cola Report for recount2:SRP029880

Date: 2019-12-25 23:50:35 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 17171 rows and 54 columns.
#>   Top rows are extracted by 'SD, CV, MAD, ATC' methods.
#>   Subgroups are detected by 'hclust, kmeans, skmeans, pam, mclust, NMF' method.
#>   Number of partitions are tried for k = 2, 3, 4, 5, 6.
#>   Performed in total 30000 partitions by row resampling.
#> 
#> Following methods can be applied to this 'ConsensusPartitionList' object:
#>  [1] "cola_report"           "collect_classes"       "collect_plots"         "collect_stats"        
#>  [5] "colnames"              "functional_enrichment" "get_anno_col"          "get_anno"             
#>  [9] "get_classes"           "get_matrix"            "get_membership"        "get_stats"            
#> [13] "is_best_k"             "is_stable_k"           "ncol"                  "nrow"                 
#> [17] "rownames"              "show"                  "suggest_best_k"        "test_to_known_factors"
#> [21] "top_rows_heatmap"      "top_rows_overlap"     
#> 
#> You can get result for a single method by, e.g. object["SD", "hclust"] or object["SD:hclust"]
#> or a subset of methods by object[c("SD", "CV")], c("hclust", "kmeans")]

The call of run_all_consensus_partition_methods() was:

#> run_all_consensus_partition_methods(data = mat, mc.cores = 4)

Dimension of the input matrix:

mat = get_matrix(res_list)
dim(mat)

#> [1] 17171    54

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, 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:kmeans	2	1.000	0.977	0.985	**
CV:NMF	2	1.000	0.975	0.990	**
MAD:hclust	3	1.000	0.964	0.983	**
MAD:kmeans	2	1.000	1.000	1.000	**
MAD:pam	2	1.000	1.000	1.000	**
MAD:mclust	2	1.000	0.974	0.989	**
ATC:hclust	3	1.000	0.987	0.994	**	2
ATC:skmeans	3	1.000	0.958	0.983	**	2
ATC:mclust	3	1.000	0.994	0.997	**
ATC:NMF	2	1.000	0.974	0.991	**
SD:pam	4	0.961	0.936	0.971	**	2,3
CV:pam	3	0.951	0.907	0.963	**
MAD:NMF	4	0.944	0.907	0.955	*	2,3
CV:skmeans	4	0.940	0.922	0.966	*	2,3
SD:NMF	4	0.929	0.900	0.954	*	2,3
ATC:pam	5	0.921	0.919	0.966	*	2,4
MAD:skmeans	3	0.909	0.929	0.962	*	2
ATC:kmeans	3	0.904	0.932	0.968	*	2
SD:skmeans	4	0.902	0.861	0.937	*	2,3
CV:mclust	4	0.887	0.893	0.928
CV:hclust	4	0.839	0.882	0.920
SD:mclust	4	0.800	0.899	0.920
CV:kmeans	2	0.633	0.936	0.956
SD:hclust	3	0.598	0.829	0.885

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

CDF of consensus matrices

Cumulative distribution function curves of consensus matrix for all methods.

collect_plots(res_list, fun = plot_ecdf)

plot of chunk collect-plots

Consensus heatmap

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

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

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

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

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

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

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

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

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

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

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

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

Membership heatmap

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

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

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

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

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

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

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

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

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

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

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

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

Signature heatmap

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

Note in following heatmaps, rows are scaled.

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

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

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

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

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

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

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

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

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

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

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

Statistics table

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

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

get_stats(res_list, k = 2)

#>             k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> SD:NMF      2 1.000           0.944       0.980          0.506 0.493   0.493
#> CV:NMF      2 1.000           0.975       0.990          0.509 0.491   0.491
#> MAD:NMF     2 1.000           0.993       0.996          0.504 0.497   0.497
#> ATC:NMF     2 1.000           0.974       0.991          0.508 0.491   0.491
#> SD:skmeans  2 1.000           0.970       0.988          0.506 0.497   0.497
#> CV:skmeans  2 1.000           0.969       0.989          0.509 0.491   0.491
#> MAD:skmeans 2 1.000           0.991       0.996          0.504 0.497   0.497
#> ATC:skmeans 2 1.000           1.000       1.000          0.510 0.491   0.491
#> SD:mclust   2 0.547           0.933       0.938          0.450 0.547   0.547
#> CV:mclust   2 0.509           0.797       0.859          0.438 0.560   0.560
#> MAD:mclust  2 1.000           0.974       0.989          0.460 0.547   0.547
#> ATC:mclust  2 0.829           0.898       0.957          0.478 0.502   0.502
#> SD:kmeans   2 1.000           0.977       0.985          0.502 0.497   0.497
#> CV:kmeans   2 0.633           0.936       0.956          0.491 0.491   0.491
#> MAD:kmeans  2 1.000           1.000       1.000          0.504 0.497   0.497
#> ATC:kmeans  2 1.000           1.000       1.000          0.510 0.491   0.491
#> SD:pam      2 0.961           0.948       0.978          0.506 0.497   0.497
#> CV:pam      2 0.858           0.960       0.974          0.501 0.491   0.491
#> MAD:pam     2 1.000           1.000       1.000          0.504 0.497   0.497
#> ATC:pam     2 1.000           1.000       1.000          0.510 0.491   0.491
#> SD:hclust   2 0.280           0.407       0.750          0.365 0.628   0.628
#> CV:hclust   2 0.537           0.731       0.878          0.200 0.927   0.927
#> MAD:hclust  2 0.855           0.948       0.975          0.509 0.491   0.491
#> ATC:hclust  2 1.000           1.000       1.000          0.510 0.491   0.491

get_stats(res_list, k = 3)

#>             k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> SD:NMF      3 0.905           0.916       0.959          0.251 0.860   0.725
#> CV:NMF      3 0.862           0.857       0.930          0.254 0.840   0.682
#> MAD:NMF     3 1.000           0.968       0.987          0.244 0.867   0.734
#> ATC:NMF     3 0.807           0.782       0.894          0.198 0.911   0.821
#> SD:skmeans  3 0.925           0.926       0.966          0.302 0.843   0.685
#> CV:skmeans  3 1.000           0.950       0.978          0.288 0.820   0.646
#> MAD:skmeans 3 0.909           0.929       0.962          0.277 0.868   0.734
#> ATC:skmeans 3 1.000           0.958       0.983          0.155 0.929   0.857
#> SD:mclust   3 0.700           0.727       0.840          0.479 0.776   0.591
#> CV:mclust   3 0.595           0.792       0.861          0.464 0.762   0.584
#> MAD:mclust  3 0.738           0.857       0.929          0.425 0.808   0.649
#> ATC:mclust  3 1.000           0.994       0.997          0.384 0.781   0.586
#> SD:kmeans   3 0.722           0.834       0.872          0.266 0.843   0.685
#> CV:kmeans   3 0.781           0.860       0.890          0.309 0.772   0.568
#> MAD:kmeans  3 0.768           0.795       0.907          0.226 0.867   0.734
#> ATC:kmeans  3 0.904           0.932       0.968          0.166 0.929   0.857
#> SD:pam      3 0.940           0.891       0.959          0.287 0.820   0.650
#> CV:pam      3 0.951           0.907       0.963          0.278 0.877   0.749
#> MAD:pam     3 0.809           0.894       0.928          0.285 0.816   0.642
#> ATC:pam     3 0.856           0.829       0.917          0.160 0.965   0.929
#> SD:hclust   3 0.598           0.829       0.885          0.617 0.603   0.437
#> CV:hclust   3 0.586           0.683       0.814          1.359 0.706   0.683
#> MAD:hclust  3 1.000           0.964       0.983          0.138 0.936   0.869
#> ATC:hclust  3 1.000           0.987       0.994          0.078 0.965   0.929

get_stats(res_list, k = 4)

#>             k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> SD:NMF      4 0.929           0.900       0.954        0.05891 0.940   0.844
#> CV:NMF      4 0.851           0.836       0.921        0.08928 0.892   0.725
#> MAD:NMF     4 0.944           0.907       0.955        0.05484 0.956   0.884
#> ATC:NMF     4 0.799           0.828       0.902        0.13679 0.859   0.663
#> SD:skmeans  4 0.902           0.861       0.937        0.08852 0.918   0.769
#> CV:skmeans  4 0.940           0.922       0.966        0.11081 0.918   0.766
#> MAD:skmeans 4 0.781           0.756       0.889        0.08471 0.904   0.746
#> ATC:skmeans 4 0.898           0.845       0.929        0.12789 0.886   0.736
#> SD:mclust   4 0.800           0.899       0.920        0.10176 0.931   0.786
#> CV:mclust   4 0.887           0.893       0.928        0.15871 0.869   0.638
#> MAD:mclust  4 0.697           0.672       0.827        0.10130 0.825   0.564
#> ATC:mclust  4 0.857           0.778       0.895        0.07664 0.940   0.825
#> SD:kmeans   4 0.759           0.708       0.850        0.10559 0.918   0.780
#> CV:kmeans   4 0.761           0.729       0.851        0.10099 0.901   0.734
#> MAD:kmeans  4 0.671           0.666       0.822        0.12913 0.953   0.877
#> ATC:kmeans  4 0.815           0.846       0.892        0.12815 0.874   0.707
#> SD:pam      4 0.961           0.936       0.971        0.10167 0.855   0.625
#> CV:pam      4 0.794           0.731       0.855        0.10677 0.869   0.662
#> MAD:pam     4 0.797           0.811       0.895        0.11480 0.909   0.751
#> ATC:pam     4 0.981           0.936       0.977        0.13463 0.877   0.730
#> SD:hclust   4 0.772           0.873       0.923        0.07114 0.968   0.917
#> CV:hclust   4 0.839           0.882       0.920        0.40363 0.695   0.518
#> MAD:hclust  4 0.995           0.958       0.982        0.00636 0.997   0.993
#> ATC:hclust  4 0.821           0.761       0.857        0.15285 0.874   0.724

get_stats(res_list, k = 5)

#>             k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> SD:NMF      5 0.790           0.749       0.868         0.0966 0.928   0.788
#> CV:NMF      5 0.857           0.787       0.895         0.0834 0.923   0.762
#> MAD:NMF     5 0.824           0.759       0.838         0.0935 0.898   0.714
#> ATC:NMF     5 0.758           0.693       0.831         0.0405 0.954   0.850
#> SD:skmeans  5 0.815           0.695       0.838         0.0513 0.979   0.927
#> CV:skmeans  5 0.797           0.729       0.838         0.0586 0.994   0.980
#> MAD:skmeans 5 0.799           0.626       0.832         0.0722 0.948   0.833
#> ATC:skmeans 5 0.858           0.850       0.897         0.0507 0.939   0.815
#> SD:mclust   5 0.733           0.773       0.847         0.0273 0.892   0.638
#> CV:mclust   5 0.880           0.891       0.864         0.0499 0.966   0.860
#> MAD:mclust  5 0.732           0.601       0.793         0.0536 0.905   0.675
#> ATC:mclust  5 0.860           0.818       0.893         0.0607 0.899   0.673
#> SD:kmeans   5 0.691           0.633       0.791         0.0678 1.000   1.000
#> CV:kmeans   5 0.725           0.728       0.771         0.0688 0.957   0.862
#> MAD:kmeans  5 0.657           0.589       0.775         0.0843 0.908   0.743
#> ATC:kmeans  5 0.689           0.747       0.834         0.0824 0.954   0.854
#> SD:pam      5 0.892           0.785       0.894         0.0453 0.970   0.894
#> CV:pam      5 0.884           0.741       0.885         0.0513 0.932   0.773
#> MAD:pam     5 0.749           0.736       0.856         0.0323 0.918   0.749
#> ATC:pam     5 0.921           0.919       0.966         0.0490 0.968   0.903
#> SD:hclust   5 0.805           0.833       0.831         0.1193 0.922   0.779
#> CV:hclust   5 0.793           0.806       0.866         0.0850 0.951   0.851
#> MAD:hclust  5 0.778           0.780       0.878         0.1955 0.874   0.703
#> ATC:hclust  5 0.846           0.893       0.951         0.0785 0.904   0.741

get_stats(res_list, k = 6)

#>             k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> SD:NMF      6 0.773           0.724       0.827         0.0683 0.911   0.692
#> CV:NMF      6 0.732           0.550       0.741         0.0657 0.924   0.703
#> MAD:NMF     6 0.757           0.719       0.833         0.0724 0.928   0.743
#> ATC:NMF     6 0.729           0.676       0.826         0.0377 0.891   0.663
#> SD:skmeans  6 0.722           0.600       0.732         0.0442 0.943   0.794
#> CV:skmeans  6 0.779           0.694       0.731         0.0452 0.921   0.710
#> MAD:skmeans 6 0.722           0.628       0.772         0.0480 0.941   0.786
#> ATC:skmeans 6 0.889           0.865       0.932         0.0427 0.992   0.970
#> SD:mclust   6 0.787           0.742       0.825         0.0543 0.971   0.874
#> CV:mclust   6 0.831           0.813       0.868         0.0297 0.983   0.920
#> MAD:mclust  6 0.752           0.656       0.801         0.0407 0.920   0.674
#> ATC:mclust  6 0.778           0.652       0.814         0.0267 0.900   0.642
#> SD:kmeans   6 0.721           0.530       0.716         0.0545 0.927   0.784
#> CV:kmeans   6 0.722           0.437       0.659         0.0479 0.973   0.901
#> MAD:kmeans  6 0.718           0.533       0.736         0.0462 0.933   0.768
#> ATC:kmeans  6 0.731           0.710       0.813         0.0506 0.979   0.924
#> SD:pam      6 0.845           0.789       0.893         0.0400 0.964   0.866
#> CV:pam      6 0.889           0.736       0.895         0.0335 0.959   0.847
#> MAD:pam     6 0.740           0.712       0.812         0.0719 0.892   0.631
#> ATC:pam     6 0.893           0.912       0.928         0.0542 0.958   0.860
#> SD:hclust   6 0.867           0.813       0.899         0.0434 0.991   0.967
#> CV:hclust   6 0.863           0.781       0.881         0.0433 0.985   0.948
#> MAD:hclust  6 0.851           0.780       0.899         0.0495 0.948   0.838
#> ATC:hclust  6 0.746           0.752       0.871         0.0759 0.947   0.833

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

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 17171 rows and 54 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#>   Subgroups are detected by 'hclust' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 3.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk SD-hclust-collect-plots

The plots are:

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

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

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

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

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

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

select_partition_number(res)

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

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.280           0.407       0.750         0.3651 0.628   0.628
#> 3 3 0.598           0.829       0.885         0.6174 0.603   0.437
#> 4 4 0.772           0.873       0.923         0.0711 0.968   0.917
#> 5 5 0.805           0.833       0.831         0.1193 0.922   0.779
#> 6 6 0.867           0.813       0.899         0.0434 0.991   0.967

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

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

suggest_best_k(res)

#> [1] 3

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
#> SRR975551     2   0.996     0.0475 0.464 0.536
#> SRR975552     2   0.996     0.0475 0.464 0.536
#> SRR975554     2   0.996     0.0475 0.464 0.536
#> SRR975553     2   0.000     0.6474 0.000 1.000
#> SRR975555     2   0.996     0.0475 0.464 0.536
#> SRR975556     2   0.000     0.6474 0.000 1.000
#> SRR975557     2   0.644     0.4167 0.164 0.836
#> SRR975558     2   0.973     0.1704 0.404 0.596
#> SRR975559     2   0.973     0.1704 0.404 0.596
#> SRR975560     2   0.000     0.6474 0.000 1.000
#> SRR975561     2   0.000     0.6474 0.000 1.000
#> SRR975562     2   0.996     0.0475 0.464 0.536
#> SRR975563     2   0.000     0.6474 0.000 1.000
#> SRR975564     2   0.996     0.0475 0.464 0.536
#> SRR975565     2   0.996     0.0475 0.464 0.536
#> SRR975566     2   0.996     0.0475 0.464 0.536
#> SRR975567     2   0.973     0.1704 0.404 0.596
#> SRR975568     2   0.996     0.0475 0.464 0.536
#> SRR975569     2   0.000     0.6474 0.000 1.000
#> SRR975570     2   0.000     0.6474 0.000 1.000
#> SRR975571     2   0.000     0.6474 0.000 1.000
#> SRR975572     2   0.000     0.6474 0.000 1.000
#> SRR975573     2   0.000     0.6474 0.000 1.000
#> SRR975574     2   0.000     0.6474 0.000 1.000
#> SRR975575     2   0.000     0.6474 0.000 1.000
#> SRR975576     2   0.000     0.6474 0.000 1.000
#> SRR975577     2   0.000     0.6474 0.000 1.000
#> SRR975578     2   0.000     0.6474 0.000 1.000
#> SRR975579     2   0.644     0.4167 0.164 0.836
#> SRR975580     2   0.000     0.6474 0.000 1.000
#> SRR975581     2   0.000     0.6474 0.000 1.000
#> SRR975582     2   0.000     0.6474 0.000 1.000
#> SRR975583     2   0.000     0.6474 0.000 1.000
#> SRR975584     2   0.000     0.6474 0.000 1.000
#> SRR975585     2   0.000     0.6474 0.000 1.000
#> SRR975586     2   0.000     0.6474 0.000 1.000
#> SRR975587     1   0.987     0.4589 0.568 0.432
#> SRR975588     2   0.000     0.6474 0.000 1.000
#> SRR975589     1   0.949     0.4103 0.632 0.368
#> SRR975590     1   0.975     0.3567 0.592 0.408
#> SRR975591     1   0.987     0.4589 0.568 0.432
#> SRR975592     1   0.855     0.4483 0.720 0.280
#> SRR975593     1   0.949     0.4103 0.632 0.368
#> SRR975594     1   0.980     0.2498 0.584 0.416
#> SRR975595     1   0.980     0.3421 0.584 0.416
#> SRR975597     1   0.980     0.3421 0.584 0.416
#> SRR975596     2   0.973     0.1704 0.404 0.596
#> SRR975598     1   0.980     0.3421 0.584 0.416
#> SRR975599     2   0.963     0.2043 0.388 0.612
#> SRR975600     2   0.992    -0.3257 0.448 0.552
#> SRR975601     1   0.987     0.4589 0.568 0.432
#> SRR975602     2   0.996     0.0475 0.464 0.536
#> SRR975603     1   0.987     0.4589 0.568 0.432
#> SRR975604     1   0.987     0.4589 0.568 0.432

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> SRR975551     1   0.312      0.824 0.892 0.108 0.000
#> SRR975552     1   0.312      0.824 0.892 0.108 0.000
#> SRR975554     1   0.216      0.820 0.936 0.064 0.000
#> SRR975553     2   0.000      0.963 0.000 1.000 0.000
#> SRR975555     1   0.348      0.815 0.872 0.128 0.000
#> SRR975556     2   0.000      0.963 0.000 1.000 0.000
#> SRR975557     2   0.934      0.374 0.208 0.512 0.280
#> SRR975558     1   0.493      0.697 0.768 0.232 0.000
#> SRR975559     1   0.341      0.797 0.876 0.124 0.000
#> SRR975560     2   0.000      0.963 0.000 1.000 0.000
#> SRR975561     2   0.000      0.963 0.000 1.000 0.000
#> SRR975562     1   0.216      0.820 0.936 0.064 0.000
#> SRR975563     2   0.000      0.963 0.000 1.000 0.000
#> SRR975564     1   0.348      0.815 0.872 0.128 0.000
#> SRR975565     1   0.341      0.817 0.876 0.124 0.000
#> SRR975566     1   0.216      0.820 0.936 0.064 0.000
#> SRR975567     1   0.493      0.697 0.768 0.232 0.000
#> SRR975568     1   0.348      0.815 0.872 0.128 0.000
#> SRR975569     2   0.000      0.963 0.000 1.000 0.000
#> SRR975570     2   0.000      0.963 0.000 1.000 0.000
#> SRR975571     2   0.000      0.963 0.000 1.000 0.000
#> SRR975572     2   0.000      0.963 0.000 1.000 0.000
#> SRR975573     2   0.000      0.963 0.000 1.000 0.000
#> SRR975574     2   0.000      0.963 0.000 1.000 0.000
#> SRR975575     2   0.000      0.963 0.000 1.000 0.000
#> SRR975576     2   0.000      0.963 0.000 1.000 0.000
#> SRR975577     2   0.000      0.963 0.000 1.000 0.000
#> SRR975578     2   0.000      0.963 0.000 1.000 0.000
#> SRR975579     2   0.934      0.374 0.208 0.512 0.280
#> SRR975580     2   0.000      0.963 0.000 1.000 0.000
#> SRR975581     2   0.000      0.963 0.000 1.000 0.000
#> SRR975582     2   0.000      0.963 0.000 1.000 0.000
#> SRR975583     2   0.000      0.963 0.000 1.000 0.000
#> SRR975584     2   0.000      0.963 0.000 1.000 0.000
#> SRR975585     2   0.000      0.963 0.000 1.000 0.000
#> SRR975586     2   0.000      0.963 0.000 1.000 0.000
#> SRR975587     3   0.573      0.875 0.324 0.000 0.676
#> SRR975588     2   0.000      0.963 0.000 1.000 0.000
#> SRR975589     1   0.355      0.683 0.868 0.000 0.132
#> SRR975590     1   0.393      0.744 0.880 0.028 0.092
#> SRR975591     3   0.573      0.875 0.324 0.000 0.676
#> SRR975592     1   0.480      0.532 0.780 0.000 0.220
#> SRR975593     1   0.355      0.683 0.868 0.000 0.132
#> SRR975594     3   0.141      0.590 0.036 0.000 0.964
#> SRR975595     1   0.377      0.752 0.888 0.028 0.084
#> SRR975597     1   0.377      0.752 0.888 0.028 0.084
#> SRR975596     1   0.341      0.797 0.876 0.124 0.000
#> SRR975598     1   0.377      0.752 0.888 0.028 0.084
#> SRR975599     1   0.806      0.247 0.532 0.068 0.400
#> SRR975600     3   0.629      0.593 0.468 0.000 0.532
#> SRR975601     3   0.573      0.875 0.324 0.000 0.676
#> SRR975602     1   0.216      0.820 0.936 0.064 0.000
#> SRR975603     3   0.573      0.875 0.324 0.000 0.676
#> SRR975604     3   0.573      0.875 0.324 0.000 0.676

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3   p4
#> SRR975551     1   0.130      0.836 0.956 0.044 0.000 0.00
#> SRR975552     1   0.130      0.836 0.956 0.044 0.000 0.00
#> SRR975554     1   0.000      0.834 1.000 0.000 0.000 0.00
#> SRR975553     2   0.000      1.000 0.000 1.000 0.000 0.00
#> SRR975555     1   0.172      0.826 0.936 0.064 0.000 0.00
#> SRR975556     2   0.000      1.000 0.000 1.000 0.000 0.00
#> SRR975557     4   0.000      1.000 0.000 0.000 0.000 1.00
#> SRR975558     1   0.406      0.748 0.832 0.108 0.000 0.06
#> SRR975559     1   0.164      0.811 0.940 0.000 0.000 0.06
#> SRR975560     2   0.000      1.000 0.000 1.000 0.000 0.00
#> SRR975561     2   0.000      1.000 0.000 1.000 0.000 0.00
#> SRR975562     1   0.000      0.834 1.000 0.000 0.000 0.00
#> SRR975563     2   0.000      1.000 0.000 1.000 0.000 0.00
#> SRR975564     1   0.172      0.826 0.936 0.064 0.000 0.00
#> SRR975565     1   0.164      0.829 0.940 0.060 0.000 0.00
#> SRR975566     1   0.000      0.834 1.000 0.000 0.000 0.00
#> SRR975567     1   0.406      0.748 0.832 0.108 0.000 0.06
#> SRR975568     1   0.172      0.826 0.936 0.064 0.000 0.00
#> SRR975569     2   0.000      1.000 0.000 1.000 0.000 0.00
#> SRR975570     2   0.000      1.000 0.000 1.000 0.000 0.00
#> SRR975571     2   0.000      1.000 0.000 1.000 0.000 0.00
#> SRR975572     2   0.000      1.000 0.000 1.000 0.000 0.00
#> SRR975573     2   0.000      1.000 0.000 1.000 0.000 0.00
#> SRR975574     2   0.000      1.000 0.000 1.000 0.000 0.00
#> SRR975575     2   0.000      1.000 0.000 1.000 0.000 0.00
#> SRR975576     2   0.000      1.000 0.000 1.000 0.000 0.00
#> SRR975577     2   0.000      1.000 0.000 1.000 0.000 0.00
#> SRR975578     2   0.000      1.000 0.000 1.000 0.000 0.00
#> SRR975579     4   0.000      1.000 0.000 0.000 0.000 1.00
#> SRR975580     2   0.000      1.000 0.000 1.000 0.000 0.00
#> SRR975581     2   0.000      1.000 0.000 1.000 0.000 0.00
#> SRR975582     2   0.000      1.000 0.000 1.000 0.000 0.00
#> SRR975583     2   0.000      1.000 0.000 1.000 0.000 0.00
#> SRR975584     2   0.000      1.000 0.000 1.000 0.000 0.00
#> SRR975585     2   0.000      1.000 0.000 1.000 0.000 0.00
#> SRR975586     2   0.000      1.000 0.000 1.000 0.000 0.00
#> SRR975587     3   0.433      0.876 0.288 0.000 0.712 0.00
#> SRR975588     2   0.000      1.000 0.000 1.000 0.000 0.00
#> SRR975589     1   0.327      0.724 0.832 0.000 0.168 0.00
#> SRR975590     1   0.276      0.770 0.872 0.000 0.128 0.00
#> SRR975591     3   0.433      0.876 0.288 0.000 0.712 0.00
#> SRR975592     1   0.410      0.576 0.744 0.000 0.256 0.00
#> SRR975593     1   0.327      0.724 0.832 0.000 0.168 0.00
#> SRR975594     3   0.000      0.353 0.000 0.000 1.000 0.00
#> SRR975595     1   0.265      0.777 0.880 0.000 0.120 0.00
#> SRR975597     1   0.265      0.777 0.880 0.000 0.120 0.00
#> SRR975596     1   0.164      0.811 0.940 0.000 0.000 0.06
#> SRR975598     1   0.265      0.777 0.880 0.000 0.120 0.00
#> SRR975599     1   0.503      0.246 0.596 0.004 0.400 0.00
#> SRR975600     3   0.493      0.586 0.432 0.000 0.568 0.00
#> SRR975601     3   0.433      0.876 0.288 0.000 0.712 0.00
#> SRR975602     1   0.000      0.834 1.000 0.000 0.000 0.00
#> SRR975603     3   0.433      0.876 0.288 0.000 0.712 0.00
#> SRR975604     3   0.433      0.876 0.288 0.000 0.712 0.00

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3   p4    p5
#> SRR975551     1   0.418      0.583 0.600 0.000 0.000 0.00 0.400
#> SRR975552     1   0.418      0.583 0.600 0.000 0.000 0.00 0.400
#> SRR975554     1   0.400      0.640 0.656 0.000 0.000 0.00 0.344
#> SRR975553     2   0.000      1.000 0.000 1.000 0.000 0.00 0.000
#> SRR975555     5   0.260      0.776 0.148 0.000 0.000 0.00 0.852
#> SRR975556     2   0.000      1.000 0.000 1.000 0.000 0.00 0.000
#> SRR975557     4   0.141      1.000 0.000 0.000 0.000 0.94 0.060
#> SRR975558     5   0.128      0.744 0.004 0.044 0.000 0.00 0.952
#> SRR975559     5   0.238      0.744 0.128 0.000 0.000 0.00 0.872
#> SRR975560     2   0.000      1.000 0.000 1.000 0.000 0.00 0.000
#> SRR975561     2   0.000      1.000 0.000 1.000 0.000 0.00 0.000
#> SRR975562     5   0.366      0.628 0.276 0.000 0.000 0.00 0.724
#> SRR975563     2   0.000      1.000 0.000 1.000 0.000 0.00 0.000
#> SRR975564     5   0.260      0.776 0.148 0.000 0.000 0.00 0.852
#> SRR975565     1   0.423      0.554 0.580 0.000 0.000 0.00 0.420
#> SRR975566     1   0.356      0.697 0.740 0.000 0.000 0.00 0.260
#> SRR975567     5   0.128      0.744 0.004 0.044 0.000 0.00 0.952
#> SRR975568     5   0.260      0.776 0.148 0.000 0.000 0.00 0.852
#> SRR975569     2   0.000      1.000 0.000 1.000 0.000 0.00 0.000
#> SRR975570     2   0.000      1.000 0.000 1.000 0.000 0.00 0.000
#> SRR975571     2   0.000      1.000 0.000 1.000 0.000 0.00 0.000
#> SRR975572     2   0.000      1.000 0.000 1.000 0.000 0.00 0.000
#> SRR975573     2   0.000      1.000 0.000 1.000 0.000 0.00 0.000
#> SRR975574     2   0.000      1.000 0.000 1.000 0.000 0.00 0.000
#> SRR975575     2   0.000      1.000 0.000 1.000 0.000 0.00 0.000
#> SRR975576     2   0.000      1.000 0.000 1.000 0.000 0.00 0.000
#> SRR975577     2   0.000      1.000 0.000 1.000 0.000 0.00 0.000
#> SRR975578     2   0.000      1.000 0.000 1.000 0.000 0.00 0.000
#> SRR975579     4   0.141      1.000 0.000 0.000 0.000 0.94 0.060
#> SRR975580     2   0.000      1.000 0.000 1.000 0.000 0.00 0.000
#> SRR975581     2   0.000      1.000 0.000 1.000 0.000 0.00 0.000
#> SRR975582     2   0.000      1.000 0.000 1.000 0.000 0.00 0.000
#> SRR975583     2   0.000      1.000 0.000 1.000 0.000 0.00 0.000
#> SRR975584     2   0.000      1.000 0.000 1.000 0.000 0.00 0.000
#> SRR975585     2   0.000      1.000 0.000 1.000 0.000 0.00 0.000
#> SRR975586     2   0.000      1.000 0.000 1.000 0.000 0.00 0.000
#> SRR975587     3   0.428      0.837 0.032 0.000 0.724 0.00 0.244
#> SRR975588     2   0.000      1.000 0.000 1.000 0.000 0.00 0.000
#> SRR975589     1   0.407      0.628 0.752 0.000 0.032 0.00 0.216
#> SRR975590     1   0.304      0.736 0.836 0.000 0.012 0.00 0.152
#> SRR975591     3   0.509      0.850 0.084 0.000 0.672 0.00 0.244
#> SRR975592     1   0.455      0.645 0.752 0.000 0.124 0.00 0.124
#> SRR975593     1   0.407      0.628 0.752 0.000 0.032 0.00 0.216
#> SRR975594     3   0.328      0.348 0.092 0.000 0.848 0.06 0.000
#> SRR975595     1   0.281      0.738 0.844 0.000 0.004 0.00 0.152
#> SRR975597     1   0.281      0.738 0.844 0.000 0.004 0.00 0.152
#> SRR975596     5   0.238      0.744 0.128 0.000 0.000 0.00 0.872
#> SRR975598     1   0.281      0.738 0.844 0.000 0.004 0.00 0.152
#> SRR975599     1   0.693      0.264 0.556 0.000 0.244 0.06 0.140
#> SRR975600     3   0.655      0.617 0.248 0.000 0.476 0.00 0.276
#> SRR975601     3   0.428      0.837 0.032 0.000 0.724 0.00 0.244
#> SRR975602     1   0.356      0.697 0.740 0.000 0.000 0.00 0.260
#> SRR975603     3   0.509      0.850 0.084 0.000 0.672 0.00 0.244
#> SRR975604     3   0.509      0.850 0.084 0.000 0.672 0.00 0.244

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5 p6
#> SRR975551     1  0.5102      0.583 0.620 0.000 0.000 0.240 0.140  0
#> SRR975552     1  0.5102      0.583 0.620 0.000 0.000 0.240 0.140  0
#> SRR975554     1  0.4881      0.592 0.656 0.000 0.000 0.136 0.208  0
#> SRR975553     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000  0
#> SRR975555     4  0.2340      0.774 0.148 0.000 0.000 0.852 0.000  0
#> SRR975556     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000  0
#> SRR975557     6  0.0000      1.000 0.000 0.000 0.000 0.000 0.000  1
#> SRR975558     4  0.1007      0.733 0.000 0.044 0.000 0.956 0.000  0
#> SRR975559     4  0.3385      0.701 0.032 0.000 0.000 0.788 0.180  0
#> SRR975560     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000  0
#> SRR975561     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000  0
#> SRR975562     4  0.5067      0.659 0.184 0.000 0.000 0.636 0.180  0
#> SRR975563     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000  0
#> SRR975564     4  0.2340      0.774 0.148 0.000 0.000 0.852 0.000  0
#> SRR975565     1  0.4951      0.571 0.620 0.000 0.000 0.276 0.104  0
#> SRR975566     1  0.3714      0.561 0.656 0.000 0.000 0.004 0.340  0
#> SRR975567     4  0.1007      0.733 0.000 0.044 0.000 0.956 0.000  0
#> SRR975568     4  0.2340      0.774 0.148 0.000 0.000 0.852 0.000  0
#> SRR975569     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000  0
#> SRR975570     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000  0
#> SRR975571     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000  0
#> SRR975572     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000  0
#> SRR975573     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000  0
#> SRR975574     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000  0
#> SRR975575     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000  0
#> SRR975576     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000  0
#> SRR975577     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000  0
#> SRR975578     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000  0
#> SRR975579     6  0.0000      1.000 0.000 0.000 0.000 0.000 0.000  1
#> SRR975580     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000  0
#> SRR975581     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000  0
#> SRR975582     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000  0
#> SRR975583     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000  0
#> SRR975584     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000  0
#> SRR975585     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000  0
#> SRR975586     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000  0
#> SRR975587     3  0.1594      0.820 0.016 0.000 0.932 0.000 0.052  0
#> SRR975588     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000  0
#> SRR975589     1  0.3221      0.595 0.828 0.000 0.076 0.096 0.000  0
#> SRR975590     1  0.0777      0.698 0.972 0.000 0.024 0.000 0.004  0
#> SRR975591     3  0.0865      0.840 0.036 0.000 0.964 0.000 0.000  0
#> SRR975592     1  0.2668      0.624 0.828 0.000 0.168 0.004 0.000  0
#> SRR975593     1  0.3221      0.595 0.828 0.000 0.076 0.096 0.000  0
#> SRR975594     3  0.3854      0.212 0.000 0.000 0.536 0.000 0.464  0
#> SRR975595     1  0.0458      0.698 0.984 0.000 0.016 0.000 0.000  0
#> SRR975597     1  0.0458      0.698 0.984 0.000 0.016 0.000 0.000  0
#> SRR975596     4  0.3385      0.701 0.032 0.000 0.000 0.788 0.180  0
#> SRR975598     1  0.0458      0.698 0.984 0.000 0.016 0.000 0.000  0
#> SRR975599     5  0.2300      0.000 0.144 0.000 0.000 0.000 0.856  0
#> SRR975600     3  0.3163      0.624 0.232 0.000 0.764 0.004 0.000  0
#> SRR975601     3  0.1594      0.820 0.016 0.000 0.932 0.000 0.052  0
#> SRR975602     1  0.3714      0.561 0.656 0.000 0.000 0.004 0.340  0
#> SRR975603     3  0.0865      0.840 0.036 0.000 0.964 0.000 0.000  0
#> SRR975604     3  0.0865      0.840 0.036 0.000 0.964 0.000 0.000  0

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

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

consensus_heatmap(res, k = 2)

plot of chunk tab-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

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 17171 rows and 54 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#>   Subgroups are detected by 'kmeans' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 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           0.977       0.985         0.5016 0.497   0.497
#> 3 3 0.722           0.834       0.872         0.2656 0.843   0.685
#> 4 4 0.759           0.708       0.850         0.1056 0.918   0.780
#> 5 5 0.691           0.633       0.791         0.0678 1.000   1.000
#> 6 6 0.721           0.530       0.716         0.0545 0.927   0.784

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
#> SRR975551     1   0.204      0.971 0.968 0.032
#> SRR975552     1   0.204      0.971 0.968 0.032
#> SRR975554     1   0.204      0.971 0.968 0.032
#> SRR975553     2   0.000      1.000 0.000 1.000
#> SRR975555     1   0.204      0.971 0.968 0.032
#> SRR975556     2   0.000      1.000 0.000 1.000
#> SRR975557     1   0.204      0.971 0.968 0.032
#> SRR975558     1   0.722      0.785 0.800 0.200
#> SRR975559     1   0.204      0.971 0.968 0.032
#> SRR975560     2   0.000      1.000 0.000 1.000
#> SRR975561     2   0.000      1.000 0.000 1.000
#> SRR975562     1   0.204      0.971 0.968 0.032
#> SRR975563     2   0.000      1.000 0.000 1.000
#> SRR975564     1   0.204      0.971 0.968 0.032
#> SRR975565     1   0.204      0.971 0.968 0.032
#> SRR975566     1   0.204      0.971 0.968 0.032
#> SRR975567     1   0.722      0.785 0.800 0.200
#> SRR975568     1   0.204      0.971 0.968 0.032
#> SRR975569     2   0.000      1.000 0.000 1.000
#> SRR975570     2   0.000      1.000 0.000 1.000
#> SRR975571     2   0.000      1.000 0.000 1.000
#> SRR975572     2   0.000      1.000 0.000 1.000
#> SRR975573     2   0.000      1.000 0.000 1.000
#> SRR975574     2   0.000      1.000 0.000 1.000
#> SRR975575     2   0.000      1.000 0.000 1.000
#> SRR975576     2   0.000      1.000 0.000 1.000
#> SRR975577     2   0.000      1.000 0.000 1.000
#> SRR975578     2   0.000      1.000 0.000 1.000
#> SRR975579     2   0.000      1.000 0.000 1.000
#> SRR975580     2   0.000      1.000 0.000 1.000
#> SRR975581     2   0.000      1.000 0.000 1.000
#> SRR975582     2   0.000      1.000 0.000 1.000
#> SRR975583     2   0.000      1.000 0.000 1.000
#> SRR975584     2   0.000      1.000 0.000 1.000
#> SRR975585     2   0.000      1.000 0.000 1.000
#> SRR975586     2   0.000      1.000 0.000 1.000
#> SRR975587     1   0.000      0.972 1.000 0.000
#> SRR975588     2   0.000      1.000 0.000 1.000
#> SRR975589     1   0.000      0.972 1.000 0.000
#> SRR975590     1   0.000      0.972 1.000 0.000
#> SRR975591     1   0.000      0.972 1.000 0.000
#> SRR975592     1   0.000      0.972 1.000 0.000
#> SRR975593     1   0.000      0.972 1.000 0.000
#> SRR975594     1   0.000      0.972 1.000 0.000
#> SRR975595     1   0.000      0.972 1.000 0.000
#> SRR975597     1   0.000      0.972 1.000 0.000
#> SRR975596     1   0.204      0.971 0.968 0.032
#> SRR975598     1   0.000      0.972 1.000 0.000
#> SRR975599     1   0.000      0.972 1.000 0.000
#> SRR975600     1   0.000      0.972 1.000 0.000
#> SRR975601     1   0.000      0.972 1.000 0.000
#> SRR975602     1   0.204      0.971 0.968 0.032
#> SRR975603     1   0.000      0.972 1.000 0.000
#> SRR975604     1   0.000      0.972 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
#> SRR975551     1  0.5098     0.8809 0.752 0.000 0.248
#> SRR975552     1  0.5098     0.8809 0.752 0.000 0.248
#> SRR975554     1  0.5098     0.8809 0.752 0.000 0.248
#> SRR975553     2  0.0592     0.9769 0.012 0.988 0.000
#> SRR975555     1  0.5098     0.8809 0.752 0.000 0.248
#> SRR975556     2  0.0000     0.9787 0.000 1.000 0.000
#> SRR975557     1  0.5948     0.0912 0.640 0.000 0.360
#> SRR975558     1  0.3412     0.7549 0.876 0.000 0.124
#> SRR975559     1  0.4974     0.8760 0.764 0.000 0.236
#> SRR975560     2  0.3412     0.8908 0.124 0.876 0.000
#> SRR975561     2  0.3192     0.9007 0.112 0.888 0.000
#> SRR975562     1  0.4974     0.8760 0.764 0.000 0.236
#> SRR975563     2  0.0000     0.9787 0.000 1.000 0.000
#> SRR975564     1  0.5098     0.8809 0.752 0.000 0.248
#> SRR975565     1  0.5098     0.8809 0.752 0.000 0.248
#> SRR975566     1  0.5098     0.8809 0.752 0.000 0.248
#> SRR975567     1  0.3412     0.7549 0.876 0.000 0.124
#> SRR975568     1  0.5098     0.8809 0.752 0.000 0.248
#> SRR975569     2  0.0000     0.9787 0.000 1.000 0.000
#> SRR975570     2  0.0000     0.9787 0.000 1.000 0.000
#> SRR975571     2  0.0592     0.9769 0.012 0.988 0.000
#> SRR975572     2  0.0000     0.9787 0.000 1.000 0.000
#> SRR975573     2  0.0592     0.9769 0.012 0.988 0.000
#> SRR975574     2  0.0592     0.9769 0.012 0.988 0.000
#> SRR975575     2  0.0000     0.9787 0.000 1.000 0.000
#> SRR975576     2  0.0000     0.9787 0.000 1.000 0.000
#> SRR975577     2  0.0592     0.9769 0.012 0.988 0.000
#> SRR975578     2  0.0592     0.9769 0.012 0.988 0.000
#> SRR975579     2  0.4974     0.7868 0.236 0.764 0.000
#> SRR975580     2  0.0000     0.9787 0.000 1.000 0.000
#> SRR975581     2  0.0000     0.9787 0.000 1.000 0.000
#> SRR975582     2  0.0592     0.9769 0.012 0.988 0.000
#> SRR975583     2  0.0000     0.9787 0.000 1.000 0.000
#> SRR975584     2  0.0592     0.9769 0.012 0.988 0.000
#> SRR975585     2  0.0000     0.9787 0.000 1.000 0.000
#> SRR975586     2  0.0592     0.9732 0.012 0.988 0.000
#> SRR975587     3  0.0000     0.7550 0.000 0.000 1.000
#> SRR975588     2  0.0000     0.9787 0.000 1.000 0.000
#> SRR975589     3  0.4842     0.6797 0.224 0.000 0.776
#> SRR975590     3  0.5529     0.5856 0.296 0.000 0.704
#> SRR975591     3  0.0000     0.7550 0.000 0.000 1.000
#> SRR975592     3  0.4605     0.6923 0.204 0.000 0.796
#> SRR975593     3  0.4842     0.6797 0.224 0.000 0.776
#> SRR975594     3  0.3038     0.6460 0.104 0.000 0.896
#> SRR975595     3  0.5905     0.4783 0.352 0.000 0.648
#> SRR975597     3  0.5905     0.4783 0.352 0.000 0.648
#> SRR975596     1  0.4974     0.8760 0.764 0.000 0.236
#> SRR975598     3  0.5905     0.4783 0.352 0.000 0.648
#> SRR975599     1  0.5497     0.5423 0.708 0.000 0.292
#> SRR975600     3  0.0000     0.7550 0.000 0.000 1.000
#> SRR975601     3  0.0000     0.7550 0.000 0.000 1.000
#> SRR975602     1  0.5098     0.8809 0.752 0.000 0.248
#> SRR975603     3  0.0000     0.7550 0.000 0.000 1.000
#> SRR975604     3  0.0000     0.7550 0.000 0.000 1.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> SRR975551     1  0.0000     0.7726 1.000 0.000 0.000 0.000
#> SRR975552     1  0.0000     0.7726 1.000 0.000 0.000 0.000
#> SRR975554     1  0.0000     0.7726 1.000 0.000 0.000 0.000
#> SRR975553     2  0.2596     0.8944 0.000 0.908 0.024 0.068
#> SRR975555     1  0.0000     0.7726 1.000 0.000 0.000 0.000
#> SRR975556     2  0.0000     0.9095 0.000 1.000 0.000 0.000
#> SRR975557     4  0.6563     0.2919 0.208 0.000 0.160 0.632
#> SRR975558     1  0.5155     0.1263 0.528 0.000 0.004 0.468
#> SRR975559     1  0.3444     0.6672 0.816 0.000 0.000 0.184
#> SRR975560     2  0.4977     0.0801 0.000 0.540 0.000 0.460
#> SRR975561     2  0.4431     0.5219 0.000 0.696 0.000 0.304
#> SRR975562     1  0.1474     0.7549 0.948 0.000 0.000 0.052
#> SRR975563     2  0.0000     0.9095 0.000 1.000 0.000 0.000
#> SRR975564     1  0.0000     0.7726 1.000 0.000 0.000 0.000
#> SRR975565     1  0.0000     0.7726 1.000 0.000 0.000 0.000
#> SRR975566     1  0.1557     0.7583 0.944 0.000 0.000 0.056
#> SRR975567     1  0.5155     0.1263 0.528 0.000 0.004 0.468
#> SRR975568     1  0.0000     0.7726 1.000 0.000 0.000 0.000
#> SRR975569     2  0.0188     0.9094 0.000 0.996 0.004 0.000
#> SRR975570     2  0.0188     0.9094 0.000 0.996 0.004 0.000
#> SRR975571     2  0.2596     0.8944 0.000 0.908 0.024 0.068
#> SRR975572     2  0.0000     0.9095 0.000 1.000 0.000 0.000
#> SRR975573     2  0.2596     0.8944 0.000 0.908 0.024 0.068
#> SRR975574     2  0.2596     0.8944 0.000 0.908 0.024 0.068
#> SRR975575     2  0.0000     0.9095 0.000 1.000 0.000 0.000
#> SRR975576     2  0.0000     0.9095 0.000 1.000 0.000 0.000
#> SRR975577     2  0.2596     0.8944 0.000 0.908 0.024 0.068
#> SRR975578     2  0.2596     0.8944 0.000 0.908 0.024 0.068
#> SRR975579     4  0.5546     0.3825 0.000 0.292 0.044 0.664
#> SRR975580     2  0.2868     0.8342 0.000 0.864 0.000 0.136
#> SRR975581     2  0.0000     0.9095 0.000 1.000 0.000 0.000
#> SRR975582     2  0.2596     0.8944 0.000 0.908 0.024 0.068
#> SRR975583     2  0.0000     0.9095 0.000 1.000 0.000 0.000
#> SRR975584     2  0.2596     0.8944 0.000 0.908 0.024 0.068
#> SRR975585     2  0.0000     0.9095 0.000 1.000 0.000 0.000
#> SRR975586     2  0.2345     0.8303 0.000 0.900 0.000 0.100
#> SRR975587     3  0.3071     0.7970 0.068 0.000 0.888 0.044
#> SRR975588     2  0.0188     0.9094 0.000 0.996 0.004 0.000
#> SRR975589     3  0.6730     0.6168 0.276 0.000 0.592 0.132
#> SRR975590     3  0.7379     0.3850 0.364 0.000 0.468 0.168
#> SRR975591     3  0.1792     0.8041 0.068 0.000 0.932 0.000
#> SRR975592     3  0.6274     0.7091 0.184 0.000 0.664 0.152
#> SRR975593     3  0.6730     0.6168 0.276 0.000 0.592 0.132
#> SRR975594     3  0.2775     0.7224 0.020 0.000 0.896 0.084
#> SRR975595     1  0.7099     0.1741 0.552 0.000 0.280 0.168
#> SRR975597     1  0.7099     0.1741 0.552 0.000 0.280 0.168
#> SRR975596     1  0.3444     0.6672 0.816 0.000 0.000 0.184
#> SRR975598     1  0.7099     0.1741 0.552 0.000 0.280 0.168
#> SRR975599     1  0.5339     0.5115 0.688 0.000 0.040 0.272
#> SRR975600     3  0.3398     0.7958 0.068 0.000 0.872 0.060
#> SRR975601     3  0.3071     0.7970 0.068 0.000 0.888 0.044
#> SRR975602     1  0.2530     0.7238 0.888 0.000 0.000 0.112
#> SRR975603     3  0.1792     0.8041 0.068 0.000 0.932 0.000
#> SRR975604     3  0.1792     0.8041 0.068 0.000 0.932 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
#> SRR975551     1  0.0162     0.6907 0.996 0.000 0.000 0.000 NA
#> SRR975552     1  0.0324     0.6915 0.992 0.000 0.000 0.004 NA
#> SRR975554     1  0.1082     0.6900 0.964 0.000 0.000 0.008 NA
#> SRR975553     2  0.4003     0.7431 0.000 0.704 0.000 0.008 NA
#> SRR975555     1  0.1106     0.6880 0.964 0.000 0.000 0.012 NA
#> SRR975556     2  0.0898     0.7992 0.000 0.972 0.000 0.008 NA
#> SRR975557     4  0.4308     0.6762 0.104 0.000 0.040 0.804 NA
#> SRR975558     1  0.6696    -0.0634 0.388 0.000 0.000 0.372 NA
#> SRR975559     1  0.5107     0.5572 0.688 0.000 0.000 0.108 NA
#> SRR975560     2  0.6534     0.1266 0.000 0.460 0.000 0.328 NA
#> SRR975561     2  0.5197     0.5221 0.000 0.680 0.000 0.204 NA
#> SRR975562     1  0.3656     0.6384 0.800 0.000 0.000 0.032 NA
#> SRR975563     2  0.0000     0.8129 0.000 1.000 0.000 0.000 NA
#> SRR975564     1  0.1670     0.6858 0.936 0.000 0.000 0.012 NA
#> SRR975565     1  0.0324     0.6913 0.992 0.000 0.000 0.004 NA
#> SRR975566     1  0.3844     0.6376 0.792 0.000 0.000 0.044 NA
#> SRR975567     1  0.6696    -0.0634 0.388 0.000 0.000 0.372 NA
#> SRR975568     1  0.1012     0.6884 0.968 0.000 0.000 0.012 NA
#> SRR975569     2  0.0290     0.8130 0.000 0.992 0.000 0.000 NA
#> SRR975570     2  0.0290     0.8130 0.000 0.992 0.000 0.000 NA
#> SRR975571     2  0.4003     0.7431 0.000 0.704 0.000 0.008 NA
#> SRR975572     2  0.0000     0.8129 0.000 1.000 0.000 0.000 NA
#> SRR975573     2  0.3730     0.7469 0.000 0.712 0.000 0.000 NA
#> SRR975574     2  0.3730     0.7469 0.000 0.712 0.000 0.000 NA
#> SRR975575     2  0.0000     0.8129 0.000 1.000 0.000 0.000 NA
#> SRR975576     2  0.0000     0.8129 0.000 1.000 0.000 0.000 NA
#> SRR975577     2  0.3730     0.7469 0.000 0.712 0.000 0.000 NA
#> SRR975578     2  0.3730     0.7469 0.000 0.712 0.000 0.000 NA
#> SRR975579     4  0.2588     0.7165 0.000 0.100 0.008 0.884 NA
#> SRR975580     2  0.5264     0.6221 0.000 0.676 0.000 0.128 NA
#> SRR975581     2  0.0000     0.8129 0.000 1.000 0.000 0.000 NA
#> SRR975582     2  0.3730     0.7469 0.000 0.712 0.000 0.000 NA
#> SRR975583     2  0.0000     0.8129 0.000 1.000 0.000 0.000 NA
#> SRR975584     2  0.3730     0.7469 0.000 0.712 0.000 0.000 NA
#> SRR975585     2  0.0000     0.8129 0.000 1.000 0.000 0.000 NA
#> SRR975586     2  0.4450     0.6282 0.000 0.760 0.000 0.132 NA
#> SRR975587     3  0.3210     0.7474 0.008 0.000 0.860 0.040 NA
#> SRR975588     2  0.0290     0.8130 0.000 0.992 0.000 0.000 NA
#> SRR975589     3  0.5814     0.6080 0.136 0.000 0.652 0.016 NA
#> SRR975590     3  0.6902     0.1891 0.324 0.000 0.392 0.004 NA
#> SRR975591     3  0.0290     0.7749 0.008 0.000 0.992 0.000 NA
#> SRR975592     3  0.4818     0.6767 0.100 0.000 0.720 0.000 NA
#> SRR975593     3  0.5814     0.6080 0.136 0.000 0.652 0.016 NA
#> SRR975594     3  0.3579     0.7085 0.000 0.000 0.828 0.072 NA
#> SRR975595     1  0.6665     0.1948 0.480 0.000 0.244 0.004 NA
#> SRR975597     1  0.6665     0.1948 0.480 0.000 0.244 0.004 NA
#> SRR975596     1  0.5197     0.5486 0.680 0.000 0.000 0.116 NA
#> SRR975598     1  0.6665     0.1948 0.480 0.000 0.244 0.004 NA
#> SRR975599     1  0.6280     0.3902 0.560 0.000 0.008 0.160 NA
#> SRR975600     3  0.1628     0.7679 0.008 0.000 0.936 0.000 NA
#> SRR975601     3  0.3229     0.7465 0.008 0.000 0.860 0.044 NA
#> SRR975602     1  0.4104     0.5870 0.748 0.000 0.000 0.032 NA
#> SRR975603     3  0.0290     0.7749 0.008 0.000 0.992 0.000 NA
#> SRR975604     3  0.0290     0.7749 0.008 0.000 0.992 0.000 NA

