0.000 0.008 0.000 NA
#> GSM1253047     5  0.1349      0.989 0.000 0.000 0.056 0.000 0.940 NA
#> GSM1253050     2  0.0717      0.921 0.000 0.976 0.000 0.008 0.000 NA
#> GSM1253051     2  0.3027      0.879 0.000 0.824 0.000 0.028 0.000 NA
#> GSM1253053     3  0.3927      0.884 0.000 0.072 0.756 0.000 0.000 NA
#> GSM1253054     5  0.1914      0.981 0.000 0.000 0.056 0.008 0.920 NA
#> GSM1253055     3  0.2697      0.901 0.000 0.048 0.876 0.000 0.008 NA
#> GSM1253079     1  0.3988      0.828 0.660 0.000 0.004 0.000 0.012 NA
#> GSM1253083     1  0.3788      0.836 0.704 0.000 0.012 0.000 0.004 NA
#> GSM1253075     1  0.3948      0.836 0.704 0.000 0.012 0.000 0.012 NA
#> GSM1253077     1  0.3670      0.836 0.704 0.000 0.012 0.000 0.000 NA
#> GSM1253076     1  0.3670      0.836 0.704 0.000 0.012 0.000 0.000 NA
#> GSM1253078     1  0.3670      0.836 0.704 0.000 0.012 0.000 0.000 NA
#> GSM1253081     1  0.1485      0.757 0.944 0.000 0.004 0.024 0.000 NA
#> GSM1253080     1  0.3699      0.828 0.660 0.000 0.000 0.000 0.004 NA
#> GSM1253082     1  0.1485      0.757 0.944 0.000 0.004 0.024 0.000 NA

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

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

consensus_heatmap(res, k = 2)

plot of chunk tab-SD-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 infection(p) disease.state(p) individual(p) k
#> SD:kmeans 56     0.018077         1.69e-08         0.955 2
#> SD:kmeans 51     0.008612         4.89e-11         0.985 3
#> SD:kmeans 56     0.000111         4.17e-13         0.934 4
#> SD:kmeans 56     0.000334         2.92e-12         0.862 5
#> SD:kmeans 56     0.000334         2.92e-12         0.862 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 51979 rows and 56 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#>   Subgroups are detected by 'skmeans' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 5.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk SD-skmeans-collect-plots

The plots are:

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

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

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

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

select_partition_number(res)

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

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.979       0.992         0.4967 0.501   0.501
#> 3 3 1.000           0.998       0.998         0.2175 0.879   0.761
#> 4 4 1.000           0.998       0.998         0.1828 0.889   0.719
#> 5 5 0.962           0.936       0.961         0.0857 0.912   0.702
#> 6 6 0.878           0.874       0.899         0.0403 0.982   0.917

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

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

suggest_best_k(res)

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

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

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

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

show/hide code output

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

#>            class entropy silhouette    p1    p2
#> GSM1253056     1   0.000      1.000 1.000 0.000
#> GSM1253057     1   0.000      1.000 1.000 0.000
#> GSM1253058     1   0.000      1.000 1.000 0.000
#> GSM1253059     1   0.000      1.000 1.000 0.000
#> GSM1253060     1   0.000      1.000 1.000 0.000
#> GSM1253061     1   0.000      1.000 1.000 0.000
#> GSM1253062     1   0.000      1.000 1.000 0.000
#> GSM1253063     1   0.000      1.000 1.000 0.000
#> GSM1253064     1   0.000      1.000 1.000 0.000
#> GSM1253065     1   0.000      1.000 1.000 0.000
#> GSM1253066     1   0.000      1.000 1.000 0.000
#> GSM1253067     1   0.000      1.000 1.000 0.000
#> GSM1253068     1   0.000      1.000 1.000 0.000
#> GSM1253069     1   0.000      1.000 1.000 0.000
#> GSM1253070     1   0.000      1.000 1.000 0.000
#> GSM1253071     1   0.000      1.000 1.000 0.000
#> GSM1253072     1   0.000      1.000 1.000 0.000
#> GSM1253073     1   0.000      1.000 1.000 0.000
#> GSM1253074     1   0.000      1.000 1.000 0.000
#> GSM1253032     1   0.000      1.000 1.000 0.000
#> GSM1253034     2   0.000      0.981 0.000 1.000
#> GSM1253039     2   0.000      0.981 0.000 1.000
#> GSM1253040     2   0.000      0.981 0.000 1.000
#> GSM1253041     2   0.000      0.981 0.000 1.000
#> GSM1253046     1   0.000      1.000 1.000 0.000
#> GSM1253048     2   0.000      0.981 0.000 1.000
#> GSM1253049     2   0.000      0.981 0.000 1.000
#> GSM1253052     2   0.000      0.981 0.000 1.000
#> GSM1253037     2   0.000      0.981 0.000 1.000
#> GSM1253028     2   0.000      0.981 0.000 1.000
#> GSM1253029     2   0.000      0.981 0.000 1.000
#> GSM1253030     2   0.000      0.981 0.000 1.000
#> GSM1253031     2   0.000      0.981 0.000 1.000
#> GSM1253033     1   0.000      1.000 1.000 0.000
#> GSM1253035     2   0.000      0.981 0.000 1.000
#> GSM1253036     2   0.000      0.981 0.000 1.000
#> GSM1253038     2   0.000      0.981 0.000 1.000
#> GSM1253042     2   0.000      0.981 0.000 1.000
#> GSM1253045     2   0.000      0.981 0.000 1.000
#> GSM1253043     2   0.000      0.981 0.000 1.000
#> GSM1253044     2   0.000      0.981 0.000 1.000
#> GSM1253047     1   0.000      1.000 1.000 0.000
#> GSM1253050     2   0.000      0.981 0.000 1.000
#> GSM1253051     2   0.000      0.981 0.000 1.000
#> GSM1253053     2   0.000      0.981 0.000 1.000
#> GSM1253054     2   0.985      0.252 0.428 0.572
#> GSM1253055     2   0.000      0.981 0.000 1.000
#> GSM1253079     1   0.000      1.000 1.000 0.000
#> GSM1253083     1   0.000      1.000 1.000 0.000
#> GSM1253075     1   0.000      1.000 1.000 0.000
#> GSM1253077     1   0.000      1.000 1.000 0.000
#> GSM1253076     1   0.000      1.000 1.000 0.000
#> GSM1253078     1   0.000      1.000 1.000 0.000
#> GSM1253081     1   0.000      1.000 1.000 0.000
#> GSM1253080     1   0.000      1.000 1.000 0.000
#> GSM1253082     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
#> GSM1253056     1  0.0237      0.997 0.996 0.000 0.004
#> GSM1253057     1  0.0000      0.999 1.000 0.000 0.000
#> GSM1253058     1  0.0237      0.997 0.996 0.000 0.004
#> GSM1253059     1  0.0237      0.997 0.996 0.000 0.004
#> GSM1253060     1  0.0237      0.997 0.996 0.000 0.004
#> GSM1253061     1  0.0000      0.999 1.000 0.000 0.000
#> GSM1253062     1  0.0000      0.999 1.000 0.000 0.000
#> GSM1253063     1  0.0237      0.997 0.996 0.000 0.004
#> GSM1253064     1  0.0000      0.999 1.000 0.000 0.000
#> GSM1253065     1  0.0237      0.997 0.996 0.000 0.004
#> GSM1253066     1  0.0000      0.999 1.000 0.000 0.000
#> GSM1253067     1  0.0237      0.997 0.996 0.000 0.004
#> GSM1253068     1  0.0000      0.999 1.000 0.000 0.000
#> GSM1253069     1  0.0000      0.999 1.000 0.000 0.000
#> GSM1253070     1  0.0000      0.999 1.000 0.000 0.000
#> GSM1253071     1  0.0237      0.997 0.996 0.000 0.004
#> GSM1253072     1  0.0000      0.999 1.000 0.000 0.000
#> GSM1253073     1  0.0237      0.997 0.996 0.000 0.004
#> GSM1253074     1  0.0000      0.999 1.000 0.000 0.000
#> GSM1253032     3  0.0237      0.993 0.004 0.000 0.996
#> GSM1253034     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253039     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253040     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253041     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253046     3  0.0237      0.993 0.004 0.000 0.996
#> GSM1253048     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253049     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253052     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253037     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253028     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253029     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253030     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253031     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253033     3  0.0237      0.993 0.004 0.000 0.996
#> GSM1253035     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253036     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253038     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253042     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253045     3  0.0237      0.990 0.000 0.004 0.996
#> GSM1253043     3  0.1411      0.963 0.000 0.036 0.964
#> GSM1253044     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253047     3  0.0237      0.993 0.004 0.000 0.996
#> GSM1253050     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253051     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253053     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253054     3  0.0237      0.993 0.004 0.000 0.996
#> GSM1253055     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253079     1  0.0000      0.999 1.000 0.000 0.000
#> GSM1253083     1  0.0000      0.999 1.000 0.000 0.000
#> GSM1253075     1  0.0000      0.999 1.000 0.000 0.000
#> GSM1253077     1  0.0000      0.999 1.000 0.000 0.000
#> GSM1253076     1  0.0000      0.999 1.000 0.000 0.000
#> GSM1253078     1  0.0000      0.999 1.000 0.000 0.000
#> GSM1253081     1  0.0000      0.999 1.000 0.000 0.000
#> GSM1253080     1  0.0000      0.999 1.000 0.000 0.000
#> GSM1253082     1  0.0237      0.997 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
#> GSM1253056     4  0.0188      1.000 0.004 0.000 0.000 0.996
#> GSM1253057     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253058     4  0.0188      1.000 0.004 0.000 0.000 0.996
#> GSM1253059     4  0.0188      1.000 0.004 0.000 0.000 0.996
#> GSM1253060     4  0.0188      1.000 0.004 0.000 0.000 0.996
#> GSM1253061     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253062     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253063     4  0.0188      1.000 0.004 0.000 0.000 0.996
#> GSM1253064     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253065     4  0.0188      1.000 0.004 0.000 0.000 0.996
#> GSM1253066     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253067     4  0.0188      1.000 0.004 0.000 0.000 0.996
#> GSM1253068     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253069     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253070     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253071     4  0.0188      1.000 0.004 0.000 0.000 0.996
#> GSM1253072     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253073     4  0.0188      1.000 0.004 0.000 0.000 0.996
#> GSM1253074     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253032     3  0.0000      0.991 0.000 0.000 1.000 0.000
#> GSM1253034     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM1253039     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM1253040     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM1253041     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM1253046     3  0.0000      0.991 0.000 0.000 1.000 0.000
#> GSM1253048     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM1253049     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM1253052     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM1253037     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM1253028     2  0.0188      0.997 0.000 0.996 0.000 0.004
#> GSM1253029     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM1253030     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM1253031     2  0.0188      0.997 0.000 0.996 0.000 0.004
#> GSM1253033     3  0.0000      0.991 0.000 0.000 1.000 0.000
#> GSM1253035     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM1253036     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM1253038     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM1253042     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM1253045     3  0.0188      0.989 0.000 0.000 0.996 0.004
#> GSM1253043     3  0.1305      0.950 0.000 0.036 0.960 0.004
#> GSM1253044     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM1253047     3  0.0000      0.991 0.000 0.000 1.000 0.000
#> GSM1253050     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM1253051     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM1253053     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> GSM1253054     3  0.0000      0.991 0.000 0.000 1.000 0.000
#> GSM1253055     2  0.0188      0.997 0.000 0.996 0.000 0.004
#> GSM1253079     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253081     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253080     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253082     1  0.0000      1.000 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
#> GSM1253056     4  0.0000      0.999 0.000 0.000 0.000 1.000 0.000
#> GSM1253057     1  0.0000      0.991 1.000 0.000 0.000 0.000 0.000
#> GSM1253058     4  0.0000      0.999 0.000 0.000 0.000 1.000 0.000
#> GSM1253059     4  0.0000      0.999 0.000 0.000 0.000 1.000 0.000
#> GSM1253060     4  0.0000      0.999 0.000 0.000 0.000 1.000 0.000
#> GSM1253061     1  0.0510      0.989 0.984 0.000 0.016 0.000 0.000
#> GSM1253062     1  0.0000      0.991 1.000 0.000 0.000 0.000 0.000
#> GSM1253063     4  0.0000      0.999 0.000 0.000 0.000 1.000 0.000
#> GSM1253064     1  0.0703      0.986 0.976 0.000 0.024 0.000 0.000
#> GSM1253065     4  0.0290      0.992 0.000 0.000 0.008 0.992 0.000
#> GSM1253066     1  0.0703      0.986 0.976 0.000 0.024 0.000 0.000
#> GSM1253067     4  0.0000      0.999 0.000 0.000 0.000 1.000 0.000
#> GSM1253068     1  0.0703      0.986 0.976 0.000 0.024 0.000 0.000
#> GSM1253069     1  0.0000      0.991 1.000 0.000 0.000 0.000 0.000
#> GSM1253070     1  0.0510      0.989 0.984 0.000 0.016 0.000 0.000
#> GSM1253071     4  0.0000      0.999 0.000 0.000 0.000 1.000 0.000
#> GSM1253072     1  0.0703      0.986 0.976 0.000 0.024 0.000 0.000
#> GSM1253073     4  0.0000      0.999 0.000 0.000 0.000 1.000 0.000
#> GSM1253074     1  0.0000      0.991 1.000 0.000 0.000 0.000 0.000
#> GSM1253032     5  0.0000      0.999 0.000 0.000 0.000 0.000 1.000
#> GSM1253034     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253039     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253040     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253041     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253046     5  0.0000      0.999 0.000 0.000 0.000 0.000 1.000
#> GSM1253048     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253049     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253052     3  0.3932      0.683 0.000 0.328 0.672 0.000 0.000
#> GSM1253037     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253028     3  0.0703      0.777 0.000 0.024 0.976 0.000 0.000
#> GSM1253029     3  0.3932      0.683 0.000 0.328 0.672 0.000 0.000
#> GSM1253030     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253031     3  0.0703      0.777 0.000 0.024 0.976 0.000 0.000
#> GSM1253033     5  0.0000      0.999 0.000 0.000 0.000 0.000 1.000
#> GSM1253035     3  0.1965      0.791 0.000 0.096 0.904 0.000 0.000
#> GSM1253036     3  0.1965      0.791 0.000 0.096 0.904 0.000 0.000
#> GSM1253038     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253042     3  0.3966      0.671 0.000 0.336 0.664 0.000 0.000
#> GSM1253045     3  0.4074      0.242 0.000 0.000 0.636 0.000 0.364
#> GSM1253043     3  0.0771      0.758 0.000 0.004 0.976 0.000 0.020
#> GSM1253044     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253047     5  0.0000      0.999 0.000 0.000 0.000 0.000 1.000
#> GSM1253050     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253051     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253053     3  0.3932      0.683 0.000 0.328 0.672 0.000 0.000
#> GSM1253054     5  0.0162      0.996 0.000 0.000 0.004 0.000 0.996
#> GSM1253055     3  0.0703      0.777 0.000 0.024 0.976 0.000 0.000
#> GSM1253079     1  0.0000      0.991 1.000 0.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000      0.991 1.000 0.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000      0.991 1.000 0.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      0.991 1.000 0.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      0.991 1.000 0.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      0.991 1.000 0.000 0.000 0.000 0.000
#> GSM1253081     1  0.0703      0.986 0.976 0.000 0.024 0.000 0.000
#> GSM1253080     1  0.0000      0.991 1.000 0.000 0.000 0.000 0.000
#> GSM1253082     1  0.0865      0.984 0.972 0.000 0.024 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
#> GSM1253056     4  0.0000      0.993 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253057     1  0.0713      0.861 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM1253058     4  0.0146      0.993 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM1253059     4  0.0146      0.993 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM1253060     4  0.0000      0.993 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253061     1  0.3221      0.820 0.736 0.000 0.000 0.000 0.000 0.264
#> GSM1253062     1  0.0458      0.864 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM1253063     4  0.0000      0.993 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253064     1  0.3464      0.796 0.688 0.000 0.000 0.000 0.000 0.312
#> GSM1253065     4  0.0937      0.956 0.000 0.000 0.000 0.960 0.000 0.040
#> GSM1253066     1  0.3464      0.796 0.688 0.000 0.000 0.000 0.000 0.312
#> GSM1253067     4  0.0146      0.993 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM1253068     1  0.3464      0.796 0.688 0.000 0.000 0.000 0.000 0.312
#> GSM1253069     1  0.0713      0.861 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM1253070     1  0.3309      0.815 0.720 0.000 0.000 0.000 0.000 0.280
#> GSM1253071     4  0.0000      0.993 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253072     1  0.3464      0.796 0.688 0.000 0.000 0.000 0.000 0.312
#> GSM1253073     4  0.0146      0.993 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM1253074     1  0.0713      0.861 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM1253032     5  0.0000      0.984 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1253034     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253039     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253040     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253041     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253046     5  0.0146      0.983 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM1253048     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253049     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253052     3  0.2730      0.751 0.000 0.192 0.808 0.000 0.000 0.000
#> GSM1253037     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253028     6  0.3833      0.895 0.000 0.000 0.444 0.000 0.000 0.556
#> GSM1253029     3  0.2730      0.751 0.000 0.192 0.808 0.000 0.000 0.000
#> GSM1253030     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253031     6  0.3833      0.895 0.000 0.000 0.444 0.000 0.000 0.556
#> GSM1253033     5  0.0260      0.982 0.000 0.000 0.000 0.000 0.992 0.008
#> GSM1253035     3  0.2001      0.564 0.000 0.040 0.912 0.000 0.000 0.048
#> GSM1253036     3  0.5184     -0.264 0.000 0.120 0.584 0.000 0.000 0.296
#> GSM1253038     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253042     3  0.2969      0.716 0.000 0.224 0.776 0.000 0.000 0.000
#> GSM1253045     6  0.4747      0.824 0.000 0.000 0.324 0.000 0.068 0.608
#> GSM1253043     6  0.3672      0.883 0.000 0.000 0.368 0.000 0.000 0.632
#> GSM1253044     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253047     5  0.0458      0.980 0.000 0.000 0.000 0.000 0.984 0.016
#> GSM1253050     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253051     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253053     3  0.2730      0.751 0.000 0.192 0.808 0.000 0.000 0.000
#> GSM1253054     5  0.1204      0.957 0.000 0.000 0.000 0.000 0.944 0.056
#> GSM1253055     3  0.0790      0.497 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM1253079     1  0.0713      0.861 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM1253083     1  0.0000      0.866 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000      0.866 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      0.866 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      0.866 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      0.866 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253081     1  0.3601      0.793 0.684 0.000 0.000 0.004 0.000 0.312
#> GSM1253080     1  0.0713      0.861 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM1253082     1  0.3601      0.793 0.684 0.000 0.000 0.004 0.000 0.312

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 infection(p) disease.state(p) individual(p) k
#> SD:skmeans 55     0.015882         6.02e-09         0.956 2
#> SD:skmeans 56     0.004693         2.40e-10         0.902 3
#> SD:skmeans 56     0.000111         2.41e-11         0.905 4
#> SD:skmeans 55     0.000418         7.90e-12         0.835 5
#> SD:skmeans 54     0.001308         2.49e-10         0.774 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 51979 rows and 56 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#>   Subgroups are detected by 'pam' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 6.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk SD-pam-collect-plots

The plots are:

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

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

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

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

select_partition_number(res)

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

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.966       0.986         0.4837 0.523   0.523
#> 3 3 0.713           0.932       0.940         0.2690 0.826   0.681
#> 4 4 0.817           0.891       0.934         0.1985 0.864   0.655
#> 5 5 1.000           0.992       0.996         0.0623 0.929   0.742
#> 6 6 0.971           0.953       0.967         0.0668 0.945   0.751

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

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

suggest_best_k(res)

#> [1] 6
#> attr(,"optional")
#> [1] 2 5

There is also optional best \(k\) = 2 5 that is worth to check.

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

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

show/hide code output

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

#>            class entropy silhouette   p1   p2
#> GSM1253056     1   0.000      0.977 1.00 0.00
#> GSM1253057     1   0.000      0.977 1.00 0.00
#> GSM1253058     1   0.000      0.977 1.00 0.00
#> GSM1253059     1   0.000      0.977 1.00 0.00
#> GSM1253060     1   0.000      0.977 1.00 0.00
#> GSM1253061     1   0.000      0.977 1.00 0.00
#> GSM1253062     1   0.000      0.977 1.00 0.00
#> GSM1253063     1   0.000      0.977 1.00 0.00
#> GSM1253064     1   0.000      0.977 1.00 0.00
#> GSM1253065     1   0.000      0.977 1.00 0.00
#> GSM1253066     1   0.000      0.977 1.00 0.00
#> GSM1253067     1   0.000      0.977 1.00 0.00
#> GSM1253068     1   0.000      0.977 1.00 0.00
#> GSM1253069     1   0.000      0.977 1.00 0.00
#> GSM1253070     1   0.000      0.977 1.00 0.00
#> GSM1253071     1   0.000      0.977 1.00 0.00
#> GSM1253072     1   0.000      0.977 1.00 0.00
#> GSM1253073     1   0.000      0.977 1.00 0.00
#> GSM1253074     1   0.000      0.977 1.00 0.00
#> GSM1253032     1   0.000      0.977 1.00 0.00
#> GSM1253034     2   0.000      1.000 0.00 1.00
#> GSM1253039     2   0.000      1.000 0.00 1.00
#> GSM1253040     2   0.000      1.000 0.00 1.00
#> GSM1253041     2   0.000      1.000 0.00 1.00
#> GSM1253046     1   0.000      0.977 1.00 0.00
#> GSM1253048     2   0.000      1.000 0.00 1.00
#> GSM1253049     2   0.000      1.000 0.00 1.00
#> GSM1253052     2   0.000      1.000 0.00 1.00
#> GSM1253037     2   0.000      1.000 0.00 1.00
#> GSM1253028     2   0.000      1.000 0.00 1.00
#> GSM1253029     2   0.000      1.000 0.00 1.00
#> GSM1253030     2   0.000      1.000 0.00 1.00
#> GSM1253031     2   0.000      1.000 0.00 1.00
#> GSM1253033     1   0.000      0.977 1.00 0.00
#> GSM1253035     2   0.000      1.000 0.00 1.00
#> GSM1253036     2   0.000      1.000 0.00 1.00
#> GSM1253038     2   0.000      1.000 0.00 1.00
#> GSM1253042     2   0.000      1.000 0.00 1.00
#> GSM1253045     1   0.971      0.355 0.60 0.40
#> GSM1253043     1   0.925      0.498 0.66 0.34
#> GSM1253044     2   0.000      1.000 0.00 1.00
#> GSM1253047     1   0.000      0.977 1.00 0.00
#> GSM1253050     2   0.000      1.000 0.00 1.00
#> GSM1253051     2   0.000      1.000 0.00 1.00
#> GSM1253053     2   0.000      1.000 0.00 1.00
#> GSM1253054     1   0.141      0.959 0.98 0.02
#> GSM1253055     2   0.000      1.000 0.00 1.00
#> GSM1253079     1   0.000      0.977 1.00 0.00
#> GSM1253083     1   0.000      0.977 1.00 0.00
#> GSM1253075     1   0.000      0.977 1.00 0.00
#> GSM1253077     1   0.000      0.977 1.00 0.00
#> GSM1253076     1   0.000      0.977 1.00 0.00
#> GSM1253078     1   0.000      0.977 1.00 0.00
#> GSM1253081     1   0.000      0.977 1.00 0.00
#> GSM1253080     1   0.000      0.977 1.00 0.00
#> GSM1253082     1   0.000      0.977 1.00 0.00

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3
#> GSM1253056     1  0.2959      0.940 0.900 0.000 0.100
#> GSM1253057     1  0.0000      0.945 1.000 0.000 0.000
#> GSM1253058     1  0.2959      0.940 0.900 0.000 0.100
#> GSM1253059     1  0.2959      0.940 0.900 0.000 0.100
#> GSM1253060     1  0.2959      0.940 0.900 0.000 0.100
#> GSM1253061     1  0.1753      0.944 0.952 0.000 0.048
#> GSM1253062     1  0.0000      0.945 1.000 0.000 0.000
#> GSM1253063     1  0.2959      0.940 0.900 0.000 0.100
#> GSM1253064     1  0.2959      0.940 0.900 0.000 0.100
#> GSM1253065     1  0.2959      0.940 0.900 0.000 0.100
#> GSM1253066     1  0.0000      0.945 1.000 0.000 0.000
#> GSM1253067     1  0.2959      0.940 0.900 0.000 0.100
#> GSM1253068     1  0.0000      0.945 1.000 0.000 0.000
#> GSM1253069     1  0.0000      0.945 1.000 0.000 0.000
#> GSM1253070     1  0.0000      0.945 1.000 0.000 0.000
#> GSM1253071     1  0.2959      0.940 0.900 0.000 0.100
#> GSM1253072     1  0.2959      0.940 0.900 0.000 0.100
#> GSM1253073     1  0.2959      0.940 0.900 0.000 0.100
#> GSM1253074     1  0.0000      0.945 1.000 0.000 0.000
#> GSM1253032     3  0.0424      0.837 0.008 0.000 0.992
#> GSM1253034     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253039     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253040     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253041     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253046     1  0.0000      0.945 1.000 0.000 0.000
#> GSM1253048     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253049     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253052     3  0.4555      0.874 0.000 0.200 0.800
#> GSM1253037     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253028     3  0.2959      0.901 0.000 0.100 0.900
#> GSM1253029     3  0.4654      0.867 0.000 0.208 0.792
#> GSM1253030     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253031     3  0.2959      0.901 0.000 0.100 0.900
#> GSM1253033     1  0.3116      0.936 0.892 0.000 0.108
#> GSM1253035     3  0.2959      0.901 0.000 0.100 0.900
#> GSM1253036     3  0.4555      0.874 0.000 0.200 0.800
#> GSM1253038     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253042     3  0.4654      0.867 0.000 0.208 0.792
#> GSM1253045     3  0.2959      0.840 0.100 0.000 0.900
#> GSM1253043     3  0.2959      0.840 0.100 0.000 0.900
#> GSM1253044     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253047     1  0.5216      0.623 0.740 0.000 0.260
#> GSM1253050     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253051     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253053     3  0.4555      0.874 0.000 0.200 0.800
#> GSM1253054     3  0.0000      0.841 0.000 0.000 1.000
#> GSM1253055     3  0.2959      0.901 0.000 0.100 0.900
#> GSM1253079     1  0.0000      0.945 1.000 0.000 0.000
#> GSM1253083     1  0.0000      0.945 1.000 0.000 0.000
#> GSM1253075     1  0.0000      0.945 1.000 0.000 0.000
#> GSM1253077     1  0.0000      0.945 1.000 0.000 0.000
#> GSM1253076     1  0.0000      0.945 1.000 0.000 0.000
#> GSM1253078     1  0.0000      0.945 1.000 0.000 0.000
#> GSM1253081     1  0.2959      0.940 0.900 0.000 0.100
#> GSM1253080     1  0.0000      0.945 1.000 0.000 0.000
#> GSM1253082     1  0.2959      0.940 0.900 0.000 0.100

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4
#> GSM1253056     4  0.2408      0.946 0.104 0.000 0.000 0.896
#> GSM1253057     1  0.0000      0.918 1.000 0.000 0.000 0.000
#> GSM1253058     4  0.2408      0.946 0.104 0.000 0.000 0.896
#> GSM1253059     4  0.2408      0.946 0.104 0.000 0.000 0.896
#> GSM1253060     4  0.2408      0.946 0.104 0.000 0.000 0.896
#> GSM1253061     1  0.0469      0.909 0.988 0.000 0.000 0.012
#> GSM1253062     1  0.0000      0.918 1.000 0.000 0.000 0.000
#> GSM1253063     4  0.2408      0.946 0.104 0.000 0.000 0.896
#> GSM1253064     1  0.3569      0.689 0.804 0.000 0.000 0.196
#> GSM1253065     4  0.2530      0.939 0.112 0.000 0.000 0.888
#> GSM1253066     1  0.0000      0.918 1.000 0.000 0.000 0.000
#> GSM1253067     4  0.2408      0.946 0.104 0.000 0.000 0.896
#> GSM1253068     1  0.0000      0.918 1.000 0.000 0.000 0.000
#> GSM1253069     1  0.0000      0.918 1.000 0.000 0.000 0.000
#> GSM1253070     1  0.0000      0.918 1.000 0.000 0.000 0.000
#> GSM1253071     4  0.2408      0.946 0.104 0.000 0.000 0.896
#> GSM1253072     1  0.0707      0.903 0.980 0.000 0.000 0.020
#> GSM1253073     4  0.2408      0.946 0.104 0.000 0.000 0.896
#> GSM1253074     1  0.0000      0.918 1.000 0.000 0.000 0.000
#> GSM1253032     3  0.4406      0.637 0.000 0.000 0.700 0.300
#> GSM1253034     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253039     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253040     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253041     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253046     1  0.2760      0.816 0.872 0.000 0.000 0.128
#> GSM1253048     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253049     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253052     3  0.1940      0.921 0.000 0.076 0.924 0.000
#> GSM1253037     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253028     3  0.0000      0.933 0.000 0.000 1.000 0.000
#> GSM1253029     3  0.2011      0.919 0.000 0.080 0.920 0.000
#> GSM1253030     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253031     3  0.0000      0.933 0.000 0.000 1.000 0.000
#> GSM1253033     1  0.6790      0.462 0.576 0.000 0.128 0.296
#> GSM1253035     3  0.0000      0.933 0.000 0.000 1.000 0.000
#> GSM1253036     3  0.1940      0.921 0.000 0.076 0.924 0.000
#> GSM1253038     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253042     3  0.2011      0.919 0.000 0.080 0.920 0.000
#> GSM1253045     3  0.0000      0.933 0.000 0.000 1.000 0.000
#> GSM1253043     3  0.0000      0.933 0.000 0.000 1.000 0.000
#> GSM1253044     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253047     1  0.6010      0.590 0.676 0.000 0.220 0.104
#> GSM1253050     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253051     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253053     3  0.1940      0.921 0.000 0.076 0.924 0.000
#> GSM1253054     3  0.2408      0.877 0.000 0.000 0.896 0.104
#> GSM1253055     3  0.0000      0.933 0.000 0.000 1.000 0.000
#> GSM1253079     1  0.0000      0.918 1.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000      0.918 1.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000      0.918 1.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      0.918 1.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      0.918 1.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      0.918 1.000 0.000 0.000 0.000
#> GSM1253081     1  0.4697      0.334 0.644 0.000 0.000 0.356
#> GSM1253080     1  0.0000      0.918 1.000 0.000 0.000 0.000
#> GSM1253082     4  0.4999      0.152 0.492 0.000 0.000 0.508

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4 p5
#> GSM1253056     4  0.0000      0.996 0.000 0.000 0.000 1.000  0
#> GSM1253057     1  0.0000      0.989 1.000 0.000 0.000 0.000  0
#> GSM1253058     4  0.0000      0.996 0.000 0.000 0.000 1.000  0
#> GSM1253059     4  0.0000      0.996 0.000 0.000 0.000 1.000  0
#> GSM1253060     4  0.0000      0.996 0.000 0.000 0.000 1.000  0
#> GSM1253061     1  0.0290      0.984 0.992 0.000 0.000 0.008  0
#> GSM1253062     1  0.0000      0.989 1.000 0.000 0.000 0.000  0
#> GSM1253063     4  0.0000      0.996 0.000 0.000 0.000 1.000  0
#> GSM1253064     1  0.0703      0.972 0.976 0.000 0.000 0.024  0
#> GSM1253065     4  0.0703      0.966 0.024 0.000 0.000 0.976  0
#> GSM1253066     1  0.0000      0.989 1.000 0.000 0.000 0.000  0
#> GSM1253067     4  0.0000      0.996 0.000 0.000 0.000 1.000  0
#> GSM1253068     1  0.0000      0.989 1.000 0.000 0.000 0.000  0
#> GSM1253069     1  0.0000      0.989 1.000 0.000 0.000 0.000  0
#> GSM1253070     1  0.0000      0.989 1.000 0.000 0.000 0.000  0
#> GSM1253071     4  0.0000      0.996 0.000 0.000 0.000 1.000  0
#> GSM1253072     1  0.0290      0.984 0.992 0.000 0.000 0.008  0
#> GSM1253073     4  0.0000      0.996 0.000 0.000 0.000 1.000  0
#> GSM1253074     1  0.0000      0.989 1.000 0.000 0.000 0.000  0
#> GSM1253032     5  0.0000      1.000 0.000 0.000 0.000 0.000  1
#> GSM1253034     2  0.0000      1.000 0.000 1.000 0.000 0.000  0
#> GSM1253039     2  0.0000      1.000 0.000 1.000 0.000 0.000  0
#> GSM1253040     2  0.0000      1.000 0.000 1.000 0.000 0.000  0
#> GSM1253041     2  0.0000      1.000 0.000 1.000 0.000 0.000  0
#> GSM1253046     5  0.0000      1.000 0.000 0.000 0.000 0.000  1
#> GSM1253048     2  0.0000      1.000 0.000 1.000 0.000 0.000  0
#> GSM1253049     2  0.0000      1.000 0.000 1.000 0.000 0.000  0
#> GSM1253052     3  0.0000      0.999 0.000 0.000 1.000 0.000  0
#> GSM1253037     2  0.0000      1.000 0.000 1.000 0.000 0.000  0
#> GSM1253028     3  0.0000      0.999 0.000 0.000 1.000 0.000  0
#> GSM1253029     3  0.0162      0.996 0.000 0.004 0.996 0.000  0
#> GSM1253030     2  0.0000      1.000 0.000 1.000 0.000 0.000  0
#> GSM1253031     3  0.0000      0.999 0.000 0.000 1.000 0.000  0
#> GSM1253033     5  0.0000      1.000 0.000 0.000 0.000 0.000  1
#> GSM1253035     3  0.0000      0.999 0.000 0.000 1.000 0.000  0
#> GSM1253036     3  0.0000      0.999 0.000 0.000 1.000 0.000  0
#> GSM1253038     2  0.0000      1.000 0.000 1.000 0.000 0.000  0
#> GSM1253042     3  0.0162      0.996 0.000 0.004 0.996 0.000  0
#> GSM1253045     3  0.0000      0.999 0.000 0.000 1.000 0.000  0
#> GSM1253043     3  0.0000      0.999 0.000 0.000 1.000 0.000  0
#> GSM1253044     2  0.0000      1.000 0.000 1.000 0.000 0.000  0
#> GSM1253047     5  0.0000      1.000 0.000 0.000 0.000 0.000  1
#> GSM1253050     2  0.0000      1.000 0.000 1.000 0.000 0.000  0
#> GSM1253051     2  0.0000      1.000 0.000 1.000 0.000 0.000  0
#> GSM1253053     3  0.0000      0.999 0.000 0.000 1.000 0.000  0
#> GSM1253054     5  0.0000      1.000 0.000 0.000 0.000 0.000  1
#> GSM1253055     3  0.0000      0.999 0.000 0.000 1.000 0.000  0
#> GSM1253079     1  0.0000      0.989 1.000 0.000 0.000 0.000  0
#> GSM1253083     1  0.0000      0.989 1.000 0.000 0.000 0.000  0
#> GSM1253075     1  0.0000      0.989 1.000 0.000 0.000 0.000  0
#> GSM1253077     1  0.0000      0.989 1.000 0.000 0.000 0.000  0
#> GSM1253076     1  0.0000      0.989 1.000 0.000 0.000 0.000  0
#> GSM1253078     1  0.0000      0.989 1.000 0.000 0.000 0.000  0
#> GSM1253081     1  0.1792      0.914 0.916 0.000 0.000 0.084  0
#> GSM1253080     1  0.0000      0.989 1.000 0.000 0.000 0.000  0
#> GSM1253082     1  0.1478      0.936 0.936 0.000 0.000 0.064  0

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4    p5    p6
#> GSM1253056     4  0.0000      0.995 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253057     1  0.0000      0.919 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253058     4  0.0000      0.995 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253059     4  0.0000      0.995 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253060     4  0.0000      0.995 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253061     6  0.3828      0.355 0.440 0.000 0.000 0.000 0.000 0.560
#> GSM1253062     1  0.2562      0.852 0.828 0.000 0.000 0.000 0.000 0.172
#> GSM1253063     4  0.0000      0.995 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253064     6  0.0865      0.926 0.036 0.000 0.000 0.000 0.000 0.964
#> GSM1253065     4  0.0858      0.962 0.004 0.000 0.000 0.968 0.000 0.028
#> GSM1253066     6  0.0865      0.926 0.036 0.000 0.000 0.000 0.000 0.964
#> GSM1253067     4  0.0000      0.995 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253068     6  0.0865      0.926 0.036 0.000 0.000 0.000 0.000 0.964
#> GSM1253069     1  0.0000      0.919 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253070     1  0.2135      0.879 0.872 0.000 0.000 0.000 0.000 0.128
#> GSM1253071     4  0.0000      0.995 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253072     6  0.0865      0.926 0.036 0.000 0.000 0.000 0.000 0.964
#> GSM1253073     4  0.0000      0.995 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253074     1  0.0000      0.919 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253032     5  0.0000      0.994 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1253034     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253039     2  0.0146      0.996 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM1253040     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253041     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253046     5  0.0000      0.994 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1253048     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253049     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253052     3  0.0146      0.984 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM1253037     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253028     3  0.0790      0.982 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM1253029     3  0.0291      0.983 0.000 0.004 0.992 0.000 0.000 0.004
#> GSM1253030     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253031     3  0.0790      0.982 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM1253033     5  0.0000      0.994 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1253035     3  0.0000      0.985 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253036     3  0.0000      0.985 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253038     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253042     3  0.0291      0.983 0.000 0.004 0.992 0.000 0.000 0.004
#> GSM1253045     3  0.0790      0.982 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM1253043     3  0.0790      0.982 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM1253044     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253047     5  0.0000      0.994 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1253050     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253051     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253053     3  0.0146      0.984 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM1253054     5  0.0632      0.978 0.000 0.000 0.000 0.000 0.976 0.024
#> GSM1253055     3  0.0713      0.983 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM1253079     1  0.0000      0.919 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253083     1  0.1327      0.912 0.936 0.000 0.000 0.000 0.000 0.064
#> GSM1253075     1  0.2562      0.852 0.828 0.000 0.000 0.000 0.000 0.172
#> GSM1253077     1  0.0000      0.919 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253076     1  0.2491      0.859 0.836 0.000 0.000 0.000 0.000 0.164
#> GSM1253078     1  0.1765      0.901 0.904 0.000 0.000 0.000 0.000 0.096
#> GSM1253081     6  0.0865      0.926 0.036 0.000 0.000 0.000 0.000 0.964
#> GSM1253080     1  0.0000      0.919 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253082     6  0.0865      0.926 0.036 0.000 0.000 0.000 0.000 0.964

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 infection(p) disease.state(p) individual(p) k
#> SD:pam 54     0.024635         4.58e-08         0.950 2
#> SD:pam 56     0.013247         4.24e-10         0.807 3
#> SD:pam 53     0.002372         1.13e-10         0.793 4
#> SD:pam 56     0.000334         2.92e-12         0.862 5
#> SD:pam 55     0.000222         1.93e-11         0.772 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 51979 rows and 56 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#>   Subgroups are detected by 'mclust' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 6.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk SD-mclust-collect-plots

The plots are:

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

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

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

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

select_partition_number(res)

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

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           1.000       1.000         0.5096 0.491   0.491
#> 3 3 0.730           0.830       0.811         0.2102 1.000   1.000
#> 4 4 0.894           0.944       0.959         0.2038 0.764   0.520
#> 5 5 0.900           0.938       0.947         0.0739 0.943   0.776
#> 6 6 0.983           0.971       0.980         0.0500 0.964   0.820

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

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

suggest_best_k(res)

#> [1] 6
#> attr(,"optional")
#> [1] 2 5

There is also optional best \(k\) = 2 5 that is worth to check.

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

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

show/hide code output

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

#>            class entropy silhouette p1 p2
#> GSM1253056     1       0          1  1  0
#> GSM1253057     1       0          1  1  0
#> GSM1253058     1       0          1  1  0
#> GSM1253059     1       0          1  1  0
#> GSM1253060     1       0          1  1  0
#> GSM1253061     1       0          1  1  0
#> GSM1253062     1       0          1  1  0
#> GSM1253063     1       0          1  1  0
#> GSM1253064     1       0          1  1  0
#> GSM1253065     1       0          1  1  0
#> GSM1253066     1       0          1  1  0
#> GSM1253067     1       0          1  1  0
#> GSM1253068     1       0          1  1  0
#> GSM1253069     1       0          1  1  0
#> GSM1253070     1       0          1  1  0
#> GSM1253071     1       0          1  1  0
#> GSM1253072     1       0          1  1  0
#> GSM1253073     1       0          1  1  0
#> GSM1253074     1       0          1  1  0
#> GSM1253032     2       0          1  0  1
#> GSM1253034     2       0          1  0  1
#> GSM1253039     2       0          1  0  1
#> GSM1253040     2       0          1  0  1
#> GSM1253041     2       0          1  0  1
#> GSM1253046     2       0          1  0  1
#> GSM1253048     2       0          1  0  1
#> GSM1253049     2       0          1  0  1
#> GSM1253052     2       0          1  0  1
#> GSM1253037     2       0          1  0  1
#> GSM1253028     2       0          1  0  1
#> GSM1253029     2       0          1  0  1
#> GSM1253030     2       0          1  0  1
#> GSM1253031     2       0          1  0  1
#> GSM1253033     2       0          1  0  1
#> GSM1253035     2       0          1  0  1
#> GSM1253036     2       0          1  0  1
#> GSM1253038     2       0          1  0  1
#> GSM1253042     2       0          1  0  1
#> GSM1253045     2       0          1  0  1
#> GSM1253043     2       0          1  0  1
#> GSM1253044     2       0          1  0  1
#> GSM1253047     2       0          1  0  1
#> GSM1253050     2       0          1  0  1
#> GSM1253051     2       0          1  0  1
#> GSM1253053     2       0          1  0  1
#> GSM1253054     2       0          1  0  1
#> GSM1253055     2       0          1  0  1
#> GSM1253079     1       0          1  1  0
#> GSM1253083     1       0          1  1  0
#> GSM1253075     1       0          1  1  0
#> GSM1253077     1       0          1  1  0
#> GSM1253076     1       0          1  1  0
#> GSM1253078     1       0          1  1  0
#> GSM1253081     1       0          1  1  0
#> GSM1253080     1       0          1  1  0
#> GSM1253082     1       0          1  1  0

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3
#> GSM1253056     1  0.3038      0.910 0.896 0.000 0.104
#> GSM1253057     1  0.0000      0.963 1.000 0.000 0.000
#> GSM1253058     1  0.5327      0.788 0.728 0.000 0.272
#> GSM1253059     1  0.5327      0.788 0.728 0.000 0.272
#> GSM1253060     1  0.0000      0.963 1.000 0.000 0.000
#> GSM1253061     1  0.0000      0.963 1.000 0.000 0.000
#> GSM1253062     1  0.0000      0.963 1.000 0.000 0.000
#> GSM1253063     1  0.3752      0.887 0.856 0.000 0.144
#> GSM1253064     1  0.0000      0.963 1.000 0.000 0.000
#> GSM1253065     1  0.0000      0.963 1.000 0.000 0.000
#> GSM1253066     1  0.0000      0.963 1.000 0.000 0.000
#> GSM1253067     1  0.4178      0.868 0.828 0.000 0.172
#> GSM1253068     1  0.0000      0.963 1.000 0.000 0.000
#> GSM1253069     1  0.0000      0.963 1.000 0.000 0.000
#> GSM1253070     1  0.3845      0.876 0.872 0.012 0.116
#> GSM1253071     1  0.0237      0.961 0.996 0.000 0.004
#> GSM1253072     1  0.0000      0.963 1.000 0.000 0.000
#> GSM1253073     1  0.3879      0.882 0.848 0.000 0.152
#> GSM1253074     1  0.0000      0.963 1.000 0.000 0.000
#> GSM1253032     2  0.5560      0.645 0.000 0.700 0.300
#> GSM1253034     2  0.6308      0.735 0.000 0.508 0.492
#> GSM1253039     2  0.6308      0.735 0.000 0.508 0.492
#> GSM1253040     2  0.6308      0.735 0.000 0.508 0.492
#> GSM1253041     2  0.6308      0.735 0.000 0.508 0.492
#> GSM1253046     2  0.5529      0.647 0.000 0.704 0.296
#> GSM1253048     2  0.6308      0.735 0.000 0.508 0.492
#> GSM1253049     2  0.6308      0.735 0.000 0.508 0.492
#> GSM1253052     2  0.0000      0.758 0.000 1.000 0.000
#> GSM1253037     2  0.6308      0.735 0.000 0.508 0.492
#> GSM1253028     2  0.2959      0.762 0.000 0.900 0.100
#> GSM1253029     2  0.0000      0.758 0.000 1.000 0.000
#> GSM1253030     2  0.6308      0.735 0.000 0.508 0.492
#> GSM1253031     2  0.5560      0.657 0.000 0.700 0.300
#> GSM1253033     2  0.5988      0.599 0.000 0.632 0.368
#> GSM1253035     2  0.0000      0.758 0.000 1.000 0.000
#> GSM1253036     2  0.2711      0.762 0.000 0.912 0.088
#> GSM1253038     2  0.6308      0.735 0.000 0.508 0.492
#> GSM1253042     2  0.0000      0.758 0.000 1.000 0.000
#> GSM1253045     2  0.4654      0.712 0.000 0.792 0.208
#> GSM1253043     2  0.1411      0.759 0.000 0.964 0.036
#> GSM1253044     2  0.6308      0.735 0.000 0.508 0.492
#> GSM1253047     2  0.5529      0.647 0.000 0.704 0.296
#> GSM1253050     2  0.6308      0.735 0.000 0.508 0.492
#> GSM1253051     2  0.6308      0.735 0.000 0.508 0.492
#> GSM1253053     2  0.0000      0.758 0.000 1.000 0.000
#> GSM1253054     2  0.4887      0.680 0.000 0.772 0.228
#> GSM1253055     2  0.0000      0.758 0.000 1.000 0.000
#> GSM1253079     1  0.0000      0.963 1.000 0.000 0.000
#> GSM1253083     1  0.0000      0.963 1.000 0.000 0.000
#> GSM1253075     1  0.0000      0.963 1.000 0.000 0.000
#> GSM1253077     1  0.0000      0.963 1.000 0.000 0.000
#> GSM1253076     1  0.0000      0.963 1.000 0.000 0.000
#> GSM1253078     1  0.0000      0.963 1.000 0.000 0.000
#> GSM1253081     1  0.0000      0.963 1.000 0.000 0.000
#> GSM1253080     1  0.0000      0.963 1.000 0.000 0.000
#> GSM1253082     1  0.0000      0.963 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
#> GSM1253056     4  0.1022      0.989 0.032 0.000 0.000 0.968
#> GSM1253057     1  0.0000      0.908 1.000 0.000 0.000 0.000
#> GSM1253058     4  0.0000      0.969 0.000 0.000 0.000 1.000
#> GSM1253059     4  0.0000      0.969 0.000 0.000 0.000 1.000
#> GSM1253060     4  0.0817      0.984 0.024 0.000 0.000 0.976
#> GSM1253061     1  0.3172      0.887 0.840 0.000 0.000 0.160
#> GSM1253062     1  0.0000      0.908 1.000 0.000 0.000 0.000
#> GSM1253063     4  0.1022      0.989 0.032 0.000 0.000 0.968
#> GSM1253064     1  0.3172      0.887 0.840 0.000 0.000 0.160
#> GSM1253065     4  0.1022      0.989 0.032 0.000 0.000 0.968
#> GSM1253066     1  0.3172      0.887 0.840 0.000 0.000 0.160
#> GSM1253067     4  0.1022      0.989 0.032 0.000 0.000 0.968
#> GSM1253068     1  0.3172      0.887 0.840 0.000 0.000 0.160
#> GSM1253069     1  0.0000      0.908 1.000 0.000 0.000 0.000
#> GSM1253070     1  0.4500      0.842 0.776 0.000 0.032 0.192
#> GSM1253071     4  0.1022      0.989 0.032 0.000 0.000 0.968
#> GSM1253072     1  0.3172      0.887 0.840 0.000 0.000 0.160
#> GSM1253073     4  0.1022      0.989 0.032 0.000 0.000 0.968
#> GSM1253074     1  0.3172      0.887 0.840 0.000 0.000 0.160
#> GSM1253032     3  0.0000      0.980 0.000 0.000 1.000 0.000
#> GSM1253034     2  0.0000      0.971 0.000 1.000 0.000 0.000
#> GSM1253039     2  0.0000      0.971 0.000 1.000 0.000 0.000
#> GSM1253040     2  0.0000      0.971 0.000 1.000 0.000 0.000
#> GSM1253041     2  0.0000      0.971 0.000 1.000 0.000 0.000
#> GSM1253046     3  0.0000      0.980 0.000 0.000 1.000 0.000
#> GSM1253048     2  0.0000      0.971 0.000 1.000 0.000 0.000
#> GSM1253049     2  0.0000      0.971 0.000 1.000 0.000 0.000
#> GSM1253052     3  0.1022      0.984 0.000 0.032 0.968 0.000
#> GSM1253037     2  0.0000      0.971 0.000 1.000 0.000 0.000
#> GSM1253028     3  0.1022      0.984 0.000 0.032 0.968 0.000
#> GSM1253029     3  0.1022      0.984 0.000 0.032 0.968 0.000
#> GSM1253030     2  0.0000      0.971 0.000 1.000 0.000 0.000
#> GSM1253031     3  0.0000      0.980 0.000 0.000 1.000 0.000
#> GSM1253033     3  0.0000      0.980 0.000 0.000 1.000 0.000
#> GSM1253035     3  0.1022      0.984 0.000 0.032 0.968 0.000
#> GSM1253036     3  0.1022      0.984 0.000 0.032 0.968 0.000
#> GSM1253038     2  0.4222      0.612 0.000 0.728 0.272 0.000
#> GSM1253042     3  0.1022      0.984 0.000 0.032 0.968 0.000
#> GSM1253045     3  0.0000      0.980 0.000 0.000 1.000 0.000
#> GSM1253043     3  0.1022      0.984 0.000 0.032 0.968 0.000
#> GSM1253044     2  0.0000      0.971 0.000 1.000 0.000 0.000
#> GSM1253047     3  0.0000      0.980 0.000 0.000 1.000 0.000
#> GSM1253050     2  0.0000      0.971 0.000 1.000 0.000 0.000
#> GSM1253051     2  0.0000      0.971 0.000 1.000 0.000 0.000
#> GSM1253053     3  0.1022      0.984 0.000 0.032 0.968 0.000
#> GSM1253054     3  0.0000      0.980 0.000 0.000 1.000 0.000
#> GSM1253055     3  0.1022      0.984 0.000 0.032 0.968 0.000
#> GSM1253079     1  0.0000      0.908 1.000 0.000 0.000 0.000
#> GSM1253083     1  0.0188      0.908 0.996 0.000 0.000 0.004
#> GSM1253075     1  0.0000      0.908 1.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      0.908 1.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      0.908 1.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      0.908 1.000 0.000 0.000 0.000
#> GSM1253081     1  0.3172      0.887 0.840 0.000 0.000 0.160
#> GSM1253080     1  0.0000      0.908 1.000 0.000 0.000 0.000
#> GSM1253082     1  0.3172      0.887 0.840 0.000 0.000 0.160

show/hide code output

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

#>            class entropy silhouette    p1 p2    p3 p4    p5
#> GSM1253056     4   0.000      1.000 0.000  0 0.000  1 0.000
#> GSM1253057     1   0.256      0.868 0.856  0 0.000  0 0.144
#> GSM1253058     4   0.000      1.000 0.000  0 0.000  1 0.000
#> GSM1253059     4   0.000      1.000 0.000  0 0.000  1 0.000
#> GSM1253060     4   0.000      1.000 0.000  0 0.000  1 0.000
#> GSM1253061     5   0.252      0.911 0.140  0 0.000  0 0.860
#> GSM1253062     1   0.256      0.868 0.856  0 0.000  0 0.144
#> GSM1253063     4   0.000      1.000 0.000  0 0.000  1 0.000
#> GSM1253064     5   0.252      0.911 0.140  0 0.000  0 0.860
#> GSM1253065     4   0.000      1.000 0.000  0 0.000  1 0.000
#> GSM1253066     5   0.252      0.911 0.140  0 0.000  0 0.860
#> GSM1253067     4   0.000      1.000 0.000  0 0.000  1 0.000
#> GSM1253068     5   0.252      0.911 0.140  0 0.000  0 0.860
#> GSM1253069     1   0.148      0.905 0.936  0 0.000  0 0.064
#> GSM1253070     5   0.569      0.266 0.088  0 0.376  0 0.536
#> GSM1253071     4   0.000      1.000 0.000  0 0.000  1 0.000
#> GSM1253072     5   0.252      0.911 0.140  0 0.000  0 0.860
#> GSM1253073     4   0.000      1.000 0.000  0 0.000  1 0.000
#> GSM1253074     1   0.300      0.814 0.812  0 0.000  0 0.188
#> GSM1253032     3   0.252      0.904 0.000  0 0.860  0 0.140
#> GSM1253034     2   0.000      1.000 0.000  1 0.000  0 0.000
#> GSM1253039     2   0.000      1.000 0.000  1 0.000  0 0.000
#> GSM1253040     2   0.000      1.000 0.000  1 0.000  0 0.000
#> GSM1253041     2   0.000      1.000 0.000  1 0.000  0 0.000
#> GSM1253046     3   0.252      0.904 0.000  0 0.860  0 0.140
#> GSM1253048     2   0.000      1.000 0.000  1 0.000  0 0.000
#> GSM1253049     2   0.000      1.000 0.000  1 0.000  0 0.000
#> GSM1253052     3   0.000      0.958 0.000  0 1.000  0 0.000
#> GSM1253037     2   0.000      1.000 0.000  1 0.000  0 0.000
#> GSM1253028     3   0.000      0.958 0.000  0 1.000  0 0.000
#> GSM1253029     3   0.000      0.958 0.000  0 1.000  0 0.000
#> GSM1253030     2   0.000      1.000 0.000  1 0.000  0 0.000
#> GSM1253031     3   0.000      0.958 0.000  0 1.000  0 0.000
#> GSM1253033     3   0.252      0.904 0.000  0 0.860  0 0.140
#> GSM1253035     3   0.000      0.958 0.000  0 1.000  0 0.000
#> GSM1253036     3   0.000      0.958 0.000  0 1.000  0 0.000
#> GSM1253038     2   0.000      1.000 0.000  1 0.000  0 0.000
#> GSM1253042     3   0.000      0.958 0.000  0 1.000  0 0.000
#> GSM1253045     3   0.000      0.958 0.000  0 1.000  0 0.000
#> GSM1253043     3   0.000      0.958 0.000  0 1.000  0 0.000
#> GSM1253044     2   0.000      1.000 0.000  1 0.000  0 0.000
#> GSM1253047     3   0.252      0.904 0.000  0 0.860  0 0.140
#> GSM1253050     2   0.000      1.000 0.000  1 0.000  0 0.000
#> GSM1253051     2   0.000      1.000 0.000  1 0.000  0 0.000
#> GSM1253053     3   0.000      0.958 0.000  0 1.000  0 0.000
#> GSM1253054     3   0.252      0.904 0.000  0 0.860  0 0.140
#> GSM1253055     3   0.000      0.958 0.000  0 1.000  0 0.000
#> GSM1253079     1   0.256      0.868 0.856  0 0.000  0 0.144
#> GSM1253083     1   0.000      0.919 1.000  0 0.000  0 0.000
#> GSM1253075     1   0.000      0.919 1.000  0 0.000  0 0.000
#> GSM1253077     1   0.000      0.919 1.000  0 0.000  0 0.000
#> GSM1253076     1   0.000      0.919 1.000  0 0.000  0 0.000
#> GSM1253078     1   0.000      0.919 1.000  0 0.000  0 0.000
#> GSM1253081     5   0.252      0.911 0.140  0 0.000  0 0.860
#> GSM1253080     1   0.000      0.919 1.000  0 0.000  0 0.000
#> GSM1253082     5   0.252      0.911 0.140  0 0.000  0 0.860

show/hide code output

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

#>            class entropy silhouette    p1 p2    p3 p4    p5    p6
#> GSM1253056     4  0.0000      1.000 0.000  0 0.000  1 0.000 0.000
#> GSM1253057     1  0.2697      0.864 0.812  0 0.000  0 0.000 0.188
#> GSM1253058     4  0.0000      1.000 0.000  0 0.000  1 0.000 0.000
#> GSM1253059     4  0.0000      1.000 0.000  0 0.000  1 0.000 0.000
#> GSM1253060     4  0.0000      1.000 0.000  0 0.000  1 0.000 0.000
#> GSM1253061     6  0.0000      0.984 0.000  0 0.000  0 0.000 1.000
#> GSM1253062     1  0.2762      0.859 0.804  0 0.000  0 0.000 0.196
#> GSM1253063     4  0.0000      1.000 0.000  0 0.000  1 0.000 0.000
#> GSM1253064     6  0.0000      0.984 0.000  0 0.000  0 0.000 1.000
#> GSM1253065     4  0.0000      1.000 0.000  0 0.000  1 0.000 0.000
#> GSM1253066     6  0.0000      0.984 0.000  0 0.000  0 0.000 1.000
#> GSM1253067     4  0.0000      1.000 0.000  0 0.000  1 0.000 0.000
#> GSM1253068     6  0.0000      0.984 0.000  0 0.000  0 0.000 1.000
#> GSM1253069     1  0.2048      0.891 0.880  0 0.000  0 0.000 0.120
#> GSM1253070     6  0.1765      0.876 0.000  0 0.000  0 0.096 0.904
#> GSM1253071     4  0.0000      1.000 0.000  0 0.000  1 0.000 0.000
#> GSM1253072     6  0.0000      0.984 0.000  0 0.000  0 0.000 1.000
#> GSM1253073     4  0.0000      1.000 0.000  0 0.000  1 0.000 0.000
#> GSM1253074     1  0.2823      0.851 0.796  0 0.000  0 0.000 0.204
#> GSM1253032     5  0.0000      1.000 0.000  0 0.000  0 1.000 0.000
#> GSM1253034     2  0.0000      1.000 0.000  1 0.000  0 0.000 0.000
#> GSM1253039     2  0.0000      1.000 0.000  1 0.000  0 0.000 0.000
#> GSM1253040     2  0.0000      1.000 0.000  1 0.000  0 0.000 0.000
#> GSM1253041     2  0.0000      1.000 0.000  1 0.000  0 0.000 0.000
#> GSM1253046     5  0.0000      1.000 0.000  0 0.000  0 1.000 0.000
#> GSM1253048     2  0.0000      1.000 0.000  1 0.000  0 0.000 0.000
#> GSM1253049     2  0.0000      1.000 0.000  1 0.000  0 0.000 0.000
#> GSM1253052     3  0.0000      0.993 0.000  0 1.000  0 0.000 0.000
#> GSM1253037     2  0.0000      1.000 0.000  1 0.000  0 0.000 0.000
#> GSM1253028     3  0.0146      0.992 0.000  0 0.996  0 0.004 0.000
#> GSM1253029     3  0.0000      0.993 0.000  0 1.000  0 0.000 0.000
#> GSM1253030     2  0.0000      1.000 0.000  1 0.000  0 0.000 0.000
#> GSM1253031     3  0.0547      0.984 0.000  0 0.980  0 0.020 0.000
#> GSM1253033     5  0.0000      1.000 0.000  0 0.000  0 1.000 0.000
#> GSM1253035     3  0.0000      0.993 0.000  0 1.000  0 0.000 0.000
#> GSM1253036     3  0.0000      0.993 0.000  0 1.000  0 0.000 0.000
#> GSM1253038     2  0.0000      1.000 0.000  1 0.000  0 0.000 0.000
#> GSM1253042     3  0.0000      0.993 0.000  0 1.000  0 0.000 0.000
#> GSM1253045     3  0.0547      0.984 0.000  0 0.980  0 0.020 0.000
#> GSM1253043     3  0.0547      0.984 0.000  0 0.980  0 0.020 0.000
#> GSM1253044     2  0.0000      1.000 0.000  1 0.000  0 0.000 0.000
#> GSM1253047     5  0.0000      1.000 0.000  0 0.000  0 1.000 0.000
#> GSM1253050     2  0.0000      1.000 0.000  1 0.000  0 0.000 0.000
#> GSM1253051     2  0.0000      1.000 0.000  1 0.000  0 0.000 0.000
#> GSM1253053     3  0.0000      0.993 0.000  0 1.000  0 0.000 0.000
#> GSM1253054     5  0.0000      1.000 0.000  0 0.000  0 1.000 0.000
#> GSM1253055     3  0.0000      0.993 0.000  0 1.000  0 0.000 0.000
#> GSM1253079     1  0.2762      0.859 0.804  0 0.000  0 0.000 0.196
#> GSM1253083     1  0.0000      0.897 1.000  0 0.000  0 0.000 0.000
#> GSM1253075     1  0.0713      0.904 0.972  0 0.000  0 0.000 0.028
#> GSM1253077     1  0.0000      0.897 1.000  0 0.000  0 0.000 0.000
#> GSM1253076     1  0.0000      0.897 1.000  0 0.000  0 0.000 0.000
#> GSM1253078     1  0.0000      0.897 1.000  0 0.000  0 0.000 0.000
#> GSM1253081     6  0.0000      0.984 0.000  0 0.000  0 0.000 1.000
#> GSM1253080     1  0.0713      0.904 0.972  0 0.000  0 0.000 0.028
#> GSM1253082     6  0.0000      0.984 0.000  0 0.000  0 0.000 1.000