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4 p5    p6
#> SRR975551     1  0.0000     0.6382 1.000 0.000 0.000 0.000 NA 0.000
#> SRR975552     1  0.0146     0.6383 0.996 0.000 0.000 0.000 NA 0.004
#> SRR975554     1  0.1909     0.6283 0.920 0.000 0.000 0.004 NA 0.052
#> SRR975553     2  0.4169     0.5570 0.000 0.532 0.000 0.012 NA 0.000
#> SRR975555     1  0.1003     0.6333 0.964 0.000 0.000 0.004 NA 0.028
#> SRR975556     2  0.2803     0.5613 0.000 0.872 0.000 0.012 NA 0.052
#> SRR975557     4  0.3390     0.7994 0.032 0.000 0.008 0.808 NA 0.152
#> SRR975558     6  0.3473     0.2404 0.192 0.000 0.004 0.024 NA 0.780
#> SRR975559     1  0.6042     0.4033 0.532 0.000 0.004 0.108 NA 0.320
#> SRR975560     6  0.5610     0.3060 0.004 0.252 0.000 0.016 NA 0.600
#> SRR975561     2  0.5454    -0.2994 0.000 0.460 0.000 0.020 NA 0.452
#> SRR975562     1  0.5304     0.4770 0.620 0.000 0.000 0.060 NA 0.280
#> SRR975563     2  0.0291     0.6778 0.000 0.992 0.000 0.004 NA 0.000
#> SRR975564     1  0.2214     0.6170 0.892 0.000 0.000 0.004 NA 0.092
#> SRR975565     1  0.0551     0.6368 0.984 0.000 0.000 0.004 NA 0.008
#> SRR975566     1  0.5469     0.5087 0.640 0.000 0.004 0.096 NA 0.228
#> SRR975567     6  0.3534     0.2405 0.200 0.000 0.004 0.024 NA 0.772
#> SRR975568     1  0.1080     0.6330 0.960 0.000 0.000 0.004 NA 0.032
#> SRR975569     2  0.0260     0.6819 0.000 0.992 0.000 0.000 NA 0.000
#> SRR975570     2  0.0260     0.6819 0.000 0.992 0.000 0.000 NA 0.000
#> SRR975571     2  0.4169     0.5570 0.000 0.532 0.000 0.012 NA 0.000
#> SRR975572     2  0.0146     0.6802 0.000 0.996 0.000 0.004 NA 0.000
#> SRR975573     2  0.3851     0.5645 0.000 0.540 0.000 0.000 NA 0.000
#> SRR975574     2  0.3851     0.5645 0.000 0.540 0.000 0.000 NA 0.000
#> SRR975575     2  0.0146     0.6802 0.000 0.996 0.000 0.004 NA 0.000
#> SRR975576     2  0.0000     0.6812 0.000 1.000 0.000 0.000 NA 0.000
#> SRR975577     2  0.3851     0.5645 0.000 0.540 0.000 0.000 NA 0.000
#> SRR975578     2  0.3851     0.5645 0.000 0.540 0.000 0.000 NA 0.000
#> SRR975579     4  0.3678     0.7855 0.000 0.016 0.000 0.748 NA 0.228
#> SRR975580     6  0.6181     0.0654 0.000 0.396 0.000 0.016 NA 0.408
#> SRR975581     2  0.0146     0.6802 0.000 0.996 0.000 0.004 NA 0.000
#> SRR975582     2  0.3851     0.5645 0.000 0.540 0.000 0.000 NA 0.000
#> SRR975583     2  0.0146     0.6802 0.000 0.996 0.000 0.004 NA 0.000
#> SRR975584     2  0.3851     0.5645 0.000 0.540 0.000 0.000 NA 0.000
#> SRR975585     2  0.0000     0.6812 0.000 1.000 0.000 0.000 NA 0.000
#> SRR975586     2  0.5358    -0.1037 0.000 0.544 0.000 0.020 NA 0.368
#> SRR975587     3  0.2979     0.7452 0.000 0.000 0.868 0.044 NA 0.036
#> SRR975588     2  0.0260     0.6819 0.000 0.992 0.000 0.000 NA 0.000
#> SRR975589     3  0.7006     0.5061 0.064 0.000 0.544 0.068 NA 0.224
#> SRR975590     1  0.7900     0.0190 0.316 0.000 0.280 0.060 NA 0.060
#> SRR975591     3  0.0000     0.7786 0.000 0.000 1.000 0.000 NA 0.000
#> SRR975592     3  0.6089     0.5980 0.088 0.000 0.648 0.048 NA 0.052
#> SRR975593     3  0.7006     0.5061 0.064 0.000 0.544 0.068 NA 0.224
#> SRR975594     3  0.4235     0.6787 0.000 0.000 0.780 0.064 NA 0.052
#> SRR975595     1  0.7595     0.2593 0.400 0.000 0.196 0.060 NA 0.048
#> SRR975597     1  0.7539     0.2632 0.408 0.000 0.196 0.060 NA 0.044
#> SRR975596     1  0.6100     0.4000 0.528 0.000 0.004 0.108 NA 0.320
#> SRR975598     1  0.7595     0.2593 0.400 0.000 0.196 0.060 NA 0.048
#> SRR975599     1  0.6868     0.2921 0.452 0.000 0.000 0.120 NA 0.120
#> SRR975600     3  0.2345     0.7562 0.000 0.000 0.904 0.028 NA 0.028
#> SRR975601     3  0.2985     0.7435 0.000 0.000 0.868 0.048 NA 0.040
#> SRR975602     1  0.5389     0.5221 0.664 0.000 0.000 0.060 NA 0.084
#> SRR975603     3  0.0000     0.7786 0.000 0.000 1.000 0.000 NA 0.000
#> SRR975604     3  0.0000     0.7786 0.000 0.000 1.000 0.000 NA 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-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

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 17171 rows and 54 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#>   Subgroups are detected by 'skmeans' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 4.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk SD-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           0.970       0.988         0.5056 0.497   0.497
#> 3 3 0.925           0.926       0.966         0.3025 0.843   0.685
#> 4 4 0.902           0.861       0.937         0.0885 0.918   0.769
#> 5 5 0.815           0.695       0.838         0.0513 0.979   0.927
#> 6 6 0.722           0.600       0.732         0.0442 0.943   0.794

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 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
#> SRR975551     1   0.000      0.977 1.000 0.000
#> SRR975552     1   0.000      0.977 1.000 0.000
#> SRR975554     1   0.000      0.977 1.000 0.000
#> SRR975553     2   0.000      1.000 0.000 1.000
#> SRR975555     1   0.000      0.977 1.000 0.000
#> SRR975556     2   0.000      1.000 0.000 1.000
#> SRR975557     1   0.000      0.977 1.000 0.000
#> SRR975558     1   0.955      0.417 0.624 0.376
#> SRR975559     1   0.000      0.977 1.000 0.000
#> SRR975560     2   0.000      1.000 0.000 1.000
#> SRR975561     2   0.000      1.000 0.000 1.000
#> SRR975562     1   0.000      0.977 1.000 0.000
#> SRR975563     2   0.000      1.000 0.000 1.000
#> SRR975564     1   0.000      0.977 1.000 0.000
#> SRR975565     1   0.000      0.977 1.000 0.000
#> SRR975566     1   0.000      0.977 1.000 0.000
#> SRR975567     1   0.866      0.604 0.712 0.288
#> SRR975568     1   0.000      0.977 1.000 0.000
#> SRR975569     2   0.000      1.000 0.000 1.000
#> SRR975570     2   0.000      1.000 0.000 1.000
#> SRR975571     2   0.000      1.000 0.000 1.000
#> SRR975572     2   0.000      1.000 0.000 1.000
#> SRR975573     2   0.000      1.000 0.000 1.000
#> SRR975574     2   0.000      1.000 0.000 1.000
#> SRR975575     2   0.000      1.000 0.000 1.000
#> SRR975576     2   0.000      1.000 0.000 1.000
#> SRR975577     2   0.000      1.000 0.000 1.000
#> SRR975578     2   0.000      1.000 0.000 1.000
#> SRR975579     2   0.000      1.000 0.000 1.000
#> SRR975580     2   0.000      1.000 0.000 1.000
#> SRR975581     2   0.000      1.000 0.000 1.000
#> SRR975582     2   0.000      1.000 0.000 1.000
#> SRR975583     2   0.000      1.000 0.000 1.000
#> SRR975584     2   0.000      1.000 0.000 1.000
#> SRR975585     2   0.000      1.000 0.000 1.000
#> SRR975586     2   0.000      1.000 0.000 1.000
#> SRR975587     1   0.000      0.977 1.000 0.000
#> SRR975588     2   0.000      1.000 0.000 1.000
#> SRR975589     1   0.000      0.977 1.000 0.000
#> SRR975590     1   0.000      0.977 1.000 0.000
#> SRR975591     1   0.000      0.977 1.000 0.000
#> SRR975592     1   0.000      0.977 1.000 0.000
#> SRR975593     1   0.000      0.977 1.000 0.000
#> SRR975594     1   0.000      0.977 1.000 0.000
#> SRR975595     1   0.000      0.977 1.000 0.000
#> SRR975597     1   0.000      0.977 1.000 0.000
#> SRR975596     1   0.000      0.977 1.000 0.000
#> SRR975598     1   0.000      0.977 1.000 0.000
#> SRR975599     1   0.000      0.977 1.000 0.000
#> SRR975600     1   0.000      0.977 1.000 0.000
#> SRR975601     1   0.000      0.977 1.000 0.000
#> SRR975602     1   0.000      0.977 1.000 0.000
#> SRR975603     1   0.000      0.977 1.000 0.000
#> SRR975604     1   0.000      0.977 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
#> SRR975551     1  0.0000      1.000 1.000  0 0.000
#> SRR975552     1  0.0000      1.000 1.000  0 0.000
#> SRR975554     1  0.0000      1.000 1.000  0 0.000
#> SRR975553     2  0.0000      1.000 0.000  1 0.000
#> SRR975555     1  0.0000      1.000 1.000  0 0.000
#> SRR975556     2  0.0000      1.000 0.000  1 0.000
#> SRR975557     3  0.6062      0.380 0.384  0 0.616
#> SRR975558     1  0.0000      1.000 1.000  0 0.000
#> SRR975559     1  0.0000      1.000 1.000  0 0.000
#> SRR975560     2  0.0000      1.000 0.000  1 0.000
#> SRR975561     2  0.0000      1.000 0.000  1 0.000
#> SRR975562     1  0.0000      1.000 1.000  0 0.000
#> SRR975563     2  0.0000      1.000 0.000  1 0.000
#> SRR975564     1  0.0000      1.000 1.000  0 0.000
#> SRR975565     1  0.0000      1.000 1.000  0 0.000
#> SRR975566     1  0.0000      1.000 1.000  0 0.000
#> SRR975567     1  0.0000      1.000 1.000  0 0.000
#> SRR975568     1  0.0000      1.000 1.000  0 0.000
#> SRR975569     2  0.0000      1.000 0.000  1 0.000
#> SRR975570     2  0.0000      1.000 0.000  1 0.000
#> SRR975571     2  0.0000      1.000 0.000  1 0.000
#> SRR975572     2  0.0000      1.000 0.000  1 0.000
#> SRR975573     2  0.0000      1.000 0.000  1 0.000
#> SRR975574     2  0.0000      1.000 0.000  1 0.000
#> SRR975575     2  0.0000      1.000 0.000  1 0.000
#> SRR975576     2  0.0000      1.000 0.000  1 0.000
#> SRR975577     2  0.0000      1.000 0.000  1 0.000
#> SRR975578     2  0.0000      1.000 0.000  1 0.000
#> SRR975579     2  0.0000      1.000 0.000  1 0.000
#> SRR975580     2  0.0000      1.000 0.000  1 0.000
#> SRR975581     2  0.0000      1.000 0.000  1 0.000
#> SRR975582     2  0.0000      1.000 0.000  1 0.000
#> SRR975583     2  0.0000      1.000 0.000  1 0.000
#> SRR975584     2  0.0000      1.000 0.000  1 0.000
#> SRR975585     2  0.0000      1.000 0.000  1 0.000
#> SRR975586     2  0.0000      1.000 0.000  1 0.000
#> SRR975587     3  0.0000      0.868 0.000  0 1.000
#> SRR975588     2  0.0000      1.000 0.000  1 0.000
#> SRR975589     3  0.0747      0.865 0.016  0 0.984
#> SRR975590     3  0.4654      0.725 0.208  0 0.792
#> SRR975591     3  0.0000      0.868 0.000  0 1.000
#> SRR975592     3  0.0592      0.866 0.012  0 0.988
#> SRR975593     3  0.0592      0.866 0.012  0 0.988
#> SRR975594     3  0.0000      0.868 0.000  0 1.000
#> SRR975595     3  0.6126      0.464 0.400  0 0.600
#> SRR975597     3  0.6126      0.464 0.400  0 0.600
#> SRR975596     1  0.0000      1.000 1.000  0 0.000
#> SRR975598     3  0.6126      0.464 0.400  0 0.600
#> SRR975599     3  0.1031      0.858 0.024  0 0.976
#> SRR975600     3  0.0000      0.868 0.000  0 1.000
#> SRR975601     3  0.0000      0.868 0.000  0 1.000
#> SRR975602     1  0.0000      1.000 1.000  0 0.000
#> SRR975603     3  0.0000      0.868 0.000  0 1.000
#> SRR975604     3  0.0000      0.868 0.000  0 1.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> SRR975551     1  0.0000      0.897 1.000 0.000 0.000 0.000
#> SRR975552     1  0.0000      0.897 1.000 0.000 0.000 0.000
#> SRR975554     1  0.0000      0.897 1.000 0.000 0.000 0.000
#> SRR975553     2  0.0336      0.982 0.000 0.992 0.000 0.008
#> SRR975555     1  0.0000      0.897 1.000 0.000 0.000 0.000
#> SRR975556     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975557     4  0.2676      0.862 0.092 0.000 0.012 0.896
#> SRR975558     4  0.1792      0.897 0.068 0.000 0.000 0.932
#> SRR975559     1  0.4804      0.345 0.616 0.000 0.000 0.384
#> SRR975560     4  0.1792      0.876 0.000 0.068 0.000 0.932
#> SRR975561     2  0.3610      0.751 0.000 0.800 0.000 0.200
#> SRR975562     1  0.0817      0.883 0.976 0.000 0.000 0.024
#> SRR975563     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975564     1  0.0000      0.897 1.000 0.000 0.000 0.000
#> SRR975565     1  0.0000      0.897 1.000 0.000 0.000 0.000
#> SRR975566     1  0.0469      0.891 0.988 0.000 0.000 0.012
#> SRR975567     4  0.1792      0.897 0.068 0.000 0.000 0.932
#> SRR975568     1  0.0000      0.897 1.000 0.000 0.000 0.000
#> SRR975569     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975570     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975571     2  0.0336      0.982 0.000 0.992 0.000 0.008
#> SRR975572     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975573     2  0.0336      0.982 0.000 0.992 0.000 0.008
#> SRR975574     2  0.0336      0.982 0.000 0.992 0.000 0.008
#> SRR975575     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975576     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975577     2  0.0336      0.982 0.000 0.992 0.000 0.008
#> SRR975578     2  0.0336      0.982 0.000 0.992 0.000 0.008
#> SRR975579     4  0.2401      0.864 0.000 0.092 0.004 0.904
#> SRR975580     2  0.0336      0.982 0.000 0.992 0.000 0.008
#> SRR975581     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975582     2  0.0336      0.982 0.000 0.992 0.000 0.008
#> SRR975583     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975584     2  0.0336      0.982 0.000 0.992 0.000 0.008
#> SRR975585     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975586     2  0.1867      0.917 0.000 0.928 0.000 0.072
#> SRR975587     3  0.0000      0.850 0.000 0.000 1.000 0.000
#> SRR975588     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975589     3  0.1059      0.841 0.016 0.000 0.972 0.012
#> SRR975590     3  0.4331      0.646 0.288 0.000 0.712 0.000
#> SRR975591     3  0.0000      0.850 0.000 0.000 1.000 0.000
#> SRR975592     3  0.0188      0.850 0.004 0.000 0.996 0.000
#> SRR975593     3  0.0657      0.845 0.004 0.000 0.984 0.012
#> SRR975594     3  0.0469      0.844 0.000 0.000 0.988 0.012
#> SRR975595     3  0.4916      0.455 0.424 0.000 0.576 0.000
#> SRR975597     3  0.4916      0.455 0.424 0.000 0.576 0.000
#> SRR975596     1  0.4817      0.335 0.612 0.000 0.000 0.388
#> SRR975598     3  0.4933      0.438 0.432 0.000 0.568 0.000
#> SRR975599     1  0.4761      0.659 0.764 0.000 0.192 0.044
#> SRR975600     3  0.0000      0.850 0.000 0.000 1.000 0.000
#> SRR975601     3  0.0000      0.850 0.000 0.000 1.000 0.000
#> SRR975602     1  0.0000      0.897 1.000 0.000 0.000 0.000
#> SRR975603     3  0.0000      0.850 0.000 0.000 1.000 0.000
#> SRR975604     3  0.0000      0.850 0.000 0.000 1.000 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
#> SRR975551     1  0.0404     0.7622 0.988 0.000 0.000 0.000 0.012
#> SRR975552     1  0.0162     0.7664 0.996 0.000 0.000 0.000 0.004
#> SRR975554     1  0.0794     0.7655 0.972 0.000 0.000 0.000 0.028
#> SRR975553     2  0.1851     0.9018 0.000 0.912 0.000 0.000 0.088
#> SRR975555     1  0.1041     0.7548 0.964 0.000 0.000 0.004 0.032
#> SRR975556     2  0.1485     0.8812 0.000 0.948 0.000 0.032 0.020
#> SRR975557     4  0.4295     0.1097 0.032 0.000 0.012 0.760 0.196
#> SRR975558     5  0.5525     0.9863 0.124 0.000 0.000 0.240 0.636
#> SRR975559     1  0.5032     0.1287 0.520 0.000 0.000 0.032 0.448
#> SRR975560     4  0.4227     0.1383 0.000 0.016 0.000 0.692 0.292
#> SRR975561     4  0.4900     0.1029 0.000 0.464 0.000 0.512 0.024
#> SRR975562     1  0.3928     0.5525 0.700 0.000 0.000 0.004 0.296
#> SRR975563     2  0.0162     0.9143 0.000 0.996 0.000 0.004 0.000
#> SRR975564     1  0.1357     0.7586 0.948 0.000 0.000 0.004 0.048
#> SRR975565     1  0.0566     0.7664 0.984 0.000 0.000 0.004 0.012
#> SRR975566     1  0.3508     0.5947 0.748 0.000 0.000 0.000 0.252
#> SRR975567     5  0.5531     0.9862 0.120 0.000 0.000 0.248 0.632
#> SRR975568     1  0.0955     0.7652 0.968 0.000 0.000 0.004 0.028
#> SRR975569     2  0.0000     0.9145 0.000 1.000 0.000 0.000 0.000
#> SRR975570     2  0.0000     0.9145 0.000 1.000 0.000 0.000 0.000
#> SRR975571     2  0.1851     0.9018 0.000 0.912 0.000 0.000 0.088
#> SRR975572     2  0.0162     0.9143 0.000 0.996 0.000 0.004 0.000
#> SRR975573     2  0.1851     0.9018 0.000 0.912 0.000 0.000 0.088
#> SRR975574     2  0.1851     0.9018 0.000 0.912 0.000 0.000 0.088
#> SRR975575     2  0.0162     0.9143 0.000 0.996 0.000 0.004 0.000
#> SRR975576     2  0.0162     0.9143 0.000 0.996 0.000 0.004 0.000
#> SRR975577     2  0.1851     0.9018 0.000 0.912 0.000 0.000 0.088
#> SRR975578     2  0.1851     0.9018 0.000 0.912 0.000 0.000 0.088
#> SRR975579     4  0.2104     0.3985 0.000 0.060 0.000 0.916 0.024
#> SRR975580     2  0.4528     0.7364 0.000 0.752 0.000 0.144 0.104
#> SRR975581     2  0.0162     0.9143 0.000 0.996 0.000 0.004 0.000
#> SRR975582     2  0.1851     0.9018 0.000 0.912 0.000 0.000 0.088
#> SRR975583     2  0.0162     0.9143 0.000 0.996 0.000 0.004 0.000
#> SRR975584     2  0.1851     0.9018 0.000 0.912 0.000 0.000 0.088
#> SRR975585     2  0.0162     0.9143 0.000 0.996 0.000 0.004 0.000
#> SRR975586     2  0.4861    -0.0591 0.000 0.548 0.000 0.428 0.024
#> SRR975587     3  0.0510     0.7789 0.000 0.000 0.984 0.000 0.016
#> SRR975588     2  0.0000     0.9145 0.000 1.000 0.000 0.000 0.000
#> SRR975589     3  0.3086     0.6720 0.004 0.000 0.816 0.000 0.180
#> SRR975590     3  0.5864     0.5285 0.300 0.000 0.572 0.000 0.128
#> SRR975591     3  0.0000     0.7791 0.000 0.000 1.000 0.000 0.000
#> SRR975592     3  0.1582     0.7703 0.028 0.000 0.944 0.000 0.028
#> SRR975593     3  0.2891     0.6782 0.000 0.000 0.824 0.000 0.176
#> SRR975594     3  0.1300     0.7692 0.000 0.000 0.956 0.028 0.016
#> SRR975595     3  0.6567     0.3638 0.360 0.000 0.432 0.000 0.208
#> SRR975597     3  0.6567     0.3638 0.360 0.000 0.432 0.000 0.208
#> SRR975596     1  0.5100     0.1169 0.516 0.000 0.000 0.036 0.448
#> SRR975598     3  0.6582     0.3284 0.376 0.000 0.416 0.000 0.208
#> SRR975599     1  0.7572     0.3331 0.500 0.000 0.104 0.168 0.228
#> SRR975600     3  0.0000     0.7791 0.000 0.000 1.000 0.000 0.000
#> SRR975601     3  0.0510     0.7789 0.000 0.000 0.984 0.000 0.016
#> SRR975602     1  0.3003     0.6518 0.812 0.000 0.000 0.000 0.188
#> SRR975603     3  0.0000     0.7791 0.000 0.000 1.000 0.000 0.000
#> SRR975604     3  0.0000     0.7791 0.000 0.000 1.000 0.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> SRR975551     1  0.1141      0.715 0.948 0.000 0.000 0.000 0.052 0.000
#> SRR975552     1  0.1010      0.726 0.960 0.000 0.000 0.000 0.036 0.004
#> SRR975554     1  0.0865      0.729 0.964 0.000 0.000 0.000 0.036 0.000
#> SRR975553     2  0.0000      0.724 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975555     1  0.1812      0.702 0.912 0.000 0.000 0.000 0.080 0.008
#> SRR975556     2  0.3864      0.385 0.000 0.520 0.000 0.000 0.000 0.480
#> SRR975557     4  0.0551      0.827 0.000 0.000 0.004 0.984 0.008 0.004
#> SRR975558     5  0.6812     -0.108 0.048 0.000 0.008 0.180 0.436 0.328
#> SRR975559     1  0.7088      0.324 0.436 0.000 0.000 0.140 0.284 0.140
#> SRR975560     6  0.5409     -0.247 0.000 0.008 0.000 0.176 0.204 0.612
#> SRR975561     6  0.5542      0.526 0.000 0.232 0.000 0.188 0.004 0.576
#> SRR975562     1  0.6206      0.451 0.552 0.000 0.000 0.056 0.252 0.140
#> SRR975563     2  0.3330      0.751 0.000 0.716 0.000 0.000 0.000 0.284
#> SRR975564     1  0.2019      0.715 0.900 0.000 0.000 0.000 0.088 0.012
#> SRR975565     1  0.0632      0.727 0.976 0.000 0.000 0.000 0.024 0.000
#> SRR975566     1  0.4372      0.628 0.744 0.000 0.000 0.040 0.176 0.040
#> SRR975567     5  0.6716     -0.105 0.048 0.000 0.004 0.180 0.440 0.328
#> SRR975568     1  0.1434      0.719 0.940 0.000 0.000 0.000 0.048 0.012
#> SRR975569     2  0.3266      0.761 0.000 0.728 0.000 0.000 0.000 0.272
#> SRR975570     2  0.3266      0.761 0.000 0.728 0.000 0.000 0.000 0.272
#> SRR975571     2  0.0000      0.724 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975572     2  0.3266      0.761 0.000 0.728 0.000 0.000 0.000 0.272
#> SRR975573     2  0.0000      0.724 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975574     2  0.0000      0.724 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975575     2  0.3266      0.761 0.000 0.728 0.000 0.000 0.000 0.272
#> SRR975576     2  0.3309      0.755 0.000 0.720 0.000 0.000 0.000 0.280
#> SRR975577     2  0.0000      0.724 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975578     2  0.0000      0.724 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975579     4  0.2146      0.815 0.000 0.004 0.000 0.880 0.000 0.116
#> SRR975580     2  0.3872     -0.088 0.000 0.604 0.000 0.004 0.000 0.392
#> SRR975581     2  0.3288      0.758 0.000 0.724 0.000 0.000 0.000 0.276
#> SRR975582     2  0.0000      0.724 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975583     2  0.3266      0.761 0.000 0.728 0.000 0.000 0.000 0.272
#> SRR975584     2  0.0000      0.724 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975585     2  0.3266      0.761 0.000 0.728 0.000 0.000 0.000 0.272
#> SRR975586     6  0.4989      0.487 0.000 0.248 0.000 0.108 0.004 0.640
#> SRR975587     3  0.1806      0.842 0.000 0.000 0.908 0.000 0.088 0.004
#> SRR975588     2  0.3266      0.761 0.000 0.728 0.000 0.000 0.000 0.272
#> SRR975589     3  0.3182      0.774 0.012 0.000 0.852 0.016 0.096 0.024
#> SRR975590     3  0.5625      0.114 0.192 0.000 0.532 0.000 0.276 0.000
#> SRR975591     3  0.0000      0.862 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975592     3  0.1812      0.838 0.008 0.000 0.912 0.000 0.080 0.000
#> SRR975593     3  0.3131      0.773 0.008 0.000 0.852 0.016 0.100 0.024
#> SRR975594     3  0.2493      0.826 0.000 0.000 0.884 0.036 0.076 0.004
#> SRR975595     5  0.6034      0.290 0.260 0.000 0.328 0.000 0.412 0.000
#> SRR975597     5  0.6044      0.290 0.264 0.000 0.328 0.000 0.408 0.000
#> SRR975596     1  0.7198      0.319 0.432 0.000 0.004 0.136 0.288 0.140
#> SRR975598     5  0.6039      0.296 0.264 0.000 0.324 0.000 0.412 0.000
#> SRR975599     5  0.6740     -0.064 0.288 0.000 0.036 0.244 0.428 0.004
#> SRR975600     3  0.0000      0.862 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975601     3  0.2001      0.838 0.000 0.000 0.900 0.004 0.092 0.004
#> SRR975602     1  0.3508      0.493 0.704 0.000 0.000 0.004 0.292 0.000
#> SRR975603     3  0.0000      0.862 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975604     3  0.0000      0.862 0.000 0.000 1.000 0.000 0.000 0.000

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

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

consensus_heatmap(res, k = 2)

plot of chunk tab-SD-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

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 17171 rows and 54 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#>   Subgroups are detected by 'pam' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 4.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk SD-pam-collect-plots

The plots are:

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

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

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

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

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

select_partition_number(res)

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

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.961           0.948       0.978         0.5062 0.497   0.497
#> 3 3 0.940           0.891       0.959         0.2866 0.820   0.650
#> 4 4 0.961           0.936       0.971         0.1017 0.855   0.625
#> 5 5 0.892           0.785       0.894         0.0453 0.970   0.894
#> 6 6 0.845           0.789       0.893         0.0400 0.964   0.866

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

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

suggest_best_k(res)

#> [1] 4
#> 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
#> SRR975551     1   0.000      0.958 1.000 0.000
#> SRR975552     1   0.680      0.778 0.820 0.180
#> SRR975554     1   0.000      0.958 1.000 0.000
#> SRR975553     2   0.000      1.000 0.000 1.000
#> SRR975555     1   0.000      0.958 1.000 0.000
#> SRR975556     2   0.000      1.000 0.000 1.000
#> SRR975557     1   0.706      0.762 0.808 0.192
#> SRR975558     1   0.971      0.389 0.600 0.400
#> SRR975559     1   0.000      0.958 1.000 0.000
#> SRR975560     2   0.000      1.000 0.000 1.000
#> SRR975561     2   0.000      1.000 0.000 1.000
#> SRR975562     1   0.000      0.958 1.000 0.000
#> SRR975563     2   0.000      1.000 0.000 1.000
#> SRR975564     1   0.000      0.958 1.000 0.000
#> SRR975565     1   0.000      0.958 1.000 0.000
#> SRR975566     1   0.000      0.958 1.000 0.000
#> SRR975567     1   0.971      0.389 0.600 0.400
#> SRR975568     1   0.000      0.958 1.000 0.000
#> SRR975569     2   0.000      1.000 0.000 1.000
#> SRR975570     2   0.000      1.000 0.000 1.000
#> SRR975571     2   0.000      1.000 0.000 1.000
#> SRR975572     2   0.000      1.000 0.000 1.000
#> SRR975573     2   0.000      1.000 0.000 1.000
#> SRR975574     2   0.000      1.000 0.000 1.000
#> SRR975575     2   0.000      1.000 0.000 1.000
#> SRR975576     2   0.000      1.000 0.000 1.000
#> SRR975577     2   0.000      1.000 0.000 1.000
#> SRR975578     2   0.000      1.000 0.000 1.000
#> SRR975579     2   0.000      1.000 0.000 1.000
#> SRR975580     2   0.000      1.000 0.000 1.000
#> SRR975581     2   0.000      1.000 0.000 1.000
#> SRR975582     2   0.000      1.000 0.000 1.000
#> SRR975583     2   0.000      1.000 0.000 1.000
#> SRR975584     2   0.000      1.000 0.000 1.000
#> SRR975585     2   0.000      1.000 0.000 1.000
#> SRR975586     2   0.000      1.000 0.000 1.000
#> SRR975587     1   0.000      0.958 1.000 0.000
#> SRR975588     2   0.000      1.000 0.000 1.000
#> SRR975589     1   0.000      0.958 1.000 0.000
#> SRR975590     1   0.000      0.958 1.000 0.000
#> SRR975591     1   0.000      0.958 1.000 0.000
#> SRR975592     1   0.000      0.958 1.000 0.000
#> SRR975593     1   0.000      0.958 1.000 0.000
#> SRR975594     1   0.000      0.958 1.000 0.000
#> SRR975595     1   0.000      0.958 1.000 0.000
#> SRR975597     1   0.000      0.958 1.000 0.000
#> SRR975596     1   0.000      0.958 1.000 0.000
#> SRR975598     1   0.000      0.958 1.000 0.000
#> SRR975599     1   0.163      0.939 0.976 0.024
#> SRR975600     1   0.000      0.958 1.000 0.000
#> SRR975601     1   0.000      0.958 1.000 0.000
#> SRR975602     1   0.000      0.958 1.000 0.000
#> SRR975603     1   0.000      0.958 1.000 0.000
#> SRR975604     1   0.000      0.958 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
#> SRR975551     1  0.0000      0.929 1.000 0.000 0.000
#> SRR975552     1  0.0000      0.929 1.000 0.000 0.000
#> SRR975554     1  0.0000      0.929 1.000 0.000 0.000
#> SRR975553     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975555     1  0.0000      0.929 1.000 0.000 0.000
#> SRR975556     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975557     3  0.6126      0.292 0.400 0.000 0.600
#> SRR975558     2  0.6225      0.233 0.432 0.568 0.000
#> SRR975559     1  0.0000      0.929 1.000 0.000 0.000
#> SRR975560     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975561     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975562     1  0.0000      0.929 1.000 0.000 0.000
#> SRR975563     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975564     1  0.0000      0.929 1.000 0.000 0.000
#> SRR975565     1  0.0000      0.929 1.000 0.000 0.000
#> SRR975566     1  0.0000      0.929 1.000 0.000 0.000
#> SRR975567     1  0.1529      0.891 0.960 0.040 0.000
#> SRR975568     1  0.0000      0.929 1.000 0.000 0.000
#> SRR975569     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975570     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975571     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975572     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975573     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975574     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975575     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975576     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975577     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975578     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975579     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975580     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975581     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975582     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975583     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975584     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975585     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975586     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975587     3  0.0000      0.918 0.000 0.000 1.000
#> SRR975588     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975589     3  0.0000      0.918 0.000 0.000 1.000
#> SRR975590     3  0.6111      0.283 0.396 0.000 0.604
#> SRR975591     3  0.0000      0.918 0.000 0.000 1.000
#> SRR975592     3  0.0424      0.912 0.008 0.000 0.992
#> SRR975593     3  0.0000      0.918 0.000 0.000 1.000
#> SRR975594     3  0.0000      0.918 0.000 0.000 1.000
#> SRR975595     1  0.5327      0.602 0.728 0.000 0.272
#> SRR975597     1  0.6026      0.373 0.624 0.000 0.376
#> SRR975596     1  0.0592      0.922 0.988 0.000 0.012
#> SRR975598     1  0.2625      0.862 0.916 0.000 0.084
#> SRR975599     1  0.5470      0.718 0.796 0.036 0.168
#> SRR975600     3  0.0000      0.918 0.000 0.000 1.000
#> SRR975601     3  0.0000      0.918 0.000 0.000 1.000
#> SRR975602     1  0.0000      0.929 1.000 0.000 0.000
#> SRR975603     3  0.0000      0.918 0.000 0.000 1.000
#> SRR975604     3  0.0000      0.918 0.000 0.000 1.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> SRR975551     4  0.3569      0.798 0.196 0.000 0.000 0.804
#> SRR975552     1  0.0000      0.931 1.000 0.000 0.000 0.000
#> SRR975554     1  0.0336      0.926 0.992 0.000 0.000 0.008
#> SRR975553     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975555     4  0.4898      0.420 0.416 0.000 0.000 0.584
#> SRR975556     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975557     1  0.0000      0.931 1.000 0.000 0.000 0.000
#> SRR975558     1  0.0524      0.924 0.988 0.008 0.000 0.004
#> SRR975559     1  0.0000      0.931 1.000 0.000 0.000 0.000
#> SRR975560     1  0.3610      0.690 0.800 0.200 0.000 0.000
#> SRR975561     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975562     1  0.0000      0.931 1.000 0.000 0.000 0.000
#> SRR975563     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975564     1  0.3444      0.700 0.816 0.000 0.000 0.184
#> SRR975565     1  0.0188      0.930 0.996 0.000 0.000 0.004
#> SRR975566     1  0.0000      0.931 1.000 0.000 0.000 0.000
#> SRR975567     1  0.0000      0.931 1.000 0.000 0.000 0.000
#> SRR975568     1  0.0188      0.930 0.996 0.000 0.000 0.004
#> SRR975569     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975570     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975571     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975572     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975573     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975574     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975575     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975576     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975577     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975578     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975579     1  0.3610      0.690 0.800 0.200 0.000 0.000
#> SRR975580     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975581     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975582     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975583     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975584     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975585     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975586     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975587     3  0.0000      0.996 0.000 0.000 1.000 0.000
#> SRR975588     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975589     3  0.0000      0.996 0.000 0.000 1.000 0.000
#> SRR975590     4  0.0188      0.863 0.000 0.000 0.004 0.996
#> SRR975591     3  0.0000      0.996 0.000 0.000 1.000 0.000
#> SRR975592     3  0.1022      0.964 0.000 0.000 0.968 0.032
#> SRR975593     3  0.0000      0.996 0.000 0.000 1.000 0.000
#> SRR975594     3  0.0000      0.996 0.000 0.000 1.000 0.000
#> SRR975595     4  0.0188      0.863 0.000 0.000 0.004 0.996
#> SRR975597     4  0.0188      0.863 0.000 0.000 0.004 0.996
#> SRR975596     1  0.0000      0.931 1.000 0.000 0.000 0.000
#> SRR975598     4  0.0188      0.863 0.000 0.000 0.004 0.996
#> SRR975599     4  0.1940      0.856 0.076 0.000 0.000 0.924
#> SRR975600     3  0.0000      0.996 0.000 0.000 1.000 0.000
#> SRR975601     3  0.0000      0.996 0.000 0.000 1.000 0.000
#> SRR975602     4  0.3610      0.797 0.200 0.000 0.000 0.800
#> SRR975603     3  0.0000      0.996 0.000 0.000 1.000 0.000
#> SRR975604     3  0.0000      0.996 0.000 0.000 1.000 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
#> SRR975551     5  0.3707      0.669 0.284 0.000 0.000 0.000 0.716
#> SRR975552     1  0.4359      0.533 0.584 0.000 0.000 0.412 0.004
#> SRR975554     1  0.1831      0.548 0.920 0.000 0.000 0.076 0.004
#> SRR975553     2  0.1671      0.945 0.000 0.924 0.000 0.076 0.000
#> SRR975555     1  0.4287     -0.440 0.540 0.000 0.000 0.000 0.460
#> SRR975556     2  0.0000      0.959 0.000 1.000 0.000 0.000 0.000
#> SRR975557     4  0.2179      0.428 0.112 0.000 0.000 0.888 0.000
#> SRR975558     1  0.4283      0.492 0.644 0.008 0.000 0.348 0.000
#> SRR975559     1  0.4015      0.592 0.652 0.000 0.000 0.348 0.000
#> SRR975560     1  0.5995      0.142 0.468 0.112 0.000 0.420 0.000
#> SRR975561     2  0.1043      0.936 0.000 0.960 0.000 0.040 0.000
#> SRR975562     1  0.4015      0.592 0.652 0.000 0.000 0.348 0.000
#> SRR975563     2  0.0000      0.959 0.000 1.000 0.000 0.000 0.000
#> SRR975564     1  0.3318      0.339 0.800 0.000 0.000 0.008 0.192
#> SRR975565     1  0.0162      0.528 0.996 0.000 0.000 0.000 0.004
#> SRR975566     1  0.3752      0.596 0.708 0.000 0.000 0.292 0.000
#> SRR975567     1  0.4283      0.486 0.544 0.000 0.000 0.456 0.000
#> SRR975568     1  0.0162      0.528 0.996 0.000 0.000 0.000 0.004
#> SRR975569     2  0.0000      0.959 0.000 1.000 0.000 0.000 0.000
#> SRR975570     2  0.0000      0.959 0.000 1.000 0.000 0.000 0.000
#> SRR975571     2  0.1671      0.945 0.000 0.924 0.000 0.076 0.000
#> SRR975572     2  0.0000      0.959 0.000 1.000 0.000 0.000 0.000
#> SRR975573     2  0.1671      0.945 0.000 0.924 0.000 0.076 0.000
#> SRR975574     2  0.1671      0.945 0.000 0.924 0.000 0.076 0.000
#> SRR975575     2  0.0000      0.959 0.000 1.000 0.000 0.000 0.000
#> SRR975576     2  0.0000      0.959 0.000 1.000 0.000 0.000 0.000
#> SRR975577     2  0.1671      0.945 0.000 0.924 0.000 0.076 0.000
#> SRR975578     2  0.1671      0.945 0.000 0.924 0.000 0.076 0.000
#> SRR975579     4  0.2377      0.555 0.000 0.128 0.000 0.872 0.000
#> SRR975580     2  0.2179      0.921 0.000 0.888 0.000 0.112 0.000
#> SRR975581     2  0.0000      0.959 0.000 1.000 0.000 0.000 0.000
#> SRR975582     2  0.1671      0.945 0.000 0.924 0.000 0.076 0.000
#> SRR975583     2  0.0000      0.959 0.000 1.000 0.000 0.000 0.000
#> SRR975584     2  0.1671      0.945 0.000 0.924 0.000 0.076 0.000
#> SRR975585     2  0.0000      0.959 0.000 1.000 0.000 0.000 0.000
#> SRR975586     2  0.0963      0.939 0.000 0.964 0.000 0.036 0.000
#> SRR975587     3  0.0000      0.996 0.000 0.000 1.000 0.000 0.000
#> SRR975588     2  0.0000      0.959 0.000 1.000 0.000 0.000 0.000
#> SRR975589     3  0.0000      0.996 0.000 0.000 1.000 0.000 0.000
#> SRR975590     5  0.0000      0.813 0.000 0.000 0.000 0.000 1.000
#> SRR975591     3  0.0000      0.996 0.000 0.000 1.000 0.000 0.000
#> SRR975592     3  0.0880      0.962 0.000 0.000 0.968 0.000 0.032
#> SRR975593     3  0.0000      0.996 0.000 0.000 1.000 0.000 0.000
#> SRR975594     3  0.0000      0.996 0.000 0.000 1.000 0.000 0.000
#> SRR975595     5  0.0000      0.813 0.000 0.000 0.000 0.000 1.000
#> SRR975597     5  0.0000      0.813 0.000 0.000 0.000 0.000 1.000
#> SRR975596     1  0.4015      0.592 0.652 0.000 0.000 0.348 0.000
#> SRR975598     5  0.0000      0.813 0.000 0.000 0.000 0.000 1.000
#> SRR975599     5  0.6031      0.452 0.352 0.000 0.000 0.128 0.520
#> SRR975600     3  0.0000      0.996 0.000 0.000 1.000 0.000 0.000
#> SRR975601     3  0.0000      0.996 0.000 0.000 1.000 0.000 0.000
#> SRR975602     5  0.3852      0.691 0.220 0.000 0.000 0.020 0.760
#> SRR975603     3  0.0000      0.996 0.000 0.000 1.000 0.000 0.000
#> SRR975604     3  0.0000      0.996 0.000 0.000 1.000 0.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> SRR975551     1  0.3330    0.64464 0.716 0.000 0.000 0.000 0.284 0.000
#> SRR975552     6  0.3152    0.45098 0.196 0.000 0.000 0.004 0.008 0.792
#> SRR975554     5  0.3797    0.19283 0.000 0.000 0.000 0.000 0.580 0.420
#> SRR975553     2  0.3288    0.78836 0.000 0.724 0.000 0.276 0.000 0.000
#> SRR975555     5  0.0632    0.83083 0.024 0.000 0.000 0.000 0.976 0.000
#> SRR975556     2  0.0000    0.86621 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975557     4  0.3555    0.55434 0.000 0.000 0.000 0.712 0.008 0.280
#> SRR975558     6  0.3398    0.43403 0.000 0.000 0.000 0.008 0.252 0.740
#> SRR975559     6  0.2738    0.68486 0.000 0.000 0.000 0.004 0.176 0.820
#> SRR975560     6  0.5244    0.00469 0.000 0.336 0.000 0.112 0.000 0.552
#> SRR975561     2  0.0508    0.86089 0.000 0.984 0.000 0.012 0.000 0.004
#> SRR975562     6  0.2738    0.68486 0.000 0.000 0.000 0.004 0.176 0.820
#> SRR975563     2  0.0000    0.86621 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975564     5  0.0806    0.83365 0.020 0.000 0.000 0.000 0.972 0.008
#> SRR975565     5  0.0632    0.83471 0.000 0.000 0.000 0.000 0.976 0.024
#> SRR975566     6  0.2948    0.67124 0.000 0.000 0.000 0.008 0.188 0.804
#> SRR975567     6  0.0260    0.59209 0.000 0.000 0.000 0.008 0.000 0.992
#> SRR975568     5  0.0632    0.83471 0.000 0.000 0.000 0.000 0.976 0.024
#> SRR975569     2  0.0000    0.86621 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975570     2  0.0000    0.86621 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975571     2  0.3288    0.78836 0.000 0.724 0.000 0.276 0.000 0.000
#> SRR975572     2  0.0000    0.86621 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975573     2  0.3221    0.79286 0.000 0.736 0.000 0.264 0.000 0.000
#> SRR975574     2  0.3266    0.79007 0.000 0.728 0.000 0.272 0.000 0.000
#> SRR975575     2  0.0000    0.86621 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975576     2  0.0000    0.86621 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975577     2  0.3288    0.78836 0.000 0.724 0.000 0.276 0.000 0.000
#> SRR975578     2  0.3288    0.78836 0.000 0.724 0.000 0.276 0.000 0.000
#> SRR975579     4  0.1251    0.62252 0.000 0.012 0.000 0.956 0.008 0.024
#> SRR975580     2  0.3448    0.78269 0.000 0.716 0.000 0.280 0.000 0.004
#> SRR975581     2  0.0000    0.86621 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975582     2  0.3266    0.79007 0.000 0.728 0.000 0.272 0.000 0.000
#> SRR975583     2  0.0000    0.86621 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975584     2  0.3288    0.78836 0.000 0.724 0.000 0.276 0.000 0.000
#> SRR975585     2  0.0000    0.86621 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975586     2  0.0291    0.86158 0.000 0.992 0.000 0.004 0.000 0.004
#> SRR975587     3  0.0000    0.99526 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975588     2  0.0000    0.86621 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975589     3  0.0000    0.99526 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975590     1  0.0000    0.86334 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR975591     3  0.0000    0.99526 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975592     3  0.0865    0.95631 0.036 0.000 0.964 0.000 0.000 0.000
#> SRR975593     3  0.0000    0.99526 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975594     3  0.0000    0.99526 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975595     1  0.0000    0.86334 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR975597     1  0.0000    0.86334 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR975596     6  0.2738    0.68486 0.000 0.000 0.000 0.004 0.176 0.820
#> SRR975598     1  0.0000    0.86334 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR975599     5  0.2915    0.65384 0.184 0.000 0.000 0.008 0.808 0.000
#> SRR975600     3  0.0000    0.99526 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975601     3  0.0000    0.99526 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975602     1  0.3652    0.70502 0.760 0.000 0.000 0.008 0.212 0.020
#> SRR975603     3  0.0000    0.99526 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975604     3  0.0000    0.99526 0.000 0.000 1.000 0.000 0.000 0.000