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 infection(p) disease.state(p) individual(p) k
#> SD:mclust 56     3.60e-03         4.20e-12         0.995 2
#> SD:mclust 56     3.60e-03         4.20e-12         0.995 3
#> SD:mclust 56     1.11e-04         4.17e-13         0.934 4
#> SD:mclust 55     3.22e-05         1.22e-12         0.837 5
#> SD:mclust 56     8.89e-05         3.40e-12         0.778 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 51979 rows and 56 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#>   Subgroups are detected by 'NMF' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 5.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk SD-NMF-collect-plots

The plots are:

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

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

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

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

select_partition_number(res)

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

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.991       0.996         0.4946 0.507   0.507
#> 3 3 0.850           0.872       0.944         0.2943 0.830   0.675
#> 4 4 0.945           0.937       0.972         0.1545 0.877   0.677
#> 5 5 0.918           0.800       0.904         0.0190 0.969   0.889
#> 6 6 0.879           0.811       0.883         0.0193 0.973   0.900

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

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

suggest_best_k(res)

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

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

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

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

show/hide code output

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

#>            class entropy silhouette    p1    p2
#> GSM1253056     1   0.000      0.993 1.000 0.000
#> GSM1253057     1   0.000      0.993 1.000 0.000
#> GSM1253058     1   0.000      0.993 1.000 0.000
#> GSM1253059     1   0.000      0.993 1.000 0.000
#> GSM1253060     1   0.000      0.993 1.000 0.000
#> GSM1253061     1   0.000      0.993 1.000 0.000
#> GSM1253062     1   0.000      0.993 1.000 0.000
#> GSM1253063     1   0.000      0.993 1.000 0.000
#> GSM1253064     1   0.000      0.993 1.000 0.000
#> GSM1253065     1   0.000      0.993 1.000 0.000
#> GSM1253066     1   0.000      0.993 1.000 0.000
#> GSM1253067     1   0.000      0.993 1.000 0.000
#> GSM1253068     1   0.000      0.993 1.000 0.000
#> GSM1253069     1   0.000      0.993 1.000 0.000
#> GSM1253070     1   0.000      0.993 1.000 0.000
#> GSM1253071     1   0.000      0.993 1.000 0.000
#> GSM1253072     1   0.000      0.993 1.000 0.000
#> GSM1253073     1   0.000      0.993 1.000 0.000
#> GSM1253074     1   0.000      0.993 1.000 0.000
#> GSM1253032     1   0.000      0.993 1.000 0.000
#> GSM1253034     2   0.000      1.000 0.000 1.000
#> GSM1253039     2   0.000      1.000 0.000 1.000
#> GSM1253040     2   0.000      1.000 0.000 1.000
#> GSM1253041     2   0.000      1.000 0.000 1.000
#> GSM1253046     1   0.000      0.993 1.000 0.000
#> GSM1253048     2   0.000      1.000 0.000 1.000
#> GSM1253049     2   0.000      1.000 0.000 1.000
#> GSM1253052     2   0.000      1.000 0.000 1.000
#> GSM1253037     2   0.000      1.000 0.000 1.000
#> GSM1253028     2   0.000      1.000 0.000 1.000
#> GSM1253029     2   0.000      1.000 0.000 1.000
#> GSM1253030     2   0.000      1.000 0.000 1.000
#> GSM1253031     2   0.000      1.000 0.000 1.000
#> GSM1253033     1   0.000      0.993 1.000 0.000
#> GSM1253035     2   0.000      1.000 0.000 1.000
#> GSM1253036     2   0.000      1.000 0.000 1.000
#> GSM1253038     2   0.000      1.000 0.000 1.000
#> GSM1253042     2   0.000      1.000 0.000 1.000
#> GSM1253045     2   0.000      1.000 0.000 1.000
#> GSM1253043     2   0.000      1.000 0.000 1.000
#> GSM1253044     2   0.000      1.000 0.000 1.000
#> GSM1253047     1   0.000      0.993 1.000 0.000
#> GSM1253050     2   0.000      1.000 0.000 1.000
#> GSM1253051     2   0.000      1.000 0.000 1.000
#> GSM1253053     2   0.000      1.000 0.000 1.000
#> GSM1253054     1   0.753      0.724 0.784 0.216
#> GSM1253055     2   0.000      1.000 0.000 1.000
#> GSM1253079     1   0.000      0.993 1.000 0.000
#> GSM1253083     1   0.000      0.993 1.000 0.000
#> GSM1253075     1   0.000      0.993 1.000 0.000
#> GSM1253077     1   0.000      0.993 1.000 0.000
#> GSM1253076     1   0.000      0.993 1.000 0.000
#> GSM1253078     1   0.000      0.993 1.000 0.000
#> GSM1253081     1   0.000      0.993 1.000 0.000
#> GSM1253080     1   0.000      0.993 1.000 0.000
#> GSM1253082     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
#> GSM1253056     1  0.0000      0.928 1.000 0.000 0.000
#> GSM1253057     1  0.1163      0.915 0.972 0.000 0.028
#> GSM1253058     1  0.0000      0.928 1.000 0.000 0.000
#> GSM1253059     1  0.0000      0.928 1.000 0.000 0.000
#> GSM1253060     1  0.0000      0.928 1.000 0.000 0.000
#> GSM1253061     1  0.0000      0.928 1.000 0.000 0.000
#> GSM1253062     1  0.0000      0.928 1.000 0.000 0.000
#> GSM1253063     1  0.0000      0.928 1.000 0.000 0.000
#> GSM1253064     1  0.0000      0.928 1.000 0.000 0.000
#> GSM1253065     1  0.0000      0.928 1.000 0.000 0.000
#> GSM1253066     1  0.0000      0.928 1.000 0.000 0.000
#> GSM1253067     1  0.0000      0.928 1.000 0.000 0.000
#> GSM1253068     1  0.0424      0.925 0.992 0.000 0.008
#> GSM1253069     1  0.1643      0.906 0.956 0.000 0.044
#> GSM1253070     3  0.5016      0.560 0.240 0.000 0.760
#> GSM1253071     1  0.0000      0.928 1.000 0.000 0.000
#> GSM1253072     1  0.0000      0.928 1.000 0.000 0.000
#> GSM1253073     1  0.0000      0.928 1.000 0.000 0.000
#> GSM1253074     1  0.4235      0.797 0.824 0.000 0.176
#> GSM1253032     3  0.0000      0.876 0.000 0.000 1.000
#> GSM1253034     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253039     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253040     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253041     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253046     3  0.0000      0.876 0.000 0.000 1.000
#> GSM1253048     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253049     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253052     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253037     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253028     2  0.5785      0.424 0.000 0.668 0.332
#> GSM1253029     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253030     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253031     3  0.6026      0.404 0.000 0.376 0.624
#> GSM1253033     3  0.0000      0.876 0.000 0.000 1.000
#> GSM1253035     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253036     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253038     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253042     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253045     3  0.0000      0.876 0.000 0.000 1.000
#> GSM1253043     3  0.0000      0.876 0.000 0.000 1.000
#> GSM1253044     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253047     3  0.0000      0.876 0.000 0.000 1.000
#> GSM1253050     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253051     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253053     2  0.0237      0.975 0.000 0.996 0.004
#> GSM1253054     3  0.0000      0.876 0.000 0.000 1.000
#> GSM1253055     3  0.6079      0.376 0.000 0.388 0.612
#> GSM1253079     1  0.0000      0.928 1.000 0.000 0.000
#> GSM1253083     1  0.6095      0.471 0.608 0.000 0.392
#> GSM1253075     1  0.3038      0.864 0.896 0.000 0.104
#> GSM1253077     1  0.6045      0.497 0.620 0.000 0.380
#> GSM1253076     1  0.2537      0.883 0.920 0.000 0.080
#> GSM1253078     1  0.4974      0.728 0.764 0.000 0.236
#> GSM1253081     1  0.0000      0.928 1.000 0.000 0.000
#> GSM1253080     1  0.5882      0.558 0.652 0.000 0.348
#> GSM1253082     1  0.0000      0.928 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
#> GSM1253056     4  0.0000      0.998 0.000 0.000 0.000 1.000
#> GSM1253057     1  0.0000      0.953 1.000 0.000 0.000 0.000
#> GSM1253058     4  0.0188      0.997 0.004 0.000 0.000 0.996
#> GSM1253059     4  0.0000      0.998 0.000 0.000 0.000 1.000
#> GSM1253060     4  0.0188      0.997 0.004 0.000 0.000 0.996
#> GSM1253061     1  0.0000      0.953 1.000 0.000 0.000 0.000
#> GSM1253062     1  0.0000      0.953 1.000 0.000 0.000 0.000
#> GSM1253063     4  0.0188      0.997 0.004 0.000 0.000 0.996
#> GSM1253064     1  0.0000      0.953 1.000 0.000 0.000 0.000
#> GSM1253065     4  0.0188      0.997 0.004 0.000 0.000 0.996
#> GSM1253066     1  0.0000      0.953 1.000 0.000 0.000 0.000
#> GSM1253067     4  0.0000      0.998 0.000 0.000 0.000 1.000
#> GSM1253068     1  0.0000      0.953 1.000 0.000 0.000 0.000
#> GSM1253069     1  0.0000      0.953 1.000 0.000 0.000 0.000
#> GSM1253070     1  0.2868      0.820 0.864 0.000 0.136 0.000
#> GSM1253071     4  0.0000      0.998 0.000 0.000 0.000 1.000
#> GSM1253072     1  0.0000      0.953 1.000 0.000 0.000 0.000
#> GSM1253073     4  0.0000      0.998 0.000 0.000 0.000 1.000
#> GSM1253074     1  0.0000      0.953 1.000 0.000 0.000 0.000
#> GSM1253032     3  0.0000      0.999 0.000 0.000 1.000 0.000
#> GSM1253034     2  0.0000      0.960 0.000 1.000 0.000 0.000
#> GSM1253039     2  0.0000      0.960 0.000 1.000 0.000 0.000
#> GSM1253040     2  0.0000      0.960 0.000 1.000 0.000 0.000
#> GSM1253041     2  0.0000      0.960 0.000 1.000 0.000 0.000
#> GSM1253046     3  0.0000      0.999 0.000 0.000 1.000 0.000
#> GSM1253048     2  0.0000      0.960 0.000 1.000 0.000 0.000
#> GSM1253049     2  0.0000      0.960 0.000 1.000 0.000 0.000
#> GSM1253052     2  0.1637      0.917 0.000 0.940 0.060 0.000
#> GSM1253037     2  0.0000      0.960 0.000 1.000 0.000 0.000
#> GSM1253028     2  0.2973      0.841 0.000 0.856 0.144 0.000
#> GSM1253029     2  0.0000      0.960 0.000 1.000 0.000 0.000
#> GSM1253030     2  0.0000      0.960 0.000 1.000 0.000 0.000
#> GSM1253031     3  0.0000      0.999 0.000 0.000 1.000 0.000
#> GSM1253033     3  0.0000      0.999 0.000 0.000 1.000 0.000
#> GSM1253035     2  0.3907      0.732 0.000 0.768 0.232 0.000
#> GSM1253036     2  0.0000      0.960 0.000 1.000 0.000 0.000
#> GSM1253038     2  0.0000      0.960 0.000 1.000 0.000 0.000
#> GSM1253042     2  0.0000      0.960 0.000 1.000 0.000 0.000
#> GSM1253045     3  0.0000      0.999 0.000 0.000 1.000 0.000
#> GSM1253043     3  0.0000      0.999 0.000 0.000 1.000 0.000
#> GSM1253044     2  0.0000      0.960 0.000 1.000 0.000 0.000
#> GSM1253047     3  0.0000      0.999 0.000 0.000 1.000 0.000
#> GSM1253050     2  0.0000      0.960 0.000 1.000 0.000 0.000
#> GSM1253051     2  0.0000      0.960 0.000 1.000 0.000 0.000
#> GSM1253053     2  0.4304      0.650 0.000 0.716 0.284 0.000
#> GSM1253054     3  0.0000      0.999 0.000 0.000 1.000 0.000
#> GSM1253055     3  0.0336      0.990 0.000 0.008 0.992 0.000
#> GSM1253079     1  0.0000      0.953 1.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000      0.953 1.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000      0.953 1.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      0.953 1.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      0.953 1.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      0.953 1.000 0.000 0.000 0.000
#> GSM1253081     1  0.4961      0.225 0.552 0.000 0.000 0.448
#> GSM1253080     1  0.0000      0.953 1.000 0.000 0.000 0.000
#> GSM1253082     1  0.4008      0.676 0.756 0.000 0.000 0.244

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4    p5
#> GSM1253056     4  0.0000     0.5359 0.000 0.000 0.000 1.000 0.000
#> GSM1253057     1  0.0000     0.9530 1.000 0.000 0.000 0.000 0.000
#> GSM1253058     3  0.4171     0.7822 0.000 0.000 0.604 0.396 0.000
#> GSM1253059     3  0.3949     0.7103 0.000 0.000 0.668 0.332 0.000
#> GSM1253060     4  0.4291    -0.7026 0.000 0.000 0.464 0.536 0.000
#> GSM1253061     1  0.0324     0.9513 0.992 0.000 0.004 0.004 0.000
#> GSM1253062     1  0.0000     0.9530 1.000 0.000 0.000 0.000 0.000
#> GSM1253063     3  0.4300     0.7598 0.000 0.000 0.524 0.476 0.000
#> GSM1253064     1  0.1041     0.9382 0.964 0.000 0.032 0.004 0.000
#> GSM1253065     4  0.1270     0.5077 0.000 0.000 0.052 0.948 0.000
#> GSM1253066     1  0.0703     0.9444 0.976 0.000 0.024 0.000 0.000
#> GSM1253067     4  0.0290     0.5338 0.000 0.000 0.008 0.992 0.000
#> GSM1253068     1  0.0404     0.9501 0.988 0.000 0.012 0.000 0.000
#> GSM1253069     1  0.0000     0.9530 1.000 0.000 0.000 0.000 0.000
#> GSM1253070     1  0.4450     0.0216 0.508 0.000 0.004 0.000 0.488
#> GSM1253071     4  0.4249    -0.6120 0.000 0.000 0.432 0.568 0.000
#> GSM1253072     1  0.0404     0.9501 0.988 0.000 0.012 0.000 0.000
#> GSM1253073     3  0.4287     0.7917 0.000 0.000 0.540 0.460 0.000
#> GSM1253074     1  0.0000     0.9530 1.000 0.000 0.000 0.000 0.000
#> GSM1253032     5  0.0000     0.8983 0.000 0.000 0.000 0.000 1.000
#> GSM1253034     2  0.0000     0.9543 0.000 1.000 0.000 0.000 0.000
#> GSM1253039     2  0.0404     0.9522 0.000 0.988 0.012 0.000 0.000
#> GSM1253040     2  0.0404     0.9522 0.000 0.988 0.012 0.000 0.000
#> GSM1253041     2  0.0162     0.9535 0.000 0.996 0.004 0.000 0.000
#> GSM1253046     5  0.0609     0.8990 0.000 0.000 0.020 0.000 0.980
#> GSM1253048     2  0.0000     0.9543 0.000 1.000 0.000 0.000 0.000
#> GSM1253049     2  0.0000     0.9543 0.000 1.000 0.000 0.000 0.000
#> GSM1253052     2  0.0566     0.9488 0.000 0.984 0.012 0.004 0.000
#> GSM1253037     2  0.0162     0.9541 0.000 0.996 0.004 0.000 0.000
#> GSM1253028     5  0.5483     0.1925 0.000 0.424 0.064 0.000 0.512
#> GSM1253029     2  0.0162     0.9535 0.000 0.996 0.004 0.000 0.000
#> GSM1253030     2  0.1671     0.9163 0.000 0.924 0.076 0.000 0.000
#> GSM1253031     5  0.1894     0.8847 0.000 0.008 0.072 0.000 0.920
#> GSM1253033     5  0.0794     0.8982 0.000 0.000 0.028 0.000 0.972
#> GSM1253035     2  0.4392     0.3266 0.000 0.612 0.008 0.000 0.380
#> GSM1253036     2  0.1851     0.9080 0.000 0.912 0.088 0.000 0.000
#> GSM1253038     2  0.0162     0.9541 0.000 0.996 0.004 0.000 0.000
#> GSM1253042     2  0.0703     0.9496 0.000 0.976 0.024 0.000 0.000
#> GSM1253045     5  0.0880     0.8954 0.000 0.000 0.032 0.000 0.968
#> GSM1253043     5  0.1908     0.8786 0.000 0.000 0.092 0.000 0.908
#> GSM1253044     2  0.0000     0.9543 0.000 1.000 0.000 0.000 0.000
#> GSM1253047     5  0.0162     0.8980 0.000 0.000 0.004 0.000 0.996
#> GSM1253050     2  0.0510     0.9512 0.000 0.984 0.016 0.000 0.000
#> GSM1253051     2  0.0000     0.9543 0.000 1.000 0.000 0.000 0.000
#> GSM1253053     2  0.3369     0.8446 0.000 0.856 0.024 0.092 0.028
#> GSM1253054     5  0.0510     0.8951 0.000 0.000 0.016 0.000 0.984
#> GSM1253055     5  0.2079     0.8533 0.000 0.064 0.020 0.000 0.916
#> GSM1253079     1  0.0000     0.9530 1.000 0.000 0.000 0.000 0.000
#> GSM1253083     1  0.0162     0.9523 0.996 0.000 0.004 0.000 0.000
#> GSM1253075     1  0.0000     0.9530 1.000 0.000 0.000 0.000 0.000
#> GSM1253077     1  0.0162     0.9523 0.996 0.000 0.004 0.000 0.000
#> GSM1253076     1  0.0000     0.9530 1.000 0.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000     0.9530 1.000 0.000 0.000 0.000 0.000
#> GSM1253081     1  0.3099     0.8177 0.848 0.000 0.028 0.124 0.000
#> GSM1253080     1  0.0000     0.9530 1.000 0.000 0.000 0.000 0.000
#> GSM1253082     1  0.1893     0.9052 0.928 0.000 0.024 0.048 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
#> GSM1253056     3  0.3547     0.9116 0.000 0.000 0.668 0.332 0.000 NA
#> GSM1253057     1  0.0984     0.9313 0.968 0.000 0.008 0.012 0.000 NA
#> GSM1253058     4  0.4079     0.5946 0.000 0.000 0.084 0.744 0.000 NA
#> GSM1253059     4  0.3612     0.6094 0.000 0.000 0.052 0.780 0.000 NA
#> GSM1253060     4  0.3103     0.5766 0.000 0.000 0.208 0.784 0.000 NA
#> GSM1253061     1  0.0862     0.9315 0.972 0.000 0.004 0.016 0.000 NA
#> GSM1253062     1  0.0858     0.9303 0.968 0.000 0.004 0.000 0.000 NA
#> GSM1253063     4  0.1265     0.6957 0.000 0.000 0.044 0.948 0.000 NA
#> GSM1253064     1  0.2542     0.8832 0.884 0.000 0.020 0.016 0.000 NA
#> GSM1253065     3  0.3508     0.8742 0.004 0.000 0.704 0.292 0.000 NA
#> GSM1253066     1  0.1511     0.9161 0.940 0.000 0.012 0.004 0.000 NA
#> GSM1253067     3  0.3782     0.8784 0.000 0.000 0.636 0.360 0.000 NA
#> GSM1253068     1  0.0806     0.9293 0.972 0.000 0.008 0.000 0.000 NA
#> GSM1253069     1  0.0717     0.9319 0.976 0.000 0.008 0.000 0.000 NA
#> GSM1253070     1  0.5391     0.0049 0.476 0.000 0.016 0.020 0.456 NA
#> GSM1253071     4  0.3298     0.5219 0.000 0.000 0.236 0.756 0.000 NA
#> GSM1253072     1  0.0458     0.9315 0.984 0.000 0.000 0.000 0.000 NA
#> GSM1253073     4  0.1908     0.6786 0.000 0.000 0.028 0.916 0.000 NA
#> GSM1253074     1  0.0881     0.9323 0.972 0.000 0.008 0.008 0.000 NA
#> GSM1253032     5  0.0000     0.8818 0.000 0.000 0.000 0.000 1.000 NA
#> GSM1253034     2  0.0458     0.8941 0.000 0.984 0.000 0.000 0.000 NA
#> GSM1253039     2  0.0865     0.8903 0.000 0.964 0.000 0.000 0.000 NA
#> GSM1253040     2  0.0713     0.8916 0.000 0.972 0.000 0.000 0.000 NA
#> GSM1253041     2  0.0146     0.8933 0.000 0.996 0.000 0.000 0.000 NA
#> GSM1253046     5  0.0260     0.8826 0.000 0.000 0.000 0.000 0.992 NA
#> GSM1253048     2  0.0146     0.8933 0.000 0.996 0.000 0.000 0.000 NA
#> GSM1253049     2  0.0260     0.8939 0.000 0.992 0.000 0.000 0.000 NA
#> GSM1253052     2  0.0870     0.8882 0.000 0.972 0.012 0.000 0.004 NA
#> GSM1253037     2  0.0260     0.8938 0.000 0.992 0.000 0.000 0.000 NA
#> GSM1253028     2  0.5927    -0.0270 0.000 0.428 0.000 0.000 0.356 NA
#> GSM1253029     2  0.0820     0.8884 0.000 0.972 0.012 0.000 0.000 NA
#> GSM1253030     2  0.3531     0.6744 0.000 0.672 0.000 0.000 0.000 NA
#> GSM1253031     5  0.3460     0.8008 0.000 0.020 0.000 0.000 0.760 NA
#> GSM1253033     5  0.1411     0.8746 0.000 0.000 0.000 0.004 0.936 NA
#> GSM1253035     2  0.4206     0.4569 0.000 0.620 0.000 0.000 0.356 NA
#> GSM1253036     2  0.3650     0.7015 0.000 0.708 0.000 0.000 0.012 NA
#> GSM1253038     2  0.0632     0.8926 0.000 0.976 0.000 0.000 0.000 NA
#> GSM1253042     2  0.0858     0.8918 0.000 0.968 0.004 0.000 0.000 NA
#> GSM1253045     5  0.1701     0.8714 0.000 0.008 0.000 0.000 0.920 NA
#> GSM1253043     5  0.3499     0.7187 0.000 0.000 0.000 0.000 0.680 NA
#> GSM1253044     2  0.0260     0.8941 0.000 0.992 0.000 0.000 0.000 NA
#> GSM1253047     5  0.0363     0.8812 0.000 0.000 0.012 0.000 0.988 NA
#> GSM1253050     2  0.0547     0.8925 0.000 0.980 0.000 0.000 0.000 NA
#> GSM1253051     2  0.0713     0.8902 0.000 0.972 0.000 0.000 0.000 NA
#> GSM1253053     2  0.3203     0.7685 0.000 0.812 0.160 0.000 0.004 NA
#> GSM1253054     5  0.1010     0.8742 0.000 0.000 0.036 0.000 0.960 NA
#> GSM1253055     5  0.4443     0.6933 0.000 0.176 0.016 0.000 0.732 NA
#> GSM1253079     1  0.0862     0.9308 0.972 0.000 0.008 0.016 0.000 NA
#> GSM1253083     1  0.0632     0.9310 0.976 0.000 0.000 0.000 0.000 NA
#> GSM1253075     1  0.0146     0.9330 0.996 0.000 0.000 0.000 0.000 NA
#> GSM1253077     1  0.0547     0.9318 0.980 0.000 0.000 0.000 0.000 NA
#> GSM1253076     1  0.0458     0.9323 0.984 0.000 0.000 0.000 0.000 NA
#> GSM1253078     1  0.0458     0.9323 0.984 0.000 0.000 0.000 0.000 NA
#> GSM1253081     1  0.3997     0.7934 0.800 0.000 0.052 0.084 0.000 NA
#> GSM1253080     1  0.0717     0.9321 0.976 0.000 0.008 0.000 0.000 NA
#> GSM1253082     1  0.2540     0.8840 0.892 0.000 0.020 0.044 0.000 NA

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

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

consensus_heatmap(res, k = 2)

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

consensus_heatmap(res, k = 3)

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

consensus_heatmap(res, k = 4)

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

consensus_heatmap(res, k = 5)

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

consensus_heatmap(res, k = 6)

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

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

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

membership_heatmap(res, k = 2)

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

membership_heatmap(res, k = 3)

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

membership_heatmap(res, k = 4)

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

membership_heatmap(res, k = 5)

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

membership_heatmap(res, k = 6)

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

Signature heatmaps where rows are scaled:

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

get_signatures(res, k = 2)

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

get_signatures(res, k = 3)

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

get_signatures(res, k = 4)

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

get_signatures(res, k = 5)

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

get_signatures(res, k = 6)

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

Signature heatmaps where rows are not scaled:

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

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

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

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

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

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

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

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

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

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

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

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk SD-NMF-signature_compare

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

which_row: row indices corresponding to the input matrix.
fdr: FDR for the differential test.
mean_x: The mean value in group x.
scaled_mean_x: The mean value in group x after rows are scaled.
km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

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

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

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

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

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

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

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

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

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

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

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

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk SD-NMF-collect-classes

test_to_known_factors(res)

#>         n infection(p) disease.state(p) individual(p) k
#> SD:NMF 56     0.018077         1.69e-08         0.955 2
#> SD:NMF 51     0.014712         8.96e-09         0.908 3
#> SD:NMF 55     0.000243         2.81e-11         0.903 4
#> SD:NMF 51     0.000491         2.54e-09         0.903 5
#> SD:NMF 53     0.000305         4.19e-10         0.882 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 51979 rows and 56 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#>   Subgroups are detected by 'hclust' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 5.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk CV-hclust-collect-plots

The plots are:

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

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

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

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

select_partition_number(res)

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

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.994       0.996         0.4909 0.507   0.507
#> 3 3 0.827           0.892       0.889         0.2508 0.860   0.723
#> 4 4 0.734           0.510       0.670         0.1276 0.717   0.437
#> 5 5 1.000           0.973       0.987         0.1243 0.850   0.586
#> 6 6 0.987           0.959       0.973         0.0103 0.991   0.959

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

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

suggest_best_k(res)

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

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
#> GSM1253056     1  0.0000      1.000 1.000 0.000
#> GSM1253057     1  0.0000      1.000 1.000 0.000
#> GSM1253058     1  0.0000      1.000 1.000 0.000
#> GSM1253059     1  0.0000      1.000 1.000 0.000
#> GSM1253060     1  0.0000      1.000 1.000 0.000
#> GSM1253061     1  0.0000      1.000 1.000 0.000
#> GSM1253062     1  0.0000      1.000 1.000 0.000
#> GSM1253063     1  0.0000      1.000 1.000 0.000
#> GSM1253064     1  0.0000      1.000 1.000 0.000
#> GSM1253065     1  0.0000      1.000 1.000 0.000
#> GSM1253066     1  0.0000      1.000 1.000 0.000
#> GSM1253067     1  0.0000      1.000 1.000 0.000
#> GSM1253068     1  0.0000      1.000 1.000 0.000
#> GSM1253069     1  0.0000      1.000 1.000 0.000
#> GSM1253070     1  0.0000      1.000 1.000 0.000
#> GSM1253071     1  0.0000      1.000 1.000 0.000
#> GSM1253072     1  0.0000      1.000 1.000 0.000
#> GSM1253073     1  0.0000      1.000 1.000 0.000
#> GSM1253074     1  0.0000      1.000 1.000 0.000
#> GSM1253032     1  0.0000      1.000 1.000 0.000
#> GSM1253034     2  0.0000      0.989 0.000 1.000
#> GSM1253039     2  0.0000      0.989 0.000 1.000
#> GSM1253040     2  0.0000      0.989 0.000 1.000
#> GSM1253041     2  0.0000      0.989 0.000 1.000
#> GSM1253046     1  0.0000      1.000 1.000 0.000
#> GSM1253048     2  0.0000      0.989 0.000 1.000
#> GSM1253049     2  0.0000      0.989 0.000 1.000
#> GSM1253052     2  0.0376      0.989 0.004 0.996
#> GSM1253037     2  0.0000      0.989 0.000 1.000
#> GSM1253028     2  0.2236      0.972 0.036 0.964
#> GSM1253029     2  0.0376      0.989 0.004 0.996
#> GSM1253030     2  0.0000      0.989 0.000 1.000
#> GSM1253031     2  0.2236      0.972 0.036 0.964
#> GSM1253033     1  0.0000      1.000 1.000 0.000
#> GSM1253035     2  0.2236      0.972 0.036 0.964
#> GSM1253036     2  0.0376      0.989 0.004 0.996
#> GSM1253038     2  0.0000      0.989 0.000 1.000
#> GSM1253042     2  0.0376      0.989 0.004 0.996
#> GSM1253045     2  0.2236      0.972 0.036 0.964
#> GSM1253043     2  0.2236      0.972 0.036 0.964
#> GSM1253044     2  0.0000      0.989 0.000 1.000
#> GSM1253047     1  0.0000      1.000 1.000 0.000
#> GSM1253050     2  0.0000      0.989 0.000 1.000
#> GSM1253051     2  0.0000      0.989 0.000 1.000
#> GSM1253053     2  0.0376      0.989 0.004 0.996
#> GSM1253054     1  0.0000      1.000 1.000 0.000
#> GSM1253055     2  0.2236      0.972 0.036 0.964
#> GSM1253079     1  0.0000      1.000 1.000 0.000
#> GSM1253083     1  0.0000      1.000 1.000 0.000
#> GSM1253075     1  0.0000      1.000 1.000 0.000
#> GSM1253077     1  0.0000      1.000 1.000 0.000
#> GSM1253076     1  0.0000      1.000 1.000 0.000
#> GSM1253078     1  0.0000      1.000 1.000 0.000
#> GSM1253081     1  0.0000      1.000 1.000 0.000
#> GSM1253080     1  0.0000      1.000 1.000 0.000
#> GSM1253082     1  0.0000      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
#> GSM1253056     3  0.0000      1.000 0.000 0.000 1.000
#> GSM1253057     1  0.6215      0.837 0.572 0.000 0.428
#> GSM1253058     3  0.0000      1.000 0.000 0.000 1.000
#> GSM1253059     3  0.0000      1.000 0.000 0.000 1.000
#> GSM1253060     3  0.0000      1.000 0.000 0.000 1.000
#> GSM1253061     1  0.6215      0.837 0.572 0.000 0.428
#> GSM1253062     1  0.6215      0.837 0.572 0.000 0.428
#> GSM1253063     3  0.0000      1.000 0.000 0.000 1.000
#> GSM1253064     1  0.6215      0.837 0.572 0.000 0.428
#> GSM1253065     3  0.0000      1.000 0.000 0.000 1.000
#> GSM1253066     1  0.6215      0.837 0.572 0.000 0.428
#> GSM1253067     3  0.0000      1.000 0.000 0.000 1.000
#> GSM1253068     1  0.6215      0.837 0.572 0.000 0.428
#> GSM1253069     1  0.6215      0.837 0.572 0.000 0.428
#> GSM1253070     1  0.6215      0.837 0.572 0.000 0.428
#> GSM1253071     3  0.0000      1.000 0.000 0.000 1.000
#> GSM1253072     1  0.6215      0.837 0.572 0.000 0.428
#> GSM1253073     3  0.0000      1.000 0.000 0.000 1.000
#> GSM1253074     1  0.6215      0.837 0.572 0.000 0.428
#> GSM1253032     1  0.0000      0.464 1.000 0.000 0.000
#> GSM1253034     2  0.0000      0.991 0.000 1.000 0.000
#> GSM1253039     2  0.0000      0.991 0.000 1.000 0.000
#> GSM1253040     2  0.0000      0.991 0.000 1.000 0.000
#> GSM1253041     2  0.0000      0.991 0.000 1.000 0.000
#> GSM1253046     1  0.0000      0.464 1.000 0.000 0.000
#> GSM1253048     2  0.0000      0.991 0.000 1.000 0.000
#> GSM1253049     2  0.0000      0.991 0.000 1.000 0.000
#> GSM1253052     2  0.0237      0.990 0.004 0.996 0.000
#> GSM1253037     2  0.0000      0.991 0.000 1.000 0.000
#> GSM1253028     2  0.1411      0.976 0.036 0.964 0.000
#> GSM1253029     2  0.0237      0.990 0.004 0.996 0.000
#> GSM1253030     2  0.0000      0.991 0.000 1.000 0.000
#> GSM1253031     2  0.1411      0.976 0.036 0.964 0.000
#> GSM1253033     1  0.0000      0.464 1.000 0.000 0.000
#> GSM1253035     2  0.1411      0.976 0.036 0.964 0.000
#> GSM1253036     2  0.0237      0.990 0.004 0.996 0.000
#> GSM1253038     2  0.0000      0.991 0.000 1.000 0.000
#> GSM1253042     2  0.0237      0.990 0.004 0.996 0.000
#> GSM1253045     2  0.1411      0.976 0.036 0.964 0.000
#> GSM1253043     2  0.1411      0.976 0.036 0.964 0.000
#> GSM1253044     2  0.0000      0.991 0.000 1.000 0.000
#> GSM1253047     1  0.0000      0.464 1.000 0.000 0.000
#> GSM1253050     2  0.0000      0.991 0.000 1.000 0.000
#> GSM1253051     2  0.0000      0.991 0.000 1.000 0.000
#> GSM1253053     2  0.0237      0.990 0.004 0.996 0.000
#> GSM1253054     1  0.0000      0.464 1.000 0.000 0.000
#> GSM1253055     2  0.1411      0.976 0.036 0.964 0.000
#> GSM1253079     1  0.6215      0.837 0.572 0.000 0.428
#> GSM1253083     1  0.6215      0.837 0.572 0.000 0.428
#> GSM1253075     1  0.6215      0.837 0.572 0.000 0.428
#> GSM1253077     1  0.6215      0.837 0.572 0.000 0.428
#> GSM1253076     1  0.6215      0.837 0.572 0.000 0.428
#> GSM1253078     1  0.6215      0.837 0.572 0.000 0.428
#> GSM1253081     1  0.6215      0.837 0.572 0.000 0.428
#> GSM1253080     1  0.6215      0.837 0.572 0.000 0.428
#> GSM1253082     1  0.6215      0.837 0.572 0.000 0.428

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4
#> GSM1253056     4   0.000      1.000 0.000 0.000 0.000 1.000
#> GSM1253057     1   0.489      0.314 0.588 0.000 0.000 0.412
#> GSM1253058     4   0.000      1.000 0.000 0.000 0.000 1.000
#> GSM1253059     4   0.000      1.000 0.000 0.000 0.000 1.000
#> GSM1253060     4   0.000      1.000 0.000 0.000 0.000 1.000
#> GSM1253061     1   0.489      0.314 0.588 0.000 0.000 0.412
#> GSM1253062     1   0.489      0.314 0.588 0.000 0.000 0.412
#> GSM1253063     4   0.000      1.000 0.000 0.000 0.000 1.000
#> GSM1253064     1   0.489      0.314 0.588 0.000 0.000 0.412
#> GSM1253065     4   0.000      1.000 0.000 0.000 0.000 1.000
#> GSM1253066     1   0.489      0.314 0.588 0.000 0.000 0.412
#> GSM1253067     4   0.000      1.000 0.000 0.000 0.000 1.000
#> GSM1253068     1   0.489      0.314 0.588 0.000 0.000 0.412
#> GSM1253069     1   0.489      0.314 0.588 0.000 0.000 0.412
#> GSM1253070     1   0.489      0.314 0.588 0.000 0.000 0.412
#> GSM1253071     4   0.000      1.000 0.000 0.000 0.000 1.000
#> GSM1253072     1   0.489      0.314 0.588 0.000 0.000 0.412
#> GSM1253073     4   0.000      1.000 0.000 0.000 0.000 1.000
#> GSM1253074     1   0.489      0.314 0.588 0.000 0.000 0.412
#> GSM1253032     2   0.480      0.999 0.340 0.656 0.004 0.000
#> GSM1253034     1   0.777     -0.158 0.412 0.344 0.244 0.000
#> GSM1253039     1   0.777     -0.158 0.412 0.344 0.244 0.000
#> GSM1253040     1   0.777     -0.158 0.412 0.344 0.244 0.000
#> GSM1253041     1   0.777     -0.158 0.412 0.344 0.244 0.000
#> GSM1253046     2   0.480      0.999 0.340 0.656 0.004 0.000
#> GSM1253048     1   0.777     -0.158 0.412 0.344 0.244 0.000
#> GSM1253049     1   0.777     -0.158 0.412 0.344 0.244 0.000
#> GSM1253052     3   0.112      0.917 0.036 0.000 0.964 0.000
#> GSM1253037     1   0.777     -0.158 0.412 0.344 0.244 0.000
#> GSM1253028     3   0.000      0.918 0.000 0.000 1.000 0.000
#> GSM1253029     3   0.112      0.917 0.036 0.000 0.964 0.000
#> GSM1253030     3   0.785      0.293 0.280 0.320 0.400 0.000
#> GSM1253031     3   0.000      0.918 0.000 0.000 1.000 0.000
#> GSM1253033     2   0.480      0.999 0.340 0.656 0.004 0.000
#> GSM1253035     3   0.000      0.918 0.000 0.000 1.000 0.000
#> GSM1253036     3   0.247      0.880 0.056 0.028 0.916 0.000
#> GSM1253038     1   0.777     -0.158 0.412 0.344 0.244 0.000
#> GSM1253042     3   0.112      0.917 0.036 0.000 0.964 0.000
#> GSM1253045     3   0.000      0.918 0.000 0.000 1.000 0.000
#> GSM1253043     3   0.000      0.918 0.000 0.000 1.000 0.000
#> GSM1253044     1   0.777     -0.158 0.412 0.344 0.244 0.000
#> GSM1253047     2   0.480      0.999 0.340 0.656 0.004 0.000
#> GSM1253050     1   0.777     -0.158 0.412 0.344 0.244 0.000
#> GSM1253051     1   0.777     -0.158 0.412 0.344 0.244 0.000
#> GSM1253053     3   0.112      0.917 0.036 0.000 0.964 0.000
#> GSM1253054     2   0.494      0.996 0.340 0.652 0.008 0.000
#> GSM1253055     3   0.000      0.918 0.000 0.000 1.000 0.000
#> GSM1253079     1   0.489      0.314 0.588 0.000 0.000 0.412
#> GSM1253083     1   0.489      0.314 0.588 0.000 0.000 0.412
#> GSM1253075     1   0.489      0.314 0.588 0.000 0.000 0.412
#> GSM1253077     1   0.489      0.314 0.588 0.000 0.000 0.412
#> GSM1253076     1   0.489      0.314 0.588 0.000 0.000 0.412
#> GSM1253078     1   0.489      0.314 0.588 0.000 0.000 0.412
#> GSM1253081     1   0.489      0.314 0.588 0.000 0.000 0.412
#> GSM1253080     1   0.489      0.314 0.588 0.000 0.000 0.412
#> GSM1253082     1   0.489      0.314 0.588 0.000 0.000 0.412

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4    p5
#> GSM1253056     4  0.0404      0.971 0.012 0.000 0.000 0.988 0.000
#> GSM1253057     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000
#> GSM1253058     4  0.0000      0.965 0.000 0.000 0.000 1.000 0.000
#> GSM1253059     4  0.0000      0.965 0.000 0.000 0.000 1.000 0.000
#> GSM1253060     4  0.0404      0.971 0.012 0.000 0.000 0.988 0.000
#> GSM1253061     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000
#> GSM1253062     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000
#> GSM1253063     4  0.0404      0.971 0.012 0.000 0.000 0.988 0.000
#> GSM1253064     1  0.0404      0.990 0.988 0.000 0.000 0.012 0.000
#> GSM1253065     4  0.2516      0.803 0.140 0.000 0.000 0.860 0.000
#> GSM1253066     1  0.0404      0.990 0.988 0.000 0.000 0.012 0.000
#> GSM1253067     4  0.0404      0.971 0.012 0.000 0.000 0.988 0.000
#> GSM1253068     1  0.0404      0.990 0.988 0.000 0.000 0.012 0.000
#> GSM1253069     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000
#> GSM1253070     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000
#> GSM1253071     4  0.0404      0.971 0.012 0.000 0.000 0.988 0.000
#> GSM1253072     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000
#> GSM1253073     4  0.0000      0.965 0.000 0.000 0.000 1.000 0.000
#> GSM1253074     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000
#> GSM1253032     5  0.0000      0.999 0.000 0.000 0.000 0.000 1.000
#> GSM1253034     2  0.0000      0.983 0.000 1.000 0.000 0.000 0.000
#> GSM1253039     2  0.0000      0.983 0.000 1.000 0.000 0.000 0.000
#> GSM1253040     2  0.0000      0.983 0.000 1.000 0.000 0.000 0.000
#> GSM1253041     2  0.0000      0.983 0.000 1.000 0.000 0.000 0.000
#> GSM1253046     5  0.0000      0.999 0.000 0.000 0.000 0.000 1.000
#> GSM1253048     2  0.0000      0.983 0.000 1.000 0.000 0.000 0.000
#> GSM1253049     2  0.0000      0.983 0.000 1.000 0.000 0.000 0.000
#> GSM1253052     3  0.0963      0.957 0.000 0.036 0.964 0.000 0.000
#> GSM1253037     2  0.0000      0.983 0.000 1.000 0.000 0.000 0.000
#> GSM1253028     3  0.0000      0.963 0.000 0.000 1.000 0.000 0.000
#> GSM1253029     3  0.0963      0.957 0.000 0.036 0.964 0.000 0.000
#> GSM1253030     2  0.2690      0.802 0.000 0.844 0.156 0.000 0.000
#> GSM1253031     3  0.0000      0.963 0.000 0.000 1.000 0.000 0.000
#> GSM1253033     5  0.0000      0.999 0.000 0.000 0.000 0.000 1.000
#> GSM1253035     3  0.0000      0.963 0.000 0.000 1.000 0.000 0.000
#> GSM1253036     3  0.2813      0.808 0.000 0.168 0.832 0.000 0.000
#> GSM1253038     2  0.0000      0.983 0.000 1.000 0.000 0.000 0.000
#> GSM1253042     3  0.0963      0.957 0.000 0.036 0.964 0.000 0.000
#> GSM1253045     3  0.0000      0.963 0.000 0.000 1.000 0.000 0.000
#> GSM1253043     3  0.0000      0.963 0.000 0.000 1.000 0.000 0.000
#> GSM1253044     2  0.0000      0.983 0.000 1.000 0.000 0.000 0.000
#> GSM1253047     5  0.0000      0.999 0.000 0.000 0.000 0.000 1.000
#> GSM1253050     2  0.0000      0.983 0.000 1.000 0.000 0.000 0.000
#> GSM1253051     2  0.0000      0.983 0.000 1.000 0.000 0.000 0.000
#> GSM1253053     3  0.0963      0.957 0.000 0.036 0.964 0.000 0.000
#> GSM1253054     5  0.0162      0.996 0.000 0.000 0.004 0.000 0.996
#> GSM1253055     3  0.0000      0.963 0.000 0.000 1.000 0.000 0.000
#> GSM1253079     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000
#> GSM1253081     1  0.0404      0.990 0.988 0.000 0.000 0.012 0.000
#> GSM1253080     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000
#> GSM1253082     1  0.0510      0.986 0.984 0.000 0.000 0.016 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
#> GSM1253056     4  0.0363      0.943 0.012 0.000 0.000 0.988 0.000 0.000
#> GSM1253057     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253058     6  0.2730      1.000 0.000 0.000 0.000 0.192 0.000 0.808
#> GSM1253059     6  0.2730      1.000 0.000 0.000 0.000 0.192 0.000 0.808
#> GSM1253060     4  0.0363      0.943 0.012 0.000 0.000 0.988 0.000 0.000
#> GSM1253061     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253062     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253063     4  0.0363      0.943 0.012 0.000 0.000 0.988 0.000 0.000
#> GSM1253064     1  0.0363      0.989 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM1253065     4  0.2260      0.714 0.140 0.000 0.000 0.860 0.000 0.000
#> GSM1253066     1  0.0363      0.989 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM1253067     4  0.1074      0.922 0.012 0.000 0.000 0.960 0.000 0.028
#> GSM1253068     1  0.0363      0.989 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM1253069     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253070     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253071     4  0.0363      0.943 0.012 0.000 0.000 0.988 0.000 0.000
#> GSM1253072     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253073     4  0.0260      0.926 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM1253074     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253032     5  0.0000      0.930 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1253034     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253039     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253040     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253041     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253046     5  0.2219      0.895 0.000 0.000 0.000 0.000 0.864 0.136
#> GSM1253048     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253049     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253052     3  0.0865      0.953 0.000 0.036 0.964 0.000 0.000 0.000
#> GSM1253037     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253028     3  0.0000      0.959 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253029     3  0.0865      0.953 0.000 0.036 0.964 0.000 0.000 0.000
#> GSM1253030     2  0.2416      0.779 0.000 0.844 0.156 0.000 0.000 0.000
#> GSM1253031     3  0.0000      0.959 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253033     5  0.2980      0.862 0.000 0.000 0.000 0.008 0.800 0.192
#> GSM1253035     3  0.0000      0.959 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253036     3  0.2527      0.785 0.000 0.168 0.832 0.000 0.000 0.000
#> GSM1253038     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253042     3  0.0865      0.953 0.000 0.036 0.964 0.000 0.000 0.000
#> GSM1253045     3  0.0000      0.959 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253043     3  0.0000      0.959 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253044     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253047     5  0.0000      0.930 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1253050     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253051     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253053     3  0.0865      0.953 0.000 0.036 0.964 0.000 0.000 0.000
#> GSM1253054     5  0.0146      0.929 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM1253055     3  0.0000      0.959 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253079     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253081     1  0.0363      0.989 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM1253080     1  0.0000      0.996 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253082     1  0.0458      0.985 0.984 0.000 0.000 0.016 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 infection(p) disease.state(p) individual(p) k
#> CV:hclust 56     0.018077         1.69e-08         0.955 2
#> CV:hclust 51     0.000101         1.43e-11         0.940 3
#> CV:hclust 25           NA         1.05e-05         0.512 4
#> CV:hclust 56     0.000334         2.92e-12         0.862 5
#> CV:hclust 56     0.000853         5.02e-11         0.923 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 51979 rows and 56 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#>   Subgroups are detected by 'kmeans' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 2.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk CV-kmeans-collect-plots

The plots are:

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

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

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

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

select_partition_number(res)

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

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           1.000       1.000         0.4934 0.507   0.507
#> 3 3 0.663           0.678       0.822         0.2841 0.875   0.757
#> 4 4 0.786           0.854       0.840         0.1329 0.803   0.535
#> 5 5 0.701           0.916       0.880         0.0673 0.935   0.758
#> 6 6 0.832           0.848       0.841         0.0468 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
#> GSM1253056     1  0.0000      1.000 1.000 0.000
#> GSM1253057     1  0.0000      1.000 1.000 0.000
#> GSM1253058     1  0.0000      1.000 1.000 0.000
#> GSM1253059     1  0.0000      1.000 1.000 0.000
#> GSM1253060     1  0.0000      1.000 1.000 0.000
#> GSM1253061     1  0.0000      1.000 1.000 0.000
#> GSM1253062     1  0.0000      1.000 1.000 0.000
#> GSM1253063     1  0.0000      1.000 1.000 0.000
#> GSM1253064     1  0.0000      1.000 1.000 0.000
#> GSM1253065     1  0.0000      1.000 1.000 0.000
#> GSM1253066     1  0.0000      1.000 1.000 0.000
#> GSM1253067     1  0.0000      1.000 1.000 0.000
#> GSM1253068     1  0.0000      1.000 1.000 0.000
#> GSM1253069     1  0.0000      1.000 1.000 0.000
#> GSM1253070     1  0.0000      1.000 1.000 0.000
#> GSM1253071     1  0.0000      1.000 1.000 0.000
#> GSM1253072     1  0.0000      1.000 1.000 0.000
#> GSM1253073     1  0.0000      1.000 1.000 0.000
#> GSM1253074     1  0.0000      1.000 1.000 0.000
#> GSM1253032     1  0.0000      1.000 1.000 0.000
#> GSM1253034     2  0.0000      1.000 0.000 1.000
#> GSM1253039     2  0.0000      1.000 0.000 1.000
#> GSM1253040     2  0.0000      1.000 0.000 1.000
#> GSM1253041     2  0.0000      1.000 0.000 1.000
#> GSM1253046     1  0.0000      1.000 1.000 0.000
#> GSM1253048     2  0.0000      1.000 0.000 1.000
#> GSM1253049     2  0.0000      1.000 0.000 1.000
#> GSM1253052     2  0.0000      1.000 0.000 1.000
#> GSM1253037     2  0.0000      1.000 0.000 1.000
#> GSM1253028     2  0.0000      1.000 0.000 1.000
#> GSM1253029     2  0.0000      1.000 0.000 1.000
#> GSM1253030     2  0.0000      1.000 0.000 1.000
#> GSM1253031     2  0.0000      1.000 0.000 1.000
#> GSM1253033     1  0.0000      1.000 1.000 0.000
#> GSM1253035     2  0.0000      1.000 0.000 1.000
#> GSM1253036     2  0.0000      1.000 0.000 1.000
#> GSM1253038     2  0.0000      1.000 0.000 1.000
#> GSM1253042     2  0.0000      1.000 0.000 1.000
#> GSM1253045     2  0.0000      1.000 0.000 1.000
#> GSM1253043     2  0.0000      1.000 0.000 1.000
#> GSM1253044     2  0.0000      1.000 0.000 1.000
#> GSM1253047     1  0.0000      1.000 1.000 0.000
#> GSM1253050     2  0.0000      1.000 0.000 1.000
#> GSM1253051     2  0.0000      1.000 0.000 1.000
#> GSM1253053     2  0.0000      1.000 0.000 1.000
#> GSM1253054     1  0.0376      0.996 0.996 0.004
#> GSM1253055     2  0.0000      1.000 0.000 1.000
#> GSM1253079     1  0.0000      1.000 1.000 0.000
#> GSM1253083     1  0.0000      1.000 1.000 0.000
#> GSM1253075     1  0.0000      1.000 1.000 0.000
#> GSM1253077     1  0.0000      1.000 1.000 0.000
#> GSM1253076     1  0.0000      1.000 1.000 0.000
#> GSM1253078     1  0.0000      1.000 1.000 0.000
#> GSM1253081     1  0.0000      1.000 1.000 0.000
#> GSM1253080     1  0.0000      1.000 1.000 0.000
#> GSM1253082     1  0.0000      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
#> GSM1253056     1  0.6274      0.569 0.544 0.000 0.456
#> GSM1253057     1  0.0000      0.802 1.000 0.000 0.000
#> GSM1253058     1  0.6274      0.569 0.544 0.000 0.456
#> GSM1253059     1  0.6274      0.569 0.544 0.000 0.456
#> GSM1253060     1  0.6274      0.569 0.544 0.000 0.456
#> GSM1253061     1  0.0000      0.802 1.000 0.000 0.000
#> GSM1253062     1  0.0000      0.802 1.000 0.000 0.000
#> GSM1253063     1  0.6274      0.569 0.544 0.000 0.456
#> GSM1253064     1  0.0000      0.802 1.000 0.000 0.000
#> GSM1253065     1  0.6274      0.569 0.544 0.000 0.456
#> GSM1253066     1  0.0000      0.802 1.000 0.000 0.000
#> GSM1253067     1  0.6274      0.569 0.544 0.000 0.456
#> GSM1253068     1  0.0000      0.802 1.000 0.000 0.000
#> GSM1253069     1  0.0000      0.802 1.000 0.000 0.000
#> GSM1253070     1  0.0892      0.789 0.980 0.000 0.020
#> GSM1253071     1  0.6274      0.569 0.544 0.000 0.456
#> GSM1253072     1  0.0000      0.802 1.000 0.000 0.000
#> GSM1253073     1  0.6274      0.569 0.544 0.000 0.456
#> GSM1253074     1  0.0000      0.802 1.000 0.000 0.000
#> GSM1253032     3  0.5882      0.716 0.348 0.000 0.652
#> GSM1253034     2  0.0000      0.807 0.000 1.000 0.000
#> GSM1253039     2  0.0000      0.807 0.000 1.000 0.000
#> GSM1253040     2  0.0000      0.807 0.000 1.000 0.000
#> GSM1253041     2  0.0000      0.807 0.000 1.000 0.000
#> GSM1253046     3  0.6045      0.694 0.380 0.000 0.620
#> GSM1253048     2  0.0000      0.807 0.000 1.000 0.000
#> GSM1253049     2  0.0000      0.807 0.000 1.000 0.000
#> GSM1253052     2  0.6045      0.524 0.000 0.620 0.380
#> GSM1253037     2  0.0000      0.807 0.000 1.000 0.000
#> GSM1253028     2  0.6252      0.404 0.000 0.556 0.444
#> GSM1253029     2  0.4654      0.710 0.000 0.792 0.208
#> GSM1253030     2  0.0000      0.807 0.000 1.000 0.000
#> GSM1253031     2  0.6252      0.404 0.000 0.556 0.444
#> GSM1253033     3  0.6026      0.696 0.376 0.000 0.624
#> GSM1253035     2  0.6062      0.517 0.000 0.616 0.384
#> GSM1253036     2  0.4654      0.710 0.000 0.792 0.208
#> GSM1253038     2  0.0000      0.807 0.000 1.000 0.000
#> GSM1253042     2  0.4654      0.710 0.000 0.792 0.208
#> GSM1253045     3  0.6483     -0.242 0.004 0.452 0.544
#> GSM1253043     3  0.6274     -0.255 0.000 0.456 0.544
#> GSM1253044     2  0.0000      0.807 0.000 1.000 0.000
#> GSM1253047     3  0.6008      0.704 0.372 0.000 0.628
#> GSM1253050     2  0.0000      0.807 0.000 1.000 0.000
#> GSM1253051     2  0.0000      0.807 0.000 1.000 0.000
#> GSM1253053     2  0.6045      0.524 0.000 0.620 0.380
#> GSM1253054     3  0.5882      0.716 0.348 0.000 0.652
#> GSM1253055     2  0.6252      0.404 0.000 0.556 0.444
#> GSM1253079     1  0.0000      0.802 1.000 0.000 0.000
#> GSM1253083     1  0.0000      0.802 1.000 0.000 0.000
#> GSM1253075     1  0.0000      0.802 1.000 0.000 0.000
#> GSM1253077     1  0.0000      0.802 1.000 0.000 0.000
#> GSM1253076     1  0.0000      0.802 1.000 0.000 0.000
#> GSM1253078     1  0.0000      0.802 1.000 0.000 0.000
#> GSM1253081     1  0.0000      0.802 1.000 0.000 0.000
#> GSM1253080     1  0.0000      0.802 1.000 0.000 0.000
#> GSM1253082     1  0.0000      0.802 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
#> GSM1253056     4  0.0000      0.996 0.000 0.000 0.000 1.000
#> GSM1253057     1  0.4250      0.998 0.724 0.000 0.000 0.276
#> GSM1253058     4  0.0592      0.989 0.000 0.000 0.016 0.984
#> GSM1253059     4  0.0592      0.989 0.000 0.000 0.016 0.984
#> GSM1253060     4  0.0000      0.996 0.000 0.000 0.000 1.000
#> GSM1253061     1  0.4250      0.998 0.724 0.000 0.000 0.276
#> GSM1253062     1  0.4250      0.998 0.724 0.000 0.000 0.276
#> GSM1253063     4  0.0000      0.996 0.000 0.000 0.000 1.000
#> GSM1253064     1  0.4250      0.998 0.724 0.000 0.000 0.276
#> GSM1253065     4  0.0000      0.996 0.000 0.000 0.000 1.000
#> GSM1253066     1  0.4250      0.998 0.724 0.000 0.000 0.276
#> GSM1253067     4  0.0000      0.996 0.000 0.000 0.000 1.000
#> GSM1253068     1  0.4250      0.998 0.724 0.000 0.000 0.276
#> GSM1253069     1  0.4250      0.998 0.724 0.000 0.000 0.276
#> GSM1253070     1  0.4304      0.988 0.716 0.000 0.000 0.284
#> GSM1253071     4  0.0000      0.996 0.000 0.000 0.000 1.000
#> GSM1253072     1  0.4250      0.998 0.724 0.000 0.000 0.276
#> GSM1253073     4  0.0188      0.995 0.000 0.000 0.004 0.996
#> GSM1253074     1  0.4250      0.998 0.724 0.000 0.000 0.276
#> GSM1253032     3  0.1059      0.703 0.016 0.000 0.972 0.012
#> GSM1253034     2  0.0000      0.874 0.000 1.000 0.000 0.000
#> GSM1253039     2  0.0592      0.874 0.016 0.984 0.000 0.000
#> GSM1253040     2  0.0592      0.874 0.016 0.984 0.000 0.000
#> GSM1253041     2  0.0000      0.874 0.000 1.000 0.000 0.000
#> GSM1253046     3  0.1677      0.693 0.040 0.000 0.948 0.012
#> GSM1253048     2  0.0000      0.874 0.000 1.000 0.000 0.000
#> GSM1253049     2  0.0592      0.874 0.016 0.984 0.000 0.000
#> GSM1253052     3  0.7576      0.619 0.260 0.256 0.484 0.000
#> GSM1253037     2  0.0592      0.874 0.016 0.984 0.000 0.000
#> GSM1253028     3  0.7159      0.693 0.260 0.188 0.552 0.000
#> GSM1253029     2  0.7249      0.177 0.260 0.540 0.200 0.000
#> GSM1253030     2  0.0592      0.874 0.016 0.984 0.000 0.000
#> GSM1253031     3  0.7159      0.693 0.260 0.188 0.552 0.000
#> GSM1253033     3  0.1724      0.692 0.020 0.000 0.948 0.032
#> GSM1253035     3  0.7557      0.625 0.260 0.252 0.488 0.000
#> GSM1253036     2  0.7249      0.177 0.260 0.540 0.200 0.000
#> GSM1253038     2  0.0592      0.874 0.016 0.984 0.000 0.000
#> GSM1253042     2  0.7249      0.177 0.260 0.540 0.200 0.000
#> GSM1253045     3  0.4576      0.736 0.260 0.012 0.728 0.000
#> GSM1253043     3  0.4576      0.736 0.260 0.012 0.728 0.000
#> GSM1253044     2  0.0000      0.874 0.000 1.000 0.000 0.000
#> GSM1253047     3  0.1677      0.693 0.040 0.000 0.948 0.012
#> GSM1253050     2  0.0000      0.874 0.000 1.000 0.000 0.000
#> GSM1253051     2  0.0000      0.874 0.000 1.000 0.000 0.000
#> GSM1253053     3  0.7576      0.619 0.260 0.256 0.484 0.000
#> GSM1253054     3  0.0592      0.706 0.016 0.000 0.984 0.000
#> GSM1253055     3  0.7159      0.693 0.260 0.188 0.552 0.000
#> GSM1253079     1  0.4250      0.998 0.724 0.000 0.000 0.276
#> GSM1253083     1  0.4250      0.998 0.724 0.000 0.000 0.276
#> GSM1253075     1  0.4250      0.998 0.724 0.000 0.000 0.276
#> GSM1253077     1  0.4250      0.998 0.724 0.000 0.000 0.276
#> GSM1253076     1  0.4250      0.998 0.724 0.000 0.000 0.276
#> GSM1253078     1  0.4250      0.998 0.724 0.000 0.000 0.276
#> GSM1253081     1  0.4304      0.989 0.716 0.000 0.000 0.284
#> GSM1253080     1  0.4250      0.998 0.724 0.000 0.000 0.276
#> GSM1253082     1  0.4304      0.989 0.716 0.000 0.000 0.284