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

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

consensus_heatmap(res, k = 2)

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

consensus_heatmap(res, k = 3)

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

consensus_heatmap(res, k = 4)

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

consensus_heatmap(res, k = 5)

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

consensus_heatmap(res, k = 6)

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

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

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

membership_heatmap(res, k = 2)

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

membership_heatmap(res, k = 3)

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

membership_heatmap(res, k = 4)

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

membership_heatmap(res, k = 5)

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

membership_heatmap(res, k = 6)

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

Signature heatmaps where rows are scaled:

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

get_signatures(res, k = 2)

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

get_signatures(res, k = 3)

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

get_signatures(res, k = 4)

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

get_signatures(res, k = 5)

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

get_signatures(res, k = 6)

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

Signature heatmaps where rows are not scaled:

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

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

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

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

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

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

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

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

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

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

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

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk SD-pam-signature_compare

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

An example of the output of tb is:

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

The columns in tb are:

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

UMAP plot which shows how samples are separated.

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

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

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

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

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

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

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

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

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

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

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

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk SD-pam-collect-classes

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 17171 rows and 54 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#>   Subgroups are detected by 'mclust' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 4.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk SD-mclust-collect-plots

The plots are:

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

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

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

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

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

select_partition_number(res)

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

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.547           0.933       0.938         0.4503 0.547   0.547
#> 3 3 0.700           0.727       0.840         0.4788 0.776   0.591
#> 4 4 0.800           0.899       0.920         0.1018 0.931   0.786
#> 5 5 0.733           0.773       0.847         0.0273 0.892   0.638
#> 6 6 0.787           0.742       0.825         0.0543 0.971   0.874

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

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

suggest_best_k(res)

#> [1] 4

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

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

show/hide code output

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

#>           class entropy silhouette    p1    p2
#> SRR975551     1   0.634      0.908 0.840 0.160
#> SRR975552     1   0.634      0.908 0.840 0.160
#> SRR975554     1   0.634      0.908 0.840 0.160
#> SRR975553     2   0.000      1.000 0.000 1.000
#> SRR975555     1   0.634      0.908 0.840 0.160
#> SRR975556     1   0.730      0.869 0.796 0.204
#> SRR975557     1   0.634      0.908 0.840 0.160
#> SRR975558     1   0.634      0.908 0.840 0.160
#> SRR975559     1   0.634      0.908 0.840 0.160
#> SRR975560     1   0.634      0.908 0.840 0.160
#> SRR975561     1   0.730      0.869 0.796 0.204
#> SRR975562     1   0.634      0.908 0.840 0.160
#> SRR975563     2   0.000      1.000 0.000 1.000
#> SRR975564     1   0.634      0.908 0.840 0.160
#> SRR975565     1   0.634      0.908 0.840 0.160
#> SRR975566     1   0.634      0.908 0.840 0.160
#> SRR975567     1   0.634      0.908 0.840 0.160
#> SRR975568     1   0.634      0.908 0.840 0.160
#> SRR975569     2   0.000      1.000 0.000 1.000
#> SRR975570     2   0.000      1.000 0.000 1.000
#> SRR975571     2   0.000      1.000 0.000 1.000
#> SRR975572     2   0.000      1.000 0.000 1.000
#> SRR975573     2   0.000      1.000 0.000 1.000
#> SRR975574     2   0.000      1.000 0.000 1.000
#> SRR975575     2   0.000      1.000 0.000 1.000
#> SRR975576     2   0.000      1.000 0.000 1.000
#> SRR975577     2   0.000      1.000 0.000 1.000
#> SRR975578     2   0.000      1.000 0.000 1.000
#> SRR975579     1   0.634      0.908 0.840 0.160
#> SRR975580     1   0.644      0.905 0.836 0.164
#> SRR975581     2   0.000      1.000 0.000 1.000
#> SRR975582     2   0.000      1.000 0.000 1.000
#> SRR975583     2   0.000      1.000 0.000 1.000
#> SRR975584     2   0.000      1.000 0.000 1.000
#> SRR975585     2   0.000      1.000 0.000 1.000
#> SRR975586     1   0.730      0.869 0.796 0.204
#> SRR975587     1   0.000      0.895 1.000 0.000
#> SRR975588     2   0.000      1.000 0.000 1.000
#> SRR975589     1   0.000      0.895 1.000 0.000
#> SRR975590     1   0.000      0.895 1.000 0.000
#> SRR975591     1   0.000      0.895 1.000 0.000
#> SRR975592     1   0.000      0.895 1.000 0.000
#> SRR975593     1   0.000      0.895 1.000 0.000
#> SRR975594     1   0.000      0.895 1.000 0.000
#> SRR975595     1   0.000      0.895 1.000 0.000
#> SRR975597     1   0.000      0.895 1.000 0.000
#> SRR975596     1   0.634      0.908 0.840 0.160
#> SRR975598     1   0.000      0.895 1.000 0.000
#> SRR975599     1   0.000      0.895 1.000 0.000
#> SRR975600     1   0.000      0.895 1.000 0.000
#> SRR975601     1   0.000      0.895 1.000 0.000
#> SRR975602     1   0.000      0.895 1.000 0.000
#> SRR975603     1   0.000      0.895 1.000 0.000
#> SRR975604     1   0.000      0.895 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
#> SRR975551     1  0.6062      0.614 0.616 0.000 0.384
#> SRR975552     1  0.6095      0.609 0.608 0.000 0.392
#> SRR975554     1  0.5138      0.646 0.748 0.000 0.252
#> SRR975553     2  0.0000      0.994 0.000 1.000 0.000
#> SRR975555     1  0.6079      0.609 0.612 0.000 0.388
#> SRR975556     1  0.1643      0.615 0.956 0.000 0.044
#> SRR975557     1  0.6140     -0.365 0.596 0.000 0.404
#> SRR975558     1  0.1643      0.615 0.956 0.000 0.044
#> SRR975559     1  0.4750      0.647 0.784 0.000 0.216
#> SRR975560     1  0.1643      0.615 0.956 0.000 0.044
#> SRR975561     1  0.1950      0.613 0.952 0.008 0.040
#> SRR975562     1  0.4702      0.649 0.788 0.000 0.212
#> SRR975563     2  0.0000      0.994 0.000 1.000 0.000
#> SRR975564     1  0.6079      0.606 0.612 0.000 0.388
#> SRR975565     1  0.6095      0.609 0.608 0.000 0.392
#> SRR975566     1  0.5968      0.438 0.636 0.000 0.364
#> SRR975567     1  0.1643      0.615 0.956 0.000 0.044
#> SRR975568     1  0.6154      0.602 0.592 0.000 0.408
#> SRR975569     2  0.0000      0.994 0.000 1.000 0.000
#> SRR975570     2  0.0000      0.994 0.000 1.000 0.000
#> SRR975571     2  0.0000      0.994 0.000 1.000 0.000
#> SRR975572     2  0.0000      0.994 0.000 1.000 0.000
#> SRR975573     2  0.0000      0.994 0.000 1.000 0.000
#> SRR975574     2  0.2796      0.890 0.092 0.908 0.000
#> SRR975575     2  0.0000      0.994 0.000 1.000 0.000
#> SRR975576     2  0.0000      0.994 0.000 1.000 0.000
#> SRR975577     2  0.0000      0.994 0.000 1.000 0.000
#> SRR975578     2  0.0000      0.994 0.000 1.000 0.000
#> SRR975579     1  0.5835     -0.158 0.660 0.000 0.340
#> SRR975580     1  0.1643      0.615 0.956 0.000 0.044
#> SRR975581     2  0.0000      0.994 0.000 1.000 0.000
#> SRR975582     2  0.0000      0.994 0.000 1.000 0.000
#> SRR975583     2  0.0000      0.994 0.000 1.000 0.000
#> SRR975584     2  0.0000      0.994 0.000 1.000 0.000
#> SRR975585     2  0.0237      0.990 0.004 0.996 0.000
#> SRR975586     1  0.4092      0.543 0.876 0.088 0.036
#> SRR975587     3  0.6045      0.757 0.380 0.000 0.620
#> SRR975588     2  0.0000      0.994 0.000 1.000 0.000
#> SRR975589     3  0.4605      0.723 0.204 0.000 0.796
#> SRR975590     3  0.4452      0.721 0.192 0.000 0.808
#> SRR975591     3  0.6045      0.757 0.380 0.000 0.620
#> SRR975592     3  0.4452      0.721 0.192 0.000 0.808
#> SRR975593     3  0.4605      0.723 0.204 0.000 0.796
#> SRR975594     3  0.6062      0.753 0.384 0.000 0.616
#> SRR975595     3  0.1163      0.591 0.028 0.000 0.972
#> SRR975597     3  0.1163      0.591 0.028 0.000 0.972
#> SRR975596     1  0.4842      0.642 0.776 0.000 0.224
#> SRR975598     3  0.1163      0.591 0.028 0.000 0.972
#> SRR975599     3  0.6095      0.747 0.392 0.000 0.608
#> SRR975600     3  0.6045      0.757 0.380 0.000 0.620
#> SRR975601     3  0.6045      0.757 0.380 0.000 0.620
#> SRR975602     3  0.4002      0.413 0.160 0.000 0.840
#> SRR975603     3  0.6045      0.757 0.380 0.000 0.620
#> SRR975604     3  0.6045      0.757 0.380 0.000 0.620

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> SRR975551     1  0.0000      0.940 1.000 0.000 0.000 0.000
#> SRR975552     1  0.0000      0.940 1.000 0.000 0.000 0.000
#> SRR975554     1  0.2759      0.921 0.904 0.000 0.044 0.052
#> SRR975553     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975555     1  0.0336      0.941 0.992 0.000 0.000 0.008
#> SRR975556     4  0.5657      0.855 0.220 0.048 0.016 0.716
#> SRR975557     4  0.1557      0.753 0.000 0.000 0.056 0.944
#> SRR975558     4  0.4399      0.874 0.224 0.000 0.016 0.760
#> SRR975559     1  0.3037      0.901 0.880 0.000 0.020 0.100
#> SRR975560     4  0.4364      0.876 0.220 0.000 0.016 0.764
#> SRR975561     4  0.5337      0.872 0.200 0.036 0.020 0.744
#> SRR975562     1  0.2271      0.926 0.916 0.000 0.008 0.076
#> SRR975563     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975564     1  0.0921      0.940 0.972 0.000 0.000 0.028
#> SRR975565     1  0.0000      0.940 1.000 0.000 0.000 0.000
#> SRR975566     1  0.2751      0.914 0.904 0.000 0.056 0.040
#> SRR975567     4  0.4399      0.874 0.224 0.000 0.016 0.760
#> SRR975568     1  0.0000      0.940 1.000 0.000 0.000 0.000
#> SRR975569     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975570     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975571     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975572     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975573     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975574     2  0.3048      0.838 0.108 0.876 0.000 0.016
#> SRR975575     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975576     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975577     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975578     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975579     4  0.1389      0.756 0.000 0.000 0.048 0.952
#> SRR975580     4  0.4364      0.876 0.220 0.000 0.016 0.764
#> SRR975581     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975582     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975583     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975584     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975585     2  0.1209      0.952 0.032 0.964 0.000 0.004
#> SRR975586     4  0.5515      0.813 0.120 0.104 0.016 0.760
#> SRR975587     3  0.0000      0.880 0.000 0.000 1.000 0.000
#> SRR975588     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975589     3  0.3444      0.822 0.184 0.000 0.816 0.000
#> SRR975590     3  0.1867      0.875 0.072 0.000 0.928 0.000
#> SRR975591     3  0.0000      0.880 0.000 0.000 1.000 0.000
#> SRR975592     3  0.1792      0.876 0.068 0.000 0.932 0.000
#> SRR975593     3  0.3311      0.829 0.172 0.000 0.828 0.000
#> SRR975594     3  0.0000      0.880 0.000 0.000 1.000 0.000
#> SRR975595     3  0.4252      0.781 0.252 0.000 0.744 0.004
#> SRR975597     3  0.4188      0.788 0.244 0.000 0.752 0.004
#> SRR975596     1  0.3215      0.900 0.876 0.000 0.032 0.092
#> SRR975598     3  0.4103      0.779 0.256 0.000 0.744 0.000
#> SRR975599     3  0.1411      0.872 0.020 0.000 0.960 0.020
#> SRR975600     3  0.0000      0.880 0.000 0.000 1.000 0.000
#> SRR975601     3  0.0000      0.880 0.000 0.000 1.000 0.000
#> SRR975602     3  0.4977      0.407 0.460 0.000 0.540 0.000
#> SRR975603     3  0.0000      0.880 0.000 0.000 1.000 0.000
#> SRR975604     3  0.0000      0.880 0.000 0.000 1.000 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
#> SRR975551     1  0.2648      0.682 0.848 0.000 0.000 0.000 0.152
#> SRR975552     1  0.2732      0.674 0.840 0.000 0.000 0.000 0.160
#> SRR975554     5  0.5926      0.630 0.164 0.000 0.204 0.008 0.624
#> SRR975553     2  0.0898      0.952 0.000 0.972 0.000 0.020 0.008
#> SRR975555     1  0.3857      0.394 0.688 0.000 0.000 0.000 0.312
#> SRR975556     5  0.1568      0.695 0.000 0.036 0.000 0.020 0.944
#> SRR975557     4  0.1750      1.000 0.000 0.000 0.028 0.936 0.036
#> SRR975558     5  0.1408      0.718 0.044 0.000 0.008 0.000 0.948
#> SRR975559     5  0.5809      0.647 0.164 0.000 0.188 0.008 0.640
#> SRR975560     5  0.0609      0.702 0.000 0.000 0.000 0.020 0.980
#> SRR975561     5  0.2270      0.662 0.000 0.076 0.000 0.020 0.904
#> SRR975562     5  0.5778      0.645 0.184 0.000 0.164 0.008 0.644
#> SRR975563     2  0.0290      0.963 0.000 0.992 0.000 0.000 0.008
#> SRR975564     5  0.5315      0.494 0.332 0.000 0.068 0.000 0.600
#> SRR975565     1  0.2648      0.682 0.848 0.000 0.000 0.000 0.152
#> SRR975566     5  0.6032      0.615 0.164 0.000 0.220 0.008 0.608
#> SRR975567     5  0.1408      0.718 0.044 0.000 0.008 0.000 0.948
#> SRR975568     1  0.2648      0.682 0.848 0.000 0.000 0.000 0.152
#> SRR975569     2  0.0000      0.968 0.000 1.000 0.000 0.000 0.000
#> SRR975570     2  0.0000      0.968 0.000 1.000 0.000 0.000 0.000
#> SRR975571     2  0.0898      0.952 0.000 0.972 0.000 0.020 0.008
#> SRR975572     2  0.0000      0.968 0.000 1.000 0.000 0.000 0.000
#> SRR975573     2  0.0000      0.968 0.000 1.000 0.000 0.000 0.000
#> SRR975574     2  0.3366      0.685 0.000 0.768 0.000 0.000 0.232
#> SRR975575     2  0.0000      0.968 0.000 1.000 0.000 0.000 0.000
#> SRR975576     2  0.0000      0.968 0.000 1.000 0.000 0.000 0.000
#> SRR975577     2  0.0000      0.968 0.000 1.000 0.000 0.000 0.000
#> SRR975578     2  0.0290      0.964 0.000 0.992 0.000 0.000 0.008
#> SRR975579     4  0.1750      1.000 0.000 0.000 0.028 0.936 0.036
#> SRR975580     5  0.1568      0.695 0.000 0.036 0.000 0.020 0.944
#> SRR975581     2  0.0898      0.952 0.000 0.972 0.000 0.020 0.008
#> SRR975582     2  0.0000      0.968 0.000 1.000 0.000 0.000 0.000
#> SRR975583     2  0.0000      0.968 0.000 1.000 0.000 0.000 0.000
#> SRR975584     2  0.0000      0.968 0.000 1.000 0.000 0.000 0.000
#> SRR975585     2  0.2329      0.836 0.000 0.876 0.000 0.000 0.124
#> SRR975586     5  0.3106      0.562 0.000 0.140 0.000 0.020 0.840
#> SRR975587     3  0.1671      0.839 0.076 0.000 0.924 0.000 0.000
#> SRR975588     2  0.0000      0.968 0.000 1.000 0.000 0.000 0.000
#> SRR975589     3  0.4127      0.811 0.156 0.000 0.792 0.028 0.024
#> SRR975590     3  0.4021      0.780 0.200 0.000 0.764 0.036 0.000
#> SRR975591     3  0.0000      0.858 0.000 0.000 1.000 0.000 0.000
#> SRR975592     3  0.3099      0.840 0.124 0.000 0.848 0.028 0.000
#> SRR975593     3  0.4127      0.811 0.156 0.000 0.792 0.028 0.024
#> SRR975594     3  0.0162      0.856 0.004 0.000 0.996 0.000 0.000
#> SRR975595     1  0.4829      0.315 0.660 0.000 0.300 0.036 0.004
#> SRR975597     1  0.4829      0.315 0.660 0.000 0.300 0.036 0.004
#> SRR975596     5  0.5809      0.647 0.164 0.000 0.188 0.008 0.640
#> SRR975598     1  0.4809      0.323 0.664 0.000 0.296 0.036 0.004
#> SRR975599     3  0.5792      0.372 0.404 0.000 0.528 0.028 0.040
#> SRR975600     3  0.1671      0.862 0.076 0.000 0.924 0.000 0.000
#> SRR975601     3  0.0703      0.857 0.024 0.000 0.976 0.000 0.000
#> SRR975602     1  0.4228      0.673 0.788 0.000 0.068 0.008 0.136
#> SRR975603     3  0.1121      0.864 0.044 0.000 0.956 0.000 0.000
#> SRR975604     3  0.0000      0.858 0.000 0.000 1.000 0.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> SRR975551     1  0.4015      0.533 0.616 0.000 0.000 0.000 0.372 0.012
#> SRR975552     1  0.4277      0.530 0.616 0.000 0.000 0.000 0.356 0.028
#> SRR975554     5  0.0547      0.901 0.000 0.000 0.020 0.000 0.980 0.000
#> SRR975553     2  0.1863      0.875 0.000 0.896 0.000 0.000 0.000 0.104
#> SRR975555     1  0.4325      0.416 0.524 0.000 0.000 0.000 0.456 0.020
#> SRR975556     6  0.3345      0.847 0.000 0.028 0.000 0.000 0.184 0.788
#> SRR975557     4  0.0146      1.000 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR975558     6  0.3868      0.499 0.000 0.000 0.000 0.000 0.492 0.508
#> SRR975559     5  0.0692      0.907 0.000 0.000 0.004 0.000 0.976 0.020
#> SRR975560     6  0.3136      0.842 0.000 0.016 0.000 0.000 0.188 0.796
#> SRR975561     6  0.3377      0.846 0.000 0.028 0.000 0.000 0.188 0.784
#> SRR975562     5  0.0363      0.902 0.000 0.000 0.000 0.000 0.988 0.012
#> SRR975563     2  0.0458      0.935 0.000 0.984 0.000 0.000 0.000 0.016
#> SRR975564     5  0.3136      0.561 0.188 0.000 0.000 0.000 0.796 0.016
#> SRR975565     1  0.4015      0.533 0.616 0.000 0.000 0.000 0.372 0.012
#> SRR975566     5  0.1461      0.878 0.000 0.000 0.044 0.000 0.940 0.016
#> SRR975567     6  0.3868      0.499 0.000 0.000 0.000 0.000 0.492 0.508
#> SRR975568     1  0.4037      0.527 0.608 0.000 0.000 0.000 0.380 0.012
#> SRR975569     2  0.0000      0.944 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975570     2  0.0000      0.944 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975571     2  0.1863      0.875 0.000 0.896 0.000 0.000 0.000 0.104
#> SRR975572     2  0.0000      0.944 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975573     2  0.0000      0.944 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975574     2  0.4170      0.484 0.000 0.660 0.000 0.000 0.032 0.308
#> SRR975575     2  0.0000      0.944 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975576     2  0.0146      0.942 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR975577     2  0.0000      0.944 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975578     2  0.0000      0.944 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975579     4  0.0146      1.000 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR975580     6  0.3269      0.847 0.000 0.024 0.000 0.000 0.184 0.792
#> SRR975581     2  0.1910      0.873 0.000 0.892 0.000 0.000 0.000 0.108
#> SRR975582     2  0.0000      0.944 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975583     2  0.0000      0.944 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975584     2  0.0000      0.944 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975585     2  0.2942      0.792 0.000 0.836 0.000 0.000 0.032 0.132
#> SRR975586     6  0.3588      0.832 0.000 0.044 0.000 0.000 0.180 0.776
#> SRR975587     3  0.1434      0.755 0.048 0.000 0.940 0.000 0.000 0.012
#> SRR975588     2  0.0000      0.944 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975589     3  0.6922      0.376 0.236 0.000 0.392 0.004 0.320 0.048
#> SRR975590     3  0.5495      0.659 0.208 0.000 0.652 0.004 0.044 0.092
#> SRR975591     3  0.0291      0.757 0.000 0.000 0.992 0.000 0.004 0.004
#> SRR975592     3  0.4605      0.699 0.176 0.000 0.732 0.004 0.028 0.060
#> SRR975593     3  0.6912      0.391 0.236 0.000 0.400 0.004 0.312 0.048
#> SRR975594     3  0.0909      0.745 0.020 0.000 0.968 0.000 0.000 0.012
#> SRR975595     1  0.5419      0.238 0.648 0.000 0.140 0.004 0.020 0.188
#> SRR975597     1  0.5419      0.238 0.648 0.000 0.140 0.004 0.020 0.188
#> SRR975596     5  0.0692      0.907 0.000 0.000 0.004 0.000 0.976 0.020
#> SRR975598     1  0.5419      0.238 0.648 0.000 0.140 0.004 0.020 0.188
#> SRR975599     3  0.6944      0.458 0.292 0.000 0.456 0.004 0.084 0.164
#> SRR975600     3  0.2163      0.757 0.096 0.000 0.892 0.000 0.008 0.004
#> SRR975601     3  0.1074      0.749 0.028 0.000 0.960 0.000 0.000 0.012
#> SRR975602     1  0.4593      0.496 0.632 0.000 0.024 0.000 0.324 0.020
#> SRR975603     3  0.1410      0.762 0.044 0.000 0.944 0.000 0.008 0.004
#> SRR975604     3  0.0146      0.756 0.000 0.000 0.996 0.000 0.004 0.000

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

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

consensus_heatmap(res, k = 2)

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

consensus_heatmap(res, k = 3)

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

consensus_heatmap(res, k = 4)

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

consensus_heatmap(res, k = 5)

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

consensus_heatmap(res, k = 6)

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

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

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

membership_heatmap(res, k = 2)

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

membership_heatmap(res, k = 3)

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

membership_heatmap(res, k = 4)

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

membership_heatmap(res, k = 5)

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

membership_heatmap(res, k = 6)

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

Signature heatmaps where rows are scaled:

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

get_signatures(res, k = 2)

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

get_signatures(res, k = 3)

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

get_signatures(res, k = 4)

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

get_signatures(res, k = 5)

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

get_signatures(res, k = 6)

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

Signature heatmaps where rows are not scaled:

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

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

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

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

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

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

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

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

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

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

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

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk SD-mclust-signature_compare

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

An example of the output of tb is:

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

The columns in tb are:

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

UMAP plot which shows how samples are separated.

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

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

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

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

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

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

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

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

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

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

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

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk SD-mclust-collect-classes

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 17171 rows and 54 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#>   Subgroups are detected by 'NMF' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 4.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk SD-NMF-collect-plots

The plots are:

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

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

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

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

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

select_partition_number(res)

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

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.944       0.980         0.5065 0.493   0.493
#> 3 3 0.905           0.916       0.959         0.2509 0.860   0.725
#> 4 4 0.929           0.900       0.954         0.0589 0.940   0.844
#> 5 5 0.790           0.749       0.868         0.0966 0.928   0.788
#> 6 6 0.773           0.724       0.827         0.0683 0.911   0.692

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 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
#> SRR975551     1   0.000     0.9772 1.000 0.000
#> SRR975552     1   0.662     0.7828 0.828 0.172
#> SRR975554     1   0.000     0.9772 1.000 0.000
#> SRR975553     2   0.000     0.9794 0.000 1.000
#> SRR975555     1   0.184     0.9518 0.972 0.028
#> SRR975556     2   0.000     0.9794 0.000 1.000
#> SRR975557     1   0.000     0.9772 1.000 0.000
#> SRR975558     2   0.998     0.0535 0.472 0.528
#> SRR975559     1   0.000     0.9772 1.000 0.000
#> SRR975560     2   0.000     0.9794 0.000 1.000
#> SRR975561     2   0.000     0.9794 0.000 1.000
#> SRR975562     1   0.000     0.9772 1.000 0.000
#> SRR975563     2   0.000     0.9794 0.000 1.000
#> SRR975564     1   0.000     0.9772 1.000 0.000
#> SRR975565     1   0.000     0.9772 1.000 0.000
#> SRR975566     1   0.000     0.9772 1.000 0.000
#> SRR975567     1   0.980     0.2804 0.584 0.416
#> SRR975568     1   0.000     0.9772 1.000 0.000
#> SRR975569     2   0.000     0.9794 0.000 1.000
#> SRR975570     2   0.000     0.9794 0.000 1.000
#> SRR975571     2   0.000     0.9794 0.000 1.000
#> SRR975572     2   0.000     0.9794 0.000 1.000
#> SRR975573     2   0.000     0.9794 0.000 1.000
#> SRR975574     2   0.000     0.9794 0.000 1.000
#> SRR975575     2   0.000     0.9794 0.000 1.000
#> SRR975576     2   0.000     0.9794 0.000 1.000
#> SRR975577     2   0.000     0.9794 0.000 1.000
#> SRR975578     2   0.000     0.9794 0.000 1.000
#> SRR975579     2   0.000     0.9794 0.000 1.000
#> SRR975580     2   0.000     0.9794 0.000 1.000
#> SRR975581     2   0.000     0.9794 0.000 1.000
#> SRR975582     2   0.000     0.9794 0.000 1.000
#> SRR975583     2   0.000     0.9794 0.000 1.000
#> SRR975584     2   0.000     0.9794 0.000 1.000
#> SRR975585     2   0.000     0.9794 0.000 1.000
#> SRR975586     2   0.000     0.9794 0.000 1.000
#> SRR975587     1   0.000     0.9772 1.000 0.000
#> SRR975588     2   0.000     0.9794 0.000 1.000
#> SRR975589     1   0.000     0.9772 1.000 0.000
#> SRR975590     1   0.000     0.9772 1.000 0.000
#> SRR975591     1   0.000     0.9772 1.000 0.000
#> SRR975592     1   0.000     0.9772 1.000 0.000
#> SRR975593     1   0.000     0.9772 1.000 0.000
#> SRR975594     1   0.000     0.9772 1.000 0.000
#> SRR975595     1   0.000     0.9772 1.000 0.000
#> SRR975597     1   0.000     0.9772 1.000 0.000
#> SRR975596     1   0.000     0.9772 1.000 0.000
#> SRR975598     1   0.000     0.9772 1.000 0.000
#> SRR975599     1   0.000     0.9772 1.000 0.000
#> SRR975600     1   0.000     0.9772 1.000 0.000
#> SRR975601     1   0.000     0.9772 1.000 0.000
#> SRR975602     1   0.000     0.9772 1.000 0.000
#> SRR975603     1   0.000     0.9772 1.000 0.000
#> SRR975604     1   0.000     0.9772 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
#> SRR975551     1  0.0000      0.906 1.000 0.000 0.000
#> SRR975552     1  0.0000      0.906 1.000 0.000 0.000
#> SRR975554     1  0.0000      0.906 1.000 0.000 0.000
#> SRR975553     2  0.0000      0.990 0.000 1.000 0.000
#> SRR975555     1  0.0000      0.906 1.000 0.000 0.000
#> SRR975556     2  0.0000      0.990 0.000 1.000 0.000
#> SRR975557     1  0.6267      0.133 0.548 0.000 0.452
#> SRR975558     1  0.1031      0.890 0.976 0.024 0.000
#> SRR975559     1  0.0000      0.906 1.000 0.000 0.000
#> SRR975560     2  0.0000      0.990 0.000 1.000 0.000
#> SRR975561     2  0.0000      0.990 0.000 1.000 0.000
#> SRR975562     1  0.0000      0.906 1.000 0.000 0.000
#> SRR975563     2  0.0000      0.990 0.000 1.000 0.000
#> SRR975564     1  0.0000      0.906 1.000 0.000 0.000
#> SRR975565     1  0.0000      0.906 1.000 0.000 0.000
#> SRR975566     1  0.0000      0.906 1.000 0.000 0.000
#> SRR975567     1  0.0237      0.903 0.996 0.004 0.000
#> SRR975568     1  0.0000      0.906 1.000 0.000 0.000
#> SRR975569     2  0.0000      0.990 0.000 1.000 0.000
#> SRR975570     2  0.0000      0.990 0.000 1.000 0.000
#> SRR975571     2  0.0000      0.990 0.000 1.000 0.000
#> SRR975572     2  0.0000      0.990 0.000 1.000 0.000
#> SRR975573     2  0.0000      0.990 0.000 1.000 0.000
#> SRR975574     2  0.0000      0.990 0.000 1.000 0.000
#> SRR975575     2  0.0000      0.990 0.000 1.000 0.000
#> SRR975576     2  0.0000      0.990 0.000 1.000 0.000
#> SRR975577     2  0.0000      0.990 0.000 1.000 0.000
#> SRR975578     2  0.0000      0.990 0.000 1.000 0.000
#> SRR975579     2  0.4796      0.718 0.000 0.780 0.220
#> SRR975580     2  0.0000      0.990 0.000 1.000 0.000
#> SRR975581     2  0.0000      0.990 0.000 1.000 0.000
#> SRR975582     2  0.0000      0.990 0.000 1.000 0.000
#> SRR975583     2  0.0000      0.990 0.000 1.000 0.000
#> SRR975584     2  0.0000      0.990 0.000 1.000 0.000
#> SRR975585     2  0.0000      0.990 0.000 1.000 0.000
#> SRR975586     2  0.0000      0.990 0.000 1.000 0.000
#> SRR975587     3  0.0237      1.000 0.004 0.000 0.996
#> SRR975588     2  0.0000      0.990 0.000 1.000 0.000
#> SRR975589     1  0.1643      0.890 0.956 0.000 0.044
#> SRR975590     1  0.5216      0.711 0.740 0.000 0.260
#> SRR975591     3  0.0237      1.000 0.004 0.000 0.996
#> SRR975592     1  0.6062      0.498 0.616 0.000 0.384
#> SRR975593     1  0.1964      0.887 0.944 0.000 0.056
#> SRR975594     3  0.0237      1.000 0.004 0.000 0.996
#> SRR975595     1  0.4702      0.769 0.788 0.000 0.212
#> SRR975597     1  0.4555      0.781 0.800 0.000 0.200
#> SRR975596     1  0.0000      0.906 1.000 0.000 0.000
#> SRR975598     1  0.4555      0.781 0.800 0.000 0.200
#> SRR975599     1  0.3192      0.851 0.888 0.000 0.112
#> SRR975600     3  0.0237      1.000 0.004 0.000 0.996
#> SRR975601     3  0.0237      1.000 0.004 0.000 0.996
#> SRR975602     1  0.0000      0.906 1.000 0.000 0.000
#> SRR975603     3  0.0237      1.000 0.004 0.000 0.996
#> SRR975604     3  0.0237      1.000 0.004 0.000 0.996

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> SRR975551     1  0.0000      0.892 1.000 0.000 0.000 0.000
#> SRR975552     1  0.0000      0.892 1.000 0.000 0.000 0.000
#> SRR975554     1  0.0000      0.892 1.000 0.000 0.000 0.000
#> SRR975553     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> SRR975555     1  0.0336      0.890 0.992 0.000 0.000 0.008
#> SRR975556     2  0.0336      0.992 0.000 0.992 0.000 0.008
#> SRR975557     4  0.0336      0.618 0.008 0.000 0.000 0.992
#> SRR975558     4  0.6714      0.550 0.360 0.100 0.000 0.540
#> SRR975559     1  0.2149      0.817 0.912 0.000 0.000 0.088
#> SRR975560     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> SRR975561     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> SRR975562     1  0.0000      0.892 1.000 0.000 0.000 0.000
#> SRR975563     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> SRR975564     1  0.0000      0.892 1.000 0.000 0.000 0.000
#> SRR975565     1  0.0000      0.892 1.000 0.000 0.000 0.000
#> SRR975566     1  0.0000      0.892 1.000 0.000 0.000 0.000
#> SRR975567     4  0.6233      0.507 0.388 0.060 0.000 0.552
#> SRR975568     1  0.0000      0.892 1.000 0.000 0.000 0.000
#> SRR975569     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> SRR975570     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> SRR975571     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> SRR975572     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> SRR975573     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> SRR975574     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> SRR975575     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> SRR975576     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> SRR975577     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> SRR975578     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> SRR975579     4  0.0592      0.616 0.000 0.016 0.000 0.984
#> SRR975580     2  0.0336      0.992 0.000 0.992 0.000 0.008
#> SRR975581     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> SRR975582     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> SRR975583     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> SRR975584     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> SRR975585     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> SRR975586     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> SRR975587     3  0.0000      1.000 0.000 0.000 1.000 0.000
#> SRR975588     2  0.0000      0.999 0.000 1.000 0.000 0.000
#> SRR975589     1  0.1716      0.865 0.936 0.000 0.064 0.000
#> SRR975590     1  0.4431      0.580 0.696 0.000 0.304 0.000
#> SRR975591     3  0.0000      1.000 0.000 0.000 1.000 0.000
#> SRR975592     1  0.5000      0.170 0.504 0.000 0.496 0.000
#> SRR975593     1  0.2469      0.834 0.892 0.000 0.108 0.000
#> SRR975594     3  0.0000      1.000 0.000 0.000 1.000 0.000
#> SRR975595     1  0.3444      0.753 0.816 0.000 0.184 0.000
#> SRR975597     1  0.2760      0.816 0.872 0.000 0.128 0.000
#> SRR975596     1  0.1637      0.844 0.940 0.000 0.000 0.060
#> SRR975598     1  0.2011      0.856 0.920 0.000 0.080 0.000
#> SRR975599     1  0.0336      0.890 0.992 0.000 0.008 0.000
#> SRR975600     3  0.0000      1.000 0.000 0.000 1.000 0.000
#> SRR975601     3  0.0000      1.000 0.000 0.000 1.000 0.000
#> SRR975602     1  0.0000      0.892 1.000 0.000 0.000 0.000
#> SRR975603     3  0.0000      1.000 0.000 0.000 1.000 0.000
#> SRR975604     3  0.0000      1.000 0.000 0.000 1.000 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
#> SRR975551     1  0.2561      0.725 0.856 0.000 0.000 0.000 0.144
#> SRR975552     1  0.2852      0.722 0.828 0.000 0.000 0.000 0.172
#> SRR975554     1  0.4302      0.186 0.520 0.000 0.000 0.000 0.480
#> SRR975553     2  0.1121      0.943 0.000 0.956 0.000 0.000 0.044
#> SRR975555     1  0.4283      0.252 0.544 0.000 0.000 0.000 0.456
#> SRR975556     2  0.1908      0.912 0.000 0.908 0.000 0.000 0.092
#> SRR975557     4  0.0000      0.845 0.000 0.000 0.000 1.000 0.000
#> SRR975558     5  0.5025      0.144 0.020 0.028 0.000 0.288 0.664
#> SRR975559     1  0.4101      0.501 0.664 0.000 0.000 0.332 0.004
#> SRR975560     2  0.4360      0.743 0.184 0.752 0.000 0.000 0.064
#> SRR975561     2  0.1544      0.926 0.000 0.932 0.000 0.000 0.068
#> SRR975562     1  0.0162      0.705 0.996 0.000 0.000 0.000 0.004
#> SRR975563     2  0.1671      0.922 0.000 0.924 0.000 0.000 0.076
#> SRR975564     5  0.2605      0.650 0.148 0.000 0.000 0.000 0.852
#> SRR975565     1  0.2966      0.714 0.816 0.000 0.000 0.000 0.184
#> SRR975566     1  0.4503      0.554 0.664 0.000 0.000 0.024 0.312
#> SRR975567     4  0.5091      0.623 0.016 0.072 0.000 0.712 0.200
#> SRR975568     5  0.2690      0.648 0.156 0.000 0.000 0.000 0.844
#> SRR975569     2  0.0510      0.946 0.000 0.984 0.000 0.000 0.016
#> SRR975570     2  0.0000      0.946 0.000 1.000 0.000 0.000 0.000
#> SRR975571     2  0.1121      0.943 0.000 0.956 0.000 0.000 0.044
#> SRR975572     2  0.0404      0.945 0.000 0.988 0.000 0.000 0.012
#> SRR975573     2  0.1121      0.943 0.000 0.956 0.000 0.000 0.044
#> SRR975574     2  0.1121      0.943 0.000 0.956 0.000 0.000 0.044
#> SRR975575     2  0.0404      0.945 0.000 0.988 0.000 0.000 0.012
#> SRR975576     2  0.0794      0.942 0.000 0.972 0.000 0.000 0.028
#> SRR975577     2  0.1121      0.943 0.000 0.956 0.000 0.000 0.044
#> SRR975578     2  0.1121      0.943 0.000 0.956 0.000 0.000 0.044
#> SRR975579     4  0.0000      0.845 0.000 0.000 0.000 1.000 0.000
#> SRR975580     2  0.4113      0.804 0.140 0.784 0.000 0.000 0.076
#> SRR975581     2  0.1043      0.938 0.000 0.960 0.000 0.000 0.040
#> SRR975582     2  0.1121      0.943 0.000 0.956 0.000 0.000 0.044
#> SRR975583     2  0.0404      0.945 0.000 0.988 0.000 0.000 0.012
#> SRR975584     2  0.1121      0.943 0.000 0.956 0.000 0.000 0.044
#> SRR975585     2  0.0510      0.945 0.000 0.984 0.000 0.000 0.016
#> SRR975586     2  0.1908      0.912 0.000 0.908 0.000 0.000 0.092
#> SRR975587     3  0.0000      0.916 0.000 0.000 1.000 0.000 0.000
#> SRR975588     2  0.0162      0.946 0.000 0.996 0.000 0.000 0.004
#> SRR975589     5  0.3163      0.645 0.164 0.000 0.012 0.000 0.824
#> SRR975590     1  0.5848      0.533 0.604 0.000 0.228 0.000 0.168
#> SRR975591     3  0.0000      0.916 0.000 0.000 1.000 0.000 0.000
#> SRR975592     3  0.5393      0.222 0.080 0.000 0.608 0.000 0.312
#> SRR975593     5  0.6949      0.160 0.388 0.000 0.144 0.032 0.436
#> SRR975594     3  0.0000      0.916 0.000 0.000 1.000 0.000 0.000
#> SRR975595     1  0.2583      0.640 0.864 0.000 0.132 0.000 0.004
#> SRR975597     1  0.3601      0.722 0.820 0.000 0.052 0.000 0.128
#> SRR975596     1  0.5334      0.395 0.672 0.000 0.000 0.148 0.180
#> SRR975598     1  0.1571      0.691 0.936 0.000 0.060 0.000 0.004
#> SRR975599     1  0.0324      0.705 0.992 0.000 0.004 0.000 0.004
#> SRR975600     5  0.4227      0.137 0.000 0.000 0.420 0.000 0.580
#> SRR975601     3  0.0000      0.916 0.000 0.000 1.000 0.000 0.000
#> SRR975602     1  0.2377      0.728 0.872 0.000 0.000 0.000 0.128
#> SRR975603     3  0.0290      0.909 0.000 0.000 0.992 0.000 0.008
#> SRR975604     3  0.0000      0.916 0.000 0.000 1.000 0.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> SRR975551     1  0.4439      0.847 0.540 0.000 0.000 0.000 0.432 0.028
#> SRR975552     1  0.4488      0.849 0.548 0.000 0.000 0.000 0.420 0.032
#> SRR975554     1  0.5887      0.367 0.404 0.000 0.000 0.000 0.200 0.396
#> SRR975553     2  0.1918      0.871 0.088 0.904 0.000 0.000 0.000 0.008
#> SRR975555     6  0.4591      0.329 0.040 0.000 0.000 0.000 0.408 0.552
#> SRR975556     2  0.3721      0.676 0.308 0.684 0.000 0.000 0.004 0.004
#> SRR975557     4  0.0000      0.745 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR975558     6  0.3100      0.768 0.012 0.004 0.000 0.028 0.108 0.848
#> SRR975559     4  0.4037      0.347 0.012 0.000 0.000 0.608 0.380 0.000
#> SRR975560     5  0.6163      0.294 0.176 0.256 0.000 0.020 0.540 0.008
#> SRR975561     2  0.3761      0.762 0.192 0.768 0.000 0.032 0.004 0.004
#> SRR975562     5  0.0508      0.449 0.004 0.000 0.000 0.000 0.984 0.012
#> SRR975563     2  0.3429      0.736 0.252 0.740 0.000 0.000 0.004 0.004
#> SRR975564     6  0.0717      0.787 0.016 0.000 0.000 0.000 0.008 0.976
#> SRR975565     1  0.4747      0.820 0.584 0.000 0.000 0.000 0.356 0.060
#> SRR975566     1  0.5277      0.829 0.528 0.000 0.000 0.008 0.384 0.080
#> SRR975567     4  0.5329      0.588 0.044 0.084 0.000 0.708 0.024 0.140
#> SRR975568     6  0.0508      0.790 0.004 0.000 0.000 0.000 0.012 0.984
#> SRR975569     2  0.0717      0.882 0.016 0.976 0.000 0.000 0.000 0.008
#> SRR975570     2  0.0508      0.884 0.012 0.984 0.000 0.000 0.004 0.000
#> SRR975571     2  0.1918      0.871 0.088 0.904 0.000 0.000 0.000 0.008
#> SRR975572     2  0.0935      0.881 0.032 0.964 0.000 0.000 0.004 0.000
#> SRR975573     2  0.1918      0.871 0.088 0.904 0.000 0.000 0.000 0.008
#> SRR975574     2  0.1918      0.871 0.088 0.904 0.000 0.000 0.000 0.008
#> SRR975575     2  0.0937      0.881 0.040 0.960 0.000 0.000 0.000 0.000
#> SRR975576     2  0.1493      0.874 0.056 0.936 0.000 0.000 0.004 0.004
#> SRR975577     2  0.1918      0.871 0.088 0.904 0.000 0.000 0.000 0.008
#> SRR975578     2  0.1918      0.871 0.088 0.904 0.000 0.000 0.000 0.008
#> SRR975579     4  0.0000      0.745 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR975580     5  0.5454      0.085 0.104 0.432 0.000 0.000 0.460 0.004
#> SRR975581     2  0.1674      0.869 0.068 0.924 0.000 0.000 0.004 0.004
#> SRR975582     2  0.1918      0.871 0.088 0.904 0.000 0.000 0.000 0.008
#> SRR975583     2  0.1364      0.877 0.048 0.944 0.000 0.000 0.004 0.004
#> SRR975584     2  0.1918      0.871 0.088 0.904 0.000 0.000 0.000 0.008
#> SRR975585     2  0.1296      0.878 0.044 0.948 0.000 0.000 0.004 0.004
#> SRR975586     2  0.3756      0.666 0.316 0.676 0.000 0.000 0.004 0.004
#> SRR975587     3  0.0146      0.914 0.004 0.000 0.996 0.000 0.000 0.000
#> SRR975588     2  0.0692      0.884 0.020 0.976 0.000 0.000 0.000 0.004
#> SRR975589     6  0.1578      0.793 0.012 0.000 0.004 0.000 0.048 0.936
#> SRR975590     1  0.5458      0.826 0.544 0.000 0.060 0.000 0.364 0.032
#> SRR975591     3  0.0260      0.912 0.000 0.000 0.992 0.000 0.000 0.008
#> SRR975592     3  0.4798      0.417 0.080 0.000 0.620 0.000 0.000 0.300
#> SRR975593     6  0.4712      0.724 0.012 0.000 0.100 0.004 0.168 0.716
#> SRR975594     3  0.0146      0.914 0.004 0.000 0.996 0.000 0.000 0.000
#> SRR975595     5  0.4293      0.184 0.164 0.000 0.096 0.000 0.736 0.004
#> SRR975597     1  0.5208      0.806 0.500 0.000 0.048 0.000 0.432 0.020
#> SRR975596     5  0.4411      0.341 0.004 0.000 0.000 0.080 0.712 0.204
#> SRR975598     5  0.2728      0.375 0.080 0.000 0.040 0.000 0.872 0.008
#> SRR975599     5  0.1036      0.437 0.024 0.000 0.004 0.000 0.964 0.008
#> SRR975600     6  0.3323      0.576 0.008 0.000 0.240 0.000 0.000 0.752
#> SRR975601     3  0.0146      0.914 0.004 0.000 0.996 0.000 0.000 0.000
#> SRR975602     1  0.4396      0.834 0.520 0.000 0.000 0.000 0.456 0.024
#> SRR975603     3  0.1471      0.871 0.004 0.000 0.932 0.000 0.000 0.064
#> SRR975604     3  0.0146      0.913 0.004 0.000 0.996 0.000 0.000 0.000