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4    p5
#> GSM1253056     4  0.2648      0.972 0.152 0.000 0.000 0.848 0.000
#> GSM1253057     1  0.0000      0.920 1.000 0.000 0.000 0.000 0.000
#> GSM1253058     4  0.4903      0.940 0.152 0.000 0.036 0.752 0.060
#> GSM1253059     4  0.4903      0.940 0.152 0.000 0.036 0.752 0.060
#> GSM1253060     4  0.2648      0.972 0.152 0.000 0.000 0.848 0.000
#> GSM1253061     1  0.2932      0.895 0.864 0.000 0.032 0.000 0.104
#> GSM1253062     1  0.0992      0.917 0.968 0.000 0.024 0.000 0.008
#> GSM1253063     4  0.2648      0.972 0.152 0.000 0.000 0.848 0.000
#> GSM1253064     1  0.4071      0.875 0.816 0.000 0.052 0.028 0.104
#> GSM1253065     4  0.3394      0.957 0.152 0.000 0.020 0.824 0.004
#> GSM1253066     1  0.3985      0.878 0.820 0.000 0.052 0.024 0.104
#> GSM1253067     4  0.3516      0.967 0.152 0.000 0.008 0.820 0.020
#> GSM1253068     1  0.3800      0.882 0.828 0.000 0.052 0.016 0.104
#> GSM1253069     1  0.0324      0.919 0.992 0.000 0.004 0.000 0.004
#> GSM1253070     1  0.3170      0.893 0.856 0.000 0.036 0.004 0.104
#> GSM1253071     4  0.2648      0.972 0.152 0.000 0.000 0.848 0.000
#> GSM1253072     1  0.3851      0.882 0.824 0.000 0.052 0.016 0.108
#> GSM1253073     4  0.3606      0.966 0.152 0.000 0.008 0.816 0.024
#> GSM1253074     1  0.0324      0.919 0.992 0.000 0.004 0.000 0.004
#> GSM1253032     5  0.3398      0.998 0.000 0.000 0.216 0.004 0.780
#> GSM1253034     2  0.0162      0.935 0.000 0.996 0.000 0.000 0.004
#> GSM1253039     2  0.3130      0.931 0.000 0.856 0.000 0.096 0.048
#> GSM1253040     2  0.3130      0.931 0.000 0.856 0.000 0.096 0.048
#> GSM1253041     2  0.0162      0.935 0.000 0.996 0.000 0.000 0.004
#> GSM1253046     5  0.3398      0.998 0.000 0.000 0.216 0.004 0.780
#> GSM1253048     2  0.0000      0.935 0.000 1.000 0.000 0.000 0.000
#> GSM1253049     2  0.3003      0.933 0.000 0.864 0.000 0.092 0.044
#> GSM1253052     3  0.2984      0.884 0.000 0.108 0.860 0.032 0.000
#> GSM1253037     2  0.3075      0.932 0.000 0.860 0.000 0.092 0.048
#> GSM1253028     3  0.2597      0.885 0.000 0.092 0.884 0.024 0.000
#> GSM1253029     3  0.4066      0.822 0.000 0.196 0.768 0.032 0.004
#> GSM1253030     2  0.2903      0.934 0.000 0.872 0.000 0.080 0.048
#> GSM1253031     3  0.2597      0.885 0.000 0.092 0.884 0.024 0.000
#> GSM1253033     5  0.3398      0.998 0.000 0.000 0.216 0.004 0.780
#> GSM1253035     3  0.2020      0.889 0.000 0.100 0.900 0.000 0.000
#> GSM1253036     3  0.3631      0.826 0.000 0.196 0.788 0.008 0.008
#> GSM1253038     2  0.3130      0.931 0.000 0.856 0.000 0.096 0.048
#> GSM1253042     3  0.4066      0.822 0.000 0.196 0.768 0.032 0.004
#> GSM1253045     3  0.2707      0.760 0.000 0.000 0.876 0.024 0.100
#> GSM1253043     3  0.2707      0.760 0.000 0.000 0.876 0.024 0.100
#> GSM1253044     2  0.0000      0.935 0.000 1.000 0.000 0.000 0.000
#> GSM1253047     5  0.3398      0.998 0.000 0.000 0.216 0.004 0.780
#> GSM1253050     2  0.0000      0.935 0.000 1.000 0.000 0.000 0.000
#> GSM1253051     2  0.0162      0.935 0.000 0.996 0.000 0.000 0.004
#> GSM1253053     3  0.2984      0.884 0.000 0.108 0.860 0.032 0.000
#> GSM1253054     5  0.3274      0.993 0.000 0.000 0.220 0.000 0.780
#> GSM1253055     3  0.2408      0.886 0.000 0.092 0.892 0.016 0.000
#> GSM1253079     1  0.0000      0.920 1.000 0.000 0.000 0.000 0.000
#> GSM1253083     1  0.0324      0.919 0.992 0.000 0.004 0.000 0.004
#> GSM1253075     1  0.0000      0.920 1.000 0.000 0.000 0.000 0.000
#> GSM1253077     1  0.0162      0.920 0.996 0.000 0.004 0.000 0.000
#> GSM1253076     1  0.0162      0.920 0.996 0.000 0.004 0.000 0.000
#> GSM1253078     1  0.0162      0.920 0.996 0.000 0.004 0.000 0.000
#> GSM1253081     1  0.4381      0.863 0.800 0.000 0.052 0.044 0.104
#> GSM1253080     1  0.0324      0.919 0.992 0.000 0.004 0.000 0.004
#> GSM1253082     1  0.4381      0.863 0.800 0.000 0.052 0.044 0.104

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4    p5    p6
#> GSM1253056     4  0.1411      0.914 0.060 0.000 0.000 0.936 0.000 0.004
#> GSM1253057     1  0.3942      0.821 0.624 0.000 0.004 0.000 0.004 0.368
#> GSM1253058     4  0.5941      0.792 0.060 0.000 0.044 0.656 0.064 0.176
#> GSM1253059     4  0.5911      0.792 0.060 0.000 0.044 0.660 0.064 0.172
#> GSM1253060     4  0.1610      0.910 0.084 0.000 0.000 0.916 0.000 0.000
#> GSM1253061     1  0.2196      0.780 0.884 0.000 0.004 0.000 0.004 0.108
#> GSM1253062     1  0.3452      0.822 0.736 0.000 0.004 0.000 0.004 0.256
#> GSM1253063     4  0.1267      0.914 0.060 0.000 0.000 0.940 0.000 0.000
#> GSM1253064     1  0.1007      0.737 0.956 0.000 0.000 0.044 0.000 0.000
#> GSM1253065     4  0.2320      0.878 0.132 0.000 0.000 0.864 0.000 0.004
#> GSM1253066     1  0.0790      0.745 0.968 0.000 0.000 0.032 0.000 0.000
#> GSM1253067     4  0.2258      0.906 0.060 0.000 0.000 0.896 0.000 0.044
#> GSM1253068     1  0.0790      0.745 0.968 0.000 0.000 0.032 0.000 0.000
#> GSM1253069     1  0.4187      0.820 0.624 0.000 0.004 0.000 0.016 0.356
#> GSM1253070     1  0.1732      0.771 0.920 0.000 0.004 0.000 0.004 0.072
#> GSM1253071     4  0.1610      0.910 0.084 0.000 0.000 0.916 0.000 0.000
#> GSM1253072     1  0.0790      0.745 0.968 0.000 0.000 0.032 0.000 0.000
#> GSM1253073     4  0.3113      0.899 0.060 0.000 0.020 0.864 0.008 0.048
#> GSM1253074     1  0.4187      0.820 0.624 0.000 0.004 0.000 0.016 0.356
#> GSM1253032     5  0.2006      0.986 0.000 0.000 0.104 0.004 0.892 0.000
#> GSM1253034     2  0.3589      0.876 0.000 0.752 0.000 0.012 0.008 0.228
#> GSM1253039     2  0.0405      0.870 0.000 0.988 0.000 0.000 0.004 0.008
#> GSM1253040     2  0.0405      0.870 0.000 0.988 0.000 0.000 0.004 0.008
#> GSM1253041     2  0.3298      0.877 0.000 0.756 0.000 0.000 0.008 0.236
#> GSM1253046     5  0.2405      0.982 0.000 0.000 0.100 0.004 0.880 0.016
#> GSM1253048     2  0.3323      0.876 0.000 0.752 0.000 0.000 0.008 0.240
#> GSM1253049     2  0.0146      0.872 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM1253052     3  0.4846      0.855 0.000 0.092 0.716 0.036 0.000 0.156
#> GSM1253037     2  0.0146      0.872 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM1253028     3  0.1556      0.856 0.000 0.080 0.920 0.000 0.000 0.000
#> GSM1253029     3  0.5426      0.826 0.000 0.148 0.656 0.036 0.000 0.160
#> GSM1253030     2  0.1261      0.873 0.000 0.952 0.000 0.024 0.000 0.024
#> GSM1253031     3  0.1556      0.856 0.000 0.080 0.920 0.000 0.000 0.000
#> GSM1253033     5  0.2870      0.973 0.000 0.000 0.100 0.004 0.856 0.040
#> GSM1253035     3  0.3852      0.872 0.000 0.092 0.800 0.020 0.000 0.088
#> GSM1253036     3  0.3219      0.837 0.000 0.148 0.820 0.012 0.000 0.020
#> GSM1253038     2  0.0405      0.870 0.000 0.988 0.000 0.000 0.004 0.008
#> GSM1253042     3  0.5426      0.826 0.000 0.148 0.656 0.036 0.000 0.160
#> GSM1253045     3  0.1858      0.766 0.000 0.000 0.904 0.000 0.092 0.004
#> GSM1253043     3  0.1806      0.770 0.000 0.000 0.908 0.000 0.088 0.004
#> GSM1253044     2  0.3323      0.876 0.000 0.752 0.000 0.000 0.008 0.240
#> GSM1253047     5  0.2149      0.985 0.000 0.000 0.104 0.004 0.888 0.004
#> GSM1253050     2  0.3323      0.876 0.000 0.752 0.000 0.000 0.008 0.240
#> GSM1253051     2  0.3589      0.876 0.000 0.752 0.000 0.012 0.008 0.228
#> GSM1253053     3  0.4846      0.855 0.000 0.092 0.716 0.036 0.000 0.156
#> GSM1253054     5  0.2053      0.983 0.000 0.000 0.108 0.000 0.888 0.004
#> GSM1253055     3  0.3439      0.870 0.000 0.080 0.832 0.020 0.000 0.068
#> GSM1253079     1  0.3930      0.822 0.628 0.000 0.004 0.000 0.004 0.364
#> GSM1253083     1  0.4224      0.826 0.660 0.000 0.012 0.000 0.016 0.312
#> GSM1253075     1  0.3972      0.827 0.664 0.000 0.012 0.000 0.004 0.320
#> GSM1253077     1  0.3789      0.826 0.660 0.000 0.008 0.000 0.000 0.332
#> GSM1253076     1  0.3789      0.826 0.660 0.000 0.008 0.000 0.000 0.332
#> GSM1253078     1  0.3789      0.826 0.660 0.000 0.008 0.000 0.000 0.332
#> GSM1253081     1  0.1444      0.713 0.928 0.000 0.000 0.072 0.000 0.000
#> GSM1253080     1  0.4187      0.820 0.624 0.000 0.004 0.000 0.016 0.356
#> GSM1253082     1  0.1444      0.713 0.928 0.000 0.000 0.072 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 infection(p) disease.state(p) individual(p) k
#> CV:kmeans 56     0.018077         1.69e-08         0.955 2
#> CV:kmeans 51     0.011237         2.87e-09         0.897 3
#> CV:kmeans 53     0.000226         6.92e-12         0.914 4
#> CV:kmeans 56     0.000334         2.92e-12         0.862 5
#> CV:kmeans 56     0.000334         2.92e-12         0.862 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 51979 rows and 56 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 5.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk CV-skmeans-collect-plots

The plots are:

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

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

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

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

select_partition_number(res)

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

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.980       0.993         0.4968 0.501   0.501
#> 3 3 1.000           0.997       0.997         0.2190 0.879   0.761
#> 4 4 1.000           0.996       0.995         0.1809 0.889   0.719
#> 5 5 0.955           0.873       0.944         0.0818 0.921   0.730
#> 6 6 0.855           0.630       0.778         0.0499 0.940   0.739

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

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

suggest_best_k(res)

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

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

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

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

show/hide code output

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

#>            class entropy silhouette    p1    p2
#> GSM1253056     1    0.00      1.000 1.000 0.000
#> GSM1253057     1    0.00      1.000 1.000 0.000
#> GSM1253058     1    0.00      1.000 1.000 0.000
#> GSM1253059     1    0.00      1.000 1.000 0.000
#> GSM1253060     1    0.00      1.000 1.000 0.000
#> GSM1253061     1    0.00      1.000 1.000 0.000
#> GSM1253062     1    0.00      1.000 1.000 0.000
#> GSM1253063     1    0.00      1.000 1.000 0.000
#> GSM1253064     1    0.00      1.000 1.000 0.000
#> GSM1253065     1    0.00      1.000 1.000 0.000
#> GSM1253066     1    0.00      1.000 1.000 0.000
#> GSM1253067     1    0.00      1.000 1.000 0.000
#> GSM1253068     1    0.00      1.000 1.000 0.000
#> GSM1253069     1    0.00      1.000 1.000 0.000
#> GSM1253070     1    0.00      1.000 1.000 0.000
#> GSM1253071     1    0.00      1.000 1.000 0.000
#> GSM1253072     1    0.00      1.000 1.000 0.000
#> GSM1253073     1    0.00      1.000 1.000 0.000
#> GSM1253074     1    0.00      1.000 1.000 0.000
#> GSM1253032     1    0.00      1.000 1.000 0.000
#> GSM1253034     2    0.00      0.982 0.000 1.000
#> GSM1253039     2    0.00      0.982 0.000 1.000
#> GSM1253040     2    0.00      0.982 0.000 1.000
#> GSM1253041     2    0.00      0.982 0.000 1.000
#> GSM1253046     1    0.00      1.000 1.000 0.000
#> GSM1253048     2    0.00      0.982 0.000 1.000
#> GSM1253049     2    0.00      0.982 0.000 1.000
#> GSM1253052     2    0.00      0.982 0.000 1.000
#> GSM1253037     2    0.00      0.982 0.000 1.000
#> GSM1253028     2    0.00      0.982 0.000 1.000
#> GSM1253029     2    0.00      0.982 0.000 1.000
#> GSM1253030     2    0.00      0.982 0.000 1.000
#> GSM1253031     2    0.00      0.982 0.000 1.000
#> GSM1253033     1    0.00      1.000 1.000 0.000
#> GSM1253035     2    0.00      0.982 0.000 1.000
#> GSM1253036     2    0.00      0.982 0.000 1.000
#> GSM1253038     2    0.00      0.982 0.000 1.000
#> GSM1253042     2    0.00      0.982 0.000 1.000
#> GSM1253045     2    0.00      0.982 0.000 1.000
#> GSM1253043     2    0.00      0.982 0.000 1.000
#> GSM1253044     2    0.00      0.982 0.000 1.000
#> GSM1253047     1    0.00      1.000 1.000 0.000
#> GSM1253050     2    0.00      0.982 0.000 1.000
#> GSM1253051     2    0.00      0.982 0.000 1.000
#> GSM1253053     2    0.00      0.982 0.000 1.000
#> GSM1253054     2    0.98      0.288 0.416 0.584
#> GSM1253055     2    0.00      0.982 0.000 1.000
#> GSM1253079     1    0.00      1.000 1.000 0.000
#> GSM1253083     1    0.00      1.000 1.000 0.000
#> GSM1253075     1    0.00      1.000 1.000 0.000
#> GSM1253077     1    0.00      1.000 1.000 0.000
#> GSM1253076     1    0.00      1.000 1.000 0.000
#> GSM1253078     1    0.00      1.000 1.000 0.000
#> GSM1253081     1    0.00      1.000 1.000 0.000
#> GSM1253080     1    0.00      1.000 1.000 0.000
#> GSM1253082     1    0.00      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
#> GSM1253056     1  0.0592      0.993 0.988 0.000 0.012
#> GSM1253057     1  0.0000      0.996 1.000 0.000 0.000
#> GSM1253058     1  0.0592      0.993 0.988 0.000 0.012
#> GSM1253059     1  0.0592      0.993 0.988 0.000 0.012
#> GSM1253060     1  0.0592      0.993 0.988 0.000 0.012
#> GSM1253061     1  0.0000      0.996 1.000 0.000 0.000
#> GSM1253062     1  0.0000      0.996 1.000 0.000 0.000
#> GSM1253063     1  0.0592      0.993 0.988 0.000 0.012
#> GSM1253064     1  0.0000      0.996 1.000 0.000 0.000
#> GSM1253065     1  0.0592      0.993 0.988 0.000 0.012
#> GSM1253066     1  0.0000      0.996 1.000 0.000 0.000
#> GSM1253067     1  0.0592      0.993 0.988 0.000 0.012
#> GSM1253068     1  0.0000      0.996 1.000 0.000 0.000
#> GSM1253069     1  0.0000      0.996 1.000 0.000 0.000
#> GSM1253070     1  0.0000      0.996 1.000 0.000 0.000
#> GSM1253071     1  0.0592      0.993 0.988 0.000 0.012
#> GSM1253072     1  0.0000      0.996 1.000 0.000 0.000
#> GSM1253073     1  0.0592      0.993 0.988 0.000 0.012
#> GSM1253074     1  0.0000      0.996 1.000 0.000 0.000
#> GSM1253032     3  0.0237      0.995 0.004 0.000 0.996
#> GSM1253034     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253039     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253040     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253041     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253046     3  0.0237      0.995 0.004 0.000 0.996
#> GSM1253048     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253049     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253052     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253037     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253028     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253029     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253030     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253031     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253033     3  0.0237      0.995 0.004 0.000 0.996
#> GSM1253035     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253036     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253038     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253042     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253045     3  0.0592      0.990 0.000 0.012 0.988
#> GSM1253043     3  0.0592      0.990 0.000 0.012 0.988
#> GSM1253044     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253047     3  0.0237      0.995 0.004 0.000 0.996
#> GSM1253050     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253051     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253053     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253054     3  0.0475      0.994 0.004 0.004 0.992
#> GSM1253055     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253079     1  0.0000      0.996 1.000 0.000 0.000
#> GSM1253083     1  0.0000      0.996 1.000 0.000 0.000
#> GSM1253075     1  0.0000      0.996 1.000 0.000 0.000
#> GSM1253077     1  0.0000      0.996 1.000 0.000 0.000
#> GSM1253076     1  0.0000      0.996 1.000 0.000 0.000
#> GSM1253078     1  0.0000      0.996 1.000 0.000 0.000
#> GSM1253081     1  0.0000      0.996 1.000 0.000 0.000
#> GSM1253080     1  0.0000      0.996 1.000 0.000 0.000
#> GSM1253082     1  0.0237      0.995 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
#> GSM1253056     4  0.0592      1.000 0.016 0.000 0.000 0.984
#> GSM1253057     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM1253058     4  0.0592      1.000 0.016 0.000 0.000 0.984
#> GSM1253059     4  0.0592      1.000 0.016 0.000 0.000 0.984
#> GSM1253060     4  0.0592      1.000 0.016 0.000 0.000 0.984
#> GSM1253061     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM1253062     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM1253063     4  0.0592      1.000 0.016 0.000 0.000 0.984
#> GSM1253064     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM1253065     4  0.0592      1.000 0.016 0.000 0.000 0.984
#> GSM1253066     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM1253067     4  0.0592      1.000 0.016 0.000 0.000 0.984
#> GSM1253068     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM1253069     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM1253070     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM1253071     4  0.0592      1.000 0.016 0.000 0.000 0.984
#> GSM1253072     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM1253073     4  0.0592      1.000 0.016 0.000 0.000 0.984
#> GSM1253074     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM1253032     3  0.0000      0.996 0.000 0.000 1.000 0.000
#> GSM1253034     2  0.0000      0.996 0.000 1.000 0.000 0.000
#> GSM1253039     2  0.0000      0.996 0.000 1.000 0.000 0.000
#> GSM1253040     2  0.0000      0.996 0.000 1.000 0.000 0.000
#> GSM1253041     2  0.0000      0.996 0.000 1.000 0.000 0.000
#> GSM1253046     3  0.0000      0.996 0.000 0.000 1.000 0.000
#> GSM1253048     2  0.0000      0.996 0.000 1.000 0.000 0.000
#> GSM1253049     2  0.0000      0.996 0.000 1.000 0.000 0.000
#> GSM1253052     2  0.0188      0.996 0.000 0.996 0.000 0.004
#> GSM1253037     2  0.0000      0.996 0.000 1.000 0.000 0.000
#> GSM1253028     2  0.0592      0.989 0.000 0.984 0.000 0.016
#> GSM1253029     2  0.0188      0.996 0.000 0.996 0.000 0.004
#> GSM1253030     2  0.0000      0.996 0.000 1.000 0.000 0.000
#> GSM1253031     2  0.0592      0.989 0.000 0.984 0.000 0.016
#> GSM1253033     3  0.0000      0.996 0.000 0.000 1.000 0.000
#> GSM1253035     2  0.0592      0.989 0.000 0.984 0.000 0.016
#> GSM1253036     2  0.0188      0.996 0.000 0.996 0.000 0.004
#> GSM1253038     2  0.0000      0.996 0.000 1.000 0.000 0.000
#> GSM1253042     2  0.0188      0.996 0.000 0.996 0.000 0.004
#> GSM1253045     3  0.0592      0.989 0.000 0.000 0.984 0.016
#> GSM1253043     3  0.0592      0.989 0.000 0.000 0.984 0.016
#> GSM1253044     2  0.0000      0.996 0.000 1.000 0.000 0.000
#> GSM1253047     3  0.0000      0.996 0.000 0.000 1.000 0.000
#> GSM1253050     2  0.0000      0.996 0.000 1.000 0.000 0.000
#> GSM1253051     2  0.0000      0.996 0.000 1.000 0.000 0.000
#> GSM1253053     2  0.0188      0.996 0.000 0.996 0.000 0.004
#> GSM1253054     3  0.0000      0.996 0.000 0.000 1.000 0.000
#> GSM1253055     2  0.0592      0.989 0.000 0.984 0.000 0.016
#> GSM1253079     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM1253081     1  0.0707      0.980 0.980 0.000 0.000 0.020
#> GSM1253080     1  0.0000      0.998 1.000 0.000 0.000 0.000
#> GSM1253082     1  0.0707      0.980 0.980 0.000 0.000 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
#> GSM1253056     4  0.0000     0.9990 0.000 0.000 0.000 1.000 0.000
#> GSM1253057     1  0.0000     0.9805 1.000 0.000 0.000 0.000 0.000
#> GSM1253058     4  0.0000     0.9990 0.000 0.000 0.000 1.000 0.000
#> GSM1253059     4  0.0000     0.9990 0.000 0.000 0.000 1.000 0.000
#> GSM1253060     4  0.0000     0.9990 0.000 0.000 0.000 1.000 0.000
#> GSM1253061     1  0.1043     0.9733 0.960 0.000 0.040 0.000 0.000
#> GSM1253062     1  0.0290     0.9796 0.992 0.000 0.008 0.000 0.000
#> GSM1253063     4  0.0000     0.9990 0.000 0.000 0.000 1.000 0.000
#> GSM1253064     1  0.1197     0.9710 0.952 0.000 0.048 0.000 0.000
#> GSM1253065     4  0.0290     0.9916 0.000 0.000 0.008 0.992 0.000
#> GSM1253066     1  0.1197     0.9710 0.952 0.000 0.048 0.000 0.000
#> GSM1253067     4  0.0000     0.9990 0.000 0.000 0.000 1.000 0.000
#> GSM1253068     1  0.1197     0.9710 0.952 0.000 0.048 0.000 0.000
#> GSM1253069     1  0.0000     0.9805 1.000 0.000 0.000 0.000 0.000
#> GSM1253070     1  0.0963     0.9744 0.964 0.000 0.036 0.000 0.000
#> GSM1253071     4  0.0000     0.9990 0.000 0.000 0.000 1.000 0.000
#> GSM1253072     1  0.1197     0.9710 0.952 0.000 0.048 0.000 0.000
#> GSM1253073     4  0.0000     0.9990 0.000 0.000 0.000 1.000 0.000
#> GSM1253074     1  0.0000     0.9805 1.000 0.000 0.000 0.000 0.000
#> GSM1253032     5  0.0000     1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM1253034     2  0.0000     0.9198 0.000 1.000 0.000 0.000 0.000
#> GSM1253039     2  0.0000     0.9198 0.000 1.000 0.000 0.000 0.000
#> GSM1253040     2  0.0000     0.9198 0.000 1.000 0.000 0.000 0.000
#> GSM1253041     2  0.0000     0.9198 0.000 1.000 0.000 0.000 0.000
#> GSM1253046     5  0.0000     1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM1253048     2  0.0000     0.9198 0.000 1.000 0.000 0.000 0.000
#> GSM1253049     2  0.0000     0.9198 0.000 1.000 0.000 0.000 0.000
#> GSM1253052     3  0.4268     0.3615 0.000 0.444 0.556 0.000 0.000
#> GSM1253037     2  0.0000     0.9198 0.000 1.000 0.000 0.000 0.000
#> GSM1253028     3  0.1282     0.7408 0.000 0.044 0.952 0.000 0.004
#> GSM1253029     3  0.4268     0.3615 0.000 0.444 0.556 0.000 0.000
#> GSM1253030     2  0.0000     0.9198 0.000 1.000 0.000 0.000 0.000
#> GSM1253031     3  0.1282     0.7408 0.000 0.044 0.952 0.000 0.004
#> GSM1253033     5  0.0000     1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM1253035     3  0.1544     0.7394 0.000 0.068 0.932 0.000 0.000
#> GSM1253036     2  0.4278    -0.0287 0.000 0.548 0.452 0.000 0.000
#> GSM1253038     2  0.0000     0.9198 0.000 1.000 0.000 0.000 0.000
#> GSM1253042     2  0.4088     0.2126 0.000 0.632 0.368 0.000 0.000
#> GSM1253045     3  0.3636     0.3983 0.000 0.000 0.728 0.000 0.272
#> GSM1253043     3  0.1197     0.6937 0.000 0.000 0.952 0.000 0.048
#> GSM1253044     2  0.0000     0.9198 0.000 1.000 0.000 0.000 0.000
#> GSM1253047     5  0.0000     1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM1253050     2  0.0000     0.9198 0.000 1.000 0.000 0.000 0.000
#> GSM1253051     2  0.0000     0.9198 0.000 1.000 0.000 0.000 0.000
#> GSM1253053     3  0.4268     0.3615 0.000 0.444 0.556 0.000 0.000
#> GSM1253054     5  0.0000     1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM1253055     3  0.1282     0.7408 0.000 0.044 0.952 0.000 0.004
#> GSM1253079     1  0.0000     0.9805 1.000 0.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000     0.9805 1.000 0.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000     0.9805 1.000 0.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000     0.9805 1.000 0.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000     0.9805 1.000 0.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000     0.9805 1.000 0.000 0.000 0.000 0.000
#> GSM1253081     1  0.1800     0.9587 0.932 0.000 0.048 0.020 0.000
#> GSM1253080     1  0.0000     0.9805 1.000 0.000 0.000 0.000 0.000
#> GSM1253082     1  0.1981     0.9521 0.924 0.000 0.048 0.028 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
#> GSM1253056     4  0.0458      0.968 0.016 0.000 0.000 0.984 0.000 0.000
#> GSM1253057     6  0.3868      0.900 0.492 0.000 0.000 0.000 0.000 0.508
#> GSM1253058     4  0.0865      0.961 0.000 0.000 0.000 0.964 0.000 0.036
#> GSM1253059     4  0.0865      0.961 0.000 0.000 0.000 0.964 0.000 0.036
#> GSM1253060     4  0.0547      0.967 0.020 0.000 0.000 0.980 0.000 0.000
#> GSM1253061     1  0.2664      0.332 0.816 0.000 0.000 0.000 0.000 0.184
#> GSM1253062     1  0.3428     -0.218 0.696 0.000 0.000 0.000 0.000 0.304
#> GSM1253063     4  0.0458      0.968 0.016 0.000 0.000 0.984 0.000 0.000
#> GSM1253064     1  0.0790      0.508 0.968 0.000 0.000 0.032 0.000 0.000
#> GSM1253065     4  0.1765      0.901 0.096 0.000 0.000 0.904 0.000 0.000
#> GSM1253066     1  0.0146      0.514 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM1253067     4  0.0547      0.965 0.000 0.000 0.000 0.980 0.000 0.020
#> GSM1253068     1  0.0000      0.514 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253069     6  0.3857      0.951 0.468 0.000 0.000 0.000 0.000 0.532
#> GSM1253070     1  0.2092      0.427 0.876 0.000 0.000 0.000 0.000 0.124
#> GSM1253071     4  0.0547      0.967 0.020 0.000 0.000 0.980 0.000 0.000
#> GSM1253072     1  0.0260      0.512 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM1253073     4  0.0632      0.964 0.000 0.000 0.000 0.976 0.000 0.024
#> GSM1253074     6  0.3857      0.951 0.468 0.000 0.000 0.000 0.000 0.532
#> GSM1253032     5  0.0000      1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1253034     2  0.0000      0.976 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253039     2  0.0000      0.976 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253040     2  0.0000      0.976 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253041     2  0.0000      0.976 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253046     5  0.0000      1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1253048     2  0.0000      0.976 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253049     2  0.0000      0.976 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253052     3  0.3468      0.548 0.000 0.284 0.712 0.000 0.000 0.004
#> GSM1253037     2  0.0000      0.976 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253028     3  0.3765      0.566 0.000 0.000 0.596 0.000 0.000 0.404
#> GSM1253029     3  0.3468      0.548 0.000 0.284 0.712 0.000 0.000 0.004
#> GSM1253030     2  0.0000      0.976 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253031     3  0.3765      0.566 0.000 0.000 0.596 0.000 0.000 0.404
#> GSM1253033     5  0.0000      1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1253035     3  0.0972      0.612 0.000 0.028 0.964 0.000 0.000 0.008
#> GSM1253036     2  0.3404      0.626 0.000 0.760 0.224 0.000 0.000 0.016
#> GSM1253038     2  0.0000      0.976 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253042     3  0.3950      0.244 0.000 0.432 0.564 0.000 0.000 0.004
#> GSM1253045     3  0.5167      0.472 0.000 0.000 0.500 0.000 0.088 0.412
#> GSM1253043     3  0.3804      0.560 0.000 0.000 0.576 0.000 0.000 0.424
#> GSM1253044     2  0.0000      0.976 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253047     5  0.0000      1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1253050     2  0.0000      0.976 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253051     2  0.0000      0.976 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253053     3  0.3468      0.548 0.000 0.284 0.712 0.000 0.000 0.004
#> GSM1253054     5  0.0000      1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1253055     3  0.0260      0.605 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM1253079     1  0.3854     -0.781 0.536 0.000 0.000 0.000 0.000 0.464
#> GSM1253083     6  0.3869      0.877 0.500 0.000 0.000 0.000 0.000 0.500
#> GSM1253075     1  0.3797     -0.684 0.580 0.000 0.000 0.000 0.000 0.420
#> GSM1253077     1  0.3868     -0.898 0.504 0.000 0.000 0.000 0.000 0.496
#> GSM1253076     1  0.3868     -0.898 0.504 0.000 0.000 0.000 0.000 0.496
#> GSM1253078     1  0.3868     -0.898 0.504 0.000 0.000 0.000 0.000 0.496
#> GSM1253081     1  0.1007      0.501 0.956 0.000 0.000 0.044 0.000 0.000
#> GSM1253080     6  0.3857      0.951 0.468 0.000 0.000 0.000 0.000 0.532
#> GSM1253082     1  0.1204      0.490 0.944 0.000 0.000 0.056 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-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 infection(p) disease.state(p) individual(p) k
#> CV:skmeans 55     0.015882         6.02e-09         0.956 2
#> CV:skmeans 56     0.004693         2.40e-10         0.902 3
#> CV:skmeans 56     0.000111         2.41e-11         0.905 4
#> CV:skmeans 50     0.001286         1.08e-10         0.837 5
#> CV:skmeans 45     0.024755         2.01e-07         0.662 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 51979 rows and 56 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#>   Subgroups are detected by 'pam' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 6.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk CV-pam-collect-plots

The plots are:

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

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

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

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

select_partition_number(res)

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

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.970       0.988         0.4906 0.514   0.514
#> 3 3 0.669           0.791       0.802         0.3289 0.788   0.596
#> 4 4 0.897           0.918       0.942         0.1522 0.880   0.650
#> 5 5 0.952           0.904       0.965         0.0502 0.903   0.645
#> 6 6 0.984           0.961       0.966         0.0575 0.943   0.735

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

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

suggest_best_k(res)

#> [1] 6
#> attr(,"optional")
#> [1] 2 5

There is also optional best \(k\) = 2 5 that is worth to check.

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

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

show/hide code output

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

#>            class entropy silhouette    p1    p2
#> GSM1253056     1  0.0000      0.980 1.000 0.000
#> GSM1253057     1  0.0000      0.980 1.000 0.000
#> GSM1253058     1  0.0000      0.980 1.000 0.000
#> GSM1253059     1  0.0000      0.980 1.000 0.000
#> GSM1253060     1  0.0000      0.980 1.000 0.000
#> GSM1253061     1  0.0000      0.980 1.000 0.000
#> GSM1253062     1  0.0000      0.980 1.000 0.000
#> GSM1253063     1  0.0000      0.980 1.000 0.000
#> GSM1253064     1  0.0000      0.980 1.000 0.000
#> GSM1253065     1  0.0000      0.980 1.000 0.000
#> GSM1253066     1  0.0000      0.980 1.000 0.000
#> GSM1253067     1  0.0000      0.980 1.000 0.000
#> GSM1253068     1  0.0000      0.980 1.000 0.000
#> GSM1253069     1  0.0000      0.980 1.000 0.000
#> GSM1253070     1  0.0000      0.980 1.000 0.000
#> GSM1253071     1  0.0000      0.980 1.000 0.000
#> GSM1253072     1  0.0000      0.980 1.000 0.000
#> GSM1253073     1  0.0000      0.980 1.000 0.000
#> GSM1253074     1  0.0000      0.980 1.000 0.000
#> GSM1253032     1  0.1184      0.966 0.984 0.016
#> GSM1253034     2  0.0000      1.000 0.000 1.000
#> GSM1253039     2  0.0000      1.000 0.000 1.000
#> GSM1253040     2  0.0000      1.000 0.000 1.000
#> GSM1253041     2  0.0000      1.000 0.000 1.000
#> GSM1253046     1  0.0000      0.980 1.000 0.000
#> GSM1253048     2  0.0000      1.000 0.000 1.000
#> GSM1253049     2  0.0000      1.000 0.000 1.000
#> GSM1253052     2  0.0000      1.000 0.000 1.000
#> GSM1253037     2  0.0000      1.000 0.000 1.000
#> GSM1253028     2  0.0000      1.000 0.000 1.000
#> GSM1253029     2  0.0000      1.000 0.000 1.000
#> GSM1253030     2  0.0000      1.000 0.000 1.000
#> GSM1253031     2  0.0000      1.000 0.000 1.000
#> GSM1253033     1  0.0000      0.980 1.000 0.000
#> GSM1253035     2  0.0000      1.000 0.000 1.000
#> GSM1253036     2  0.0000      1.000 0.000 1.000
#> GSM1253038     2  0.0000      1.000 0.000 1.000
#> GSM1253042     2  0.0000      1.000 0.000 1.000
#> GSM1253045     2  0.0000      1.000 0.000 1.000
#> GSM1253043     1  0.9866      0.259 0.568 0.432
#> GSM1253044     2  0.0000      1.000 0.000 1.000
#> GSM1253047     1  0.0376      0.977 0.996 0.004
#> GSM1253050     2  0.0000      1.000 0.000 1.000
#> GSM1253051     2  0.0000      1.000 0.000 1.000
#> GSM1253053     2  0.0000      1.000 0.000 1.000
#> GSM1253054     1  0.7299      0.742 0.796 0.204
#> GSM1253055     2  0.0000      1.000 0.000 1.000
#> GSM1253079     1  0.0000      0.980 1.000 0.000
#> GSM1253083     1  0.0000      0.980 1.000 0.000
#> GSM1253075     1  0.0000      0.980 1.000 0.000
#> GSM1253077     1  0.0000      0.980 1.000 0.000
#> GSM1253076     1  0.0000      0.980 1.000 0.000
#> GSM1253078     1  0.0000      0.980 1.000 0.000
#> GSM1253081     1  0.0000      0.980 1.000 0.000
#> GSM1253080     1  0.0000      0.980 1.000 0.000
#> GSM1253082     1  0.0000      0.980 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
#> GSM1253056     1  0.0000      0.864 1.000 0.000 0.000
#> GSM1253057     3  0.6126      0.861 0.400 0.000 0.600
#> GSM1253058     1  0.0000      0.864 1.000 0.000 0.000
#> GSM1253059     1  0.0000      0.864 1.000 0.000 0.000
#> GSM1253060     1  0.0000      0.864 1.000 0.000 0.000
#> GSM1253061     1  0.1031      0.835 0.976 0.000 0.024
#> GSM1253062     3  0.6126      0.861 0.400 0.000 0.600
#> GSM1253063     1  0.0000      0.864 1.000 0.000 0.000
#> GSM1253064     1  0.0000      0.864 1.000 0.000 0.000
#> GSM1253065     1  0.0000      0.864 1.000 0.000 0.000
#> GSM1253066     3  0.6126      0.861 0.400 0.000 0.600
#> GSM1253067     1  0.0000      0.864 1.000 0.000 0.000
#> GSM1253068     3  0.6126      0.861 0.400 0.000 0.600
#> GSM1253069     3  0.6126      0.861 0.400 0.000 0.600
#> GSM1253070     3  0.6274      0.785 0.456 0.000 0.544
#> GSM1253071     1  0.0000      0.864 1.000 0.000 0.000
#> GSM1253072     1  0.4555      0.452 0.800 0.000 0.200
#> GSM1253073     1  0.0000      0.864 1.000 0.000 0.000
#> GSM1253074     3  0.6140      0.857 0.404 0.000 0.596
#> GSM1253032     1  0.7492      0.437 0.608 0.340 0.052
#> GSM1253034     2  0.5882      0.851 0.000 0.652 0.348
#> GSM1253039     2  0.5882      0.851 0.000 0.652 0.348
#> GSM1253040     2  0.5882      0.851 0.000 0.652 0.348
#> GSM1253041     2  0.5882      0.851 0.000 0.652 0.348
#> GSM1253046     3  0.8047      0.677 0.256 0.112 0.632
#> GSM1253048     2  0.5882      0.851 0.000 0.652 0.348
#> GSM1253049     2  0.5882      0.851 0.000 0.652 0.348
#> GSM1253052     2  0.0000      0.789 0.000 1.000 0.000
#> GSM1253037     2  0.5882      0.851 0.000 0.652 0.348
#> GSM1253028     2  0.1860      0.763 0.000 0.948 0.052
#> GSM1253029     2  0.0000      0.789 0.000 1.000 0.000
#> GSM1253030     2  0.5882      0.851 0.000 0.652 0.348
#> GSM1253031     2  0.1860      0.763 0.000 0.948 0.052
#> GSM1253033     1  0.5138      0.662 0.828 0.120 0.052
#> GSM1253035     2  0.1860      0.763 0.000 0.948 0.052
#> GSM1253036     2  0.0000      0.789 0.000 1.000 0.000
#> GSM1253038     2  0.5882      0.851 0.000 0.652 0.348
#> GSM1253042     2  0.0000      0.789 0.000 1.000 0.000
#> GSM1253045     3  0.6192      0.328 0.000 0.420 0.580
#> GSM1253043     3  0.8731      0.296 0.116 0.368 0.516
#> GSM1253044     2  0.5882      0.851 0.000 0.652 0.348
#> GSM1253047     3  0.8103      0.668 0.248 0.120 0.632
#> GSM1253050     2  0.5882      0.851 0.000 0.652 0.348
#> GSM1253051     2  0.5882      0.851 0.000 0.652 0.348
#> GSM1253053     2  0.0892      0.780 0.000 0.980 0.020
#> GSM1253054     1  0.7607      0.414 0.584 0.364 0.052
#> GSM1253055     2  0.1860      0.763 0.000 0.948 0.052
#> GSM1253079     3  0.6126      0.861 0.400 0.000 0.600
#> GSM1253083     3  0.6126      0.861 0.400 0.000 0.600
#> GSM1253075     3  0.6126      0.861 0.400 0.000 0.600
#> GSM1253077     3  0.6126      0.861 0.400 0.000 0.600
#> GSM1253076     3  0.6126      0.861 0.400 0.000 0.600
#> GSM1253078     3  0.6126      0.861 0.400 0.000 0.600
#> GSM1253081     1  0.0424      0.856 0.992 0.000 0.008
#> GSM1253080     3  0.6126      0.861 0.400 0.000 0.600
#> GSM1253082     1  0.0747      0.848 0.984 0.000 0.016

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4
#> GSM1253056     4  0.1867      0.904 0.072 0.000 0.000 0.928
#> GSM1253057     1  0.0000      0.962 1.000 0.000 0.000 0.000
#> GSM1253058     4  0.1867      0.904 0.072 0.000 0.000 0.928
#> GSM1253059     4  0.1867      0.904 0.072 0.000 0.000 0.928
#> GSM1253060     4  0.1867      0.904 0.072 0.000 0.000 0.928
#> GSM1253061     4  0.3688      0.830 0.208 0.000 0.000 0.792
#> GSM1253062     1  0.0000      0.962 1.000 0.000 0.000 0.000
#> GSM1253063     4  0.1867      0.904 0.072 0.000 0.000 0.928
#> GSM1253064     4  0.3528      0.845 0.192 0.000 0.000 0.808
#> GSM1253065     4  0.2011      0.901 0.080 0.000 0.000 0.920
#> GSM1253066     1  0.0000      0.962 1.000 0.000 0.000 0.000
#> GSM1253067     4  0.1867      0.904 0.072 0.000 0.000 0.928
#> GSM1253068     1  0.0000      0.962 1.000 0.000 0.000 0.000
#> GSM1253069     1  0.0000      0.962 1.000 0.000 0.000 0.000
#> GSM1253070     1  0.2011      0.885 0.920 0.000 0.000 0.080
#> GSM1253071     4  0.1867      0.904 0.072 0.000 0.000 0.928
#> GSM1253072     4  0.4977      0.375 0.460 0.000 0.000 0.540
#> GSM1253073     4  0.1867      0.904 0.072 0.000 0.000 0.928
#> GSM1253074     1  0.0188      0.959 0.996 0.000 0.000 0.004
#> GSM1253032     4  0.4543      0.459 0.000 0.000 0.324 0.676
#> GSM1253034     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253039     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253040     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253041     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253046     1  0.4362      0.804 0.816 0.000 0.096 0.088
#> GSM1253048     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253049     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253052     3  0.2011      0.934 0.000 0.080 0.920 0.000
#> GSM1253037     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253028     3  0.0000      0.960 0.000 0.000 1.000 0.000
#> GSM1253029     3  0.2011      0.934 0.000 0.080 0.920 0.000
#> GSM1253030     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253031     3  0.0000      0.960 0.000 0.000 1.000 0.000
#> GSM1253033     4  0.2805      0.792 0.012 0.000 0.100 0.888
#> GSM1253035     3  0.0000      0.960 0.000 0.000 1.000 0.000
#> GSM1253036     3  0.2011      0.934 0.000 0.080 0.920 0.000
#> GSM1253038     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253042     3  0.2011      0.934 0.000 0.080 0.920 0.000
#> GSM1253045     3  0.0000      0.960 0.000 0.000 1.000 0.000
#> GSM1253043     3  0.0000      0.960 0.000 0.000 1.000 0.000
#> GSM1253044     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253047     1  0.5610      0.698 0.720 0.000 0.176 0.104
#> GSM1253050     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253051     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253053     3  0.1022      0.954 0.000 0.032 0.968 0.000
#> GSM1253054     3  0.1867      0.917 0.000 0.000 0.928 0.072
#> GSM1253055     3  0.0000      0.960 0.000 0.000 1.000 0.000
#> GSM1253079     1  0.0000      0.962 1.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000      0.962 1.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000      0.962 1.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      0.962 1.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      0.962 1.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      0.962 1.000 0.000 0.000 0.000
#> GSM1253081     4  0.3311      0.861 0.172 0.000 0.000 0.828
#> GSM1253080     1  0.0000      0.962 1.000 0.000 0.000 0.000
#> GSM1253082     4  0.3400      0.856 0.180 0.000 0.000 0.820

show/hide code output

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

#>            class entropy silhouette    p1 p2    p3    p4    p5
#> GSM1253056     4  0.0000      0.885 0.000  0 0.000 1.000 0.000
#> GSM1253057     1  0.0000      0.924 1.000  0 0.000 0.000 0.000
#> GSM1253058     4  0.0000      0.885 0.000  0 0.000 1.000 0.000
#> GSM1253059     4  0.0000      0.885 0.000  0 0.000 1.000 0.000
#> GSM1253060     4  0.0000      0.885 0.000  0 0.000 1.000 0.000
#> GSM1253061     1  0.4088      0.406 0.632  0 0.000 0.368 0.000
#> GSM1253062     1  0.0000      0.924 1.000  0 0.000 0.000 0.000
#> GSM1253063     4  0.0000      0.885 0.000  0 0.000 1.000 0.000
#> GSM1253064     1  0.4088      0.406 0.632  0 0.000 0.368 0.000
#> GSM1253065     4  0.0162      0.882 0.004  0 0.000 0.996 0.000
#> GSM1253066     1  0.0000      0.924 1.000  0 0.000 0.000 0.000
#> GSM1253067     4  0.0000      0.885 0.000  0 0.000 1.000 0.000
#> GSM1253068     1  0.0000      0.924 1.000  0 0.000 0.000 0.000
#> GSM1253069     1  0.0000      0.924 1.000  0 0.000 0.000 0.000
#> GSM1253070     1  0.0609      0.909 0.980  0 0.000 0.020 0.000
#> GSM1253071     4  0.0000      0.885 0.000  0 0.000 1.000 0.000
#> GSM1253072     1  0.3730      0.569 0.712  0 0.000 0.288 0.000
#> GSM1253073     4  0.0000      0.885 0.000  0 0.000 1.000 0.000
#> GSM1253074     1  0.0162      0.921 0.996  0 0.000 0.004 0.000
#> GSM1253032     5  0.0000      0.998 0.000  0 0.000 0.000 1.000
#> GSM1253034     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM1253039     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM1253040     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM1253041     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM1253046     5  0.0000      0.998 0.000  0 0.000 0.000 1.000
#> GSM1253048     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM1253049     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM1253052     3  0.0000      0.996 0.000  0 1.000 0.000 0.000
#> GSM1253037     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM1253028     3  0.0290      0.995 0.000  0 0.992 0.000 0.008
#> GSM1253029     3  0.0000      0.996 0.000  0 1.000 0.000 0.000
#> GSM1253030     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM1253031     3  0.0290      0.995 0.000  0 0.992 0.000 0.008
#> GSM1253033     5  0.0290      0.990 0.000  0 0.000 0.008 0.992
#> GSM1253035     3  0.0000      0.996 0.000  0 1.000 0.000 0.000
#> GSM1253036     3  0.0000      0.996 0.000  0 1.000 0.000 0.000
#> GSM1253038     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM1253042     3  0.0000      0.996 0.000  0 1.000 0.000 0.000
#> GSM1253045     3  0.0290      0.995 0.000  0 0.992 0.000 0.008
#> GSM1253043     3  0.0290      0.995 0.000  0 0.992 0.000 0.008
#> GSM1253044     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM1253047     5  0.0000      0.998 0.000  0 0.000 0.000 1.000
#> GSM1253050     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM1253051     2  0.0000      1.000 0.000  1 0.000 0.000 0.000
#> GSM1253053     3  0.0000      0.996 0.000  0 1.000 0.000 0.000
#> GSM1253054     5  0.0000      0.998 0.000  0 0.000 0.000 1.000
#> GSM1253055     3  0.0290      0.995 0.000  0 0.992 0.000 0.008
#> GSM1253079     1  0.0000      0.924 1.000  0 0.000 0.000 0.000
#> GSM1253083     1  0.0000      0.924 1.000  0 0.000 0.000 0.000
#> GSM1253075     1  0.0000      0.924 1.000  0 0.000 0.000 0.000
#> GSM1253077     1  0.0000      0.924 1.000  0 0.000 0.000 0.000
#> GSM1253076     1  0.0000      0.924 1.000  0 0.000 0.000 0.000
#> GSM1253078     1  0.0000      0.924 1.000  0 0.000 0.000 0.000
#> GSM1253081     4  0.4210      0.255 0.412  0 0.000 0.588 0.000
#> GSM1253080     1  0.0000      0.924 1.000  0 0.000 0.000 0.000
#> GSM1253082     4  0.4249      0.193 0.432  0 0.000 0.568 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
#> GSM1253056     4  0.0000      0.999 0.000  0 0.000 1.000  0 0.000
#> GSM1253057     1  0.0000      0.927 1.000  0 0.000 0.000  0 0.000
#> GSM1253058     4  0.0000      0.999 0.000  0 0.000 1.000  0 0.000
#> GSM1253059     4  0.0000      0.999 0.000  0 0.000 1.000  0 0.000
#> GSM1253060     4  0.0000      0.999 0.000  0 0.000 1.000  0 0.000
#> GSM1253061     6  0.3384      0.876 0.120  0 0.000 0.068  0 0.812
#> GSM1253062     1  0.2664      0.834 0.816  0 0.000 0.000  0 0.184
#> GSM1253063     4  0.0000      0.999 0.000  0 0.000 1.000  0 0.000
#> GSM1253064     6  0.1838      0.946 0.016  0 0.000 0.068  0 0.916
#> GSM1253065     4  0.0146      0.995 0.000  0 0.000 0.996  0 0.004
#> GSM1253066     6  0.1610      0.907 0.084  0 0.000 0.000  0 0.916
#> GSM1253067     4  0.0000      0.999 0.000  0 0.000 1.000  0 0.000
#> GSM1253068     6  0.1610      0.907 0.084  0 0.000 0.000  0 0.916
#> GSM1253069     1  0.0000      0.927 1.000  0 0.000 0.000  0 0.000
#> GSM1253070     1  0.3076      0.702 0.760  0 0.000 0.000  0 0.240
#> GSM1253071     4  0.0000      0.999 0.000  0 0.000 1.000  0 0.000
#> GSM1253072     6  0.1838      0.946 0.016  0 0.000 0.068  0 0.916
#> GSM1253073     4  0.0000      0.999 0.000  0 0.000 1.000  0 0.000
#> GSM1253074     1  0.0000      0.927 1.000  0 0.000 0.000  0 0.000
#> GSM1253032     5  0.0000      1.000 0.000  0 0.000 0.000  1 0.000
#> GSM1253034     2  0.0000      1.000 0.000  1 0.000 0.000  0 0.000
#> GSM1253039     2  0.0000      1.000 0.000  1 0.000 0.000  0 0.000
#> GSM1253040     2  0.0000      1.000 0.000  1 0.000 0.000  0 0.000
#> GSM1253041     2  0.0000      1.000 0.000  1 0.000 0.000  0 0.000
#> GSM1253046     5  0.0000      1.000 0.000  0 0.000 0.000  1 0.000
#> GSM1253048     2  0.0000      1.000 0.000  1 0.000 0.000  0 0.000
#> GSM1253049     2  0.0000      1.000 0.000  1 0.000 0.000  0 0.000
#> GSM1253052     3  0.1610      0.949 0.000  0 0.916 0.000  0 0.084
#> GSM1253037     2  0.0000      1.000 0.000  1 0.000 0.000  0 0.000
#> GSM1253028     3  0.0000      0.972 0.000  0 1.000 0.000  0 0.000
#> GSM1253029     3  0.1610      0.949 0.000  0 0.916 0.000  0 0.084
#> GSM1253030     2  0.0000      1.000 0.000  1 0.000 0.000  0 0.000
#> GSM1253031     3  0.0000      0.972 0.000  0 1.000 0.000  0 0.000
#> GSM1253033     5  0.0000      1.000 0.000  0 0.000 0.000  1 0.000
#> GSM1253035     3  0.0000      0.972 0.000  0 1.000 0.000  0 0.000
#> GSM1253036     3  0.0000      0.972 0.000  0 1.000 0.000  0 0.000
#> GSM1253038     2  0.0000      1.000 0.000  1 0.000 0.000  0 0.000
#> GSM1253042     3  0.1610      0.949 0.000  0 0.916 0.000  0 0.084
#> GSM1253045     3  0.0000      0.972 0.000  0 1.000 0.000  0 0.000
#> GSM1253043     3  0.0000      0.972 0.000  0 1.000 0.000  0 0.000
#> GSM1253044     2  0.0000      1.000 0.000  1 0.000 0.000  0 0.000
#> GSM1253047     5  0.0000      1.000 0.000  0 0.000 0.000  1 0.000
#> GSM1253050     2  0.0000      1.000 0.000  1 0.000 0.000  0 0.000
#> GSM1253051     2  0.0000      1.000 0.000  1 0.000 0.000  0 0.000
#> GSM1253053     3  0.1610      0.949 0.000  0 0.916 0.000  0 0.084
#> GSM1253054     5  0.0000      1.000 0.000  0 0.000 0.000  1 0.000
#> GSM1253055     3  0.0000      0.972 0.000  0 1.000 0.000  0 0.000
#> GSM1253079     1  0.0937      0.917 0.960  0 0.000 0.000  0 0.040
#> GSM1253083     1  0.1204      0.920 0.944  0 0.000 0.000  0 0.056
#> GSM1253075     1  0.1387      0.917 0.932  0 0.000 0.000  0 0.068
#> GSM1253077     1  0.0146      0.927 0.996  0 0.000 0.000  0 0.004
#> GSM1253076     1  0.1910      0.895 0.892  0 0.000 0.000  0 0.108
#> GSM1253078     1  0.1501      0.912 0.924  0 0.000 0.000  0 0.076
#> GSM1253081     6  0.1838      0.946 0.016  0 0.000 0.068  0 0.916
#> GSM1253080     1  0.0000      0.927 1.000  0 0.000 0.000  0 0.000
#> GSM1253082     6  0.1838      0.946 0.016  0 0.000 0.068  0 0.916

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 infection(p) disease.state(p) individual(p) k
#> CV:pam 55     0.021088         2.77e-08         0.962 2
#> CV:pam 51     0.002346         2.27e-08         0.663 3
#> CV:pam 54     0.004017         2.84e-10         0.605 4
#> CV:pam 52     0.000510         2.18e-11         0.817 5
#> CV:pam 56     0.000239         1.10e-11         0.786 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 51979 rows and 56 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 6.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk CV-mclust-collect-plots

The plots are:

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

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

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

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

select_partition_number(res)

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

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.998       0.999         0.5095 0.491   0.491
#> 3 3 0.906           0.963       0.961         0.2396 0.873   0.741
#> 4 4 0.877           0.871       0.927         0.1868 0.845   0.594
#> 5 5 0.907           0.937       0.920         0.0597 0.953   0.809
#> 6 6 0.990           0.983       0.988         0.0541 0.964   0.820

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

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

suggest_best_k(res)

#> [1] 6
#> attr(,"optional")
#> [1] 2 3 5

There is also optional best \(k\) = 2 3 5 that is worth to check.

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

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

show/hide code output

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

#>            class entropy silhouette    p1    p2
#> GSM1253056     1   0.000      0.998 1.000 0.000
#> GSM1253057     1   0.000      0.998 1.000 0.000
#> GSM1253058     1   0.000      0.998 1.000 0.000
#> GSM1253059     1   0.000      0.998 1.000 0.000
#> GSM1253060     1   0.000      0.998 1.000 0.000
#> GSM1253061     1   0.000      0.998 1.000 0.000
#> GSM1253062     1   0.000      0.998 1.000 0.000
#> GSM1253063     1   0.000      0.998 1.000 0.000
#> GSM1253064     1   0.000      0.998 1.000 0.000
#> GSM1253065     1   0.000      0.998 1.000 0.000
#> GSM1253066     1   0.000      0.998 1.000 0.000
#> GSM1253067     1   0.000      0.998 1.000 0.000
#> GSM1253068     1   0.000      0.998 1.000 0.000
#> GSM1253069     1   0.000      0.998 1.000 0.000
#> GSM1253070     1   0.343      0.932 0.936 0.064
#> GSM1253071     1   0.000      0.998 1.000 0.000
#> GSM1253072     1   0.000      0.998 1.000 0.000
#> GSM1253073     1   0.000      0.998 1.000 0.000
#> GSM1253074     1   0.000      0.998 1.000 0.000
#> GSM1253032     2   0.000      1.000 0.000 1.000
#> GSM1253034     2   0.000      1.000 0.000 1.000
#> GSM1253039     2   0.000      1.000 0.000 1.000
#> GSM1253040     2   0.000      1.000 0.000 1.000
#> GSM1253041     2   0.000      1.000 0.000 1.000
#> GSM1253046     2   0.000      1.000 0.000 1.000
#> GSM1253048     2   0.000      1.000 0.000 1.000
#> GSM1253049     2   0.000      1.000 0.000 1.000
#> GSM1253052     2   0.000      1.000 0.000 1.000
#> GSM1253037     2   0.000      1.000 0.000 1.000
#> GSM1253028     2   0.000      1.000 0.000 1.000
#> GSM1253029     2   0.000      1.000 0.000 1.000
#> GSM1253030     2   0.000      1.000 0.000 1.000
#> GSM1253031     2   0.000      1.000 0.000 1.000
#> GSM1253033     2   0.000      1.000 0.000 1.000
#> GSM1253035     2   0.000      1.000 0.000 1.000
#> GSM1253036     2   0.000      1.000 0.000 1.000
#> GSM1253038     2   0.000      1.000 0.000 1.000
#> GSM1253042     2   0.000      1.000 0.000 1.000
#> GSM1253045     2   0.000      1.000 0.000 1.000
#> GSM1253043     2   0.000      1.000 0.000 1.000
#> GSM1253044     2   0.000      1.000 0.000 1.000
#> GSM1253047     2   0.000      1.000 0.000 1.000
#> GSM1253050     2   0.000      1.000 0.000 1.000
#> GSM1253051     2   0.000      1.000 0.000 1.000
#> GSM1253053     2   0.000      1.000 0.000 1.000
#> GSM1253054     2   0.000      1.000 0.000 1.000
#> GSM1253055     2   0.000      1.000 0.000 1.000
#> GSM1253079     1   0.000      0.998 1.000 0.000
#> GSM1253083     1   0.000      0.998 1.000 0.000
#> GSM1253075     1   0.000      0.998 1.000 0.000
#> GSM1253077     1   0.000      0.998 1.000 0.000
#> GSM1253076     1   0.000      0.998 1.000 0.000
#> GSM1253078     1   0.000      0.998 1.000 0.000
#> GSM1253081     1   0.000      0.998 1.000 0.000
#> GSM1253080     1   0.000      0.998 1.000 0.000
#> GSM1253082     1   0.000      0.998 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
#> GSM1253056     1  0.1289      0.980 0.968 0.000 0.032
#> GSM1253057     1  0.0000      0.989 1.000 0.000 0.000
#> GSM1253058     1  0.1529      0.976 0.960 0.000 0.040
#> GSM1253059     1  0.1529      0.976 0.960 0.000 0.040
#> GSM1253060     1  0.1289      0.980 0.968 0.000 0.032
#> GSM1253061     1  0.0000      0.989 1.000 0.000 0.000
#> GSM1253062     1  0.0000      0.989 1.000 0.000 0.000
#> GSM1253063     1  0.1289      0.980 0.968 0.000 0.032
#> GSM1253064     1  0.0000      0.989 1.000 0.000 0.000
#> GSM1253065     1  0.1289      0.980 0.968 0.000 0.032
#> GSM1253066     1  0.0000      0.989 1.000 0.000 0.000
#> GSM1253067     1  0.1289      0.980 0.968 0.000 0.032
#> GSM1253068     1  0.0000      0.989 1.000 0.000 0.000
#> GSM1253069     1  0.0000      0.989 1.000 0.000 0.000
#> GSM1253070     1  0.1529      0.963 0.960 0.000 0.040
#> GSM1253071     1  0.1289      0.980 0.968 0.000 0.032
#> GSM1253072     1  0.0000      0.989 1.000 0.000 0.000
#> GSM1253073     1  0.1289      0.980 0.968 0.000 0.032
#> GSM1253074     1  0.0000      0.989 1.000 0.000 0.000
#> GSM1253032     3  0.1289      0.897 0.000 0.032 0.968
#> GSM1253034     2  0.0000      0.988 0.000 1.000 0.000
#> GSM1253039     2  0.0000      0.988 0.000 1.000 0.000
#> GSM1253040     2  0.0000      0.988 0.000 1.000 0.000
#> GSM1253041     2  0.0000      0.988 0.000 1.000 0.000
#> GSM1253046     3  0.1289      0.897 0.000 0.032 0.968
#> GSM1253048     2  0.0000      0.988 0.000 1.000 0.000
#> GSM1253049     2  0.0000      0.988 0.000 1.000 0.000
#> GSM1253052     3  0.4504      0.903 0.000 0.196 0.804
#> GSM1253037     2  0.0000      0.988 0.000 1.000 0.000
#> GSM1253028     3  0.4121      0.905 0.000 0.168 0.832
#> GSM1253029     3  0.4504      0.903 0.000 0.196 0.804
#> GSM1253030     2  0.0000      0.988 0.000 1.000 0.000
#> GSM1253031     2  0.3551      0.838 0.000 0.868 0.132
#> GSM1253033     3  0.1289      0.897 0.000 0.032 0.968
#> GSM1253035     3  0.4504      0.903 0.000 0.196 0.804
#> GSM1253036     2  0.0237      0.984 0.000 0.996 0.004
#> GSM1253038     2  0.0000      0.988 0.000 1.000 0.000
#> GSM1253042     3  0.4555      0.900 0.000 0.200 0.800
#> GSM1253045     3  0.2448      0.910 0.000 0.076 0.924
#> GSM1253043     3  0.2878      0.914 0.000 0.096 0.904
#> GSM1253044     2  0.0000      0.988 0.000 1.000 0.000
#> GSM1253047     3  0.1289      0.897 0.000 0.032 0.968
#> GSM1253050     2  0.0000      0.988 0.000 1.000 0.000
#> GSM1253051     2  0.0000      0.988 0.000 1.000 0.000
#> GSM1253053     3  0.4504      0.903 0.000 0.196 0.804
#> GSM1253054     3  0.2261      0.909 0.000 0.068 0.932
#> GSM1253055     3  0.4504      0.903 0.000 0.196 0.804
#> GSM1253079     1  0.0000      0.989 1.000 0.000 0.000
#> GSM1253083     1  0.0000      0.989 1.000 0.000 0.000
#> GSM1253075     1  0.0000      0.989 1.000 0.000 0.000
#> GSM1253077     1  0.0000      0.989 1.000 0.000 0.000
#> GSM1253076     1  0.0000      0.989 1.000 0.000 0.000
#> GSM1253078     1  0.0000      0.989 1.000 0.000 0.000
#> GSM1253081     1  0.0000      0.989 1.000 0.000 0.000
#> GSM1253080     1  0.0000      0.989 1.000 0.000 0.000
#> GSM1253082     1  0.0000      0.989 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
#> GSM1253056     4  0.4972      0.740 0.000 0.000 0.456 0.544
#> GSM1253057     1  0.4972      1.000 0.544 0.000 0.000 0.456
#> GSM1253058     4  0.4972      0.740 0.000 0.000 0.456 0.544
#> GSM1253059     4  0.4972      0.740 0.000 0.000 0.456 0.544
#> GSM1253060     4  0.4955      0.741 0.000 0.000 0.444 0.556
#> GSM1253061     4  0.0000      0.518 0.000 0.000 0.000 1.000
#> GSM1253062     1  0.4972      1.000 0.544 0.000 0.000 0.456
#> GSM1253063     4  0.4972      0.740 0.000 0.000 0.456 0.544
#> GSM1253064     4  0.0592      0.532 0.000 0.000 0.016 0.984
#> GSM1253065     4  0.4948      0.741 0.000 0.000 0.440 0.560
#> GSM1253066     4  0.0000      0.518 0.000 0.000 0.000 1.000
#> GSM1253067     4  0.4972      0.740 0.000 0.000 0.456 0.544
#> GSM1253068     4  0.0000      0.518 0.000 0.000 0.000 1.000
#> GSM1253069     1  0.4972      1.000 0.544 0.000 0.000 0.456
#> GSM1253070     4  0.3900      0.536 0.164 0.000 0.020 0.816
#> GSM1253071     4  0.4955      0.741 0.000 0.000 0.444 0.556
#> GSM1253072     4  0.0000      0.518 0.000 0.000 0.000 1.000
#> GSM1253073     4  0.4972      0.740 0.000 0.000 0.456 0.544
#> GSM1253074     1  0.4972      1.000 0.544 0.000 0.000 0.456
#> GSM1253032     3  0.4972      0.997 0.456 0.000 0.544 0.000
#> GSM1253034     2  0.0000      0.963 0.000 1.000 0.000 0.000
#> GSM1253039     2  0.0000      0.963 0.000 1.000 0.000 0.000
#> GSM1253040     2  0.0000      0.963 0.000 1.000 0.000 0.000
#> GSM1253041     2  0.0000      0.963 0.000 1.000 0.000 0.000
#> GSM1253046     3  0.4972      0.997 0.456 0.000 0.544 0.000
#> GSM1253048     2  0.0000      0.963 0.000 1.000 0.000 0.000
#> GSM1253049     2  0.0000      0.963 0.000 1.000 0.000 0.000
#> GSM1253052     3  0.4972      0.997 0.456 0.000 0.544 0.000
#> GSM1253037     2  0.0000      0.963 0.000 1.000 0.000 0.000
#> GSM1253028     3  0.4972      0.997 0.456 0.000 0.544 0.000
#> GSM1253029     3  0.4972      0.997 0.456 0.000 0.544 0.000
#> GSM1253030     2  0.0336      0.957 0.008 0.992 0.000 0.000
#> GSM1253031     3  0.5564      0.980 0.436 0.020 0.544 0.000
#> GSM1253033     3  0.4972      0.997 0.456 0.000 0.544 0.000
#> GSM1253035     3  0.4972      0.997 0.456 0.000 0.544 0.000
#> GSM1253036     3  0.5564      0.980 0.436 0.020 0.544 0.000
#> GSM1253038     2  0.5929      0.435 0.296 0.640 0.064 0.000
#> GSM1253042     3  0.4972      0.997 0.456 0.000 0.544 0.000
#> GSM1253045     3  0.4972      0.997 0.456 0.000 0.544 0.000
#> GSM1253043     3  0.4972      0.997 0.456 0.000 0.544 0.000
#> GSM1253044     2  0.0000      0.963 0.000 1.000 0.000 0.000
#> GSM1253047     3  0.4972      0.997 0.456 0.000 0.544 0.000
#> GSM1253050     2  0.0000      0.963 0.000 1.000 0.000 0.000
#> GSM1253051     2  0.0000      0.963 0.000 1.000 0.000 0.000
#> GSM1253053     3  0.4972      0.997 0.456 0.000 0.544 0.000
#> GSM1253054     3  0.4972      0.997 0.456 0.000 0.544 0.000
#> GSM1253055     3  0.4972      0.997 0.456 0.000 0.544 0.000
#> GSM1253079     1  0.4972      1.000 0.544 0.000 0.000 0.456
#> GSM1253083     1  0.4972      1.000 0.544 0.000 0.000 0.456
#> GSM1253075     1  0.4972      1.000 0.544 0.000 0.000 0.456
#> GSM1253077     1  0.4972      1.000 0.544 0.000 0.000 0.456
#> GSM1253076     1  0.4972      1.000 0.544 0.000 0.000 0.456
#> GSM1253078     1  0.4972      1.000 0.544 0.000 0.000 0.456
#> GSM1253081     4  0.0000      0.518 0.000 0.000 0.000 1.000
#> GSM1253080     1  0.4972      1.000 0.544 0.000 0.000 0.456
#> GSM1253082     4  0.0000      0.518 0.000 0.000 0.000 1.000

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4    p5
#> GSM1253056     4  0.0290      0.997 0.008 0.000 0.000 0.992 0.000
#> GSM1253057     1  0.1270      0.941 0.948 0.000 0.000 0.000 0.052
#> GSM1253058     4  0.0000      0.991 0.000 0.000 0.000 1.000 0.000
#> GSM1253059     4  0.0000      0.991 0.000 0.000 0.000 1.000 0.000
#> GSM1253060     4  0.0290      0.997 0.008 0.000 0.000 0.992 0.000
#> GSM1253061     5  0.3636      0.938 0.272 0.000 0.000 0.000 0.728
#> GSM1253062     1  0.1270      0.941 0.948 0.000 0.000 0.000 0.052
#> GSM1253063     4  0.0290      0.997 0.008 0.000 0.000 0.992 0.000
#> GSM1253064     5  0.3636      0.938 0.272 0.000 0.000 0.000 0.728
#> GSM1253065     4  0.0290      0.997 0.008 0.000 0.000 0.992 0.000
#> GSM1253066     5  0.3707      0.939 0.284 0.000 0.000 0.000 0.716
#> GSM1253067     4  0.0290      0.997 0.008 0.000 0.000 0.992 0.000
#> GSM1253068     5  0.3707      0.939 0.284 0.000 0.000 0.000 0.716
#> GSM1253069     1  0.1197      0.943 0.952 0.000 0.000 0.000 0.048
#> GSM1253070     5  0.6381      0.629 0.240 0.000 0.196 0.008 0.556
#> GSM1253071     4  0.0290      0.997 0.008 0.000 0.000 0.992 0.000
#> GSM1253072     5  0.3707      0.939 0.284 0.000 0.000 0.000 0.716
#> GSM1253073     4  0.0290      0.997 0.008 0.000 0.000 0.992 0.000
#> GSM1253074     1  0.2230      0.855 0.884 0.000 0.000 0.000 0.116
#> GSM1253032     3  0.3636      0.814 0.000 0.000 0.728 0.000 0.272
#> GSM1253034     2  0.0000      0.992 0.000 1.000 0.000 0.000 0.000
#> GSM1253039     2  0.0000      0.992 0.000 1.000 0.000 0.000 0.000
#> GSM1253040     2  0.0000      0.992 0.000 1.000 0.000 0.000 0.000
#> GSM1253041     2  0.0000      0.992 0.000 1.000 0.000 0.000 0.000
#> GSM1253046     3  0.3636      0.814 0.000 0.000 0.728 0.000 0.272
#> GSM1253048     2  0.0000      0.992 0.000 1.000 0.000 0.000 0.000
#> GSM1253049     2  0.0000      0.992 0.000 1.000 0.000 0.000 0.000
#> GSM1253052     3  0.0000      0.919 0.000 0.000 1.000 0.000 0.000
#> GSM1253037     2  0.0000      0.992 0.000 1.000 0.000 0.000 0.000
#> GSM1253028     3  0.0000      0.919 0.000 0.000 1.000 0.000 0.000
#> GSM1253029     3  0.0000      0.919 0.000 0.000 1.000 0.000 0.000
#> GSM1253030     2  0.0162      0.989 0.000 0.996 0.004 0.000 0.000
#> GSM1253031     3  0.0000      0.919 0.000 0.000 1.000 0.000 0.000
#> GSM1253033     3  0.3636      0.814 0.000 0.000 0.728 0.000 0.272
#> GSM1253035     3  0.0000      0.919 0.000 0.000 1.000 0.000 0.000
#> GSM1253036     3  0.0703      0.907 0.000 0.024 0.976 0.000 0.000
#> GSM1253038     2  0.1544      0.918 0.000 0.932 0.068 0.000 0.000
#> GSM1253042     3  0.0000      0.919 0.000 0.000 1.000 0.000 0.000
#> GSM1253045     3  0.0000      0.919 0.000 0.000 1.000 0.000 0.000
#> GSM1253043     3  0.0000      0.919 0.000 0.000 1.000 0.000 0.000
#> GSM1253044     2  0.0000      0.992 0.000 1.000 0.000 0.000 0.000
#> GSM1253047     3  0.3636      0.814 0.000 0.000 0.728 0.000 0.272
#> GSM1253050     2  0.0000      0.992 0.000 1.000 0.000 0.000 0.000
#> GSM1253051     2  0.0000      0.992 0.000 1.000 0.000 0.000 0.000
#> GSM1253053     3  0.0000      0.919 0.000 0.000 1.000 0.000 0.000
#> GSM1253054     3  0.3636      0.814 0.000 0.000 0.728 0.000 0.272
#> GSM1253055     3  0.0000      0.919 0.000 0.000 1.000 0.000 0.000
#> GSM1253079     1  0.1410      0.934 0.940 0.000 0.000 0.000 0.060
#> GSM1253083     1  0.0000      0.954 1.000 0.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000      0.954 1.000 0.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      0.954 1.000 0.000 0.000 0.000 0.000
#> GSM1253076     1  0.0162      0.950 0.996 0.000 0.000 0.004 0.000
#> GSM1253078     1  0.0000      0.954 1.000 0.000 0.000 0.000 0.000
#> GSM1253081     5  0.3707      0.939 0.284 0.000 0.000 0.000 0.716
#> GSM1253080     1  0.0000      0.954 1.000 0.000 0.000 0.000 0.000
#> GSM1253082     5  0.3636      0.938 0.272 0.000 0.000 0.000 0.728

show/hide code output

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

#>            class entropy silhouette    p1 p2 p3 p4    p5    p6
#> GSM1253056     4  0.0000      1.000 0.000  0  0  1 0.000 0.000
#> GSM1253057     1  0.2135      0.899 0.872  0  0  0 0.000 0.128
#> GSM1253058     4  0.0000      1.000 0.000  0  0  1 0.000 0.000
#> GSM1253059     4  0.0000      1.000 0.000  0  0  1 0.000 0.000
#> GSM1253060     4  0.0000      1.000 0.000  0  0  1 0.000 0.000
#> GSM1253061     6  0.0000      0.999 0.000  0  0  0 0.000 1.000
#> GSM1253062     1  0.2300      0.889 0.856  0  0  0 0.000 0.144
#> GSM1253063     4  0.0000      1.000 0.000  0  0  1 0.000 0.000
#> GSM1253064     6  0.0000      0.999 0.000  0  0  0 0.000 1.000
#> GSM1253065     4  0.0000      1.000 0.000  0  0  1 0.000 0.000
#> GSM1253066     6  0.0000      0.999 0.000  0  0  0 0.000 1.000
#> GSM1253067     4  0.0000      1.000 0.000  0  0  1 0.000 0.000
#> GSM1253068     6  0.0000      0.999 0.000  0  0  0 0.000 1.000
#> GSM1253069     1  0.1387      0.920 0.932  0  0  0 0.000 0.068
#> GSM1253070     6  0.0146      0.995 0.000  0  0  0 0.004 0.996
#> GSM1253071     4  0.0000      1.000 0.000  0  0  1 0.000 0.000
#> GSM1253072     6  0.0000      0.999 0.000  0  0  0 0.000 1.000
#> GSM1253073     4  0.0000      1.000 0.000  0  0  1 0.000 0.000
#> GSM1253074     1  0.2260      0.893 0.860  0  0  0 0.000 0.140
#> GSM1253032     5  0.0000      1.000 0.000  0  0  0 1.000 0.000
#> GSM1253034     2  0.0000      1.000 0.000  1  0  0 0.000 0.000
#> GSM1253039     2  0.0000      1.000 0.000  1  0  0 0.000 0.000
#> GSM1253040     2  0.0000      1.000 0.000  1  0  0 0.000 0.000
#> GSM1253041     2  0.0000      1.000 0.000  1  0  0 0.000 0.000
#> GSM1253046     5  0.0000      1.000 0.000  0  0  0 1.000 0.000
#> GSM1253048     2  0.0000      1.000 0.000  1  0  0 0.000 0.000
#> GSM1253049     2  0.0000      1.000 0.000  1  0  0 0.000 0.000
#> GSM1253052     3  0.0000      1.000 0.000  0  1  0 0.000 0.000
#> GSM1253037     2  0.0000      1.000 0.000  1  0  0 0.000 0.000
#> GSM1253028     3  0.0000      1.000 0.000  0  1  0 0.000 0.000
#> GSM1253029     3  0.0000      1.000 0.000  0  1  0 0.000 0.000
#> GSM1253030     2  0.0000      1.000 0.000  1  0  0 0.000 0.000
#> GSM1253031     3  0.0000      1.000 0.000  0  1  0 0.000 0.000
#> GSM1253033     5  0.0000      1.000 0.000  0  0  0 1.000 0.000
#> GSM1253035     3  0.0000      1.000 0.000  0  1  0 0.000 0.000
#> GSM1253036     3  0.0000      1.000 0.000  0  1  0 0.000 0.000
#> GSM1253038     2  0.0000      1.000 0.000  1  0  0 0.000 0.000
#> GSM1253042     3  0.0000      1.000 0.000  0  1  0 0.000 0.000
#> GSM1253045     3  0.0000      1.000 0.000  0  1  0 0.000 0.000
#> GSM1253043     3  0.0000      1.000 0.000  0  1  0 0.000 0.000
#> GSM1253044     2  0.0000      1.000 0.000  1  0  0 0.000 0.000
#> GSM1253047     5  0.0000      1.000 0.000  0  0  0 1.000 0.000
#> GSM1253050     2  0.0000      1.000 0.000  1  0  0 0.000 0.000
#> GSM1253051     2  0.0000      1.000 0.000  1  0  0 0.000 0.000
#> GSM1253053     3  0.0000      1.000 0.000  0  1  0 0.000 0.000
#> GSM1253054     5  0.0000      1.000 0.000  0  0  0 1.000 0.000
#> GSM1253055     3  0.0000      1.000 0.000  0  1  0 0.000 0.000
#> GSM1253079     1  0.2527      0.866 0.832  0  0  0 0.000 0.168
#> GSM1253083     1  0.0000      0.930 1.000  0  0  0 0.000 0.000
#> GSM1253075     1  0.0000      0.930 1.000  0  0  0 0.000 0.000
#> GSM1253077     1  0.0000      0.930 1.000  0  0  0 0.000 0.000
#> GSM1253076     1  0.0000      0.930 1.000  0  0  0 0.000 0.000
#> GSM1253078     1  0.0000      0.930 1.000  0  0  0 0.000 0.000
#> GSM1253081     6  0.0000      0.999 0.000  0  0  0 0.000 1.000
#> GSM1253080     1  0.0000      0.930 1.000  0  0  0 0.000 0.000
#> GSM1253082     6  0.0000      0.999 0.000  0  0  0 0.000 1.000

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 infection(p) disease.state(p) individual(p) k
#> CV:mclust 56     3.60e-03         4.20e-12         0.995 2
#> CV:mclust 56     4.69e-03         2.85e-11         0.932 3
#> CV:mclust 55     3.17e-05         4.79e-14         0.806 4
#> CV:mclust 56     3.15e-05         6.30e-13         0.853 5
#> CV:mclust 56     8.89e-05         3.40e-12         0.778 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 51979 rows and 56 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#>   Subgroups are detected by 'NMF' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 5.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk CV-NMF-collect-plots

The plots are:

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

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

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

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

select_partition_number(res)

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

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.986       0.994        0.49523 0.507   0.507
#> 3 3 0.786           0.808       0.921        0.30173 0.829   0.672
#> 4 4 0.927           0.886       0.955        0.15249 0.834   0.582
#> 5 5 0.945           0.884       0.963        0.00267 0.960   0.858
#> 6 6 0.842           0.785       0.881        0.01852 0.974   0.904

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

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

suggest_best_k(res)

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

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

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

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

show/hide code output

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

#>            class entropy silhouette   p1   p2
#> GSM1253056     1   0.000      0.990 1.00 0.00
#> GSM1253057     1   0.000      0.990 1.00 0.00
#> GSM1253058     1   0.000      0.990 1.00 0.00
#> GSM1253059     1   0.000      0.990 1.00 0.00
#> GSM1253060     1   0.000      0.990 1.00 0.00
#> GSM1253061     1   0.000      0.990 1.00 0.00
#> GSM1253062     1   0.000      0.990 1.00 0.00
#> GSM1253063     1   0.000      0.990 1.00 0.00
#> GSM1253064     1   0.000      0.990 1.00 0.00
#> GSM1253065     1   0.000      0.990 1.00 0.00
#> GSM1253066     1   0.000      0.990 1.00 0.00
#> GSM1253067     1   0.000      0.990 1.00 0.00
#> GSM1253068     1   0.000      0.990 1.00 0.00
#> GSM1253069     1   0.000      0.990 1.00 0.00
#> GSM1253070     1   0.000      0.990 1.00 0.00
#> GSM1253071     1   0.000      0.990 1.00 0.00
#> GSM1253072     1   0.000      0.990 1.00 0.00
#> GSM1253073     1   0.000      0.990 1.00 0.00
#> GSM1253074     1   0.000      0.990 1.00 0.00
#> GSM1253032     1   0.000      0.990 1.00 0.00
#> GSM1253034     2   0.000      1.000 0.00 1.00
#> GSM1253039     2   0.000      1.000 0.00 1.00
#> GSM1253040     2   0.000      1.000 0.00 1.00
#> GSM1253041     2   0.000      1.000 0.00 1.00
#> GSM1253046     1   0.000      0.990 1.00 0.00
#> GSM1253048     2   0.000      1.000 0.00 1.00
#> GSM1253049     2   0.000      1.000 0.00 1.00
#> GSM1253052     2   0.000      1.000 0.00 1.00
#> GSM1253037     2   0.000      1.000 0.00 1.00
#> GSM1253028     2   0.000      1.000 0.00 1.00
#> GSM1253029     2   0.000      1.000 0.00 1.00
#> GSM1253030     2   0.000      1.000 0.00 1.00
#> GSM1253031     2   0.000      1.000 0.00 1.00
#> GSM1253033     1   0.000      0.990 1.00 0.00
#> GSM1253035     2   0.000      1.000 0.00 1.00
#> GSM1253036     2   0.000      1.000 0.00 1.00
#> GSM1253038     2   0.000      1.000 0.00 1.00
#> GSM1253042     2   0.000      1.000 0.00 1.00
#> GSM1253045     2   0.000      1.000 0.00 1.00
#> GSM1253043     2   0.000      1.000 0.00 1.00
#> GSM1253044     2   0.000      1.000 0.00 1.00
#> GSM1253047     1   0.000      0.990 1.00 0.00
#> GSM1253050     2   0.000      1.000 0.00 1.00
#> GSM1253051     2   0.000      1.000 0.00 1.00
#> GSM1253053     2   0.000      1.000 0.00 1.00
#> GSM1253054     1   0.904      0.529 0.68 0.32
#> GSM1253055     2   0.000      1.000 0.00 1.00
#> GSM1253079     1   0.000      0.990 1.00 0.00
#> GSM1253083     1   0.000      0.990 1.00 0.00
#> GSM1253075     1   0.000      0.990 1.00 0.00
#> GSM1253077     1   0.000      0.990 1.00 0.00
#> GSM1253076     1   0.000      0.990 1.00 0.00
#> GSM1253078     1   0.000      0.990 1.00 0.00
#> GSM1253081     1   0.000      0.990 1.00 0.00
#> GSM1253080     1   0.000      0.990 1.00 0.00
#> GSM1253082     1   0.000      0.990 1.00 0.00

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3
#> GSM1253056     1  0.0000      0.895 1.000 0.000 0.000
#> GSM1253057     1  0.4931      0.756 0.768 0.000 0.232
#> GSM1253058     1  0.0000      0.895 1.000 0.000 0.000
#> GSM1253059     1  0.0000      0.895 1.000 0.000 0.000
#> GSM1253060     1  0.0000      0.895 1.000 0.000 0.000
#> GSM1253061     1  0.0000      0.895 1.000 0.000 0.000
#> GSM1253062     1  0.4346      0.803 0.816 0.000 0.184
#> GSM1253063     1  0.0000      0.895 1.000 0.000 0.000
#> GSM1253064     1  0.2796      0.864 0.908 0.000 0.092
#> GSM1253065     1  0.0000      0.895 1.000 0.000 0.000
#> GSM1253066     1  0.1411      0.886 0.964 0.000 0.036
#> GSM1253067     1  0.0000      0.895 1.000 0.000 0.000
#> GSM1253068     1  0.4504      0.793 0.804 0.000 0.196
#> GSM1253069     1  0.0237      0.894 0.996 0.000 0.004
#> GSM1253070     3  0.3619      0.709 0.136 0.000 0.864
#> GSM1253071     1  0.0000      0.895 1.000 0.000 0.000
#> GSM1253072     1  0.0000      0.895 1.000 0.000 0.000
#> GSM1253073     1  0.0000      0.895 1.000 0.000 0.000
#> GSM1253074     1  0.3192      0.853 0.888 0.000 0.112
#> GSM1253032     3  0.0000      0.852 0.000 0.000 1.000
#> GSM1253034     2  0.0000      0.948 0.000 1.000 0.000
#> GSM1253039     2  0.0000      0.948 0.000 1.000 0.000
#> GSM1253040     2  0.0000      0.948 0.000 1.000 0.000
#> GSM1253041     2  0.0000      0.948 0.000 1.000 0.000
#> GSM1253046     3  0.0000      0.852 0.000 0.000 1.000
#> GSM1253048     2  0.0000      0.948 0.000 1.000 0.000
#> GSM1253049     2  0.0000      0.948 0.000 1.000 0.000
#> GSM1253052     2  0.1411      0.918 0.000 0.964 0.036
#> GSM1253037     2  0.0000      0.948 0.000 1.000 0.000
#> GSM1253028     2  0.6168      0.302 0.000 0.588 0.412
#> GSM1253029     2  0.0000      0.948 0.000 1.000 0.000
#> GSM1253030     2  0.0000      0.948 0.000 1.000 0.000
#> GSM1253031     2  0.6295      0.153 0.000 0.528 0.472
#> GSM1253033     3  0.0000      0.852 0.000 0.000 1.000
#> GSM1253035     2  0.0747      0.936 0.000 0.984 0.016
#> GSM1253036     2  0.0000      0.948 0.000 1.000 0.000
#> GSM1253038     2  0.0000      0.948 0.000 1.000 0.000
#> GSM1253042     2  0.0000      0.948 0.000 1.000 0.000
#> GSM1253045     3  0.0000      0.852 0.000 0.000 1.000
#> GSM1253043     3  0.0237      0.850 0.000 0.004 0.996
#> GSM1253044     2  0.0000      0.948 0.000 1.000 0.000
#> GSM1253047     3  0.0000      0.852 0.000 0.000 1.000
#> GSM1253050     2  0.0000      0.948 0.000 1.000 0.000
#> GSM1253051     2  0.0000      0.948 0.000 1.000 0.000
#> GSM1253053     2  0.0000      0.948 0.000 1.000 0.000
#> GSM1253054     3  0.0000      0.852 0.000 0.000 1.000
#> GSM1253055     3  0.6305     -0.140 0.000 0.484 0.516
#> GSM1253079     1  0.3879      0.827 0.848 0.000 0.152
#> GSM1253083     1  0.1163      0.889 0.972 0.000 0.028
#> GSM1253075     3  0.6309     -0.275 0.496 0.000 0.504
#> GSM1253077     1  0.6280      0.310 0.540 0.000 0.460
#> GSM1253076     1  0.5216      0.723 0.740 0.000 0.260
#> GSM1253078     1  0.5785      0.613 0.668 0.000 0.332
#> GSM1253081     1  0.0000      0.895 1.000 0.000 0.000
#> GSM1253080     1  0.5497      0.680 0.708 0.000 0.292
#> GSM1253082     1  0.0000      0.895 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
#> GSM1253056     4  0.0188     0.9967 0.000 0.000 0.004 0.996
#> GSM1253057     1  0.0000     0.9403 1.000 0.000 0.000 0.000
#> GSM1253058     4  0.0000     0.9979 0.000 0.000 0.000 1.000
#> GSM1253059     4  0.0188     0.9948 0.004 0.000 0.000 0.996
#> GSM1253060     4  0.0188     0.9967 0.000 0.000 0.004 0.996
#> GSM1253061     1  0.0336     0.9366 0.992 0.000 0.000 0.008
#> GSM1253062     1  0.0000     0.9403 1.000 0.000 0.000 0.000
#> GSM1253063     4  0.0000     0.9979 0.000 0.000 0.000 1.000
#> GSM1253064     1  0.0336     0.9371 0.992 0.000 0.000 0.008
#> GSM1253065     4  0.0188     0.9967 0.000 0.000 0.004 0.996
#> GSM1253066     1  0.0376     0.9376 0.992 0.000 0.004 0.004
#> GSM1253067     4  0.0000     0.9979 0.000 0.000 0.000 1.000
#> GSM1253068     1  0.0336     0.9368 0.992 0.000 0.008 0.000
#> GSM1253069     1  0.0000     0.9403 1.000 0.000 0.000 0.000
#> GSM1253070     1  0.4103     0.6497 0.744 0.000 0.256 0.000
#> GSM1253071     4  0.0000     0.9979 0.000 0.000 0.000 1.000
#> GSM1253072     1  0.0469     0.9346 0.988 0.000 0.000 0.012
#> GSM1253073     4  0.0000     0.9979 0.000 0.000 0.000 1.000
#> GSM1253074     1  0.0000     0.9403 1.000 0.000 0.000 0.000
#> GSM1253032     3  0.0000     0.9280 0.000 0.000 1.000 0.000
#> GSM1253034     2  0.0000     0.9425 0.000 1.000 0.000 0.000
#> GSM1253039     2  0.0000     0.9425 0.000 1.000 0.000 0.000
#> GSM1253040     2  0.0000     0.9425 0.000 1.000 0.000 0.000
#> GSM1253041     2  0.0000     0.9425 0.000 1.000 0.000 0.000
#> GSM1253046     3  0.0000     0.9280 0.000 0.000 1.000 0.000
#> GSM1253048     2  0.0000     0.9425 0.000 1.000 0.000 0.000
#> GSM1253049     2  0.0000     0.9425 0.000 1.000 0.000 0.000
#> GSM1253052     2  0.4855     0.3339 0.000 0.600 0.400 0.000
#> GSM1253037     2  0.0000     0.9425 0.000 1.000 0.000 0.000
#> GSM1253028     2  0.4382     0.5786 0.000 0.704 0.296 0.000
#> GSM1253029     2  0.0188     0.9396 0.000 0.996 0.004 0.000
#> GSM1253030     2  0.0000     0.9425 0.000 1.000 0.000 0.000
#> GSM1253031     3  0.1118     0.9075 0.000 0.036 0.964 0.000
#> GSM1253033     3  0.0000     0.9280 0.000 0.000 1.000 0.000
#> GSM1253035     3  0.4985     0.0102 0.000 0.468 0.532 0.000
#> GSM1253036     2  0.0000     0.9425 0.000 1.000 0.000 0.000
#> GSM1253038     2  0.0000     0.9425 0.000 1.000 0.000 0.000
#> GSM1253042     2  0.0000     0.9425 0.000 1.000 0.000 0.000
#> GSM1253045     3  0.0336     0.9235 0.008 0.000 0.992 0.000
#> GSM1253043     3  0.0188     0.9270 0.000 0.004 0.996 0.000
#> GSM1253044     2  0.0000     0.9425 0.000 1.000 0.000 0.000
#> GSM1253047     3  0.0000     0.9280 0.000 0.000 1.000 0.000
#> GSM1253050     2  0.0000     0.9425 0.000 1.000 0.000 0.000
#> GSM1253051     2  0.0000     0.9425 0.000 1.000 0.000 0.000
#> GSM1253053     2  0.3610     0.7333 0.000 0.800 0.200 0.000
#> GSM1253054     3  0.0000     0.9280 0.000 0.000 1.000 0.000
#> GSM1253055     3  0.0817     0.9161 0.000 0.024 0.976 0.000
#> GSM1253079     1  0.0000     0.9403 1.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000     0.9403 1.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000     0.9403 1.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000     0.9403 1.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000     0.9403 1.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000     0.9403 1.000 0.000 0.000 0.000
#> GSM1253081     1  0.4730     0.4647 0.636 0.000 0.000 0.364
#> GSM1253080     1  0.0000     0.9403 1.000 0.000 0.000 0.000
#> GSM1253082     1  0.4804     0.4194 0.616 0.000 0.000 0.384

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4    p5
#> GSM1253056     4  0.0162     0.7805 0.000 0.000 0.004 0.996 0.000
#> GSM1253057     1  0.0000     0.9607 1.000 0.000 0.000 0.000 0.000
#> GSM1253058     4  0.3707     0.2030 0.000 0.000 0.284 0.716 0.000
#> GSM1253059     3  0.3661     0.0000 0.000 0.000 0.724 0.276 0.000
#> GSM1253060     4  0.0510     0.7791 0.000 0.000 0.016 0.984 0.000
#> GSM1253061     1  0.0000     0.9607 1.000 0.000 0.000 0.000 0.000
#> GSM1253062     1  0.0162     0.9579 0.996 0.000 0.004 0.000 0.000
#> GSM1253063     4  0.0794     0.7739 0.000 0.000 0.028 0.972 0.000
#> GSM1253064     1  0.0880     0.9312 0.968 0.000 0.000 0.032 0.000
#> GSM1253065     4  0.0404     0.7765 0.000 0.000 0.012 0.988 0.000
#> GSM1253066     1  0.0000     0.9607 1.000 0.000 0.000 0.000 0.000
#> GSM1253067     4  0.0290     0.7810 0.000 0.000 0.008 0.992 0.000
#> GSM1253068     1  0.0000     0.9607 1.000 0.000 0.000 0.000 0.000
#> GSM1253069     1  0.0000     0.9607 1.000 0.000 0.000 0.000 0.000
#> GSM1253070     1  0.2843     0.7852 0.848 0.000 0.008 0.000 0.144
#> GSM1253071     4  0.0162     0.7805 0.000 0.000 0.004 0.996 0.000
#> GSM1253072     1  0.0000     0.9607 1.000 0.000 0.000 0.000 0.000
#> GSM1253073     4  0.1478     0.7424 0.000 0.000 0.064 0.936 0.000
#> GSM1253074     1  0.0000     0.9607 1.000 0.000 0.000 0.000 0.000
#> GSM1253032     5  0.0000     0.9911 0.000 0.000 0.000 0.000 1.000
#> GSM1253034     2  0.0000     0.9860 0.000 1.000 0.000 0.000 0.000
#> GSM1253039     2  0.0000     0.9860 0.000 1.000 0.000 0.000 0.000
#> GSM1253040     2  0.0000     0.9860 0.000 1.000 0.000 0.000 0.000
#> GSM1253041     2  0.0000     0.9860 0.000 1.000 0.000 0.000 0.000
#> GSM1253046     5  0.0162     0.9909 0.000 0.000 0.004 0.000 0.996
#> GSM1253048     2  0.0000     0.9860 0.000 1.000 0.000 0.000 0.000
#> GSM1253049     2  0.0000     0.9860 0.000 1.000 0.000 0.000 0.000
#> GSM1253052     2  0.0771     0.9709 0.000 0.976 0.004 0.000 0.020
#> GSM1253037     2  0.0000     0.9860 0.000 1.000 0.000 0.000 0.000
#> GSM1253028     2  0.2470     0.8660 0.000 0.884 0.012 0.000 0.104
#> GSM1253029     2  0.0162     0.9843 0.000 0.996 0.004 0.000 0.000
#> GSM1253030     2  0.0290     0.9823 0.000 0.992 0.008 0.000 0.000
#> GSM1253031     5  0.0566     0.9851 0.000 0.004 0.012 0.000 0.984
#> GSM1253033     5  0.0162     0.9909 0.000 0.000 0.004 0.000 0.996
#> GSM1253035     2  0.1410     0.9333 0.000 0.940 0.000 0.000 0.060
#> GSM1253036     2  0.0290     0.9822 0.000 0.992 0.008 0.000 0.000
#> GSM1253038     2  0.0000     0.9860 0.000 1.000 0.000 0.000 0.000
#> GSM1253042     2  0.0000     0.9860 0.000 1.000 0.000 0.000 0.000
#> GSM1253045     5  0.0162     0.9907 0.000 0.000 0.004 0.000 0.996
#> GSM1253043     5  0.0510     0.9870 0.000 0.000 0.016 0.000 0.984
#> GSM1253044     2  0.0000     0.9860 0.000 1.000 0.000 0.000 0.000
#> GSM1253047     5  0.0000     0.9911 0.000 0.000 0.000 0.000 1.000
#> GSM1253050     2  0.0000     0.9860 0.000 1.000 0.000 0.000 0.000
#> GSM1253051     2  0.0000     0.9860 0.000 1.000 0.000 0.000 0.000
#> GSM1253053     2  0.0579     0.9775 0.000 0.984 0.008 0.000 0.008
#> GSM1253054     5  0.0162     0.9898 0.000 0.000 0.004 0.000 0.996
#> GSM1253055     5  0.0807     0.9743 0.000 0.012 0.012 0.000 0.976
#> GSM1253079     1  0.0000     0.9607 1.000 0.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000     0.9607 1.000 0.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000     0.9607 1.000 0.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000     0.9607 1.000 0.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000     0.9607 1.000 0.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000     0.9607 1.000 0.000 0.000 0.000 0.000
#> GSM1253081     4  0.4294     0.0579 0.468 0.000 0.000 0.532 0.000
#> GSM1253080     1  0.0000     0.9607 1.000 0.000 0.000 0.000 0.000
#> GSM1253082     1  0.4138     0.3109 0.616 0.000 0.000 0.384 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
#> GSM1253056     4  0.0146     0.4482 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM1253057     1  0.0146     0.9499 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM1253058     6  0.4695     0.0000 0.000 0.000 0.044 0.448 0.000 0.508
#> GSM1253059     3  0.5444     0.3285 0.000 0.000 0.576 0.216 0.000 0.208
#> GSM1253060     4  0.3727     0.0355 0.000 0.000 0.388 0.612 0.000 0.000
#> GSM1253061     1  0.0858     0.9449 0.968 0.000 0.028 0.000 0.000 0.004
#> GSM1253062     1  0.0603     0.9477 0.980 0.000 0.004 0.000 0.000 0.016
#> GSM1253063     4  0.3868    -0.3878 0.000 0.000 0.496 0.504 0.000 0.000
#> GSM1253064     1  0.2094     0.9042 0.908 0.000 0.004 0.064 0.000 0.024
#> GSM1253065     4  0.0790     0.4035 0.000 0.000 0.000 0.968 0.000 0.032
#> GSM1253066     1  0.1138     0.9405 0.960 0.000 0.004 0.012 0.000 0.024
#> GSM1253067     4  0.0458     0.4511 0.000 0.000 0.016 0.984 0.000 0.000
#> GSM1253068     1  0.0748     0.9469 0.976 0.000 0.004 0.004 0.000 0.016
#> GSM1253069     1  0.0146     0.9499 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM1253070     1  0.3968     0.7054 0.756 0.000 0.060 0.000 0.180 0.004
#> GSM1253071     4  0.3565     0.2706 0.000 0.000 0.304 0.692 0.000 0.004
#> GSM1253072     1  0.0964     0.9455 0.968 0.000 0.012 0.004 0.000 0.016
#> GSM1253073     3  0.4072     0.1609 0.000 0.000 0.544 0.448 0.000 0.008
#> GSM1253074     1  0.0146     0.9499 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM1253032     5  0.0000     0.8924 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1253034     2  0.0291     0.9410 0.000 0.992 0.004 0.000 0.000 0.004
#> GSM1253039     2  0.0291     0.9406 0.000 0.992 0.004 0.000 0.000 0.004
#> GSM1253040     2  0.0291     0.9406 0.000 0.992 0.004 0.000 0.000 0.004
#> GSM1253041     2  0.0260     0.9402 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM1253046     5  0.0260     0.8928 0.000 0.000 0.008 0.000 0.992 0.000
#> GSM1253048     2  0.0622     0.9393 0.000 0.980 0.008 0.000 0.000 0.012
#> GSM1253049     2  0.0000     0.9405 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253052     2  0.0912     0.9349 0.000 0.972 0.004 0.012 0.004 0.008
#> GSM1253037     2  0.0146     0.9406 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM1253028     2  0.4322     0.7356 0.000 0.736 0.192 0.000 0.052 0.020
#> GSM1253029     2  0.0405     0.9396 0.000 0.988 0.004 0.000 0.000 0.008
#> GSM1253030     2  0.2814     0.8329 0.000 0.820 0.172 0.000 0.000 0.008
#> GSM1253031     5  0.2963     0.8470 0.000 0.004 0.152 0.000 0.828 0.016
#> GSM1253033     5  0.1806     0.8688 0.000 0.000 0.088 0.000 0.908 0.004
#> GSM1253035     2  0.2518     0.8749 0.000 0.880 0.012 0.000 0.092 0.016
#> GSM1253036     2  0.2896     0.8414 0.000 0.824 0.160 0.000 0.000 0.016
#> GSM1253038     2  0.0520     0.9401 0.000 0.984 0.008 0.000 0.000 0.008
#> GSM1253042     2  0.1003     0.9382 0.000 0.964 0.020 0.000 0.000 0.016
#> GSM1253045     5  0.2358     0.8658 0.000 0.000 0.108 0.000 0.876 0.016
#> GSM1253043     5  0.3952     0.7782 0.000 0.000 0.212 0.000 0.736 0.052
#> GSM1253044     2  0.0717     0.9387 0.000 0.976 0.008 0.000 0.000 0.016
#> GSM1253047     5  0.0146     0.8921 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM1253050     2  0.1003     0.9376 0.000 0.964 0.016 0.000 0.000 0.020
#> GSM1253051     2  0.0909     0.9387 0.000 0.968 0.012 0.000 0.000 0.020
#> GSM1253053     2  0.3959     0.7730 0.000 0.792 0.004 0.132 0.024 0.048
#> GSM1253054     5  0.0363     0.8907 0.000 0.000 0.000 0.000 0.988 0.012
#> GSM1253055     5  0.3357     0.7305 0.000 0.144 0.020 0.000 0.816 0.020
#> GSM1253079     1  0.0146     0.9499 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM1253083     1  0.0547     0.9442 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM1253075     1  0.0363     0.9493 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM1253077     1  0.0000     0.9500 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253076     1  0.0146     0.9500 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM1253078     1  0.0000     0.9500 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253081     1  0.3790     0.7529 0.772 0.000 0.020 0.184 0.000 0.024
#> GSM1253080     1  0.0146     0.9499 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM1253082     1  0.3233     0.8276 0.828 0.000 0.016 0.132 0.000 0.024

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 infection(p) disease.state(p) individual(p) k
#> CV:NMF 56     0.018077         1.69e-08         0.955 2
#> CV:NMF 51     0.014712         8.96e-09         0.908 3
#> CV:NMF 52     0.000833         2.25e-10         0.893 4
#> CV:NMF 52     0.000833         3.91e-10         0.883 5
#> CV:NMF 47     0.000274         8.31e-09         0.704 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 51979 rows and 56 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#>   Subgroups are detected by 'hclust' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 5.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk MAD-hclust-collect-plots

The plots are:

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

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

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

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

select_partition_number(res)

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

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           1.000       1.000         0.4933 0.507   0.507
#> 3 3 0.827           0.957       0.944         0.2618 0.860   0.723
#> 4 4 1.000           1.000       1.000         0.1167 0.938   0.832
#> 5 5 1.000           0.998       0.981         0.1128 0.914   0.719
#> 6 6 1.000           0.941       0.983         0.0171 0.995   0.976

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

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

suggest_best_k(res)

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

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

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

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

show/hide code output

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

#>            class entropy silhouette    p1    p2
#> GSM1253056     1  0.0000      1.000 1.000 0.000
#> GSM1253057     1  0.0000      1.000 1.000 0.000
#> GSM1253058     1  0.0000      1.000 1.000 0.000
#> GSM1253059     1  0.0000      1.000 1.000 0.000
#> GSM1253060     1  0.0000      1.000 1.000 0.000
#> GSM1253061     1  0.0000      1.000 1.000 0.000
#> GSM1253062     1  0.0000      1.000 1.000 0.000
#> GSM1253063     1  0.0000      1.000 1.000 0.000
#> GSM1253064     1  0.0000      1.000 1.000 0.000
#> GSM1253065     1  0.0000      1.000 1.000 0.000
#> GSM1253066     1  0.0000      1.000 1.000 0.000
#> GSM1253067     1  0.0000      1.000 1.000 0.000
#> GSM1253068     1  0.0000      1.000 1.000 0.000
#> GSM1253069     1  0.0000      1.000 1.000 0.000
#> GSM1253070     1  0.0000      1.000 1.000 0.000
#> GSM1253071     1  0.0000      1.000 1.000 0.000
#> GSM1253072     1  0.0000      1.000 1.000 0.000
#> GSM1253073     1  0.0000      1.000 1.000 0.000
#> GSM1253074     1  0.0000      1.000 1.000 0.000
#> GSM1253032     1  0.0000      1.000 1.000 0.000
#> GSM1253034     2  0.0000      1.000 0.000 1.000
#> GSM1253039     2  0.0000      1.000 0.000 1.000
#> GSM1253040     2  0.0000      1.000 0.000 1.000
#> GSM1253041     2  0.0000      1.000 0.000 1.000
#> GSM1253046     1  0.0000      1.000 1.000 0.000
#> GSM1253048     2  0.0000      1.000 0.000 1.000
#> GSM1253049     2  0.0000      1.000 0.000 1.000
#> GSM1253052     2  0.0000      1.000 0.000 1.000
#> GSM1253037     2  0.0000      1.000 0.000 1.000
#> GSM1253028     2  0.0000      1.000 0.000 1.000
#> GSM1253029     2  0.0000      1.000 0.000 1.000
#> GSM1253030     2  0.0000      1.000 0.000 1.000
#> GSM1253031     2  0.0000      1.000 0.000 1.000
#> GSM1253033     1  0.0000      1.000 1.000 0.000
#> GSM1253035     2  0.0000      1.000 0.000 1.000
#> GSM1253036     2  0.0000      1.000 0.000 1.000
#> GSM1253038     2  0.0000      1.000 0.000 1.000
#> GSM1253042     2  0.0000      1.000 0.000 1.000
#> GSM1253045     2  0.0000      1.000 0.000 1.000
#> GSM1253043     2  0.0376      0.996 0.004 0.996
#> GSM1253044     2  0.0000      1.000 0.000 1.000
#> GSM1253047     1  0.0000      1.000 1.000 0.000
#> GSM1253050     2  0.0000      1.000 0.000 1.000
#> GSM1253051     2  0.0000      1.000 0.000 1.000
#> GSM1253053     2  0.0000      1.000 0.000 1.000
#> GSM1253054     1  0.0000      1.000 1.000 0.000
#> GSM1253055     2  0.0000      1.000 0.000 1.000
#> GSM1253079     1  0.0000      1.000 1.000 0.000
#> GSM1253083     1  0.0000      1.000 1.000 0.000
#> GSM1253075     1  0.0000      1.000 1.000 0.000
#> GSM1253077     1  0.0000      1.000 1.000 0.000
#> GSM1253076     1  0.0000      1.000 1.000 0.000
#> GSM1253078     1  0.0000      1.000 1.000 0.000
#> GSM1253081     1  0.0000      1.000 1.000 0.000
#> GSM1253080     1  0.0000      1.000 1.000 0.000
#> GSM1253082     1  0.0000      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
#> GSM1253056     3  0.4842      1.000 0.224 0.000 0.776
#> GSM1253057     1  0.0000      0.937 1.000 0.000 0.000
#> GSM1253058     3  0.4842      1.000 0.224 0.000 0.776
#> GSM1253059     3  0.4842      1.000 0.224 0.000 0.776
#> GSM1253060     3  0.4842      1.000 0.224 0.000 0.776
#> GSM1253061     1  0.0000      0.937 1.000 0.000 0.000
#> GSM1253062     1  0.0000      0.937 1.000 0.000 0.000
#> GSM1253063     3  0.4842      1.000 0.224 0.000 0.776
#> GSM1253064     1  0.0000      0.937 1.000 0.000 0.000
#> GSM1253065     3  0.4842      1.000 0.224 0.000 0.776
#> GSM1253066     1  0.0000      0.937 1.000 0.000 0.000
#> GSM1253067     3  0.4842      1.000 0.224 0.000 0.776
#> GSM1253068     1  0.0000      0.937 1.000 0.000 0.000
#> GSM1253069     1  0.0000      0.937 1.000 0.000 0.000
#> GSM1253070     1  0.0000      0.937 1.000 0.000 0.000
#> GSM1253071     3  0.4842      1.000 0.224 0.000 0.776
#> GSM1253072     1  0.0000      0.937 1.000 0.000 0.000
#> GSM1253073     3  0.4842      1.000 0.224 0.000 0.776
#> GSM1253074     1  0.0000      0.937 1.000 0.000 0.000
#> GSM1253032     1  0.4842      0.761 0.776 0.000 0.224
#> GSM1253034     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253039     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253040     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253041     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253046     1  0.4842      0.761 0.776 0.000 0.224
#> GSM1253048     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253049     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253052     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253037     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253028     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253029     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253030     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253031     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253033     1  0.4842      0.761 0.776 0.000 0.224
#> GSM1253035     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253036     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253038     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253042     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253045     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253043     2  0.0237      0.996 0.000 0.996 0.004
#> GSM1253044     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253047     1  0.4842      0.761 0.776 0.000 0.224
#> GSM1253050     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253051     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253053     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253054     1  0.4842      0.761 0.776 0.000 0.224
#> GSM1253055     2  0.0000      1.000 0.000 1.000 0.000
#> GSM1253079     1  0.0000      0.937 1.000 0.000 0.000
#> GSM1253083     1  0.0000      0.937 1.000 0.000 0.000
#> GSM1253075     1  0.0000      0.937 1.000 0.000 0.000
#> GSM1253077     1  0.0000      0.937 1.000 0.000 0.000
#> GSM1253076     1  0.0000      0.937 1.000 0.000 0.000
#> GSM1253078     1  0.0000      0.937 1.000 0.000 0.000
#> GSM1253081     1  0.0000      0.937 1.000 0.000 0.000
#> GSM1253080     1  0.0000      0.937 1.000 0.000 0.000
#> GSM1253082     1  0.0000      0.937 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
#> GSM1253056     4  0.0000      1.000  0 0.000 0.000  1
#> GSM1253057     1  0.0000      1.000  1 0.000 0.000  0
#> GSM1253058     4  0.0000      1.000  0 0.000 0.000  1
#> GSM1253059     4  0.0000      1.000  0 0.000 0.000  1
#> GSM1253060     4  0.0000      1.000  0 0.000 0.000  1
#> GSM1253061     1  0.0000      1.000  1 0.000 0.000  0
#> GSM1253062     1  0.0000      1.000  1 0.000 0.000  0
#> GSM1253063     4  0.0000      1.000  0 0.000 0.000  1
#> GSM1253064     1  0.0000      1.000  1 0.000 0.000  0
#> GSM1253065     4  0.0000      1.000  0 0.000 0.000  1
#> GSM1253066     1  0.0000      1.000  1 0.000 0.000  0
#> GSM1253067     4  0.0000      1.000  0 0.000 0.000  1
#> GSM1253068     1  0.0000      1.000  1 0.000 0.000  0
#> GSM1253069     1  0.0000      1.000  1 0.000 0.000  0
#> GSM1253070     1  0.0000      1.000  1 0.000 0.000  0
#> GSM1253071     4  0.0000      1.000  0 0.000 0.000  1
#> GSM1253072     1  0.0000      1.000  1 0.000 0.000  0
#> GSM1253073     4  0.0000      1.000  0 0.000 0.000  1
#> GSM1253074     1  0.0000      1.000  1 0.000 0.000  0
#> GSM1253032     3  0.0000      1.000  0 0.000 1.000  0
#> GSM1253034     2  0.0000      1.000  0 1.000 0.000  0
#> GSM1253039     2  0.0000      1.000  0 1.000 0.000  0
#> GSM1253040     2  0.0000      1.000  0 1.000 0.000  0
#> GSM1253041     2  0.0000      1.000  0 1.000 0.000  0
#> GSM1253046     3  0.0000      1.000  0 0.000 1.000  0
#> GSM1253048     2  0.0000      1.000  0 1.000 0.000  0
#> GSM1253049     2  0.0000      1.000  0 1.000 0.000  0
#> GSM1253052     2  0.0000      1.000  0 1.000 0.000  0
#> GSM1253037     2  0.0000      1.000  0 1.000 0.000  0
#> GSM1253028     2  0.0000      1.000  0 1.000 0.000  0
#> GSM1253029     2  0.0000      1.000  0 1.000 0.000  0
#> GSM1253030     2  0.0000      1.000  0 1.000 0.000  0
#> GSM1253031     2  0.0000      1.000  0 1.000 0.000  0
#> GSM1253033     3  0.0000      1.000  0 0.000 1.000  0
#> GSM1253035     2  0.0000      1.000  0 1.000 0.000  0
#> GSM1253036     2  0.0000      1.000  0 1.000 0.000  0
#> GSM1253038     2  0.0000      1.000  0 1.000 0.000  0
#> GSM1253042     2  0.0000      1.000  0 1.000 0.000  0
#> GSM1253045     2  0.0000      1.000  0 1.000 0.000  0
#> GSM1253043     2  0.0188      0.996  0 0.996 0.004  0
#> GSM1253044     2  0.0000      1.000  0 1.000 0.000  0
#> GSM1253047     3  0.0000      1.000  0 0.000 1.000  0
#> GSM1253050     2  0.0000      1.000  0 1.000 0.000  0
#> GSM1253051     2  0.0000      1.000  0 1.000 0.000  0
#> GSM1253053     2  0.0000      1.000  0 1.000 0.000  0
#> GSM1253054     3  0.0000      1.000  0 0.000 1.000  0
#> GSM1253055     2  0.0000      1.000  0 1.000 0.000  0
#> GSM1253079     1  0.0000      1.000  1 0.000 0.000  0
#> GSM1253083     1  0.0000      1.000  1 0.000 0.000  0
#> GSM1253075     1  0.0000      1.000  1 0.000 0.000  0
#> GSM1253077     1  0.0000      1.000  1 0.000 0.000  0
#> GSM1253076     1  0.0000      1.000  1 0.000 0.000  0
#> GSM1253078     1  0.0000      1.000  1 0.000 0.000  0
#> GSM1253081     1  0.0000      1.000  1 0.000 0.000  0
#> GSM1253080     1  0.0000      1.000  1 0.000 0.000  0
#> GSM1253082     1  0.0000      1.000  1 0.000 0.000  0

show/hide code output

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

#>            class entropy silhouette p1    p2    p3 p4    p5
#> GSM1253056     4   0.000      1.000  0 0.000 0.000  1 0.000
#> GSM1253057     1   0.000      1.000  1 0.000 0.000  0 0.000
#> GSM1253058     4   0.000      1.000  0 0.000 0.000  1 0.000
#> GSM1253059     4   0.000      1.000  0 0.000 0.000  1 0.000
#> GSM1253060     4   0.000      1.000  0 0.000 0.000  1 0.000
#> GSM1253061     1   0.000      1.000  1 0.000 0.000  0 0.000
#> GSM1253062     1   0.000      1.000  1 0.000 0.000  0 0.000
#> GSM1253063     4   0.000      1.000  0 0.000 0.000  1 0.000
#> GSM1253064     1   0.000      1.000  1 0.000 0.000  0 0.000
#> GSM1253065     4   0.000      1.000  0 0.000 0.000  1 0.000
#> GSM1253066     1   0.000      1.000  1 0.000 0.000  0 0.000
#> GSM1253067     4   0.000      1.000  0 0.000 0.000  1 0.000
#> GSM1253068     1   0.000      1.000  1 0.000 0.000  0 0.000
#> GSM1253069     1   0.000      1.000  1 0.000 0.000  0 0.000
#> GSM1253070     1   0.000      1.000  1 0.000 0.000  0 0.000
#> GSM1253071     4   0.000      1.000  0 0.000 0.000  1 0.000
#> GSM1253072     1   0.000      1.000  1 0.000 0.000  0 0.000
#> GSM1253073     4   0.000      1.000  0 0.000 0.000  1 0.000
#> GSM1253074     1   0.000      1.000  1 0.000 0.000  0 0.000
#> GSM1253032     5   0.000      0.987  0 0.000 0.000  0 1.000
#> GSM1253034     2   0.000      1.000  0 1.000 0.000  0 0.000
#> GSM1253039     2   0.000      1.000  0 1.000 0.000  0 0.000
#> GSM1253040     2   0.000      1.000  0 1.000 0.000  0 0.000
#> GSM1253041     2   0.000      1.000  0 1.000 0.000  0 0.000
#> GSM1253046     5   0.000      0.987  0 0.000 0.000  0 1.000
#> GSM1253048     2   0.000      1.000  0 1.000 0.000  0 0.000
#> GSM1253049     2   0.000      1.000  0 1.000 0.000  0 0.000
#> GSM1253052     3   0.185      0.999  0 0.088 0.912  0 0.000
#> GSM1253037     2   0.000      1.000  0 1.000 0.000  0 0.000
#> GSM1253028     3   0.185      0.999  0 0.088 0.912  0 0.000
#> GSM1253029     3   0.185      0.999  0 0.088 0.912  0 0.000
#> GSM1253030     2   0.000      1.000  0 1.000 0.000  0 0.000
#> GSM1253031     3   0.185      0.999  0 0.088 0.912  0 0.000
#> GSM1253033     5   0.185      0.946  0 0.000 0.088  0 0.912
#> GSM1253035     3   0.185      0.999  0 0.088 0.912  0 0.000
#> GSM1253036     3   0.185      0.999  0 0.088 0.912  0 0.000
#> GSM1253038     2   0.000      1.000  0 1.000 0.000  0 0.000
#> GSM1253042     3   0.185      0.999  0 0.088 0.912  0 0.000
#> GSM1253045     3   0.185      0.999  0 0.088 0.912  0 0.000
#> GSM1253043     3   0.195      0.995  0 0.084 0.912  0 0.004
#> GSM1253044     2   0.000      1.000  0 1.000 0.000  0 0.000
#> GSM1253047     5   0.000      0.987  0 0.000 0.000  0 1.000
#> GSM1253050     2   0.000      1.000  0 1.000 0.000  0 0.000
#> GSM1253051     2   0.000      1.000  0 1.000 0.000  0 0.000
#> GSM1253053     3   0.185      0.999  0 0.088 0.912  0 0.000
#> GSM1253054     5   0.000      0.987  0 0.000 0.000  0 1.000
#> GSM1253055     3   0.185      0.999  0 0.088 0.912  0 0.000
#> GSM1253079     1   0.000      1.000  1 0.000 0.000  0 0.000
#> GSM1253083     1   0.000      1.000  1 0.000 0.000  0 0.000
#> GSM1253075     1   0.000      1.000  1 0.000 0.000  0 0.000
#> GSM1253077     1   0.000      1.000  1 0.000 0.000  0 0.000
#> GSM1253076     1   0.000      1.000  1 0.000 0.000  0 0.000
#> GSM1253078     1   0.000      1.000  1 0.000 0.000  0 0.000
#> GSM1253081     1   0.000      1.000  1 0.000 0.000  0 0.000
#> GSM1253080     1   0.000      1.000  1 0.000 0.000  0 0.000
#> GSM1253082     1   0.000      1.000  1 0.000 0.000  0 0.000

show/hide code output

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

#>            class entropy silhouette p1 p2    p3    p4    p5    p6
#> GSM1253056     4  0.0000      0.916  0  0 0.000 1.000 0.000 0.000
#> GSM1253057     1  0.0000      1.000  1  0 0.000 0.000 0.000 0.000
#> GSM1253058     4  0.3756     -0.190  0  0 0.000 0.600 0.000 0.400
#> GSM1253059     6  0.3288      0.000  0  0 0.000 0.276 0.000 0.724
#> GSM1253060     4  0.0000      0.916  0  0 0.000 1.000 0.000 0.000
#> GSM1253061     1  0.0000      1.000  1  0 0.000 0.000 0.000 0.000
#> GSM1253062     1  0.0000      1.000  1  0 0.000 0.000 0.000 0.000
#> GSM1253063     4  0.0000      0.916  0  0 0.000 1.000 0.000 0.000
#> GSM1253064     1  0.0000      1.000  1  0 0.000 0.000 0.000 0.000
#> GSM1253065     4  0.0000      0.916  0  0 0.000 1.000 0.000 0.000
#> GSM1253066     1  0.0000      1.000  1  0 0.000 0.000 0.000 0.000
#> GSM1253067     4  0.0000      0.916  0  0 0.000 1.000 0.000 0.000
#> GSM1253068     1  0.0000      1.000  1  0 0.000 0.000 0.000 0.000
#> GSM1253069     1  0.0000      1.000  1  0 0.000 0.000 0.000 0.000
#> GSM1253070     1  0.0000      1.000  1  0 0.000 0.000 0.000 0.000
#> GSM1253071     4  0.0000      0.916  0  0 0.000 1.000 0.000 0.000
#> GSM1253072     1  0.0000      1.000  1  0 0.000 0.000 0.000 0.000
#> GSM1253073     4  0.0000      0.916  0  0 0.000 1.000 0.000 0.000
#> GSM1253074     1  0.0000      1.000  1  0 0.000 0.000 0.000 0.000
#> GSM1253032     5  0.0000      0.940  0  0 0.000 0.000 1.000 0.000
#> GSM1253034     2  0.0000      1.000  0  1 0.000 0.000 0.000 0.000
#> GSM1253039     2  0.0000      1.000  0  1 0.000 0.000 0.000 0.000
#> GSM1253040     2  0.0000      1.000  0  1 0.000 0.000 0.000 0.000
#> GSM1253041     2  0.0000      1.000  0  1 0.000 0.000 0.000 0.000
#> GSM1253046     5  0.0000      0.940  0  0 0.000 0.000 1.000 0.000
#> GSM1253048     2  0.0000      1.000  0  1 0.000 0.000 0.000 0.000
#> GSM1253049     2  0.0000      1.000  0  1 0.000 0.000 0.000 0.000
#> GSM1253052     3  0.0000      1.000  0  0 1.000 0.000 0.000 0.000
#> GSM1253037     2  0.0000      1.000  0  1 0.000 0.000 0.000 0.000
#> GSM1253028     3  0.0000      1.000  0  0 1.000 0.000 0.000 0.000
#> GSM1253029     3  0.0000      1.000  0  0 1.000 0.000 0.000 0.000
#> GSM1253030     2  0.0000      1.000  0  1 0.000 0.000 0.000 0.000
#> GSM1253031     3  0.0000      1.000  0  0 1.000 0.000 0.000 0.000
#> GSM1253033     5  0.3288      0.726  0  0 0.000 0.000 0.724 0.276
#> GSM1253035     3  0.0000      1.000  0  0 1.000 0.000 0.000 0.000
#> GSM1253036     3  0.0000      1.000  0  0 1.000 0.000 0.000 0.000
#> GSM1253038     2  0.0000      1.000  0  1 0.000 0.000 0.000 0.000
#> GSM1253042     3  0.0000      1.000  0  0 1.000 0.000 0.000 0.000
#> GSM1253045     3  0.0000      1.000  0  0 1.000 0.000 0.000 0.000
#> GSM1253043     3  0.0146      0.996  0  0 0.996 0.000 0.004 0.000
#> GSM1253044     2  0.0000      1.000  0  1 0.000 0.000 0.000 0.000
#> GSM1253047     5  0.0000      0.940  0  0 0.000 0.000 1.000 0.000
#> GSM1253050     2  0.0000      1.000  0  1 0.000 0.000 0.000 0.000
#> GSM1253051     2  0.0000      1.000  0  1 0.000 0.000 0.000 0.000
#> GSM1253053     3  0.0000      1.000  0  0 1.000 0.000 0.000 0.000
#> GSM1253054     5  0.0000      0.940  0  0 0.000 0.000 1.000 0.000
#> GSM1253055     3  0.0000      1.000  0  0 1.000 0.000 0.000 0.000
#> GSM1253079     1  0.0000      1.000  1  0 0.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000      1.000  1  0 0.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000      1.000  1  0 0.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      1.000  1  0 0.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      1.000  1  0 0.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      1.000  1  0 0.000 0.000 0.000 0.000
#> GSM1253081     1  0.0000      1.000  1  0 0.000 0.000 0.000 0.000
#> GSM1253080     1  0.0000      1.000  1  0 0.000 0.000 0.000 0.000
#> GSM1253082     1  0.0000      1.000  1  0 0.000 0.000 0.000 0.000