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

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

consensus_heatmap(res, k = 2)

plot of chunk tab-SD-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

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 17171 rows and 54 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#>   Subgroups are detected by 'hclust' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 4.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk CV-hclust-collect-plots

The plots are:

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

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

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

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

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

select_partition_number(res)

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

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.537           0.731       0.878         0.2001 0.927   0.927
#> 3 3 0.586           0.683       0.814         1.3586 0.706   0.683
#> 4 4 0.839           0.882       0.920         0.4036 0.695   0.518
#> 5 5 0.793           0.806       0.866         0.0850 0.951   0.851
#> 6 6 0.863           0.781       0.881         0.0433 0.985   0.948

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

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

suggest_best_k(res)

#> [1] 4

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

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

show/hide code output

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

#>           class entropy silhouette    p1    p2
#> SRR975551     1  0.2423      0.807 0.960 0.040
#> SRR975552     1  0.2423      0.807 0.960 0.040
#> SRR975554     1  0.2423      0.807 0.960 0.040
#> SRR975553     1  0.0000      0.806 1.000 0.000
#> SRR975555     1  0.2423      0.807 0.960 0.040
#> SRR975556     1  0.0000      0.806 1.000 0.000
#> SRR975557     2  0.9896      1.000 0.440 0.560
#> SRR975558     1  0.2423      0.807 0.960 0.040
#> SRR975559     1  0.2423      0.807 0.960 0.040
#> SRR975560     1  0.0000      0.806 1.000 0.000
#> SRR975561     1  0.0376      0.802 0.996 0.004
#> SRR975562     1  0.2423      0.807 0.960 0.040
#> SRR975563     1  0.0000      0.806 1.000 0.000
#> SRR975564     1  0.2423      0.807 0.960 0.040
#> SRR975565     1  0.2423      0.807 0.960 0.040
#> SRR975566     1  0.2423      0.807 0.960 0.040
#> SRR975567     1  0.2423      0.807 0.960 0.040
#> SRR975568     1  0.2423      0.807 0.960 0.040
#> SRR975569     1  0.0000      0.806 1.000 0.000
#> SRR975570     1  0.0000      0.806 1.000 0.000
#> SRR975571     1  0.0000      0.806 1.000 0.000
#> SRR975572     1  0.0000      0.806 1.000 0.000
#> SRR975573     1  0.0000      0.806 1.000 0.000
#> SRR975574     1  0.0000      0.806 1.000 0.000
#> SRR975575     1  0.0000      0.806 1.000 0.000
#> SRR975576     1  0.0000      0.806 1.000 0.000
#> SRR975577     1  0.0000      0.806 1.000 0.000
#> SRR975578     1  0.0000      0.806 1.000 0.000
#> SRR975579     2  0.9896      1.000 0.440 0.560
#> SRR975580     1  0.0000      0.806 1.000 0.000
#> SRR975581     1  0.0000      0.806 1.000 0.000
#> SRR975582     1  0.0000      0.806 1.000 0.000
#> SRR975583     1  0.0000      0.806 1.000 0.000
#> SRR975584     1  0.0000      0.806 1.000 0.000
#> SRR975585     1  0.0000      0.806 1.000 0.000
#> SRR975586     1  0.0000      0.806 1.000 0.000
#> SRR975587     1  0.9896      0.410 0.560 0.440
#> SRR975588     1  0.0000      0.806 1.000 0.000
#> SRR975589     1  0.9286      0.545 0.656 0.344
#> SRR975590     1  0.9000      0.571 0.684 0.316
#> SRR975591     1  0.9896      0.410 0.560 0.440
#> SRR975592     1  0.9286      0.545 0.656 0.344
#> SRR975593     1  0.9286      0.545 0.656 0.344
#> SRR975594     1  0.9896      0.410 0.560 0.440
#> SRR975595     1  0.9170      0.557 0.668 0.332
#> SRR975597     1  0.9170      0.557 0.668 0.332
#> SRR975596     1  0.2423      0.807 0.960 0.040
#> SRR975598     1  0.9170      0.557 0.668 0.332
#> SRR975599     1  0.5629      0.736 0.868 0.132
#> SRR975600     1  0.9286      0.545 0.656 0.344
#> SRR975601     1  0.9896      0.410 0.560 0.440
#> SRR975602     1  0.2423      0.807 0.960 0.040
#> SRR975603     1  0.9896      0.410 0.560 0.440
#> SRR975604     1  0.9896      0.410 0.560 0.440

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> SRR975551     2  0.6225      0.616 0.432 0.568 0.000
#> SRR975552     2  0.6225      0.616 0.432 0.568 0.000
#> SRR975554     2  0.6225      0.616 0.432 0.568 0.000
#> SRR975553     2  0.0000      0.673 0.000 1.000 0.000
#> SRR975555     2  0.6225      0.616 0.432 0.568 0.000
#> SRR975556     2  0.0000      0.673 0.000 1.000 0.000
#> SRR975557     1  0.6225      1.000 0.568 0.432 0.000
#> SRR975558     2  0.5948      0.632 0.360 0.640 0.000
#> SRR975559     2  0.6225      0.616 0.432 0.568 0.000
#> SRR975560     2  0.1964      0.666 0.056 0.944 0.000
#> SRR975561     2  0.0237      0.668 0.004 0.996 0.000
#> SRR975562     2  0.6225      0.616 0.432 0.568 0.000
#> SRR975563     2  0.0000      0.673 0.000 1.000 0.000
#> SRR975564     2  0.6225      0.616 0.432 0.568 0.000
#> SRR975565     2  0.6225      0.616 0.432 0.568 0.000
#> SRR975566     2  0.6225      0.616 0.432 0.568 0.000
#> SRR975567     2  0.5835      0.635 0.340 0.660 0.000
#> SRR975568     2  0.6225      0.616 0.432 0.568 0.000
#> SRR975569     2  0.0000      0.673 0.000 1.000 0.000
#> SRR975570     2  0.0000      0.673 0.000 1.000 0.000
#> SRR975571     2  0.0000      0.673 0.000 1.000 0.000
#> SRR975572     2  0.0000      0.673 0.000 1.000 0.000
#> SRR975573     2  0.0000      0.673 0.000 1.000 0.000
#> SRR975574     2  0.0000      0.673 0.000 1.000 0.000
#> SRR975575     2  0.0000      0.673 0.000 1.000 0.000
#> SRR975576     2  0.0000      0.673 0.000 1.000 0.000
#> SRR975577     2  0.0000      0.673 0.000 1.000 0.000
#> SRR975578     2  0.0000      0.673 0.000 1.000 0.000
#> SRR975579     1  0.6225      1.000 0.568 0.432 0.000
#> SRR975580     2  0.1964      0.666 0.056 0.944 0.000
#> SRR975581     2  0.0000      0.673 0.000 1.000 0.000
#> SRR975582     2  0.0000      0.673 0.000 1.000 0.000
#> SRR975583     2  0.0000      0.673 0.000 1.000 0.000
#> SRR975584     2  0.0000      0.673 0.000 1.000 0.000
#> SRR975585     2  0.0000      0.673 0.000 1.000 0.000
#> SRR975586     2  0.0000      0.673 0.000 1.000 0.000
#> SRR975587     3  0.0000      0.834 0.000 0.000 1.000
#> SRR975588     2  0.0000      0.673 0.000 1.000 0.000
#> SRR975589     3  0.6286      0.790 0.136 0.092 0.772
#> SRR975590     2  0.8889      0.495 0.164 0.560 0.276
#> SRR975591     3  0.1289      0.853 0.000 0.032 0.968
#> SRR975592     3  0.6286      0.790 0.136 0.092 0.772
#> SRR975593     3  0.6286      0.790 0.136 0.092 0.772
#> SRR975594     3  0.0000      0.834 0.000 0.000 1.000
#> SRR975595     2  0.8801      0.485 0.148 0.560 0.292
#> SRR975597     2  0.8801      0.485 0.148 0.560 0.292
#> SRR975596     2  0.6225      0.616 0.432 0.568 0.000
#> SRR975598     2  0.8801      0.485 0.148 0.560 0.292
#> SRR975599     2  0.8297      0.588 0.348 0.560 0.092
#> SRR975600     3  0.6208      0.793 0.136 0.088 0.776
#> SRR975601     3  0.0000      0.834 0.000 0.000 1.000
#> SRR975602     2  0.6225      0.616 0.432 0.568 0.000
#> SRR975603     3  0.1289      0.853 0.000 0.032 0.968
#> SRR975604     3  0.1289      0.853 0.000 0.032 0.968

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> SRR975551     1  0.1022      0.895 0.968 0.032 0.000 0.000
#> SRR975552     1  0.1022      0.895 0.968 0.032 0.000 0.000
#> SRR975554     1  0.1022      0.895 0.968 0.032 0.000 0.000
#> SRR975553     2  0.0000      0.990 0.000 1.000 0.000 0.000
#> SRR975555     1  0.1022      0.895 0.968 0.032 0.000 0.000
#> SRR975556     2  0.0000      0.990 0.000 1.000 0.000 0.000
#> SRR975557     4  0.3610      1.000 0.000 0.200 0.000 0.800
#> SRR975558     1  0.2469      0.813 0.892 0.108 0.000 0.000
#> SRR975559     1  0.0707      0.877 0.980 0.020 0.000 0.000
#> SRR975560     2  0.1557      0.912 0.056 0.944 0.000 0.000
#> SRR975561     2  0.1211      0.944 0.000 0.960 0.000 0.040
#> SRR975562     1  0.1474      0.885 0.948 0.052 0.000 0.000
#> SRR975563     2  0.0000      0.990 0.000 1.000 0.000 0.000
#> SRR975564     1  0.1022      0.895 0.968 0.032 0.000 0.000
#> SRR975565     1  0.1022      0.895 0.968 0.032 0.000 0.000
#> SRR975566     1  0.0707      0.877 0.980 0.020 0.000 0.000
#> SRR975567     1  0.2760      0.789 0.872 0.128 0.000 0.000
#> SRR975568     1  0.1022      0.895 0.968 0.032 0.000 0.000
#> SRR975569     2  0.0000      0.990 0.000 1.000 0.000 0.000
#> SRR975570     2  0.0000      0.990 0.000 1.000 0.000 0.000
#> SRR975571     2  0.0000      0.990 0.000 1.000 0.000 0.000
#> SRR975572     2  0.0000      0.990 0.000 1.000 0.000 0.000
#> SRR975573     2  0.0000      0.990 0.000 1.000 0.000 0.000
#> SRR975574     2  0.0000      0.990 0.000 1.000 0.000 0.000
#> SRR975575     2  0.0000      0.990 0.000 1.000 0.000 0.000
#> SRR975576     2  0.0000      0.990 0.000 1.000 0.000 0.000
#> SRR975577     2  0.0000      0.990 0.000 1.000 0.000 0.000
#> SRR975578     2  0.0000      0.990 0.000 1.000 0.000 0.000
#> SRR975579     4  0.3610      1.000 0.000 0.200 0.000 0.800
#> SRR975580     2  0.1557      0.912 0.056 0.944 0.000 0.000
#> SRR975581     2  0.0000      0.990 0.000 1.000 0.000 0.000
#> SRR975582     2  0.0000      0.990 0.000 1.000 0.000 0.000
#> SRR975583     2  0.0000      0.990 0.000 1.000 0.000 0.000
#> SRR975584     2  0.0000      0.990 0.000 1.000 0.000 0.000
#> SRR975585     2  0.0000      0.990 0.000 1.000 0.000 0.000
#> SRR975586     2  0.0000      0.990 0.000 1.000 0.000 0.000
#> SRR975587     3  0.0000      0.758 0.000 0.000 1.000 0.000
#> SRR975588     2  0.0000      0.990 0.000 1.000 0.000 0.000
#> SRR975589     3  0.7058      0.649 0.228 0.000 0.572 0.200
#> SRR975590     1  0.6367      0.697 0.692 0.032 0.076 0.200
#> SRR975591     3  0.1022      0.767 0.032 0.000 0.968 0.000
#> SRR975592     3  0.6790      0.666 0.228 0.000 0.604 0.168
#> SRR975593     3  0.7058      0.649 0.228 0.000 0.572 0.200
#> SRR975594     3  0.0000      0.758 0.000 0.000 1.000 0.000
#> SRR975595     1  0.6609      0.678 0.676 0.032 0.092 0.200
#> SRR975597     1  0.6609      0.678 0.676 0.032 0.092 0.200
#> SRR975596     1  0.0707      0.877 0.980 0.020 0.000 0.000
#> SRR975598     1  0.6609      0.678 0.676 0.032 0.092 0.200
#> SRR975599     1  0.3215      0.842 0.876 0.032 0.092 0.000
#> SRR975600     3  0.6761      0.669 0.224 0.000 0.608 0.168
#> SRR975601     3  0.0000      0.758 0.000 0.000 1.000 0.000
#> SRR975602     1  0.1022      0.895 0.968 0.032 0.000 0.000
#> SRR975603     3  0.1022      0.767 0.032 0.000 0.968 0.000
#> SRR975604     3  0.1022      0.767 0.032 0.000 0.968 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
#> SRR975551     1  0.0609      0.705 0.980 0.000 0.000 0.000 0.020
#> SRR975552     1  0.0609      0.705 0.980 0.000 0.000 0.000 0.020
#> SRR975554     1  0.0290      0.711 0.992 0.000 0.000 0.000 0.008
#> SRR975553     2  0.0000      0.988 0.000 1.000 0.000 0.000 0.000
#> SRR975555     1  0.3395      0.586 0.764 0.000 0.000 0.000 0.236
#> SRR975556     2  0.0000      0.988 0.000 1.000 0.000 0.000 0.000
#> SRR975557     4  0.2377      1.000 0.000 0.128 0.000 0.872 0.000
#> SRR975558     5  0.4280      0.726 0.140 0.088 0.000 0.000 0.772
#> SRR975559     5  0.4101      0.794 0.372 0.000 0.000 0.000 0.628
#> SRR975560     2  0.1484      0.927 0.008 0.944 0.000 0.000 0.048
#> SRR975561     2  0.2074      0.865 0.000 0.896 0.000 0.104 0.000
#> SRR975562     5  0.4201      0.756 0.408 0.000 0.000 0.000 0.592
#> SRR975563     2  0.0000      0.988 0.000 1.000 0.000 0.000 0.000
#> SRR975564     1  0.3983      0.406 0.660 0.000 0.000 0.000 0.340
#> SRR975565     1  0.2516      0.678 0.860 0.000 0.000 0.000 0.140
#> SRR975566     1  0.3305      0.351 0.776 0.000 0.000 0.000 0.224
#> SRR975567     5  0.4617      0.715 0.148 0.108 0.000 0.000 0.744
#> SRR975568     1  0.3395      0.586 0.764 0.000 0.000 0.000 0.236
#> SRR975569     2  0.0000      0.988 0.000 1.000 0.000 0.000 0.000
#> SRR975570     2  0.0000      0.988 0.000 1.000 0.000 0.000 0.000
#> SRR975571     2  0.0000      0.988 0.000 1.000 0.000 0.000 0.000
#> SRR975572     2  0.0000      0.988 0.000 1.000 0.000 0.000 0.000
#> SRR975573     2  0.0000      0.988 0.000 1.000 0.000 0.000 0.000
#> SRR975574     2  0.0000      0.988 0.000 1.000 0.000 0.000 0.000
#> SRR975575     2  0.0000      0.988 0.000 1.000 0.000 0.000 0.000
#> SRR975576     2  0.0000      0.988 0.000 1.000 0.000 0.000 0.000
#> SRR975577     2  0.0000      0.988 0.000 1.000 0.000 0.000 0.000
#> SRR975578     2  0.0000      0.988 0.000 1.000 0.000 0.000 0.000
#> SRR975579     4  0.2377      1.000 0.000 0.128 0.000 0.872 0.000
#> SRR975580     2  0.1484      0.927 0.008 0.944 0.000 0.000 0.048
#> SRR975581     2  0.0000      0.988 0.000 1.000 0.000 0.000 0.000
#> SRR975582     2  0.0000      0.988 0.000 1.000 0.000 0.000 0.000
#> SRR975583     2  0.0000      0.988 0.000 1.000 0.000 0.000 0.000
#> SRR975584     2  0.0000      0.988 0.000 1.000 0.000 0.000 0.000
#> SRR975585     2  0.0000      0.988 0.000 1.000 0.000 0.000 0.000
#> SRR975586     2  0.0000      0.988 0.000 1.000 0.000 0.000 0.000
#> SRR975587     3  0.1732      0.682 0.000 0.000 0.920 0.000 0.080
#> SRR975588     2  0.0000      0.988 0.000 1.000 0.000 0.000 0.000
#> SRR975589     3  0.7586      0.576 0.160 0.000 0.512 0.128 0.200
#> SRR975590     1  0.5322      0.645 0.708 0.000 0.016 0.128 0.148
#> SRR975591     3  0.0880      0.713 0.000 0.000 0.968 0.000 0.032
#> SRR975592     3  0.7325      0.601 0.160 0.000 0.544 0.108 0.188
#> SRR975593     3  0.7586      0.576 0.160 0.000 0.512 0.128 0.200
#> SRR975594     3  0.1732      0.682 0.000 0.000 0.920 0.000 0.080
#> SRR975595     1  0.5620      0.641 0.696 0.000 0.032 0.128 0.144
#> SRR975597     1  0.5620      0.641 0.696 0.000 0.032 0.128 0.144
#> SRR975596     5  0.4114      0.792 0.376 0.000 0.000 0.000 0.624
#> SRR975598     1  0.5620      0.641 0.696 0.000 0.032 0.128 0.144
#> SRR975599     1  0.2473      0.702 0.896 0.000 0.032 0.000 0.072
#> SRR975600     3  0.7295      0.605 0.156 0.000 0.548 0.108 0.188
#> SRR975601     3  0.1732      0.682 0.000 0.000 0.920 0.000 0.080
#> SRR975602     1  0.0000      0.711 1.000 0.000 0.000 0.000 0.000
#> SRR975603     3  0.0880      0.713 0.000 0.000 0.968 0.000 0.032
#> SRR975604     3  0.0880      0.713 0.000 0.000 0.968 0.000 0.032

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> SRR975551     1  0.0790      0.644 0.968 0.000 0.000 0.032 0.000 0.000
#> SRR975552     1  0.0790      0.644 0.968 0.000 0.000 0.032 0.000 0.000
#> SRR975554     1  0.1528      0.651 0.936 0.000 0.048 0.016 0.000 0.000
#> SRR975553     2  0.0000      0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975555     1  0.3515      0.499 0.676 0.000 0.000 0.324 0.000 0.000
#> SRR975556     2  0.0000      0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975557     5  0.0000      1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR975558     4  0.0632      0.714 0.000 0.024 0.000 0.976 0.000 0.000
#> SRR975559     4  0.3126      0.816 0.248 0.000 0.000 0.752 0.000 0.000
#> SRR975560     2  0.1806      0.900 0.004 0.908 0.000 0.088 0.000 0.000
#> SRR975561     2  0.2969      0.726 0.000 0.776 0.000 0.000 0.224 0.000
#> SRR975562     4  0.3330      0.784 0.284 0.000 0.000 0.716 0.000 0.000
#> SRR975563     2  0.0000      0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975564     1  0.3810      0.370 0.572 0.000 0.000 0.428 0.000 0.000
#> SRR975565     1  0.2631      0.622 0.820 0.000 0.000 0.180 0.000 0.000
#> SRR975566     1  0.3076      0.334 0.760 0.000 0.000 0.240 0.000 0.000
#> SRR975567     4  0.1434      0.718 0.012 0.048 0.000 0.940 0.000 0.000
#> SRR975568     1  0.3515      0.499 0.676 0.000 0.000 0.324 0.000 0.000
#> SRR975569     2  0.0000      0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975570     2  0.0000      0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975571     2  0.0000      0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975572     2  0.0000      0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975573     2  0.0000      0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975574     2  0.0000      0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975575     2  0.0000      0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975576     2  0.0000      0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975577     2  0.0000      0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975578     2  0.0000      0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975579     5  0.0000      1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR975580     2  0.1753      0.904 0.004 0.912 0.000 0.084 0.000 0.000
#> SRR975581     2  0.0000      0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975582     2  0.0000      0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975583     2  0.0000      0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975584     2  0.0000      0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975585     2  0.0000      0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975586     2  0.0000      0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975587     6  0.0000      1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR975588     2  0.0000      0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975589     3  0.0000      0.665 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975590     1  0.3883      0.590 0.656 0.000 0.332 0.012 0.000 0.000
#> SRR975591     3  0.3867      0.295 0.000 0.000 0.512 0.000 0.000 0.488
#> SRR975592     3  0.0790      0.675 0.000 0.000 0.968 0.000 0.000 0.032
#> SRR975593     3  0.0000      0.665 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975594     6  0.0000      1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR975595     1  0.3843      0.507 0.548 0.000 0.452 0.000 0.000 0.000
#> SRR975597     1  0.3843      0.507 0.548 0.000 0.452 0.000 0.000 0.000
#> SRR975596     4  0.3151      0.815 0.252 0.000 0.000 0.748 0.000 0.000
#> SRR975598     1  0.3843      0.507 0.548 0.000 0.452 0.000 0.000 0.000
#> SRR975599     1  0.3151      0.613 0.748 0.000 0.252 0.000 0.000 0.000
#> SRR975600     3  0.0865      0.674 0.000 0.000 0.964 0.000 0.000 0.036
#> SRR975601     6  0.0000      1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR975602     1  0.0363      0.648 0.988 0.000 0.000 0.012 0.000 0.000
#> SRR975603     3  0.3867      0.295 0.000 0.000 0.512 0.000 0.000 0.488
#> SRR975604     3  0.3868      0.278 0.000 0.000 0.504 0.000 0.000 0.496

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

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 17171 rows and 54 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#>   Subgroups are detected by 'kmeans' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 2.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk CV-kmeans-collect-plots

The plots are:

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

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

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

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

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

select_partition_number(res)

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

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.633           0.936       0.956         0.4908 0.491   0.491
#> 3 3 0.781           0.860       0.890         0.3090 0.772   0.568
#> 4 4 0.761           0.729       0.851         0.1010 0.901   0.734
#> 5 5 0.725           0.728       0.771         0.0688 0.957   0.862
#> 6 6 0.722           0.437       0.659         0.0479 0.973   0.901

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
#> SRR975551     1   0.482      0.928 0.896 0.104
#> SRR975552     1   0.781      0.766 0.768 0.232
#> SRR975554     1   0.482      0.928 0.896 0.104
#> SRR975553     2   0.118      0.976 0.016 0.984
#> SRR975555     1   0.482      0.928 0.896 0.104
#> SRR975556     2   0.118      0.976 0.016 0.984
#> SRR975557     2   0.000      0.963 0.000 1.000
#> SRR975558     2   0.961      0.329 0.384 0.616
#> SRR975559     1   0.482      0.928 0.896 0.104
#> SRR975560     2   0.118      0.976 0.016 0.984
#> SRR975561     2   0.000      0.963 0.000 1.000
#> SRR975562     1   0.482      0.928 0.896 0.104
#> SRR975563     2   0.118      0.976 0.016 0.984
#> SRR975564     1   0.482      0.928 0.896 0.104
#> SRR975565     1   0.482      0.928 0.896 0.104
#> SRR975566     1   0.482      0.928 0.896 0.104
#> SRR975567     2   0.625      0.810 0.156 0.844
#> SRR975568     1   0.482      0.928 0.896 0.104
#> SRR975569     2   0.118      0.976 0.016 0.984
#> SRR975570     2   0.118      0.976 0.016 0.984
#> SRR975571     2   0.118      0.976 0.016 0.984
#> SRR975572     2   0.118      0.976 0.016 0.984
#> SRR975573     2   0.118      0.976 0.016 0.984
#> SRR975574     2   0.118      0.976 0.016 0.984
#> SRR975575     2   0.118      0.976 0.016 0.984
#> SRR975576     2   0.118      0.976 0.016 0.984
#> SRR975577     2   0.118      0.976 0.016 0.984
#> SRR975578     2   0.118      0.976 0.016 0.984
#> SRR975579     2   0.000      0.963 0.000 1.000
#> SRR975580     2   0.118      0.976 0.016 0.984
#> SRR975581     2   0.118      0.976 0.016 0.984
#> SRR975582     2   0.118      0.976 0.016 0.984
#> SRR975583     2   0.118      0.976 0.016 0.984
#> SRR975584     2   0.118      0.976 0.016 0.984
#> SRR975585     2   0.118      0.976 0.016 0.984
#> SRR975586     2   0.118      0.976 0.016 0.984
#> SRR975587     1   0.000      0.938 1.000 0.000
#> SRR975588     2   0.118      0.976 0.016 0.984
#> SRR975589     1   0.000      0.938 1.000 0.000
#> SRR975590     1   0.000      0.938 1.000 0.000
#> SRR975591     1   0.000      0.938 1.000 0.000
#> SRR975592     1   0.000      0.938 1.000 0.000
#> SRR975593     1   0.000      0.938 1.000 0.000
#> SRR975594     1   0.000      0.938 1.000 0.000
#> SRR975595     1   0.000      0.938 1.000 0.000
#> SRR975597     1   0.000      0.938 1.000 0.000
#> SRR975596     1   0.482      0.928 0.896 0.104
#> SRR975598     1   0.000      0.938 1.000 0.000
#> SRR975599     1   0.482      0.928 0.896 0.104
#> SRR975600     1   0.000      0.938 1.000 0.000
#> SRR975601     1   0.000      0.938 1.000 0.000
#> SRR975602     1   0.482      0.928 0.896 0.104
#> SRR975603     1   0.000      0.938 1.000 0.000
#> SRR975604     1   0.000      0.938 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
#> SRR975551     1  0.5201     0.8231 0.760 0.004 0.236
#> SRR975552     1  0.4575     0.8028 0.812 0.004 0.184
#> SRR975554     1  0.5201     0.8231 0.760 0.004 0.236
#> SRR975553     2  0.0000     0.9824 0.000 1.000 0.000
#> SRR975555     1  0.5201     0.8231 0.760 0.004 0.236
#> SRR975556     2  0.0000     0.9824 0.000 1.000 0.000
#> SRR975557     1  0.6215    -0.0177 0.572 0.428 0.000
#> SRR975558     1  0.2918     0.6919 0.924 0.044 0.032
#> SRR975559     1  0.1525     0.7112 0.964 0.004 0.032
#> SRR975560     1  0.5216     0.4752 0.740 0.260 0.000
#> SRR975561     2  0.4399     0.8082 0.188 0.812 0.000
#> SRR975562     1  0.5201     0.8231 0.760 0.004 0.236
#> SRR975563     2  0.0000     0.9824 0.000 1.000 0.000
#> SRR975564     1  0.5201     0.8231 0.760 0.004 0.236
#> SRR975565     1  0.5201     0.8231 0.760 0.004 0.236
#> SRR975566     1  0.5201     0.8231 0.760 0.004 0.236
#> SRR975567     1  0.2918     0.6919 0.924 0.044 0.032
#> SRR975568     1  0.5201     0.8231 0.760 0.004 0.236
#> SRR975569     2  0.0000     0.9824 0.000 1.000 0.000
#> SRR975570     2  0.0000     0.9824 0.000 1.000 0.000
#> SRR975571     2  0.0000     0.9824 0.000 1.000 0.000
#> SRR975572     2  0.0000     0.9824 0.000 1.000 0.000
#> SRR975573     2  0.0000     0.9824 0.000 1.000 0.000
#> SRR975574     2  0.0000     0.9824 0.000 1.000 0.000
#> SRR975575     2  0.0000     0.9824 0.000 1.000 0.000
#> SRR975576     2  0.0000     0.9824 0.000 1.000 0.000
#> SRR975577     2  0.0000     0.9824 0.000 1.000 0.000
#> SRR975578     2  0.0000     0.9824 0.000 1.000 0.000
#> SRR975579     2  0.4974     0.7604 0.236 0.764 0.000
#> SRR975580     2  0.0000     0.9824 0.000 1.000 0.000
#> SRR975581     2  0.0000     0.9824 0.000 1.000 0.000
#> SRR975582     2  0.0000     0.9824 0.000 1.000 0.000
#> SRR975583     2  0.0000     0.9824 0.000 1.000 0.000
#> SRR975584     2  0.0000     0.9824 0.000 1.000 0.000
#> SRR975585     2  0.0000     0.9824 0.000 1.000 0.000
#> SRR975586     2  0.0000     0.9824 0.000 1.000 0.000
#> SRR975587     3  0.0237     0.8998 0.004 0.000 0.996
#> SRR975588     2  0.0000     0.9824 0.000 1.000 0.000
#> SRR975589     3  0.1753     0.8888 0.048 0.000 0.952
#> SRR975590     3  0.4346     0.7792 0.184 0.000 0.816
#> SRR975591     3  0.0000     0.8997 0.000 0.000 1.000
#> SRR975592     3  0.1031     0.8968 0.024 0.000 0.976
#> SRR975593     3  0.1753     0.8888 0.048 0.000 0.952
#> SRR975594     3  0.0237     0.8998 0.004 0.000 0.996
#> SRR975595     3  0.4750     0.7400 0.216 0.000 0.784
#> SRR975597     3  0.4750     0.7400 0.216 0.000 0.784
#> SRR975596     1  0.4784     0.8108 0.796 0.004 0.200
#> SRR975598     3  0.5465     0.6004 0.288 0.000 0.712
#> SRR975599     1  0.5201     0.8231 0.760 0.004 0.236
#> SRR975600     3  0.0000     0.8997 0.000 0.000 1.000
#> SRR975601     3  0.0237     0.8998 0.004 0.000 0.996
#> SRR975602     1  0.5201     0.8231 0.760 0.004 0.236
#> SRR975603     3  0.0000     0.8997 0.000 0.000 1.000
#> SRR975604     3  0.0000     0.8997 0.000 0.000 1.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> SRR975551     1  0.0188      0.769 0.996 0.000 0.000 0.004
#> SRR975552     1  0.0592      0.766 0.984 0.000 0.000 0.016
#> SRR975554     1  0.0188      0.769 0.996 0.000 0.000 0.004
#> SRR975553     2  0.3071      0.901 0.000 0.888 0.044 0.068
#> SRR975555     1  0.0188      0.769 0.996 0.000 0.000 0.004
#> SRR975556     2  0.0336      0.917 0.000 0.992 0.000 0.008
#> SRR975557     4  0.5977      0.360 0.220 0.080 0.008 0.692
#> SRR975558     1  0.5093      0.423 0.640 0.012 0.000 0.348
#> SRR975559     1  0.3801      0.606 0.780 0.000 0.000 0.220
#> SRR975560     1  0.5898      0.332 0.604 0.048 0.000 0.348
#> SRR975561     4  0.4999      0.368 0.000 0.492 0.000 0.508
#> SRR975562     1  0.0336      0.768 0.992 0.000 0.000 0.008
#> SRR975563     2  0.0000      0.923 0.000 1.000 0.000 0.000
#> SRR975564     1  0.0707      0.768 0.980 0.000 0.000 0.020
#> SRR975565     1  0.0188      0.769 0.996 0.000 0.000 0.004
#> SRR975566     1  0.0336      0.768 0.992 0.000 0.000 0.008
#> SRR975567     1  0.5110      0.413 0.636 0.012 0.000 0.352
#> SRR975568     1  0.0707      0.768 0.980 0.000 0.000 0.020
#> SRR975569     2  0.0000      0.923 0.000 1.000 0.000 0.000
#> SRR975570     2  0.0000      0.923 0.000 1.000 0.000 0.000
#> SRR975571     2  0.3071      0.901 0.000 0.888 0.044 0.068
#> SRR975572     2  0.0000      0.923 0.000 1.000 0.000 0.000
#> SRR975573     2  0.3071      0.901 0.000 0.888 0.044 0.068
#> SRR975574     2  0.3071      0.901 0.000 0.888 0.044 0.068
#> SRR975575     2  0.0000      0.923 0.000 1.000 0.000 0.000
#> SRR975576     2  0.0000      0.923 0.000 1.000 0.000 0.000
#> SRR975577     2  0.3071      0.901 0.000 0.888 0.044 0.068
#> SRR975578     2  0.3071      0.901 0.000 0.888 0.044 0.068
#> SRR975579     4  0.4836      0.635 0.000 0.320 0.008 0.672
#> SRR975580     2  0.3037      0.900 0.000 0.888 0.036 0.076
#> SRR975581     2  0.0000      0.923 0.000 1.000 0.000 0.000
#> SRR975582     2  0.3071      0.901 0.000 0.888 0.044 0.068
#> SRR975583     2  0.0000      0.923 0.000 1.000 0.000 0.000
#> SRR975584     2  0.3071      0.901 0.000 0.888 0.044 0.068
#> SRR975585     2  0.0000      0.923 0.000 1.000 0.000 0.000
#> SRR975586     2  0.2149      0.810 0.000 0.912 0.000 0.088
#> SRR975587     3  0.2759      0.863 0.052 0.000 0.904 0.044
#> SRR975588     2  0.0000      0.923 0.000 1.000 0.000 0.000
#> SRR975589     3  0.5376      0.813 0.088 0.000 0.736 0.176
#> SRR975590     3  0.7762      0.224 0.380 0.000 0.384 0.236
#> SRR975591     3  0.1474      0.864 0.052 0.000 0.948 0.000
#> SRR975592     3  0.5076      0.823 0.072 0.000 0.756 0.172
#> SRR975593     3  0.5334      0.814 0.088 0.000 0.740 0.172
#> SRR975594     3  0.2759      0.863 0.052 0.000 0.904 0.044
#> SRR975595     1  0.7745     -0.237 0.412 0.000 0.352 0.236
#> SRR975597     1  0.7745     -0.237 0.412 0.000 0.352 0.236
#> SRR975596     1  0.2281      0.723 0.904 0.000 0.000 0.096
#> SRR975598     1  0.7679     -0.137 0.448 0.000 0.316 0.236
#> SRR975599     1  0.2647      0.713 0.880 0.000 0.000 0.120
#> SRR975600     3  0.3312      0.859 0.052 0.000 0.876 0.072
#> SRR975601     3  0.2759      0.863 0.052 0.000 0.904 0.044
#> SRR975602     1  0.2149      0.734 0.912 0.000 0.000 0.088
#> SRR975603     3  0.1474      0.864 0.052 0.000 0.948 0.000
#> SRR975604     3  0.1474      0.864 0.052 0.000 0.948 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
#> SRR975551     1  0.0162      0.804 0.996 0.000 0.000 0.004 0.000
#> SRR975552     1  0.0898      0.808 0.972 0.000 0.000 0.008 0.020
#> SRR975554     1  0.0693      0.806 0.980 0.000 0.000 0.012 0.008
#> SRR975553     2  0.3999      0.711 0.000 0.656 0.000 0.000 0.344
#> SRR975555     1  0.2233      0.789 0.904 0.000 0.000 0.016 0.080
#> SRR975556     2  0.2280      0.688 0.000 0.880 0.000 0.000 0.120
#> SRR975557     4  0.2584      0.653 0.052 0.032 0.008 0.904 0.004
#> SRR975558     1  0.6120      0.568 0.580 0.004 0.000 0.172 0.244
#> SRR975559     1  0.3810      0.755 0.812 0.000 0.000 0.088 0.100
#> SRR975560     1  0.6841      0.494 0.552 0.044 0.000 0.156 0.248
#> SRR975561     4  0.5889      0.395 0.000 0.392 0.000 0.504 0.104
#> SRR975562     1  0.1768      0.804 0.924 0.000 0.000 0.004 0.072
#> SRR975563     2  0.0000      0.779 0.000 1.000 0.000 0.000 0.000
#> SRR975564     1  0.2208      0.804 0.908 0.000 0.000 0.020 0.072
#> SRR975565     1  0.1018      0.807 0.968 0.000 0.000 0.016 0.016
#> SRR975566     1  0.1638      0.804 0.932 0.000 0.000 0.004 0.064
#> SRR975567     1  0.6326      0.507 0.552 0.004 0.000 0.216 0.228
#> SRR975568     1  0.1943      0.801 0.924 0.000 0.000 0.020 0.056
#> SRR975569     2  0.0162      0.779 0.000 0.996 0.000 0.000 0.004
#> SRR975570     2  0.0162      0.779 0.000 0.996 0.000 0.000 0.004
#> SRR975571     2  0.3999      0.711 0.000 0.656 0.000 0.000 0.344
#> SRR975572     2  0.0000      0.779 0.000 1.000 0.000 0.000 0.000
#> SRR975573     2  0.3999      0.711 0.000 0.656 0.000 0.000 0.344
#> SRR975574     2  0.4015      0.710 0.000 0.652 0.000 0.000 0.348
#> SRR975575     2  0.0000      0.779 0.000 1.000 0.000 0.000 0.000
#> SRR975576     2  0.0000      0.779 0.000 1.000 0.000 0.000 0.000
#> SRR975577     2  0.4015      0.710 0.000 0.652 0.000 0.000 0.348
#> SRR975578     2  0.4015      0.710 0.000 0.652 0.000 0.000 0.348
#> SRR975579     4  0.2179      0.709 0.000 0.100 0.000 0.896 0.004
#> SRR975580     2  0.4150      0.642 0.000 0.612 0.000 0.000 0.388
#> SRR975581     2  0.0000      0.779 0.000 1.000 0.000 0.000 0.000
#> SRR975582     2  0.4015      0.710 0.000 0.652 0.000 0.000 0.348
#> SRR975583     2  0.0000      0.779 0.000 1.000 0.000 0.000 0.000
#> SRR975584     2  0.4015      0.710 0.000 0.652 0.000 0.000 0.348
#> SRR975585     2  0.0000      0.779 0.000 1.000 0.000 0.000 0.000
#> SRR975586     2  0.3184      0.614 0.000 0.852 0.000 0.048 0.100
#> SRR975587     3  0.2769      0.749 0.000 0.000 0.876 0.032 0.092
#> SRR975588     2  0.0162      0.779 0.000 0.996 0.000 0.000 0.004
#> SRR975589     3  0.5329      0.502 0.036 0.000 0.684 0.044 0.236
#> SRR975590     5  0.7547      0.917 0.268 0.000 0.324 0.040 0.368
#> SRR975591     3  0.0000      0.784 0.000 0.000 1.000 0.000 0.000
#> SRR975592     3  0.4775      0.575 0.028 0.000 0.740 0.040 0.192
#> SRR975593     3  0.5275      0.509 0.036 0.000 0.692 0.044 0.228
#> SRR975594     3  0.2769      0.749 0.000 0.000 0.876 0.032 0.092
#> SRR975595     5  0.7540      0.939 0.268 0.000 0.316 0.040 0.376
#> SRR975597     5  0.7540      0.939 0.268 0.000 0.316 0.040 0.376
#> SRR975596     1  0.3255      0.774 0.848 0.000 0.000 0.052 0.100
#> SRR975598     5  0.7534      0.857 0.328 0.000 0.260 0.040 0.372
#> SRR975599     1  0.3438      0.613 0.808 0.000 0.000 0.020 0.172
#> SRR975600     3  0.2409      0.749 0.000 0.000 0.900 0.032 0.068
#> SRR975601     3  0.2769      0.749 0.000 0.000 0.876 0.032 0.092
#> SRR975602     1  0.3399      0.620 0.812 0.000 0.000 0.020 0.168
#> SRR975603     3  0.0000      0.784 0.000 0.000 1.000 0.000 0.000
#> SRR975604     3  0.0000      0.784 0.000 0.000 1.000 0.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> SRR975551     1  0.1141    0.71619 0.948 0.000 0.000 0.000 0.052 0.000
#> SRR975552     1  0.2537    0.72346 0.872 0.000 0.000 0.000 0.096 0.032
#> SRR975554     1  0.1890    0.71520 0.916 0.000 0.000 0.000 0.060 0.024
#> SRR975553     2  0.0146    0.41600 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR975555     1  0.4261    0.68518 0.732 0.000 0.000 0.000 0.156 0.112
#> SRR975556     6  0.4334    0.67235 0.000 0.408 0.000 0.000 0.024 0.568
#> SRR975557     4  0.0508    0.64551 0.012 0.000 0.000 0.984 0.000 0.004
#> SRR975558     1  0.6375    0.45314 0.480 0.000 0.000 0.028 0.252 0.240
#> SRR975559     1  0.3956    0.68100 0.796 0.000 0.000 0.028 0.080 0.096
#> SRR975560     1  0.7152    0.36362 0.424 0.032 0.000 0.036 0.208 0.300
#> SRR975561     4  0.7053   -0.00791 0.000 0.164 0.000 0.404 0.104 0.328
#> SRR975562     1  0.3286    0.69940 0.832 0.000 0.000 0.012 0.044 0.112
#> SRR975563     2  0.3995   -0.19010 0.000 0.516 0.000 0.000 0.004 0.480
#> SRR975564     1  0.3878    0.70316 0.772 0.000 0.000 0.000 0.112 0.116
#> SRR975565     1  0.2586    0.72063 0.868 0.000 0.000 0.000 0.100 0.032
#> SRR975566     1  0.1767    0.71579 0.932 0.000 0.000 0.012 0.036 0.020
#> SRR975567     1  0.6990    0.39265 0.452 0.000 0.000 0.092 0.232 0.224
#> SRR975568     1  0.3958    0.70021 0.764 0.000 0.000 0.000 0.128 0.108
#> SRR975569     2  0.3991   -0.17453 0.000 0.524 0.000 0.000 0.004 0.472
#> SRR975570     2  0.3991   -0.17453 0.000 0.524 0.000 0.000 0.004 0.472
#> SRR975571     2  0.0146    0.41600 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR975572     2  0.3995   -0.19010 0.000 0.516 0.000 0.000 0.004 0.480
#> SRR975573     2  0.0000    0.41828 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975574     2  0.0000    0.41828 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975575     2  0.3995   -0.19010 0.000 0.516 0.000 0.000 0.004 0.480
#> SRR975576     2  0.3993   -0.18220 0.000 0.520 0.000 0.000 0.004 0.476
#> SRR975577     2  0.0000    0.41828 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975578     2  0.0146    0.41600 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR975579     4  0.0725    0.66084 0.000 0.012 0.000 0.976 0.000 0.012
#> SRR975580     2  0.4687   -0.02939 0.000 0.684 0.000 0.000 0.136 0.180
#> SRR975581     2  0.3866   -0.18860 0.000 0.516 0.000 0.000 0.000 0.484
#> SRR975582     2  0.0000    0.41828 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975583     2  0.3995   -0.19010 0.000 0.516 0.000 0.000 0.004 0.480
#> SRR975584     2  0.0000    0.41828 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975585     2  0.3995   -0.18792 0.000 0.516 0.000 0.000 0.004 0.480
#> SRR975586     6  0.5672    0.71644 0.000 0.360 0.000 0.020 0.100 0.520
#> SRR975587     3  0.3325    0.65979 0.000 0.000 0.820 0.000 0.096 0.084
#> SRR975588     2  0.3991   -0.17453 0.000 0.524 0.000 0.000 0.004 0.472
#> SRR975589     3  0.5871    0.38981 0.032 0.000 0.572 0.012 0.300 0.084
#> SRR975590     5  0.5204    0.93890 0.128 0.000 0.204 0.000 0.652 0.016
#> SRR975591     3  0.0000    0.71847 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975592     3  0.5421    0.38940 0.024 0.000 0.612 0.012 0.292 0.060
#> SRR975593     3  0.5798    0.39629 0.032 0.000 0.584 0.012 0.292 0.080
#> SRR975594     3  0.3325    0.65979 0.000 0.000 0.820 0.000 0.096 0.084
#> SRR975595     5  0.4653    0.96349 0.120 0.000 0.196 0.000 0.684 0.000
#> SRR975597     5  0.4653    0.96349 0.120 0.000 0.196 0.000 0.684 0.000
#> SRR975596     1  0.4061    0.68235 0.784 0.000 0.000 0.024 0.080 0.112
#> SRR975598     5  0.4701    0.93185 0.148 0.000 0.168 0.000 0.684 0.000
#> SRR975599     1  0.5074    0.31569 0.572 0.000 0.000 0.012 0.356 0.060
#> SRR975600     3  0.3646    0.63063 0.000 0.000 0.800 0.008 0.132 0.060
#> SRR975601     3  0.3325    0.65979 0.000 0.000 0.820 0.000 0.096 0.084
#> SRR975602     1  0.4917    0.41294 0.620 0.000 0.000 0.012 0.308 0.060
#> SRR975603     3  0.0000    0.71847 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975604     3  0.0000    0.71847 0.000 0.000 1.000 0.000 0.000 0.000

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

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

consensus_heatmap(res, k = 2)

plot of chunk tab-CV-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

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 17171 rows and 54 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#>   Subgroups are detected by 'skmeans' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 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 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           0.969       0.989         0.5093 0.491   0.491
#> 3 3 1.000           0.950       0.978         0.2882 0.820   0.646
#> 4 4 0.940           0.922       0.966         0.1108 0.918   0.766
#> 5 5 0.797           0.729       0.838         0.0586 0.994   0.980
#> 6 6 0.779           0.694       0.731         0.0452 0.921   0.710

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 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
#> SRR975551     1   0.000      0.999 1.000 0.000
#> SRR975552     1   0.224      0.961 0.964 0.036
#> SRR975554     1   0.000      0.999 1.000 0.000
#> SRR975553     2   0.000      0.977 0.000 1.000
#> SRR975555     1   0.000      0.999 1.000 0.000
#> SRR975556     2   0.000      0.977 0.000 1.000
#> SRR975557     2   0.000      0.977 0.000 1.000
#> SRR975558     2   0.998      0.116 0.472 0.528
#> SRR975559     1   0.000      0.999 1.000 0.000
#> SRR975560     2   0.000      0.977 0.000 1.000
#> SRR975561     2   0.000      0.977 0.000 1.000
#> SRR975562     1   0.000      0.999 1.000 0.000
#> SRR975563     2   0.000      0.977 0.000 1.000
#> SRR975564     1   0.000      0.999 1.000 0.000
#> SRR975565     1   0.000      0.999 1.000 0.000
#> SRR975566     1   0.000      0.999 1.000 0.000
#> SRR975567     2   0.506      0.861 0.112 0.888
#> SRR975568     1   0.000      0.999 1.000 0.000
#> SRR975569     2   0.000      0.977 0.000 1.000
#> SRR975570     2   0.000      0.977 0.000 1.000
#> SRR975571     2   0.000      0.977 0.000 1.000
#> SRR975572     2   0.000      0.977 0.000 1.000
#> SRR975573     2   0.000      0.977 0.000 1.000
#> SRR975574     2   0.000      0.977 0.000 1.000
#> SRR975575     2   0.000      0.977 0.000 1.000
#> SRR975576     2   0.000      0.977 0.000 1.000
#> SRR975577     2   0.000      0.977 0.000 1.000
#> SRR975578     2   0.000      0.977 0.000 1.000
#> SRR975579     2   0.000      0.977 0.000 1.000
#> SRR975580     2   0.000      0.977 0.000 1.000
#> SRR975581     2   0.000      0.977 0.000 1.000
#> SRR975582     2   0.000      0.977 0.000 1.000
#> SRR975583     2   0.000      0.977 0.000 1.000
#> SRR975584     2   0.000      0.977 0.000 1.000
#> SRR975585     2   0.000      0.977 0.000 1.000
#> SRR975586     2   0.000      0.977 0.000 1.000
#> SRR975587     1   0.000      0.999 1.000 0.000
#> SRR975588     2   0.000      0.977 0.000 1.000
#> SRR975589     1   0.000      0.999 1.000 0.000
#> SRR975590     1   0.000      0.999 1.000 0.000
#> SRR975591     1   0.000      0.999 1.000 0.000
#> SRR975592     1   0.000      0.999 1.000 0.000
#> SRR975593     1   0.000      0.999 1.000 0.000
#> SRR975594     1   0.000      0.999 1.000 0.000
#> SRR975595     1   0.000      0.999 1.000 0.000
#> SRR975597     1   0.000      0.999 1.000 0.000
#> SRR975596     1   0.000      0.999 1.000 0.000
#> SRR975598     1   0.000      0.999 1.000 0.000
#> SRR975599     1   0.000      0.999 1.000 0.000
#> SRR975600     1   0.000      0.999 1.000 0.000
#> SRR975601     1   0.000      0.999 1.000 0.000
#> SRR975602     1   0.000      0.999 1.000 0.000
#> SRR975603     1   0.000      0.999 1.000 0.000
#> SRR975604     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
#> SRR975551     1  0.0237      0.962 0.996 0.000 0.004
#> SRR975552     1  0.0237      0.962 0.996 0.000 0.004
#> SRR975554     1  0.0237      0.962 0.996 0.000 0.004
#> SRR975553     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975555     1  0.0237      0.962 0.996 0.000 0.004
#> SRR975556     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975557     2  0.6001      0.740 0.176 0.772 0.052
#> SRR975558     1  0.1163      0.941 0.972 0.000 0.028
#> SRR975559     1  0.0000      0.960 1.000 0.000 0.000
#> SRR975560     2  0.4796      0.729 0.220 0.780 0.000
#> SRR975561     2  0.0237      0.979 0.004 0.996 0.000
#> SRR975562     1  0.0237      0.962 0.996 0.000 0.004
#> SRR975563     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975564     1  0.0237      0.962 0.996 0.000 0.004
#> SRR975565     1  0.0237      0.962 0.996 0.000 0.004
#> SRR975566     1  0.0237      0.962 0.996 0.000 0.004
#> SRR975567     1  0.1163      0.941 0.972 0.000 0.028
#> SRR975568     1  0.0237      0.962 0.996 0.000 0.004
#> SRR975569     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975570     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975571     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975572     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975573     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975574     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975575     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975576     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975577     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975578     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975579     2  0.0237      0.979 0.004 0.996 0.000
#> SRR975580     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975581     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975582     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975583     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975584     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975585     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975586     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975587     3  0.0000      0.985 0.000 0.000 1.000
#> SRR975588     2  0.0000      0.981 0.000 1.000 0.000
#> SRR975589     3  0.0000      0.985 0.000 0.000 1.000
#> SRR975590     3  0.1163      0.970 0.028 0.000 0.972
#> SRR975591     3  0.0000      0.985 0.000 0.000 1.000
#> SRR975592     3  0.0000      0.985 0.000 0.000 1.000
#> SRR975593     3  0.0000      0.985 0.000 0.000 1.000
#> SRR975594     3  0.0000      0.985 0.000 0.000 1.000
#> SRR975595     3  0.1860      0.955 0.052 0.000 0.948
#> SRR975597     3  0.1860      0.955 0.052 0.000 0.948
#> SRR975596     1  0.0000      0.960 1.000 0.000 0.000
#> SRR975598     3  0.1860      0.955 0.052 0.000 0.948
#> SRR975599     1  0.6252      0.176 0.556 0.000 0.444
#> SRR975600     3  0.0000      0.985 0.000 0.000 1.000
#> SRR975601     3  0.0000      0.985 0.000 0.000 1.000
#> SRR975602     1  0.0237      0.962 0.996 0.000 0.004
#> SRR975603     3  0.0000      0.985 0.000 0.000 1.000
#> SRR975604     3  0.0000      0.985 0.000 0.000 1.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> SRR975551     1  0.0000      0.967 1.000 0.000 0.000 0.000
#> SRR975552     1  0.0188      0.965 0.996 0.000 0.000 0.004
#> SRR975554     1  0.0000      0.967 1.000 0.000 0.000 0.000
#> SRR975553     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> SRR975555     1  0.0188      0.965 0.996 0.000 0.000 0.004
#> SRR975556     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> SRR975557     4  0.0188      0.955 0.000 0.004 0.000 0.996
#> SRR975558     4  0.3400      0.770 0.180 0.000 0.000 0.820
#> SRR975559     1  0.3569      0.750 0.804 0.000 0.000 0.196
#> SRR975560     4  0.0188      0.955 0.000 0.004 0.000 0.996
#> SRR975561     4  0.0707      0.945 0.000 0.020 0.000 0.980
#> SRR975562     1  0.0000      0.967 1.000 0.000 0.000 0.000
#> SRR975563     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> SRR975564     1  0.0000      0.967 1.000 0.000 0.000 0.000
#> SRR975565     1  0.0000      0.967 1.000 0.000 0.000 0.000
#> SRR975566     1  0.0188      0.965 0.996 0.000 0.000 0.004
#> SRR975567     4  0.0188      0.953 0.004 0.000 0.000 0.996
#> SRR975568     1  0.0000      0.967 1.000 0.000 0.000 0.000
#> SRR975569     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> SRR975570     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> SRR975571     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> SRR975572     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> SRR975573     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> SRR975574     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> SRR975575     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> SRR975576     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> SRR975577     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> SRR975578     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> SRR975579     4  0.0336      0.954 0.000 0.008 0.000 0.992
#> SRR975580     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> SRR975581     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> SRR975582     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> SRR975583     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> SRR975584     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> SRR975585     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> SRR975586     2  0.4941      0.210 0.000 0.564 0.000 0.436
#> SRR975587     3  0.0000      0.929 0.000 0.000 1.000 0.000
#> SRR975588     2  0.0000      0.977 0.000 1.000 0.000 0.000
#> SRR975589     3  0.0000      0.929 0.000 0.000 1.000 0.000
#> SRR975590     3  0.1022      0.910 0.032 0.000 0.968 0.000
#> SRR975591     3  0.0000      0.929 0.000 0.000 1.000 0.000
#> SRR975592     3  0.0000      0.929 0.000 0.000 1.000 0.000
#> SRR975593     3  0.0000      0.929 0.000 0.000 1.000 0.000
#> SRR975594     3  0.0000      0.929 0.000 0.000 1.000 0.000
#> SRR975595     3  0.4018      0.752 0.224 0.000 0.772 0.004
#> SRR975597     3  0.4018      0.752 0.224 0.000 0.772 0.004
#> SRR975596     1  0.2921      0.827 0.860 0.000 0.000 0.140
#> SRR975598     3  0.4699      0.605 0.320 0.000 0.676 0.004
#> SRR975599     1  0.0188      0.965 0.996 0.000 0.000 0.004
#> SRR975600     3  0.0000      0.929 0.000 0.000 1.000 0.000
#> SRR975601     3  0.0000      0.929 0.000 0.000 1.000 0.000
#> SRR975602     1  0.0188      0.965 0.996 0.000 0.000 0.004
#> SRR975603     3  0.0000      0.929 0.000 0.000 1.000 0.000
#> SRR975604     3  0.0000      0.929 0.000 0.000 1.000 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
#> SRR975551     1  0.0510      0.833 0.984 0.000 0.000 0.000 0.016
#> SRR975552     1  0.1410      0.835 0.940 0.000 0.000 0.000 0.060
#> SRR975554     1  0.0880      0.835 0.968 0.000 0.000 0.000 0.032
#> SRR975553     2  0.3857      0.778 0.000 0.688 0.000 0.312 0.000
#> SRR975555     1  0.3177      0.793 0.792 0.000 0.000 0.000 0.208
#> SRR975556     2  0.1792      0.768 0.000 0.916 0.000 0.084 0.000
#> SRR975557     4  0.4235      0.675 0.000 0.000 0.000 0.576 0.424
#> SRR975558     5  0.5283      0.202 0.188 0.000 0.000 0.136 0.676
#> SRR975559     1  0.4451      0.409 0.644 0.000 0.000 0.016 0.340
#> SRR975560     4  0.4268      0.467 0.000 0.000 0.000 0.556 0.444
#> SRR975561     4  0.5019      0.646 0.000 0.052 0.000 0.632 0.316
#> SRR975562     1  0.1704      0.823 0.928 0.000 0.000 0.004 0.068
#> SRR975563     2  0.0000      0.824 0.000 1.000 0.000 0.000 0.000
#> SRR975564     1  0.2732      0.806 0.840 0.000 0.000 0.000 0.160
#> SRR975565     1  0.1851      0.828 0.912 0.000 0.000 0.000 0.088
#> SRR975566     1  0.1792      0.801 0.916 0.000 0.000 0.000 0.084
#> SRR975567     5  0.4171     -0.531 0.000 0.000 0.000 0.396 0.604
#> SRR975568     1  0.2852      0.803 0.828 0.000 0.000 0.000 0.172
#> SRR975569     2  0.0000      0.824 0.000 1.000 0.000 0.000 0.000
#> SRR975570     2  0.0000      0.824 0.000 1.000 0.000 0.000 0.000
#> SRR975571     2  0.3857      0.778 0.000 0.688 0.000 0.312 0.000
#> SRR975572     2  0.0000      0.824 0.000 1.000 0.000 0.000 0.000
#> SRR975573     2  0.3857      0.778 0.000 0.688 0.000 0.312 0.000
#> SRR975574     2  0.3857      0.778 0.000 0.688 0.000 0.312 0.000
#> SRR975575     2  0.0000      0.824 0.000 1.000 0.000 0.000 0.000
#> SRR975576     2  0.0000      0.824 0.000 1.000 0.000 0.000 0.000
#> SRR975577     2  0.3857      0.778 0.000 0.688 0.000 0.312 0.000
#> SRR975578     2  0.3857      0.778 0.000 0.688 0.000 0.312 0.000
#> SRR975579     4  0.4341      0.704 0.000 0.004 0.000 0.592 0.404
#> SRR975580     2  0.4367      0.723 0.000 0.620 0.000 0.372 0.008
#> SRR975581     2  0.0000      0.824 0.000 1.000 0.000 0.000 0.000
#> SRR975582     2  0.3857      0.778 0.000 0.688 0.000 0.312 0.000
#> SRR975583     2  0.0000      0.824 0.000 1.000 0.000 0.000 0.000
#> SRR975584     2  0.3857      0.778 0.000 0.688 0.000 0.312 0.000
#> SRR975585     2  0.0000      0.824 0.000 1.000 0.000 0.000 0.000
#> SRR975586     2  0.4235      0.129 0.000 0.576 0.000 0.424 0.000
#> SRR975587     3  0.0510      0.881 0.000 0.000 0.984 0.000 0.016
#> SRR975588     2  0.0000      0.824 0.000 1.000 0.000 0.000 0.000
#> SRR975589     3  0.0566      0.881 0.000 0.000 0.984 0.004 0.012
#> SRR975590     3  0.3229      0.805 0.032 0.000 0.840 0.000 0.128
#> SRR975591     3  0.0162      0.881 0.000 0.000 0.996 0.004 0.000
#> SRR975592     3  0.0404      0.881 0.000 0.000 0.988 0.000 0.012
#> SRR975593     3  0.0566      0.881 0.000 0.000 0.984 0.004 0.012
#> SRR975594     3  0.0510      0.881 0.000 0.000 0.984 0.000 0.016
#> SRR975595     3  0.5871      0.598 0.184 0.000 0.604 0.000 0.212
#> SRR975597     3  0.5841      0.602 0.180 0.000 0.608 0.000 0.212
#> SRR975596     1  0.3961      0.601 0.736 0.000 0.000 0.016 0.248
#> SRR975598     3  0.6315      0.463 0.260 0.000 0.528 0.000 0.212
#> SRR975599     1  0.3616      0.719 0.768 0.000 0.004 0.004 0.224
#> SRR975600     3  0.0162      0.881 0.000 0.000 0.996 0.004 0.000
#> SRR975601     3  0.0510      0.881 0.000 0.000 0.984 0.000 0.016
#> SRR975602     1  0.2773      0.771 0.836 0.000 0.000 0.000 0.164
#> SRR975603     3  0.0162      0.881 0.000 0.000 0.996 0.004 0.000
#> SRR975604     3  0.0162      0.881 0.000 0.000 0.996 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
#> SRR975551     1  0.0717      0.661 0.976 0.008 0.000 0.000 0.000 0.016
#> SRR975552     1  0.1588      0.647 0.924 0.004 0.000 0.000 0.000 0.072
#> SRR975554     1  0.1714      0.653 0.908 0.000 0.000 0.000 0.000 0.092
#> SRR975553     5  0.0146      0.954 0.000 0.000 0.000 0.004 0.996 0.000
#> SRR975555     1  0.4598      0.502 0.592 0.048 0.000 0.000 0.000 0.360
#> SRR975556     2  0.4018      0.683 0.000 0.656 0.000 0.000 0.324 0.020
#> SRR975557     4  0.0458      0.678 0.000 0.000 0.000 0.984 0.000 0.016
#> SRR975558     6  0.5225      0.000 0.112 0.012 0.000 0.248 0.000 0.628
#> SRR975559     1  0.5235      0.217 0.612 0.016 0.000 0.088 0.000 0.284
#> SRR975560     4  0.6374      0.288 0.004 0.184 0.000 0.492 0.028 0.292
#> SRR975561     4  0.1493      0.660 0.000 0.056 0.000 0.936 0.004 0.004
#> SRR975562     1  0.3829      0.601 0.760 0.060 0.000 0.000 0.000 0.180
#> SRR975563     2  0.3854      0.900 0.000 0.536 0.000 0.000 0.464 0.000
#> SRR975564     1  0.3938      0.515 0.660 0.016 0.000 0.000 0.000 0.324
#> SRR975565     1  0.2558      0.625 0.840 0.004 0.000 0.000 0.000 0.156
#> SRR975566     1  0.1765      0.642 0.924 0.024 0.000 0.000 0.000 0.052
#> SRR975567     4  0.4399      0.210 0.004 0.028 0.000 0.616 0.000 0.352
#> SRR975568     1  0.3867      0.512 0.660 0.012 0.000 0.000 0.000 0.328
#> SRR975569     2  0.3857      0.904 0.000 0.532 0.000 0.000 0.468 0.000
#> SRR975570     2  0.3857      0.904 0.000 0.532 0.000 0.000 0.468 0.000
#> SRR975571     5  0.0146      0.954 0.000 0.000 0.000 0.004 0.996 0.000
#> SRR975572     2  0.3857      0.904 0.000 0.532 0.000 0.000 0.468 0.000
#> SRR975573     5  0.0000      0.957 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR975574     5  0.0000      0.957 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR975575     2  0.3857      0.904 0.000 0.532 0.000 0.000 0.468 0.000
#> SRR975576     2  0.3857      0.904 0.000 0.532 0.000 0.000 0.468 0.000
#> SRR975577     5  0.0000      0.957 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR975578     5  0.0146      0.954 0.000 0.004 0.000 0.000 0.996 0.000
#> SRR975579     4  0.0000      0.683 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR975580     5  0.3695      0.648 0.000 0.184 0.000 0.004 0.772 0.040
#> SRR975581     2  0.3857      0.904 0.000 0.532 0.000 0.000 0.468 0.000
#> SRR975582     5  0.0000      0.957 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR975583     2  0.3857      0.904 0.000 0.532 0.000 0.000 0.468 0.000
#> SRR975584     5  0.0000      0.957 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR975585     2  0.3857      0.904 0.000 0.532 0.000 0.000 0.468 0.000
#> SRR975586     2  0.5583      0.327 0.000 0.600 0.000 0.244 0.136 0.020
#> SRR975587     3  0.1334      0.806 0.000 0.020 0.948 0.000 0.000 0.032
#> SRR975588     2  0.3857      0.904 0.000 0.532 0.000 0.000 0.468 0.000
#> SRR975589     3  0.1838      0.787 0.000 0.016 0.916 0.000 0.000 0.068
#> SRR975590     3  0.5761      0.617 0.052 0.156 0.628 0.000 0.000 0.164
#> SRR975591     3  0.0146      0.806 0.000 0.004 0.996 0.000 0.000 0.000
#> SRR975592     3  0.1257      0.807 0.000 0.020 0.952 0.000 0.000 0.028
#> SRR975593     3  0.2030      0.786 0.000 0.028 0.908 0.000 0.000 0.064
#> SRR975594     3  0.0891      0.808 0.000 0.008 0.968 0.000 0.000 0.024
#> SRR975595     3  0.7050      0.416 0.080 0.244 0.412 0.000 0.000 0.264
#> SRR975597     3  0.7040      0.419 0.080 0.244 0.416 0.000 0.000 0.260
#> SRR975596     1  0.4907      0.361 0.636 0.020 0.000 0.052 0.000 0.292
#> SRR975598     3  0.7234      0.373 0.100 0.244 0.384 0.000 0.000 0.272
#> SRR975599     1  0.5894      0.303 0.472 0.244 0.000 0.000 0.000 0.284
#> SRR975600     3  0.0000      0.807 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975601     3  0.1168      0.807 0.000 0.016 0.956 0.000 0.000 0.028
#> SRR975602     1  0.4792      0.521 0.668 0.132 0.000 0.000 0.000 0.200
#> SRR975603     3  0.0146      0.806 0.000 0.004 0.996 0.000 0.000 0.000
#> SRR975604     3  0.0146      0.806 0.000 0.004 0.996 0.000 0.000 0.000

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

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

consensus_heatmap(res, k = 2)

plot of chunk tab-CV-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

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 17171 rows and 54 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#>   Subgroups are detected by 'pam' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 3.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk CV-pam-collect-plots

The plots are:

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

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

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

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

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

select_partition_number(res)

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

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.858           0.960       0.974         0.5014 0.491   0.491
#> 3 3 0.951           0.907       0.963         0.2779 0.877   0.749
#> 4 4 0.794           0.731       0.855         0.1068 0.869   0.662
#> 5 5 0.884           0.741       0.885         0.0513 0.932   0.773
#> 6 6 0.889           0.736       0.895         0.0335 0.959   0.847

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

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

suggest_best_k(res)

#> [1] 3

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

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

show/hide code output

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

#>           class entropy silhouette    p1    p2
#> SRR975551     1   0.295      0.940 0.948 0.052
#> SRR975552     1   0.730      0.811 0.796 0.204
#> SRR975554     1   0.295      0.940 0.948 0.052
#> SRR975553     2   0.000      1.000 0.000 1.000
#> SRR975555     1   0.722      0.816 0.800 0.200
#> SRR975556     2   0.000      1.000 0.000 1.000
#> SRR975557     2   0.000      1.000 0.000 1.000
#> SRR975558     2   0.000      1.000 0.000 1.000
#> SRR975559     1   0.295      0.940 0.948 0.052
#> SRR975560     2   0.000      1.000 0.000 1.000
#> SRR975561     2   0.000      1.000 0.000 1.000
#> SRR975562     1   0.295      0.940 0.948 0.052
#> SRR975563     2   0.000      1.000 0.000 1.000
#> SRR975564     1   0.689      0.832 0.816 0.184
#> SRR975565     1   0.722      0.816 0.800 0.200
#> SRR975566     1   0.295      0.940 0.948 0.052
#> SRR975567     2   0.000      1.000 0.000 1.000
#> SRR975568     1   0.722      0.816 0.800 0.200
#> SRR975569     2   0.000      1.000 0.000 1.000
#> SRR975570     2   0.000      1.000 0.000 1.000
#> SRR975571     2   0.000      1.000 0.000 1.000
#> SRR975572     2   0.000      1.000 0.000 1.000
#> SRR975573     2   0.000      1.000 0.000 1.000
#> SRR975574     2   0.000      1.000 0.000 1.000
#> SRR975575     2   0.000      1.000 0.000 1.000
#> SRR975576     2   0.000      1.000 0.000 1.000
#> SRR975577     2   0.000      1.000 0.000 1.000
#> SRR975578     2   0.000      1.000 0.000 1.000
#> SRR975579     2   0.000      1.000 0.000 1.000
#> SRR975580     2   0.000      1.000 0.000 1.000
#> SRR975581     2   0.000      1.000 0.000 1.000
#> SRR975582     2   0.000      1.000 0.000 1.000
#> SRR975583     2   0.000      1.000 0.000 1.000
#> SRR975584     2   0.000      1.000 0.000 1.000
#> SRR975585     2   0.000      1.000 0.000 1.000
#> SRR975586     2   0.000      1.000 0.000 1.000
#> SRR975587     1   0.000      0.946 1.000 0.000
#> SRR975588     2   0.000      1.000 0.000 1.000
#> SRR975589     1   0.000      0.946 1.000 0.000
#> SRR975590     1   0.000      0.946 1.000 0.000
#> SRR975591     1   0.000      0.946 1.000 0.000
#> SRR975592     1   0.000      0.946 1.000 0.000
#> SRR975593     1   0.000      0.946 1.000 0.000
#> SRR975594     1   0.000      0.946 1.000 0.000
#> SRR975595     1   0.000      0.946 1.000 0.000
#> SRR975597     1   0.000      0.946 1.000 0.000
#> SRR975596     1   0.295      0.940 0.948 0.052
#> SRR975598     1   0.000      0.946 1.000 0.000
#> SRR975599     1   0.295      0.940 0.948 0.052
#> SRR975600     1   0.000      0.946 1.000 0.000
#> SRR975601     1   0.000      0.946 1.000 0.000
#> SRR975602     1   0.295      0.940 0.948 0.052
#> SRR975603     1   0.000      0.946 1.000 0.000
#> SRR975604     1   0.000      0.946 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
#> SRR975551     1  0.0000      0.927 1.000 0.000 0.000
#> SRR975552     1  0.0000      0.927 1.000 0.000 0.000
#> SRR975554     1  0.0000      0.927 1.000 0.000 0.000
#> SRR975553     2  0.0000      0.966 0.000 1.000 0.000
#> SRR975555     1  0.0000      0.927 1.000 0.000 0.000
#> SRR975556     2  0.0000      0.966 0.000 1.000 0.000
#> SRR975557     2  0.1289      0.939 0.032 0.968 0.000
#> SRR975558     2  0.6305      0.109 0.484 0.516 0.000
#> SRR975559     1  0.0000      0.927 1.000 0.000 0.000
#> SRR975560     2  0.0424      0.960 0.008 0.992 0.000
#> SRR975561     2  0.0000      0.966 0.000 1.000 0.000
#> SRR975562     1  0.0000      0.927 1.000 0.000 0.000
#> SRR975563     2  0.0000      0.966 0.000 1.000 0.000
#> SRR975564     1  0.0000      0.927 1.000 0.000 0.000
#> SRR975565     1  0.0000      0.927 1.000 0.000 0.000
#> SRR975566     1  0.0000      0.927 1.000 0.000 0.000
#> SRR975567     2  0.5678      0.550 0.316 0.684 0.000
#> SRR975568     1  0.0000      0.927 1.000 0.000 0.000
#> SRR975569     2  0.0000      0.966 0.000 1.000 0.000
#> SRR975570     2  0.0000      0.966 0.000 1.000 0.000
#> SRR975571     2  0.0000      0.966 0.000 1.000 0.000
#> SRR975572     2  0.0000      0.966 0.000 1.000 0.000
#> SRR975573     2  0.0000      0.966 0.000 1.000 0.000
#> SRR975574     2  0.0000      0.966 0.000 1.000 0.000
#> SRR975575     2  0.0000      0.966 0.000 1.000 0.000
#> SRR975576     2  0.0000      0.966 0.000 1.000 0.000
#> SRR975577     2  0.0000      0.966 0.000 1.000 0.000
#> SRR975578     2  0.0000      0.966 0.000 1.000 0.000
#> SRR975579     2  0.0000      0.966 0.000 1.000 0.000
#> SRR975580     2  0.0000      0.966 0.000 1.000 0.000
#> SRR975581     2  0.0000      0.966 0.000 1.000 0.000
#> SRR975582     2  0.0000      0.966 0.000 1.000 0.000
#> SRR975583     2  0.0000      0.966 0.000 1.000 0.000
#> SRR975584     2  0.0000      0.966 0.000 1.000 0.000
#> SRR975585     2  0.0000      0.966 0.000 1.000 0.000
#> SRR975586     2  0.0000      0.966 0.000 1.000 0.000
#> SRR975587     3  0.0000      0.985 0.000 0.000 1.000
#> SRR975588     2  0.0000      0.966 0.000 1.000 0.000
#> SRR975589     3  0.0000      0.985 0.000 0.000 1.000
#> SRR975590     3  0.2261      0.927 0.068 0.000 0.932
#> SRR975591     3  0.0000      0.985 0.000 0.000 1.000
#> SRR975592     3  0.2261      0.927 0.068 0.000 0.932
#> SRR975593     3  0.0000      0.985 0.000 0.000 1.000
#> SRR975594     3  0.0000      0.985 0.000 0.000 1.000
#> SRR975595     1  0.6154      0.344 0.592 0.000 0.408
#> SRR975597     1  0.6204      0.300 0.576 0.000 0.424
#> SRR975596     1  0.2356      0.871 0.928 0.000 0.072
#> SRR975598     1  0.3482      0.817 0.872 0.000 0.128
#> SRR975599     1  0.0000      0.927 1.000 0.000 0.000
#> SRR975600     3  0.0000      0.985 0.000 0.000 1.000
#> SRR975601     3  0.0000      0.985 0.000 0.000 1.000
#> SRR975602     1  0.0000      0.927 1.000 0.000 0.000
#> SRR975603     3  0.0000      0.985 0.000 0.000 1.000
#> SRR975604     3  0.0000      0.985 0.000 0.000 1.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> SRR975551     1  0.0000     0.6070 1.000 0.000 0.000 0.000
#> SRR975552     1  0.4072     0.3172 0.748 0.000 0.000 0.252
#> SRR975554     1  0.2469     0.5292 0.892 0.000 0.000 0.108
#> SRR975553     2  0.0188     0.9907 0.000 0.996 0.000 0.004
#> SRR975555     1  0.0188     0.6066 0.996 0.000 0.000 0.004
#> SRR975556     2  0.0000     0.9912 0.000 1.000 0.000 0.000
#> SRR975557     4  0.5792     0.5280 0.056 0.296 0.000 0.648
#> SRR975558     4  0.6454     0.4893 0.380 0.076 0.000 0.544
#> SRR975559     4  0.4985     0.4032 0.468 0.000 0.000 0.532
#> SRR975560     4  0.5263     0.3676 0.008 0.448 0.000 0.544
#> SRR975561     2  0.2647     0.8545 0.000 0.880 0.000 0.120
#> SRR975562     1  0.4697    -0.0233 0.644 0.000 0.000 0.356
#> SRR975563     2  0.0000     0.9912 0.000 1.000 0.000 0.000
#> SRR975564     1  0.1022     0.5938 0.968 0.000 0.000 0.032
#> SRR975565     1  0.4877    -0.2027 0.592 0.000 0.000 0.408
#> SRR975566     4  0.4985     0.4032 0.468 0.000 0.000 0.532
#> SRR975567     4  0.7152     0.5397 0.284 0.172 0.000 0.544
#> SRR975568     1  0.3610     0.4075 0.800 0.000 0.000 0.200
#> SRR975569     2  0.0000     0.9912 0.000 1.000 0.000 0.000
#> SRR975570     2  0.0000     0.9912 0.000 1.000 0.000 0.000
#> SRR975571     2  0.0188     0.9907 0.000 0.996 0.000 0.004
#> SRR975572     2  0.0000     0.9912 0.000 1.000 0.000 0.000
#> SRR975573     2  0.0188     0.9907 0.000 0.996 0.000 0.004
#> SRR975574     2  0.0188     0.9907 0.000 0.996 0.000 0.004
#> SRR975575     2  0.0000     0.9912 0.000 1.000 0.000 0.000
#> SRR975576     2  0.0000     0.9912 0.000 1.000 0.000 0.000
#> SRR975577     2  0.0188     0.9907 0.000 0.996 0.000 0.004
#> SRR975578     2  0.0188     0.9907 0.000 0.996 0.000 0.004
#> SRR975579     4  0.4713     0.5010 0.000 0.360 0.000 0.640
#> SRR975580     2  0.0336     0.9875 0.000 0.992 0.000 0.008
#> SRR975581     2  0.0000     0.9912 0.000 1.000 0.000 0.000
#> SRR975582     2  0.0188     0.9907 0.000 0.996 0.000 0.004
#> SRR975583     2  0.0000     0.9912 0.000 1.000 0.000 0.000
#> SRR975584     2  0.0188     0.9907 0.000 0.996 0.000 0.004
#> SRR975585     2  0.0000     0.9912 0.000 1.000 0.000 0.000
#> SRR975586     2  0.0336     0.9849 0.000 0.992 0.000 0.008
#> SRR975587     3  0.0000     0.9181 0.000 0.000 1.000 0.000
#> SRR975588     2  0.0000     0.9912 0.000 1.000 0.000 0.000
#> SRR975589     3  0.3074     0.8440 0.000 0.000 0.848 0.152
#> SRR975590     1  0.7760     0.1637 0.408 0.000 0.240 0.352
#> SRR975591     3  0.0000     0.9181 0.000 0.000 1.000 0.000
#> SRR975592     3  0.6893     0.3924 0.300 0.000 0.564 0.136
#> SRR975593     3  0.3172     0.8390 0.000 0.000 0.840 0.160
#> SRR975594     3  0.0000     0.9181 0.000 0.000 1.000 0.000
#> SRR975595     1  0.6426     0.4791 0.568 0.000 0.080 0.352
#> SRR975597     1  0.6186     0.4960 0.584 0.000 0.064 0.352
#> SRR975596     4  0.4981     0.4041 0.464 0.000 0.000 0.536
#> SRR975598     1  0.5420     0.5226 0.624 0.000 0.024 0.352
#> SRR975599     1  0.3726     0.5710 0.788 0.000 0.000 0.212
#> SRR975600     3  0.0592     0.9131 0.000 0.000 0.984 0.016
#> SRR975601     3  0.0000     0.9181 0.000 0.000 1.000 0.000
#> SRR975602     1  0.0000     0.6070 1.000 0.000 0.000 0.000
#> SRR975603     3  0.0000     0.9181 0.000 0.000 1.000 0.000
#> SRR975604     3  0.0000     0.9181 0.000 0.000 1.000 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
#> SRR975551     1  0.4397     0.5263 0.696 0.000 0.000 0.028 0.276
#> SRR975552     1  0.5642     0.3954 0.636 0.000 0.000 0.184 0.180
#> SRR975554     1  0.0865     0.7152 0.972 0.000 0.000 0.004 0.024
#> SRR975553     2  0.0404     0.9479 0.000 0.988 0.000 0.012 0.000
#> SRR975555     1  0.1444     0.7131 0.948 0.000 0.000 0.012 0.040
#> SRR975556     2  0.0000     0.9493 0.000 1.000 0.000 0.000 0.000
#> SRR975557     4  0.0404     0.4371 0.000 0.012 0.000 0.988 0.000
#> SRR975558     1  0.5557    -0.5187 0.468 0.068 0.000 0.464 0.000
#> SRR975559     4  0.4452     0.4753 0.496 0.000 0.000 0.500 0.004
#> SRR975560     2  0.5177    -0.0111 0.040 0.488 0.000 0.472 0.000
#> SRR975561     2  0.4287     0.3165 0.000 0.540 0.000 0.460 0.000
#> SRR975562     1  0.2519     0.6486 0.884 0.000 0.000 0.100 0.016
#> SRR975563     2  0.0000     0.9493 0.000 1.000 0.000 0.000 0.000
#> SRR975564     1  0.1106     0.7161 0.964 0.000 0.000 0.012 0.024
#> SRR975565     1  0.0000     0.7010 1.000 0.000 0.000 0.000 0.000
#> SRR975566     4  0.4307     0.4713 0.500 0.000 0.000 0.500 0.000
#> SRR975567     4  0.5276     0.4765 0.436 0.048 0.000 0.516 0.000
#> SRR975568     1  0.1106     0.7161 0.964 0.000 0.000 0.012 0.024
#> SRR975569     2  0.0000     0.9493 0.000 1.000 0.000 0.000 0.000
#> SRR975570     2  0.0000     0.9493 0.000 1.000 0.000 0.000 0.000
#> SRR975571     2  0.0404     0.9479 0.000 0.988 0.000 0.012 0.000
#> SRR975572     2  0.0000     0.9493 0.000 1.000 0.000 0.000 0.000
#> SRR975573     2  0.0404     0.9479 0.000 0.988 0.000 0.012 0.000
#> SRR975574     2  0.0404     0.9479 0.000 0.988 0.000 0.012 0.000
#> SRR975575     2  0.0000     0.9493 0.000 1.000 0.000 0.000 0.000
#> SRR975576     2  0.0000     0.9493 0.000 1.000 0.000 0.000 0.000
#> SRR975577     2  0.0404     0.9479 0.000 0.988 0.000 0.012 0.000
#> SRR975578     2  0.0404     0.9479 0.000 0.988 0.000 0.012 0.000
#> SRR975579     4  0.1792     0.4138 0.000 0.084 0.000 0.916 0.000
#> SRR975580     2  0.0510     0.9456 0.000 0.984 0.000 0.016 0.000
#> SRR975581     2  0.0000     0.9493 0.000 1.000 0.000 0.000 0.000
#> SRR975582     2  0.0404     0.9479 0.000 0.988 0.000 0.012 0.000
#> SRR975583     2  0.0000     0.9493 0.000 1.000 0.000 0.000 0.000
#> SRR975584     2  0.0404     0.9479 0.000 0.988 0.000 0.012 0.000
#> SRR975585     2  0.0000     0.9493 0.000 1.000 0.000 0.000 0.000
#> SRR975586     2  0.0404     0.9421 0.000 0.988 0.000 0.012 0.000
#> SRR975587     3  0.0000     0.9458 0.000 0.000 1.000 0.000 0.000
#> SRR975588     2  0.0000     0.9493 0.000 1.000 0.000 0.000 0.000
#> SRR975589     3  0.2891     0.7921 0.000 0.000 0.824 0.000 0.176
#> SRR975590     5  0.0162     0.8515 0.004 0.000 0.000 0.000 0.996
#> SRR975591     3  0.0000     0.9458 0.000 0.000 1.000 0.000 0.000
#> SRR975592     5  0.4300    -0.0282 0.000 0.000 0.476 0.000 0.524
#> SRR975593     3  0.2966     0.7829 0.000 0.000 0.816 0.000 0.184
#> SRR975594     3  0.0000     0.9458 0.000 0.000 1.000 0.000 0.000
#> SRR975595     5  0.0000     0.8544 0.000 0.000 0.000 0.000 1.000
#> SRR975597     5  0.0000     0.8544 0.000 0.000 0.000 0.000 1.000
#> SRR975596     4  0.4306     0.4734 0.492 0.000 0.000 0.508 0.000
#> SRR975598     5  0.0000     0.8544 0.000 0.000 0.000 0.000 1.000
#> SRR975599     1  0.4731     0.1912 0.528 0.000 0.000 0.016 0.456
#> SRR975600     3  0.0510     0.9372 0.000 0.000 0.984 0.000 0.016
#> SRR975601     3  0.0000     0.9458 0.000 0.000 1.000 0.000 0.000
#> SRR975602     1  0.3214     0.6763 0.844 0.000 0.000 0.036 0.120
#> SRR975603     3  0.0000     0.9458 0.000 0.000 1.000 0.000 0.000
#> SRR975604     3  0.0000     0.9458 0.000 0.000 1.000 0.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> SRR975551     1  0.6116     0.0408 0.360 0.000 0.000 0.000 0.340 0.300
#> SRR975552     6  0.5554     0.2888 0.276 0.000 0.000 0.000 0.180 0.544
#> SRR975554     1  0.2793     0.4694 0.800 0.000 0.000 0.000 0.000 0.200
#> SRR975553     2  0.1176     0.9463 0.000 0.956 0.000 0.024 0.000 0.020
#> SRR975555     1  0.0000     0.6310 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR975556     2  0.0146     0.9531 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR975557     4  0.0547     0.6416 0.000 0.000 0.000 0.980 0.000 0.020
#> SRR975558     1  0.3944    -0.0195 0.568 0.004 0.000 0.000 0.000 0.428
#> SRR975559     6  0.0547     0.7149 0.020 0.000 0.000 0.000 0.000 0.980
#> SRR975560     2  0.4623     0.2170 0.016 0.540 0.000 0.016 0.000 0.428
#> SRR975561     4  0.3727     0.3755 0.000 0.388 0.000 0.612 0.000 0.000
#> SRR975562     6  0.4095    -0.0227 0.480 0.000 0.000 0.000 0.008 0.512
#> SRR975563     2  0.0000     0.9536 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975564     1  0.0000     0.6310 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR975565     1  0.0000     0.6310 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR975566     6  0.0632     0.7155 0.024 0.000 0.000 0.000 0.000 0.976
#> SRR975567     6  0.3618     0.6191 0.124 0.032 0.000 0.032 0.000 0.812
#> SRR975568     1  0.0000     0.6310 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR975569     2  0.0000     0.9536 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975570     2  0.0000     0.9536 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975571     2  0.1176     0.9463 0.000 0.956 0.000 0.024 0.000 0.020
#> SRR975572     2  0.0000     0.9536 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975573     2  0.0993     0.9479 0.000 0.964 0.000 0.024 0.000 0.012
#> SRR975574     2  0.1176     0.9463 0.000 0.956 0.000 0.024 0.000 0.020
#> SRR975575     2  0.0000     0.9536 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975576     2  0.0000     0.9536 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975577     2  0.1176     0.9463 0.000 0.956 0.000 0.024 0.000 0.020
#> SRR975578     2  0.1176     0.9463 0.000 0.956 0.000 0.024 0.000 0.020
#> SRR975579     4  0.0692     0.6424 0.000 0.004 0.000 0.976 0.000 0.020
#> SRR975580     2  0.1261     0.9439 0.000 0.952 0.000 0.024 0.000 0.024
#> SRR975581     2  0.0000     0.9536 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975582     2  0.1176     0.9463 0.000 0.956 0.000 0.024 0.000 0.020
#> SRR975583     2  0.0000     0.9536 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975584     2  0.1176     0.9463 0.000 0.956 0.000 0.024 0.000 0.020
#> SRR975585     2  0.0000     0.9536 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975586     2  0.0000     0.9536 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975587     3  0.0000     0.9463 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975588     2  0.0000     0.9536 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975589     3  0.2703     0.7948 0.004 0.000 0.824 0.000 0.172 0.000
#> SRR975590     5  0.0000     0.8351 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR975591     3  0.0000     0.9463 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975592     5  0.3862    -0.0346 0.000 0.000 0.476 0.000 0.524 0.000
#> SRR975593     3  0.2664     0.7835 0.000 0.000 0.816 0.000 0.184 0.000
#> SRR975594     3  0.0000     0.9463 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975595     5  0.0000     0.8351 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR975597     5  0.0000     0.8351 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR975596     6  0.0713     0.7158 0.028 0.000 0.000 0.000 0.000 0.972
#> SRR975598     5  0.0000     0.8351 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR975599     1  0.4385     0.2997 0.532 0.000 0.000 0.000 0.444 0.024
#> SRR975600     3  0.0458     0.9378 0.000 0.000 0.984 0.000 0.016 0.000
#> SRR975601     3  0.0000     0.9463 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975602     1  0.5877     0.0819 0.428 0.000 0.000 0.000 0.200 0.372
#> SRR975603     3  0.0000     0.9463 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975604     3  0.0000     0.9463 0.000 0.000 1.000 0.000 0.000 0.000

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

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

consensus_heatmap(res, k = 2)

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

consensus_heatmap(res, k = 3)

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

consensus_heatmap(res, k = 4)

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

consensus_heatmap(res, k = 5)

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

consensus_heatmap(res, k = 6)

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

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

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

membership_heatmap(res, k = 2)

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

membership_heatmap(res, k = 3)

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

membership_heatmap(res, k = 4)

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

membership_heatmap(res, k = 5)

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

membership_heatmap(res, k = 6)

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

Signature heatmaps where rows are scaled:

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

get_signatures(res, k = 2)

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

get_signatures(res, k = 3)

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

get_signatures(res, k = 4)

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

get_signatures(res, k = 5)

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

get_signatures(res, k = 6)

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

Signature heatmaps where rows are not scaled:

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

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

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

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

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

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

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

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

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

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

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

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk CV-pam-signature_compare

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

An example of the output of tb is:

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

The columns in tb are:

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

UMAP plot which shows how samples are separated.