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

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

consensus_heatmap(res, k = 2)

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

consensus_heatmap(res, k = 3)

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

consensus_heatmap(res, k = 4)

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

consensus_heatmap(res, k = 5)

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

consensus_heatmap(res, k = 6)

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

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

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

membership_heatmap(res, k = 2)

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

membership_heatmap(res, k = 3)

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

membership_heatmap(res, k = 4)

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

membership_heatmap(res, k = 5)

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

membership_heatmap(res, k = 6)

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

Signature heatmaps where rows are scaled:

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

get_signatures(res, k = 2)

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

get_signatures(res, k = 3)

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

get_signatures(res, k = 4)

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

get_signatures(res, k = 5)

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

get_signatures(res, k = 6)

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

Signature heatmaps where rows are not scaled:

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

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

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

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

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

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

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

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

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

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

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

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk MAD-hclust-signature_compare

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

which_row: row indices corresponding to the input matrix.
fdr: FDR for the differential test.
mean_x: The mean value in group x.
scaled_mean_x: The mean value in group x after rows are scaled.
km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

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

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

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

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

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

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

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

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

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

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

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

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk MAD-hclust-collect-classes

test_to_known_factors(res)

#>             n infection(p) disease.state(p) individual(p) k
#> MAD:hclust 56     0.018077         1.69e-08         0.955 2
#> MAD:hclust 56     0.000786         1.93e-09         0.944 3
#> MAD:hclust 56     0.000111         2.78e-11         0.909 4
#> MAD:hclust 56     0.000334         2.92e-12         0.862 5
#> MAD:hclust 54     0.000524         2.07e-11         0.813 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 51979 rows and 56 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           0.992       0.996         0.4945 0.507   0.507
#> 3 3 0.710           0.728       0.804         0.2749 0.964   0.932
#> 4 4 0.781           0.843       0.845         0.1269 0.695   0.424
#> 5 5 0.742           0.902       0.869         0.0723 0.953   0.820
#> 6 6 0.815           0.857       0.852         0.0519 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
#> GSM1253056     1   0.000      0.994 1.0 0.0
#> GSM1253057     1   0.000      0.994 1.0 0.0
#> GSM1253058     1   0.000      0.994 1.0 0.0
#> GSM1253059     1   0.000      0.994 1.0 0.0
#> GSM1253060     1   0.000      0.994 1.0 0.0
#> GSM1253061     1   0.000      0.994 1.0 0.0
#> GSM1253062     1   0.000      0.994 1.0 0.0
#> GSM1253063     1   0.000      0.994 1.0 0.0
#> GSM1253064     1   0.000      0.994 1.0 0.0
#> GSM1253065     1   0.000      0.994 1.0 0.0
#> GSM1253066     1   0.000      0.994 1.0 0.0
#> GSM1253067     1   0.000      0.994 1.0 0.0
#> GSM1253068     1   0.000      0.994 1.0 0.0
#> GSM1253069     1   0.000      0.994 1.0 0.0
#> GSM1253070     1   0.000      0.994 1.0 0.0
#> GSM1253071     1   0.000      0.994 1.0 0.0
#> GSM1253072     1   0.000      0.994 1.0 0.0
#> GSM1253073     1   0.000      0.994 1.0 0.0
#> GSM1253074     1   0.000      0.994 1.0 0.0
#> GSM1253032     1   0.000      0.994 1.0 0.0
#> GSM1253034     2   0.000      1.000 0.0 1.0
#> GSM1253039     2   0.000      1.000 0.0 1.0
#> GSM1253040     2   0.000      1.000 0.0 1.0
#> GSM1253041     2   0.000      1.000 0.0 1.0
#> GSM1253046     1   0.000      0.994 1.0 0.0
#> GSM1253048     2   0.000      1.000 0.0 1.0
#> GSM1253049     2   0.000      1.000 0.0 1.0
#> GSM1253052     2   0.000      1.000 0.0 1.0
#> GSM1253037     2   0.000      1.000 0.0 1.0
#> GSM1253028     2   0.000      1.000 0.0 1.0
#> GSM1253029     2   0.000      1.000 0.0 1.0
#> GSM1253030     2   0.000      1.000 0.0 1.0
#> GSM1253031     2   0.000      1.000 0.0 1.0
#> GSM1253033     1   0.000      0.994 1.0 0.0
#> GSM1253035     2   0.000      1.000 0.0 1.0
#> GSM1253036     2   0.000      1.000 0.0 1.0
#> GSM1253038     2   0.000      1.000 0.0 1.0
#> GSM1253042     2   0.000      1.000 0.0 1.0
#> GSM1253045     2   0.000      1.000 0.0 1.0
#> GSM1253043     2   0.000      1.000 0.0 1.0
#> GSM1253044     2   0.000      1.000 0.0 1.0
#> GSM1253047     1   0.000      0.994 1.0 0.0
#> GSM1253050     2   0.000      1.000 0.0 1.0
#> GSM1253051     2   0.000      1.000 0.0 1.0
#> GSM1253053     2   0.000      1.000 0.0 1.0
#> GSM1253054     1   0.722      0.750 0.8 0.2
#> GSM1253055     2   0.000      1.000 0.0 1.0
#> GSM1253079     1   0.000      0.994 1.0 0.0
#> GSM1253083     1   0.000      0.994 1.0 0.0
#> GSM1253075     1   0.000      0.994 1.0 0.0
#> GSM1253077     1   0.000      0.994 1.0 0.0
#> GSM1253076     1   0.000      0.994 1.0 0.0
#> GSM1253078     1   0.000      0.994 1.0 0.0
#> GSM1253081     1   0.000      0.994 1.0 0.0
#> GSM1253080     1   0.000      0.994 1.0 0.0
#> GSM1253082     1   0.000      0.994 1.0 0.0

show/hide code output

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

#>            class entropy silhouette    p1    p2 p3
#> GSM1253056     1  0.6308      0.617 0.508 0.000 NA
#> GSM1253057     1  0.0000      0.804 1.000 0.000 NA
#> GSM1253058     1  0.6308      0.617 0.508 0.000 NA
#> GSM1253059     1  0.6308      0.617 0.508 0.000 NA
#> GSM1253060     1  0.6308      0.617 0.508 0.000 NA
#> GSM1253061     1  0.0000      0.804 1.000 0.000 NA
#> GSM1253062     1  0.0000      0.804 1.000 0.000 NA
#> GSM1253063     1  0.6308      0.617 0.508 0.000 NA
#> GSM1253064     1  0.0000      0.804 1.000 0.000 NA
#> GSM1253065     1  0.6308      0.617 0.508 0.000 NA
#> GSM1253066     1  0.0000      0.804 1.000 0.000 NA
#> GSM1253067     1  0.6308      0.617 0.508 0.000 NA
#> GSM1253068     1  0.0000      0.804 1.000 0.000 NA
#> GSM1253069     1  0.0237      0.803 0.996 0.000 NA
#> GSM1253070     1  0.0237      0.803 0.996 0.000 NA
#> GSM1253071     1  0.6308      0.617 0.508 0.000 NA
#> GSM1253072     1  0.0000      0.804 1.000 0.000 NA
#> GSM1253073     1  0.6308      0.617 0.508 0.000 NA
#> GSM1253074     1  0.0237      0.803 0.996 0.000 NA
#> GSM1253032     1  0.9944      0.244 0.372 0.284 NA
#> GSM1253034     2  0.5431      0.852 0.000 0.716 NA
#> GSM1253039     2  0.5431      0.852 0.000 0.716 NA
#> GSM1253040     2  0.5431      0.852 0.000 0.716 NA
#> GSM1253041     2  0.5431      0.852 0.000 0.716 NA
#> GSM1253046     1  0.9517      0.376 0.476 0.212 NA
#> GSM1253048     2  0.5431      0.852 0.000 0.716 NA
#> GSM1253049     2  0.5431      0.852 0.000 0.716 NA
#> GSM1253052     2  0.0000      0.805 0.000 1.000 NA
#> GSM1253037     2  0.5431      0.852 0.000 0.716 NA
#> GSM1253028     2  0.1411      0.790 0.000 0.964 NA
#> GSM1253029     2  0.5058      0.848 0.000 0.756 NA
#> GSM1253030     2  0.5431      0.852 0.000 0.716 NA
#> GSM1253031     2  0.1031      0.796 0.000 0.976 NA
#> GSM1253033     1  0.9616      0.363 0.444 0.212 NA
#> GSM1253035     2  0.0000      0.805 0.000 1.000 NA
#> GSM1253036     2  0.3038      0.828 0.000 0.896 NA
#> GSM1253038     2  0.5431      0.852 0.000 0.716 NA
#> GSM1253042     2  0.0000      0.805 0.000 1.000 NA
#> GSM1253045     2  0.4796      0.658 0.000 0.780 NA
#> GSM1253043     2  0.4796      0.658 0.000 0.780 NA
#> GSM1253044     2  0.5431      0.852 0.000 0.716 NA
#> GSM1253047     1  0.9895      0.261 0.404 0.284 NA
#> GSM1253050     2  0.5431      0.852 0.000 0.716 NA
#> GSM1253051     2  0.5431      0.852 0.000 0.716 NA
#> GSM1253053     2  0.0000      0.805 0.000 1.000 NA
#> GSM1253054     2  0.9925     -0.122 0.336 0.384 NA
#> GSM1253055     2  0.1411      0.790 0.000 0.964 NA
#> GSM1253079     1  0.0000      0.804 1.000 0.000 NA
#> GSM1253083     1  0.0237      0.803 0.996 0.000 NA
#> GSM1253075     1  0.0000      0.804 1.000 0.000 NA
#> GSM1253077     1  0.0237      0.803 0.996 0.000 NA
#> GSM1253076     1  0.0237      0.803 0.996 0.000 NA
#> GSM1253078     1  0.0237      0.803 0.996 0.000 NA
#> GSM1253081     1  0.0000      0.804 1.000 0.000 NA
#> GSM1253080     1  0.0237      0.803 0.996 0.000 NA
#> GSM1253082     1  0.0000      0.804 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
#> GSM1253056     4  0.4454      0.998 0.308 0.000 0.000 0.692
#> GSM1253057     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253058     4  0.4769      0.994 0.308 0.000 0.008 0.684
#> GSM1253059     4  0.4769      0.994 0.308 0.000 0.008 0.684
#> GSM1253060     4  0.4454      0.998 0.308 0.000 0.000 0.692
#> GSM1253061     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253062     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253063     4  0.4454      0.998 0.308 0.000 0.000 0.692
#> GSM1253064     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253065     4  0.4454      0.998 0.308 0.000 0.000 0.692
#> GSM1253066     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253067     4  0.4454      0.998 0.308 0.000 0.000 0.692
#> GSM1253068     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253069     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253070     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253071     4  0.4454      0.998 0.308 0.000 0.000 0.692
#> GSM1253072     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253073     4  0.4454      0.998 0.308 0.000 0.000 0.692
#> GSM1253074     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253032     3  0.4769      0.534 0.008 0.000 0.684 0.308
#> GSM1253034     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253039     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253040     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253041     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253046     3  0.5786      0.497 0.052 0.000 0.640 0.308
#> GSM1253048     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253049     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253052     3  0.4877      0.467 0.000 0.408 0.592 0.000
#> GSM1253037     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253028     3  0.4804      0.491 0.000 0.384 0.616 0.000
#> GSM1253029     2  0.4564      0.320 0.000 0.672 0.328 0.000
#> GSM1253030     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253031     3  0.4817      0.488 0.000 0.388 0.612 0.000
#> GSM1253033     3  0.5186      0.497 0.016 0.000 0.640 0.344
#> GSM1253035     3  0.4877      0.467 0.000 0.408 0.592 0.000
#> GSM1253036     3  0.4999      0.255 0.000 0.492 0.508 0.000
#> GSM1253038     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253042     3  0.4877      0.467 0.000 0.408 0.592 0.000
#> GSM1253045     3  0.0336      0.582 0.000 0.008 0.992 0.000
#> GSM1253043     3  0.0336      0.582 0.000 0.008 0.992 0.000
#> GSM1253044     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253047     3  0.4769      0.534 0.008 0.000 0.684 0.308
#> GSM1253050     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253051     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253053     3  0.4877      0.467 0.000 0.408 0.592 0.000
#> GSM1253054     3  0.4769      0.534 0.008 0.000 0.684 0.308
#> GSM1253055     3  0.4804      0.491 0.000 0.384 0.616 0.000
#> GSM1253079     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253081     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253080     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253082     1  0.0000      1.000 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
#> GSM1253056     4   0.265      0.980 0.152 0.000 0.000 0.848 0.000
#> GSM1253057     1   0.000      0.898 1.000 0.000 0.000 0.000 0.000
#> GSM1253058     4   0.440      0.938 0.152 0.000 0.000 0.760 0.088
#> GSM1253059     4   0.451      0.935 0.152 0.000 0.000 0.752 0.096
#> GSM1253060     4   0.265      0.980 0.152 0.000 0.000 0.848 0.000
#> GSM1253061     1   0.311      0.856 0.800 0.000 0.000 0.000 0.200
#> GSM1253062     1   0.000      0.898 1.000 0.000 0.000 0.000 0.000
#> GSM1253063     4   0.265      0.980 0.152 0.000 0.000 0.848 0.000
#> GSM1253064     1   0.327      0.849 0.780 0.000 0.000 0.000 0.220
#> GSM1253065     4   0.265      0.980 0.152 0.000 0.000 0.848 0.000
#> GSM1253066     1   0.327      0.849 0.780 0.000 0.000 0.000 0.220
#> GSM1253067     4   0.281      0.979 0.152 0.000 0.000 0.844 0.004
#> GSM1253068     1   0.327      0.849 0.780 0.000 0.000 0.000 0.220
#> GSM1253069     1   0.000      0.898 1.000 0.000 0.000 0.000 0.000
#> GSM1253070     1   0.314      0.855 0.796 0.000 0.000 0.000 0.204
#> GSM1253071     4   0.265      0.980 0.152 0.000 0.000 0.848 0.000
#> GSM1253072     1   0.327      0.849 0.780 0.000 0.000 0.000 0.220
#> GSM1253073     4   0.314      0.976 0.152 0.000 0.000 0.832 0.016
#> GSM1253074     1   0.000      0.898 1.000 0.000 0.000 0.000 0.000
#> GSM1253032     5   0.395      0.985 0.000 0.000 0.332 0.000 0.668
#> GSM1253034     2   0.179      0.936 0.000 0.916 0.000 0.084 0.000
#> GSM1253039     2   0.208      0.934 0.000 0.908 0.000 0.084 0.008
#> GSM1253040     2   0.029      0.965 0.000 0.992 0.000 0.000 0.008
#> GSM1253041     2   0.000      0.967 0.000 1.000 0.000 0.000 0.000
#> GSM1253046     5   0.423      0.973 0.012 0.000 0.312 0.000 0.676
#> GSM1253048     2   0.000      0.967 0.000 1.000 0.000 0.000 0.000
#> GSM1253049     2   0.000      0.967 0.000 1.000 0.000 0.000 0.000
#> GSM1253052     3   0.497      0.880 0.000 0.260 0.672 0.068 0.000
#> GSM1253037     2   0.000      0.967 0.000 1.000 0.000 0.000 0.000
#> GSM1253028     3   0.351      0.867 0.000 0.252 0.748 0.000 0.000
#> GSM1253029     3   0.530      0.797 0.000 0.328 0.604 0.068 0.000
#> GSM1253030     2   0.208      0.934 0.000 0.908 0.000 0.084 0.008
#> GSM1253031     3   0.353      0.868 0.000 0.256 0.744 0.000 0.000
#> GSM1253033     5   0.419      0.974 0.000 0.000 0.304 0.012 0.684
#> GSM1253035     3   0.497      0.880 0.000 0.260 0.672 0.068 0.000
#> GSM1253036     3   0.368      0.855 0.000 0.280 0.720 0.000 0.000
#> GSM1253038     2   0.000      0.967 0.000 1.000 0.000 0.000 0.000
#> GSM1253042     3   0.497      0.880 0.000 0.260 0.672 0.068 0.000
#> GSM1253045     3   0.000      0.501 0.000 0.000 1.000 0.000 0.000
#> GSM1253043     3   0.000      0.501 0.000 0.000 1.000 0.000 0.000
#> GSM1253044     2   0.000      0.967 0.000 1.000 0.000 0.000 0.000
#> GSM1253047     5   0.395      0.985 0.000 0.000 0.332 0.000 0.668
#> GSM1253050     2   0.029      0.965 0.000 0.992 0.000 0.000 0.008
#> GSM1253051     2   0.179      0.936 0.000 0.916 0.000 0.084 0.000
#> GSM1253053     3   0.497      0.880 0.000 0.260 0.672 0.068 0.000
#> GSM1253054     5   0.395      0.985 0.000 0.000 0.332 0.000 0.668
#> GSM1253055     3   0.492      0.879 0.000 0.252 0.680 0.068 0.000
#> GSM1253079     1   0.000      0.898 1.000 0.000 0.000 0.000 0.000
#> GSM1253083     1   0.000      0.898 1.000 0.000 0.000 0.000 0.000
#> GSM1253075     1   0.000      0.898 1.000 0.000 0.000 0.000 0.000
#> GSM1253077     1   0.000      0.898 1.000 0.000 0.000 0.000 0.000
#> GSM1253076     1   0.000      0.898 1.000 0.000 0.000 0.000 0.000
#> GSM1253078     1   0.000      0.898 1.000 0.000 0.000 0.000 0.000
#> GSM1253081     1   0.402      0.828 0.752 0.000 0.000 0.028 0.220
#> GSM1253080     1   0.000      0.898 1.000 0.000 0.000 0.000 0.000
#> GSM1253082     1   0.402      0.828 0.752 0.000 0.000 0.028 0.220

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4    p5 p6
#> GSM1253056     4  0.1946      0.959 0.072 0.000 0.012 0.912 0.000 NA
#> GSM1253057     1  0.0405      0.803 0.988 0.000 0.008 0.000 0.000 NA
#> GSM1253058     4  0.4621      0.890 0.072 0.000 0.060 0.768 0.012 NA
#> GSM1253059     4  0.4879      0.861 0.072 0.000 0.048 0.740 0.012 NA
#> GSM1253060     4  0.1444      0.960 0.072 0.000 0.000 0.928 0.000 NA
#> GSM1253061     1  0.3965      0.729 0.604 0.000 0.008 0.000 0.000 NA
#> GSM1253062     1  0.0260      0.804 0.992 0.000 0.008 0.000 0.000 NA
#> GSM1253063     4  0.1444      0.960 0.072 0.000 0.000 0.928 0.000 NA
#> GSM1253064     1  0.3944      0.718 0.568 0.000 0.000 0.004 0.000 NA
#> GSM1253065     4  0.2058      0.958 0.072 0.000 0.012 0.908 0.000 NA
#> GSM1253066     1  0.3810      0.720 0.572 0.000 0.000 0.000 0.000 NA
#> GSM1253067     4  0.2151      0.958 0.072 0.000 0.016 0.904 0.000 NA
#> GSM1253068     1  0.3937      0.720 0.572 0.000 0.004 0.000 0.000 NA
#> GSM1253069     1  0.0291      0.803 0.992 0.000 0.004 0.000 0.000 NA
#> GSM1253070     1  0.4057      0.728 0.600 0.000 0.012 0.000 0.000 NA
#> GSM1253071     4  0.1444      0.960 0.072 0.000 0.000 0.928 0.000 NA
#> GSM1253072     1  0.3937      0.720 0.572 0.000 0.004 0.000 0.000 NA
#> GSM1253073     4  0.2039      0.956 0.072 0.000 0.004 0.908 0.000 NA
#> GSM1253074     1  0.0508      0.804 0.984 0.000 0.012 0.000 0.000 NA
#> GSM1253032     5  0.0547      0.982 0.000 0.000 0.020 0.000 0.980 NA
#> GSM1253034     2  0.3081      0.851 0.000 0.776 0.000 0.000 0.004 NA
#> GSM1253039     2  0.3370      0.852 0.000 0.772 0.000 0.012 0.004 NA
#> GSM1253040     2  0.0725      0.923 0.000 0.976 0.000 0.012 0.000 NA
#> GSM1253041     2  0.0146      0.925 0.000 0.996 0.000 0.004 0.000 NA
#> GSM1253046     5  0.0622      0.979 0.000 0.000 0.012 0.000 0.980 NA
#> GSM1253048     2  0.0260      0.925 0.000 0.992 0.000 0.000 0.000 NA
#> GSM1253049     2  0.0000      0.925 0.000 1.000 0.000 0.000 0.000 NA
#> GSM1253052     3  0.4486      0.879 0.000 0.124 0.728 0.008 0.000 NA
#> GSM1253037     2  0.0000      0.925 0.000 1.000 0.000 0.000 0.000 NA
#> GSM1253028     3  0.3584      0.842 0.000 0.108 0.824 0.044 0.016 NA
#> GSM1253029     3  0.4739      0.870 0.000 0.136 0.712 0.008 0.004 NA
#> GSM1253030     2  0.3192      0.851 0.000 0.776 0.000 0.004 0.004 NA
#> GSM1253031     3  0.3483      0.845 0.000 0.116 0.824 0.044 0.008 NA
#> GSM1253033     5  0.1765      0.960 0.000 0.000 0.024 0.000 0.924 NA
#> GSM1253035     3  0.4240      0.880 0.000 0.124 0.736 0.000 0.000 NA
#> GSM1253036     3  0.3331      0.843 0.000 0.136 0.816 0.044 0.004 NA
#> GSM1253038     2  0.0622      0.923 0.000 0.980 0.000 0.012 0.000 NA
#> GSM1253042     3  0.4486      0.879 0.000 0.124 0.728 0.008 0.000 NA
#> GSM1253045     3  0.3607      0.729 0.000 0.000 0.812 0.040 0.124 NA
#> GSM1253043     3  0.3607      0.729 0.000 0.000 0.812 0.040 0.124 NA
#> GSM1253044     2  0.0146      0.925 0.000 0.996 0.000 0.004 0.000 NA
#> GSM1253047     5  0.0909      0.981 0.000 0.000 0.020 0.000 0.968 NA
#> GSM1253050     2  0.0146      0.925 0.000 0.996 0.000 0.000 0.000 NA
#> GSM1253051     2  0.3081      0.851 0.000 0.776 0.000 0.000 0.004 NA
#> GSM1253053     3  0.4486      0.879 0.000 0.124 0.728 0.008 0.000 NA
#> GSM1253054     5  0.1092      0.979 0.000 0.000 0.020 0.000 0.960 NA
#> GSM1253055     3  0.4506      0.876 0.000 0.108 0.736 0.000 0.016 NA
#> GSM1253079     1  0.0405      0.803 0.988 0.000 0.008 0.000 0.000 NA
#> GSM1253083     1  0.1010      0.802 0.960 0.000 0.036 0.000 0.004 NA
#> GSM1253075     1  0.0603      0.804 0.980 0.000 0.016 0.000 0.004 NA
#> GSM1253077     1  0.0935      0.802 0.964 0.000 0.032 0.000 0.004 NA
#> GSM1253076     1  0.0935      0.803 0.964 0.000 0.032 0.000 0.004 NA
#> GSM1253078     1  0.0935      0.802 0.964 0.000 0.032 0.000 0.004 NA
#> GSM1253081     1  0.4366      0.703 0.548 0.000 0.000 0.024 0.000 NA
#> GSM1253080     1  0.0922      0.803 0.968 0.000 0.024 0.000 0.004 NA
#> GSM1253082     1  0.4366      0.703 0.548 0.000 0.000 0.024 0.000 NA

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

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

consensus_heatmap(res, k = 2)

plot of chunk tab-MAD-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 infection(p) disease.state(p) individual(p) k
#> MAD:kmeans 56     0.018077         1.69e-08         0.955 2
#> MAD:kmeans 51     0.008612         4.89e-11         0.985 3
#> MAD:kmeans 45     0.001509         1.02e-09         0.803 4
#> MAD:kmeans 56     0.000334         2.92e-12         0.862 5
#> MAD:kmeans 56     0.000334         2.92e-12         0.862 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 51979 rows and 56 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#>   Subgroups are detected by 'skmeans' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 5.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk MAD-skmeans-collect-plots

The plots are:

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

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

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

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

select_partition_number(res)

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

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.987       0.994         0.4977 0.501   0.501
#> 3 3 1.000           0.946       0.974         0.1988 0.894   0.790
#> 4 4 1.000           0.956       0.985         0.1829 0.889   0.726
#> 5 5 0.931           0.918       0.961         0.0919 0.931   0.767
#> 6 6 0.890           0.894       0.913         0.0389 0.947   0.783

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

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

suggest_best_k(res)

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

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

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

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

show/hide code output

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

#>            class entropy silhouette    p1    p2
#> GSM1253056     1   0.000      0.999 1.000 0.000
#> GSM1253057     1   0.000      0.999 1.000 0.000
#> GSM1253058     1   0.000      0.999 1.000 0.000
#> GSM1253059     1   0.000      0.999 1.000 0.000
#> GSM1253060     1   0.000      0.999 1.000 0.000
#> GSM1253061     1   0.000      0.999 1.000 0.000
#> GSM1253062     1   0.000      0.999 1.000 0.000
#> GSM1253063     1   0.000      0.999 1.000 0.000
#> GSM1253064     1   0.000      0.999 1.000 0.000
#> GSM1253065     1   0.000      0.999 1.000 0.000
#> GSM1253066     1   0.000      0.999 1.000 0.000
#> GSM1253067     1   0.000      0.999 1.000 0.000
#> GSM1253068     1   0.000      0.999 1.000 0.000
#> GSM1253069     1   0.000      0.999 1.000 0.000
#> GSM1253070     1   0.000      0.999 1.000 0.000
#> GSM1253071     1   0.000      0.999 1.000 0.000
#> GSM1253072     1   0.000      0.999 1.000 0.000
#> GSM1253073     1   0.000      0.999 1.000 0.000
#> GSM1253074     1   0.000      0.999 1.000 0.000
#> GSM1253032     1   0.184      0.971 0.972 0.028
#> GSM1253034     2   0.000      0.988 0.000 1.000
#> GSM1253039     2   0.000      0.988 0.000 1.000
#> GSM1253040     2   0.000      0.988 0.000 1.000
#> GSM1253041     2   0.000      0.988 0.000 1.000
#> GSM1253046     1   0.000      0.999 1.000 0.000
#> GSM1253048     2   0.000      0.988 0.000 1.000
#> GSM1253049     2   0.000      0.988 0.000 1.000
#> GSM1253052     2   0.000      0.988 0.000 1.000
#> GSM1253037     2   0.000      0.988 0.000 1.000
#> GSM1253028     2   0.000      0.988 0.000 1.000
#> GSM1253029     2   0.000      0.988 0.000 1.000
#> GSM1253030     2   0.000      0.988 0.000 1.000
#> GSM1253031     2   0.000      0.988 0.000 1.000
#> GSM1253033     1   0.000      0.999 1.000 0.000
#> GSM1253035     2   0.000      0.988 0.000 1.000
#> GSM1253036     2   0.000      0.988 0.000 1.000
#> GSM1253038     2   0.000      0.988 0.000 1.000
#> GSM1253042     2   0.000      0.988 0.000 1.000
#> GSM1253045     2   0.000      0.988 0.000 1.000
#> GSM1253043     2   0.000      0.988 0.000 1.000
#> GSM1253044     2   0.000      0.988 0.000 1.000
#> GSM1253047     1   0.000      0.999 1.000 0.000
#> GSM1253050     2   0.000      0.988 0.000 1.000
#> GSM1253051     2   0.000      0.988 0.000 1.000
#> GSM1253053     2   0.000      0.988 0.000 1.000
#> GSM1253054     2   0.861      0.602 0.284 0.716
#> GSM1253055     2   0.000      0.988 0.000 1.000
#> GSM1253079     1   0.000      0.999 1.000 0.000
#> GSM1253083     1   0.000      0.999 1.000 0.000
#> GSM1253075     1   0.000      0.999 1.000 0.000
#> GSM1253077     1   0.000      0.999 1.000 0.000
#> GSM1253076     1   0.000      0.999 1.000 0.000
#> GSM1253078     1   0.000      0.999 1.000 0.000
#> GSM1253081     1   0.000      0.999 1.000 0.000
#> GSM1253080     1   0.000      0.999 1.000 0.000
#> GSM1253082     1   0.000      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
#> GSM1253056     1  0.1643      0.969 0.956 0.000 0.044
#> GSM1253057     1  0.0000      0.985 1.000 0.000 0.000
#> GSM1253058     1  0.1643      0.969 0.956 0.000 0.044
#> GSM1253059     1  0.1643      0.969 0.956 0.000 0.044
#> GSM1253060     1  0.1643      0.969 0.956 0.000 0.044
#> GSM1253061     1  0.0000      0.985 1.000 0.000 0.000
#> GSM1253062     1  0.0000      0.985 1.000 0.000 0.000
#> GSM1253063     1  0.1643      0.969 0.956 0.000 0.044
#> GSM1253064     1  0.0000      0.985 1.000 0.000 0.000
#> GSM1253065     1  0.1643      0.969 0.956 0.000 0.044
#> GSM1253066     1  0.0000      0.985 1.000 0.000 0.000
#> GSM1253067     1  0.1643      0.969 0.956 0.000 0.044
#> GSM1253068     1  0.0000      0.985 1.000 0.000 0.000
#> GSM1253069     1  0.0000      0.985 1.000 0.000 0.000
#> GSM1253070     1  0.0000      0.985 1.000 0.000 0.000
#> GSM1253071     1  0.1643      0.969 0.956 0.000 0.044
#> GSM1253072     1  0.0000      0.985 1.000 0.000 0.000
#> GSM1253073     1  0.1643      0.969 0.956 0.000 0.044
#> GSM1253074     1  0.0000      0.985 1.000 0.000 0.000
#> GSM1253032     3  0.1529      0.907 0.040 0.000 0.960
#> GSM1253034     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253039     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253040     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253041     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253046     3  0.1643      0.907 0.044 0.000 0.956
#> GSM1253048     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253049     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253052     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253037     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253028     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253029     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253030     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253031     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253033     3  0.1529      0.907 0.040 0.000 0.960
#> GSM1253035     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253036     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253038     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253042     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253045     3  0.6215      0.216 0.000 0.428 0.572
#> GSM1253043     2  0.6095      0.259 0.000 0.608 0.392
#> GSM1253044     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253047     3  0.1643      0.907 0.044 0.000 0.956
#> GSM1253050     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253051     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253053     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253054     3  0.1765      0.906 0.040 0.004 0.956
#> GSM1253055     2  0.0000      0.979 0.000 1.000 0.000
#> GSM1253079     1  0.0000      0.985 1.000 0.000 0.000
#> GSM1253083     1  0.0000      0.985 1.000 0.000 0.000
#> GSM1253075     1  0.0000      0.985 1.000 0.000 0.000
#> GSM1253077     1  0.0000      0.985 1.000 0.000 0.000
#> GSM1253076     1  0.0000      0.985 1.000 0.000 0.000
#> GSM1253078     1  0.0000      0.985 1.000 0.000 0.000
#> GSM1253081     1  0.0000      0.985 1.000 0.000 0.000
#> GSM1253080     1  0.0000      0.985 1.000 0.000 0.000
#> GSM1253082     1  0.0592      0.981 0.988 0.000 0.012

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4
#> GSM1253056     4  0.0188      1.000 0.004 0.000 0.000 0.996
#> GSM1253057     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253058     4  0.0188      1.000 0.004 0.000 0.000 0.996
#> GSM1253059     4  0.0188      1.000 0.004 0.000 0.000 0.996
#> GSM1253060     4  0.0188      1.000 0.004 0.000 0.000 0.996
#> GSM1253061     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253062     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253063     4  0.0188      1.000 0.004 0.000 0.000 0.996
#> GSM1253064     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253065     4  0.0188      1.000 0.004 0.000 0.000 0.996
#> GSM1253066     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253067     4  0.0188      1.000 0.004 0.000 0.000 0.996
#> GSM1253068     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253069     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253070     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253071     4  0.0188      1.000 0.004 0.000 0.000 0.996
#> GSM1253072     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253073     4  0.0188      1.000 0.004 0.000 0.000 0.996
#> GSM1253074     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253032     3  0.0000      0.893 0.000 0.000 1.000 0.000
#> GSM1253034     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> GSM1253039     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> GSM1253040     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> GSM1253041     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> GSM1253046     3  0.0000      0.893 0.000 0.000 1.000 0.000
#> GSM1253048     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> GSM1253049     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> GSM1253052     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> GSM1253037     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> GSM1253028     2  0.0188      0.975 0.000 0.996 0.000 0.004
#> GSM1253029     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> GSM1253030     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> GSM1253031     2  0.0188      0.975 0.000 0.996 0.000 0.004
#> GSM1253033     3  0.0000      0.893 0.000 0.000 1.000 0.000
#> GSM1253035     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> GSM1253036     2  0.0188      0.975 0.000 0.996 0.000 0.004
#> GSM1253038     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> GSM1253042     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> GSM1253045     3  0.4978      0.342 0.000 0.384 0.612 0.004
#> GSM1253043     2  0.5060      0.194 0.000 0.584 0.412 0.004
#> GSM1253044     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> GSM1253047     3  0.0000      0.893 0.000 0.000 1.000 0.000
#> GSM1253050     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> GSM1253051     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> GSM1253053     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> GSM1253054     3  0.0000      0.893 0.000 0.000 1.000 0.000
#> GSM1253055     2  0.0188      0.975 0.000 0.996 0.000 0.004
#> GSM1253079     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253081     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253080     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253082     1  0.0000      1.000 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
#> GSM1253056     4  0.0000      1.000 0.000 0.000 0.000  1 0.000
#> GSM1253057     1  0.0000      0.992 1.000 0.000 0.000  0 0.000
#> GSM1253058     4  0.0000      1.000 0.000 0.000 0.000  1 0.000
#> GSM1253059     4  0.0000      1.000 0.000 0.000 0.000  1 0.000
#> GSM1253060     4  0.0000      1.000 0.000 0.000 0.000  1 0.000
#> GSM1253061     1  0.0609      0.989 0.980 0.000 0.020  0 0.000
#> GSM1253062     1  0.0162      0.992 0.996 0.000 0.004  0 0.000
#> GSM1253063     4  0.0000      1.000 0.000 0.000 0.000  1 0.000
#> GSM1253064     1  0.0609      0.989 0.980 0.000 0.020  0 0.000
#> GSM1253065     4  0.0000      1.000 0.000 0.000 0.000  1 0.000
#> GSM1253066     1  0.0609      0.989 0.980 0.000 0.020  0 0.000
#> GSM1253067     4  0.0000      1.000 0.000 0.000 0.000  1 0.000
#> GSM1253068     1  0.0609      0.989 0.980 0.000 0.020  0 0.000
#> GSM1253069     1  0.0000      0.992 1.000 0.000 0.000  0 0.000
#> GSM1253070     1  0.0510      0.990 0.984 0.000 0.016  0 0.000
#> GSM1253071     4  0.0000      1.000 0.000 0.000 0.000  1 0.000
#> GSM1253072     1  0.0609      0.989 0.980 0.000 0.020  0 0.000
#> GSM1253073     4  0.0000      1.000 0.000 0.000 0.000  1 0.000
#> GSM1253074     1  0.0000      0.992 1.000 0.000 0.000  0 0.000
#> GSM1253032     5  0.0000      0.988 0.000 0.000 0.000  0 1.000
#> GSM1253034     2  0.0000      0.879 0.000 1.000 0.000  0 0.000
#> GSM1253039     2  0.0000      0.879 0.000 1.000 0.000  0 0.000
#> GSM1253040     2  0.0000      0.879 0.000 1.000 0.000  0 0.000
#> GSM1253041     2  0.0000      0.879 0.000 1.000 0.000  0 0.000
#> GSM1253046     5  0.0000      0.988 0.000 0.000 0.000  0 1.000
#> GSM1253048     2  0.0000      0.879 0.000 1.000 0.000  0 0.000
#> GSM1253049     2  0.0000      0.879 0.000 1.000 0.000  0 0.000
#> GSM1253052     2  0.4138      0.438 0.000 0.616 0.384  0 0.000
#> GSM1253037     2  0.0000      0.879 0.000 1.000 0.000  0 0.000
#> GSM1253028     3  0.0880      0.934 0.000 0.032 0.968  0 0.000
#> GSM1253029     2  0.4138      0.438 0.000 0.616 0.384  0 0.000
#> GSM1253030     2  0.0000      0.879 0.000 1.000 0.000  0 0.000
#> GSM1253031     3  0.0703      0.933 0.000 0.024 0.976  0 0.000
#> GSM1253033     5  0.0000      0.988 0.000 0.000 0.000  0 1.000
#> GSM1253035     3  0.2813      0.816 0.000 0.168 0.832  0 0.000
#> GSM1253036     3  0.2179      0.892 0.000 0.112 0.888  0 0.000
#> GSM1253038     2  0.0000      0.879 0.000 1.000 0.000  0 0.000
#> GSM1253042     2  0.4138      0.438 0.000 0.616 0.384  0 0.000
#> GSM1253045     3  0.0798      0.919 0.000 0.008 0.976  0 0.016
#> GSM1253043     3  0.0693      0.925 0.000 0.012 0.980  0 0.008
#> GSM1253044     2  0.0000      0.879 0.000 1.000 0.000  0 0.000
#> GSM1253047     5  0.0162      0.987 0.000 0.000 0.004  0 0.996
#> GSM1253050     2  0.0000      0.879 0.000 1.000 0.000  0 0.000
#> GSM1253051     2  0.0000      0.879 0.000 1.000 0.000  0 0.000
#> GSM1253053     2  0.4138      0.438 0.000 0.616 0.384  0 0.000
#> GSM1253054     5  0.1270      0.955 0.000 0.000 0.052  0 0.948
#> GSM1253055     3  0.1270      0.929 0.000 0.052 0.948  0 0.000
#> GSM1253079     1  0.0000      0.992 1.000 0.000 0.000  0 0.000
#> GSM1253083     1  0.0000      0.992 1.000 0.000 0.000  0 0.000
#> GSM1253075     1  0.0000      0.992 1.000 0.000 0.000  0 0.000
#> GSM1253077     1  0.0000      0.992 1.000 0.000 0.000  0 0.000
#> GSM1253076     1  0.0000      0.992 1.000 0.000 0.000  0 0.000
#> GSM1253078     1  0.0000      0.992 1.000 0.000 0.000  0 0.000
#> GSM1253081     1  0.0609      0.989 0.980 0.000 0.020  0 0.000
#> GSM1253080     1  0.0000      0.992 1.000 0.000 0.000  0 0.000
#> GSM1253082     1  0.0609      0.989 0.980 0.000 0.020  0 0.000

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4    p5    p6
#> GSM1253056     4  0.0000      0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253057     1  0.0146      0.913 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM1253058     4  0.0000      0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253059     4  0.0000      0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253060     4  0.0146      0.996 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM1253061     1  0.3094      0.877 0.824 0.000 0.036 0.000 0.000 0.140
#> GSM1253062     1  0.0146      0.912 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM1253063     4  0.0000      0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253064     1  0.3523      0.863 0.780 0.000 0.040 0.000 0.000 0.180
#> GSM1253065     4  0.0291      0.992 0.000 0.000 0.004 0.992 0.000 0.004
#> GSM1253066     1  0.3523      0.863 0.780 0.000 0.040 0.000 0.000 0.180
#> GSM1253067     4  0.0000      0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253068     1  0.3523      0.863 0.780 0.000 0.040 0.000 0.000 0.180
#> GSM1253069     1  0.0146      0.913 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM1253070     1  0.2826      0.883 0.844 0.000 0.028 0.000 0.000 0.128
#> GSM1253071     4  0.0000      0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253072     1  0.3523      0.863 0.780 0.000 0.040 0.000 0.000 0.180
#> GSM1253073     4  0.0000      0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253074     1  0.0000      0.913 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253032     5  0.0000      0.945 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1253034     2  0.0000      0.940 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253039     2  0.0000      0.940 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253040     2  0.0000      0.940 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253041     2  0.0000      0.940 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253046     5  0.1367      0.939 0.000 0.000 0.044 0.000 0.944 0.012
#> GSM1253048     2  0.0000      0.940 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253049     2  0.0000      0.940 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253052     3  0.3050      0.862 0.000 0.236 0.764 0.000 0.000 0.000
#> GSM1253037     2  0.0000      0.940 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253028     6  0.3244      0.957 0.000 0.000 0.268 0.000 0.000 0.732
#> GSM1253029     3  0.3076      0.857 0.000 0.240 0.760 0.000 0.000 0.000
#> GSM1253030     2  0.0000      0.940 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253031     6  0.3244      0.957 0.000 0.000 0.268 0.000 0.000 0.732
#> GSM1253033     5  0.1594      0.936 0.000 0.000 0.052 0.000 0.932 0.016
#> GSM1253035     3  0.2365      0.686 0.000 0.072 0.888 0.000 0.000 0.040
#> GSM1253036     2  0.6082     -0.320 0.000 0.396 0.292 0.000 0.000 0.312
#> GSM1253038     2  0.0000      0.940 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253042     3  0.3050      0.862 0.000 0.236 0.764 0.000 0.000 0.000
#> GSM1253045     6  0.2902      0.917 0.000 0.000 0.196 0.000 0.004 0.800
#> GSM1253043     6  0.3101      0.955 0.000 0.000 0.244 0.000 0.000 0.756
#> GSM1253044     2  0.0000      0.940 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253047     5  0.1563      0.934 0.000 0.000 0.012 0.000 0.932 0.056
#> GSM1253050     2  0.0000      0.940 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253051     2  0.0000      0.940 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253053     3  0.3050      0.862 0.000 0.236 0.764 0.000 0.000 0.000
#> GSM1253054     5  0.1967      0.920 0.000 0.000 0.012 0.000 0.904 0.084
#> GSM1253055     3  0.2170      0.560 0.000 0.012 0.888 0.000 0.000 0.100
#> GSM1253079     1  0.0000      0.913 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253083     1  0.0146      0.913 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM1253075     1  0.0146      0.913 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM1253077     1  0.0146      0.913 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM1253076     1  0.0146      0.913 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM1253078     1  0.0146      0.913 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM1253081     1  0.3523      0.863 0.780 0.000 0.040 0.000 0.000 0.180
#> GSM1253080     1  0.0146      0.913 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM1253082     1  0.3663      0.860 0.776 0.000 0.040 0.004 0.000 0.180

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 infection(p) disease.state(p) individual(p) k
#> MAD:skmeans 56     0.013575         3.63e-09         0.949 2
#> MAD:skmeans 54     0.006642         7.33e-10         0.903 3
#> MAD:skmeans 54     0.000178         8.70e-11         0.880 4
#> MAD:skmeans 52     0.000821         1.18e-11         0.874 5
#> MAD:skmeans 55     0.001056         1.02e-10         0.777 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 51979 rows and 56 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#>   Subgroups are detected by 'pam' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 6.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk MAD-pam-collect-plots

The plots are:

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

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

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

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

select_partition_number(res)

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

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.992       0.996         0.4945 0.507   0.507
#> 3 3 0.739           0.865       0.864         0.2706 0.860   0.731
#> 4 4 0.933           0.937       0.967         0.1988 0.832   0.584
#> 5 5 1.000           0.941       0.979         0.0451 0.934   0.745
#> 6 6 0.948           0.975       0.970         0.0521 0.949   0.764

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

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

suggest_best_k(res)

#> [1] 6
#> attr(,"optional")
#> [1] 2 4 5

There is also optional best \(k\) = 2 4 5 that is worth to check.

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

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

show/hide code output

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

#>            class entropy silhouette    p1    p2
#> GSM1253056     1  0.0000      0.994 1.000 0.000
#> GSM1253057     1  0.0000      0.994 1.000 0.000
#> GSM1253058     1  0.0000      0.994 1.000 0.000
#> GSM1253059     1  0.0000      0.994 1.000 0.000
#> GSM1253060     1  0.0000      0.994 1.000 0.000
#> GSM1253061     1  0.0000      0.994 1.000 0.000
#> GSM1253062     1  0.0000      0.994 1.000 0.000
#> GSM1253063     1  0.0000      0.994 1.000 0.000
#> GSM1253064     1  0.0000      0.994 1.000 0.000
#> GSM1253065     1  0.0000      0.994 1.000 0.000
#> GSM1253066     1  0.0000      0.994 1.000 0.000
#> GSM1253067     1  0.0000      0.994 1.000 0.000
#> GSM1253068     1  0.0000      0.994 1.000 0.000
#> GSM1253069     1  0.0000      0.994 1.000 0.000
#> GSM1253070     1  0.0000      0.994 1.000 0.000
#> GSM1253071     1  0.0000      0.994 1.000 0.000
#> GSM1253072     1  0.0000      0.994 1.000 0.000
#> GSM1253073     1  0.0000      0.994 1.000 0.000
#> GSM1253074     1  0.0000      0.994 1.000 0.000
#> GSM1253032     1  0.0000      0.994 1.000 0.000
#> GSM1253034     2  0.0000      1.000 0.000 1.000
#> GSM1253039     2  0.0000      1.000 0.000 1.000
#> GSM1253040     2  0.0000      1.000 0.000 1.000
#> GSM1253041     2  0.0000      1.000 0.000 1.000
#> GSM1253046     1  0.0000      0.994 1.000 0.000
#> GSM1253048     2  0.0000      1.000 0.000 1.000
#> GSM1253049     2  0.0000      1.000 0.000 1.000
#> GSM1253052     2  0.0000      1.000 0.000 1.000
#> GSM1253037     2  0.0000      1.000 0.000 1.000
#> GSM1253028     2  0.0000      1.000 0.000 1.000
#> GSM1253029     2  0.0000      1.000 0.000 1.000
#> GSM1253030     2  0.0000      1.000 0.000 1.000
#> GSM1253031     2  0.0000      1.000 0.000 1.000
#> GSM1253033     1  0.0000      0.994 1.000 0.000
#> GSM1253035     2  0.0000      1.000 0.000 1.000
#> GSM1253036     2  0.0000      1.000 0.000 1.000
#> GSM1253038     2  0.0000      1.000 0.000 1.000
#> GSM1253042     2  0.0000      1.000 0.000 1.000
#> GSM1253045     2  0.0672      0.992 0.008 0.992
#> GSM1253043     2  0.0000      1.000 0.000 1.000
#> GSM1253044     2  0.0000      1.000 0.000 1.000
#> GSM1253047     1  0.0000      0.994 1.000 0.000
#> GSM1253050     2  0.0000      1.000 0.000 1.000
#> GSM1253051     2  0.0000      1.000 0.000 1.000
#> GSM1253053     2  0.0000      1.000 0.000 1.000
#> GSM1253054     1  0.7219      0.750 0.800 0.200
#> GSM1253055     2  0.0000      1.000 0.000 1.000
#> GSM1253079     1  0.0000      0.994 1.000 0.000
#> GSM1253083     1  0.0000      0.994 1.000 0.000
#> GSM1253075     1  0.0000      0.994 1.000 0.000
#> GSM1253077     1  0.0000      0.994 1.000 0.000
#> GSM1253076     1  0.0000      0.994 1.000 0.000
#> GSM1253078     1  0.0000      0.994 1.000 0.000
#> GSM1253081     1  0.0000      0.994 1.000 0.000
#> GSM1253080     1  0.0000      0.994 1.000 0.000
#> GSM1253082     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
#> GSM1253056     1  0.5431      0.813 0.716 0.284 0.000
#> GSM1253057     1  0.0000      0.865 1.000 0.000 0.000
#> GSM1253058     1  0.5431      0.813 0.716 0.284 0.000
#> GSM1253059     1  0.5431      0.813 0.716 0.284 0.000
#> GSM1253060     1  0.5431      0.813 0.716 0.284 0.000
#> GSM1253061     1  0.0000      0.865 1.000 0.000 0.000
#> GSM1253062     1  0.0000      0.865 1.000 0.000 0.000
#> GSM1253063     1  0.5431      0.813 0.716 0.284 0.000
#> GSM1253064     1  0.5327      0.817 0.728 0.272 0.000
#> GSM1253065     1  0.5431      0.813 0.716 0.284 0.000
#> GSM1253066     1  0.0000      0.865 1.000 0.000 0.000
#> GSM1253067     1  0.5431      0.813 0.716 0.284 0.000
#> GSM1253068     1  0.0000      0.865 1.000 0.000 0.000
#> GSM1253069     1  0.0000      0.865 1.000 0.000 0.000
#> GSM1253070     1  0.0000      0.865 1.000 0.000 0.000
#> GSM1253071     1  0.5431      0.813 0.716 0.284 0.000
#> GSM1253072     1  0.0000      0.865 1.000 0.000 0.000
#> GSM1253073     1  0.5431      0.813 0.716 0.284 0.000
#> GSM1253074     1  0.0000      0.865 1.000 0.000 0.000
#> GSM1253032     3  0.5431      0.600 0.000 0.284 0.716
#> GSM1253034     2  0.5431      1.000 0.000 0.716 0.284
#> GSM1253039     2  0.5431      1.000 0.000 0.716 0.284
#> GSM1253040     2  0.5431      1.000 0.000 0.716 0.284
#> GSM1253041     2  0.5431      1.000 0.000 0.716 0.284
#> GSM1253046     1  0.1765      0.859 0.956 0.040 0.004
#> GSM1253048     2  0.5431      1.000 0.000 0.716 0.284
#> GSM1253049     2  0.5431      1.000 0.000 0.716 0.284
#> GSM1253052     3  0.1529      0.882 0.000 0.040 0.960
#> GSM1253037     2  0.5431      1.000 0.000 0.716 0.284
#> GSM1253028     3  0.0000      0.895 0.000 0.000 1.000
#> GSM1253029     3  0.1964      0.863 0.000 0.056 0.944
#> GSM1253030     2  0.5431      1.000 0.000 0.716 0.284
#> GSM1253031     3  0.0000      0.895 0.000 0.000 1.000
#> GSM1253033     1  0.9809      0.386 0.432 0.284 0.284
#> GSM1253035     3  0.0000      0.895 0.000 0.000 1.000
#> GSM1253036     3  0.1529      0.882 0.000 0.040 0.960
#> GSM1253038     2  0.5431      1.000 0.000 0.716 0.284
#> GSM1253042     3  0.1529      0.882 0.000 0.040 0.960
#> GSM1253045     3  0.0424      0.889 0.008 0.000 0.992
#> GSM1253043     3  0.0000      0.895 0.000 0.000 1.000
#> GSM1253044     2  0.5431      1.000 0.000 0.716 0.284
#> GSM1253047     1  0.5098      0.586 0.752 0.000 0.248
#> GSM1253050     2  0.5431      1.000 0.000 0.716 0.284
#> GSM1253051     2  0.5431      1.000 0.000 0.716 0.284
#> GSM1253053     3  0.1529      0.882 0.000 0.040 0.960
#> GSM1253054     3  0.5325      0.635 0.004 0.248 0.748
#> GSM1253055     3  0.0000      0.895 0.000 0.000 1.000
#> GSM1253079     1  0.0000      0.865 1.000 0.000 0.000
#> GSM1253083     1  0.0000      0.865 1.000 0.000 0.000
#> GSM1253075     1  0.0000      0.865 1.000 0.000 0.000
#> GSM1253077     1  0.0000      0.865 1.000 0.000 0.000
#> GSM1253076     1  0.0000      0.865 1.000 0.000 0.000
#> GSM1253078     1  0.0000      0.865 1.000 0.000 0.000
#> GSM1253081     1  0.5397      0.815 0.720 0.280 0.000
#> GSM1253080     1  0.0000      0.865 1.000 0.000 0.000
#> GSM1253082     1  0.5397      0.815 0.720 0.280 0.000

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4
#> GSM1253056     4   0.000      0.905 0.000 0.000 0.000 1.000
#> GSM1253057     1   0.000      0.986 1.000 0.000 0.000 0.000
#> GSM1253058     4   0.000      0.905 0.000 0.000 0.000 1.000
#> GSM1253059     4   0.000      0.905 0.000 0.000 0.000 1.000
#> GSM1253060     4   0.000      0.905 0.000 0.000 0.000 1.000
#> GSM1253061     1   0.000      0.986 1.000 0.000 0.000 0.000
#> GSM1253062     1   0.000      0.986 1.000 0.000 0.000 0.000
#> GSM1253063     4   0.000      0.905 0.000 0.000 0.000 1.000
#> GSM1253064     4   0.441      0.631 0.300 0.000 0.000 0.700
#> GSM1253065     4   0.000      0.905 0.000 0.000 0.000 1.000
#> GSM1253066     1   0.000      0.986 1.000 0.000 0.000 0.000
#> GSM1253067     4   0.000      0.905 0.000 0.000 0.000 1.000
#> GSM1253068     1   0.000      0.986 1.000 0.000 0.000 0.000
#> GSM1253069     1   0.000      0.986 1.000 0.000 0.000 0.000
#> GSM1253070     1   0.000      0.986 1.000 0.000 0.000 0.000
#> GSM1253071     4   0.000      0.905 0.000 0.000 0.000 1.000
#> GSM1253072     1   0.000      0.986 1.000 0.000 0.000 0.000
#> GSM1253073     4   0.000      0.905 0.000 0.000 0.000 1.000
#> GSM1253074     1   0.000      0.986 1.000 0.000 0.000 0.000
#> GSM1253032     4   0.494      0.312 0.000 0.000 0.436 0.564
#> GSM1253034     2   0.000      1.000 0.000 1.000 0.000 0.000
#> GSM1253039     2   0.000      1.000 0.000 1.000 0.000 0.000
#> GSM1253040     2   0.000      1.000 0.000 1.000 0.000 0.000
#> GSM1253041     2   0.000      1.000 0.000 1.000 0.000 0.000
#> GSM1253046     1   0.323      0.882 0.880 0.000 0.072 0.048
#> GSM1253048     2   0.000      1.000 0.000 1.000 0.000 0.000
#> GSM1253049     2   0.000      1.000 0.000 1.000 0.000 0.000
#> GSM1253052     3   0.194      0.943 0.000 0.076 0.924 0.000
#> GSM1253037     2   0.000      1.000 0.000 1.000 0.000 0.000
#> GSM1253028     3   0.000      0.960 0.000 0.000 1.000 0.000
#> GSM1253029     3   0.222      0.929 0.000 0.092 0.908 0.000
#> GSM1253030     2   0.000      1.000 0.000 1.000 0.000 0.000
#> GSM1253031     3   0.000      0.960 0.000 0.000 1.000 0.000
#> GSM1253033     4   0.413      0.819 0.108 0.000 0.064 0.828
#> GSM1253035     3   0.000      0.960 0.000 0.000 1.000 0.000
#> GSM1253036     3   0.194      0.943 0.000 0.076 0.924 0.000
#> GSM1253038     2   0.000      1.000 0.000 1.000 0.000 0.000
#> GSM1253042     3   0.194      0.943 0.000 0.076 0.924 0.000
#> GSM1253045     3   0.000      0.960 0.000 0.000 1.000 0.000
#> GSM1253043     3   0.000      0.960 0.000 0.000 1.000 0.000
#> GSM1253044     2   0.000      1.000 0.000 1.000 0.000 0.000
#> GSM1253047     1   0.276      0.863 0.872 0.000 0.128 0.000
#> GSM1253050     2   0.000      1.000 0.000 1.000 0.000 0.000
#> GSM1253051     2   0.000      1.000 0.000 1.000 0.000 0.000
#> GSM1253053     3   0.194      0.943 0.000 0.076 0.924 0.000
#> GSM1253054     3   0.000      0.960 0.000 0.000 1.000 0.000
#> GSM1253055     3   0.000      0.960 0.000 0.000 1.000 0.000
#> GSM1253079     1   0.000      0.986 1.000 0.000 0.000 0.000
#> GSM1253083     1   0.000      0.986 1.000 0.000 0.000 0.000
#> GSM1253075     1   0.000      0.986 1.000 0.000 0.000 0.000
#> GSM1253077     1   0.000      0.986 1.000 0.000 0.000 0.000
#> GSM1253076     1   0.000      0.986 1.000 0.000 0.000 0.000
#> GSM1253078     1   0.000      0.986 1.000 0.000 0.000 0.000
#> GSM1253081     4   0.281      0.839 0.132 0.000 0.000 0.868
#> GSM1253080     1   0.000      0.986 1.000 0.000 0.000 0.000
#> GSM1253082     4   0.317      0.817 0.160 0.000 0.000 0.840

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4    p5
#> GSM1253056     4   0.000      0.876 0.000 0.000 0.000 1.000 0.000
#> GSM1253057     1   0.000      0.985 1.000 0.000 0.000 0.000 0.000
#> GSM1253058     4   0.000      0.876 0.000 0.000 0.000 1.000 0.000
#> GSM1253059     4   0.000      0.876 0.000 0.000 0.000 1.000 0.000
#> GSM1253060     4   0.000      0.876 0.000 0.000 0.000 1.000 0.000
#> GSM1253061     1   0.000      0.985 1.000 0.000 0.000 0.000 0.000
#> GSM1253062     1   0.000      0.985 1.000 0.000 0.000 0.000 0.000
#> GSM1253063     4   0.000      0.876 0.000 0.000 0.000 1.000 0.000
#> GSM1253064     1   0.318      0.697 0.792 0.000 0.000 0.208 0.000
#> GSM1253065     4   0.000      0.876 0.000 0.000 0.000 1.000 0.000
#> GSM1253066     1   0.000      0.985 1.000 0.000 0.000 0.000 0.000
#> GSM1253067     4   0.000      0.876 0.000 0.000 0.000 1.000 0.000
#> GSM1253068     1   0.000      0.985 1.000 0.000 0.000 0.000 0.000
#> GSM1253069     1   0.000      0.985 1.000 0.000 0.000 0.000 0.000
#> GSM1253070     1   0.000      0.985 1.000 0.000 0.000 0.000 0.000
#> GSM1253071     4   0.000      0.876 0.000 0.000 0.000 1.000 0.000
#> GSM1253072     1   0.000      0.985 1.000 0.000 0.000 0.000 0.000
#> GSM1253073     4   0.000      0.876 0.000 0.000 0.000 1.000 0.000
#> GSM1253074     1   0.000      0.985 1.000 0.000 0.000 0.000 0.000
#> GSM1253032     5   0.000      0.998 0.000 0.000 0.000 0.000 1.000
#> GSM1253034     2   0.000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253039     2   0.000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253040     2   0.000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253041     2   0.000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253046     5   0.000      0.998 0.000 0.000 0.000 0.000 1.000
#> GSM1253048     2   0.000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253049     2   0.000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253052     3   0.000      0.996 0.000 0.000 1.000 0.000 0.000
#> GSM1253037     2   0.000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253028     3   0.000      0.996 0.000 0.000 1.000 0.000 0.000
#> GSM1253029     3   0.088      0.961 0.000 0.032 0.968 0.000 0.000
#> GSM1253030     2   0.000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253031     3   0.000      0.996 0.000 0.000 1.000 0.000 0.000
#> GSM1253033     5   0.000      0.998 0.000 0.000 0.000 0.000 1.000
#> GSM1253035     3   0.000      0.996 0.000 0.000 1.000 0.000 0.000
#> GSM1253036     3   0.000      0.996 0.000 0.000 1.000 0.000 0.000
#> GSM1253038     2   0.000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253042     3   0.000      0.996 0.000 0.000 1.000 0.000 0.000
#> GSM1253045     3   0.000      0.996 0.000 0.000 1.000 0.000 0.000
#> GSM1253043     3   0.000      0.996 0.000 0.000 1.000 0.000 0.000
#> GSM1253044     2   0.000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253047     5   0.000      0.998 0.000 0.000 0.000 0.000 1.000
#> GSM1253050     2   0.000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253051     2   0.000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253053     3   0.000      0.996 0.000 0.000 1.000 0.000 0.000
#> GSM1253054     5   0.029      0.992 0.000 0.000 0.008 0.000 0.992
#> GSM1253055     3   0.000      0.996 0.000 0.000 1.000 0.000 0.000
#> GSM1253079     1   0.000      0.985 1.000 0.000 0.000 0.000 0.000
#> GSM1253083     1   0.000      0.985 1.000 0.000 0.000 0.000 0.000
#> GSM1253075     1   0.000      0.985 1.000 0.000 0.000 0.000 0.000
#> GSM1253077     1   0.000      0.985 1.000 0.000 0.000 0.000 0.000
#> GSM1253076     1   0.000      0.985 1.000 0.000 0.000 0.000 0.000
#> GSM1253078     1   0.000      0.985 1.000 0.000 0.000 0.000 0.000
#> GSM1253081     4   0.423      0.297 0.424 0.000 0.000 0.576 0.000
#> GSM1253080     1   0.000      0.985 1.000 0.000 0.000 0.000 0.000
#> GSM1253082     4   0.430      0.125 0.480 0.000 0.000 0.520 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
#> GSM1253056     4  0.0000      1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253057     1  0.0000      0.985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253058     4  0.0000      1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253059     4  0.0000      1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253060     4  0.0000      1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253061     1  0.2340      0.799 0.852 0.000 0.000 0.000 0.000 0.148
#> GSM1253062     1  0.0000      0.985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253063     4  0.0000      1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253064     6  0.2633      0.963 0.104 0.000 0.000 0.032 0.000 0.864
#> GSM1253065     4  0.0000      1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253066     6  0.2219      0.964 0.136 0.000 0.000 0.000 0.000 0.864
#> GSM1253067     4  0.0000      1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253068     6  0.2219      0.964 0.136 0.000 0.000 0.000 0.000 0.864
#> GSM1253069     1  0.0000      0.985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253070     1  0.0363      0.974 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM1253071     4  0.0000      1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253072     6  0.2219      0.964 0.136 0.000 0.000 0.000 0.000 0.864
#> GSM1253073     4  0.0000      1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253074     1  0.0000      0.985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253032     5  0.0000      0.993 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1253034     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253039     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253040     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253041     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253046     5  0.0000      0.993 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1253048     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253049     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253052     3  0.0865      0.938 0.000 0.000 0.964 0.000 0.000 0.036
#> GSM1253037     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253028     3  0.1814      0.932 0.000 0.000 0.900 0.000 0.000 0.100
#> GSM1253029     3  0.1649      0.917 0.000 0.032 0.932 0.000 0.000 0.036
#> GSM1253030     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253031     3  0.1814      0.932 0.000 0.000 0.900 0.000 0.000 0.100
#> GSM1253033     5  0.0000      0.993 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1253035     3  0.0000      0.941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253036     3  0.1556      0.936 0.000 0.000 0.920 0.000 0.000 0.080
#> GSM1253038     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253042     3  0.0865      0.938 0.000 0.000 0.964 0.000 0.000 0.036
#> GSM1253045     3  0.1814      0.932 0.000 0.000 0.900 0.000 0.000 0.100
#> GSM1253043     3  0.1814      0.932 0.000 0.000 0.900 0.000 0.000 0.100
#> GSM1253044     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253047     5  0.0000      0.993 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1253050     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253051     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253053     3  0.0865      0.938 0.000 0.000 0.964 0.000 0.000 0.036
#> GSM1253054     5  0.0806      0.974 0.000 0.000 0.008 0.000 0.972 0.020
#> GSM1253055     3  0.0865      0.938 0.000 0.000 0.964 0.000 0.000 0.036
#> GSM1253079     1  0.0000      0.985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000      0.985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000      0.985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      0.985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      0.985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      0.985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253081     6  0.2679      0.958 0.096 0.000 0.000 0.040 0.000 0.864
#> GSM1253080     1  0.0000      0.985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253082     6  0.2697      0.953 0.092 0.000 0.000 0.044 0.000 0.864

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 infection(p) disease.state(p) individual(p) k
#> MAD:pam 56     0.018077         1.69e-08         0.955 2
#> MAD:pam 55     0.011292         1.36e-10         0.845 3
#> MAD:pam 55     0.009848         5.06e-10         0.657 4
#> MAD:pam 54     0.001542         2.07e-11         0.842 5
#> MAD:pam 56     0.000488         2.57e-11         0.785 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 51979 rows and 56 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#>   Subgroups are detected by 'mclust' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 6.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk MAD-mclust-collect-plots

The plots are:

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

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

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

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

select_partition_number(res)

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

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           1.000       1.000         0.5096 0.491   0.491
#> 3 3 0.778           0.767       0.890         0.2096 0.873   0.745
#> 4 4 0.889           0.906       0.938         0.2110 0.816   0.551
#> 5 5 0.911           0.934       0.930         0.0638 0.928   0.729
#> 6 6 1.000           0.996       0.998         0.0553 0.949   0.757

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

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

suggest_best_k(res)

#> [1] 6
#> attr(,"optional")
#> [1] 2 5

There is also optional best \(k\) = 2 5 that is worth to check.

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

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

show/hide code output

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

#>            class entropy silhouette p1 p2
#> GSM1253056     1       0          1  1  0
#> GSM1253057     1       0          1  1  0
#> GSM1253058     1       0          1  1  0
#> GSM1253059     1       0          1  1  0
#> GSM1253060     1       0          1  1  0
#> GSM1253061     1       0          1  1  0
#> GSM1253062     1       0          1  1  0
#> GSM1253063     1       0          1  1  0
#> GSM1253064     1       0          1  1  0
#> GSM1253065     1       0          1  1  0
#> GSM1253066     1       0          1  1  0
#> GSM1253067     1       0          1  1  0
#> GSM1253068     1       0          1  1  0
#> GSM1253069     1       0          1  1  0
#> GSM1253070     1       0          1  1  0
#> GSM1253071     1       0          1  1  0
#> GSM1253072     1       0          1  1  0
#> GSM1253073     1       0          1  1  0
#> GSM1253074     1       0          1  1  0
#> GSM1253032     2       0          1  0  1
#> GSM1253034     2       0          1  0  1
#> GSM1253039     2       0          1  0  1
#> GSM1253040     2       0          1  0  1
#> GSM1253041     2       0          1  0  1
#> GSM1253046     2       0          1  0  1
#> GSM1253048     2       0          1  0  1
#> GSM1253049     2       0          1  0  1
#> GSM1253052     2       0          1  0  1
#> GSM1253037     2       0          1  0  1
#> GSM1253028     2       0          1  0  1
#> GSM1253029     2       0          1  0  1
#> GSM1253030     2       0          1  0  1
#> GSM1253031     2       0          1  0  1
#> GSM1253033     2       0          1  0  1
#> GSM1253035     2       0          1  0  1
#> GSM1253036     2       0          1  0  1
#> GSM1253038     2       0          1  0  1
#> GSM1253042     2       0          1  0  1
#> GSM1253045     2       0          1  0  1
#> GSM1253043     2       0          1  0  1
#> GSM1253044     2       0          1  0  1
#> GSM1253047     2       0          1  0  1
#> GSM1253050     2       0          1  0  1
#> GSM1253051     2       0          1  0  1
#> GSM1253053     2       0          1  0  1
#> GSM1253054     2       0          1  0  1
#> GSM1253055     2       0          1  0  1
#> GSM1253079     1       0          1  1  0
#> GSM1253083     1       0          1  1  0
#> GSM1253075     1       0          1  1  0
#> GSM1253077     1       0          1  1  0
#> GSM1253076     1       0          1  1  0
#> GSM1253078     1       0          1  1  0
#> GSM1253081     1       0          1  1  0
#> GSM1253080     1       0          1  1  0
#> GSM1253082     1       0          1  1  0

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3
#> GSM1253056     3  0.6286      0.542 0.464 0.000 0.536
#> GSM1253057     1  0.0000      0.890 1.000 0.000 0.000
#> GSM1253058     3  0.5760      0.599 0.328 0.000 0.672
#> GSM1253059     3  0.5760      0.599 0.328 0.000 0.672
#> GSM1253060     1  0.5760      0.105 0.672 0.000 0.328
#> GSM1253061     1  0.0000      0.890 1.000 0.000 0.000
#> GSM1253062     1  0.0000      0.890 1.000 0.000 0.000
#> GSM1253063     3  0.6286      0.542 0.464 0.000 0.536
#> GSM1253064     1  0.0000      0.890 1.000 0.000 0.000
#> GSM1253065     1  0.6192     -0.275 0.580 0.000 0.420
#> GSM1253066     1  0.0000      0.890 1.000 0.000 0.000
#> GSM1253067     3  0.6286      0.542 0.464 0.000 0.536
#> GSM1253068     1  0.0000      0.890 1.000 0.000 0.000
#> GSM1253069     1  0.0000      0.890 1.000 0.000 0.000
#> GSM1253070     1  0.5529      0.390 0.704 0.000 0.296
#> GSM1253071     1  0.6126     -0.200 0.600 0.000 0.400
#> GSM1253072     1  0.0000      0.890 1.000 0.000 0.000
#> GSM1253073     3  0.6286      0.542 0.464 0.000 0.536
#> GSM1253074     1  0.0000      0.890 1.000 0.000 0.000
#> GSM1253032     3  0.4796      0.281 0.000 0.220 0.780
#> GSM1253034     2  0.0000      0.935 0.000 1.000 0.000
#> GSM1253039     2  0.0000      0.935 0.000 1.000 0.000
#> GSM1253040     2  0.0000      0.935 0.000 1.000 0.000
#> GSM1253041     2  0.0000      0.935 0.000 1.000 0.000
#> GSM1253046     2  0.6669      0.435 0.008 0.524 0.468
#> GSM1253048     2  0.0000      0.935 0.000 1.000 0.000
#> GSM1253049     2  0.0000      0.935 0.000 1.000 0.000
#> GSM1253052     2  0.1289      0.934 0.000 0.968 0.032
#> GSM1253037     2  0.0000      0.935 0.000 1.000 0.000
#> GSM1253028     2  0.1163      0.934 0.000 0.972 0.028
#> GSM1253029     2  0.1289      0.934 0.000 0.968 0.032
#> GSM1253030     2  0.0000      0.935 0.000 1.000 0.000
#> GSM1253031     2  0.3038      0.889 0.000 0.896 0.104
#> GSM1253033     3  0.5220      0.304 0.012 0.208 0.780
#> GSM1253035     2  0.1289      0.934 0.000 0.968 0.032
#> GSM1253036     2  0.1163      0.934 0.000 0.972 0.028
#> GSM1253038     2  0.0424      0.935 0.000 0.992 0.008
#> GSM1253042     2  0.1289      0.934 0.000 0.968 0.032
#> GSM1253045     2  0.2959      0.890 0.000 0.900 0.100
#> GSM1253043     2  0.1163      0.934 0.000 0.972 0.028
#> GSM1253044     2  0.0000      0.935 0.000 1.000 0.000
#> GSM1253047     2  0.6291      0.450 0.000 0.532 0.468
#> GSM1253050     2  0.0000      0.935 0.000 1.000 0.000
#> GSM1253051     2  0.0000      0.935 0.000 1.000 0.000
#> GSM1253053     2  0.1289      0.934 0.000 0.968 0.032
#> GSM1253054     2  0.5785      0.652 0.000 0.668 0.332
#> GSM1253055     2  0.1289      0.934 0.000 0.968 0.032
#> GSM1253079     1  0.0000      0.890 1.000 0.000 0.000
#> GSM1253083     1  0.0000      0.890 1.000 0.000 0.000
#> GSM1253075     1  0.0000      0.890 1.000 0.000 0.000
#> GSM1253077     1  0.0000      0.890 1.000 0.000 0.000
#> GSM1253076     1  0.0000      0.890 1.000 0.000 0.000
#> GSM1253078     1  0.0000      0.890 1.000 0.000 0.000
#> GSM1253081     1  0.0000      0.890 1.000 0.000 0.000
#> GSM1253080     1  0.0000      0.890 1.000 0.000 0.000
#> GSM1253082     1  0.0000      0.890 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
#> GSM1253056     4  0.0000      1.000 0.000 0.000 0.000 1.000
#> GSM1253057     1  0.0000      0.776 1.000 0.000 0.000 0.000
#> GSM1253058     4  0.0000      1.000 0.000 0.000 0.000 1.000
#> GSM1253059     4  0.0000      1.000 0.000 0.000 0.000 1.000
#> GSM1253060     4  0.0000      1.000 0.000 0.000 0.000 1.000
#> GSM1253061     1  0.4746      0.688 0.632 0.000 0.000 0.368
#> GSM1253062     1  0.0000      0.776 1.000 0.000 0.000 0.000
#> GSM1253063     4  0.0000      1.000 0.000 0.000 0.000 1.000
#> GSM1253064     1  0.4746      0.688 0.632 0.000 0.000 0.368
#> GSM1253065     4  0.0000      1.000 0.000 0.000 0.000 1.000
#> GSM1253066     1  0.4746      0.688 0.632 0.000 0.000 0.368
#> GSM1253067     4  0.0000      1.000 0.000 0.000 0.000 1.000
#> GSM1253068     1  0.4746      0.688 0.632 0.000 0.000 0.368
#> GSM1253069     1  0.0000      0.776 1.000 0.000 0.000 0.000
#> GSM1253070     1  0.4746      0.688 0.632 0.000 0.000 0.368
#> GSM1253071     4  0.0000      1.000 0.000 0.000 0.000 1.000
#> GSM1253072     1  0.4746      0.688 0.632 0.000 0.000 0.368
#> GSM1253073     4  0.0000      1.000 0.000 0.000 0.000 1.000
#> GSM1253074     1  0.4746      0.688 0.632 0.000 0.000 0.368
#> GSM1253032     3  0.0000      1.000 0.000 0.000 1.000 0.000
#> GSM1253034     2  0.0000      0.991 0.000 1.000 0.000 0.000
#> GSM1253039     2  0.0000      0.991 0.000 1.000 0.000 0.000
#> GSM1253040     2  0.0000      0.991 0.000 1.000 0.000 0.000
#> GSM1253041     2  0.0000      0.991 0.000 1.000 0.000 0.000
#> GSM1253046     3  0.0000      1.000 0.000 0.000 1.000 0.000
#> GSM1253048     2  0.0000      0.991 0.000 1.000 0.000 0.000
#> GSM1253049     2  0.0000      0.991 0.000 1.000 0.000 0.000
#> GSM1253052     3  0.0000      1.000 0.000 0.000 1.000 0.000
#> GSM1253037     2  0.0000      0.991 0.000 1.000 0.000 0.000
#> GSM1253028     3  0.0000      1.000 0.000 0.000 1.000 0.000
#> GSM1253029     3  0.0000      1.000 0.000 0.000 1.000 0.000
#> GSM1253030     2  0.0000      0.991 0.000 1.000 0.000 0.000
#> GSM1253031     3  0.0000      1.000 0.000 0.000 1.000 0.000
#> GSM1253033     3  0.0000      1.000 0.000 0.000 1.000 0.000
#> GSM1253035     3  0.0000      1.000 0.000 0.000 1.000 0.000
#> GSM1253036     3  0.0000      1.000 0.000 0.000 1.000 0.000
#> GSM1253038     2  0.2216      0.892 0.000 0.908 0.092 0.000
#> GSM1253042     3  0.0000      1.000 0.000 0.000 1.000 0.000
#> GSM1253045     3  0.0000      1.000 0.000 0.000 1.000 0.000
#> GSM1253043     3  0.0000      1.000 0.000 0.000 1.000 0.000
#> GSM1253044     2  0.0000      0.991 0.000 1.000 0.000 0.000
#> GSM1253047     3  0.0000      1.000 0.000 0.000 1.000 0.000
#> GSM1253050     2  0.0000      0.991 0.000 1.000 0.000 0.000
#> GSM1253051     2  0.0000      0.991 0.000 1.000 0.000 0.000
#> GSM1253053     3  0.0000      1.000 0.000 0.000 1.000 0.000
#> GSM1253054     3  0.0000      1.000 0.000 0.000 1.000 0.000
#> GSM1253055     3  0.0000      1.000 0.000 0.000 1.000 0.000
#> GSM1253079     1  0.0000      0.776 1.000 0.000 0.000 0.000
#> GSM1253083     1  0.1716      0.769 0.936 0.000 0.000 0.064
#> GSM1253075     1  0.0000      0.776 1.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      0.776 1.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      0.776 1.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      0.776 1.000 0.000 0.000 0.000
#> GSM1253081     1  0.4746      0.688 0.632 0.000 0.000 0.368
#> GSM1253080     1  0.0707      0.775 0.980 0.000 0.000 0.020
#> GSM1253082     1  0.4746      0.688 0.632 0.000 0.000 0.368

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3 p4    p5
#> GSM1253056     4   0.000      1.000 0.000 0.000 0.000  1 0.000
#> GSM1253057     1   0.000      1.000 1.000 0.000 0.000  0 0.000
#> GSM1253058     4   0.000      1.000 0.000 0.000 0.000  1 0.000
#> GSM1253059     4   0.000      1.000 0.000 0.000 0.000  1 0.000
#> GSM1253060     4   0.000      1.000 0.000 0.000 0.000  1 0.000
#> GSM1253061     5   0.366      1.000 0.276 0.000 0.000  0 0.724
#> GSM1253062     1   0.000      1.000 1.000 0.000 0.000  0 0.000
#> GSM1253063     4   0.000      1.000 0.000 0.000 0.000  1 0.000
#> GSM1253064     5   0.366      1.000 0.276 0.000 0.000  0 0.724
#> GSM1253065     4   0.000      1.000 0.000 0.000 0.000  1 0.000
#> GSM1253066     5   0.366      1.000 0.276 0.000 0.000  0 0.724
#> GSM1253067     4   0.000      1.000 0.000 0.000 0.000  1 0.000
#> GSM1253068     5   0.366      1.000 0.276 0.000 0.000  0 0.724
#> GSM1253069     1   0.000      1.000 1.000 0.000 0.000  0 0.000
#> GSM1253070     3   0.678     -0.361 0.276 0.000 0.376  0 0.348
#> GSM1253071     4   0.000      1.000 0.000 0.000 0.000  1 0.000
#> GSM1253072     5   0.366      1.000 0.276 0.000 0.000  0 0.724
#> GSM1253073     4   0.000      1.000 0.000 0.000 0.000  1 0.000
#> GSM1253074     1   0.000      1.000 1.000 0.000 0.000  0 0.000
#> GSM1253032     3   0.000      0.786 0.000 0.000 1.000  0 0.000
#> GSM1253034     2   0.000      1.000 0.000 1.000 0.000  0 0.000
#> GSM1253039     2   0.000      1.000 0.000 1.000 0.000  0 0.000
#> GSM1253040     2   0.000      1.000 0.000 1.000 0.000  0 0.000
#> GSM1253041     2   0.000      1.000 0.000 1.000 0.000  0 0.000
#> GSM1253046     3   0.000      0.786 0.000 0.000 1.000  0 0.000
#> GSM1253048     2   0.000      1.000 0.000 1.000 0.000  0 0.000
#> GSM1253049     2   0.000      1.000 0.000 1.000 0.000  0 0.000
#> GSM1253052     3   0.366      0.885 0.000 0.000 0.724  0 0.276
#> GSM1253037     2   0.000      1.000 0.000 1.000 0.000  0 0.000
#> GSM1253028     3   0.366      0.885 0.000 0.000 0.724  0 0.276
#> GSM1253029     3   0.379      0.884 0.000 0.004 0.724  0 0.272
#> GSM1253030     2   0.000      1.000 0.000 1.000 0.000  0 0.000
#> GSM1253031     3   0.366      0.885 0.000 0.000 0.724  0 0.276
#> GSM1253033     3   0.000      0.786 0.000 0.000 1.000  0 0.000
#> GSM1253035     3   0.366      0.885 0.000 0.000 0.724  0 0.276
#> GSM1253036     3   0.366      0.885 0.000 0.000 0.724  0 0.276
#> GSM1253038     2   0.000      1.000 0.000 1.000 0.000  0 0.000
#> GSM1253042     3   0.366      0.885 0.000 0.000 0.724  0 0.276
#> GSM1253045     3   0.366      0.885 0.000 0.000 0.724  0 0.276
#> GSM1253043     3   0.366      0.885 0.000 0.000 0.724  0 0.276
#> GSM1253044     2   0.000      1.000 0.000 1.000 0.000  0 0.000
#> GSM1253047     3   0.000      0.786 0.000 0.000 1.000  0 0.000
#> GSM1253050     2   0.000      1.000 0.000 1.000 0.000  0 0.000
#> GSM1253051     2   0.000      1.000 0.000 1.000 0.000  0 0.000
#> GSM1253053     3   0.366      0.885 0.000 0.000 0.724  0 0.276
#> GSM1253054     3   0.000      0.786 0.000 0.000 1.000  0 0.000
#> GSM1253055     3   0.366      0.885 0.000 0.000 0.724  0 0.276
#> GSM1253079     1   0.000      1.000 1.000 0.000 0.000  0 0.000
#> GSM1253083     1   0.000      1.000 1.000 0.000 0.000  0 0.000
#> GSM1253075     1   0.000      1.000 1.000 0.000 0.000  0 0.000
#> GSM1253077     1   0.000      1.000 1.000 0.000 0.000  0 0.000
#> GSM1253076     1   0.000      1.000 1.000 0.000 0.000  0 0.000
#> GSM1253078     1   0.000      1.000 1.000 0.000 0.000  0 0.000
#> GSM1253081     5   0.366      1.000 0.276 0.000 0.000  0 0.724
#> GSM1253080     1   0.000      1.000 1.000 0.000 0.000  0 0.000
#> GSM1253082     5   0.366      1.000 0.276 0.000 0.000  0 0.724

show/hide code output

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

#>            class entropy silhouette    p1 p2 p3 p4 p5    p6
#> GSM1253056     4   0.000      1.000 0.000  0  0  1  0 0.000
#> GSM1253057     1   0.000      0.990 1.000  0  0  0  0 0.000
#> GSM1253058     4   0.000      1.000 0.000  0  0  1  0 0.000
#> GSM1253059     4   0.000      1.000 0.000  0  0  1  0 0.000
#> GSM1253060     4   0.000      1.000 0.000  0  0  1  0 0.000
#> GSM1253061     6   0.000      1.000 0.000  0  0  0  0 1.000
#> GSM1253062     1   0.000      0.990 1.000  0  0  0  0 0.000
#> GSM1253063     4   0.000      1.000 0.000  0  0  1  0 0.000
#> GSM1253064     6   0.000      1.000 0.000  0  0  0  0 1.000
#> GSM1253065     4   0.000      1.000 0.000  0  0  1  0 0.000
#> GSM1253066     6   0.000      1.000 0.000  0  0  0  0 1.000
#> GSM1253067     4   0.000      1.000 0.000  0  0  1  0 0.000
#> GSM1253068     6   0.000      1.000 0.000  0  0  0  0 1.000
#> GSM1253069     1   0.000      0.990 1.000  0  0  0  0 0.000
#> GSM1253070     6   0.000      1.000 0.000  0  0  0  0 1.000
#> GSM1253071     4   0.000      1.000 0.000  0  0  1  0 0.000
#> GSM1253072     6   0.000      1.000 0.000  0  0  0  0 1.000
#> GSM1253073     4   0.000      1.000 0.000  0  0  1  0 0.000
#> GSM1253074     1   0.171      0.894 0.908  0  0  0  0 0.092
#> GSM1253032     5   0.000      1.000 0.000  0  0  0  1 0.000
#> GSM1253034     2   0.000      1.000 0.000  1  0  0  0 0.000
#> GSM1253039     2   0.000      1.000 0.000  1  0  0  0 0.000
#> GSM1253040     2   0.000      1.000 0.000  1  0  0  0 0.000
#> GSM1253041     2   0.000      1.000 0.000  1  0  0  0 0.000
#> GSM1253046     5   0.000      1.000 0.000  0  0  0  1 0.000
#> GSM1253048     2   0.000      1.000 0.000  1  0  0  0 0.000
#> GSM1253049     2   0.000      1.000 0.000  1  0  0  0 0.000
#> GSM1253052     3   0.000      1.000 0.000  0  1  0  0 0.000
#> GSM1253037     2   0.000      1.000 0.000  1  0  0  0 0.000
#> GSM1253028     3   0.000      1.000 0.000  0  1  0  0 0.000
#> GSM1253029     3   0.000      1.000 0.000  0  1  0  0 0.000
#> GSM1253030     2   0.000      1.000 0.000  1  0  0  0 0.000
#> GSM1253031     3   0.000      1.000 0.000  0  1  0  0 0.000
#> GSM1253033     5   0.000      1.000 0.000  0  0  0  1 0.000
#> GSM1253035     3   0.000      1.000 0.000  0  1  0  0 0.000
#> GSM1253036     3   0.000      1.000 0.000  0  1  0  0 0.000
#> GSM1253038     2   0.000      1.000 0.000  1  0  0  0 0.000
#> GSM1253042     3   0.000      1.000 0.000  0  1  0  0 0.000
#> GSM1253045     3   0.000      1.000 0.000  0  1  0  0 0.000
#> GSM1253043     3   0.000      1.000 0.000  0  1  0  0 0.000
#> GSM1253044     2   0.000      1.000 0.000  1  0  0  0 0.000
#> GSM1253047     5   0.000      1.000 0.000  0  0  0  1 0.000
#> GSM1253050     2   0.000      1.000 0.000  1  0  0  0 0.000
#> GSM1253051     2   0.000      1.000 0.000  1  0  0  0 0.000
#> GSM1253053     3   0.000      1.000 0.000  0  1  0  0 0.000
#> GSM1253054     5   0.000      1.000 0.000  0  0  0  1 0.000
#> GSM1253055     3   0.000      1.000 0.000  0  1  0  0 0.000
#> GSM1253079     1   0.000      0.990 1.000  0  0  0  0 0.000
#> GSM1253083     1   0.000      0.990 1.000  0  0  0  0 0.000
#> GSM1253075     1   0.000      0.990 1.000  0  0  0  0 0.000
#> GSM1253077     1   0.000      0.990 1.000  0  0  0  0 0.000
#> GSM1253076     1   0.000      0.990 1.000  0  0  0  0 0.000
#> GSM1253078     1   0.000      0.990 1.000  0  0  0  0 0.000
#> GSM1253081     6   0.000      1.000 0.000  0  0  0  0 1.000
#> GSM1253080     1   0.000      0.990 1.000  0  0  0  0 0.000
#> GSM1253082     6   0.000      1.000 0.000  0  0  0  0 1.000

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 infection(p) disease.state(p) individual(p) k
#> MAD:mclust 56     3.60e-03         4.20e-12         0.995 2
#> MAD:mclust 48     9.80e-05         1.38e-10         0.911 3
#> MAD:mclust 56     1.11e-04         4.17e-13         0.934 4
#> MAD:mclust 55     3.22e-05         1.22e-12         0.837 5
#> MAD:mclust 56     8.89e-05         3.40e-12         0.778 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 51979 rows and 56 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#>   Subgroups are detected by 'NMF' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 5.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk MAD-NMF-collect-plots

The plots are:

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

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

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

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

select_partition_number(res)

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

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.984       0.994         0.4954 0.507   0.507
#> 3 3 0.782           0.837       0.925         0.3365 0.778   0.578
#> 4 4 0.980           0.933       0.974         0.1139 0.817   0.524
#> 5 5 0.938           0.903       0.944         0.0156 0.971   0.894
#> 6 6 0.874           0.836       0.903         0.0195 0.982   0.933

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

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

suggest_best_k(res)

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

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

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

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

show/hide code output

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

#>            class entropy silhouette    p1    p2
#> GSM1253056     1   0.000      0.989 1.000 0.000
#> GSM1253057     1   0.000      0.989 1.000 0.000
#> GSM1253058     1   0.000      0.989 1.000 0.000
#> GSM1253059     1   0.000      0.989 1.000 0.000
#> GSM1253060     1   0.000      0.989 1.000 0.000
#> GSM1253061     1   0.000      0.989 1.000 0.000
#> GSM1253062     1   0.000      0.989 1.000 0.000
#> GSM1253063     1   0.000      0.989 1.000 0.000
#> GSM1253064     1   0.000      0.989 1.000 0.000
#> GSM1253065     1   0.000      0.989 1.000 0.000
#> GSM1253066     1   0.000      0.989 1.000 0.000
#> GSM1253067     1   0.000      0.989 1.000 0.000
#> GSM1253068     1   0.000      0.989 1.000 0.000
#> GSM1253069     1   0.000      0.989 1.000 0.000
#> GSM1253070     1   0.000      0.989 1.000 0.000
#> GSM1253071     1   0.000      0.989 1.000 0.000
#> GSM1253072     1   0.000      0.989 1.000 0.000
#> GSM1253073     1   0.000      0.989 1.000 0.000
#> GSM1253074     1   0.000      0.989 1.000 0.000
#> GSM1253032     1   0.000      0.989 1.000 0.000
#> GSM1253034     2   0.000      1.000 0.000 1.000
#> GSM1253039     2   0.000      1.000 0.000 1.000
#> GSM1253040     2   0.000      1.000 0.000 1.000
#> GSM1253041     2   0.000      1.000 0.000 1.000
#> GSM1253046     1   0.000      0.989 1.000 0.000
#> GSM1253048     2   0.000      1.000 0.000 1.000
#> GSM1253049     2   0.000      1.000 0.000 1.000
#> GSM1253052     2   0.000      1.000 0.000 1.000
#> GSM1253037     2   0.000      1.000 0.000 1.000
#> GSM1253028     2   0.000      1.000 0.000 1.000
#> GSM1253029     2   0.000      1.000 0.000 1.000
#> GSM1253030     2   0.000      1.000 0.000 1.000
#> GSM1253031     2   0.000      1.000 0.000 1.000
#> GSM1253033     1   0.000      0.989 1.000 0.000
#> GSM1253035     2   0.000      1.000 0.000 1.000
#> GSM1253036     2   0.000      1.000 0.000 1.000
#> GSM1253038     2   0.000      1.000 0.000 1.000
#> GSM1253042     2   0.000      1.000 0.000 1.000
#> GSM1253045     2   0.000      1.000 0.000 1.000
#> GSM1253043     2   0.000      1.000 0.000 1.000
#> GSM1253044     2   0.000      1.000 0.000 1.000
#> GSM1253047     1   0.000      0.989 1.000 0.000
#> GSM1253050     2   0.000      1.000 0.000 1.000
#> GSM1253051     2   0.000      1.000 0.000 1.000
#> GSM1253053     2   0.000      1.000 0.000 1.000
#> GSM1253054     1   0.932      0.466 0.652 0.348
#> GSM1253055     2   0.000      1.000 0.000 1.000
#> GSM1253079     1   0.000      0.989 1.000 0.000
#> GSM1253083     1   0.000      0.989 1.000 0.000
#> GSM1253075     1   0.000      0.989 1.000 0.000
#> GSM1253077     1   0.000      0.989 1.000 0.000
#> GSM1253076     1   0.000      0.989 1.000 0.000
#> GSM1253078     1   0.000      0.989 1.000 0.000
#> GSM1253081     1   0.000      0.989 1.000 0.000
#> GSM1253080     1   0.000      0.989 1.000 0.000
#> GSM1253082     1   0.000      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
#> GSM1253056     1  0.0000      0.867 1.000 0.000 0.000
#> GSM1253057     3  0.6260      0.142 0.448 0.000 0.552
#> GSM1253058     1  0.0000      0.867 1.000 0.000 0.000
#> GSM1253059     1  0.0000      0.867 1.000 0.000 0.000
#> GSM1253060     1  0.0000      0.867 1.000 0.000 0.000
#> GSM1253061     1  0.4062      0.782 0.836 0.000 0.164
#> GSM1253062     1  0.6111      0.382 0.604 0.000 0.396
#> GSM1253063     1  0.0000      0.867 1.000 0.000 0.000
#> GSM1253064     1  0.4235      0.772 0.824 0.000 0.176
#> GSM1253065     1  0.0000      0.867 1.000 0.000 0.000
#> GSM1253066     1  0.4399      0.759 0.812 0.000 0.188
#> GSM1253067     1  0.0000      0.867 1.000 0.000 0.000
#> GSM1253068     1  0.5968      0.465 0.636 0.000 0.364
#> GSM1253069     3  0.4796      0.706 0.220 0.000 0.780
#> GSM1253070     3  0.0747      0.831 0.016 0.000 0.984
#> GSM1253071     1  0.0000      0.867 1.000 0.000 0.000
#> GSM1253072     1  0.3941      0.788 0.844 0.000 0.156
#> GSM1253073     1  0.0000      0.867 1.000 0.000 0.000
#> GSM1253074     3  0.4291      0.755 0.180 0.000 0.820
#> GSM1253032     3  0.0661      0.825 0.004 0.008 0.988
#> GSM1253034     2  0.0000      0.999 0.000 1.000 0.000
#> GSM1253039     2  0.0000      0.999 0.000 1.000 0.000
#> GSM1253040     2  0.0000      0.999 0.000 1.000 0.000
#> GSM1253041     2  0.0000      0.999 0.000 1.000 0.000
#> GSM1253046     3  0.0000      0.827 0.000 0.000 1.000
#> GSM1253048     2  0.0000      0.999 0.000 1.000 0.000
#> GSM1253049     2  0.0000      0.999 0.000 1.000 0.000
#> GSM1253052     2  0.0000      0.999 0.000 1.000 0.000
#> GSM1253037     2  0.0000      0.999 0.000 1.000 0.000
#> GSM1253028     2  0.0747      0.982 0.000 0.984 0.016
#> GSM1253029     2  0.0000      0.999 0.000 1.000 0.000
#> GSM1253030     2  0.0000      0.999 0.000 1.000 0.000
#> GSM1253031     2  0.0000      0.999 0.000 1.000 0.000
#> GSM1253033     3  0.2448      0.818 0.076 0.000 0.924
#> GSM1253035     2  0.0000      0.999 0.000 1.000 0.000
#> GSM1253036     2  0.0000      0.999 0.000 1.000 0.000
#> GSM1253038     2  0.0000      0.999 0.000 1.000 0.000
#> GSM1253042     2  0.0000      0.999 0.000 1.000 0.000
#> GSM1253045     3  0.3038      0.773 0.000 0.104 0.896
#> GSM1253043     3  0.6286      0.171 0.000 0.464 0.536
#> GSM1253044     2  0.0000      0.999 0.000 1.000 0.000
#> GSM1253047     3  0.0000      0.827 0.000 0.000 1.000
#> GSM1253050     2  0.0000      0.999 0.000 1.000 0.000
#> GSM1253051     2  0.0000      0.999 0.000 1.000 0.000
#> GSM1253053     2  0.0000      0.999 0.000 1.000 0.000
#> GSM1253054     3  0.1289      0.813 0.000 0.032 0.968
#> GSM1253055     2  0.0000      0.999 0.000 1.000 0.000
#> GSM1253079     1  0.6180      0.323 0.584 0.000 0.416
#> GSM1253083     3  0.0592      0.831 0.012 0.000 0.988
#> GSM1253075     3  0.5529      0.579 0.296 0.000 0.704
#> GSM1253077     3  0.0592      0.831 0.012 0.000 0.988
#> GSM1253076     3  0.4178      0.762 0.172 0.000 0.828
#> GSM1253078     3  0.3619      0.789 0.136 0.000 0.864
#> GSM1253081     1  0.0237      0.865 0.996 0.000 0.004
#> GSM1253080     3  0.2537      0.818 0.080 0.000 0.920
#> GSM1253082     1  0.0000      0.867 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
#> GSM1253056     4   0.000      0.947 0.00 0.000 0.000 1.00
#> GSM1253057     1   0.000      0.977 1.00 0.000 0.000 0.00
#> GSM1253058     4   0.000      0.947 0.00 0.000 0.000 1.00
#> GSM1253059     4   0.000      0.947 0.00 0.000 0.000 1.00
#> GSM1253060     4   0.000      0.947 0.00 0.000 0.000 1.00
#> GSM1253061     1   0.000      0.977 1.00 0.000 0.000 0.00
#> GSM1253062     1   0.000      0.977 1.00 0.000 0.000 0.00
#> GSM1253063     4   0.000      0.947 0.00 0.000 0.000 1.00
#> GSM1253064     1   0.000      0.977 1.00 0.000 0.000 0.00
#> GSM1253065     4   0.000      0.947 0.00 0.000 0.000 1.00
#> GSM1253066     1   0.000      0.977 1.00 0.000 0.000 0.00
#> GSM1253067     4   0.000      0.947 0.00 0.000 0.000 1.00
#> GSM1253068     1   0.000      0.977 1.00 0.000 0.000 0.00
#> GSM1253069     1   0.000      0.977 1.00 0.000 0.000 0.00
#> GSM1253070     1   0.000      0.977 1.00 0.000 0.000 0.00
#> GSM1253071     4   0.000      0.947 0.00 0.000 0.000 1.00
#> GSM1253072     1   0.000      0.977 1.00 0.000 0.000 0.00
#> GSM1253073     4   0.000      0.947 0.00 0.000 0.000 1.00
#> GSM1253074     1   0.000      0.977 1.00 0.000 0.000 0.00
#> GSM1253032     3   0.000      0.964 0.00 0.000 1.000 0.00
#> GSM1253034     2   0.000      0.972 0.00 1.000 0.000 0.00
#> GSM1253039     2   0.000      0.972 0.00 1.000 0.000 0.00
#> GSM1253040     2   0.000      0.972 0.00 1.000 0.000 0.00
#> GSM1253041     2   0.000      0.972 0.00 1.000 0.000 0.00
#> GSM1253046     3   0.000      0.964 0.00 0.000 1.000 0.00
#> GSM1253048     2   0.000      0.972 0.00 1.000 0.000 0.00
#> GSM1253049     2   0.000      0.972 0.00 1.000 0.000 0.00
#> GSM1253052     2   0.164      0.922 0.00 0.940 0.060 0.00
#> GSM1253037     2   0.000      0.972 0.00 1.000 0.000 0.00
#> GSM1253028     2   0.000      0.972 0.00 1.000 0.000 0.00
#> GSM1253029     2   0.000      0.972 0.00 1.000 0.000 0.00
#> GSM1253030     2   0.000      0.972 0.00 1.000 0.000 0.00
#> GSM1253031     3   0.322      0.802 0.00 0.164 0.836 0.00
#> GSM1253033     3   0.000      0.964 0.00 0.000 1.000 0.00
#> GSM1253035     2   0.215      0.893 0.00 0.912 0.088 0.00
#> GSM1253036     2   0.000      0.972 0.00 1.000 0.000 0.00
#> GSM1253038     2   0.000      0.972 0.00 1.000 0.000 0.00
#> GSM1253042     2   0.000      0.972 0.00 1.000 0.000 0.00
#> GSM1253045     3   0.000      0.964 0.00 0.000 1.000 0.00
#> GSM1253043     3   0.000      0.964 0.00 0.000 1.000 0.00
#> GSM1253044     2   0.000      0.972 0.00 1.000 0.000 0.00
#> GSM1253047     3   0.000      0.964 0.00 0.000 1.000 0.00
#> GSM1253050     2   0.000      0.972 0.00 1.000 0.000 0.00
#> GSM1253051     2   0.000      0.972 0.00 1.000 0.000 0.00
#> GSM1253053     2   0.456      0.509 0.00 0.672 0.328 0.00
#> GSM1253054     3   0.000      0.964 0.00 0.000 1.000 0.00
#> GSM1253055     3   0.179      0.910 0.00 0.068 0.932 0.00
#> GSM1253079     1   0.000      0.977 1.00 0.000 0.000 0.00
#> GSM1253083     1   0.000      0.977 1.00 0.000 0.000 0.00
#> GSM1253075     1   0.000      0.977 1.00 0.000 0.000 0.00
#> GSM1253077     1   0.000      0.977 1.00 0.000 0.000 0.00
#> GSM1253076     1   0.000      0.977 1.00 0.000 0.000 0.00
#> GSM1253078     1   0.000      0.977 1.00 0.000 0.000 0.00
#> GSM1253081     4   0.479      0.356 0.38 0.000 0.000 0.62
#> GSM1253080     1   0.000      0.977 1.00 0.000 0.000 0.00
#> GSM1253082     1   0.471      0.392 0.64 0.000 0.000 0.36

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4    p5
#> GSM1253056     3  0.4088      0.843 0.000 0.000 0.632 0.368 0.000
#> GSM1253057     1  0.0000      0.967 1.000 0.000 0.000 0.000 0.000
#> GSM1253058     4  0.1043      0.942 0.000 0.000 0.040 0.960 0.000
#> GSM1253059     4  0.1043      0.915 0.000 0.000 0.040 0.960 0.000
#> GSM1253060     4  0.1270      0.928 0.000 0.000 0.052 0.948 0.000
#> GSM1253061     1  0.0162      0.965 0.996 0.000 0.000 0.004 0.000
#> GSM1253062     1  0.0162      0.965 0.996 0.000 0.004 0.000 0.000
#> GSM1253063     4  0.0162      0.951 0.000 0.000 0.004 0.996 0.000
#> GSM1253064     1  0.0290      0.963 0.992 0.000 0.008 0.000 0.000
#> GSM1253065     3  0.3305      0.834 0.000 0.000 0.776 0.224 0.000
#> GSM1253066     1  0.0000      0.967 1.000 0.000 0.000 0.000 0.000
#> GSM1253067     3  0.3876      0.886 0.000 0.000 0.684 0.316 0.000
#> GSM1253068     1  0.0000      0.967 1.000 0.000 0.000 0.000 0.000
#> GSM1253069     1  0.0000      0.967 1.000 0.000 0.000 0.000 0.000
#> GSM1253070     1  0.4722      0.363 0.608 0.000 0.024 0.000 0.368
#> GSM1253071     4  0.0963      0.947 0.000 0.000 0.036 0.964 0.000
#> GSM1253072     1  0.0000      0.967 1.000 0.000 0.000 0.000 0.000
#> GSM1253073     4  0.0162      0.949 0.000 0.000 0.004 0.996 0.000
#> GSM1253074     1  0.0000      0.967 1.000 0.000 0.000 0.000 0.000
#> GSM1253032     5  0.0162      0.917 0.000 0.000 0.004 0.000 0.996
#> GSM1253034     2  0.0290      0.943 0.000 0.992 0.008 0.000 0.000
#> GSM1253039     2  0.0290      0.943 0.000 0.992 0.008 0.000 0.000
#> GSM1253040     2  0.0000      0.944 0.000 1.000 0.000 0.000 0.000
#> GSM1253041     2  0.0000      0.944 0.000 1.000 0.000 0.000 0.000
#> GSM1253046     5  0.0000      0.918 0.000 0.000 0.000 0.000 1.000
#> GSM1253048     2  0.0000      0.944 0.000 1.000 0.000 0.000 0.000
#> GSM1253049     2  0.0000      0.944 0.000 1.000 0.000 0.000 0.000
#> GSM1253052     2  0.0693      0.934 0.000 0.980 0.012 0.000 0.008
#> GSM1253037     2  0.0000      0.944 0.000 1.000 0.000 0.000 0.000
#> GSM1253028     2  0.4199      0.720 0.000 0.764 0.056 0.000 0.180
#> GSM1253029     2  0.0000      0.944 0.000 1.000 0.000 0.000 0.000
#> GSM1253030     2  0.0794      0.932 0.000 0.972 0.028 0.000 0.000
#> GSM1253031     5  0.1597      0.904 0.000 0.012 0.048 0.000 0.940
#> GSM1253033     5  0.0703      0.916 0.000 0.000 0.024 0.000 0.976
#> GSM1253035     2  0.3885      0.628 0.000 0.724 0.008 0.000 0.268
#> GSM1253036     2  0.1168      0.925 0.000 0.960 0.032 0.000 0.008
#> GSM1253038     2  0.0290      0.943 0.000 0.992 0.008 0.000 0.000
#> GSM1253042     2  0.0000      0.944 0.000 1.000 0.000 0.000 0.000
#> GSM1253045     5  0.1197      0.911 0.000 0.000 0.048 0.000 0.952
#> GSM1253043     5  0.1043      0.913 0.000 0.000 0.040 0.000 0.960
#> GSM1253044     2  0.0000      0.944 0.000 1.000 0.000 0.000 0.000
#> GSM1253047     5  0.0404      0.915 0.000 0.000 0.012 0.000 0.988
#> GSM1253050     2  0.0000      0.944 0.000 1.000 0.000 0.000 0.000
#> GSM1253051     2  0.0162      0.944 0.000 0.996 0.004 0.000 0.000
#> GSM1253053     2  0.4620      0.524 0.000 0.652 0.320 0.000 0.028
#> GSM1253054     5  0.1121      0.900 0.000 0.000 0.044 0.000 0.956
#> GSM1253055     5  0.4130      0.516 0.000 0.292 0.012 0.000 0.696
#> GSM1253079     1  0.0000      0.967 1.000 0.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000      0.967 1.000 0.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000      0.967 1.000 0.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      0.967 1.000 0.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      0.967 1.000 0.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      0.967 1.000 0.000 0.000 0.000 0.000
#> GSM1253081     1  0.2426      0.874 0.900 0.000 0.036 0.064 0.000
#> GSM1253080     1  0.0000      0.967 1.000 0.000 0.000 0.000 0.000
#> GSM1253082     1  0.0865      0.945 0.972 0.000 0.004 0.024 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
#> GSM1253056     3  0.3371      0.853 0.000 0.000 0.708 0.292 0.000 NA
#> GSM1253057     1  0.0653      0.939 0.980 0.000 0.004 0.004 0.000 NA
#> GSM1253058     4  0.3121      0.791 0.004 0.000 0.116 0.836 0.000 NA
#> GSM1253059     4  0.2311      0.777 0.000 0.000 0.104 0.880 0.000 NA
#> GSM1253060     4  0.1814      0.842 0.000 0.000 0.100 0.900 0.000 NA
#> GSM1253061     1  0.0458      0.937 0.984 0.000 0.000 0.000 0.000 NA
#> GSM1253062     1  0.0914      0.935 0.968 0.000 0.016 0.000 0.000 NA
#> GSM1253063     4  0.0820      0.851 0.000 0.000 0.012 0.972 0.000 NA
#> GSM1253064     1  0.2361      0.891 0.896 0.000 0.008 0.032 0.000 NA
#> GSM1253065     3  0.2260      0.811 0.000 0.000 0.860 0.140 0.000 NA
#> GSM1253066     1  0.1149      0.929 0.960 0.000 0.008 0.008 0.000 NA
#> GSM1253067     3  0.3221      0.878 0.000 0.000 0.736 0.264 0.000 NA
#> GSM1253068     1  0.0692      0.938 0.976 0.000 0.004 0.000 0.000 NA
#> GSM1253069     1  0.0603      0.939 0.980 0.000 0.004 0.000 0.000 NA
#> GSM1253070     1  0.5338      0.142 0.508 0.000 0.020 0.000 0.412 NA
#> GSM1253071     4  0.1858      0.840 0.000 0.000 0.092 0.904 0.000 NA
#> GSM1253072     1  0.0713      0.935 0.972 0.000 0.000 0.000 0.000 NA
#> GSM1253073     4  0.2163      0.813 0.000 0.000 0.016 0.892 0.000 NA
#> GSM1253074     1  0.0458      0.939 0.984 0.000 0.000 0.000 0.000 NA
#> GSM1253032     5  0.0363      0.798 0.000 0.000 0.000 0.000 0.988 NA
#> GSM1253034     2  0.0260      0.929 0.000 0.992 0.000 0.000 0.000 NA
#> GSM1253039     2  0.0260      0.929 0.000 0.992 0.000 0.000 0.000 NA
#> GSM1253040     2  0.0146      0.929 0.000 0.996 0.000 0.000 0.000 NA
#> GSM1253041     2  0.0260      0.928 0.000 0.992 0.000 0.000 0.000 NA
#> GSM1253046     5  0.0547      0.797 0.000 0.000 0.000 0.000 0.980 NA
#> GSM1253048     2  0.0000      0.929 0.000 1.000 0.000 0.000 0.000 NA
#> GSM1253049     2  0.0146      0.929 0.000 0.996 0.000 0.000 0.000 NA
#> GSM1253052     2  0.1082      0.916 0.000 0.956 0.000 0.004 0.000 NA
#> GSM1253037     2  0.0000      0.929 0.000 1.000 0.000 0.000 0.000 NA
#> GSM1253028     5  0.5479      0.361 0.000 0.368 0.000 0.000 0.500 NA
#> GSM1253029     2  0.0790      0.922 0.000 0.968 0.000 0.000 0.000 NA
#> GSM1253030     2  0.3446      0.664 0.000 0.692 0.000 0.000 0.000 NA
#> GSM1253031     5  0.3044      0.768 0.000 0.048 0.000 0.000 0.836 NA
#> GSM1253033     5  0.1332      0.794 0.000 0.000 0.012 0.008 0.952 NA
#> GSM1253035     2  0.4230      0.344 0.000 0.612 0.000 0.000 0.364 NA
#> GSM1253036     2  0.3108      0.811 0.000 0.828 0.000 0.000 0.044 NA
#> GSM1253038     2  0.0260      0.928 0.000 0.992 0.000 0.000 0.000 NA
#> GSM1253042     2  0.0790      0.923 0.000 0.968 0.000 0.000 0.000 NA
#> GSM1253045     5  0.2558      0.768 0.000 0.000 0.004 0.000 0.840 NA
#> GSM1253043     5  0.3371      0.673 0.000 0.000 0.000 0.000 0.708 NA
#> GSM1253044     2  0.0260      0.928 0.000 0.992 0.000 0.000 0.000 NA
#> GSM1253047     5  0.0790      0.795 0.000 0.000 0.000 0.000 0.968 NA
#> GSM1253050     2  0.0146      0.929 0.000 0.996 0.000 0.000 0.000 NA
#> GSM1253051     2  0.0458      0.926 0.000 0.984 0.000 0.000 0.000 NA
#> GSM1253053     2  0.3736      0.775 0.000 0.792 0.144 0.004 0.004 NA
#> GSM1253054     5  0.1333      0.791 0.000 0.000 0.008 0.000 0.944 NA
#> GSM1253055     5  0.4787      0.443 0.000 0.336 0.000 0.000 0.596 NA
#> GSM1253079     1  0.0551      0.940 0.984 0.000 0.004 0.008 0.000 NA
#> GSM1253083     1  0.0458      0.939 0.984 0.000 0.000 0.000 0.000 NA
#> GSM1253075     1  0.0146      0.940 0.996 0.000 0.000 0.000 0.000 NA
#> GSM1253077     1  0.0458      0.939 0.984 0.000 0.000 0.000 0.000 NA
#> GSM1253076     1  0.0000      0.939 1.000 0.000 0.000 0.000 0.000 NA
#> GSM1253078     1  0.0146      0.939 0.996 0.000 0.000 0.000 0.000 NA
#> GSM1253081     1  0.3425      0.825 0.836 0.000 0.048 0.084 0.000 NA
#> GSM1253080     1  0.0458      0.939 0.984 0.000 0.000 0.000 0.000 NA
#> GSM1253082     1  0.2657      0.866 0.880 0.000 0.020 0.076 0.000 NA

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

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

consensus_heatmap(res, k = 2)

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

consensus_heatmap(res, k = 3)

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

consensus_heatmap(res, k = 4)

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

consensus_heatmap(res, k = 5)

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

consensus_heatmap(res, k = 6)

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

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

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

membership_heatmap(res, k = 2)

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

membership_heatmap(res, k = 3)

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

membership_heatmap(res, k = 4)

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

membership_heatmap(res, k = 5)

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

membership_heatmap(res, k = 6)

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

Signature heatmaps where rows are scaled:

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

get_signatures(res, k = 2)

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

get_signatures(res, k = 3)

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

get_signatures(res, k = 4)

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

get_signatures(res, k = 5)

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

get_signatures(res, k = 6)

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

Signature heatmaps where rows are not scaled:

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

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

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

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

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

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

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

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

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

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

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

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk MAD-NMF-signature_compare

# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)

An example of the output of tb is:

#>   which_row         fdr    mean_1    mean_2 scaled_mean_1 scaled_mean_2 km
#> 1        38 0.042760348  8.373488  9.131774    -0.5533452     0.5164555  1
#> 2        40 0.018707592  7.106213  8.469186    -0.6173731     0.5762149  1
#> 3        55 0.019134737 10.221463 11.207825    -0.6159697     0.5749050  1
#> 4        59 0.006059896  5.921854  7.869574    -0.6899429     0.6439467  1
#> 5        60 0.018055526  8.928898 10.211722    -0.6204761     0.5791110  1
#> 6        98 0.009384629 15.714769 14.887706     0.6635654    -0.6193277  2
...

The columns in tb are:

which_row: row indices corresponding to the input matrix.
fdr: FDR for the differential test.
mean_x: The mean value in group x.
scaled_mean_x: The mean value in group x after rows are scaled.
km: Row groups if k-means clustering is applied to rows.

UMAP plot which shows how samples are separated.