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

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

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

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

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

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

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

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

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

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

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

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk CV-pam-collect-classes

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 17171 rows and 54 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#>   Subgroups are detected by 'mclust' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 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 CV-mclust-collect-plots

The plots are:

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

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

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

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

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

select_partition_number(res)

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

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.509           0.797       0.859         0.4384 0.560   0.560
#> 3 3 0.595           0.792       0.861         0.4645 0.762   0.584
#> 4 4 0.887           0.893       0.928         0.1587 0.869   0.638
#> 5 5 0.880           0.891       0.864         0.0499 0.966   0.860
#> 6 6 0.831           0.813       0.868         0.0297 0.983   0.920

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

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

suggest_best_k(res)

#> [1] 4

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

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

show/hide code output

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

#>           class entropy silhouette    p1    p2
#> SRR975551     1   0.000      0.766 1.000 0.000
#> SRR975552     1   0.000      0.766 1.000 0.000
#> SRR975554     1   0.000      0.766 1.000 0.000
#> SRR975553     2   0.973      0.870 0.404 0.596
#> SRR975555     1   0.000      0.766 1.000 0.000
#> SRR975556     1   0.358      0.681 0.932 0.068
#> SRR975557     1   0.000      0.766 1.000 0.000
#> SRR975558     1   0.000      0.766 1.000 0.000
#> SRR975559     1   0.000      0.766 1.000 0.000
#> SRR975560     1   0.118      0.751 0.984 0.016
#> SRR975561     1   0.184      0.737 0.972 0.028
#> SRR975562     1   0.000      0.766 1.000 0.000
#> SRR975563     2   0.900      0.984 0.316 0.684
#> SRR975564     1   0.000      0.766 1.000 0.000
#> SRR975565     1   0.000      0.766 1.000 0.000
#> SRR975566     1   0.000      0.766 1.000 0.000
#> SRR975567     1   0.000      0.766 1.000 0.000
#> SRR975568     1   0.000      0.766 1.000 0.000
#> SRR975569     2   0.900      0.984 0.316 0.684
#> SRR975570     2   0.900      0.984 0.316 0.684
#> SRR975571     2   0.973      0.870 0.404 0.596
#> SRR975572     2   0.900      0.984 0.316 0.684
#> SRR975573     2   0.900      0.984 0.316 0.684
#> SRR975574     1   0.992     -0.560 0.552 0.448
#> SRR975575     2   0.900      0.984 0.316 0.684
#> SRR975576     2   0.900      0.984 0.316 0.684
#> SRR975577     2   0.900      0.984 0.316 0.684
#> SRR975578     2   0.900      0.984 0.316 0.684
#> SRR975579     1   0.141      0.747 0.980 0.020
#> SRR975580     1   0.141      0.747 0.980 0.020
#> SRR975581     2   0.904      0.980 0.320 0.680
#> SRR975582     2   0.900      0.984 0.316 0.684
#> SRR975583     2   0.900      0.984 0.316 0.684
#> SRR975584     2   0.900      0.984 0.316 0.684
#> SRR975585     2   0.900      0.984 0.316 0.684
#> SRR975586     1   0.358      0.681 0.932 0.068
#> SRR975587     1   0.900      0.750 0.684 0.316
#> SRR975588     2   0.900      0.984 0.316 0.684
#> SRR975589     1   0.900      0.750 0.684 0.316
#> SRR975590     1   0.900      0.750 0.684 0.316
#> SRR975591     1   0.900      0.750 0.684 0.316
#> SRR975592     1   0.900      0.750 0.684 0.316
#> SRR975593     1   0.900      0.750 0.684 0.316
#> SRR975594     1   0.900      0.750 0.684 0.316
#> SRR975595     1   0.900      0.750 0.684 0.316
#> SRR975597     1   0.900      0.750 0.684 0.316
#> SRR975596     1   0.000      0.766 1.000 0.000
#> SRR975598     1   0.900      0.750 0.684 0.316
#> SRR975599     1   0.900      0.750 0.684 0.316
#> SRR975600     1   0.900      0.750 0.684 0.316
#> SRR975601     1   0.900      0.750 0.684 0.316
#> SRR975602     1   0.653      0.760 0.832 0.168
#> SRR975603     1   0.900      0.750 0.684 0.316
#> SRR975604     1   0.900      0.750 0.684 0.316

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> SRR975551     1  0.0237      0.833 0.996 0.004 0.000
#> SRR975552     1  0.4477      0.856 0.864 0.068 0.068
#> SRR975554     1  0.2496      0.889 0.928 0.068 0.004
#> SRR975553     2  0.1525      0.949 0.004 0.964 0.032
#> SRR975555     1  0.2261      0.888 0.932 0.068 0.000
#> SRR975556     3  0.7983      0.518 0.104 0.264 0.632
#> SRR975557     3  0.6148      0.672 0.076 0.148 0.776
#> SRR975558     3  0.6252      0.662 0.144 0.084 0.772
#> SRR975559     1  0.7176      0.582 0.684 0.068 0.248
#> SRR975560     3  0.6252      0.662 0.144 0.084 0.772
#> SRR975561     3  0.6208      0.669 0.076 0.152 0.772
#> SRR975562     1  0.2496      0.889 0.928 0.068 0.004
#> SRR975563     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975564     1  0.2496      0.889 0.928 0.068 0.004
#> SRR975565     1  0.2261      0.888 0.932 0.068 0.000
#> SRR975566     1  0.5153      0.824 0.832 0.068 0.100
#> SRR975567     3  0.6252      0.662 0.144 0.084 0.772
#> SRR975568     1  0.2261      0.888 0.932 0.068 0.000
#> SRR975569     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975570     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975571     2  0.1525      0.949 0.004 0.964 0.032
#> SRR975572     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975573     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975574     2  0.3879      0.780 0.000 0.848 0.152
#> SRR975575     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975576     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975577     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975578     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975579     3  0.6122      0.671 0.072 0.152 0.776
#> SRR975580     3  0.7692      0.581 0.136 0.184 0.680
#> SRR975581     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975582     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975583     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975584     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975585     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975586     3  0.7764      0.472 0.068 0.328 0.604
#> SRR975587     3  0.3038      0.733 0.104 0.000 0.896
#> SRR975588     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975589     3  0.5327      0.583 0.272 0.000 0.728
#> SRR975590     3  0.5835      0.572 0.340 0.000 0.660
#> SRR975591     3  0.1529      0.736 0.040 0.000 0.960
#> SRR975592     3  0.5327      0.583 0.272 0.000 0.728
#> SRR975593     3  0.5327      0.583 0.272 0.000 0.728
#> SRR975594     3  0.1753      0.736 0.048 0.000 0.952
#> SRR975595     3  0.5835      0.572 0.340 0.000 0.660
#> SRR975597     3  0.5835      0.572 0.340 0.000 0.660
#> SRR975596     1  0.7022      0.617 0.700 0.068 0.232
#> SRR975598     3  0.5835      0.572 0.340 0.000 0.660
#> SRR975599     3  0.4062      0.727 0.164 0.000 0.836
#> SRR975600     3  0.1529      0.736 0.040 0.000 0.960
#> SRR975601     3  0.3038      0.733 0.104 0.000 0.896
#> SRR975602     1  0.2448      0.807 0.924 0.000 0.076
#> SRR975603     3  0.1529      0.736 0.040 0.000 0.960
#> SRR975604     3  0.1529      0.736 0.040 0.000 0.960

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> SRR975551     1  0.0188      0.930 0.996 0.000 0.000 0.004
#> SRR975552     1  0.1211      0.926 0.960 0.000 0.000 0.040
#> SRR975554     1  0.0937      0.936 0.976 0.000 0.012 0.012
#> SRR975553     2  0.1022      0.969 0.000 0.968 0.000 0.032
#> SRR975555     1  0.0469      0.937 0.988 0.000 0.000 0.012
#> SRR975556     4  0.2313      0.906 0.044 0.032 0.000 0.924
#> SRR975557     4  0.1792      0.924 0.068 0.000 0.000 0.932
#> SRR975558     4  0.1792      0.924 0.068 0.000 0.000 0.932
#> SRR975559     1  0.2300      0.910 0.924 0.000 0.028 0.048
#> SRR975560     4  0.1792      0.924 0.068 0.000 0.000 0.932
#> SRR975561     4  0.1792      0.924 0.068 0.000 0.000 0.932
#> SRR975562     1  0.0937      0.936 0.976 0.000 0.012 0.012
#> SRR975563     2  0.0000      0.993 0.000 1.000 0.000 0.000
#> SRR975564     1  0.0469      0.937 0.988 0.000 0.000 0.012
#> SRR975565     1  0.0469      0.937 0.988 0.000 0.000 0.012
#> SRR975566     1  0.0469      0.937 0.988 0.000 0.000 0.012
#> SRR975567     4  0.1792      0.924 0.068 0.000 0.000 0.932
#> SRR975568     1  0.0469      0.937 0.988 0.000 0.000 0.012
#> SRR975569     2  0.0000      0.993 0.000 1.000 0.000 0.000
#> SRR975570     2  0.0000      0.993 0.000 1.000 0.000 0.000
#> SRR975571     2  0.1022      0.969 0.000 0.968 0.000 0.032
#> SRR975572     2  0.0000      0.993 0.000 1.000 0.000 0.000
#> SRR975573     2  0.0000      0.993 0.000 1.000 0.000 0.000
#> SRR975574     4  0.4898      0.303 0.000 0.416 0.000 0.584
#> SRR975575     2  0.0000      0.993 0.000 1.000 0.000 0.000
#> SRR975576     2  0.0000      0.993 0.000 1.000 0.000 0.000
#> SRR975577     2  0.0000      0.993 0.000 1.000 0.000 0.000
#> SRR975578     2  0.0000      0.993 0.000 1.000 0.000 0.000
#> SRR975579     4  0.1902      0.923 0.064 0.004 0.000 0.932
#> SRR975580     4  0.1902      0.923 0.064 0.004 0.000 0.932
#> SRR975581     2  0.1022      0.969 0.000 0.968 0.000 0.032
#> SRR975582     2  0.0000      0.993 0.000 1.000 0.000 0.000
#> SRR975583     2  0.0000      0.993 0.000 1.000 0.000 0.000
#> SRR975584     2  0.0000      0.993 0.000 1.000 0.000 0.000
#> SRR975585     2  0.0000      0.993 0.000 1.000 0.000 0.000
#> SRR975586     4  0.3082      0.862 0.032 0.084 0.000 0.884
#> SRR975587     3  0.0469      0.848 0.000 0.000 0.988 0.012
#> SRR975588     2  0.0000      0.993 0.000 1.000 0.000 0.000
#> SRR975589     3  0.3908      0.816 0.212 0.000 0.784 0.004
#> SRR975590     3  0.5500      0.795 0.224 0.000 0.708 0.068
#> SRR975591     3  0.0000      0.850 0.000 0.000 1.000 0.000
#> SRR975592     3  0.3908      0.816 0.212 0.000 0.784 0.004
#> SRR975593     3  0.3908      0.816 0.212 0.000 0.784 0.004
#> SRR975594     3  0.0000      0.850 0.000 0.000 1.000 0.000
#> SRR975595     3  0.5500      0.795 0.224 0.000 0.708 0.068
#> SRR975597     3  0.5500      0.795 0.224 0.000 0.708 0.068
#> SRR975596     1  0.1733      0.924 0.948 0.000 0.024 0.028
#> SRR975598     3  0.5500      0.795 0.224 0.000 0.708 0.068
#> SRR975599     1  0.7638      0.150 0.448 0.000 0.220 0.332
#> SRR975600     3  0.0000      0.850 0.000 0.000 1.000 0.000
#> SRR975601     3  0.0336      0.849 0.000 0.000 0.992 0.008
#> SRR975602     1  0.1209      0.914 0.964 0.000 0.032 0.004
#> SRR975603     3  0.0000      0.850 0.000 0.000 1.000 0.000
#> SRR975604     3  0.0000      0.850 0.000 0.000 1.000 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
#> SRR975551     1  0.0693      0.864 0.980 0.000 0.000 0.012 0.008
#> SRR975552     1  0.2605      0.866 0.852 0.000 0.000 0.148 0.000
#> SRR975554     1  0.2233      0.902 0.904 0.000 0.000 0.080 0.016
#> SRR975553     2  0.1800      0.958 0.000 0.932 0.048 0.020 0.000
#> SRR975555     1  0.1478      0.900 0.936 0.000 0.000 0.064 0.000
#> SRR975556     4  0.4256      0.809 0.004 0.052 0.160 0.780 0.004
#> SRR975557     4  0.1612      0.852 0.024 0.000 0.016 0.948 0.012
#> SRR975558     4  0.1124      0.856 0.036 0.000 0.000 0.960 0.004
#> SRR975559     1  0.3656      0.803 0.784 0.000 0.000 0.196 0.020
#> SRR975560     4  0.1285      0.856 0.036 0.000 0.004 0.956 0.004
#> SRR975561     4  0.3545      0.835 0.020 0.008 0.140 0.828 0.004
#> SRR975562     1  0.2110      0.902 0.912 0.000 0.000 0.072 0.016
#> SRR975563     2  0.0290      0.980 0.000 0.992 0.008 0.000 0.000
#> SRR975564     1  0.2020      0.899 0.900 0.000 0.000 0.100 0.000
#> SRR975565     1  0.1608      0.901 0.928 0.000 0.000 0.072 0.000
#> SRR975566     1  0.2017      0.903 0.912 0.000 0.000 0.080 0.008
#> SRR975567     4  0.1124      0.856 0.036 0.000 0.000 0.960 0.004
#> SRR975568     1  0.1732      0.901 0.920 0.000 0.000 0.080 0.000
#> SRR975569     2  0.0693      0.977 0.000 0.980 0.008 0.012 0.000
#> SRR975570     2  0.0404      0.979 0.000 0.988 0.012 0.000 0.000
#> SRR975571     2  0.1800      0.958 0.000 0.932 0.048 0.020 0.000
#> SRR975572     2  0.0000      0.979 0.000 1.000 0.000 0.000 0.000
#> SRR975573     2  0.0693      0.977 0.000 0.980 0.008 0.012 0.000
#> SRR975574     4  0.6333      0.424 0.000 0.328 0.176 0.496 0.000
#> SRR975575     2  0.0000      0.979 0.000 1.000 0.000 0.000 0.000
#> SRR975576     2  0.0162      0.979 0.000 0.996 0.004 0.000 0.000
#> SRR975577     2  0.0807      0.977 0.000 0.976 0.012 0.012 0.000
#> SRR975578     2  0.1907      0.956 0.000 0.928 0.044 0.028 0.000
#> SRR975579     4  0.1679      0.856 0.020 0.004 0.016 0.948 0.012
#> SRR975580     4  0.2426      0.854 0.008 0.016 0.064 0.908 0.004
#> SRR975581     2  0.1626      0.962 0.000 0.940 0.044 0.016 0.000
#> SRR975582     2  0.0703      0.977 0.000 0.976 0.024 0.000 0.000
#> SRR975583     2  0.0000      0.979 0.000 1.000 0.000 0.000 0.000
#> SRR975584     2  0.1106      0.974 0.000 0.964 0.024 0.012 0.000
#> SRR975585     2  0.0000      0.979 0.000 1.000 0.000 0.000 0.000
#> SRR975586     4  0.5065      0.769 0.004 0.120 0.148 0.724 0.004
#> SRR975587     3  0.3274      0.992 0.000 0.000 0.780 0.000 0.220
#> SRR975588     2  0.0404      0.979 0.000 0.988 0.012 0.000 0.000
#> SRR975589     5  0.3482      0.813 0.012 0.000 0.168 0.008 0.812
#> SRR975590     5  0.0404      0.881 0.012 0.000 0.000 0.000 0.988
#> SRR975591     3  0.3242      0.994 0.000 0.000 0.784 0.000 0.216
#> SRR975592     5  0.3399      0.809 0.012 0.000 0.172 0.004 0.812
#> SRR975593     5  0.3482      0.813 0.012 0.000 0.168 0.008 0.812
#> SRR975594     3  0.3242      0.994 0.000 0.000 0.784 0.000 0.216
#> SRR975595     5  0.0404      0.881 0.012 0.000 0.000 0.000 0.988
#> SRR975597     5  0.0404      0.881 0.012 0.000 0.000 0.000 0.988
#> SRR975596     1  0.2616      0.893 0.880 0.000 0.000 0.100 0.020
#> SRR975598     5  0.0404      0.881 0.012 0.000 0.000 0.000 0.988
#> SRR975599     1  0.7213      0.120 0.448 0.000 0.028 0.248 0.276
#> SRR975600     3  0.3491      0.977 0.000 0.000 0.768 0.004 0.228
#> SRR975601     3  0.3274      0.992 0.000 0.000 0.780 0.000 0.220
#> SRR975602     1  0.0992      0.862 0.968 0.000 0.000 0.008 0.024
#> SRR975603     3  0.3242      0.994 0.000 0.000 0.784 0.000 0.216
#> SRR975604     3  0.3242      0.994 0.000 0.000 0.784 0.000 0.216

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> SRR975551     1  0.1075      0.894 0.952 0.000 0.000 0.048 0.000 0.000
#> SRR975552     1  0.2121      0.890 0.892 0.000 0.000 0.096 0.012 0.000
#> SRR975554     1  0.1267      0.916 0.940 0.000 0.000 0.060 0.000 0.000
#> SRR975553     2  0.2664      0.838 0.000 0.816 0.000 0.000 0.184 0.000
#> SRR975555     1  0.0713      0.916 0.972 0.000 0.000 0.028 0.000 0.000
#> SRR975556     5  0.4189      0.163 0.000 0.020 0.000 0.376 0.604 0.000
#> SRR975557     4  0.3954      0.664 0.056 0.000 0.000 0.740 0.204 0.000
#> SRR975558     4  0.1204      0.759 0.056 0.000 0.000 0.944 0.000 0.000
#> SRR975559     1  0.2020      0.890 0.896 0.000 0.000 0.096 0.008 0.000
#> SRR975560     4  0.2978      0.729 0.056 0.012 0.000 0.860 0.072 0.000
#> SRR975561     5  0.6666      0.364 0.052 0.176 0.000 0.384 0.388 0.000
#> SRR975562     1  0.0937      0.917 0.960 0.000 0.000 0.040 0.000 0.000
#> SRR975563     2  0.1765      0.892 0.000 0.904 0.000 0.000 0.096 0.000
#> SRR975564     1  0.1267      0.915 0.940 0.000 0.000 0.060 0.000 0.000
#> SRR975565     1  0.0458      0.918 0.984 0.000 0.000 0.016 0.000 0.000
#> SRR975566     1  0.0858      0.917 0.968 0.000 0.000 0.028 0.004 0.000
#> SRR975567     4  0.1204      0.759 0.056 0.000 0.000 0.944 0.000 0.000
#> SRR975568     1  0.1075      0.918 0.952 0.000 0.000 0.048 0.000 0.000
#> SRR975569     2  0.0547      0.900 0.000 0.980 0.000 0.000 0.020 0.000
#> SRR975570     2  0.0632      0.897 0.000 0.976 0.000 0.000 0.024 0.000
#> SRR975571     2  0.2664      0.838 0.000 0.816 0.000 0.000 0.184 0.000
#> SRR975572     2  0.0632      0.897 0.000 0.976 0.000 0.000 0.024 0.000
#> SRR975573     2  0.0547      0.901 0.000 0.980 0.000 0.000 0.020 0.000
#> SRR975574     5  0.5095      0.506 0.000 0.312 0.000 0.104 0.584 0.000
#> SRR975575     2  0.0632      0.897 0.000 0.976 0.000 0.000 0.024 0.000
#> SRR975576     2  0.1765      0.892 0.000 0.904 0.000 0.000 0.096 0.000
#> SRR975577     2  0.2219      0.874 0.000 0.864 0.000 0.000 0.136 0.000
#> SRR975578     2  0.3198      0.731 0.000 0.740 0.000 0.000 0.260 0.000
#> SRR975579     4  0.5725      0.450 0.052 0.064 0.000 0.548 0.336 0.000
#> SRR975580     4  0.3809      0.485 0.008 0.012 0.000 0.716 0.264 0.000
#> SRR975581     2  0.1141      0.893 0.000 0.948 0.000 0.000 0.052 0.000
#> SRR975582     2  0.1910      0.887 0.000 0.892 0.000 0.000 0.108 0.000
#> SRR975583     2  0.0632      0.897 0.000 0.976 0.000 0.000 0.024 0.000
#> SRR975584     2  0.2219      0.874 0.000 0.864 0.000 0.000 0.136 0.000
#> SRR975585     2  0.0632      0.897 0.000 0.976 0.000 0.000 0.024 0.000
#> SRR975586     5  0.6057      0.573 0.008 0.268 0.000 0.240 0.484 0.000
#> SRR975587     3  0.0713      0.968 0.000 0.000 0.972 0.000 0.028 0.000
#> SRR975588     2  0.0632      0.897 0.000 0.976 0.000 0.000 0.024 0.000
#> SRR975589     6  0.4225      0.780 0.000 0.000 0.192 0.064 0.008 0.736
#> SRR975590     6  0.0363      0.855 0.000 0.000 0.012 0.000 0.000 0.988
#> SRR975591     3  0.0000      0.969 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975592     6  0.3337      0.738 0.000 0.000 0.260 0.000 0.004 0.736
#> SRR975593     6  0.4172      0.779 0.000 0.000 0.200 0.056 0.008 0.736
#> SRR975594     3  0.0713      0.968 0.000 0.000 0.972 0.000 0.028 0.000
#> SRR975595     6  0.0260      0.853 0.000 0.000 0.000 0.000 0.008 0.992
#> SRR975597     6  0.0260      0.853 0.000 0.000 0.000 0.000 0.008 0.992
#> SRR975596     1  0.1812      0.903 0.912 0.000 0.000 0.080 0.008 0.000
#> SRR975598     6  0.0405      0.851 0.004 0.000 0.000 0.000 0.008 0.988
#> SRR975599     1  0.5204      0.258 0.536 0.000 0.000 0.364 0.000 0.100
#> SRR975600     3  0.1858      0.871 0.000 0.000 0.904 0.000 0.004 0.092
#> SRR975601     3  0.0713      0.968 0.000 0.000 0.972 0.000 0.028 0.000
#> SRR975602     1  0.1141      0.896 0.948 0.000 0.000 0.052 0.000 0.000
#> SRR975603     3  0.0000      0.969 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975604     3  0.0000      0.969 0.000 0.000 1.000 0.000 0.000 0.000

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

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

consensus_heatmap(res, k = 2)

plot of chunk tab-CV-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

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 17171 rows and 54 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#>   Subgroups are detected by 'NMF' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 2.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

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           0.975       0.990         0.5092 0.491   0.491
#> 3 3 0.862           0.857       0.930         0.2541 0.840   0.682
#> 4 4 0.851           0.836       0.921         0.0893 0.892   0.725
#> 5 5 0.857           0.787       0.895         0.0834 0.923   0.762
#> 6 6 0.732           0.550       0.741         0.0657 0.924   0.703

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
#> SRR975551     1   0.000      0.984 1.000 0.000
#> SRR975552     1   0.204      0.954 0.968 0.032
#> SRR975554     1   0.000      0.984 1.000 0.000
#> SRR975553     2   0.000      0.995 0.000 1.000
#> SRR975555     1   0.000      0.984 1.000 0.000
#> SRR975556     2   0.000      0.995 0.000 1.000
#> SRR975557     2   0.000      0.995 0.000 1.000
#> SRR975558     1   0.966      0.350 0.608 0.392
#> SRR975559     1   0.000      0.984 1.000 0.000
#> SRR975560     2   0.000      0.995 0.000 1.000
#> SRR975561     2   0.000      0.995 0.000 1.000
#> SRR975562     1   0.000      0.984 1.000 0.000
#> SRR975563     2   0.000      0.995 0.000 1.000
#> SRR975564     1   0.000      0.984 1.000 0.000
#> SRR975565     1   0.000      0.984 1.000 0.000
#> SRR975566     1   0.000      0.984 1.000 0.000
#> SRR975567     2   0.529      0.860 0.120 0.880
#> SRR975568     1   0.000      0.984 1.000 0.000
#> SRR975569     2   0.000      0.995 0.000 1.000
#> SRR975570     2   0.000      0.995 0.000 1.000
#> SRR975571     2   0.000      0.995 0.000 1.000
#> SRR975572     2   0.000      0.995 0.000 1.000
#> SRR975573     2   0.000      0.995 0.000 1.000
#> SRR975574     2   0.000      0.995 0.000 1.000
#> SRR975575     2   0.000      0.995 0.000 1.000
#> SRR975576     2   0.000      0.995 0.000 1.000
#> SRR975577     2   0.000      0.995 0.000 1.000
#> SRR975578     2   0.000      0.995 0.000 1.000
#> SRR975579     2   0.000      0.995 0.000 1.000
#> SRR975580     2   0.000      0.995 0.000 1.000
#> SRR975581     2   0.000      0.995 0.000 1.000
#> SRR975582     2   0.000      0.995 0.000 1.000
#> SRR975583     2   0.000      0.995 0.000 1.000
#> SRR975584     2   0.000      0.995 0.000 1.000
#> SRR975585     2   0.000      0.995 0.000 1.000
#> SRR975586     2   0.000      0.995 0.000 1.000
#> SRR975587     1   0.000      0.984 1.000 0.000
#> SRR975588     2   0.000      0.995 0.000 1.000
#> SRR975589     1   0.000      0.984 1.000 0.000
#> SRR975590     1   0.000      0.984 1.000 0.000
#> SRR975591     1   0.000      0.984 1.000 0.000
#> SRR975592     1   0.000      0.984 1.000 0.000
#> SRR975593     1   0.000      0.984 1.000 0.000
#> SRR975594     1   0.000      0.984 1.000 0.000
#> SRR975595     1   0.000      0.984 1.000 0.000
#> SRR975597     1   0.000      0.984 1.000 0.000
#> SRR975596     1   0.000      0.984 1.000 0.000
#> SRR975598     1   0.000      0.984 1.000 0.000
#> SRR975599     1   0.000      0.984 1.000 0.000
#> SRR975600     1   0.000      0.984 1.000 0.000
#> SRR975601     1   0.000      0.984 1.000 0.000
#> SRR975602     1   0.000      0.984 1.000 0.000
#> SRR975603     1   0.000      0.984 1.000 0.000
#> SRR975604     1   0.000      0.984 1.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> SRR975551     1  0.2356      0.890 0.928 0.000 0.072
#> SRR975552     1  0.2356      0.890 0.928 0.000 0.072
#> SRR975554     1  0.2356      0.890 0.928 0.000 0.072
#> SRR975553     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975555     1  0.2356      0.890 0.928 0.000 0.072
#> SRR975556     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975557     2  0.4291      0.815 0.180 0.820 0.000
#> SRR975558     1  0.0000      0.853 1.000 0.000 0.000
#> SRR975559     1  0.0000      0.853 1.000 0.000 0.000
#> SRR975560     2  0.4002      0.821 0.160 0.840 0.000
#> SRR975561     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975562     1  0.2356      0.890 0.928 0.000 0.072
#> SRR975563     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975564     1  0.2356      0.890 0.928 0.000 0.072
#> SRR975565     1  0.2356      0.890 0.928 0.000 0.072
#> SRR975566     1  0.1289      0.872 0.968 0.000 0.032
#> SRR975567     1  0.0000      0.853 1.000 0.000 0.000
#> SRR975568     1  0.2356      0.890 0.928 0.000 0.072
#> SRR975569     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975570     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975571     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975572     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975573     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975574     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975575     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975576     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975577     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975578     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975579     2  0.2356      0.926 0.072 0.928 0.000
#> SRR975580     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975581     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975582     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975583     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975584     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975585     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975586     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975587     3  0.0000      0.846 0.000 0.000 1.000
#> SRR975588     2  0.0000      0.983 0.000 1.000 0.000
#> SRR975589     1  0.5216      0.686 0.740 0.000 0.260
#> SRR975590     3  0.5882      0.430 0.348 0.000 0.652
#> SRR975591     3  0.0237      0.843 0.004 0.000 0.996
#> SRR975592     3  0.2261      0.805 0.068 0.000 0.932
#> SRR975593     1  0.5678      0.590 0.684 0.000 0.316
#> SRR975594     3  0.0000      0.846 0.000 0.000 1.000
#> SRR975595     3  0.6062      0.342 0.384 0.000 0.616
#> SRR975597     3  0.6168      0.255 0.412 0.000 0.588
#> SRR975596     1  0.0000      0.853 1.000 0.000 0.000
#> SRR975598     1  0.6274      0.186 0.544 0.000 0.456
#> SRR975599     1  0.5650      0.598 0.688 0.000 0.312
#> SRR975600     3  0.0000      0.846 0.000 0.000 1.000
#> SRR975601     3  0.0000      0.846 0.000 0.000 1.000
#> SRR975602     1  0.2356      0.890 0.928 0.000 0.072
#> SRR975603     3  0.0000      0.846 0.000 0.000 1.000
#> SRR975604     3  0.0000      0.846 0.000 0.000 1.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> SRR975551     1  0.0000      0.791 1.000 0.000 0.000 0.000
#> SRR975552     1  0.0000      0.791 1.000 0.000 0.000 0.000
#> SRR975554     1  0.0000      0.791 1.000 0.000 0.000 0.000
#> SRR975553     2  0.0000      0.975 0.000 1.000 0.000 0.000
#> SRR975555     1  0.2469      0.779 0.892 0.000 0.000 0.108
#> SRR975556     2  0.0000      0.975 0.000 1.000 0.000 0.000
#> SRR975557     4  0.0000      0.736 0.000 0.000 0.000 1.000
#> SRR975558     1  0.3688      0.704 0.792 0.000 0.000 0.208
#> SRR975559     4  0.4804      0.491 0.384 0.000 0.000 0.616
#> SRR975560     2  0.2761      0.869 0.048 0.904 0.000 0.048
#> SRR975561     2  0.4916      0.273 0.000 0.576 0.000 0.424
#> SRR975562     1  0.0000      0.791 1.000 0.000 0.000 0.000
#> SRR975563     2  0.0000      0.975 0.000 1.000 0.000 0.000
#> SRR975564     1  0.2760      0.771 0.872 0.000 0.000 0.128
#> SRR975565     1  0.2011      0.786 0.920 0.000 0.000 0.080
#> SRR975566     1  0.1211      0.774 0.960 0.000 0.000 0.040
#> SRR975567     4  0.3074      0.725 0.152 0.000 0.000 0.848
#> SRR975568     1  0.2760      0.771 0.872 0.000 0.000 0.128
#> SRR975569     2  0.0000      0.975 0.000 1.000 0.000 0.000
#> SRR975570     2  0.0000      0.975 0.000 1.000 0.000 0.000
#> SRR975571     2  0.0000      0.975 0.000 1.000 0.000 0.000
#> SRR975572     2  0.0000      0.975 0.000 1.000 0.000 0.000
#> SRR975573     2  0.0000      0.975 0.000 1.000 0.000 0.000
#> SRR975574     2  0.0000      0.975 0.000 1.000 0.000 0.000
#> SRR975575     2  0.0000      0.975 0.000 1.000 0.000 0.000
#> SRR975576     2  0.0000      0.975 0.000 1.000 0.000 0.000
#> SRR975577     2  0.0000      0.975 0.000 1.000 0.000 0.000
#> SRR975578     2  0.0000      0.975 0.000 1.000 0.000 0.000
#> SRR975579     4  0.2760      0.662 0.000 0.128 0.000 0.872
#> SRR975580     2  0.0000      0.975 0.000 1.000 0.000 0.000
#> SRR975581     2  0.0000      0.975 0.000 1.000 0.000 0.000
#> SRR975582     2  0.0000      0.975 0.000 1.000 0.000 0.000
#> SRR975583     2  0.0000      0.975 0.000 1.000 0.000 0.000
#> SRR975584     2  0.0000      0.975 0.000 1.000 0.000 0.000
#> SRR975585     2  0.0000      0.975 0.000 1.000 0.000 0.000
#> SRR975586     2  0.0000      0.975 0.000 1.000 0.000 0.000
#> SRR975587     3  0.0000      0.998 0.000 0.000 1.000 0.000
#> SRR975588     2  0.0000      0.975 0.000 1.000 0.000 0.000
#> SRR975589     1  0.4017      0.770 0.828 0.000 0.044 0.128
#> SRR975590     1  0.4985      0.324 0.532 0.000 0.468 0.000
#> SRR975591     3  0.0000      0.998 0.000 0.000 1.000 0.000
#> SRR975592     3  0.0469      0.982 0.012 0.000 0.988 0.000
#> SRR975593     1  0.4720      0.662 0.720 0.000 0.264 0.016
#> SRR975594     3  0.0000      0.998 0.000 0.000 1.000 0.000
#> SRR975595     1  0.4898      0.448 0.584 0.000 0.416 0.000
#> SRR975597     1  0.4830      0.492 0.608 0.000 0.392 0.000
#> SRR975596     1  0.4933      0.216 0.568 0.000 0.000 0.432
#> SRR975598     1  0.3486      0.719 0.812 0.000 0.188 0.000
#> SRR975599     1  0.1389      0.782 0.952 0.000 0.048 0.000
#> SRR975600     3  0.0000      0.998 0.000 0.000 1.000 0.000
#> SRR975601     3  0.0000      0.998 0.000 0.000 1.000 0.000
#> SRR975602     1  0.0000      0.791 1.000 0.000 0.000 0.000
#> SRR975603     3  0.0000      0.998 0.000 0.000 1.000 0.000
#> SRR975604     3  0.0000      0.998 0.000 0.000 1.000 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
#> SRR975551     1  0.0000     0.8137 1.000 0.000 0.000 0.000 0.000
#> SRR975552     1  0.0000     0.8137 1.000 0.000 0.000 0.000 0.000
#> SRR975554     1  0.2648     0.6866 0.848 0.000 0.000 0.000 0.152
#> SRR975553     2  0.1851     0.9377 0.000 0.912 0.000 0.000 0.088
#> SRR975555     5  0.4201     0.3772 0.408 0.000 0.000 0.000 0.592
#> SRR975556     2  0.0162     0.9488 0.000 0.996 0.000 0.000 0.004
#> SRR975557     4  0.0000     0.7432 0.000 0.000 0.000 1.000 0.000
#> SRR975558     5  0.2130     0.7841 0.080 0.012 0.000 0.000 0.908
#> SRR975559     4  0.3932     0.5119 0.328 0.000 0.000 0.672 0.000
#> SRR975560     2  0.4703     0.6513 0.024 0.732 0.000 0.212 0.032
#> SRR975561     4  0.2068     0.7012 0.000 0.092 0.000 0.904 0.004
#> SRR975562     1  0.0000     0.8137 1.000 0.000 0.000 0.000 0.000
#> SRR975563     2  0.0162     0.9488 0.000 0.996 0.000 0.000 0.004
#> SRR975564     5  0.1965     0.7949 0.096 0.000 0.000 0.000 0.904
#> SRR975565     1  0.3039     0.6585 0.808 0.000 0.000 0.000 0.192
#> SRR975566     1  0.4227     0.0616 0.580 0.000 0.000 0.000 0.420
#> SRR975567     4  0.4828     0.1765 0.012 0.008 0.000 0.572 0.408
#> SRR975568     5  0.2020     0.7955 0.100 0.000 0.000 0.000 0.900
#> SRR975569     2  0.0609     0.9475 0.000 0.980 0.000 0.000 0.020
#> SRR975570     2  0.0162     0.9488 0.000 0.996 0.000 0.000 0.004
#> SRR975571     2  0.1851     0.9377 0.000 0.912 0.000 0.000 0.088
#> SRR975572     2  0.0000     0.9489 0.000 1.000 0.000 0.000 0.000
#> SRR975573     2  0.1851     0.9377 0.000 0.912 0.000 0.000 0.088
#> SRR975574     2  0.1851     0.9377 0.000 0.912 0.000 0.000 0.088
#> SRR975575     2  0.0000     0.9489 0.000 1.000 0.000 0.000 0.000
#> SRR975576     2  0.0162     0.9488 0.000 0.996 0.000 0.000 0.004
#> SRR975577     2  0.1792     0.9388 0.000 0.916 0.000 0.000 0.084
#> SRR975578     2  0.1792     0.9388 0.000 0.916 0.000 0.000 0.084
#> SRR975579     4  0.0000     0.7432 0.000 0.000 0.000 1.000 0.000
#> SRR975580     2  0.1792     0.9388 0.000 0.916 0.000 0.000 0.084
#> SRR975581     2  0.0162     0.9488 0.000 0.996 0.000 0.000 0.004
#> SRR975582     2  0.1851     0.9377 0.000 0.912 0.000 0.000 0.088
#> SRR975583     2  0.0162     0.9488 0.000 0.996 0.000 0.000 0.004
#> SRR975584     2  0.1851     0.9377 0.000 0.912 0.000 0.000 0.088
#> SRR975585     2  0.0162     0.9488 0.000 0.996 0.000 0.000 0.004
#> SRR975586     2  0.0162     0.9488 0.000 0.996 0.000 0.000 0.004
#> SRR975587     3  0.0000     0.8969 0.000 0.000 1.000 0.000 0.000
#> SRR975588     2  0.0162     0.9488 0.000 0.996 0.000 0.000 0.004
#> SRR975589     5  0.2124     0.7956 0.096 0.000 0.004 0.000 0.900
#> SRR975590     1  0.3177     0.7384 0.792 0.000 0.208 0.000 0.000
#> SRR975591     3  0.0000     0.8969 0.000 0.000 1.000 0.000 0.000
#> SRR975592     3  0.3003     0.7413 0.000 0.000 0.812 0.000 0.188
#> SRR975593     5  0.4069     0.7098 0.096 0.000 0.112 0.000 0.792
#> SRR975594     3  0.0000     0.8969 0.000 0.000 1.000 0.000 0.000
#> SRR975595     1  0.3366     0.7138 0.768 0.000 0.232 0.000 0.000
#> SRR975597     1  0.3143     0.7405 0.796 0.000 0.204 0.000 0.000
#> SRR975596     5  0.6137     0.0714 0.132 0.000 0.000 0.392 0.476
#> SRR975598     1  0.2329     0.7851 0.876 0.000 0.124 0.000 0.000
#> SRR975599     1  0.0162     0.8137 0.996 0.000 0.004 0.000 0.000
#> SRR975600     3  0.4287     0.2579 0.000 0.000 0.540 0.000 0.460
#> SRR975601     3  0.0000     0.8969 0.000 0.000 1.000 0.000 0.000
#> SRR975602     1  0.0000     0.8137 1.000 0.000 0.000 0.000 0.000
#> SRR975603     3  0.0000     0.8969 0.000 0.000 1.000 0.000 0.000
#> SRR975604     3  0.0000     0.8969 0.000 0.000 1.000 0.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> SRR975551     1  0.0000     0.7900 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR975552     1  0.0260     0.7908 0.992 0.000 0.000 0.000 0.008 0.000
#> SRR975554     1  0.2340     0.7254 0.852 0.000 0.000 0.000 0.148 0.000
#> SRR975553     2  0.0000     0.6605 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975555     5  0.3912     0.4915 0.224 0.000 0.000 0.000 0.732 0.044
#> SRR975556     6  0.3864     0.1211 0.000 0.480 0.000 0.000 0.000 0.520
#> SRR975557     4  0.0000     0.7541 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR975558     5  0.0547     0.7234 0.000 0.000 0.000 0.000 0.980 0.020
#> SRR975559     4  0.4074     0.6559 0.140 0.000 0.000 0.752 0.000 0.108
#> SRR975560     6  0.4779     0.0911 0.000 0.308 0.000 0.016 0.044 0.632
#> SRR975561     4  0.2841     0.6830 0.000 0.012 0.000 0.824 0.000 0.164
#> SRR975562     1  0.3916     0.6578 0.680 0.000 0.000 0.000 0.020 0.300
#> SRR975563     6  0.3864     0.1211 0.000 0.480 0.000 0.000 0.000 0.520
#> SRR975564     5  0.0000     0.7232 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR975565     1  0.2941     0.6817 0.780 0.000 0.000 0.000 0.220 0.000
#> SRR975566     1  0.5168     0.2672 0.552 0.000 0.000 0.004 0.360 0.084
#> SRR975567     4  0.5911     0.3202 0.000 0.000 0.000 0.456 0.228 0.316
#> SRR975568     5  0.0260     0.7208 0.000 0.000 0.000 0.000 0.992 0.008
#> SRR975569     2  0.2996     0.5105 0.000 0.772 0.000 0.000 0.000 0.228
#> SRR975570     2  0.3330     0.4456 0.000 0.716 0.000 0.000 0.000 0.284
#> SRR975571     2  0.0000     0.6605 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975572     2  0.3737     0.2319 0.000 0.608 0.000 0.000 0.000 0.392
#> SRR975573     2  0.0000     0.6605 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975574     2  0.0146     0.6603 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR975575     2  0.3774     0.1806 0.000 0.592 0.000 0.000 0.000 0.408
#> SRR975576     2  0.3862    -0.1501 0.000 0.524 0.000 0.000 0.000 0.476
#> SRR975577     2  0.0000     0.6605 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975578     2  0.0146     0.6603 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR975579     4  0.0000     0.7541 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR975580     2  0.1967     0.5442 0.012 0.904 0.000 0.000 0.000 0.084
#> SRR975581     2  0.3727     0.2405 0.000 0.612 0.000 0.000 0.000 0.388
#> SRR975582     2  0.0000     0.6605 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975583     6  0.3868     0.0591 0.000 0.496 0.000 0.000 0.000 0.504
#> SRR975584     2  0.0632     0.6376 0.000 0.976 0.000 0.000 0.000 0.024
#> SRR975585     2  0.3823     0.0661 0.000 0.564 0.000 0.000 0.000 0.436
#> SRR975586     6  0.3864     0.1211 0.000 0.480 0.000 0.000 0.000 0.520
#> SRR975587     3  0.0000     0.9615 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975588     2  0.3482     0.3970 0.000 0.684 0.000 0.000 0.000 0.316
#> SRR975589     5  0.2941     0.6429 0.000 0.000 0.000 0.000 0.780 0.220
#> SRR975590     1  0.2219     0.7713 0.864 0.000 0.136 0.000 0.000 0.000
#> SRR975591     3  0.0000     0.9615 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975592     3  0.2871     0.7160 0.000 0.000 0.804 0.000 0.192 0.004
#> SRR975593     5  0.4585     0.5849 0.000 0.000 0.068 0.000 0.648 0.284
#> SRR975594     3  0.0000     0.9615 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975595     1  0.4386     0.7211 0.708 0.000 0.200 0.000 0.000 0.092
#> SRR975597     1  0.3971     0.7432 0.748 0.000 0.184 0.000 0.000 0.068
#> SRR975596     6  0.6641    -0.5347 0.032 0.000 0.000 0.248 0.336 0.384
#> SRR975598     1  0.3747     0.7757 0.784 0.000 0.104 0.000 0.000 0.112
#> SRR975599     1  0.2703     0.7661 0.824 0.000 0.000 0.000 0.004 0.172
#> SRR975600     5  0.4184    -0.0456 0.000 0.000 0.484 0.000 0.504 0.012
#> SRR975601     3  0.0000     0.9615 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975602     1  0.1075     0.7896 0.952 0.000 0.000 0.000 0.000 0.048
#> SRR975603     3  0.0000     0.9615 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975604     3  0.0000     0.9615 0.000 0.000 1.000 0.000 0.000 0.000

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

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

consensus_heatmap(res, k = 2)

plot of chunk tab-CV-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

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 17171 rows and 54 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#>   Subgroups are detected by 'hclust' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 3.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk MAD-hclust-collect-plots

The plots are:

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

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

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

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

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

select_partition_number(res)

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

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.855           0.948       0.975        0.50852 0.491   0.491
#> 3 3 1.000           0.964       0.983        0.13771 0.936   0.869
#> 4 4 0.995           0.958       0.982        0.00636 0.997   0.993
#> 5 5 0.778           0.780       0.878        0.19555 0.874   0.703
#> 6 6 0.851           0.780       0.899        0.04948 0.948   0.838

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

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

suggest_best_k(res)

#> [1] 3

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

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

show/hide code output

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

#>           class entropy silhouette    p1    p2
#> SRR975551     1   0.000      0.977 1.000 0.000
#> SRR975552     1   0.000      0.977 1.000 0.000
#> SRR975554     1   0.000      0.977 1.000 0.000
#> SRR975553     2   0.000      0.967 0.000 1.000
#> SRR975555     1   0.000      0.977 1.000 0.000
#> SRR975556     2   0.000      0.967 0.000 1.000
#> SRR975557     2   0.722      0.774 0.200 0.800
#> SRR975558     1   0.714      0.763 0.804 0.196
#> SRR975559     1   0.000      0.977 1.000 0.000
#> SRR975560     2   0.000      0.967 0.000 1.000
#> SRR975561     2   0.000      0.967 0.000 1.000
#> SRR975562     1   0.000      0.977 1.000 0.000
#> SRR975563     2   0.000      0.967 0.000 1.000
#> SRR975564     1   0.000      0.977 1.000 0.000
#> SRR975565     1   0.000      0.977 1.000 0.000
#> SRR975566     1   0.000      0.977 1.000 0.000
#> SRR975567     1   0.714      0.763 0.804 0.196
#> SRR975568     1   0.000      0.977 1.000 0.000
#> SRR975569     2   0.000      0.967 0.000 1.000
#> SRR975570     2   0.000      0.967 0.000 1.000
#> SRR975571     2   0.000      0.967 0.000 1.000
#> SRR975572     2   0.000      0.967 0.000 1.000
#> SRR975573     2   0.000      0.967 0.000 1.000
#> SRR975574     2   0.000      0.967 0.000 1.000
#> SRR975575     2   0.000      0.967 0.000 1.000
#> SRR975576     2   0.000      0.967 0.000 1.000
#> SRR975577     2   0.000      0.967 0.000 1.000
#> SRR975578     2   0.000      0.967 0.000 1.000
#> SRR975579     2   0.722      0.774 0.200 0.800
#> SRR975580     2   0.000      0.967 0.000 1.000
#> SRR975581     2   0.000      0.967 0.000 1.000
#> SRR975582     2   0.000      0.967 0.000 1.000
#> SRR975583     2   0.000      0.967 0.000 1.000
#> SRR975584     2   0.000      0.967 0.000 1.000
#> SRR975585     2   0.000      0.967 0.000 1.000
#> SRR975586     2   0.000      0.967 0.000 1.000
#> SRR975587     1   0.184      0.962 0.972 0.028
#> SRR975588     2   0.000      0.967 0.000 1.000
#> SRR975589     1   0.000      0.977 1.000 0.000
#> SRR975590     1   0.000      0.977 1.000 0.000
#> SRR975591     1   0.184      0.962 0.972 0.028
#> SRR975592     1   0.000      0.977 1.000 0.000
#> SRR975593     1   0.000      0.977 1.000 0.000
#> SRR975594     2   0.722      0.774 0.200 0.800
#> SRR975595     1   0.000      0.977 1.000 0.000
#> SRR975597     1   0.000      0.977 1.000 0.000
#> SRR975596     1   0.000      0.977 1.000 0.000
#> SRR975598     1   0.000      0.977 1.000 0.000
#> SRR975599     2   0.722      0.774 0.200 0.800
#> SRR975600     1   0.184      0.962 0.972 0.028
#> SRR975601     1   0.184      0.962 0.972 0.028
#> SRR975602     1   0.000      0.977 1.000 0.000
#> SRR975603     1   0.184      0.962 0.972 0.028
#> SRR975604     1   0.184      0.962 0.972 0.028