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

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

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

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

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

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

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

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

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

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

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

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk MAD-NMF-collect-classes

test_to_known_factors(res)

#>          n infection(p) disease.state(p) individual(p) k
#> MAD:NMF 55     0.015882         6.02e-09         0.956 2
#> MAD:NMF 51     0.004809         1.14e-08         0.819 3
#> MAD:NMF 54     0.000556         7.17e-11         0.899 4
#> MAD:NMF 55     0.000190         2.25e-10         0.951 5
#> MAD:NMF 52     0.000387         1.02e-09         0.875 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 51979 rows and 56 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 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-hclust-collect-plots

The plots are:

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

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

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

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

select_partition_number(res)

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

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.963       0.986         0.4871 0.507   0.507
#> 3 3 0.899           0.933       0.922         0.1696 0.914   0.831
#> 4 4 1.000           0.960       0.984         0.0912 0.960   0.904
#> 5 5 1.000           0.960       0.984         0.1360 0.916   0.779
#> 6 6 1.000           0.987       0.993         0.0152 0.988   0.961

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

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

suggest_best_k(res)

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

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

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

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

show/hide code output

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

#>            class entropy silhouette  p1  p2
#> GSM1253056     1   0.000      1.000 1.0 0.0
#> GSM1253057     1   0.000      1.000 1.0 0.0
#> GSM1253058     1   0.000      1.000 1.0 0.0
#> GSM1253059     1   0.000      1.000 1.0 0.0
#> GSM1253060     1   0.000      1.000 1.0 0.0
#> GSM1253061     1   0.000      1.000 1.0 0.0
#> GSM1253062     1   0.000      1.000 1.0 0.0
#> GSM1253063     1   0.000      1.000 1.0 0.0
#> GSM1253064     1   0.000      1.000 1.0 0.0
#> GSM1253065     1   0.000      1.000 1.0 0.0
#> GSM1253066     1   0.000      1.000 1.0 0.0
#> GSM1253067     1   0.000      1.000 1.0 0.0
#> GSM1253068     1   0.000      1.000 1.0 0.0
#> GSM1253069     1   0.000      1.000 1.0 0.0
#> GSM1253070     1   0.000      1.000 1.0 0.0
#> GSM1253071     1   0.000      1.000 1.0 0.0
#> GSM1253072     1   0.000      1.000 1.0 0.0
#> GSM1253073     1   0.000      1.000 1.0 0.0
#> GSM1253074     1   0.000      1.000 1.0 0.0
#> GSM1253032     1   0.000      1.000 1.0 0.0
#> GSM1253034     2   0.000      0.963 0.0 1.0
#> GSM1253039     2   0.000      0.963 0.0 1.0
#> GSM1253040     2   0.000      0.963 0.0 1.0
#> GSM1253041     2   0.000      0.963 0.0 1.0
#> GSM1253046     1   0.000      1.000 1.0 0.0
#> GSM1253048     2   0.000      0.963 0.0 1.0
#> GSM1253049     2   0.000      0.963 0.0 1.0
#> GSM1253052     2   0.000      0.963 0.0 1.0
#> GSM1253037     2   0.000      0.963 0.0 1.0
#> GSM1253028     2   0.000      0.963 0.0 1.0
#> GSM1253029     2   0.000      0.963 0.0 1.0
#> GSM1253030     2   0.000      0.963 0.0 1.0
#> GSM1253031     2   0.000      0.963 0.0 1.0
#> GSM1253033     1   0.000      1.000 1.0 0.0
#> GSM1253035     2   0.000      0.963 0.0 1.0
#> GSM1253036     2   0.000      0.963 0.0 1.0
#> GSM1253038     2   0.000      0.963 0.0 1.0
#> GSM1253042     2   0.000      0.963 0.0 1.0
#> GSM1253045     2   0.971      0.364 0.4 0.6
#> GSM1253043     2   0.971      0.364 0.4 0.6
#> GSM1253044     2   0.000      0.963 0.0 1.0
#> GSM1253047     1   0.000      1.000 1.0 0.0
#> GSM1253050     2   0.000      0.963 0.0 1.0
#> GSM1253051     2   0.000      0.963 0.0 1.0
#> GSM1253053     2   0.000      0.963 0.0 1.0
#> GSM1253054     1   0.000      1.000 1.0 0.0
#> GSM1253055     2   0.000      0.963 0.0 1.0
#> GSM1253079     1   0.000      1.000 1.0 0.0
#> GSM1253083     1   0.000      1.000 1.0 0.0
#> GSM1253075     1   0.000      1.000 1.0 0.0
#> GSM1253077     1   0.000      1.000 1.0 0.0
#> GSM1253076     1   0.000      1.000 1.0 0.0
#> GSM1253078     1   0.000      1.000 1.0 0.0
#> GSM1253081     1   0.000      1.000 1.0 0.0
#> GSM1253080     1   0.000      1.000 1.0 0.0
#> GSM1253082     1   0.000      1.000 1.0 0.0

show/hide code output

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

#>            class entropy silhouette    p1  p2    p3
#> GSM1253056     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253057     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253058     1   0.588      0.595 0.652 0.0 0.348
#> GSM1253059     1   0.613      0.517 0.600 0.0 0.400
#> GSM1253060     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253061     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253062     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253063     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253064     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253065     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253066     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253067     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253068     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253069     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253070     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253071     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253072     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253073     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253074     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253032     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253034     2   0.000      1.000 0.000 1.0 0.000
#> GSM1253039     2   0.000      1.000 0.000 1.0 0.000
#> GSM1253040     2   0.000      1.000 0.000 1.0 0.000
#> GSM1253041     2   0.000      1.000 0.000 1.0 0.000
#> GSM1253046     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253048     2   0.000      1.000 0.000 1.0 0.000
#> GSM1253049     2   0.000      1.000 0.000 1.0 0.000
#> GSM1253052     3   0.613      0.862 0.000 0.4 0.600
#> GSM1253037     2   0.000      1.000 0.000 1.0 0.000
#> GSM1253028     3   0.613      0.862 0.000 0.4 0.600
#> GSM1253029     3   0.613      0.862 0.000 0.4 0.600
#> GSM1253030     2   0.000      1.000 0.000 1.0 0.000
#> GSM1253031     3   0.613      0.862 0.000 0.4 0.600
#> GSM1253033     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253035     3   0.613      0.862 0.000 0.4 0.600
#> GSM1253036     3   0.613      0.862 0.000 0.4 0.600
#> GSM1253038     2   0.000      1.000 0.000 1.0 0.000
#> GSM1253042     3   0.613      0.862 0.000 0.4 0.600
#> GSM1253045     3   0.000      0.532 0.000 0.0 1.000
#> GSM1253043     3   0.000      0.532 0.000 0.0 1.000
#> GSM1253044     2   0.000      1.000 0.000 1.0 0.000
#> GSM1253047     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253050     2   0.000      1.000 0.000 1.0 0.000
#> GSM1253051     2   0.000      1.000 0.000 1.0 0.000
#> GSM1253053     3   0.613      0.862 0.000 0.4 0.600
#> GSM1253054     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253055     3   0.613      0.862 0.000 0.4 0.600
#> GSM1253079     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253083     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253075     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253077     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253076     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253078     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253081     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253080     1   0.000      0.979 1.000 0.0 0.000
#> GSM1253082     1   0.000      0.979 1.000 0.0 0.000

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4
#> GSM1253056     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253057     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253058     4  0.1716      0.880 0.064 0.000 0.000 0.936
#> GSM1253059     4  0.0000      0.879 0.000 0.000 0.000 1.000
#> GSM1253060     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253061     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253062     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253063     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253064     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253065     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253066     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253067     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253068     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253069     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253070     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253071     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253072     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253073     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253074     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253032     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253034     2  0.0000      0.997 0.000 1.000 0.000 0.000
#> GSM1253039     2  0.0000      0.997 0.000 1.000 0.000 0.000
#> GSM1253040     2  0.0000      0.997 0.000 1.000 0.000 0.000
#> GSM1253041     2  0.0000      0.997 0.000 1.000 0.000 0.000
#> GSM1253046     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253048     2  0.0000      0.997 0.000 1.000 0.000 0.000
#> GSM1253049     2  0.0000      0.997 0.000 1.000 0.000 0.000
#> GSM1253052     3  0.0000      0.914 0.000 0.000 1.000 0.000
#> GSM1253037     2  0.0000      0.997 0.000 1.000 0.000 0.000
#> GSM1253028     3  0.0000      0.914 0.000 0.000 1.000 0.000
#> GSM1253029     3  0.0000      0.914 0.000 0.000 1.000 0.000
#> GSM1253030     2  0.0000      0.997 0.000 1.000 0.000 0.000
#> GSM1253031     3  0.0000      0.914 0.000 0.000 1.000 0.000
#> GSM1253033     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253035     3  0.0000      0.914 0.000 0.000 1.000 0.000
#> GSM1253036     3  0.0000      0.914 0.000 0.000 1.000 0.000
#> GSM1253038     2  0.0000      0.997 0.000 1.000 0.000 0.000
#> GSM1253042     3  0.0000      0.914 0.000 0.000 1.000 0.000
#> GSM1253045     3  0.4855      0.413 0.000 0.000 0.600 0.400
#> GSM1253043     3  0.4855      0.413 0.000 0.000 0.600 0.400
#> GSM1253044     2  0.0000      0.997 0.000 1.000 0.000 0.000
#> GSM1253047     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253050     2  0.0000      0.997 0.000 1.000 0.000 0.000
#> GSM1253051     2  0.0817      0.970 0.000 0.976 0.024 0.000
#> GSM1253053     3  0.0000      0.914 0.000 0.000 1.000 0.000
#> GSM1253054     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253055     3  0.0000      0.914 0.000 0.000 1.000 0.000
#> GSM1253079     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253081     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253080     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253082     1  0.0000      1.000 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
#> GSM1253056     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253057     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253058     4  0.1478      0.871 0.064 0.000 0.000 0.936  0
#> GSM1253059     4  0.0000      0.871 0.000 0.000 0.000 1.000  0
#> GSM1253060     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253061     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253062     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253063     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253064     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253065     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253066     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253067     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253068     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253069     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253070     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253071     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253072     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253073     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253074     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253032     5  0.0000      1.000 0.000 0.000 0.000 0.000  1
#> GSM1253034     2  0.0000      0.997 0.000 1.000 0.000 0.000  0
#> GSM1253039     2  0.0000      0.997 0.000 1.000 0.000 0.000  0
#> GSM1253040     2  0.0000      0.997 0.000 1.000 0.000 0.000  0
#> GSM1253041     2  0.0000      0.997 0.000 1.000 0.000 0.000  0
#> GSM1253046     5  0.0000      1.000 0.000 0.000 0.000 0.000  1
#> GSM1253048     2  0.0000      0.997 0.000 1.000 0.000 0.000  0
#> GSM1253049     2  0.0000      0.997 0.000 1.000 0.000 0.000  0
#> GSM1253052     3  0.0000      0.914 0.000 0.000 1.000 0.000  0
#> GSM1253037     2  0.0000      0.997 0.000 1.000 0.000 0.000  0
#> GSM1253028     3  0.0000      0.914 0.000 0.000 1.000 0.000  0
#> GSM1253029     3  0.0000      0.914 0.000 0.000 1.000 0.000  0
#> GSM1253030     2  0.0000      0.997 0.000 1.000 0.000 0.000  0
#> GSM1253031     3  0.0000      0.914 0.000 0.000 1.000 0.000  0
#> GSM1253033     5  0.0000      1.000 0.000 0.000 0.000 0.000  1
#> GSM1253035     3  0.0000      0.914 0.000 0.000 1.000 0.000  0
#> GSM1253036     3  0.0000      0.914 0.000 0.000 1.000 0.000  0
#> GSM1253038     2  0.0000      0.997 0.000 1.000 0.000 0.000  0
#> GSM1253042     3  0.0000      0.914 0.000 0.000 1.000 0.000  0
#> GSM1253045     3  0.4182      0.412 0.000 0.000 0.600 0.400  0
#> GSM1253043     3  0.4182      0.412 0.000 0.000 0.600 0.400  0
#> GSM1253044     2  0.0000      0.997 0.000 1.000 0.000 0.000  0
#> GSM1253047     5  0.0000      1.000 0.000 0.000 0.000 0.000  1
#> GSM1253050     2  0.0000      0.997 0.000 1.000 0.000 0.000  0
#> GSM1253051     2  0.0703      0.970 0.000 0.976 0.024 0.000  0
#> GSM1253053     3  0.0000      0.914 0.000 0.000 1.000 0.000  0
#> GSM1253054     5  0.0000      1.000 0.000 0.000 0.000 0.000  1
#> GSM1253055     3  0.0000      0.914 0.000 0.000 1.000 0.000  0
#> GSM1253079     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253083     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253075     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253077     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253076     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253078     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253081     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253080     1  0.0000      1.000 1.000 0.000 0.000 0.000  0
#> GSM1253082     1  0.0000      1.000 1.000 0.000 0.000 0.000  0

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4 p5    p6
#> GSM1253056     1  0.0865      0.972 0.964 0.000 0.000 0.000  0 0.036
#> GSM1253057     1  0.0000      0.990 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253058     4  0.1500      0.851 0.052 0.000 0.000 0.936  0 0.012
#> GSM1253059     4  0.0000      0.849 0.000 0.000 0.000 1.000  0 0.000
#> GSM1253060     1  0.0865      0.972 0.964 0.000 0.000 0.000  0 0.036
#> GSM1253061     1  0.0000      0.990 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253062     1  0.0000      0.990 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253063     1  0.0865      0.972 0.964 0.000 0.000 0.000  0 0.036
#> GSM1253064     1  0.0000      0.990 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253065     1  0.0865      0.972 0.964 0.000 0.000 0.000  0 0.036
#> GSM1253066     1  0.0000      0.990 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253067     1  0.0865      0.972 0.964 0.000 0.000 0.000  0 0.036
#> GSM1253068     1  0.0000      0.990 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253069     1  0.0000      0.990 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253070     1  0.0000      0.990 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253071     1  0.0865      0.972 0.964 0.000 0.000 0.000  0 0.036
#> GSM1253072     1  0.0000      0.990 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253073     1  0.0865      0.972 0.964 0.000 0.000 0.000  0 0.036
#> GSM1253074     1  0.0000      0.990 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253032     5  0.0000      1.000 0.000 0.000 0.000 0.000  1 0.000
#> GSM1253034     2  0.0000      0.997 0.000 1.000 0.000 0.000  0 0.000
#> GSM1253039     2  0.0000      0.997 0.000 1.000 0.000 0.000  0 0.000
#> GSM1253040     2  0.0000      0.997 0.000 1.000 0.000 0.000  0 0.000
#> GSM1253041     2  0.0000      0.997 0.000 1.000 0.000 0.000  0 0.000
#> GSM1253046     5  0.0000      1.000 0.000 0.000 0.000 0.000  1 0.000
#> GSM1253048     2  0.0000      0.997 0.000 1.000 0.000 0.000  0 0.000
#> GSM1253049     2  0.0000      0.997 0.000 1.000 0.000 0.000  0 0.000
#> GSM1253052     3  0.0000      1.000 0.000 0.000 1.000 0.000  0 0.000
#> GSM1253037     2  0.0000      0.997 0.000 1.000 0.000 0.000  0 0.000
#> GSM1253028     3  0.0000      1.000 0.000 0.000 1.000 0.000  0 0.000
#> GSM1253029     3  0.0000      1.000 0.000 0.000 1.000 0.000  0 0.000
#> GSM1253030     2  0.0000      0.997 0.000 1.000 0.000 0.000  0 0.000
#> GSM1253031     3  0.0000      1.000 0.000 0.000 1.000 0.000  0 0.000
#> GSM1253033     5  0.0000      1.000 0.000 0.000 0.000 0.000  1 0.000
#> GSM1253035     3  0.0000      1.000 0.000 0.000 1.000 0.000  0 0.000
#> GSM1253036     3  0.0000      1.000 0.000 0.000 1.000 0.000  0 0.000
#> GSM1253038     2  0.0000      0.997 0.000 1.000 0.000 0.000  0 0.000
#> GSM1253042     3  0.0000      1.000 0.000 0.000 1.000 0.000  0 0.000
#> GSM1253045     6  0.0865      1.000 0.000 0.000 0.036 0.000  0 0.964
#> GSM1253043     6  0.0865      1.000 0.000 0.000 0.036 0.000  0 0.964
#> GSM1253044     2  0.0000      0.997 0.000 1.000 0.000 0.000  0 0.000
#> GSM1253047     5  0.0000      1.000 0.000 0.000 0.000 0.000  1 0.000
#> GSM1253050     2  0.0000      0.997 0.000 1.000 0.000 0.000  0 0.000
#> GSM1253051     2  0.0632      0.970 0.000 0.976 0.024 0.000  0 0.000
#> GSM1253053     3  0.0000      1.000 0.000 0.000 1.000 0.000  0 0.000
#> GSM1253054     5  0.0000      1.000 0.000 0.000 0.000 0.000  1 0.000
#> GSM1253055     3  0.0000      1.000 0.000 0.000 1.000 0.000  0 0.000
#> GSM1253079     1  0.0000      0.990 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253083     1  0.0000      0.990 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253075     1  0.0000      0.990 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253077     1  0.0000      0.990 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253076     1  0.0000      0.990 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253078     1  0.0000      0.990 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253081     1  0.0000      0.990 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253080     1  0.0000      0.990 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253082     1  0.0000      0.990 1.000 0.000 0.000 0.000  0 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 infection(p) disease.state(p) individual(p) k
#> ATC:hclust 54       0.0246         4.58e-08         0.950 2
#> ATC:hclust 56       0.0238         2.72e-09         0.851 3
#> ATC:hclust 54       0.0457         1.51e-07         0.938 4
#> ATC:hclust 54       0.0203         1.75e-09         0.912 5
#> ATC:hclust 56       0.0300         3.73e-09         0.810 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 51979 rows and 56 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           0.992       0.996         0.4795 0.523   0.523
#> 3 3 0.679           0.664       0.864         0.2393 0.908   0.825
#> 4 4 0.729           0.794       0.808         0.1589 0.801   0.568
#> 5 5 0.687           0.889       0.871         0.0827 0.938   0.781
#> 6 6 0.754           0.817       0.876         0.0507 0.995   0.976

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
#> GSM1253056     1    0.00      0.994 1.000 0.000
#> GSM1253057     1    0.00      0.994 1.000 0.000
#> GSM1253058     1    0.00      0.994 1.000 0.000
#> GSM1253059     1    0.00      0.994 1.000 0.000
#> GSM1253060     1    0.00      0.994 1.000 0.000
#> GSM1253061     1    0.00      0.994 1.000 0.000
#> GSM1253062     1    0.00      0.994 1.000 0.000
#> GSM1253063     1    0.00      0.994 1.000 0.000
#> GSM1253064     1    0.00      0.994 1.000 0.000
#> GSM1253065     1    0.00      0.994 1.000 0.000
#> GSM1253066     1    0.00      0.994 1.000 0.000
#> GSM1253067     1    0.00      0.994 1.000 0.000
#> GSM1253068     1    0.00      0.994 1.000 0.000
#> GSM1253069     1    0.00      0.994 1.000 0.000
#> GSM1253070     1    0.00      0.994 1.000 0.000
#> GSM1253071     1    0.00      0.994 1.000 0.000
#> GSM1253072     1    0.00      0.994 1.000 0.000
#> GSM1253073     1    0.00      0.994 1.000 0.000
#> GSM1253074     1    0.00      0.994 1.000 0.000
#> GSM1253032     1    0.00      0.994 1.000 0.000
#> GSM1253034     2    0.00      1.000 0.000 1.000
#> GSM1253039     2    0.00      1.000 0.000 1.000
#> GSM1253040     2    0.00      1.000 0.000 1.000
#> GSM1253041     2    0.00      1.000 0.000 1.000
#> GSM1253046     1    0.00      0.994 1.000 0.000
#> GSM1253048     2    0.00      1.000 0.000 1.000
#> GSM1253049     2    0.00      1.000 0.000 1.000
#> GSM1253052     2    0.00      1.000 0.000 1.000
#> GSM1253037     2    0.00      1.000 0.000 1.000
#> GSM1253028     2    0.00      1.000 0.000 1.000
#> GSM1253029     2    0.00      1.000 0.000 1.000
#> GSM1253030     2    0.00      1.000 0.000 1.000
#> GSM1253031     2    0.00      1.000 0.000 1.000
#> GSM1253033     1    0.00      0.994 1.000 0.000
#> GSM1253035     2    0.00      1.000 0.000 1.000
#> GSM1253036     2    0.00      1.000 0.000 1.000
#> GSM1253038     2    0.00      1.000 0.000 1.000
#> GSM1253042     2    0.00      1.000 0.000 1.000
#> GSM1253045     1    0.00      0.994 1.000 0.000
#> GSM1253043     1    0.73      0.744 0.796 0.204
#> GSM1253044     2    0.00      1.000 0.000 1.000
#> GSM1253047     1    0.00      0.994 1.000 0.000
#> GSM1253050     2    0.00      1.000 0.000 1.000
#> GSM1253051     2    0.00      1.000 0.000 1.000
#> GSM1253053     2    0.00      1.000 0.000 1.000
#> GSM1253054     1    0.00      0.994 1.000 0.000
#> GSM1253055     2    0.00      1.000 0.000 1.000
#> GSM1253079     1    0.00      0.994 1.000 0.000
#> GSM1253083     1    0.00      0.994 1.000 0.000
#> GSM1253075     1    0.00      0.994 1.000 0.000
#> GSM1253077     1    0.00      0.994 1.000 0.000
#> GSM1253076     1    0.00      0.994 1.000 0.000
#> GSM1253078     1    0.00      0.994 1.000 0.000
#> GSM1253081     1    0.00      0.994 1.000 0.000
#> GSM1253080     1    0.00      0.994 1.000 0.000
#> GSM1253082     1    0.00      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
#> GSM1253056     1   0.382      0.854 0.852 0.000 0.148
#> GSM1253057     1   0.000      0.914 1.000 0.000 0.000
#> GSM1253058     1   0.484      0.814 0.776 0.000 0.224
#> GSM1253059     1   0.624      0.592 0.560 0.000 0.440
#> GSM1253060     1   0.382      0.854 0.852 0.000 0.148
#> GSM1253061     1   0.000      0.914 1.000 0.000 0.000
#> GSM1253062     1   0.000      0.914 1.000 0.000 0.000
#> GSM1253063     1   0.382      0.854 0.852 0.000 0.148
#> GSM1253064     1   0.000      0.914 1.000 0.000 0.000
#> GSM1253065     1   0.382      0.854 0.852 0.000 0.148
#> GSM1253066     1   0.000      0.914 1.000 0.000 0.000
#> GSM1253067     1   0.382      0.854 0.852 0.000 0.148
#> GSM1253068     1   0.000      0.914 1.000 0.000 0.000
#> GSM1253069     1   0.000      0.914 1.000 0.000 0.000
#> GSM1253070     1   0.000      0.914 1.000 0.000 0.000
#> GSM1253071     1   0.382      0.854 0.852 0.000 0.148
#> GSM1253072     1   0.000      0.914 1.000 0.000 0.000
#> GSM1253073     1   0.382      0.854 0.852 0.000 0.148
#> GSM1253074     1   0.000      0.914 1.000 0.000 0.000
#> GSM1253032     1   0.493      0.754 0.768 0.000 0.232
#> GSM1253034     2   0.000      0.742 0.000 1.000 0.000
#> GSM1253039     2   0.000      0.742 0.000 1.000 0.000
#> GSM1253040     2   0.000      0.742 0.000 1.000 0.000
#> GSM1253041     2   0.000      0.742 0.000 1.000 0.000
#> GSM1253046     1   0.327      0.848 0.884 0.000 0.116
#> GSM1253048     2   0.000      0.742 0.000 1.000 0.000
#> GSM1253049     2   0.000      0.742 0.000 1.000 0.000
#> GSM1253052     2   0.631     -0.489 0.000 0.500 0.500
#> GSM1253037     2   0.000      0.742 0.000 1.000 0.000
#> GSM1253028     3   0.606      0.443 0.000 0.384 0.616
#> GSM1253029     2   0.631     -0.489 0.000 0.500 0.500
#> GSM1253030     2   0.000      0.742 0.000 1.000 0.000
#> GSM1253031     2   0.631     -0.489 0.000 0.500 0.500
#> GSM1253033     1   0.590      0.610 0.648 0.000 0.352
#> GSM1253035     3   0.631      0.348 0.000 0.500 0.500
#> GSM1253036     3   0.631      0.348 0.000 0.500 0.500
#> GSM1253038     2   0.000      0.742 0.000 1.000 0.000
#> GSM1253042     3   0.631      0.348 0.000 0.500 0.500
#> GSM1253045     3   0.382      0.416 0.148 0.000 0.852
#> GSM1253043     3   0.469      0.446 0.096 0.052 0.852
#> GSM1253044     2   0.000      0.742 0.000 1.000 0.000
#> GSM1253047     1   0.429      0.799 0.820 0.000 0.180
#> GSM1253050     2   0.000      0.742 0.000 1.000 0.000
#> GSM1253051     2   0.000      0.742 0.000 1.000 0.000
#> GSM1253053     2   0.631     -0.489 0.000 0.500 0.500
#> GSM1253054     1   0.590      0.610 0.648 0.000 0.352
#> GSM1253055     2   0.631     -0.489 0.000 0.500 0.500
#> GSM1253079     1   0.000      0.914 1.000 0.000 0.000
#> GSM1253083     1   0.000      0.914 1.000 0.000 0.000
#> GSM1253075     1   0.000      0.914 1.000 0.000 0.000
#> GSM1253077     1   0.000      0.914 1.000 0.000 0.000
#> GSM1253076     1   0.000      0.914 1.000 0.000 0.000
#> GSM1253078     1   0.000      0.914 1.000 0.000 0.000
#> GSM1253081     1   0.000      0.914 1.000 0.000 0.000
#> GSM1253080     1   0.000      0.914 1.000 0.000 0.000
#> GSM1253082     1   0.000      0.914 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
#> GSM1253056     4  0.0000     0.8942 0.000 0.000 0.000 1.000
#> GSM1253057     1  0.4999     0.7948 0.508 0.000 0.000 0.492
#> GSM1253058     4  0.2741     0.7784 0.096 0.000 0.012 0.892
#> GSM1253059     4  0.5690     0.5385 0.268 0.000 0.060 0.672
#> GSM1253060     4  0.0000     0.8942 0.000 0.000 0.000 1.000
#> GSM1253061     1  0.4999     0.7948 0.508 0.000 0.000 0.492
#> GSM1253062     1  0.4999     0.7948 0.508 0.000 0.000 0.492
#> GSM1253063     4  0.0188     0.8892 0.004 0.000 0.000 0.996
#> GSM1253064     1  0.4999     0.7948 0.508 0.000 0.000 0.492
#> GSM1253065     4  0.0817     0.8537 0.024 0.000 0.000 0.976
#> GSM1253066     1  0.4999     0.7948 0.508 0.000 0.000 0.492
#> GSM1253067     4  0.0000     0.8942 0.000 0.000 0.000 1.000
#> GSM1253068     1  0.4999     0.7948 0.508 0.000 0.000 0.492
#> GSM1253069     1  0.4999     0.7948 0.508 0.000 0.000 0.492
#> GSM1253070     1  0.4898     0.7016 0.584 0.000 0.000 0.416
#> GSM1253071     4  0.0000     0.8942 0.000 0.000 0.000 1.000
#> GSM1253072     1  0.4999     0.7948 0.508 0.000 0.000 0.492
#> GSM1253073     4  0.0000     0.8942 0.000 0.000 0.000 1.000
#> GSM1253074     1  0.4999     0.7948 0.508 0.000 0.000 0.492
#> GSM1253032     1  0.6586     0.2156 0.628 0.000 0.156 0.216
#> GSM1253034     2  0.1302     0.9643 0.044 0.956 0.000 0.000
#> GSM1253039     2  0.1302     0.9643 0.044 0.956 0.000 0.000
#> GSM1253040     2  0.0000     0.9809 0.000 1.000 0.000 0.000
#> GSM1253041     2  0.0000     0.9809 0.000 1.000 0.000 0.000
#> GSM1253046     1  0.6781     0.3182 0.596 0.000 0.148 0.256
#> GSM1253048     2  0.0000     0.9809 0.000 1.000 0.000 0.000
#> GSM1253049     2  0.0000     0.9809 0.000 1.000 0.000 0.000
#> GSM1253052     3  0.3764     0.8992 0.000 0.216 0.784 0.000
#> GSM1253037     2  0.0000     0.9809 0.000 1.000 0.000 0.000
#> GSM1253028     3  0.3266     0.8706 0.000 0.168 0.832 0.000
#> GSM1253029     3  0.4635     0.8853 0.028 0.216 0.756 0.000
#> GSM1253030     2  0.1867     0.9474 0.072 0.928 0.000 0.000
#> GSM1253031     3  0.3764     0.8992 0.000 0.216 0.784 0.000
#> GSM1253033     1  0.5875     0.0526 0.692 0.000 0.204 0.104
#> GSM1253035     3  0.3764     0.8992 0.000 0.216 0.784 0.000
#> GSM1253036     3  0.4904     0.8780 0.040 0.216 0.744 0.000
#> GSM1253038     2  0.0000     0.9809 0.000 1.000 0.000 0.000
#> GSM1253042     3  0.3764     0.8992 0.000 0.216 0.784 0.000
#> GSM1253045     3  0.3311     0.6429 0.172 0.000 0.828 0.000
#> GSM1253043     3  0.3311     0.6429 0.172 0.000 0.828 0.000
#> GSM1253044     2  0.0000     0.9809 0.000 1.000 0.000 0.000
#> GSM1253047     1  0.6703     0.2861 0.612 0.000 0.156 0.232
#> GSM1253050     2  0.0000     0.9809 0.000 1.000 0.000 0.000
#> GSM1253051     2  0.1867     0.9474 0.072 0.928 0.000 0.000
#> GSM1253053     3  0.3764     0.8992 0.000 0.216 0.784 0.000
#> GSM1253054     1  0.5982     0.0603 0.684 0.000 0.204 0.112
#> GSM1253055     3  0.3764     0.8992 0.000 0.216 0.784 0.000
#> GSM1253079     1  0.4999     0.7948 0.508 0.000 0.000 0.492
#> GSM1253083     1  0.4999     0.7948 0.508 0.000 0.000 0.492
#> GSM1253075     1  0.4999     0.7948 0.508 0.000 0.000 0.492
#> GSM1253077     1  0.4999     0.7948 0.508 0.000 0.000 0.492
#> GSM1253076     1  0.4999     0.7948 0.508 0.000 0.000 0.492
#> GSM1253078     1  0.4999     0.7948 0.508 0.000 0.000 0.492
#> GSM1253081     1  0.4999     0.7948 0.508 0.000 0.000 0.492
#> GSM1253080     1  0.4999     0.7948 0.508 0.000 0.000 0.492
#> GSM1253082     1  0.4999     0.7948 0.508 0.000 0.000 0.492

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4    p5
#> GSM1253056     4  0.3612      0.882 0.268 0.000 0.000 0.732 0.000
#> GSM1253057     1  0.0000      0.960 1.000 0.000 0.000 0.000 0.000
#> GSM1253058     4  0.5150      0.687 0.132 0.000 0.048 0.744 0.076
#> GSM1253059     4  0.6117      0.490 0.088 0.000 0.048 0.636 0.228
#> GSM1253060     4  0.3636      0.881 0.272 0.000 0.000 0.728 0.000
#> GSM1253061     1  0.0000      0.960 1.000 0.000 0.000 0.000 0.000
#> GSM1253062     1  0.0162      0.960 0.996 0.000 0.000 0.004 0.000
#> GSM1253063     4  0.3707      0.873 0.284 0.000 0.000 0.716 0.000
#> GSM1253064     1  0.1571      0.940 0.936 0.000 0.060 0.004 0.000
#> GSM1253065     4  0.5218      0.754 0.336 0.000 0.060 0.604 0.000
#> GSM1253066     1  0.1809      0.937 0.928 0.000 0.060 0.012 0.000
#> GSM1253067     4  0.3612      0.882 0.268 0.000 0.000 0.732 0.000
#> GSM1253068     1  0.1809      0.937 0.928 0.000 0.060 0.012 0.000
#> GSM1253069     1  0.0000      0.960 1.000 0.000 0.000 0.000 0.000
#> GSM1253070     1  0.1444      0.909 0.948 0.000 0.000 0.012 0.040
#> GSM1253071     4  0.3612      0.880 0.268 0.000 0.000 0.732 0.000
#> GSM1253072     1  0.1809      0.937 0.928 0.000 0.060 0.012 0.000
#> GSM1253073     4  0.3661      0.880 0.276 0.000 0.000 0.724 0.000
#> GSM1253074     1  0.0000      0.960 1.000 0.000 0.000 0.000 0.000
#> GSM1253032     5  0.3988      0.849 0.252 0.000 0.000 0.016 0.732
#> GSM1253034     2  0.3216      0.895 0.000 0.848 0.000 0.108 0.044
#> GSM1253039     2  0.3216      0.895 0.000 0.848 0.000 0.108 0.044
#> GSM1253040     2  0.0000      0.946 0.000 1.000 0.000 0.000 0.000
#> GSM1253041     2  0.0000      0.946 0.000 1.000 0.000 0.000 0.000
#> GSM1253046     5  0.4661      0.798 0.324 0.000 0.012 0.012 0.652
#> GSM1253048     2  0.0000      0.946 0.000 1.000 0.000 0.000 0.000
#> GSM1253049     2  0.0000      0.946 0.000 1.000 0.000 0.000 0.000
#> GSM1253052     3  0.3293      0.908 0.000 0.108 0.852 0.012 0.028
#> GSM1253037     2  0.0000      0.946 0.000 1.000 0.000 0.000 0.000
#> GSM1253028     3  0.2694      0.908 0.000 0.108 0.876 0.008 0.008
#> GSM1253029     3  0.4142      0.884 0.000 0.108 0.812 0.044 0.036
#> GSM1253030     2  0.3916      0.867 0.000 0.804 0.000 0.104 0.092
#> GSM1253031     3  0.2694      0.908 0.000 0.108 0.876 0.008 0.008
#> GSM1253033     5  0.3016      0.791 0.132 0.000 0.000 0.020 0.848
#> GSM1253035     3  0.2127      0.909 0.000 0.108 0.892 0.000 0.000
#> GSM1253036     3  0.4289      0.869 0.000 0.108 0.804 0.040 0.048
#> GSM1253038     2  0.0609      0.941 0.000 0.980 0.000 0.020 0.000
#> GSM1253042     3  0.3293      0.908 0.000 0.108 0.852 0.012 0.028
#> GSM1253045     3  0.5128      0.641 0.000 0.000 0.656 0.076 0.268
#> GSM1253043     3  0.5128      0.641 0.000 0.000 0.656 0.076 0.268
#> GSM1253044     2  0.0000      0.946 0.000 1.000 0.000 0.000 0.000
#> GSM1253047     5  0.4213      0.825 0.308 0.000 0.000 0.012 0.680
#> GSM1253050     2  0.0000      0.946 0.000 1.000 0.000 0.000 0.000
#> GSM1253051     2  0.3916      0.867 0.000 0.804 0.000 0.104 0.092
#> GSM1253053     3  0.3293      0.908 0.000 0.108 0.852 0.012 0.028
#> GSM1253054     5  0.3098      0.810 0.148 0.000 0.000 0.016 0.836
#> GSM1253055     3  0.2445      0.909 0.000 0.108 0.884 0.004 0.004
#> GSM1253079     1  0.0162      0.960 0.996 0.000 0.000 0.004 0.000
#> GSM1253083     1  0.0162      0.960 0.996 0.000 0.000 0.004 0.000
#> GSM1253075     1  0.0162      0.960 0.996 0.000 0.000 0.004 0.000
#> GSM1253077     1  0.0162      0.960 0.996 0.000 0.000 0.004 0.000
#> GSM1253076     1  0.0290      0.957 0.992 0.000 0.000 0.008 0.000
#> GSM1253078     1  0.0162      0.960 0.996 0.000 0.000 0.004 0.000
#> GSM1253081     1  0.1809      0.937 0.928 0.000 0.060 0.012 0.000
#> GSM1253080     1  0.1697      0.939 0.932 0.000 0.060 0.008 0.000
#> GSM1253082     1  0.1697      0.939 0.932 0.000 0.060 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
#> GSM1253056     4  0.2260      0.843 0.140 0.000 0.000 0.860 0.000 0.000
#> GSM1253057     1  0.0000      0.920 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253058     4  0.5126     -0.453 0.056 0.000 0.000 0.564 0.016 0.364
#> GSM1253059     6  0.5655      0.000 0.028 0.000 0.000 0.360 0.084 0.528
#> GSM1253060     4  0.2783      0.837 0.148 0.000 0.000 0.836 0.000 0.016
#> GSM1253061     1  0.0363      0.917 0.988 0.000 0.012 0.000 0.000 0.000
#> GSM1253062     1  0.0000      0.920 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253063     4  0.2692      0.839 0.148 0.000 0.000 0.840 0.000 0.012
#> GSM1253064     1  0.3128      0.866 0.844 0.000 0.052 0.008 0.000 0.096
#> GSM1253065     4  0.4631      0.655 0.160 0.000 0.000 0.704 0.004 0.132
#> GSM1253066     1  0.4021      0.834 0.788 0.000 0.052 0.024 0.004 0.132
#> GSM1253067     4  0.2260      0.843 0.140 0.000 0.000 0.860 0.000 0.000
#> GSM1253068     1  0.4021      0.834 0.788 0.000 0.052 0.024 0.004 0.132
#> GSM1253069     1  0.0000      0.920 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253070     1  0.0547      0.904 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM1253071     4  0.2340      0.838 0.148 0.000 0.000 0.852 0.000 0.000
#> GSM1253072     1  0.4021      0.834 0.788 0.000 0.052 0.024 0.004 0.132
#> GSM1253073     4  0.2553      0.843 0.144 0.000 0.000 0.848 0.000 0.008
#> GSM1253074     1  0.0000      0.920 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253032     5  0.2445      0.871 0.108 0.000 0.000 0.020 0.872 0.000
#> GSM1253034     2  0.3526      0.863 0.000 0.828 0.000 0.056 0.028 0.088
#> GSM1253039     2  0.3526      0.863 0.000 0.828 0.000 0.056 0.028 0.088
#> GSM1253040     2  0.0260      0.923 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM1253041     2  0.0260      0.923 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM1253046     5  0.3352      0.832 0.172 0.000 0.012 0.016 0.800 0.000
#> GSM1253048     2  0.0260      0.923 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM1253049     2  0.0000      0.923 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253052     3  0.2359      0.870 0.000 0.052 0.904 0.016 0.004 0.024
#> GSM1253037     2  0.0000      0.923 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253028     3  0.2095      0.870 0.000 0.052 0.916 0.004 0.016 0.012
#> GSM1253029     3  0.3037      0.850 0.000 0.052 0.864 0.016 0.004 0.064
#> GSM1253030     2  0.4124      0.782 0.000 0.728 0.000 0.036 0.012 0.224
#> GSM1253031     3  0.2095      0.870 0.000 0.052 0.916 0.004 0.016 0.012
#> GSM1253033     5  0.1785      0.834 0.048 0.000 0.000 0.016 0.928 0.008
#> GSM1253035     3  0.1141      0.872 0.000 0.052 0.948 0.000 0.000 0.000
#> GSM1253036     3  0.3567      0.783 0.000 0.052 0.804 0.000 0.008 0.136
#> GSM1253038     2  0.1421      0.910 0.000 0.944 0.000 0.028 0.028 0.000
#> GSM1253042     3  0.2359      0.870 0.000 0.052 0.904 0.016 0.004 0.024
#> GSM1253045     3  0.5396      0.483 0.000 0.000 0.564 0.000 0.152 0.284
#> GSM1253043     3  0.5396      0.483 0.000 0.000 0.564 0.000 0.152 0.284
#> GSM1253044     2  0.0000      0.923 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253047     5  0.2968      0.846 0.168 0.000 0.000 0.016 0.816 0.000
#> GSM1253050     2  0.0000      0.923 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253051     2  0.4124      0.782 0.000 0.728 0.000 0.036 0.012 0.224
#> GSM1253053     3  0.2359      0.870 0.000 0.052 0.904 0.016 0.004 0.024
#> GSM1253054     5  0.1738      0.841 0.052 0.000 0.000 0.016 0.928 0.004
#> GSM1253055     3  0.2095      0.870 0.000 0.052 0.916 0.004 0.016 0.012
#> GSM1253079     1  0.0000      0.920 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000      0.920 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000      0.920 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      0.920 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      0.920 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      0.920 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253081     1  0.4021      0.834 0.788 0.000 0.052 0.024 0.004 0.132
#> GSM1253080     1  0.3598      0.852 0.816 0.000 0.052 0.012 0.004 0.116
#> GSM1253082     1  0.3319      0.862 0.836 0.000 0.052 0.016 0.000 0.096

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 infection(p) disease.state(p) individual(p) k
#> ATC:kmeans 56     0.030714         2.22e-07         0.937 2
#> ATC:kmeans 45     0.109327         4.72e-06         0.908 3
#> ATC:kmeans 51     0.000363         9.82e-13         0.899 4
#> ATC:kmeans 55     0.000418         7.69e-12         0.811 5
#> ATC:kmeans 52     0.000821         1.44e-10         0.778 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 51979 rows and 56 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'skmeans' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 5.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk ATC-skmeans-collect-plots

The plots are:

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

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

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

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

select_partition_number(res)

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

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           1.000       1.000         0.4934 0.507   0.507
#> 3 3 0.787           0.910       0.926         0.1922 0.909   0.821
#> 4 4 0.821           0.958       0.911         0.1215 0.889   0.733
#> 5 5 0.917           0.974       0.970         0.0700 0.973   0.911
#> 6 6 0.949           0.930       0.961         0.0412 0.995   0.981

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

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

suggest_best_k(res)

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

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
#> GSM1253056     1       0          1  1  0
#> GSM1253057     1       0          1  1  0
#> GSM1253058     1       0          1  1  0
#> GSM1253059     1       0          1  1  0
#> GSM1253060     1       0          1  1  0
#> GSM1253061     1       0          1  1  0
#> GSM1253062     1       0          1  1  0
#> GSM1253063     1       0          1  1  0
#> GSM1253064     1       0          1  1  0
#> GSM1253065     1       0          1  1  0
#> GSM1253066     1       0          1  1  0
#> GSM1253067     1       0          1  1  0
#> GSM1253068     1       0          1  1  0
#> GSM1253069     1       0          1  1  0
#> GSM1253070     1       0          1  1  0
#> GSM1253071     1       0          1  1  0
#> GSM1253072     1       0          1  1  0
#> GSM1253073     1       0          1  1  0
#> GSM1253074     1       0          1  1  0
#> GSM1253032     1       0          1  1  0
#> GSM1253034     2       0          1  0  1
#> GSM1253039     2       0          1  0  1
#> GSM1253040     2       0          1  0  1
#> GSM1253041     2       0          1  0  1
#> GSM1253046     1       0          1  1  0
#> GSM1253048     2       0          1  0  1
#> GSM1253049     2       0          1  0  1
#> GSM1253052     2       0          1  0  1
#> GSM1253037     2       0          1  0  1
#> GSM1253028     2       0          1  0  1
#> GSM1253029     2       0          1  0  1
#> GSM1253030     2       0          1  0  1
#> GSM1253031     2       0          1  0  1
#> GSM1253033     1       0          1  1  0
#> GSM1253035     2       0          1  0  1
#> GSM1253036     2       0          1  0  1
#> GSM1253038     2       0          1  0  1
#> GSM1253042     2       0          1  0  1
#> GSM1253045     2       0          1  0  1
#> GSM1253043     2       0          1  0  1
#> GSM1253044     2       0          1  0  1
#> GSM1253047     1       0          1  1  0
#> GSM1253050     2       0          1  0  1
#> GSM1253051     2       0          1  0  1
#> GSM1253053     2       0          1  0  1
#> GSM1253054     1       0          1  1  0
#> GSM1253055     2       0          1  0  1
#> GSM1253079     1       0          1  1  0
#> GSM1253083     1       0          1  1  0
#> GSM1253075     1       0          1  1  0
#> GSM1253077     1       0          1  1  0
#> GSM1253076     1       0          1  1  0
#> GSM1253078     1       0          1  1  0
#> GSM1253081     1       0          1  1  0
#> GSM1253080     1       0          1  1  0
#> GSM1253082     1       0          1  1  0

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3
#> GSM1253056     1   0.497      0.745 0.764 0.000 0.236
#> GSM1253057     1   0.000      0.878 1.000 0.000 0.000
#> GSM1253058     1   0.502      0.740 0.760 0.000 0.240
#> GSM1253059     1   0.502      0.740 0.760 0.000 0.240
#> GSM1253060     1   0.497      0.745 0.764 0.000 0.236
#> GSM1253061     1   0.000      0.878 1.000 0.000 0.000
#> GSM1253062     1   0.000      0.878 1.000 0.000 0.000
#> GSM1253063     1   0.497      0.745 0.764 0.000 0.236
#> GSM1253064     1   0.000      0.878 1.000 0.000 0.000
#> GSM1253065     1   0.497      0.745 0.764 0.000 0.236
#> GSM1253066     1   0.000      0.878 1.000 0.000 0.000
#> GSM1253067     1   0.497      0.745 0.764 0.000 0.236
#> GSM1253068     1   0.000      0.878 1.000 0.000 0.000
#> GSM1253069     1   0.000      0.878 1.000 0.000 0.000
#> GSM1253070     1   0.000      0.878 1.000 0.000 0.000
#> GSM1253071     1   0.497      0.745 0.764 0.000 0.236
#> GSM1253072     1   0.000      0.878 1.000 0.000 0.000
#> GSM1253073     1   0.497      0.745 0.764 0.000 0.236
#> GSM1253074     1   0.000      0.878 1.000 0.000 0.000
#> GSM1253032     3   0.593      1.000 0.356 0.000 0.644
#> GSM1253034     2   0.000      0.991 0.000 1.000 0.000
#> GSM1253039     2   0.000      0.991 0.000 1.000 0.000
#> GSM1253040     2   0.000      0.991 0.000 1.000 0.000
#> GSM1253041     2   0.000      0.991 0.000 1.000 0.000
#> GSM1253046     3   0.593      1.000 0.356 0.000 0.644
#> GSM1253048     2   0.000      0.991 0.000 1.000 0.000
#> GSM1253049     2   0.000      0.991 0.000 1.000 0.000
#> GSM1253052     2   0.000      0.991 0.000 1.000 0.000
#> GSM1253037     2   0.000      0.991 0.000 1.000 0.000
#> GSM1253028     2   0.000      0.991 0.000 1.000 0.000
#> GSM1253029     2   0.000      0.991 0.000 1.000 0.000
#> GSM1253030     2   0.000      0.991 0.000 1.000 0.000
#> GSM1253031     2   0.000      0.991 0.000 1.000 0.000
#> GSM1253033     3   0.593      1.000 0.356 0.000 0.644
#> GSM1253035     2   0.000      0.991 0.000 1.000 0.000
#> GSM1253036     2   0.000      0.991 0.000 1.000 0.000
#> GSM1253038     2   0.000      0.991 0.000 1.000 0.000
#> GSM1253042     2   0.000      0.991 0.000 1.000 0.000
#> GSM1253045     2   0.327      0.896 0.000 0.884 0.116
#> GSM1253043     2   0.327      0.896 0.000 0.884 0.116
#> GSM1253044     2   0.000      0.991 0.000 1.000 0.000
#> GSM1253047     3   0.593      1.000 0.356 0.000 0.644
#> GSM1253050     2   0.000      0.991 0.000 1.000 0.000
#> GSM1253051     2   0.000      0.991 0.000 1.000 0.000
#> GSM1253053     2   0.000      0.991 0.000 1.000 0.000
#> GSM1253054     3   0.593      1.000 0.356 0.000 0.644
#> GSM1253055     2   0.000      0.991 0.000 1.000 0.000
#> GSM1253079     1   0.000      0.878 1.000 0.000 0.000
#> GSM1253083     1   0.000      0.878 1.000 0.000 0.000
#> GSM1253075     1   0.000      0.878 1.000 0.000 0.000
#> GSM1253077     1   0.000      0.878 1.000 0.000 0.000
#> GSM1253076     1   0.000      0.878 1.000 0.000 0.000
#> GSM1253078     1   0.000      0.878 1.000 0.000 0.000
#> GSM1253081     1   0.000      0.878 1.000 0.000 0.000
#> GSM1253080     1   0.000      0.878 1.000 0.000 0.000
#> GSM1253082     1   0.000      0.878 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
#> GSM1253056     4  0.4661      0.966 0.348 0.000 0.000 0.652
#> GSM1253057     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253058     4  0.4193      0.893 0.268 0.000 0.000 0.732
#> GSM1253059     4  0.4343      0.888 0.264 0.000 0.004 0.732
#> GSM1253060     4  0.4679      0.962 0.352 0.000 0.000 0.648
#> GSM1253061     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253062     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253063     4  0.4661      0.966 0.348 0.000 0.000 0.652
#> GSM1253064     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253065     4  0.4679      0.962 0.352 0.000 0.000 0.648
#> GSM1253066     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253067     4  0.4643      0.964 0.344 0.000 0.000 0.656
#> GSM1253068     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253069     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253070     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253071     4  0.4661      0.966 0.348 0.000 0.000 0.652
#> GSM1253072     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253073     4  0.4661      0.966 0.348 0.000 0.000 0.652
#> GSM1253074     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253032     3  0.3400      0.998 0.180 0.000 0.820 0.000
#> GSM1253034     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253039     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253040     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253041     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253046     3  0.3400      0.998 0.180 0.000 0.820 0.000
#> GSM1253048     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253049     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253052     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253037     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253028     2  0.0188      0.960 0.000 0.996 0.000 0.004
#> GSM1253029     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253030     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253031     2  0.0188      0.960 0.000 0.996 0.000 0.004
#> GSM1253033     3  0.3356      0.994 0.176 0.000 0.824 0.000
#> GSM1253035     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253036     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253038     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253042     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253045     2  0.7105      0.461 0.000 0.556 0.176 0.268
#> GSM1253043     2  0.7105      0.461 0.000 0.556 0.176 0.268
#> GSM1253044     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253047     3  0.3400      0.998 0.180 0.000 0.820 0.000
#> GSM1253050     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253051     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253053     2  0.0000      0.962 0.000 1.000 0.000 0.000
#> GSM1253054     3  0.3400      0.998 0.180 0.000 0.820 0.000
#> GSM1253055     2  0.0188      0.960 0.000 0.996 0.000 0.004
#> GSM1253079     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253081     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253080     1  0.0000      1.000 1.000 0.000 0.000 0.000
#> GSM1253082     1  0.0000      1.000 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
#> GSM1253056     4  0.3177      0.914 0.208 0.000 0.000 0.792 0.000
#> GSM1253057     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000
#> GSM1253058     4  0.0000      0.667 0.000 0.000 0.000 1.000 0.000
#> GSM1253059     4  0.0404      0.660 0.000 0.000 0.000 0.988 0.012
#> GSM1253060     4  0.3210      0.910 0.212 0.000 0.000 0.788 0.000
#> GSM1253061     1  0.0162      0.998 0.996 0.000 0.004 0.000 0.000
#> GSM1253062     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000
#> GSM1253063     4  0.3177      0.914 0.208 0.000 0.000 0.792 0.000
#> GSM1253064     1  0.0162      0.998 0.996 0.000 0.004 0.000 0.000
#> GSM1253065     4  0.3177      0.914 0.208 0.000 0.000 0.792 0.000
#> GSM1253066     1  0.0162      0.998 0.996 0.000 0.004 0.000 0.000
#> GSM1253067     4  0.3143      0.913 0.204 0.000 0.000 0.796 0.000
#> GSM1253068     1  0.0162      0.998 0.996 0.000 0.004 0.000 0.000
#> GSM1253069     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000
#> GSM1253070     1  0.0162      0.998 0.996 0.000 0.004 0.000 0.000
#> GSM1253071     4  0.3143      0.913 0.204 0.000 0.000 0.796 0.000
#> GSM1253072     1  0.0162      0.998 0.996 0.000 0.004 0.000 0.000
#> GSM1253073     4  0.3177      0.914 0.208 0.000 0.000 0.792 0.000
#> GSM1253074     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000
#> GSM1253032     5  0.0510      0.994 0.016 0.000 0.000 0.000 0.984
#> GSM1253034     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000
#> GSM1253039     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000
#> GSM1253040     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000
#> GSM1253041     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000
#> GSM1253046     5  0.0510      0.994 0.016 0.000 0.000 0.000 0.984
#> GSM1253048     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000
#> GSM1253049     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000
#> GSM1253052     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000
#> GSM1253037     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000
#> GSM1253028     2  0.0290      0.992 0.000 0.992 0.008 0.000 0.000
#> GSM1253029     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000
#> GSM1253030     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000
#> GSM1253031     2  0.0404      0.989 0.000 0.988 0.012 0.000 0.000
#> GSM1253033     5  0.0290      0.983 0.008 0.000 0.000 0.000 0.992
#> GSM1253035     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000
#> GSM1253036     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000
#> GSM1253038     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000
#> GSM1253042     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000
#> GSM1253045     3  0.0162      0.985 0.000 0.004 0.996 0.000 0.000
#> GSM1253043     3  0.0404      0.985 0.000 0.012 0.988 0.000 0.000
#> GSM1253044     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000
#> GSM1253047     5  0.0609      0.989 0.020 0.000 0.000 0.000 0.980
#> GSM1253050     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000
#> GSM1253051     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000
#> GSM1253053     2  0.0000      0.999 0.000 1.000 0.000 0.000 0.000
#> GSM1253054     5  0.0510      0.994 0.016 0.000 0.000 0.000 0.984
#> GSM1253055     2  0.0290      0.992 0.000 0.992 0.008 0.000 0.000
#> GSM1253079     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000
#> GSM1253081     1  0.0162      0.998 0.996 0.000 0.004 0.000 0.000
#> GSM1253080     1  0.0000      0.998 1.000 0.000 0.000 0.000 0.000
#> GSM1253082     1  0.0162      0.998 0.996 0.000 0.004 0.000 0.000

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4 p5    p6
#> GSM1253056     4  0.1075      0.932 0.048 0.000 0.000 0.952  0 0.000
#> GSM1253057     1  0.0000      0.996 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253058     4  0.3409      0.379 0.000 0.000 0.000 0.700  0 0.300
#> GSM1253059     6  0.2562      0.000 0.000 0.000 0.000 0.172  0 0.828
#> GSM1253060     4  0.1471      0.910 0.064 0.000 0.000 0.932  0 0.004
#> GSM1253061     1  0.0291      0.994 0.992 0.000 0.000 0.004  0 0.004
#> GSM1253062     1  0.0000      0.996 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253063     4  0.1219      0.931 0.048 0.000 0.000 0.948  0 0.004
#> GSM1253064     1  0.0291      0.994 0.992 0.000 0.000 0.004  0 0.004
#> GSM1253065     4  0.1285      0.928 0.052 0.000 0.000 0.944  0 0.004
#> GSM1253066     1  0.0291      0.994 0.992 0.000 0.000 0.004  0 0.004
#> GSM1253067     4  0.1219      0.929 0.048 0.000 0.000 0.948  0 0.004
#> GSM1253068     1  0.0291      0.994 0.992 0.000 0.000 0.004  0 0.004
#> GSM1253069     1  0.0000      0.996 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253070     1  0.0146      0.995 0.996 0.000 0.000 0.000  0 0.004
#> GSM1253071     4  0.1075      0.932 0.048 0.000 0.000 0.952  0 0.000
#> GSM1253072     1  0.0291      0.994 0.992 0.000 0.000 0.004  0 0.004
#> GSM1253073     4  0.1075      0.932 0.048 0.000 0.000 0.952  0 0.000
#> GSM1253074     1  0.0000      0.996 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253032     5  0.0000      1.000 0.000 0.000 0.000 0.000  1 0.000
#> GSM1253034     2  0.0000      0.945 0.000 1.000 0.000 0.000  0 0.000
#> GSM1253039     2  0.0000      0.945 0.000 1.000 0.000 0.000  0 0.000
#> GSM1253040     2  0.0000      0.945 0.000 1.000 0.000 0.000  0 0.000
#> GSM1253041     2  0.0000      0.945 0.000 1.000 0.000 0.000  0 0.000
#> GSM1253046     5  0.0000      1.000 0.000 0.000 0.000 0.000  1 0.000
#> GSM1253048     2  0.0000      0.945 0.000 1.000 0.000 0.000  0 0.000
#> GSM1253049     2  0.0000      0.945 0.000 1.000 0.000 0.000  0 0.000
#> GSM1253052     2  0.1556      0.927 0.000 0.920 0.000 0.000  0 0.080
#> GSM1253037     2  0.0000      0.945 0.000 1.000 0.000 0.000  0 0.000
#> GSM1253028     2  0.3417      0.850 0.000 0.796 0.044 0.000  0 0.160
#> GSM1253029     2  0.1556      0.927 0.000 0.920 0.000 0.000  0 0.080
#> GSM1253030     2  0.0260      0.942 0.000 0.992 0.000 0.000  0 0.008
#> GSM1253031     2  0.3344      0.856 0.000 0.804 0.044 0.000  0 0.152
#> GSM1253033     5  0.0000      1.000 0.000 0.000 0.000 0.000  1 0.000
#> GSM1253035     2  0.2135      0.905 0.000 0.872 0.000 0.000  0 0.128
#> GSM1253036     2  0.2260      0.898 0.000 0.860 0.000 0.000  0 0.140
#> GSM1253038     2  0.0000      0.945 0.000 1.000 0.000 0.000  0 0.000
#> GSM1253042     2  0.1556      0.927 0.000 0.920 0.000 0.000  0 0.080
#> GSM1253045     3  0.1074      0.969 0.000 0.000 0.960 0.028  0 0.012
#> GSM1253043     3  0.0000      0.969 0.000 0.000 1.000 0.000  0 0.000
#> GSM1253044     2  0.0000      0.945 0.000 1.000 0.000 0.000  0 0.000
#> GSM1253047     5  0.0000      1.000 0.000 0.000 0.000 0.000  1 0.000
#> GSM1253050     2  0.0000      0.945 0.000 1.000 0.000 0.000  0 0.000
#> GSM1253051     2  0.0000      0.945 0.000 1.000 0.000 0.000  0 0.000
#> GSM1253053     2  0.1714      0.923 0.000 0.908 0.000 0.000  0 0.092
#> GSM1253054     5  0.0000      1.000 0.000 0.000 0.000 0.000  1 0.000
#> GSM1253055     2  0.3417      0.850 0.000 0.796 0.044 0.000  0 0.160
#> GSM1253079     1  0.0000      0.996 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253083     1  0.0000      0.996 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253075     1  0.0000      0.996 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253077     1  0.0000      0.996 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253076     1  0.0000      0.996 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253078     1  0.0000      0.996 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253081     1  0.0508      0.987 0.984 0.000 0.000 0.012  0 0.004
#> GSM1253080     1  0.0000      0.996 1.000 0.000 0.000 0.000  0 0.000
#> GSM1253082     1  0.0405      0.991 0.988 0.000 0.000 0.008  0 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-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 infection(p) disease.state(p) individual(p) k
#> ATC:skmeans 56     0.018077         1.69e-08         0.955 2
#> ATC:skmeans 56     0.004693         2.78e-10         0.907 3
#> ATC:skmeans 54     0.000178         8.70e-11         0.880 4
#> ATC:skmeans 56     0.000334         2.11e-10         0.784 5
#> ATC:skmeans 54     0.000524         1.24e-09         0.745 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 51979 rows and 56 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'pam' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 6.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk ATC-pam-collect-plots

The plots are:

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

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

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

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

select_partition_number(res)

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

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           1.000       1.000         0.4778 0.523   0.523
#> 3 3 1.000           0.992       0.997         0.2118 0.873   0.762
#> 4 4 0.784           0.822       0.890         0.2758 0.843   0.627
#> 5 5 0.776           0.873       0.892         0.0445 0.911   0.689
#> 6 6 0.936           0.915       0.954         0.0315 0.981   0.912

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

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

suggest_best_k(res)

#> [1] 6
#> attr(,"optional")
#> [1] 2 3

There is also optional best \(k\) = 2 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
#> GSM1253056     1       0          1  1  0
#> GSM1253057     1       0          1  1  0
#> GSM1253058     1       0          1  1  0
#> GSM1253059     1       0          1  1  0
#> GSM1253060     1       0          1  1  0
#> GSM1253061     1       0          1  1  0
#> GSM1253062     1       0          1  1  0
#> GSM1253063     1       0          1  1  0
#> GSM1253064     1       0          1  1  0
#> GSM1253065     1       0          1  1  0
#> GSM1253066     1       0          1  1  0
#> GSM1253067     1       0          1  1  0
#> GSM1253068     1       0          1  1  0
#> GSM1253069     1       0          1  1  0
#> GSM1253070     1       0          1  1  0
#> GSM1253071     1       0          1  1  0
#> GSM1253072     1       0          1  1  0
#> GSM1253073     1       0          1  1  0
#> GSM1253074     1       0          1  1  0
#> GSM1253032     1       0          1  1  0
#> GSM1253034     2       0          1  0  1
#> GSM1253039     2       0          1  0  1
#> GSM1253040     2       0          1  0  1
#> GSM1253041     2       0          1  0  1
#> GSM1253046     1       0          1  1  0
#> GSM1253048     2       0          1  0  1
#> GSM1253049     2       0          1  0  1
#> GSM1253052     2       0          1  0  1
#> GSM1253037     2       0          1  0  1
#> GSM1253028     2       0          1  0  1
#> GSM1253029     2       0          1  0  1
#> GSM1253030     2       0          1  0  1
#> GSM1253031     2       0          1  0  1
#> GSM1253033     1       0          1  1  0
#> GSM1253035     2       0          1  0  1
#> GSM1253036     2       0          1  0  1
#> GSM1253038     2       0          1  0  1
#> GSM1253042     2       0          1  0  1
#> GSM1253045     1       0          1  1  0
#> GSM1253043     1       0          1  1  0
#> GSM1253044     2       0          1  0  1
#> GSM1253047     1       0          1  1  0
#> GSM1253050     2       0          1  0  1
#> GSM1253051     2       0          1  0  1
#> GSM1253053     2       0          1  0  1
#> GSM1253054     1       0          1  1  0
#> GSM1253055     2       0          1  0  1
#> GSM1253079     1       0          1  1  0
#> GSM1253083     1       0          1  1  0
#> GSM1253075     1       0          1  1  0
#> GSM1253077     1       0          1  1  0
#> GSM1253076     1       0          1  1  0
#> GSM1253078     1       0          1  1  0
#> GSM1253081     1       0          1  1  0
#> GSM1253080     1       0          1  1  0
#> GSM1253082     1       0          1  1  0

show/hide code output

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

#>            class entropy silhouette p1    p2    p3
#> GSM1253056     1    0.00      1.000  1 0.000 0.000
#> GSM1253057     1    0.00      1.000  1 0.000 0.000
#> GSM1253058     1    0.00      1.000  1 0.000 0.000
#> GSM1253059     1    0.00      1.000  1 0.000 0.000
#> GSM1253060     1    0.00      1.000  1 0.000 0.000
#> GSM1253061     1    0.00      1.000  1 0.000 0.000
#> GSM1253062     1    0.00      1.000  1 0.000 0.000
#> GSM1253063     1    0.00      1.000  1 0.000 0.000
#> GSM1253064     1    0.00      1.000  1 0.000 0.000
#> GSM1253065     1    0.00      1.000  1 0.000 0.000
#> GSM1253066     1    0.00      1.000  1 0.000 0.000
#> GSM1253067     1    0.00      1.000  1 0.000 0.000
#> GSM1253068     1    0.00      1.000  1 0.000 0.000
#> GSM1253069     1    0.00      1.000  1 0.000 0.000
#> GSM1253070     1    0.00      1.000  1 0.000 0.000
#> GSM1253071     1    0.00      1.000  1 0.000 0.000
#> GSM1253072     1    0.00      1.000  1 0.000 0.000
#> GSM1253073     1    0.00      1.000  1 0.000 0.000
#> GSM1253074     1    0.00      1.000  1 0.000 0.000
#> GSM1253032     1    0.00      1.000  1 0.000 0.000
#> GSM1253034     2    0.00      1.000  0 1.000 0.000
#> GSM1253039     2    0.00      1.000  0 1.000 0.000
#> GSM1253040     2    0.00      1.000  0 1.000 0.000
#> GSM1253041     2    0.00      1.000  0 1.000 0.000
#> GSM1253046     1    0.00      1.000  1 0.000 0.000
#> GSM1253048     2    0.00      1.000  0 1.000 0.000
#> GSM1253049     2    0.00      1.000  0 1.000 0.000
#> GSM1253052     3    0.00      0.983  0 0.000 1.000
#> GSM1253037     2    0.00      1.000  0 1.000 0.000
#> GSM1253028     3    0.00      0.983  0 0.000 1.000
#> GSM1253029     3    0.00      0.983  0 0.000 1.000
#> GSM1253030     2    0.00      1.000  0 1.000 0.000
#> GSM1253031     3    0.00      0.983  0 0.000 1.000
#> GSM1253033     1    0.00      1.000  1 0.000 0.000
#> GSM1253035     3    0.00      0.983  0 0.000 1.000
#> GSM1253036     3    0.00      0.983  0 0.000 1.000
#> GSM1253038     2    0.00      1.000  0 1.000 0.000
#> GSM1253042     3    0.00      0.983  0 0.000 1.000
#> GSM1253045     3    0.00      0.983  0 0.000 1.000
#> GSM1253043     3    0.00      0.983  0 0.000 1.000
#> GSM1253044     2    0.00      1.000  0 1.000 0.000
#> GSM1253047     1    0.00      1.000  1 0.000 0.000
#> GSM1253050     2    0.00      1.000  0 1.000 0.000
#> GSM1253051     3    0.44      0.768  0 0.188 0.812
#> GSM1253053     3    0.00      0.983  0 0.000 1.000
#> GSM1253054     1    0.00      1.000  1 0.000 0.000
#> GSM1253055     3    0.00      0.983  0 0.000 1.000
#> GSM1253079     1    0.00      1.000  1 0.000 0.000
#> GSM1253083     1    0.00      1.000  1 0.000 0.000
#> GSM1253075     1    0.00      1.000  1 0.000 0.000
#> GSM1253077     1    0.00      1.000  1 0.000 0.000
#> GSM1253076     1    0.00      1.000  1 0.000 0.000
#> GSM1253078     1    0.00      1.000  1 0.000 0.000
#> GSM1253081     1    0.00      1.000  1 0.000 0.000
#> GSM1253080     1    0.00      1.000  1 0.000 0.000
#> GSM1253082     1    0.00      1.000  1 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
#> GSM1253056     4  0.0000      0.750 0.000 0.000 0.000 1.000
#> GSM1253057     1  0.3873      0.754 0.772 0.000 0.000 0.228
#> GSM1253058     4  0.4072      0.759 0.252 0.000 0.000 0.748
#> GSM1253059     4  0.4072      0.759 0.252 0.000 0.000 0.748
#> GSM1253060     4  0.3688      0.770 0.208 0.000 0.000 0.792
#> GSM1253061     1  0.2921      0.802 0.860 0.000 0.000 0.140
#> GSM1253062     1  0.0000      0.820 1.000 0.000 0.000 0.000
#> GSM1253063     4  0.0000      0.750 0.000 0.000 0.000 1.000
#> GSM1253064     1  0.3801      0.751 0.780 0.000 0.000 0.220
#> GSM1253065     4  0.0000      0.750 0.000 0.000 0.000 1.000
#> GSM1253066     1  0.4072      0.739 0.748 0.000 0.000 0.252
#> GSM1253067     4  0.3975      0.764 0.240 0.000 0.000 0.760
#> GSM1253068     1  0.4072      0.739 0.748 0.000 0.000 0.252
#> GSM1253069     1  0.3400      0.783 0.820 0.000 0.000 0.180
#> GSM1253070     1  0.1211      0.798 0.960 0.000 0.000 0.040
#> GSM1253071     4  0.4072      0.759 0.252 0.000 0.000 0.748
#> GSM1253072     1  0.4072      0.739 0.748 0.000 0.000 0.252
#> GSM1253073     4  0.0000      0.750 0.000 0.000 0.000 1.000
#> GSM1253074     1  0.3024      0.797 0.852 0.000 0.000 0.148
#> GSM1253032     1  0.4992     -0.355 0.524 0.000 0.000 0.476
#> GSM1253034     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253039     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253040     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253041     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253046     1  0.4356      0.723 0.708 0.000 0.000 0.292
#> GSM1253048     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253049     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253052     3  0.0000      0.982 0.000 0.000 1.000 0.000
#> GSM1253037     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253028     3  0.0000      0.982 0.000 0.000 1.000 0.000
#> GSM1253029     3  0.0000      0.982 0.000 0.000 1.000 0.000
#> GSM1253030     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253031     3  0.0000      0.982 0.000 0.000 1.000 0.000
#> GSM1253033     1  0.1716      0.780 0.936 0.000 0.000 0.064
#> GSM1253035     3  0.0000      0.982 0.000 0.000 1.000 0.000
#> GSM1253036     3  0.0000      0.982 0.000 0.000 1.000 0.000
#> GSM1253038     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253042     3  0.0000      0.982 0.000 0.000 1.000 0.000
#> GSM1253045     3  0.0000      0.982 0.000 0.000 1.000 0.000
#> GSM1253043     3  0.0000      0.982 0.000 0.000 1.000 0.000
#> GSM1253044     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253047     1  0.0000      0.820 1.000 0.000 0.000 0.000
#> GSM1253050     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> GSM1253051     3  0.3486      0.768 0.000 0.188 0.812 0.000
#> GSM1253053     3  0.0000      0.982 0.000 0.000 1.000 0.000
#> GSM1253054     1  0.2530      0.728 0.888 0.000 0.000 0.112
#> GSM1253055     3  0.0000      0.982 0.000 0.000 1.000 0.000
#> GSM1253079     1  0.0000      0.820 1.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000      0.820 1.000 0.000 0.000 0.000
#> GSM1253075     1  0.0188      0.820 0.996 0.000 0.000 0.004
#> GSM1253077     1  0.0000      0.820 1.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      0.820 1.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      0.820 1.000 0.000 0.000 0.000
#> GSM1253081     4  0.4522      0.296 0.320 0.000 0.000 0.680
#> GSM1253080     1  0.4072      0.739 0.748 0.000 0.000 0.252
#> GSM1253082     4  0.4981      0.304 0.464 0.000 0.000 0.536

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4    p5
#> GSM1253056     4  0.0162      0.849 0.004 0.000 0.000 0.996 0.000
#> GSM1253057     1  0.2516      0.830 0.860 0.000 0.000 0.140 0.000
#> GSM1253058     4  0.2732      0.850 0.160 0.000 0.000 0.840 0.000
#> GSM1253059     4  0.3875      0.825 0.160 0.000 0.000 0.792 0.048
#> GSM1253060     4  0.2329      0.865 0.124 0.000 0.000 0.876 0.000
#> GSM1253061     1  0.1608      0.852 0.928 0.000 0.000 0.072 0.000
#> GSM1253062     1  0.0000      0.873 1.000 0.000 0.000 0.000 0.000
#> GSM1253063     4  0.0162      0.849 0.004 0.000 0.000 0.996 0.000
#> GSM1253064     1  0.1792      0.859 0.916 0.000 0.000 0.084 0.000
#> GSM1253065     4  0.0162      0.849 0.004 0.000 0.000 0.996 0.000
#> GSM1253066     1  0.2690      0.821 0.844 0.000 0.000 0.156 0.000
#> GSM1253067     4  0.2605      0.859 0.148 0.000 0.000 0.852 0.000
#> GSM1253068     1  0.2690      0.821 0.844 0.000 0.000 0.156 0.000
#> GSM1253069     1  0.1851      0.861 0.912 0.000 0.000 0.088 0.000
#> GSM1253070     1  0.1357      0.836 0.948 0.000 0.000 0.048 0.004
#> GSM1253071     4  0.2732      0.850 0.160 0.000 0.000 0.840 0.000
#> GSM1253072     1  0.2690      0.821 0.844 0.000 0.000 0.156 0.000
#> GSM1253073     4  0.0162      0.849 0.004 0.000 0.000 0.996 0.000
#> GSM1253074     1  0.1410      0.871 0.940 0.000 0.000 0.060 0.000
#> GSM1253032     5  0.5162      0.849 0.308 0.000 0.000 0.064 0.628
#> GSM1253034     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253039     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253040     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253041     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253046     5  0.5696      0.742 0.172 0.000 0.000 0.200 0.628
#> GSM1253048     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253049     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253052     3  0.0000      0.919 0.000 0.000 1.000 0.000 0.000
#> GSM1253037     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253028     3  0.0000      0.919 0.000 0.000 1.000 0.000 0.000
#> GSM1253029     3  0.0000      0.919 0.000 0.000 1.000 0.000 0.000
#> GSM1253030     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253031     3  0.0000      0.919 0.000 0.000 1.000 0.000 0.000
#> GSM1253033     5  0.3492      0.775 0.188 0.000 0.000 0.016 0.796
#> GSM1253035     3  0.0000      0.919 0.000 0.000 1.000 0.000 0.000
#> GSM1253036     3  0.0000      0.919 0.000 0.000 1.000 0.000 0.000
#> GSM1253038     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253042     3  0.0000      0.919 0.000 0.000 1.000 0.000 0.000
#> GSM1253045     3  0.4251      0.635 0.000 0.000 0.624 0.004 0.372
#> GSM1253043     3  0.4251      0.635 0.000 0.000 0.624 0.004 0.372
#> GSM1253044     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253047     5  0.4101      0.813 0.372 0.000 0.000 0.000 0.628
#> GSM1253050     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253051     3  0.3003      0.731 0.000 0.188 0.812 0.000 0.000
#> GSM1253053     3  0.0000      0.919 0.000 0.000 1.000 0.000 0.000
#> GSM1253054     5  0.5162      0.849 0.308 0.000 0.000 0.064 0.628
#> GSM1253055     3  0.0000      0.919 0.000 0.000 1.000 0.000 0.000
#> GSM1253079     1  0.0000      0.873 1.000 0.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000      0.873 1.000 0.000 0.000 0.000 0.000
#> GSM1253075     1  0.0162      0.873 0.996 0.000 0.000 0.004 0.000
#> GSM1253077     1  0.0000      0.873 1.000 0.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      0.873 1.000 0.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      0.873 1.000 0.000 0.000 0.000 0.000
#> GSM1253081     1  0.3561      0.719 0.740 0.000 0.000 0.260 0.000
#> GSM1253080     1  0.2690      0.821 0.844 0.000 0.000 0.156 0.000
#> GSM1253082     1  0.2891      0.703 0.824 0.000 0.000 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
#> GSM1253056     4  0.0000      0.968 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253057     1  0.1334      0.943 0.948 0.000 0.000 0.020 0.032 0.000
#> GSM1253058     4  0.0632      0.963 0.024 0.000 0.000 0.976 0.000 0.000
#> GSM1253059     6  0.4648     -0.230 0.040 0.000 0.000 0.464 0.000 0.496
#> GSM1253060     4  0.0458      0.969 0.016 0.000 0.000 0.984 0.000 0.000
#> GSM1253061     1  0.1141      0.928 0.948 0.000 0.000 0.052 0.000 0.000
#> GSM1253062     1  0.0000      0.950 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253063     4  0.0000      0.968 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1253064     1  0.0937      0.938 0.960 0.000 0.000 0.040 0.000 0.000
#> GSM1253065     4  0.0777      0.943 0.004 0.000 0.000 0.972 0.024 0.000
#> GSM1253066     1  0.1564      0.939 0.936 0.000 0.000 0.024 0.040 0.000
#> GSM1253067     4  0.0458      0.969 0.016 0.000 0.000 0.984 0.000 0.000
#> GSM1253068     1  0.1564      0.939 0.936 0.000 0.000 0.024 0.040 0.000
#> GSM1253069     1  0.0820      0.949 0.972 0.000 0.000 0.012 0.016 0.000
#> GSM1253070     1  0.2432      0.856 0.876 0.000 0.000 0.024 0.100 0.000
#> GSM1253071     4  0.0632      0.963 0.024 0.000 0.000 0.976 0.000 0.000
#> GSM1253072     1  0.1564      0.939 0.936 0.000 0.000 0.024 0.040 0.000
#> GSM1253073     4  0.0458      0.956 0.000 0.000 0.000 0.984 0.016 0.000
#> GSM1253074     1  0.0820      0.949 0.972 0.000 0.000 0.016 0.012 0.000
#> GSM1253032     5  0.1418      0.956 0.032 0.000 0.000 0.024 0.944 0.000
#> GSM1253034     2  0.0458      0.989 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM1253039     2  0.0458      0.989 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM1253040     2  0.0000      0.994 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253041     2  0.0000      0.994 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253046     5  0.0458      0.915 0.000 0.000 0.000 0.016 0.984 0.000
#> GSM1253048     2  0.0000      0.994 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253049     2  0.0000      0.994 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253052     3  0.0000      0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253037     2  0.0000      0.994 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253028     3  0.0000      0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253029     3  0.0000      0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253030     2  0.0458      0.989 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM1253031     3  0.0000      0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253033     5  0.1464      0.944 0.016 0.000 0.000 0.004 0.944 0.036
#> GSM1253035     3  0.0000      0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253036     3  0.0000      0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253038     2  0.0458      0.989 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM1253042     3  0.0000      0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253045     6  0.3198      0.589 0.000 0.000 0.260 0.000 0.000 0.740
#> GSM1253043     6  0.3198      0.589 0.000 0.000 0.260 0.000 0.000 0.740
#> GSM1253044     2  0.0000      0.994 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253047     5  0.1267      0.940 0.060 0.000 0.000 0.000 0.940 0.000
#> GSM1253050     2  0.0000      0.994 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253051     3  0.3136      0.639 0.000 0.188 0.796 0.000 0.016 0.000
#> GSM1253053     3  0.0000      0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253054     5  0.1418      0.956 0.032 0.000 0.000 0.024 0.944 0.000
#> GSM1253055     3  0.0000      0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1253079     1  0.0000      0.950 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000      0.950 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253075     1  0.0146      0.950 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM1253077     1  0.0000      0.950 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      0.950 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      0.950 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1253081     1  0.2867      0.869 0.848 0.000 0.000 0.112 0.040 0.000
#> GSM1253080     1  0.1564      0.939 0.936 0.000 0.000 0.024 0.040 0.000
#> GSM1253082     1  0.2454      0.822 0.840 0.000 0.000 0.160 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 infection(p) disease.state(p) individual(p) k
#> ATC:pam 56     0.030714         2.22e-07         0.937 2
#> ATC:pam 56     0.023827         6.27e-10         0.856 3
#> ATC:pam 53     0.006453         1.27e-10         0.856 4
#> ATC:pam 56     0.000334         7.23e-13         0.865 5
#> ATC:pam 55     0.001056         3.22e-11         0.711 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 51979 rows and 56 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 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 ATC-mclust-collect-plots

The plots are:

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

All the plots in panels can be made by individual functions and they are plotted later in this section.

select_partition_number() produces several plots showing different statistics for choosing “optimized” k. There are following statistics:

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

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

select_partition_number(res)

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

The numeric values for all these statistics can be obtained by get_stats().

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.981       0.990         0.5082 0.491   0.491
#> 3 3 0.631           0.831       0.864         0.2671 0.671   0.437
#> 4 4 1.000           0.962       0.978         0.1553 0.884   0.678
#> 5 5 0.783           0.856       0.871         0.0602 0.932   0.741
#> 6 6 0.833           0.899       0.906         0.0506 0.933   0.688

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
#> 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
#> GSM1253056     1  0.0376      0.997 0.996 0.004
#> GSM1253057     1  0.0000      0.999 1.000 0.000
#> GSM1253058     1  0.0376      0.997 0.996 0.004
#> GSM1253059     1  0.0376      0.997 0.996 0.004
#> GSM1253060     1  0.0376      0.997 0.996 0.004
#> GSM1253061     1  0.0000      0.999 1.000 0.000
#> GSM1253062     1  0.0000      0.999 1.000 0.000
#> GSM1253063     1  0.0376      0.997 0.996 0.004
#> GSM1253064     1  0.0000      0.999 1.000 0.000
#> GSM1253065     1  0.0376      0.997 0.996 0.004
#> GSM1253066     1  0.0000      0.999 1.000 0.000
#> GSM1253067     1  0.0376      0.997 0.996 0.004
#> GSM1253068     1  0.0000      0.999 1.000 0.000
#> GSM1253069     1  0.0000      0.999 1.000 0.000
#> GSM1253070     1  0.0000      0.999 1.000 0.000
#> GSM1253071     1  0.0376      0.997 0.996 0.004
#> GSM1253072     1  0.0000      0.999 1.000 0.000
#> GSM1253073     1  0.0376      0.997 0.996 0.004
#> GSM1253074     1  0.0000      0.999 1.000 0.000
#> GSM1253032     2  0.4939      0.887 0.108 0.892
#> GSM1253034     2  0.0000      0.981 0.000 1.000
#> GSM1253039     2  0.0000      0.981 0.000 1.000
#> GSM1253040     2  0.0000      0.981 0.000 1.000
#> GSM1253041     2  0.0000      0.981 0.000 1.000
#> GSM1253046     2  0.5946      0.847 0.144 0.856
#> GSM1253048     2  0.0000      0.981 0.000 1.000
#> GSM1253049     2  0.0000      0.981 0.000 1.000
#> GSM1253052     2  0.0000      0.981 0.000 1.000
#> GSM1253037     2  0.0000      0.981 0.000 1.000
#> GSM1253028     2  0.0000      0.981 0.000 1.000
#> GSM1253029     2  0.0000      0.981 0.000 1.000
#> GSM1253030     2  0.0000      0.981 0.000 1.000
#> GSM1253031     2  0.0000      0.981 0.000 1.000
#> GSM1253033     2  0.1414      0.968 0.020 0.980
#> GSM1253035     2  0.0000      0.981 0.000 1.000
#> GSM1253036     2  0.0000      0.981 0.000 1.000
#> GSM1253038     2  0.0000      0.981 0.000 1.000
#> GSM1253042     2  0.0000      0.981 0.000 1.000
#> GSM1253045     2  0.0672      0.976 0.008 0.992
#> GSM1253043     2  0.0672      0.976 0.008 0.992
#> GSM1253044     2  0.0000      0.981 0.000 1.000
#> GSM1253047     2  0.7056      0.783 0.192 0.808
#> GSM1253050     2  0.0000      0.981 0.000 1.000
#> GSM1253051     2  0.0000      0.981 0.000 1.000
#> GSM1253053     2  0.0000      0.981 0.000 1.000
#> GSM1253054     2  0.2603      0.949 0.044 0.956
#> GSM1253055     2  0.0000      0.981 0.000 1.000
#> GSM1253079     1  0.0000      0.999 1.000 0.000
#> GSM1253083     1  0.0000      0.999 1.000 0.000
#> GSM1253075     1  0.0000      0.999 1.000 0.000
#> GSM1253077     1  0.0000      0.999 1.000 0.000
#> GSM1253076     1  0.0000      0.999 1.000 0.000
#> GSM1253078     1  0.0000      0.999 1.000 0.000
#> GSM1253081     1  0.0000      0.999 1.000 0.000
#> GSM1253080     1  0.0000      0.999 1.000 0.000
#> GSM1253082     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
#> GSM1253056     3  0.5431      0.692 0.284 0.000 0.716
#> GSM1253057     1  0.0000      0.938 1.000 0.000 0.000
#> GSM1253058     3  0.5397      0.694 0.280 0.000 0.720
#> GSM1253059     3  0.5397      0.694 0.280 0.000 0.720
#> GSM1253060     3  0.5431      0.692 0.284 0.000 0.716
#> GSM1253061     1  0.1964      0.924 0.944 0.000 0.056
#> GSM1253062     1  0.0424      0.936 0.992 0.000 0.008
#> GSM1253063     3  0.5431      0.692 0.284 0.000 0.716
#> GSM1253064     1  0.2066      0.923 0.940 0.000 0.060
#> GSM1253065     3  0.5431      0.692 0.284 0.000 0.716
#> GSM1253066     1  0.2066      0.923 0.940 0.000 0.060
#> GSM1253067     3  0.5431      0.692 0.284 0.000 0.716
#> GSM1253068     1  0.2066      0.923 0.940 0.000 0.060
#> GSM1253069     1  0.0237      0.937 0.996 0.000 0.004
#> GSM1253070     1  0.5988      0.433 0.632 0.000 0.368
#> GSM1253071     3  0.5431      0.692 0.284 0.000 0.716
#> GSM1253072     1  0.2066      0.923 0.940 0.000 0.060
#> GSM1253073     3  0.5431      0.692 0.284 0.000 0.716
#> GSM1253074     1  0.1643      0.917 0.956 0.000 0.044
#> GSM1253032     3  0.3038      0.749 0.104 0.000 0.896
#> GSM1253034     2  0.0000      0.994 0.000 1.000 0.000
#> GSM1253039     2  0.0000      0.994 0.000 1.000 0.000
#> GSM1253040     2  0.0000      0.994 0.000 1.000 0.000
#> GSM1253041     2  0.0000      0.994 0.000 1.000 0.000
#> GSM1253046     3  0.3272      0.750 0.104 0.004 0.892
#> GSM1253048     2  0.0000      0.994 0.000 1.000 0.000
#> GSM1253049     2  0.0000      0.994 0.000 1.000 0.000
#> GSM1253052     3  0.5363      0.686 0.000 0.276 0.724
#> GSM1253037     2  0.0000      0.994 0.000 1.000 0.000
#> GSM1253028     3  0.5363      0.684 0.000 0.276 0.724
#> GSM1253029     3  0.5363      0.686 0.000 0.276 0.724
#> GSM1253030     2  0.1031      0.974 0.000 0.976 0.024
#> GSM1253031     3  0.6490      0.700 0.036 0.256 0.708
#> GSM1253033     3  0.2625      0.747 0.084 0.000 0.916
#> GSM1253035     3  0.5760      0.647 0.000 0.328 0.672
#> GSM1253036     3  0.5733      0.651 0.000 0.324 0.676
#> GSM1253038     2  0.0000      0.994 0.000 1.000 0.000
#> GSM1253042     3  0.5363      0.686 0.000 0.276 0.724
#> GSM1253045     3  0.2866      0.745 0.076 0.008 0.916
#> GSM1253043     3  0.2866      0.745 0.076 0.008 0.916
#> GSM1253044     2  0.0000      0.994 0.000 1.000 0.000
#> GSM1253047     3  0.3349      0.748 0.108 0.004 0.888
#> GSM1253050     2  0.0000      0.994 0.000 1.000 0.000
#> GSM1253051     2  0.1163      0.967 0.000 0.972 0.028
#> GSM1253053     3  0.5327      0.687 0.000 0.272 0.728
#> GSM1253054     3  0.3193      0.750 0.100 0.004 0.896
#> GSM1253055     3  0.5706      0.653 0.000 0.320 0.680
#> GSM1253079     1  0.0424      0.937 0.992 0.000 0.008
#> GSM1253083     1  0.1529      0.920 0.960 0.000 0.040
#> GSM1253075     1  0.1163      0.928 0.972 0.000 0.028
#> GSM1253077     1  0.0000      0.938 1.000 0.000 0.000
#> GSM1253076     1  0.1643      0.917 0.956 0.000 0.044
#> GSM1253078     1  0.1031      0.930 0.976 0.000 0.024
#> GSM1253081     1  0.2066      0.923 0.940 0.000 0.060
#> GSM1253080     1  0.0237      0.937 0.996 0.000 0.004
#> GSM1253082     1  0.2165      0.919 0.936 0.000 0.064

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4
#> GSM1253056     4  0.0336      0.991 0.008 0.000 0.000 0.992
#> GSM1253057     1  0.0336      0.982 0.992 0.000 0.000 0.008
#> GSM1253058     4  0.0336      0.981 0.000 0.000 0.008 0.992
#> GSM1253059     4  0.0469      0.977 0.000 0.000 0.012 0.988
#> GSM1253060     4  0.0707      0.983 0.020 0.000 0.000 0.980
#> GSM1253061     1  0.1118      0.977 0.964 0.000 0.000 0.036
#> GSM1253062     1  0.0000      0.982 1.000 0.000 0.000 0.000
#> GSM1253063     4  0.0469      0.991 0.012 0.000 0.000 0.988
#> GSM1253064     1  0.1211      0.975 0.960 0.000 0.000 0.040
#> GSM1253065     4  0.0469      0.991 0.012 0.000 0.000 0.988
#> GSM1253066     1  0.1118      0.977 0.964 0.000 0.000 0.036
#> GSM1253067     4  0.0336      0.991 0.008 0.000 0.000 0.992
#> GSM1253068     1  0.1118      0.977 0.964 0.000 0.000 0.036
#> GSM1253069     1  0.0000      0.982 1.000 0.000 0.000 0.000
#> GSM1253070     3  0.4420      0.702 0.240 0.000 0.748 0.012
#> GSM1253071     4  0.0336      0.991 0.008 0.000 0.000 0.992
#> GSM1253072     1  0.1118      0.977 0.964 0.000 0.000 0.036
#> GSM1253073     4  0.0469      0.991 0.012 0.000 0.000 0.988
#> GSM1253074     1  0.0469      0.981 0.988 0.000 0.000 0.012
#> GSM1253032     3  0.1722      0.940 0.048 0.000 0.944 0.008
#> GSM1253034     2  0.0336      0.965 0.000 0.992 0.008 0.000
#> GSM1253039     2  0.0000      0.968 0.000 1.000 0.000 0.000
#> GSM1253040     2  0.0000      0.968 0.000 1.000 0.000 0.000
#> GSM1253041     2  0.0000      0.968 0.000 1.000 0.000 0.000
#> GSM1253046     3  0.1722      0.940 0.048 0.000 0.944 0.008
#> GSM1253048     2  0.0336      0.965 0.000 0.992 0.008 0.000
#> GSM1253049     2  0.0000      0.968 0.000 1.000 0.000 0.000
#> GSM1253052     3  0.0000      0.965 0.000 0.000 1.000 0.000
#> GSM1253037     2  0.0000      0.968 0.000 1.000 0.000 0.000
#> GSM1253028     3  0.0000      0.965 0.000 0.000 1.000 0.000
#> GSM1253029     3  0.0000      0.965 0.000 0.000 1.000 0.000
#> GSM1253030     2  0.2921      0.850 0.000 0.860 0.140 0.000
#> GSM1253031     3  0.0000      0.965 0.000 0.000 1.000 0.000
#> GSM1253033     3  0.1022      0.953 0.032 0.000 0.968 0.000
#> GSM1253035     3  0.0000      0.965 0.000 0.000 1.000 0.000
#> GSM1253036     3  0.0000      0.965 0.000 0.000 1.000 0.000
#> GSM1253038     2  0.0000      0.968 0.000 1.000 0.000 0.000
#> GSM1253042     3  0.0000      0.965 0.000 0.000 1.000 0.000
#> GSM1253045     3  0.0000      0.965 0.000 0.000 1.000 0.000
#> GSM1253043     3  0.0000      0.965 0.000 0.000 1.000 0.000
#> GSM1253044     2  0.0188      0.967 0.000 0.996 0.004 0.000
#> GSM1253047     3  0.2101      0.927 0.060 0.000 0.928 0.012
#> GSM1253050     2  0.0000      0.968 0.000 1.000 0.000 0.000
#> GSM1253051     2  0.3074      0.837 0.000 0.848 0.152 0.000
#> GSM1253053     3  0.0000      0.965 0.000 0.000 1.000 0.000
#> GSM1253054     3  0.1677      0.945 0.040 0.000 0.948 0.012
#> GSM1253055     3  0.0000      0.965 0.000 0.000 1.000 0.000
#> GSM1253079     1  0.0000      0.982 1.000 0.000 0.000 0.000
#> GSM1253083     1  0.0000      0.982 1.000 0.000 0.000 0.000
#> GSM1253075     1  0.0000      0.982 1.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      0.982 1.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      0.982 1.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      0.982 1.000 0.000 0.000 0.000
#> GSM1253081     1  0.1474      0.966 0.948 0.000 0.000 0.052
#> GSM1253080     1  0.0707      0.981 0.980 0.000 0.000 0.020
#> GSM1253082     1  0.1211      0.975 0.960 0.000 0.000 0.040

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4    p5
#> GSM1253056     4  0.0404      0.932 0.012 0.000 0.000 0.988 0.000
#> GSM1253057     1  0.0000      0.899 1.000 0.000 0.000 0.000 0.000
#> GSM1253058     4  0.3318      0.789 0.000 0.000 0.008 0.800 0.192
#> GSM1253059     4  0.3318      0.789 0.000 0.000 0.008 0.800 0.192
#> GSM1253060     4  0.0703      0.921 0.024 0.000 0.000 0.976 0.000
#> GSM1253061     5  0.6071      0.994 0.236 0.000 0.000 0.192 0.572
#> GSM1253062     1  0.0000      0.899 1.000 0.000 0.000 0.000 0.000
#> GSM1253063     4  0.0404      0.932 0.012 0.000 0.000 0.988 0.000
#> GSM1253064     5  0.6071      0.994 0.236 0.000 0.000 0.192 0.572
#> GSM1253065     4  0.0510      0.930 0.016 0.000 0.000 0.984 0.000
#> GSM1253066     5  0.6071      0.994 0.236 0.000 0.000 0.192 0.572
#> GSM1253067     4  0.0566      0.931 0.012 0.000 0.000 0.984 0.004
#> GSM1253068     5  0.6071      0.994 0.236 0.000 0.000 0.192 0.572
#> GSM1253069     1  0.0000      0.899 1.000 0.000 0.000 0.000 0.000
#> GSM1253070     1  0.6561     -0.195 0.424 0.000 0.204 0.000 0.372
#> GSM1253071     4  0.0566      0.931 0.012 0.000 0.000 0.984 0.004
#> GSM1253072     5  0.6071      0.994 0.236 0.000 0.000 0.192 0.572
#> GSM1253073     4  0.0404      0.932 0.012 0.000 0.000 0.988 0.000
#> GSM1253074     1  0.1965      0.809 0.904 0.000 0.000 0.000 0.096
#> GSM1253032     3  0.6181      0.639 0.196 0.000 0.552 0.000 0.252
#> GSM1253034     2  0.0290      0.974 0.000 0.992 0.008 0.000 0.000
#> GSM1253039     2  0.0162      0.975 0.000 0.996 0.004 0.000 0.000
#> GSM1253040     2  0.0000      0.976 0.000 1.000 0.000 0.000 0.000
#> GSM1253041     2  0.0000      0.976 0.000 1.000 0.000 0.000 0.000
#> GSM1253046     3  0.6187      0.637 0.200 0.000 0.552 0.000 0.248
#> GSM1253048     2  0.0290      0.974 0.000 0.992 0.008 0.000 0.000
#> GSM1253049     2  0.0000      0.976 0.000 1.000 0.000 0.000 0.000
#> GSM1253052     3  0.0162      0.832 0.000 0.004 0.996 0.000 0.000
#> GSM1253037     2  0.0000      0.976 0.000 1.000 0.000 0.000 0.000
#> GSM1253028     3  0.0324      0.832 0.000 0.004 0.992 0.000 0.004
#> GSM1253029     3  0.0162      0.832 0.000 0.004 0.996 0.000 0.000
#> GSM1253030     2  0.2127      0.893 0.000 0.892 0.108 0.000 0.000
#> GSM1253031     3  0.0162      0.832 0.000 0.000 0.996 0.000 0.004
#> GSM1253033     3  0.6021      0.660 0.188 0.000 0.580 0.000 0.232
#> GSM1253035     3  0.0000      0.832 0.000 0.000 1.000 0.000 0.000
#> GSM1253036     3  0.0162      0.832 0.000 0.000 0.996 0.000 0.004
#> GSM1253038     2  0.0000      0.976 0.000 1.000 0.000 0.000 0.000
#> GSM1253042     3  0.0162      0.832 0.000 0.004 0.996 0.000 0.000
#> GSM1253045     3  0.4479      0.711 0.000 0.184 0.744 0.000 0.072
#> GSM1253043     3  0.4593      0.710 0.000 0.184 0.736 0.000 0.080
#> GSM1253044     2  0.0162      0.976 0.000 0.996 0.004 0.000 0.000
#> GSM1253047     3  0.6259      0.580 0.248 0.000 0.540 0.000 0.212
#> GSM1253050     2  0.0000      0.976 0.000 1.000 0.000 0.000 0.000
#> GSM1253051     2  0.2280      0.881 0.000 0.880 0.120 0.000 0.000
#> GSM1253053     3  0.0324      0.832 0.000 0.004 0.992 0.000 0.004
#> GSM1253054     3  0.6155      0.643 0.192 0.000 0.556 0.000 0.252
#> GSM1253055     3  0.0162      0.832 0.000 0.000 0.996 0.000 0.004
#> GSM1253079     1  0.0162      0.896 0.996 0.000 0.000 0.000 0.004
#> GSM1253083     1  0.0162      0.896 0.996 0.000 0.000 0.000 0.004
#> GSM1253075     1  0.0000      0.899 1.000 0.000 0.000 0.000 0.000
#> GSM1253077     1  0.0000      0.899 1.000 0.000 0.000 0.000 0.000
#> GSM1253076     1  0.0000      0.899 1.000 0.000 0.000 0.000 0.000
#> GSM1253078     1  0.0000      0.899 1.000 0.000 0.000 0.000 0.000
#> GSM1253081     5  0.6085      0.966 0.216 0.000 0.000 0.212 0.572
#> GSM1253080     1  0.3749      0.634 0.816 0.000 0.000 0.104 0.080
#> GSM1253082     5  0.6071      0.994 0.236 0.000 0.000 0.192 0.572

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4    p5    p6
#> GSM1253056     4  0.2527      0.933 0.168 0.000 0.000 0.832 0.000 0.000
#> GSM1253057     6  0.1387      1.000 0.068 0.000 0.000 0.000 0.000 0.932
#> GSM1253058     4  0.1015      0.797 0.004 0.000 0.004 0.968 0.012 0.012
#> GSM1253059     4  0.1015      0.797 0.004 0.000 0.004 0.968 0.012 0.012
#> GSM1253060     4  0.3190      0.896 0.220 0.000 0.000 0.772 0.000 0.008
#> GSM1253061     1  0.0865      0.897 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM1253062     6  0.1387      1.000 0.068 0.000 0.000 0.000 0.000 0.932
#> GSM1253063     4  0.2562      0.933 0.172 0.000 0.000 0.828 0.000 0.000
#> GSM1253064     1  0.0865      0.897 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM1253065     4  0.2631      0.930 0.180 0.000 0.000 0.820 0.000 0.000
#> GSM1253066     1  0.0865      0.897 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM1253067     4  0.2491      0.933 0.164 0.000 0.000 0.836 0.000 0.000
#> GSM1253068     1  0.0865      0.897 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM1253069     6  0.1387      1.000 0.068 0.000 0.000 0.000 0.000 0.932
#> GSM1253070     1  0.3885      0.695 0.736 0.000 0.000 0.000 0.044 0.220
#> GSM1253071     4  0.2631      0.931 0.180 0.000 0.000 0.820 0.000 0.000
#> GSM1253072     1  0.0865      0.897 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM1253073     4  0.2562      0.934 0.172 0.000 0.000 0.828 0.000 0.000
#> GSM1253074     1  0.3446      0.605 0.692 0.000 0.000 0.000 0.000 0.308
#> GSM1253032     5  0.1251      0.883 0.024 0.000 0.012 0.000 0.956 0.008
#> GSM1253034     2  0.0291      0.966 0.004 0.992 0.004 0.000 0.000 0.000
#> GSM1253039     2  0.0000      0.969 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253040     2  0.0000      0.969 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253041     2  0.0000      0.969 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253046     5  0.3482      0.823 0.024 0.000 0.012 0.000 0.796 0.168
#> GSM1253048     2  0.0291      0.966 0.004 0.992 0.004 0.000 0.000 0.000
#> GSM1253049     2  0.0000      0.969 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253052     3  0.1675      0.883 0.000 0.024 0.936 0.000 0.032 0.008
#> GSM1253037     2  0.0000      0.969 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253028     3  0.2905      0.858 0.004 0.000 0.856 0.000 0.092 0.048
#> GSM1253029     3  0.1663      0.882 0.004 0.024 0.940 0.000 0.024 0.008
#> GSM1253030     2  0.2939      0.845 0.000 0.848 0.120 0.000 0.016 0.016
#> GSM1253031     3  0.1924      0.885 0.004 0.000 0.920 0.000 0.028 0.048
#> GSM1253033     5  0.1710      0.862 0.020 0.000 0.028 0.000 0.936 0.016
#> GSM1253035     3  0.0862      0.890 0.004 0.000 0.972 0.000 0.016 0.008
#> GSM1253036     3  0.1636      0.887 0.004 0.000 0.936 0.000 0.024 0.036
#> GSM1253038     2  0.0000      0.969 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253042     3  0.1663      0.882 0.004 0.024 0.940 0.000 0.024 0.008
#> GSM1253045     3  0.3721      0.672 0.004 0.000 0.684 0.000 0.308 0.004
#> GSM1253043     3  0.3753      0.686 0.004 0.000 0.696 0.000 0.292 0.008
#> GSM1253044     2  0.0000      0.969 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253047     5  0.3834      0.814 0.044 0.000 0.012 0.000 0.776 0.168
#> GSM1253050     2  0.0000      0.969 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1253051     2  0.2806      0.839 0.000 0.844 0.136 0.000 0.016 0.004
#> GSM1253053     3  0.1675      0.883 0.000 0.024 0.936 0.000 0.032 0.008
#> GSM1253054     5  0.1251      0.883 0.024 0.000 0.012 0.000 0.956 0.008
#> GSM1253055     3  0.1938      0.884 0.004 0.000 0.920 0.000 0.036 0.040
#> GSM1253079     6  0.1387      1.000 0.068 0.000 0.000 0.000 0.000 0.932
#> GSM1253083     6  0.1387      1.000 0.068 0.000 0.000 0.000 0.000 0.932
#> GSM1253075     6  0.1387      1.000 0.068 0.000 0.000 0.000 0.000 0.932
#> GSM1253077     6  0.1387      1.000 0.068 0.000 0.000 0.000 0.000 0.932
#> GSM1253076     6  0.1387      1.000 0.068 0.000 0.000 0.000 0.000 0.932
#> GSM1253078     6  0.1387      1.000 0.068 0.000 0.000 0.000 0.000 0.932
#> GSM1253081     1  0.0363      0.869 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM1253080     1  0.2823      0.774 0.796 0.000 0.000 0.000 0.000 0.204
#> GSM1253082     1  0.0508      0.880 0.984 0.000 0.000 0.004 0.000 0.012

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 infection(p) disease.state(p) individual(p) k
#> ATC:mclust 56     3.60e-03         4.20e-12         0.995 2
#> ATC:mclust 55     1.57e-05         1.41e-08         0.749 3
#> ATC:mclust 56     4.80e-05         1.44e-12         0.933 4
#> ATC:mclust 55     3.22e-05         1.22e-12         0.837 5
#> ATC:mclust 56     1.06e-04         4.21e-12         0.740 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 51979 rows and 56 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           0.986       0.994         0.4952 0.507   0.507
#> 3 3 0.628           0.624       0.782         0.2583 0.960   0.921
#> 4 4 0.580           0.785       0.783         0.0948 0.798   0.578
#> 5 5 0.758           0.827       0.882         0.0742 0.920   0.747
#> 6 6 0.742           0.727       0.854         0.0351 0.977   0.917

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
#> GSM1253056     1   0.000      0.990 1.000 0.000
#> GSM1253057     1   0.000      0.990 1.000 0.000
#> GSM1253058     1   0.000      0.990 1.000 0.000
#> GSM1253059     1   0.861      0.607 0.716 0.284
#> GSM1253060     1   0.000      0.990 1.000 0.000
#> GSM1253061     1   0.000      0.990 1.000 0.000
#> GSM1253062     1   0.000      0.990 1.000 0.000
#> GSM1253063     1   0.000      0.990 1.000 0.000
#> GSM1253064     1   0.000      0.990 1.000 0.000
#> GSM1253065     1   0.000      0.990 1.000 0.000
#> GSM1253066     1   0.000      0.990 1.000 0.000
#> GSM1253067     1   0.000      0.990 1.000 0.000
#> GSM1253068     1   0.000      0.990 1.000 0.000
#> GSM1253069     1   0.000      0.990 1.000 0.000
#> GSM1253070     1   0.000      0.990 1.000 0.000
#> GSM1253071     1   0.000      0.990 1.000 0.000
#> GSM1253072     1   0.000      0.990 1.000 0.000
#> GSM1253073     1   0.000      0.990 1.000 0.000
#> GSM1253074     1   0.000      0.990 1.000 0.000
#> GSM1253032     1   0.000      0.990 1.000 0.000
#> GSM1253034     2   0.000      1.000 0.000 1.000
#> GSM1253039     2   0.000      1.000 0.000 1.000
#> GSM1253040     2   0.000      1.000 0.000 1.000
#> GSM1253041     2   0.000      1.000 0.000 1.000
#> GSM1253046     1   0.000      0.990 1.000 0.000
#> GSM1253048     2   0.000      1.000 0.000 1.000
#> GSM1253049     2   0.000      1.000 0.000 1.000
#> GSM1253052     2   0.000      1.000 0.000 1.000
#> GSM1253037     2   0.000      1.000 0.000 1.000
#> GSM1253028     2   0.000      1.000 0.000 1.000
#> GSM1253029     2   0.000      1.000 0.000 1.000
#> GSM1253030     2   0.000      1.000 0.000 1.000
#> GSM1253031     2   0.000      1.000 0.000 1.000
#> GSM1253033     1   0.242      0.951 0.960 0.040
#> GSM1253035     2   0.000      1.000 0.000 1.000
#> GSM1253036     2   0.000      1.000 0.000 1.000
#> GSM1253038     2   0.000      1.000 0.000 1.000
#> GSM1253042     2   0.000      1.000 0.000 1.000
#> GSM1253045     2   0.000      1.000 0.000 1.000
#> GSM1253043     2   0.000      1.000 0.000 1.000
#> GSM1253044     2   0.000      1.000 0.000 1.000
#> GSM1253047     1   0.000      0.990 1.000 0.000
#> GSM1253050     2   0.000      1.000 0.000 1.000
#> GSM1253051     2   0.000      1.000 0.000 1.000
#> GSM1253053     2   0.000      1.000 0.000 1.000
#> GSM1253054     1   0.000      0.990 1.000 0.000
#> GSM1253055     2   0.000      1.000 0.000 1.000
#> GSM1253079     1   0.000      0.990 1.000 0.000
#> GSM1253083     1   0.000      0.990 1.000 0.000
#> GSM1253075     1   0.000      0.990 1.000 0.000
#> GSM1253077     1   0.000      0.990 1.000 0.000
#> GSM1253076     1   0.000      0.990 1.000 0.000
#> GSM1253078     1   0.000      0.990 1.000 0.000
#> GSM1253081     1   0.000      0.990 1.000 0.000
#> GSM1253080     1   0.000      0.990 1.000 0.000
#> GSM1253082     1   0.000      0.990 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
#> GSM1253056     1  0.5016     0.5276 0.760 0.000 0.240
#> GSM1253057     1  0.1031     0.6132 0.976 0.000 0.024
#> GSM1253058     1  0.7378     0.0947 0.560 0.036 0.404
#> GSM1253059     3  0.9042    -0.0803 0.356 0.144 0.500
#> GSM1253060     1  0.5016     0.5276 0.760 0.000 0.240
#> GSM1253061     1  0.2959     0.5929 0.900 0.000 0.100
#> GSM1253062     1  0.2261     0.6023 0.932 0.000 0.068
#> GSM1253063     1  0.5016     0.5276 0.760 0.000 0.240
#> GSM1253064     1  0.3686     0.5792 0.860 0.000 0.140
#> GSM1253065     1  0.5016     0.5276 0.760 0.000 0.240
#> GSM1253066     1  0.1411     0.6139 0.964 0.000 0.036
#> GSM1253067     1  0.5016     0.5276 0.760 0.000 0.240
#> GSM1253068     1  0.4504     0.5764 0.804 0.000 0.196
#> GSM1253069     1  0.5254     0.5312 0.736 0.000 0.264
#> GSM1253070     1  0.5926     0.4354 0.644 0.000 0.356
#> GSM1253071     1  0.5016     0.5276 0.760 0.000 0.240
#> GSM1253072     1  0.3816     0.5980 0.852 0.000 0.148
#> GSM1253073     1  0.5016     0.5276 0.760 0.000 0.240
#> GSM1253074     1  0.5859     0.4501 0.656 0.000 0.344
#> GSM1253032     1  0.5926     0.4354 0.644 0.000 0.356
#> GSM1253034     2  0.1031     0.8857 0.000 0.976 0.024
#> GSM1253039     2  0.3816     0.8291 0.000 0.852 0.148
#> GSM1253040     2  0.1964     0.8787 0.000 0.944 0.056
#> GSM1253041     2  0.3619     0.8390 0.000 0.864 0.136
#> GSM1253046     1  0.5926     0.4354 0.644 0.000 0.356
#> GSM1253048     2  0.0747     0.8847 0.000 0.984 0.016
#> GSM1253049     2  0.3116     0.8571 0.000 0.892 0.108
#> GSM1253052     2  0.1163     0.8859 0.000 0.972 0.028
#> GSM1253037     2  0.2878     0.8629 0.000 0.904 0.096
#> GSM1253028     2  0.3752     0.8303 0.000 0.856 0.144
#> GSM1253029     2  0.1529     0.8855 0.000 0.960 0.040
#> GSM1253030     2  0.0592     0.8860 0.000 0.988 0.012
#> GSM1253031     2  0.3752     0.8303 0.000 0.856 0.144
#> GSM1253033     3  0.9735    -0.0664 0.316 0.244 0.440
#> GSM1253035     2  0.3686     0.8326 0.000 0.860 0.140
#> GSM1253036     2  0.3752     0.8303 0.000 0.856 0.144
#> GSM1253038     2  0.1753     0.8833 0.000 0.952 0.048
#> GSM1253042     2  0.0424     0.8855 0.000 0.992 0.008
#> GSM1253045     2  0.8338     0.1758 0.084 0.516 0.400
#> GSM1253043     2  0.3879     0.8243 0.000 0.848 0.152
#> GSM1253044     2  0.3412     0.8480 0.000 0.876 0.124
#> GSM1253047     1  0.5926     0.4354 0.644 0.000 0.356
#> GSM1253050     2  0.3192     0.8549 0.000 0.888 0.112
#> GSM1253051     2  0.0592     0.8849 0.000 0.988 0.012
#> GSM1253053     2  0.0592     0.8846 0.000 0.988 0.012
#> GSM1253054     1  0.8143     0.2338 0.560 0.080 0.360
#> GSM1253055     2  0.3752     0.8303 0.000 0.856 0.144
#> GSM1253079     1  0.3551     0.5825 0.868 0.000 0.132
#> GSM1253083     1  0.4931     0.5553 0.768 0.000 0.232
#> GSM1253075     1  0.3192     0.6091 0.888 0.000 0.112
#> GSM1253077     1  0.5497     0.5048 0.708 0.000 0.292
#> GSM1253076     1  0.3038     0.6090 0.896 0.000 0.104
#> GSM1253078     1  0.3686     0.6001 0.860 0.000 0.140
#> GSM1253081     1  0.5016     0.5276 0.760 0.000 0.240
#> GSM1253080     1  0.5016     0.5502 0.760 0.000 0.240
#> GSM1253082     1  0.5016     0.5276 0.760 0.000 0.240

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4
#> GSM1253056     4  0.4406      0.904 0.300 0.000 0.000 0.700
#> GSM1253057     1  0.0817      0.870 0.976 0.000 0.000 0.024
#> GSM1253058     4  0.5475      0.797 0.236 0.024 0.024 0.716
#> GSM1253059     4  0.5596      0.720 0.232 0.040 0.016 0.712
#> GSM1253060     4  0.4431      0.902 0.304 0.000 0.000 0.696
#> GSM1253061     1  0.2466      0.831 0.900 0.000 0.004 0.096
#> GSM1253062     1  0.1211      0.864 0.960 0.000 0.000 0.040
#> GSM1253063     4  0.4406      0.904 0.300 0.000 0.000 0.700
#> GSM1253064     1  0.2924      0.827 0.884 0.000 0.016 0.100
#> GSM1253065     4  0.4431      0.902 0.304 0.000 0.000 0.696
#> GSM1253066     1  0.3862      0.766 0.824 0.000 0.024 0.152
#> GSM1253067     4  0.4406      0.904 0.300 0.000 0.000 0.700
#> GSM1253068     1  0.3107      0.816 0.884 0.000 0.036 0.080
#> GSM1253069     1  0.0707      0.864 0.980 0.000 0.020 0.000
#> GSM1253070     1  0.3625      0.637 0.828 0.000 0.160 0.012
#> GSM1253071     4  0.4454      0.889 0.308 0.000 0.000 0.692
#> GSM1253072     1  0.3279      0.812 0.872 0.000 0.032 0.096
#> GSM1253073     4  0.4406      0.904 0.300 0.000 0.000 0.700
#> GSM1253074     1  0.1635      0.849 0.948 0.000 0.044 0.008
#> GSM1253032     3  0.7000      0.721 0.404 0.028 0.512 0.056
#> GSM1253034     2  0.2489      0.844 0.000 0.912 0.068 0.020
#> GSM1253039     2  0.4820      0.760 0.000 0.772 0.168 0.060
#> GSM1253040     2  0.2546      0.844 0.000 0.912 0.060 0.028
#> GSM1253041     2  0.3398      0.845 0.000 0.872 0.068 0.060
#> GSM1253046     3  0.6257      0.674 0.436 0.000 0.508 0.056
#> GSM1253048     2  0.0707      0.854 0.000 0.980 0.020 0.000
#> GSM1253049     2  0.2021      0.850 0.000 0.936 0.040 0.024
#> GSM1253052     2  0.4123      0.830 0.000 0.820 0.136 0.044
#> GSM1253037     2  0.3015      0.833 0.000 0.884 0.092 0.024
#> GSM1253028     2  0.4508      0.784 0.004 0.764 0.216 0.016
#> GSM1253029     2  0.3876      0.834 0.000 0.836 0.124 0.040
#> GSM1253030     2  0.3763      0.816 0.000 0.832 0.144 0.024
#> GSM1253031     2  0.5327      0.756 0.000 0.720 0.220 0.060
#> GSM1253033     3  0.7649      0.724 0.300 0.116 0.548 0.036
#> GSM1253035     2  0.3597      0.832 0.000 0.836 0.148 0.016
#> GSM1253036     2  0.3324      0.836 0.000 0.852 0.136 0.012
#> GSM1253038     2  0.2313      0.849 0.000 0.924 0.044 0.032
#> GSM1253042     2  0.4088      0.830 0.000 0.820 0.140 0.040
#> GSM1253045     3  0.7381      0.309 0.180 0.328 0.492 0.000
#> GSM1253043     2  0.7291      0.544 0.148 0.636 0.172 0.044
#> GSM1253044     2  0.2675      0.852 0.000 0.908 0.044 0.048
#> GSM1253047     3  0.6252      0.680 0.432 0.000 0.512 0.056
#> GSM1253050     2  0.2882      0.837 0.000 0.892 0.084 0.024
#> GSM1253051     2  0.2266      0.849 0.000 0.912 0.084 0.004
#> GSM1253053     2  0.3999      0.831 0.000 0.824 0.140 0.036
#> GSM1253054     3  0.7636      0.747 0.332 0.072 0.536 0.060
#> GSM1253055     2  0.4661      0.657 0.000 0.652 0.348 0.000
#> GSM1253079     1  0.1022      0.867 0.968 0.000 0.000 0.032
#> GSM1253083     1  0.0469      0.866 0.988 0.000 0.000 0.012
#> GSM1253075     1  0.0469      0.871 0.988 0.000 0.000 0.012
#> GSM1253077     1  0.0927      0.857 0.976 0.000 0.008 0.016
#> GSM1253076     1  0.0817      0.866 0.976 0.000 0.000 0.024
#> GSM1253078     1  0.0921      0.864 0.972 0.000 0.000 0.028
#> GSM1253081     1  0.4843     -0.197 0.604 0.000 0.000 0.396
#> GSM1253080     1  0.2131      0.851 0.932 0.000 0.036 0.032
#> GSM1253082     4  0.4999      0.521 0.492 0.000 0.000 0.508

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4 p5
#> GSM1253056     4  0.2329      0.822 0.124 0.000 0.000 0.876 NA
#> GSM1253057     1  0.0727      0.902 0.980 0.000 0.004 0.004 NA
#> GSM1253058     4  0.4563      0.646 0.032 0.004 0.008 0.732 NA
#> GSM1253059     4  0.4971      0.469 0.020 0.000 0.004 0.504 NA
#> GSM1253060     4  0.4269      0.674 0.300 0.000 0.000 0.684 NA
#> GSM1253061     1  0.1121      0.897 0.956 0.000 0.000 0.044 NA
#> GSM1253062     1  0.2284      0.881 0.896 0.000 0.004 0.004 NA
#> GSM1253063     4  0.2818      0.822 0.132 0.000 0.000 0.856 NA
#> GSM1253064     1  0.1408      0.895 0.948 0.000 0.000 0.044 NA
#> GSM1253065     4  0.4642      0.617 0.328 0.000 0.004 0.648 NA
#> GSM1253066     1  0.2233      0.873 0.904 0.000 0.000 0.080 NA
#> GSM1253067     4  0.2513      0.819 0.116 0.000 0.000 0.876 NA
#> GSM1253068     1  0.1981      0.883 0.920 0.000 0.000 0.064 NA
#> GSM1253069     1  0.1087      0.902 0.968 0.000 0.008 0.008 NA
#> GSM1253070     1  0.4076      0.721 0.768 0.000 0.200 0.020 NA
#> GSM1253071     4  0.3719      0.805 0.116 0.000 0.000 0.816 NA
#> GSM1253072     1  0.2046      0.881 0.916 0.000 0.000 0.068 NA
#> GSM1253073     4  0.3044      0.816 0.148 0.000 0.004 0.840 NA
#> GSM1253074     1  0.1059      0.901 0.968 0.000 0.008 0.020 NA
#> GSM1253032     3  0.2353      0.727 0.060 0.000 0.908 0.028 NA
#> GSM1253034     2  0.0162      0.959 0.000 0.996 0.000 0.000 NA
#> GSM1253039     2  0.0290      0.957 0.000 0.992 0.000 0.000 NA
#> GSM1253040     2  0.0162      0.958 0.000 0.996 0.000 0.000 NA
#> GSM1253041     2  0.0290      0.958 0.000 0.992 0.000 0.000 NA
#> GSM1253046     3  0.2879      0.709 0.080 0.000 0.880 0.032 NA
#> GSM1253048     2  0.0290      0.958 0.000 0.992 0.008 0.000 NA
#> GSM1253049     2  0.0162      0.958 0.000 0.996 0.000 0.000 NA
#> GSM1253052     2  0.1612      0.950 0.000 0.948 0.024 0.012 NA
#> GSM1253037     2  0.0162      0.958 0.000 0.996 0.000 0.000 NA
#> GSM1253028     3  0.5173      0.182 0.000 0.460 0.500 0.000 NA
#> GSM1253029     2  0.1372      0.951 0.000 0.956 0.024 0.004 NA
#> GSM1253030     2  0.4023      0.821 0.000 0.812 0.048 0.020 NA
#> GSM1253031     3  0.4477      0.651 0.000 0.252 0.708 0.000 NA
#> GSM1253033     3  0.1016      0.738 0.004 0.008 0.972 0.012 NA
#> GSM1253035     2  0.2482      0.902 0.000 0.892 0.084 0.000 NA
#> GSM1253036     2  0.2871      0.885 0.000 0.872 0.088 0.000 NA
#> GSM1253038     2  0.0290      0.957 0.000 0.992 0.000 0.000 NA
#> GSM1253042     2  0.1106      0.954 0.000 0.964 0.012 0.000 NA
#> GSM1253045     3  0.1799      0.745 0.012 0.028 0.940 0.000 NA
#> GSM1253043     3  0.4697      0.677 0.008 0.224 0.720 0.000 NA
#> GSM1253044     2  0.0833      0.957 0.000 0.976 0.016 0.004 NA
#> GSM1253047     3  0.2615      0.719 0.080 0.000 0.892 0.020 NA
#> GSM1253050     2  0.0162      0.958 0.000 0.996 0.000 0.000 NA
#> GSM1253051     2  0.1901      0.937 0.000 0.932 0.040 0.004 NA
#> GSM1253053     2  0.1653      0.948 0.000 0.944 0.028 0.004 NA
#> GSM1253054     3  0.2273      0.740 0.048 0.008 0.920 0.016 NA
#> GSM1253055     3  0.4920      0.497 0.000 0.348 0.620 0.008 NA
#> GSM1253079     1  0.2011      0.884 0.908 0.000 0.000 0.004 NA
#> GSM1253083     1  0.1764      0.890 0.928 0.000 0.008 0.000 NA
#> GSM1253075     1  0.1764      0.891 0.928 0.000 0.008 0.000 NA
#> GSM1253077     1  0.2077      0.883 0.908 0.000 0.008 0.000 NA
#> GSM1253076     1  0.1956      0.887 0.916 0.000 0.008 0.000 NA
#> GSM1253078     1  0.3171      0.809 0.816 0.000 0.008 0.000 NA
#> GSM1253081     1  0.2136      0.869 0.904 0.000 0.000 0.088 NA
#> GSM1253080     1  0.1492      0.898 0.948 0.000 0.008 0.040 NA
#> GSM1253082     1  0.3242      0.761 0.816 0.000 0.000 0.172 NA

show/hide code output

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

#>            class entropy silhouette    p1    p2    p3    p4    p5 p6
#> GSM1253056     4  0.1970      0.604 0.060 0.000 0.028 0.912 0.000 NA
#> GSM1253057     1  0.0582      0.902 0.984 0.000 0.004 0.004 0.004 NA
#> GSM1253058     4  0.3791     -0.240 0.004 0.000 0.300 0.688 0.000 NA
#> GSM1253059     3  0.4275      0.000 0.004 0.000 0.592 0.388 0.000 NA
#> GSM1253060     4  0.4353      0.561 0.204 0.000 0.060 0.724 0.000 NA
#> GSM1253061     1  0.1844      0.892 0.924 0.000 0.024 0.048 0.000 NA
#> GSM1253062     1  0.1382      0.894 0.948 0.000 0.036 0.000 0.008 NA
#> GSM1253063     4  0.4385      0.579 0.120 0.000 0.100 0.756 0.000 NA
#> GSM1253064     1  0.2085      0.893 0.912 0.000 0.024 0.056 0.008 NA
#> GSM1253065     4  0.4864      0.528 0.220 0.000 0.072 0.688 0.008 NA
#> GSM1253066     1  0.2670      0.865 0.872 0.000 0.040 0.084 0.004 NA
#> GSM1253067     4  0.2594      0.573 0.048 0.000 0.040 0.892 0.004 NA
#> GSM1253068     1  0.2237      0.878 0.896 0.000 0.036 0.068 0.000 NA
#> GSM1253069     1  0.0912      0.901 0.972 0.000 0.004 0.008 0.012 NA
#> GSM1253070     1  0.4069      0.736 0.760 0.000 0.028 0.012 0.188 NA
#> GSM1253071     4  0.3794      0.277 0.040 0.000 0.216 0.744 0.000 NA
#> GSM1253072     1  0.2685      0.866 0.872 0.000 0.044 0.080 0.000 NA
#> GSM1253073     4  0.4030      0.611 0.132 0.000 0.068 0.780 0.000 NA
#> GSM1253074     1  0.1116      0.901 0.960 0.000 0.004 0.028 0.008 NA
#> GSM1253032     5  0.0951      0.755 0.020 0.000 0.000 0.004 0.968 NA
#> GSM1253034     2  0.0547      0.882 0.000 0.980 0.000 0.000 0.000 NA
#> GSM1253039     2  0.1531      0.858 0.000 0.928 0.004 0.000 0.000 NA
#> GSM1253040     2  0.0790      0.877 0.000 0.968 0.000 0.000 0.000 NA
#> GSM1253041     2  0.0260      0.880 0.000 0.992 0.000 0.000 0.000 NA
#> GSM1253046     5  0.1074      0.753 0.028 0.000 0.000 0.000 0.960 NA
#> GSM1253048     2  0.0547      0.879 0.000 0.980 0.000 0.000 0.000 NA
#> GSM1253049     2  0.0713      0.877 0.000 0.972 0.000 0.000 0.000 NA
#> GSM1253052     2  0.1075      0.877 0.000 0.952 0.000 0.000 0.000 NA
#> GSM1253037     2  0.0260      0.881 0.000 0.992 0.000 0.000 0.000 NA
#> GSM1253028     2  0.6459     -0.242 0.000 0.348 0.004 0.008 0.324 NA
#> GSM1253029     2  0.0713      0.881 0.000 0.972 0.000 0.000 0.000 NA
#> GSM1253030     2  0.4520      0.530 0.000 0.580 0.016 0.008 0.004 NA
#> GSM1253031     5  0.5852      0.472 0.000 0.240 0.004 0.000 0.516 NA
#> GSM1253033     5  0.1657      0.744 0.000 0.000 0.016 0.000 0.928 NA
#> GSM1253035     2  0.3682      0.768 0.000 0.792 0.008 0.000 0.052 NA
#> GSM1253036     2  0.3915      0.685 0.000 0.704 0.004 0.000 0.020 NA
#> GSM1253038     2  0.1531      0.859 0.000 0.928 0.004 0.000 0.000 NA
#> GSM1253042     2  0.0865      0.875 0.000 0.964 0.000 0.000 0.000 NA
#> GSM1253045     5  0.2660      0.736 0.008 0.016 0.004 0.000 0.872 NA
#> GSM1253043     5  0.5400      0.592 0.000 0.112 0.024 0.000 0.628 NA
#> GSM1253044     2  0.0937      0.874 0.000 0.960 0.000 0.000 0.000 NA
#> GSM1253047     5  0.0935      0.752 0.032 0.000 0.000 0.000 0.964 NA
#> GSM1253050     2  0.0260      0.880 0.000 0.992 0.000 0.000 0.000 NA
#> GSM1253051     2  0.2814      0.795 0.000 0.820 0.008 0.000 0.000 NA
#> GSM1253053     2  0.1753      0.855 0.000 0.912 0.000 0.000 0.004 NA
#> GSM1253054     5  0.1368      0.756 0.012 0.004 0.008 0.004 0.956 NA
#> GSM1253055     5  0.6377      0.382 0.000 0.276 0.012 0.004 0.444 NA
#> GSM1253079     1  0.1080      0.899 0.960 0.000 0.032 0.000 0.004 NA
#> GSM1253083     1  0.2113      0.881 0.912 0.000 0.048 0.000 0.008 NA
#> GSM1253075     1  0.1511      0.892 0.944 0.000 0.032 0.000 0.012 NA
#> GSM1253077     1  0.2414      0.871 0.896 0.000 0.056 0.000 0.012 NA
#> GSM1253076     1  0.2484      0.876 0.896 0.000 0.056 0.004 0.012 NA
#> GSM1253078     1  0.3174      0.831 0.840 0.000 0.108 0.000 0.012 NA
#> GSM1253081     1  0.3125      0.852 0.852 0.000 0.040 0.092 0.004 NA
#> GSM1253080     1  0.1679      0.900 0.936 0.000 0.016 0.036 0.012 NA
#> GSM1253082     1  0.3617      0.790 0.800 0.000 0.044 0.144 0.000 NA

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

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

consensus_heatmap(res, k = 2)

plot of chunk tab-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 infection(p) disease.state(p) individual(p) k
#> ATC:NMF 56     0.018077         1.69e-08         0.955 2
#> ATC:NMF 46     0.004646         5.67e-10         0.929 3
#> ATC:NMF 54     0.002595         1.39e-09         0.853 4
#> ATC:NMF 53     0.000226         9.38e-11         0.826 5
#> ATC:NMF 50     0.000460         1.38e-09         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.

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