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> SRR975551     1   0.000      0.962 1.000 0.000 0.000
#> SRR975552     1   0.000      0.962 1.000 0.000 0.000
#> SRR975554     1   0.000      0.962 1.000 0.000 0.000
#> SRR975553     2   0.000      1.000 0.000 1.000 0.000
#> SRR975555     1   0.000      0.962 1.000 0.000 0.000
#> SRR975556     2   0.000      1.000 0.000 1.000 0.000
#> SRR975557     3   0.000      0.974 0.000 0.000 1.000
#> SRR975558     1   0.450      0.721 0.804 0.196 0.000
#> SRR975559     1   0.000      0.962 1.000 0.000 0.000
#> SRR975560     2   0.000      1.000 0.000 1.000 0.000
#> SRR975561     2   0.000      1.000 0.000 1.000 0.000
#> SRR975562     1   0.000      0.962 1.000 0.000 0.000
#> SRR975563     2   0.000      1.000 0.000 1.000 0.000
#> SRR975564     1   0.000      0.962 1.000 0.000 0.000
#> SRR975565     1   0.000      0.962 1.000 0.000 0.000
#> SRR975566     1   0.000      0.962 1.000 0.000 0.000
#> SRR975567     1   0.450      0.721 0.804 0.196 0.000
#> SRR975568     1   0.000      0.962 1.000 0.000 0.000
#> SRR975569     2   0.000      1.000 0.000 1.000 0.000
#> SRR975570     2   0.000      1.000 0.000 1.000 0.000
#> SRR975571     2   0.000      1.000 0.000 1.000 0.000
#> SRR975572     2   0.000      1.000 0.000 1.000 0.000
#> SRR975573     2   0.000      1.000 0.000 1.000 0.000
#> SRR975574     2   0.000      1.000 0.000 1.000 0.000
#> SRR975575     2   0.000      1.000 0.000 1.000 0.000
#> SRR975576     2   0.000      1.000 0.000 1.000 0.000
#> SRR975577     2   0.000      1.000 0.000 1.000 0.000
#> SRR975578     2   0.000      1.000 0.000 1.000 0.000
#> SRR975579     3   0.000      0.974 0.000 0.000 1.000
#> SRR975580     2   0.000      1.000 0.000 1.000 0.000
#> SRR975581     2   0.000      1.000 0.000 1.000 0.000
#> SRR975582     2   0.000      1.000 0.000 1.000 0.000
#> SRR975583     2   0.000      1.000 0.000 1.000 0.000
#> SRR975584     2   0.000      1.000 0.000 1.000 0.000
#> SRR975585     2   0.000      1.000 0.000 1.000 0.000
#> SRR975586     2   0.000      1.000 0.000 1.000 0.000
#> SRR975587     1   0.245      0.920 0.924 0.000 0.076
#> SRR975588     2   0.000      1.000 0.000 1.000 0.000
#> SRR975589     1   0.000      0.962 1.000 0.000 0.000
#> SRR975590     1   0.000      0.962 1.000 0.000 0.000
#> SRR975591     1   0.245      0.920 0.924 0.000 0.076
#> SRR975592     1   0.000      0.962 1.000 0.000 0.000
#> SRR975593     1   0.000      0.962 1.000 0.000 0.000
#> SRR975594     3   0.000      0.974 0.000 0.000 1.000
#> SRR975595     1   0.000      0.962 1.000 0.000 0.000
#> SRR975597     1   0.000      0.962 1.000 0.000 0.000
#> SRR975596     1   0.000      0.962 1.000 0.000 0.000
#> SRR975598     1   0.000      0.962 1.000 0.000 0.000
#> SRR975599     3   0.245      0.917 0.076 0.000 0.924
#> SRR975600     1   0.245      0.920 0.924 0.000 0.076
#> SRR975601     1   0.245      0.920 0.924 0.000 0.076
#> SRR975602     1   0.000      0.962 1.000 0.000 0.000
#> SRR975603     1   0.245      0.920 0.924 0.000 0.076
#> SRR975604     1   0.245      0.920 0.924 0.000 0.076

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> SRR975551     1  0.0000      0.959 1.000 0.000 0.000 0.000
#> SRR975552     1  0.0000      0.959 1.000 0.000 0.000 0.000
#> SRR975554     1  0.0000      0.959 1.000 0.000 0.000 0.000
#> SRR975553     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975555     1  0.0188      0.958 0.996 0.000 0.004 0.000
#> SRR975556     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975557     4  0.0000      1.000 0.000 0.000 0.000 1.000
#> SRR975558     1  0.3751      0.700 0.800 0.196 0.004 0.000
#> SRR975559     1  0.0188      0.958 0.996 0.000 0.004 0.000
#> SRR975560     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975561     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975562     1  0.0188      0.958 0.996 0.000 0.004 0.000
#> SRR975563     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975564     1  0.0188      0.958 0.996 0.000 0.004 0.000
#> SRR975565     1  0.0000      0.959 1.000 0.000 0.000 0.000
#> SRR975566     1  0.0000      0.959 1.000 0.000 0.000 0.000
#> SRR975567     1  0.3751      0.700 0.800 0.196 0.004 0.000
#> SRR975568     1  0.0188      0.958 0.996 0.000 0.004 0.000
#> SRR975569     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975570     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975571     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975572     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975573     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975574     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975575     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975576     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975577     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975578     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975579     4  0.0000      1.000 0.000 0.000 0.000 1.000
#> SRR975580     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975581     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975582     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975583     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975584     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975585     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975586     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975587     1  0.1940      0.918 0.924 0.000 0.076 0.000
#> SRR975588     2  0.0000      1.000 0.000 1.000 0.000 0.000
#> SRR975589     1  0.0000      0.959 1.000 0.000 0.000 0.000
#> SRR975590     1  0.0000      0.959 1.000 0.000 0.000 0.000
#> SRR975591     1  0.1940      0.918 0.924 0.000 0.076 0.000
#> SRR975592     1  0.0000      0.959 1.000 0.000 0.000 0.000
#> SRR975593     1  0.0000      0.959 1.000 0.000 0.000 0.000
#> SRR975594     3  0.0188      0.803 0.000 0.000 0.996 0.004
#> SRR975595     1  0.0000      0.959 1.000 0.000 0.000 0.000
#> SRR975597     1  0.0000      0.959 1.000 0.000 0.000 0.000
#> SRR975596     1  0.0188      0.958 0.996 0.000 0.004 0.000
#> SRR975598     1  0.0000      0.959 1.000 0.000 0.000 0.000
#> SRR975599     3  0.2125      0.808 0.076 0.000 0.920 0.004
#> SRR975600     1  0.1940      0.918 0.924 0.000 0.076 0.000
#> SRR975601     1  0.1940      0.918 0.924 0.000 0.076 0.000
#> SRR975602     1  0.0000      0.959 1.000 0.000 0.000 0.000
#> SRR975603     1  0.1940      0.918 0.924 0.000 0.076 0.000
#> SRR975604     1  0.1940      0.918 0.924 0.000 0.076 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
#> SRR975551     1   0.130      0.720 0.956 0.000 0.028  0 0.016
#> SRR975552     1   0.130      0.720 0.956 0.000 0.028  0 0.016
#> SRR975554     1   0.191      0.740 0.908 0.000 0.092  0 0.000
#> SRR975553     2   0.000      0.995 0.000 1.000 0.000  0 0.000
#> SRR975555     1   0.460      0.436 0.656 0.000 0.316  0 0.028
#> SRR975556     2   0.000      0.995 0.000 1.000 0.000  0 0.000
#> SRR975557     4   0.000      1.000 0.000 0.000 0.000  1 0.000
#> SRR975558     3   0.587      0.429 0.092 0.140 0.692  0 0.076
#> SRR975559     3   0.482      0.319 0.456 0.000 0.524  0 0.020
#> SRR975560     2   0.152      0.944 0.000 0.944 0.012  0 0.044
#> SRR975561     2   0.000      0.995 0.000 1.000 0.000  0 0.000
#> SRR975562     1   0.332      0.624 0.820 0.000 0.160  0 0.020
#> SRR975563     2   0.000      0.995 0.000 1.000 0.000  0 0.000
#> SRR975564     1   0.472      0.381 0.628 0.000 0.344  0 0.028
#> SRR975565     1   0.177      0.706 0.932 0.000 0.052  0 0.016
#> SRR975566     1   0.191      0.740 0.908 0.000 0.092  0 0.000
#> SRR975567     3   0.587      0.429 0.092 0.140 0.692  0 0.076
#> SRR975568     1   0.460      0.436 0.656 0.000 0.316  0 0.028
#> SRR975569     2   0.000      0.995 0.000 1.000 0.000  0 0.000
#> SRR975570     2   0.000      0.995 0.000 1.000 0.000  0 0.000
#> SRR975571     2   0.000      0.995 0.000 1.000 0.000  0 0.000
#> SRR975572     2   0.000      0.995 0.000 1.000 0.000  0 0.000
#> SRR975573     2   0.000      0.995 0.000 1.000 0.000  0 0.000
#> SRR975574     2   0.000      0.995 0.000 1.000 0.000  0 0.000
#> SRR975575     2   0.000      0.995 0.000 1.000 0.000  0 0.000
#> SRR975576     2   0.000      0.995 0.000 1.000 0.000  0 0.000
#> SRR975577     2   0.000      0.995 0.000 1.000 0.000  0 0.000
#> SRR975578     2   0.000      0.995 0.000 1.000 0.000  0 0.000
#> SRR975579     4   0.000      1.000 0.000 0.000 0.000  1 0.000
#> SRR975580     2   0.152      0.944 0.000 0.944 0.012  0 0.044
#> SRR975581     2   0.000      0.995 0.000 1.000 0.000  0 0.000
#> SRR975582     2   0.000      0.995 0.000 1.000 0.000  0 0.000
#> SRR975583     2   0.000      0.995 0.000 1.000 0.000  0 0.000
#> SRR975584     2   0.000      0.995 0.000 1.000 0.000  0 0.000
#> SRR975585     2   0.000      0.995 0.000 1.000 0.000  0 0.000
#> SRR975586     2   0.000      0.995 0.000 1.000 0.000  0 0.000
#> SRR975587     3   0.161      0.706 0.072 0.000 0.928  0 0.000
#> SRR975588     2   0.000      0.995 0.000 1.000 0.000  0 0.000
#> SRR975589     3   0.428      0.155 0.452 0.000 0.548  0 0.000
#> SRR975590     1   0.223      0.731 0.884 0.000 0.116  0 0.000
#> SRR975591     3   0.161      0.706 0.072 0.000 0.928  0 0.000
#> SRR975592     1   0.366      0.598 0.724 0.000 0.276  0 0.000
#> SRR975593     3   0.428      0.155 0.452 0.000 0.548  0 0.000
#> SRR975594     5   0.167      0.870 0.000 0.000 0.076  0 0.924
#> SRR975595     1   0.337      0.656 0.768 0.000 0.232  0 0.000
#> SRR975597     1   0.337      0.656 0.768 0.000 0.232  0 0.000
#> SRR975596     3   0.482      0.319 0.456 0.000 0.524  0 0.020
#> SRR975598     1   0.334      0.657 0.772 0.000 0.228  0 0.000
#> SRR975599     5   0.311      0.872 0.036 0.000 0.112  0 0.852
#> SRR975600     3   0.161      0.706 0.072 0.000 0.928  0 0.000
#> SRR975601     3   0.161      0.706 0.072 0.000 0.928  0 0.000
#> SRR975602     1   0.191      0.740 0.908 0.000 0.092  0 0.000
#> SRR975603     3   0.161      0.706 0.072 0.000 0.928  0 0.000
#> SRR975604     3   0.161      0.706 0.072 0.000 0.928  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
#> SRR975551     1  0.2219      0.591 0.864 0.000 0.000 0.136 0.000  0
#> SRR975552     1  0.2219      0.591 0.864 0.000 0.000 0.136 0.000  0
#> SRR975554     1  0.0291      0.631 0.992 0.000 0.004 0.000 0.004  0
#> SRR975553     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000  0
#> SRR975555     1  0.3823      0.196 0.564 0.000 0.000 0.436 0.000  0
#> SRR975556     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000  0
#> SRR975557     6  0.0000      1.000 0.000 0.000 0.000 0.000 0.000  1
#> SRR975558     4  0.0000      0.601 0.000 0.000 0.000 1.000 0.000  0
#> SRR975559     4  0.3706      0.529 0.380 0.000 0.000 0.620 0.000  0
#> SRR975560     2  0.2730      0.782 0.000 0.808 0.000 0.192 0.000  0
#> SRR975561     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000  0
#> SRR975562     1  0.3175      0.444 0.744 0.000 0.000 0.256 0.000  0
#> SRR975563     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000  0
#> SRR975564     1  0.3854      0.130 0.536 0.000 0.000 0.464 0.000  0
#> SRR975565     1  0.2454      0.579 0.840 0.000 0.000 0.160 0.000  0
#> SRR975566     1  0.0291      0.631 0.992 0.000 0.004 0.000 0.004  0
#> SRR975567     4  0.0000      0.601 0.000 0.000 0.000 1.000 0.000  0
#> SRR975568     1  0.3823      0.196 0.564 0.000 0.000 0.436 0.000  0
#> SRR975569     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000  0
#> SRR975570     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000  0
#> SRR975571     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000  0
#> SRR975572     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000  0
#> SRR975573     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000  0
#> SRR975574     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000  0
#> SRR975575     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000  0
#> SRR975576     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000  0
#> SRR975577     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000  0
#> SRR975578     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000  0
#> SRR975579     6  0.0000      1.000 0.000 0.000 0.000 0.000 0.000  1
#> SRR975580     2  0.2730      0.782 0.000 0.808 0.000 0.192 0.000  0
#> SRR975581     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000  0
#> SRR975582     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000  0
#> SRR975583     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000  0
#> SRR975584     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000  0
#> SRR975585     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000  0
#> SRR975586     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000  0
#> SRR975587     3  0.0000      0.993 0.000 0.000 1.000 0.000 0.000  0
#> SRR975588     2  0.0000      0.982 0.000 1.000 0.000 0.000 0.000  0
#> SRR975589     1  0.5974      0.191 0.440 0.000 0.312 0.248 0.000  0
#> SRR975590     1  0.0858      0.631 0.968 0.000 0.028 0.000 0.004  0
#> SRR975591     3  0.0000      0.993 0.000 0.000 1.000 0.000 0.000  0
#> SRR975592     1  0.3351      0.545 0.712 0.000 0.288 0.000 0.000  0
#> SRR975593     1  0.5974      0.191 0.440 0.000 0.312 0.248 0.000  0
#> SRR975594     5  0.0632      0.887 0.000 0.000 0.024 0.000 0.976  0
#> SRR975595     1  0.3050      0.588 0.764 0.000 0.236 0.000 0.000  0
#> SRR975597     1  0.3050      0.588 0.764 0.000 0.236 0.000 0.000  0
#> SRR975596     4  0.3706      0.529 0.380 0.000 0.000 0.620 0.000  0
#> SRR975598     1  0.3023      0.589 0.768 0.000 0.232 0.000 0.000  0
#> SRR975599     5  0.1863      0.888 0.036 0.000 0.044 0.000 0.920  0
#> SRR975600     3  0.0713      0.965 0.000 0.000 0.972 0.028 0.000  0
#> SRR975601     3  0.0000      0.993 0.000 0.000 1.000 0.000 0.000  0
#> SRR975602     1  0.0291      0.631 0.992 0.000 0.004 0.000 0.004  0
#> SRR975603     3  0.0000      0.993 0.000 0.000 1.000 0.000 0.000  0
#> SRR975604     3  0.0000      0.993 0.000 0.000 1.000 0.000 0.000  0

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

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

consensus_heatmap(res, k = 2)

plot of chunk tab-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

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 17171 rows and 54 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#>   Subgroups are detected by 'kmeans' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 2.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk MAD-kmeans-collect-plots

The plots are:

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

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

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

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

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

select_partition_number(res)

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

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           1.000       1.000         0.5036 0.497   0.497
#> 3 3 0.768           0.795       0.907         0.2259 0.867   0.734
#> 4 4 0.671           0.666       0.822         0.1291 0.953   0.877
#> 5 5 0.657           0.589       0.775         0.0843 0.908   0.743
#> 6 6 0.718           0.533       0.736         0.0462 0.933   0.768

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
#> SRR975551     1       0          1  1  0
#> SRR975552     1       0          1  1  0
#> SRR975554     1       0          1  1  0
#> SRR975553     2       0          1  0  1
#> SRR975555     1       0          1  1  0
#> SRR975556     2       0          1  0  1
#> SRR975557     1       0          1  1  0
#> SRR975558     1       0          1  1  0
#> SRR975559     1       0          1  1  0
#> SRR975560     2       0          1  0  1
#> SRR975561     2       0          1  0  1
#> SRR975562     1       0          1  1  0
#> SRR975563     2       0          1  0  1
#> SRR975564     1       0          1  1  0
#> SRR975565     1       0          1  1  0
#> SRR975566     1       0          1  1  0
#> SRR975567     1       0          1  1  0
#> SRR975568     1       0          1  1  0
#> SRR975569     2       0          1  0  1
#> SRR975570     2       0          1  0  1
#> SRR975571     2       0          1  0  1
#> SRR975572     2       0          1  0  1
#> SRR975573     2       0          1  0  1
#> SRR975574     2       0          1  0  1
#> SRR975575     2       0          1  0  1
#> SRR975576     2       0          1  0  1
#> SRR975577     2       0          1  0  1
#> SRR975578     2       0          1  0  1
#> SRR975579     2       0          1  0  1
#> SRR975580     2       0          1  0  1
#> SRR975581     2       0          1  0  1
#> SRR975582     2       0          1  0  1
#> SRR975583     2       0          1  0  1
#> SRR975584     2       0          1  0  1
#> SRR975585     2       0          1  0  1
#> SRR975586     2       0          1  0  1
#> SRR975587     1       0          1  1  0
#> SRR975588     2       0          1  0  1
#> SRR975589     1       0          1  1  0
#> SRR975590     1       0          1  1  0
#> SRR975591     1       0          1  1  0
#> SRR975592     1       0          1  1  0
#> SRR975593     1       0          1  1  0
#> SRR975594     1       0          1  1  0
#> SRR975595     1       0          1  1  0
#> SRR975597     1       0          1  1  0
#> SRR975596     1       0          1  1  0
#> SRR975598     1       0          1  1  0
#> SRR975599     1       0          1  1  0
#> SRR975600     1       0          1  1  0
#> SRR975601     1       0          1  1  0
#> SRR975602     1       0          1  1  0
#> SRR975603     1       0          1  1  0
#> SRR975604     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
#> SRR975551     1  0.0000      0.876 1.000 0.000 0.000
#> SRR975552     1  0.0000      0.876 1.000 0.000 0.000
#> SRR975554     1  0.0000      0.876 1.000 0.000 0.000
#> SRR975553     2  0.0237      0.978 0.000 0.996 0.004
#> SRR975555     1  0.0000      0.876 1.000 0.000 0.000
#> SRR975556     2  0.1163      0.962 0.000 0.972 0.028
#> SRR975557     3  0.1860      0.585 0.052 0.000 0.948
#> SRR975558     1  0.3412      0.739 0.876 0.000 0.124
#> SRR975559     1  0.0000      0.876 1.000 0.000 0.000
#> SRR975560     2  0.3412      0.888 0.000 0.876 0.124
#> SRR975561     2  0.3038      0.907 0.000 0.896 0.104
#> SRR975562     1  0.0000      0.876 1.000 0.000 0.000
#> SRR975563     2  0.0000      0.978 0.000 1.000 0.000
#> SRR975564     1  0.0000      0.876 1.000 0.000 0.000
#> SRR975565     1  0.0000      0.876 1.000 0.000 0.000
#> SRR975566     1  0.0000      0.876 1.000 0.000 0.000
#> SRR975567     1  0.3412      0.739 0.876 0.000 0.124
#> SRR975568     1  0.0000      0.876 1.000 0.000 0.000
#> SRR975569     2  0.0000      0.978 0.000 1.000 0.000
#> SRR975570     2  0.0000      0.978 0.000 1.000 0.000
#> SRR975571     2  0.0237      0.978 0.000 0.996 0.004
#> SRR975572     2  0.0000      0.978 0.000 1.000 0.000
#> SRR975573     2  0.0237      0.978 0.000 0.996 0.004
#> SRR975574     2  0.0237      0.978 0.000 0.996 0.004
#> SRR975575     2  0.0000      0.978 0.000 1.000 0.000
#> SRR975576     2  0.0000      0.978 0.000 1.000 0.000
#> SRR975577     2  0.0237      0.978 0.000 0.996 0.004
#> SRR975578     2  0.0237      0.978 0.000 0.996 0.004
#> SRR975579     3  0.6305     -0.315 0.000 0.484 0.516
#> SRR975580     2  0.2878      0.913 0.000 0.904 0.096
#> SRR975581     2  0.0000      0.978 0.000 1.000 0.000
#> SRR975582     2  0.0237      0.978 0.000 0.996 0.004
#> SRR975583     2  0.0000      0.978 0.000 1.000 0.000
#> SRR975584     2  0.0237      0.978 0.000 0.996 0.004
#> SRR975585     2  0.0000      0.978 0.000 1.000 0.000
#> SRR975586     2  0.3038      0.907 0.000 0.896 0.104
#> SRR975587     1  0.6307     -0.266 0.512 0.000 0.488
#> SRR975588     2  0.0000      0.978 0.000 1.000 0.000
#> SRR975589     1  0.3412      0.793 0.876 0.000 0.124
#> SRR975590     1  0.3752      0.772 0.856 0.000 0.144
#> SRR975591     3  0.6140      0.523 0.404 0.000 0.596
#> SRR975592     1  0.3752      0.772 0.856 0.000 0.144
#> SRR975593     1  0.3619      0.779 0.864 0.000 0.136
#> SRR975594     3  0.3482      0.628 0.128 0.000 0.872
#> SRR975595     1  0.1964      0.853 0.944 0.000 0.056
#> SRR975597     1  0.1964      0.853 0.944 0.000 0.056
#> SRR975596     1  0.0000      0.876 1.000 0.000 0.000
#> SRR975598     1  0.1964      0.853 0.944 0.000 0.056
#> SRR975599     3  0.3686      0.630 0.140 0.000 0.860
#> SRR975600     1  0.6305     -0.260 0.516 0.000 0.484
#> SRR975601     3  0.6126      0.525 0.400 0.000 0.600
#> SRR975602     1  0.0237      0.875 0.996 0.000 0.004
#> SRR975603     3  0.6140      0.523 0.404 0.000 0.596
#> SRR975604     3  0.6126      0.525 0.400 0.000 0.600

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> SRR975551     1  0.1118     0.7421 0.964 0.000 0.000 0.036
#> SRR975552     1  0.0707     0.7445 0.980 0.000 0.000 0.020
#> SRR975554     1  0.0817     0.7441 0.976 0.000 0.000 0.024
#> SRR975553     2  0.2450     0.8752 0.000 0.912 0.072 0.016
#> SRR975555     1  0.0592     0.7447 0.984 0.000 0.000 0.016
#> SRR975556     2  0.3056     0.8158 0.000 0.888 0.072 0.040
#> SRR975557     4  0.4511     0.4855 0.008 0.000 0.268 0.724
#> SRR975558     1  0.7760     0.0728 0.392 0.000 0.236 0.372
#> SRR975559     1  0.4458     0.6678 0.808 0.000 0.116 0.076
#> SRR975560     2  0.6716     0.4338 0.000 0.568 0.112 0.320
#> SRR975561     2  0.6167     0.5478 0.000 0.648 0.096 0.256
#> SRR975562     1  0.2334     0.7302 0.908 0.000 0.004 0.088
#> SRR975563     2  0.0000     0.8867 0.000 1.000 0.000 0.000
#> SRR975564     1  0.0921     0.7450 0.972 0.000 0.000 0.028
#> SRR975565     1  0.0707     0.7445 0.980 0.000 0.000 0.020
#> SRR975566     1  0.4093     0.6845 0.832 0.000 0.096 0.072
#> SRR975567     1  0.7760     0.0728 0.392 0.000 0.236 0.372
#> SRR975568     1  0.0707     0.7448 0.980 0.000 0.000 0.020
#> SRR975569     2  0.0188     0.8863 0.000 0.996 0.004 0.000
#> SRR975570     2  0.0000     0.8867 0.000 1.000 0.000 0.000
#> SRR975571     2  0.2450     0.8752 0.000 0.912 0.072 0.016
#> SRR975572     2  0.0000     0.8867 0.000 1.000 0.000 0.000
#> SRR975573     2  0.2450     0.8752 0.000 0.912 0.072 0.016
#> SRR975574     2  0.2450     0.8752 0.000 0.912 0.072 0.016
#> SRR975575     2  0.0000     0.8867 0.000 1.000 0.000 0.000
#> SRR975576     2  0.0000     0.8867 0.000 1.000 0.000 0.000
#> SRR975577     2  0.2450     0.8752 0.000 0.912 0.072 0.016
#> SRR975578     2  0.2450     0.8752 0.000 0.912 0.072 0.016
#> SRR975579     4  0.3400     0.4676 0.000 0.180 0.000 0.820
#> SRR975580     2  0.6521     0.5415 0.000 0.620 0.124 0.256
#> SRR975581     2  0.0000     0.8867 0.000 1.000 0.000 0.000
#> SRR975582     2  0.2450     0.8752 0.000 0.912 0.072 0.016
#> SRR975583     2  0.0000     0.8867 0.000 1.000 0.000 0.000
#> SRR975584     2  0.2450     0.8752 0.000 0.912 0.072 0.016
#> SRR975585     2  0.0000     0.8867 0.000 1.000 0.000 0.000
#> SRR975586     2  0.6140     0.5484 0.000 0.652 0.096 0.252
#> SRR975587     3  0.5337     0.7288 0.260 0.000 0.696 0.044
#> SRR975588     2  0.0000     0.8867 0.000 1.000 0.000 0.000
#> SRR975589     1  0.6393     0.0509 0.480 0.000 0.456 0.064
#> SRR975590     1  0.5374     0.4798 0.704 0.000 0.244 0.052
#> SRR975591     3  0.3311     0.8152 0.172 0.000 0.828 0.000
#> SRR975592     1  0.5807     0.2250 0.596 0.000 0.364 0.040
#> SRR975593     1  0.6395     0.0347 0.476 0.000 0.460 0.064
#> SRR975594     3  0.5992    -0.2641 0.040 0.000 0.516 0.444
#> SRR975595     1  0.3732     0.6823 0.852 0.000 0.092 0.056
#> SRR975597     1  0.3486     0.6858 0.864 0.000 0.092 0.044
#> SRR975596     1  0.4646     0.6629 0.796 0.000 0.120 0.084
#> SRR975598     1  0.3732     0.6823 0.852 0.000 0.092 0.056
#> SRR975599     4  0.6979     0.1039 0.120 0.000 0.376 0.504
#> SRR975600     3  0.3539     0.8110 0.176 0.000 0.820 0.004
#> SRR975601     3  0.4868     0.7475 0.256 0.000 0.720 0.024
#> SRR975602     1  0.1940     0.7285 0.924 0.000 0.000 0.076
#> SRR975603     3  0.3311     0.8152 0.172 0.000 0.828 0.000
#> SRR975604     3  0.3311     0.8152 0.172 0.000 0.828 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
#> SRR975551     1  0.0955      0.783 0.968 0.000 0.000 0.004 0.028
#> SRR975552     1  0.0324      0.784 0.992 0.000 0.000 0.004 0.004
#> SRR975554     1  0.1043      0.785 0.960 0.000 0.000 0.000 0.040
#> SRR975553     2  0.4465      0.726 0.000 0.736 0.060 0.000 0.204
#> SRR975555     1  0.0865      0.784 0.972 0.000 0.000 0.004 0.024
#> SRR975556     2  0.5025      0.420 0.000 0.704 0.000 0.124 0.172
#> SRR975557     4  0.4024      0.567 0.000 0.000 0.220 0.752 0.028
#> SRR975558     5  0.8003      0.528 0.228 0.000 0.108 0.248 0.416
#> SRR975559     1  0.5542      0.562 0.632 0.000 0.084 0.008 0.276
#> SRR975560     5  0.6756      0.171 0.000 0.268 0.000 0.344 0.388
#> SRR975561     2  0.6724     -0.216 0.000 0.420 0.000 0.284 0.296
#> SRR975562     1  0.4090      0.683 0.716 0.000 0.000 0.016 0.268
#> SRR975563     2  0.0000      0.770 0.000 1.000 0.000 0.000 0.000
#> SRR975564     1  0.1282      0.772 0.952 0.000 0.000 0.004 0.044
#> SRR975565     1  0.0324      0.784 0.992 0.000 0.000 0.004 0.004
#> SRR975566     1  0.4668      0.668 0.724 0.000 0.048 0.008 0.220
#> SRR975567     5  0.8003      0.528 0.228 0.000 0.108 0.248 0.416
#> SRR975568     1  0.0566      0.783 0.984 0.000 0.000 0.004 0.012
#> SRR975569     2  0.0162      0.769 0.000 0.996 0.000 0.000 0.004
#> SRR975570     2  0.0000      0.770 0.000 1.000 0.000 0.000 0.000
#> SRR975571     2  0.4465      0.726 0.000 0.736 0.060 0.000 0.204
#> SRR975572     2  0.0000      0.770 0.000 1.000 0.000 0.000 0.000
#> SRR975573     2  0.4434      0.726 0.000 0.736 0.056 0.000 0.208
#> SRR975574     2  0.4434      0.726 0.000 0.736 0.056 0.000 0.208
#> SRR975575     2  0.0000      0.770 0.000 1.000 0.000 0.000 0.000
#> SRR975576     2  0.0000      0.770 0.000 1.000 0.000 0.000 0.000
#> SRR975577     2  0.4434      0.726 0.000 0.736 0.056 0.000 0.208
#> SRR975578     2  0.4434      0.726 0.000 0.736 0.056 0.000 0.208
#> SRR975579     4  0.1549      0.336 0.000 0.040 0.000 0.944 0.016
#> SRR975580     2  0.6784     -0.247 0.000 0.368 0.000 0.280 0.352
#> SRR975581     2  0.0000      0.770 0.000 1.000 0.000 0.000 0.000
#> SRR975582     2  0.4434      0.726 0.000 0.736 0.056 0.000 0.208
#> SRR975583     2  0.0000      0.770 0.000 1.000 0.000 0.000 0.000
#> SRR975584     2  0.4434      0.726 0.000 0.736 0.056 0.000 0.208
#> SRR975585     2  0.0000      0.770 0.000 1.000 0.000 0.000 0.000
#> SRR975586     2  0.6715     -0.213 0.000 0.424 0.000 0.284 0.292
#> SRR975587     3  0.4695      0.621 0.124 0.000 0.764 0.016 0.096
#> SRR975588     2  0.0000      0.770 0.000 1.000 0.000 0.000 0.000
#> SRR975589     3  0.5957      0.507 0.236 0.000 0.588 0.000 0.176
#> SRR975590     1  0.6096      0.406 0.604 0.000 0.252 0.016 0.128
#> SRR975591     3  0.1478      0.679 0.064 0.000 0.936 0.000 0.000
#> SRR975592     3  0.6441      0.337 0.352 0.000 0.508 0.016 0.124
#> SRR975593     3  0.5957      0.507 0.236 0.000 0.588 0.000 0.176
#> SRR975594     3  0.5751     -0.301 0.004 0.000 0.516 0.404 0.076
#> SRR975595     1  0.5451      0.660 0.700 0.000 0.104 0.024 0.172
#> SRR975597     1  0.5009      0.671 0.736 0.000 0.104 0.016 0.144
#> SRR975596     1  0.5704      0.550 0.616 0.000 0.084 0.012 0.288
#> SRR975598     1  0.5451      0.660 0.700 0.000 0.104 0.024 0.172
#> SRR975599     4  0.7745      0.318 0.076 0.000 0.280 0.428 0.216
#> SRR975600     3  0.2426      0.672 0.064 0.000 0.900 0.000 0.036
#> SRR975601     3  0.3977      0.637 0.100 0.000 0.812 0.008 0.080
#> SRR975602     1  0.3944      0.734 0.768 0.000 0.000 0.032 0.200
#> SRR975603     3  0.1478      0.679 0.064 0.000 0.936 0.000 0.000
#> SRR975604     3  0.1638      0.678 0.064 0.000 0.932 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
#> SRR975551     1  0.0717      0.705 0.976 0.000 0.000 0.008 0.016 0.000
#> SRR975552     1  0.0260      0.707 0.992 0.000 0.000 0.000 0.008 0.000
#> SRR975554     1  0.2186      0.701 0.908 0.000 0.000 0.008 0.048 0.036
#> SRR975553     2  0.0551      0.574 0.000 0.984 0.000 0.008 0.004 0.004
#> SRR975555     1  0.1552      0.701 0.940 0.000 0.000 0.004 0.020 0.036
#> SRR975556     5  0.6169      0.000 0.000 0.336 0.000 0.008 0.428 0.228
#> SRR975557     4  0.2448      0.607 0.000 0.000 0.052 0.884 0.000 0.064
#> SRR975558     6  0.4535      0.276 0.140 0.000 0.096 0.024 0.000 0.740
#> SRR975559     1  0.7663      0.435 0.448 0.000 0.084 0.064 0.144 0.260
#> SRR975560     6  0.4854      0.440 0.000 0.188 0.000 0.012 0.112 0.688
#> SRR975561     6  0.5956      0.151 0.000 0.256 0.000 0.012 0.208 0.524
#> SRR975562     1  0.6415      0.522 0.520 0.000 0.000 0.052 0.184 0.244
#> SRR975563     2  0.3647      0.522 0.000 0.640 0.000 0.000 0.360 0.000
#> SRR975564     1  0.2015      0.689 0.916 0.000 0.000 0.016 0.012 0.056
#> SRR975565     1  0.0146      0.706 0.996 0.000 0.000 0.000 0.004 0.000
#> SRR975566     1  0.6844      0.547 0.576 0.000 0.060 0.060 0.136 0.168
#> SRR975567     6  0.4535      0.276 0.140 0.000 0.096 0.024 0.000 0.740
#> SRR975568     1  0.1590      0.694 0.936 0.000 0.000 0.008 0.008 0.048
#> SRR975569     2  0.3563      0.543 0.000 0.664 0.000 0.000 0.336 0.000
#> SRR975570     2  0.3578      0.541 0.000 0.660 0.000 0.000 0.340 0.000
#> SRR975571     2  0.0551      0.574 0.000 0.984 0.000 0.008 0.004 0.004
#> SRR975572     2  0.3634      0.530 0.000 0.644 0.000 0.000 0.356 0.000
#> SRR975573     2  0.0000      0.581 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975574     2  0.0000      0.581 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975575     2  0.3634      0.530 0.000 0.644 0.000 0.000 0.356 0.000
#> SRR975576     2  0.3647      0.522 0.000 0.640 0.000 0.000 0.360 0.000
#> SRR975577     2  0.0000      0.581 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975578     2  0.0000      0.581 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975579     4  0.3166      0.520 0.000 0.008 0.000 0.800 0.008 0.184
#> SRR975580     6  0.5539      0.273 0.000 0.292 0.000 0.008 0.136 0.564
#> SRR975581     2  0.3647      0.522 0.000 0.640 0.000 0.000 0.360 0.000
#> SRR975582     2  0.0000      0.581 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975583     2  0.3634      0.530 0.000 0.644 0.000 0.000 0.356 0.000
#> SRR975584     2  0.0000      0.581 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975585     2  0.3634      0.530 0.000 0.644 0.000 0.000 0.356 0.000
#> SRR975586     6  0.5918      0.165 0.000 0.252 0.000 0.012 0.204 0.532
#> SRR975587     3  0.4193      0.639 0.052 0.000 0.780 0.016 0.136 0.016
#> SRR975588     2  0.3578      0.541 0.000 0.660 0.000 0.000 0.340 0.000
#> SRR975589     3  0.5702      0.590 0.092 0.000 0.688 0.032 0.064 0.124
#> SRR975590     1  0.6713      0.134 0.436 0.000 0.300 0.024 0.228 0.012
#> SRR975591     3  0.0000      0.740 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975592     3  0.6105      0.476 0.220 0.000 0.560 0.016 0.192 0.012
#> SRR975593     3  0.5649      0.591 0.092 0.000 0.692 0.032 0.060 0.124
#> SRR975594     4  0.6213      0.326 0.000 0.000 0.400 0.444 0.108 0.048
#> SRR975595     1  0.5652      0.585 0.588 0.000 0.068 0.024 0.304 0.016
#> SRR975597     1  0.5124      0.602 0.644 0.000 0.068 0.020 0.264 0.004
#> SRR975596     1  0.7776      0.420 0.428 0.000 0.084 0.068 0.152 0.268
#> SRR975598     1  0.5652      0.585 0.588 0.000 0.068 0.024 0.304 0.016
#> SRR975599     4  0.7427      0.524 0.060 0.000 0.140 0.488 0.236 0.076
#> SRR975600     3  0.1269      0.732 0.000 0.000 0.956 0.012 0.012 0.020
#> SRR975601     3  0.4025      0.644 0.032 0.000 0.796 0.016 0.128 0.028
#> SRR975602     1  0.5125      0.634 0.656 0.000 0.000 0.060 0.244 0.040
#> SRR975603     3  0.0000      0.740 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975604     3  0.0146      0.738 0.000 0.000 0.996 0.000 0.004 0.000

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

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

consensus_heatmap(res, k = 2)

plot of chunk tab-MAD-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

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 17171 rows and 54 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#>   Subgroups are detected by 'skmeans' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 3.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

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           0.991       0.996         0.5044 0.497   0.497
#> 3 3 0.909           0.929       0.962         0.2770 0.868   0.734
#> 4 4 0.781           0.756       0.889         0.0847 0.904   0.746
#> 5 5 0.799           0.626       0.832         0.0722 0.948   0.833
#> 6 6 0.722           0.628       0.772         0.0480 0.941   0.786

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

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

suggest_best_k(res)

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

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

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

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

show/hide code output

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

#>           class entropy silhouette    p1    p2
#> SRR975551     1   0.000      0.992 1.000 0.000
#> SRR975552     1   0.000      0.992 1.000 0.000
#> SRR975554     1   0.000      0.992 1.000 0.000
#> SRR975553     2   0.000      1.000 0.000 1.000
#> SRR975555     1   0.000      0.992 1.000 0.000
#> SRR975556     2   0.000      1.000 0.000 1.000
#> SRR975557     1   0.000      0.992 1.000 0.000
#> SRR975558     1   0.722      0.752 0.800 0.200
#> SRR975559     1   0.000      0.992 1.000 0.000
#> SRR975560     2   0.000      1.000 0.000 1.000
#> SRR975561     2   0.000      1.000 0.000 1.000
#> SRR975562     1   0.000      0.992 1.000 0.000
#> SRR975563     2   0.000      1.000 0.000 1.000
#> SRR975564     1   0.000      0.992 1.000 0.000
#> SRR975565     1   0.000      0.992 1.000 0.000
#> SRR975566     1   0.000      0.992 1.000 0.000
#> SRR975567     1   0.163      0.970 0.976 0.024
#> SRR975568     1   0.000      0.992 1.000 0.000
#> SRR975569     2   0.000      1.000 0.000 1.000
#> SRR975570     2   0.000      1.000 0.000 1.000
#> SRR975571     2   0.000      1.000 0.000 1.000
#> SRR975572     2   0.000      1.000 0.000 1.000
#> SRR975573     2   0.000      1.000 0.000 1.000
#> SRR975574     2   0.000      1.000 0.000 1.000
#> SRR975575     2   0.000      1.000 0.000 1.000
#> SRR975576     2   0.000      1.000 0.000 1.000
#> SRR975577     2   0.000      1.000 0.000 1.000
#> SRR975578     2   0.000      1.000 0.000 1.000
#> SRR975579     2   0.000      1.000 0.000 1.000
#> SRR975580     2   0.000      1.000 0.000 1.000
#> SRR975581     2   0.000      1.000 0.000 1.000
#> SRR975582     2   0.000      1.000 0.000 1.000
#> SRR975583     2   0.000      1.000 0.000 1.000
#> SRR975584     2   0.000      1.000 0.000 1.000
#> SRR975585     2   0.000      1.000 0.000 1.000
#> SRR975586     2   0.000      1.000 0.000 1.000
#> SRR975587     1   0.000      0.992 1.000 0.000
#> SRR975588     2   0.000      1.000 0.000 1.000
#> SRR975589     1   0.000      0.992 1.000 0.000
#> SRR975590     1   0.000      0.992 1.000 0.000
#> SRR975591     1   0.000      0.992 1.000 0.000
#> SRR975592     1   0.000      0.992 1.000 0.000
#> SRR975593     1   0.000      0.992 1.000 0.000
#> SRR975594     1   0.000      0.992 1.000 0.000
#> SRR975595     1   0.000      0.992 1.000 0.000
#> SRR975597     1   0.000      0.992 1.000 0.000
#> SRR975596     1   0.000      0.992 1.000 0.000
#> SRR975598     1   0.000      0.992 1.000 0.000
#> SRR975599     1   0.000      0.992 1.000 0.000
#> SRR975600     1   0.000      0.992 1.000 0.000
#> SRR975601     1   0.000      0.992 1.000 0.000
#> SRR975602     1   0.000      0.992 1.000 0.000
#> SRR975603     1   0.000      0.992 1.000 0.000
#> SRR975604     1   0.000      0.992 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
#> SRR975551     1   0.000      0.891 1.000  0 0.000
#> SRR975552     1   0.000      0.891 1.000  0 0.000
#> SRR975554     1   0.000      0.891 1.000  0 0.000
#> SRR975553     2   0.000      1.000 0.000  1 0.000
#> SRR975555     1   0.000      0.891 1.000  0 0.000
#> SRR975556     2   0.000      1.000 0.000  1 0.000
#> SRR975557     3   0.000      1.000 0.000  0 1.000
#> SRR975558     1   0.000      0.891 1.000  0 0.000
#> SRR975559     1   0.000      0.891 1.000  0 0.000
#> SRR975560     2   0.000      1.000 0.000  1 0.000
#> SRR975561     2   0.000      1.000 0.000  1 0.000
#> SRR975562     1   0.000      0.891 1.000  0 0.000
#> SRR975563     2   0.000      1.000 0.000  1 0.000
#> SRR975564     1   0.000      0.891 1.000  0 0.000
#> SRR975565     1   0.000      0.891 1.000  0 0.000
#> SRR975566     1   0.000      0.891 1.000  0 0.000
#> SRR975567     1   0.000      0.891 1.000  0 0.000
#> SRR975568     1   0.000      0.891 1.000  0 0.000
#> SRR975569     2   0.000      1.000 0.000  1 0.000
#> SRR975570     2   0.000      1.000 0.000  1 0.000
#> SRR975571     2   0.000      1.000 0.000  1 0.000
#> SRR975572     2   0.000      1.000 0.000  1 0.000
#> SRR975573     2   0.000      1.000 0.000  1 0.000
#> SRR975574     2   0.000      1.000 0.000  1 0.000
#> SRR975575     2   0.000      1.000 0.000  1 0.000
#> SRR975576     2   0.000      1.000 0.000  1 0.000
#> SRR975577     2   0.000      1.000 0.000  1 0.000
#> SRR975578     2   0.000      1.000 0.000  1 0.000
#> SRR975579     2   0.000      1.000 0.000  1 0.000
#> SRR975580     2   0.000      1.000 0.000  1 0.000
#> SRR975581     2   0.000      1.000 0.000  1 0.000
#> SRR975582     2   0.000      1.000 0.000  1 0.000
#> SRR975583     2   0.000      1.000 0.000  1 0.000
#> SRR975584     2   0.000      1.000 0.000  1 0.000
#> SRR975585     2   0.000      1.000 0.000  1 0.000
#> SRR975586     2   0.000      1.000 0.000  1 0.000
#> SRR975587     3   0.000      1.000 0.000  0 1.000
#> SRR975588     2   0.000      1.000 0.000  1 0.000
#> SRR975589     1   0.593      0.594 0.644  0 0.356
#> SRR975590     1   0.593      0.594 0.644  0 0.356
#> SRR975591     3   0.000      1.000 0.000  0 1.000
#> SRR975592     1   0.601      0.566 0.628  0 0.372
#> SRR975593     1   0.595      0.588 0.640  0 0.360
#> SRR975594     3   0.000      1.000 0.000  0 1.000
#> SRR975595     1   0.455      0.775 0.800  0 0.200
#> SRR975597     1   0.455      0.775 0.800  0 0.200
#> SRR975596     1   0.000      0.891 1.000  0 0.000
#> SRR975598     1   0.455      0.775 0.800  0 0.200
#> SRR975599     3   0.000      1.000 0.000  0 1.000
#> SRR975600     3   0.000      1.000 0.000  0 1.000
#> SRR975601     3   0.000      1.000 0.000  0 1.000
#> SRR975602     1   0.000      0.891 1.000  0 0.000
#> SRR975603     3   0.000      1.000 0.000  0 1.000
#> SRR975604     3   0.000      1.000 0.000  0 1.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> SRR975551     1  0.0000     0.8472 1.000 0.000 0.000 0.000
#> SRR975552     1  0.0000     0.8472 1.000 0.000 0.000 0.000
#> SRR975554     1  0.0000     0.8472 1.000 0.000 0.000 0.000
#> SRR975553     2  0.0000     0.9587 0.000 1.000 0.000 0.000
#> SRR975555     1  0.0000     0.8472 1.000 0.000 0.000 0.000
#> SRR975556     2  0.0188     0.9554 0.000 0.996 0.000 0.004
#> SRR975557     3  0.5257     0.4567 0.008 0.000 0.548 0.444
#> SRR975558     4  0.7058     0.2481 0.344 0.000 0.136 0.520
#> SRR975559     1  0.3617     0.7455 0.860 0.000 0.076 0.064
#> SRR975560     4  0.4382     0.3675 0.000 0.296 0.000 0.704
#> SRR975561     2  0.4040     0.6649 0.000 0.752 0.000 0.248
#> SRR975562     1  0.1474     0.8233 0.948 0.000 0.000 0.052
#> SRR975563     2  0.0000     0.9587 0.000 1.000 0.000 0.000
#> SRR975564     1  0.0188     0.8460 0.996 0.000 0.000 0.004
#> SRR975565     1  0.0000     0.8472 1.000 0.000 0.000 0.000
#> SRR975566     1  0.2089     0.8133 0.932 0.000 0.020 0.048
#> SRR975567     4  0.6885     0.2023 0.372 0.000 0.112 0.516
#> SRR975568     1  0.0000     0.8472 1.000 0.000 0.000 0.000
#> SRR975569     2  0.0000     0.9587 0.000 1.000 0.000 0.000
#> SRR975570     2  0.0000     0.9587 0.000 1.000 0.000 0.000
#> SRR975571     2  0.0000     0.9587 0.000 1.000 0.000 0.000
#> SRR975572     2  0.0000     0.9587 0.000 1.000 0.000 0.000
#> SRR975573     2  0.0000     0.9587 0.000 1.000 0.000 0.000
#> SRR975574     2  0.0000     0.9587 0.000 1.000 0.000 0.000
#> SRR975575     2  0.0000     0.9587 0.000 1.000 0.000 0.000
#> SRR975576     2  0.0000     0.9587 0.000 1.000 0.000 0.000
#> SRR975577     2  0.0000     0.9587 0.000 1.000 0.000 0.000
#> SRR975578     2  0.0000     0.9587 0.000 1.000 0.000 0.000
#> SRR975579     4  0.4699     0.2809 0.000 0.320 0.004 0.676
#> SRR975580     2  0.3907     0.6891 0.000 0.768 0.000 0.232
#> SRR975581     2  0.0000     0.9587 0.000 1.000 0.000 0.000
#> SRR975582     2  0.0000     0.9587 0.000 1.000 0.000 0.000
#> SRR975583     2  0.0000     0.9587 0.000 1.000 0.000 0.000
#> SRR975584     2  0.0000     0.9587 0.000 1.000 0.000 0.000
#> SRR975585     2  0.0000     0.9587 0.000 1.000 0.000 0.000
#> SRR975586     2  0.4040     0.6649 0.000 0.752 0.000 0.248
#> SRR975587     3  0.2149     0.7302 0.088 0.000 0.912 0.000
#> SRR975588     2  0.0000     0.9587 0.000 1.000 0.000 0.000
#> SRR975589     3  0.6074     0.2339 0.340 0.000 0.600 0.060
#> SRR975590     1  0.4697     0.4321 0.644 0.000 0.356 0.000
#> SRR975591     3  0.0000     0.7630 0.000 0.000 1.000 0.000
#> SRR975592     1  0.4996     0.0432 0.516 0.000 0.484 0.000
#> SRR975593     3  0.5986     0.2898 0.320 0.000 0.620 0.060
#> SRR975594     3  0.3907     0.6834 0.000 0.000 0.768 0.232
#> SRR975595     1  0.3074     0.7548 0.848 0.000 0.152 0.000
#> SRR975597     1  0.3074     0.7548 0.848 0.000 0.152 0.000
#> SRR975596     1  0.3900     0.7270 0.844 0.000 0.084 0.072
#> SRR975598     1  0.3074     0.7548 0.848 0.000 0.152 0.000
#> SRR975599     3  0.4567     0.6699 0.016 0.000 0.740 0.244
#> SRR975600     3  0.0188     0.7621 0.000 0.000 0.996 0.004
#> SRR975601     3  0.2342     0.7500 0.008 0.000 0.912 0.080
#> SRR975602     1  0.0000     0.8472 1.000 0.000 0.000 0.000
#> SRR975603     3  0.0188     0.7621 0.000 0.000 0.996 0.004
#> SRR975604     3  0.0336     0.7635 0.000 0.000 0.992 0.008

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> SRR975551     1  0.0451    0.79049 0.988 0.000 0.000 0.004 0.008
#> SRR975552     1  0.0693    0.79090 0.980 0.000 0.000 0.008 0.012
#> SRR975554     1  0.0510    0.78916 0.984 0.000 0.000 0.000 0.016
#> SRR975553     2  0.1502    0.88258 0.000 0.940 0.000 0.056 0.004
#> SRR975555     1  0.0404    0.79064 0.988 0.000 0.000 0.000 0.012
#> SRR975556     2  0.2172    0.82742 0.000 0.908 0.000 0.076 0.016
#> SRR975557     4  0.6137   -0.06114 0.000 0.000 0.392 0.476 0.132
#> SRR975558     5  0.1281    0.38743 0.032 0.000 0.012 0.000 0.956
#> SRR975559     5  0.4907    0.32650 0.488 0.000 0.000 0.024 0.488
#> SRR975560     4  0.5456    0.25881 0.000 0.060 0.000 0.484 0.456
#> SRR975561     2  0.4978    0.11538 0.000 0.496 0.000 0.476 0.028
#> SRR975562     1  0.4243    0.35666 0.712 0.000 0.000 0.024 0.264
#> SRR975563     2  0.0162    0.89017 0.000 0.996 0.000 0.000 0.004
#> SRR975564     1  0.1768    0.74953 0.924 0.000 0.000 0.004 0.072
#> SRR975565     1  0.0404    0.79059 0.988 0.000 0.000 0.000 0.012
#> SRR975566     1  0.4404    0.24004 0.684 0.000 0.000 0.024 0.292
#> SRR975567     5  0.1444    0.39827 0.040 0.000 0.012 0.000 0.948
#> SRR975568     1  0.0703    0.78753 0.976 0.000 0.000 0.000 0.024
#> SRR975569     2  0.0000    0.89024 0.000 1.000 0.000 0.000 0.000
#> SRR975570     2  0.0000    0.89024 0.000 1.000 0.000 0.000 0.000
#> SRR975571     2  0.1502    0.88258 0.000 0.940 0.000 0.056 0.004
#> SRR975572     2  0.0162    0.89017 0.000 0.996 0.000 0.000 0.004
#> SRR975573     2  0.1502    0.88258 0.000 0.940 0.000 0.056 0.004
#> SRR975574     2  0.1502    0.88258 0.000 0.940 0.000 0.056 0.004
#> SRR975575     2  0.0162    0.89017 0.000 0.996 0.000 0.000 0.004
#> SRR975576     2  0.0162    0.89017 0.000 0.996 0.000 0.000 0.004
#> SRR975577     2  0.1502    0.88258 0.000 0.940 0.000 0.056 0.004
#> SRR975578     2  0.1502    0.88258 0.000 0.940 0.000 0.056 0.004
#> SRR975579     4  0.3857    0.47069 0.000 0.088 0.052 0.832 0.028
#> SRR975580     2  0.5176    0.20955 0.000 0.492 0.000 0.468 0.040
#> SRR975581     2  0.0162    0.89017 0.000 0.996 0.000 0.000 0.004
#> SRR975582     2  0.1502    0.88258 0.000 0.940 0.000 0.056 0.004
#> SRR975583     2  0.0162    0.89017 0.000 0.996 0.000 0.000 0.004
#> SRR975584     2  0.1502    0.88258 0.000 0.940 0.000 0.056 0.004
#> SRR975585     2  0.0162    0.89017 0.000 0.996 0.000 0.000 0.004
#> SRR975586     2  0.5296    0.08208 0.000 0.484 0.000 0.468 0.048
#> SRR975587     3  0.1670    0.63818 0.052 0.000 0.936 0.012 0.000
#> SRR975588     2  0.0000    0.89024 0.000 1.000 0.000 0.000 0.000
#> SRR975589     3  0.5967    0.31990 0.056 0.000 0.508 0.024 0.412
#> SRR975590     1  0.4971    0.42452 0.628 0.000 0.332 0.036 0.004
#> SRR975591     3  0.2424    0.66811 0.000 0.000 0.868 0.000 0.132
#> SRR975592     3  0.5338    0.00385 0.456 0.000 0.504 0.024 0.016
#> SRR975593     3  0.5853    0.33424 0.048 0.000 0.516 0.024 0.412
#> SRR975594     3  0.3424    0.36759 0.000 0.000 0.760 0.240 0.000
#> SRR975595     1  0.4043    0.67792 0.792 0.000 0.160 0.036 0.012
#> SRR975597     1  0.4012    0.67098 0.788 0.000 0.168 0.036 0.008
#> SRR975596     5  0.4979    0.34455 0.480 0.000 0.000 0.028 0.492
#> SRR975598     1  0.3962    0.68501 0.800 0.000 0.152 0.036 0.012
#> SRR975599     3  0.4986    0.17863 0.032 0.000 0.608 0.356 0.004
#> SRR975600     3  0.2605    0.66359 0.000 0.000 0.852 0.000 0.148
#> SRR975601     3  0.0912    0.63177 0.012 0.000 0.972 0.016 0.000
#> SRR975602     1  0.1153    0.78001 0.964 0.000 0.004 0.024 0.008
#> SRR975603     3  0.2424    0.66811 0.000 0.000 0.868 0.000 0.132
#> SRR975604     3  0.1608    0.66177 0.000 0.000 0.928 0.000 0.072

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> SRR975551     1  0.0725     0.7243 0.976 0.000 0.000 0.012 0.000 0.012
#> SRR975552     1  0.1226     0.7221 0.952 0.000 0.000 0.040 0.004 0.004
#> SRR975554     1  0.1757     0.7075 0.916 0.000 0.000 0.076 0.000 0.008
#> SRR975553     2  0.0000     0.7498 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975555     1  0.1620     0.7190 0.940 0.000 0.000 0.024 0.012 0.024
#> SRR975556     2  0.3869     0.2617 0.000 0.500 0.000 0.000 0.000 0.500
#> SRR975557     5  0.2766     0.6280 0.000 0.000 0.124 0.020 0.852 0.004
#> SRR975558     4  0.4348     0.4367 0.024 0.000 0.056 0.788 0.032 0.100
#> SRR975559     4  0.4242     0.3029 0.412 0.000 0.012 0.572 0.004 0.000
#> SRR975560     6  0.4660     0.1884 0.000 0.008 0.000 0.308 0.048 0.636
#> SRR975561     6  0.4612     0.5245 0.000 0.284 0.000 0.008 0.052 0.656
#> SRR975562     1  0.4415     0.0674 0.556 0.000 0.000 0.420 0.020 0.004
#> SRR975563     2  0.3175     0.8007 0.000 0.744 0.000 0.000 0.000 0.256
#> SRR975564     1  0.2306     0.6779 0.888 0.000 0.000 0.092 0.004 0.016
#> SRR975565     1  0.0806     0.7216 0.972 0.000 0.000 0.020 0.000 0.008
#> SRR975566     1  0.4032     0.4539 0.696 0.000 0.012 0.280 0.008 0.004
#> SRR975567     4  0.4356     0.4560 0.040 0.000 0.044 0.792 0.032 0.092
#> SRR975568     1  0.1605     0.7114 0.936 0.000 0.000 0.044 0.004 0.016
#> SRR975569     2  0.3151     0.8002 0.000 0.748 0.000 0.000 0.000 0.252
#> SRR975570     2  0.3175     0.8007 0.000 0.744 0.000 0.000 0.000 0.256
#> SRR975571     2  0.0000     0.7498 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975572     2  0.3175     0.8007 0.000 0.744 0.000 0.000 0.000 0.256
#> SRR975573     2  0.0000     0.7498 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975574     2  0.0000     0.7498 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975575     2  0.3175     0.8007 0.000 0.744 0.000 0.000 0.000 0.256
#> SRR975576     2  0.3175     0.8007 0.000 0.744 0.000 0.000 0.000 0.256
#> SRR975577     2  0.0000     0.7498 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975578     2  0.0000     0.7498 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975579     5  0.2420     0.5230 0.000 0.004 0.000 0.004 0.864 0.128
#> SRR975580     6  0.4790     0.5998 0.000 0.368 0.000 0.016 0.032 0.584
#> SRR975581     2  0.3175     0.8007 0.000 0.744 0.000 0.000 0.000 0.256
#> SRR975582     2  0.0000     0.7498 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975583     2  0.3175     0.8007 0.000 0.744 0.000 0.000 0.000 0.256
#> SRR975584     2  0.0000     0.7498 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975585     2  0.3175     0.8007 0.000 0.744 0.000 0.000 0.000 0.256
#> SRR975586     6  0.4075     0.6487 0.000 0.204 0.000 0.016 0.036 0.744
#> SRR975587     3  0.3023     0.6768 0.008 0.000 0.872 0.032 0.052 0.036
#> SRR975588     2  0.3175     0.8007 0.000 0.744 0.000 0.000 0.000 0.256
#> SRR975589     3  0.4476     0.5929 0.012 0.000 0.680 0.276 0.012 0.020
#> SRR975590     1  0.6170     0.3186 0.540 0.000 0.324 0.072 0.024 0.040
#> SRR975591     3  0.0858     0.7484 0.000 0.000 0.968 0.028 0.004 0.000
#> SRR975592     3  0.5743     0.4024 0.288 0.000 0.588 0.088 0.020 0.016
#> SRR975593     3  0.4291     0.5834 0.008 0.000 0.676 0.292 0.012 0.012
#> SRR975594     5  0.4786     0.2934 0.000 0.000 0.468 0.012 0.492 0.028
#> SRR975595     1  0.6060     0.5973 0.664 0.000 0.116 0.104 0.048 0.068
#> SRR975597     1  0.5903     0.5992 0.676 0.000 0.124 0.088 0.044 0.068
#> SRR975596     4  0.4209     0.3078 0.396 0.000 0.012 0.588 0.004 0.000
#> SRR975598     1  0.6060     0.5973 0.664 0.000 0.116 0.104 0.048 0.068
#> SRR975599     5  0.5914     0.5501 0.032 0.000 0.228 0.068 0.628 0.044
#> SRR975600     3  0.1364     0.7457 0.000 0.000 0.944 0.048 0.004 0.004
#> SRR975601     3  0.3320     0.6388 0.000 0.000 0.844 0.032 0.076 0.048
#> SRR975602     1  0.3300     0.6873 0.832 0.000 0.000 0.116 0.032 0.020
#> SRR975603     3  0.0858     0.7484 0.000 0.000 0.968 0.028 0.004 0.000
#> SRR975604     3  0.0653     0.7367 0.000 0.000 0.980 0.004 0.012 0.004

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

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

consensus_heatmap(res, k = 2)

plot of chunk tab-MAD-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

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 17171 rows and 54 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#>   Subgroups are detected by 'pam' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 2.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk MAD-pam-collect-plots

The plots are:

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

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

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

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

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

select_partition_number(res)

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

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           1.000       1.000         0.5037 0.497   0.497
#> 3 3 0.809           0.894       0.928         0.2848 0.816   0.642
#> 4 4 0.797           0.811       0.895         0.1148 0.909   0.751
#> 5 5 0.749           0.736       0.856         0.0323 0.918   0.749
#> 6 6 0.740           0.712       0.812         0.0719 0.892   0.631

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
#> SRR975551     1  0.0000      1.000 1.000 0.000
#> SRR975552     1  0.0000      1.000 1.000 0.000
#> SRR975554     1  0.0000      1.000 1.000 0.000
#> SRR975553     2  0.0000      1.000 0.000 1.000
#> SRR975555     1  0.0000      1.000 1.000 0.000
#> SRR975556     2  0.0000      1.000 0.000 1.000
#> SRR975557     1  0.0000      1.000 1.000 0.000
#> SRR975558     1  0.0672      0.992 0.992 0.008
#> SRR975559     1  0.0000      1.000 1.000 0.000
#> SRR975560     2  0.0000      1.000 0.000 1.000
#> SRR975561     2  0.0000      1.000 0.000 1.000
#> SRR975562     1  0.0000      1.000 1.000 0.000
#> SRR975563     2  0.0000      1.000 0.000 1.000
#> SRR975564     1  0.0000      1.000 1.000 0.000
#> SRR975565     1  0.0000      1.000 1.000 0.000
#> SRR975566     1  0.0000      1.000 1.000 0.000
#> SRR975567     1  0.0000      1.000 1.000 0.000
#> SRR975568     1  0.0000      1.000 1.000 0.000
#> SRR975569     2  0.0000      1.000 0.000 1.000
#> SRR975570     2  0.0000      1.000 0.000 1.000
#> SRR975571     2  0.0000      1.000 0.000 1.000
#> SRR975572     2  0.0000      1.000 0.000 1.000
#> SRR975573     2  0.0000      1.000 0.000 1.000
#> SRR975574     2  0.0000      1.000 0.000 1.000
#> SRR975575     2  0.0000      1.000 0.000 1.000
#> SRR975576     2  0.0000      1.000 0.000 1.000
#> SRR975577     2  0.0000      1.000 0.000 1.000
#> SRR975578     2  0.0000      1.000 0.000 1.000
#> SRR975579     2  0.0000      1.000 0.000 1.000
#> SRR975580     2  0.0000      1.000 0.000 1.000
#> SRR975581     2  0.0000      1.000 0.000 1.000
#> SRR975582     2  0.0000      1.000 0.000 1.000
#> SRR975583     2  0.0000      1.000 0.000 1.000
#> SRR975584     2  0.0000      1.000 0.000 1.000
#> SRR975585     2  0.0000      1.000 0.000 1.000
#> SRR975586     2  0.0000      1.000 0.000 1.000
#> SRR975587     1  0.0000      1.000 1.000 0.000
#> SRR975588     2  0.0000      1.000 0.000 1.000
#> SRR975589     1  0.0000      1.000 1.000 0.000
#> SRR975590     1  0.0000      1.000 1.000 0.000
#> SRR975591     1  0.0000      1.000 1.000 0.000
#> SRR975592     1  0.0000      1.000 1.000 0.000
#> SRR975593     1  0.0000      1.000 1.000 0.000
#> SRR975594     1  0.0000      1.000 1.000 0.000
#> SRR975595     1  0.0000      1.000 1.000 0.000
#> SRR975597     1  0.0000      1.000 1.000 0.000
#> SRR975596     1  0.0000      1.000 1.000 0.000
#> SRR975598     1  0.0000      1.000 1.000 0.000
#> SRR975599     1  0.0000      1.000 1.000 0.000
#> SRR975600     1  0.0000      1.000 1.000 0.000
#> SRR975601     1  0.0000      1.000 1.000 0.000
#> SRR975602     1  0.0000      1.000 1.000 0.000
#> SRR975603     1  0.0000      1.000 1.000 0.000
#> SRR975604     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
#> SRR975551     1  0.0000      0.788 1.000 0.000 0.000
#> SRR975552     1  0.0000      0.788 1.000 0.000 0.000
#> SRR975554     1  0.5058      0.859 0.756 0.000 0.244
#> SRR975553     2  0.0000      0.980 0.000 1.000 0.000
#> SRR975555     1  0.0424      0.795 0.992 0.000 0.008
#> SRR975556     2  0.0000      0.980 0.000 1.000 0.000
#> SRR975557     3  0.0237      0.896 0.004 0.000 0.996
#> SRR975558     2  0.7001      0.706 0.200 0.716 0.084
#> SRR975559     1  0.5216      0.844 0.740 0.000 0.260
#> SRR975560     2  0.4452      0.811 0.192 0.808 0.000
#> SRR975561     2  0.0000      0.980 0.000 1.000 0.000
#> SRR975562     1  0.5098      0.857 0.752 0.000 0.248
#> SRR975563     2  0.0000      0.980 0.000 1.000 0.000
#> SRR975564     1  0.4452      0.888 0.808 0.000 0.192
#> SRR975565     1  0.1163      0.809 0.972 0.000 0.028
#> SRR975566     3  0.3752      0.783 0.144 0.000 0.856
#> SRR975567     3  0.5465      0.645 0.288 0.000 0.712
#> SRR975568     1  0.4235      0.883 0.824 0.000 0.176
#> SRR975569     2  0.0000      0.980 0.000 1.000 0.000
#> SRR975570     2  0.0000      0.980 0.000 1.000 0.000
#> SRR975571     2  0.0000      0.980 0.000 1.000 0.000
#> SRR975572     2  0.0000      0.980 0.000 1.000 0.000
#> SRR975573     2  0.0000      0.980 0.000 1.000 0.000
#> SRR975574     2  0.0000      0.980 0.000 1.000 0.000
#> SRR975575     2  0.0000      0.980 0.000 1.000 0.000
#> SRR975576     2  0.0000      0.980 0.000 1.000 0.000
#> SRR975577     2  0.0000      0.980 0.000 1.000 0.000
#> SRR975578     2  0.0000      0.980 0.000 1.000 0.000
#> SRR975579     2  0.2261      0.928 0.068 0.932 0.000
#> SRR975580     2  0.0000      0.980 0.000 1.000 0.000
#> SRR975581     2  0.0000      0.980 0.000 1.000 0.000
#> SRR975582     2  0.0000      0.980 0.000 1.000 0.000
#> SRR975583     2  0.0000      0.980 0.000 1.000 0.000
#> SRR975584     2  0.0000      0.980 0.000 1.000 0.000
#> SRR975585     2  0.0000      0.980 0.000 1.000 0.000
#> SRR975586     2  0.0000      0.980 0.000 1.000 0.000
#> SRR975587     3  0.1964      0.870 0.056 0.000 0.944
#> SRR975588     2  0.0000      0.980 0.000 1.000 0.000
#> SRR975589     3  0.0000      0.898 0.000 0.000 1.000
#> SRR975590     1  0.4605      0.885 0.796 0.000 0.204
#> SRR975591     3  0.0000      0.898 0.000 0.000 1.000
#> SRR975592     3  0.3192      0.811 0.112 0.000 0.888
#> SRR975593     3  0.0000      0.898 0.000 0.000 1.000
#> SRR975594     3  0.0000      0.898 0.000 0.000 1.000
#> SRR975595     1  0.4887      0.864 0.772 0.000 0.228
#> SRR975597     1  0.4555      0.886 0.800 0.000 0.200
#> SRR975596     3  0.4654      0.692 0.208 0.000 0.792
#> SRR975598     1  0.4504      0.887 0.804 0.000 0.196
#> SRR975599     3  0.5465      0.517 0.288 0.000 0.712
#> SRR975600     3  0.0000      0.898 0.000 0.000 1.000
#> SRR975601     3  0.1860      0.872 0.052 0.000 0.948
#> SRR975602     1  0.4504      0.887 0.804 0.000 0.196
#> SRR975603     3  0.0000      0.898 0.000 0.000 1.000
#> SRR975604     3  0.0000      0.898 0.000 0.000 1.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> SRR975551     1  0.0000     0.8842 1.000 0.000 0.000 0.000
#> SRR975552     1  0.2149     0.8103 0.912 0.000 0.000 0.088
#> SRR975554     4  0.7072     0.6189 0.336 0.000 0.140 0.524
#> SRR975553     2  0.0336     0.9090 0.000 0.992 0.000 0.008
#> SRR975555     1  0.0000     0.8842 1.000 0.000 0.000 0.000
#> SRR975556     2  0.1716     0.8719 0.000 0.936 0.000 0.064
#> SRR975557     3  0.1302     0.9082 0.000 0.000 0.956 0.044
#> SRR975558     4  0.1474     0.6714 0.000 0.000 0.052 0.948
#> SRR975559     4  0.7096     0.6237 0.332 0.000 0.144 0.524
#> SRR975560     2  0.4941     0.5020 0.000 0.564 0.000 0.436
#> SRR975561     2  0.3907     0.7360 0.000 0.768 0.000 0.232
#> SRR975562     4  0.5985     0.7537 0.168 0.000 0.140 0.692
#> SRR975563     2  0.0000     0.9094 0.000 1.000 0.000 0.000
#> SRR975564     1  0.0895     0.8757 0.976 0.000 0.004 0.020
#> SRR975565     1  0.0376     0.8833 0.992 0.000 0.004 0.004
#> SRR975566     4  0.7109     0.5977 0.144 0.000 0.336 0.520
#> SRR975567     4  0.1474     0.6714 0.000 0.000 0.052 0.948
#> SRR975568     1  0.2053     0.8177 0.924 0.000 0.072 0.004
#> SRR975569     2  0.0000     0.9094 0.000 1.000 0.000 0.000
#> SRR975570     2  0.0000     0.9094 0.000 1.000 0.000 0.000
#> SRR975571     2  0.0336     0.9090 0.000 0.992 0.000 0.008
#> SRR975572     2  0.0000     0.9094 0.000 1.000 0.000 0.000
#> SRR975573     2  0.0336     0.9090 0.000 0.992 0.000 0.008
#> SRR975574     2  0.0336     0.9090 0.000 0.992 0.000 0.008
#> SRR975575     2  0.0000     0.9094 0.000 1.000 0.000 0.000
#> SRR975576     2  0.0000     0.9094 0.000 1.000 0.000 0.000
#> SRR975577     2  0.0336     0.9090 0.000 0.992 0.000 0.008
#> SRR975578     2  0.0336     0.9090 0.000 0.992 0.000 0.008
#> SRR975579     2  0.4992     0.4428 0.000 0.524 0.000 0.476
#> SRR975580     2  0.4933     0.5081 0.000 0.568 0.000 0.432
#> SRR975581     2  0.0000     0.9094 0.000 1.000 0.000 0.000
#> SRR975582     2  0.0336     0.9090 0.000 0.992 0.000 0.008
#> SRR975583     2  0.0000     0.9094 0.000 1.000 0.000 0.000
#> SRR975584     2  0.0336     0.9090 0.000 0.992 0.000 0.008
#> SRR975585     2  0.0000     0.9094 0.000 1.000 0.000 0.000
#> SRR975586     2  0.4916     0.5098 0.000 0.576 0.000 0.424
#> SRR975587     3  0.3074     0.8045 0.152 0.000 0.848 0.000
#> SRR975588     2  0.0000     0.9094 0.000 1.000 0.000 0.000
#> SRR975589     3  0.0000     0.9248 0.000 0.000 1.000 0.000
#> SRR975590     1  0.2469     0.7876 0.892 0.000 0.108 0.000
#> SRR975591     3  0.0000     0.9248 0.000 0.000 1.000 0.000
#> SRR975592     3  0.3074     0.7575 0.152 0.000 0.848 0.000
#> SRR975593     3  0.0000     0.9248 0.000 0.000 1.000 0.000
#> SRR975594     3  0.1489     0.9070 0.004 0.000 0.952 0.044
#> SRR975595     1  0.0707     0.8808 0.980 0.000 0.020 0.000
#> SRR975597     1  0.1211     0.8671 0.960 0.000 0.040 0.000
#> SRR975596     4  0.5948     0.7552 0.160 0.000 0.144 0.696
#> SRR975598     1  0.0469     0.8835 0.988 0.000 0.012 0.000
#> SRR975599     1  0.7450    -0.0201 0.424 0.000 0.404 0.172
#> SRR975600     3  0.0000     0.9248 0.000 0.000 1.000 0.000
#> SRR975601     3  0.2921     0.8164 0.140 0.000 0.860 0.000
#> SRR975602     1  0.0000     0.8842 1.000 0.000 0.000 0.000
#> SRR975603     3  0.0000     0.9248 0.000 0.000 1.000 0.000
#> SRR975604     3  0.0000     0.9248 0.000 0.000 1.000 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
#> SRR975551     1  0.0404      0.898 0.988 0.000 0.000 0.000 0.012
#> SRR975552     1  0.2471      0.832 0.864 0.000 0.000 0.000 0.136
#> SRR975554     3  0.6801      0.285 0.312 0.000 0.376 0.000 0.312
#> SRR975553     2  0.2719      0.867 0.000 0.852 0.000 0.144 0.004
#> SRR975555     1  0.0290      0.899 0.992 0.000 0.000 0.000 0.008
#> SRR975556     2  0.1197      0.872 0.000 0.952 0.000 0.048 0.000
#> SRR975557     4  0.5122      0.312 0.000 0.000 0.312 0.628 0.060
#> SRR975558     3  0.6572      0.351 0.000 0.000 0.460 0.228 0.312
#> SRR975559     3  0.4584      0.593 0.028 0.000 0.660 0.000 0.312
#> SRR975560     2  0.5172      0.624 0.000 0.616 0.000 0.324 0.060
#> SRR975561     2  0.2929      0.772 0.000 0.820 0.000 0.180 0.000
#> SRR975562     3  0.4348      0.595 0.016 0.000 0.668 0.000 0.316
#> SRR975563     2  0.0000      0.892 0.000 1.000 0.000 0.000 0.000
#> SRR975564     1  0.0880      0.894 0.968 0.000 0.000 0.000 0.032
#> SRR975565     1  0.3430      0.668 0.776 0.000 0.004 0.000 0.220
#> SRR975566     3  0.5672      0.538 0.104 0.000 0.584 0.000 0.312
#> SRR975567     3  0.6572      0.351 0.000 0.000 0.460 0.228 0.312
#> SRR975568     1  0.2344      0.854 0.904 0.000 0.064 0.000 0.032
#> SRR975569     2  0.0000      0.892 0.000 1.000 0.000 0.000 0.000
#> SRR975570     2  0.0000      0.892 0.000 1.000 0.000 0.000 0.000
#> SRR975571     2  0.2719      0.867 0.000 0.852 0.000 0.144 0.004
#> SRR975572     2  0.0000      0.892 0.000 1.000 0.000 0.000 0.000
#> SRR975573     2  0.2329      0.874 0.000 0.876 0.000 0.124 0.000
#> SRR975574     2  0.2536      0.872 0.000 0.868 0.000 0.128 0.004
#> SRR975575     2  0.0000      0.892 0.000 1.000 0.000 0.000 0.000
#> SRR975576     2  0.0000      0.892 0.000 1.000 0.000 0.000 0.000
#> SRR975577     2  0.2719      0.867 0.000 0.852 0.000 0.144 0.004
#> SRR975578     2  0.2719      0.867 0.000 0.852 0.000 0.144 0.004
#> SRR975579     4  0.0404      0.422 0.000 0.000 0.000 0.988 0.012
#> SRR975580     2  0.4101      0.660 0.000 0.628 0.000 0.372 0.000
#> SRR975581     2  0.0000      0.892 0.000 1.000 0.000 0.000 0.000
#> SRR975582     2  0.2536      0.872 0.000 0.868 0.000 0.128 0.004
#> SRR975583     2  0.0000      0.892 0.000 1.000 0.000 0.000 0.000
#> SRR975584     2  0.2719      0.867 0.000 0.852 0.000 0.144 0.004
#> SRR975585     2  0.0000      0.892 0.000 1.000 0.000 0.000 0.000
#> SRR975586     2  0.3336      0.710 0.000 0.772 0.000 0.228 0.000
#> SRR975587     5  0.5441      0.803 0.080 0.000 0.324 0.000 0.596
#> SRR975588     2  0.0000      0.892 0.000 1.000 0.000 0.000 0.000
#> SRR975589     3  0.0000      0.620 0.000 0.000 1.000 0.000 0.000
#> SRR975590     1  0.1041      0.899 0.964 0.000 0.032 0.000 0.004
#> SRR975591     3  0.0000      0.620 0.000 0.000 1.000 0.000 0.000
#> SRR975592     3  0.3661      0.195 0.276 0.000 0.724 0.000 0.000
#> SRR975593     3  0.0000      0.620 0.000 0.000 1.000 0.000 0.000
#> SRR975594     5  0.4138      0.740 0.000 0.000 0.384 0.000 0.616
#> SRR975595     1  0.2077      0.870 0.908 0.000 0.084 0.000 0.008
#> SRR975597     1  0.2077      0.870 0.908 0.000 0.084 0.000 0.008
#> SRR975596     3  0.4419      0.595 0.020 0.000 0.668 0.000 0.312
#> SRR975598     1  0.2077      0.870 0.908 0.000 0.084 0.000 0.008
#> SRR975599     5  0.7316      0.492 0.188 0.000 0.196 0.084 0.532
#> SRR975600     3  0.0000      0.620 0.000 0.000 1.000 0.000 0.000
#> SRR975601     5  0.5315      0.805 0.068 0.000 0.332 0.000 0.600
#> SRR975602     1  0.0290      0.898 0.992 0.000 0.000 0.000 0.008
#> SRR975603     3  0.0000      0.620 0.000 0.000 1.000 0.000 0.000
#> SRR975604     3  0.0000      0.620 0.000 0.000 1.000 0.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> SRR975551     1  0.0000      0.800 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR975552     1  0.4022      0.706 0.792 0.064 0.000 0.108 0.036 0.000
#> SRR975554     1  0.6141     -0.250 0.400 0.000 0.352 0.004 0.244 0.000
#> SRR975553     6  0.0000      0.827 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR975555     1  0.0458      0.802 0.984 0.000 0.000 0.000 0.016 0.000
#> SRR975556     2  0.3911      0.925 0.000 0.624 0.000 0.008 0.000 0.368
#> SRR975557     4  0.2536      0.733 0.000 0.000 0.116 0.864 0.020 0.000
#> SRR975558     3  0.6976      0.230 0.000 0.372 0.380 0.144 0.104 0.000
#> SRR975559     3  0.4237      0.638 0.048 0.000 0.704 0.004 0.244 0.000
#> SRR975560     6  0.5571      0.150 0.000 0.372 0.000 0.144 0.000 0.484
#> SRR975561     2  0.4292      0.779 0.000 0.628 0.000 0.032 0.000 0.340
#> SRR975562     3  0.3872      0.642 0.020 0.000 0.712 0.004 0.264 0.000
#> SRR975563     2  0.3684      0.936 0.000 0.628 0.000 0.000 0.000 0.372
#> SRR975564     1  0.0603      0.799 0.980 0.000 0.004 0.000 0.016 0.000
#> SRR975565     1  0.3011      0.640 0.800 0.004 0.004 0.000 0.192 0.000
#> SRR975566     3  0.5576      0.517 0.184 0.000 0.568 0.004 0.244 0.000
#> SRR975567     3  0.7262      0.263 0.000 0.320 0.380 0.144 0.156 0.000
#> SRR975568     1  0.1659      0.790 0.940 0.020 0.028 0.004 0.008 0.000
#> SRR975569     2  0.3684      0.936 0.000 0.628 0.000 0.000 0.000 0.372
#> SRR975570     2  0.3684      0.936 0.000 0.628 0.000 0.000 0.000 0.372
#> SRR975571     6  0.0000      0.827 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR975572     2  0.3684      0.936 0.000 0.628 0.000 0.000 0.000 0.372
#> SRR975573     6  0.1444      0.765 0.000 0.072 0.000 0.000 0.000 0.928
#> SRR975574     6  0.1141      0.791 0.000 0.052 0.000 0.000 0.000 0.948
#> SRR975575     2  0.3684      0.936 0.000 0.628 0.000 0.000 0.000 0.372
#> SRR975576     2  0.3684      0.936 0.000 0.628 0.000 0.000 0.000 0.372
#> SRR975577     6  0.0000      0.827 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR975578     6  0.0000      0.827 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR975579     4  0.2100      0.749 0.000 0.004 0.000 0.884 0.000 0.112
#> SRR975580     6  0.4316      0.395 0.000 0.312 0.000 0.040 0.000 0.648
#> SRR975581     2  0.3684      0.936 0.000 0.628 0.000 0.000 0.000 0.372
#> SRR975582     6  0.1141      0.791 0.000 0.052 0.000 0.000 0.000 0.948
#> SRR975583     2  0.3684      0.936 0.000 0.628 0.000 0.000 0.000 0.372
#> SRR975584     6  0.0000      0.827 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR975585     2  0.3684      0.936 0.000 0.628 0.000 0.000 0.000 0.372
#> SRR975586     2  0.2250      0.440 0.000 0.896 0.000 0.040 0.000 0.064
#> SRR975587     5  0.3595      0.843 0.008 0.000 0.288 0.000 0.704 0.000
#> SRR975588     2  0.3684      0.936 0.000 0.628 0.000 0.000 0.000 0.372
#> SRR975589     3  0.0000      0.680 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975590     1  0.1124      0.807 0.956 0.000 0.036 0.000 0.008 0.000
#> SRR975591     3  0.0000      0.680 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975592     3  0.3309      0.310 0.280 0.000 0.720 0.000 0.000 0.000
#> SRR975593     3  0.0000      0.680 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975594     5  0.3351      0.843 0.000 0.000 0.288 0.000 0.712 0.000
#> SRR975595     1  0.3381      0.739 0.800 0.000 0.156 0.000 0.044 0.000
#> SRR975597     1  0.3381      0.739 0.800 0.000 0.156 0.000 0.044 0.000
#> SRR975596     3  0.4117      0.645 0.032 0.004 0.716 0.004 0.244 0.000
#> SRR975598     1  0.3381      0.739 0.800 0.000 0.156 0.000 0.044 0.000
#> SRR975599     5  0.6416      0.457 0.068 0.124 0.156 0.036 0.616 0.000
#> SRR975600     3  0.0000      0.680 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975601     5  0.3489      0.845 0.004 0.000 0.288 0.000 0.708 0.000
#> SRR975602     1  0.1549      0.801 0.936 0.000 0.020 0.000 0.044 0.000
#> SRR975603     3  0.0000      0.680 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975604     3  0.0000      0.680 0.000 0.000 1.000 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-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

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 17171 rows and 54 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#>   Subgroups are detected by 'mclust' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 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-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           0.974       0.989         0.4602 0.547   0.547
#> 3 3 0.738           0.857       0.929         0.4250 0.808   0.649
#> 4 4 0.697           0.672       0.827         0.1013 0.825   0.564
#> 5 5 0.732           0.601       0.793         0.0536 0.905   0.675
#> 6 6 0.752           0.656       0.801         0.0407 0.920   0.674

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
#> SRR975551     1   0.000      0.982 1.000 0.000
#> SRR975552     1   0.000      0.982 1.000 0.000
#> SRR975554     1   0.000      0.982 1.000 0.000
#> SRR975553     2   0.000      1.000 0.000 1.000
#> SRR975555     1   0.000      0.982 1.000 0.000
#> SRR975556     1   0.541      0.858 0.876 0.124
#> SRR975557     1   0.000      0.982 1.000 0.000
#> SRR975558     1   0.000      0.982 1.000 0.000
#> SRR975559     1   0.000      0.982 1.000 0.000
#> SRR975560     1   0.000      0.982 1.000 0.000
#> SRR975561     1   0.917      0.523 0.668 0.332
#> SRR975562     1   0.000      0.982 1.000 0.000
#> SRR975563     2   0.000      1.000 0.000 1.000
#> SRR975564     1   0.000      0.982 1.000 0.000
#> SRR975565     1   0.000      0.982 1.000 0.000
#> SRR975566     1   0.000      0.982 1.000 0.000
#> SRR975567     1   0.000      0.982 1.000 0.000
#> SRR975568     1   0.000      0.982 1.000 0.000
#> SRR975569     2   0.000      1.000 0.000 1.000
#> SRR975570     2   0.000      1.000 0.000 1.000
#> SRR975571     2   0.000      1.000 0.000 1.000
#> SRR975572     2   0.000      1.000 0.000 1.000
#> SRR975573     2   0.000      1.000 0.000 1.000
#> SRR975574     2   0.000      1.000 0.000 1.000
#> SRR975575     2   0.000      1.000 0.000 1.000
#> SRR975576     2   0.000      1.000 0.000 1.000
#> SRR975577     2   0.000      1.000 0.000 1.000
#> SRR975578     2   0.000      1.000 0.000 1.000
#> SRR975579     1   0.000      0.982 1.000 0.000
#> SRR975580     1   0.000      0.982 1.000 0.000
#> SRR975581     2   0.000      1.000 0.000 1.000
#> SRR975582     2   0.000      1.000 0.000 1.000
#> SRR975583     2   0.000      1.000 0.000 1.000
#> SRR975584     2   0.000      1.000 0.000 1.000
#> SRR975585     2   0.000      1.000 0.000 1.000
#> SRR975586     1   0.644      0.808 0.836 0.164
#> SRR975587     1   0.000      0.982 1.000 0.000
#> SRR975588     2   0.000      1.000 0.000 1.000
#> SRR975589     1   0.000      0.982 1.000 0.000
#> SRR975590     1   0.000      0.982 1.000 0.000
#> SRR975591     1   0.000      0.982 1.000 0.000
#> SRR975592     1   0.000      0.982 1.000 0.000
#> SRR975593     1   0.000      0.982 1.000 0.000
#> SRR975594     1   0.000      0.982 1.000 0.000
#> SRR975595     1   0.000      0.982 1.000 0.000
#> SRR975597     1   0.000      0.982 1.000 0.000
#> SRR975596     1   0.000      0.982 1.000 0.000
#> SRR975598     1   0.000      0.982 1.000 0.000
#> SRR975599     1   0.000      0.982 1.000 0.000
#> SRR975600     1   0.000      0.982 1.000 0.000
#> SRR975601     1   0.000      0.982 1.000 0.000
#> SRR975602     1   0.000      0.982 1.000 0.000
#> SRR975603     1   0.000      0.982 1.000 0.000
#> SRR975604     1   0.000      0.982 1.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3
#> SRR975551     1  0.3752      0.830 0.856 0.000 0.144
#> SRR975552     1  0.3752      0.830 0.856 0.000 0.144
#> SRR975554     1  0.3686      0.832 0.860 0.000 0.140
#> SRR975553     2  0.0000      0.997 0.000 1.000 0.000
#> SRR975555     1  0.3752      0.830 0.856 0.000 0.144
#> SRR975556     3  0.0237      0.892 0.000 0.004 0.996
#> SRR975557     3  0.3752      0.822 0.144 0.000 0.856
#> SRR975558     3  0.0000      0.893 0.000 0.000 1.000
#> SRR975559     1  0.2356      0.860 0.928 0.000 0.072
#> SRR975560     3  0.0000      0.893 0.000 0.000 1.000
#> SRR975561     3  0.0592      0.886 0.000 0.012 0.988
#> SRR975562     1  0.3267      0.842 0.884 0.000 0.116
#> SRR975563     2  0.0000      0.997 0.000 1.000 0.000
#> SRR975564     1  0.3752      0.830 0.856 0.000 0.144
#> SRR975565     1  0.3752      0.830 0.856 0.000 0.144
#> SRR975566     1  0.2261      0.860 0.932 0.000 0.068
#> SRR975567     3  0.0000      0.893 0.000 0.000 1.000
#> SRR975568     1  0.3752      0.830 0.856 0.000 0.144
#> SRR975569     2  0.0000      0.997 0.000 1.000 0.000
#> SRR975570     2  0.0000      0.997 0.000 1.000 0.000
#> SRR975571     2  0.0000      0.997 0.000 1.000 0.000
#> SRR975572     2  0.0000      0.997 0.000 1.000 0.000
#> SRR975573     2  0.0000      0.997 0.000 1.000 0.000
#> SRR975574     2  0.1643      0.951 0.000 0.956 0.044
#> SRR975575     2  0.0000      0.997 0.000 1.000 0.000
#> SRR975576     2  0.0000      0.997 0.000 1.000 0.000
#> SRR975577     2  0.0000      0.997 0.000 1.000 0.000
#> SRR975578     2  0.0000      0.997 0.000 1.000 0.000
#> SRR975579     3  0.3686      0.825 0.140 0.000 0.860
#> SRR975580     3  0.0000      0.893 0.000 0.000 1.000
#> SRR975581     2  0.0000      0.997 0.000 1.000 0.000
#> SRR975582     2  0.0000      0.997 0.000 1.000 0.000
#> SRR975583     2  0.0000      0.997 0.000 1.000 0.000
#> SRR975584     2  0.0000      0.997 0.000 1.000 0.000
#> SRR975585     2  0.0237      0.993 0.000 0.996 0.004
#> SRR975586     3  0.0237      0.892 0.000 0.004 0.996
#> SRR975587     1  0.3192      0.798 0.888 0.000 0.112
#> SRR975588     2  0.0000      0.997 0.000 1.000 0.000
#> SRR975589     1  0.0592      0.857 0.988 0.000 0.012
#> SRR975590     1  0.0000      0.858 1.000 0.000 0.000
#> SRR975591     1  0.6026      0.337 0.624 0.000 0.376
#> SRR975592     1  0.0592      0.857 0.988 0.000 0.012
#> SRR975593     1  0.0592      0.857 0.988 0.000 0.012
#> SRR975594     3  0.3941      0.815 0.156 0.000 0.844
#> SRR975595     1  0.0000      0.858 1.000 0.000 0.000
#> SRR975597     1  0.0000      0.858 1.000 0.000 0.000
#> SRR975596     1  0.2356      0.860 0.928 0.000 0.072
#> SRR975598     1  0.0000      0.858 1.000 0.000 0.000
#> SRR975599     3  0.6286      0.171 0.464 0.000 0.536
#> SRR975600     1  0.3192      0.798 0.888 0.000 0.112
#> SRR975601     1  0.6026      0.337 0.624 0.000 0.376
#> SRR975602     1  0.0424      0.858 0.992 0.000 0.008
#> SRR975603     1  0.3192      0.798 0.888 0.000 0.112
#> SRR975604     1  0.6026      0.337 0.624 0.000 0.376

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> SRR975551     1  0.6621      0.575 0.628 0.000 0.184 0.188
#> SRR975552     1  0.6689      0.574 0.620 0.000 0.184 0.196
#> SRR975554     1  0.6709      0.358 0.616 0.000 0.172 0.212
#> SRR975553     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975555     1  0.6689      0.574 0.620 0.000 0.184 0.196
#> SRR975556     3  0.1302      0.601 0.000 0.044 0.956 0.000
#> SRR975557     3  0.3486      0.592 0.000 0.000 0.812 0.188
#> SRR975558     3  0.0188      0.621 0.000 0.000 0.996 0.004
#> SRR975559     4  0.6548      0.736 0.188 0.000 0.176 0.636
#> SRR975560     3  0.0188      0.622 0.000 0.004 0.996 0.000
#> SRR975561     3  0.3764      0.402 0.000 0.216 0.784 0.000
#> SRR975562     1  0.6805      0.348 0.604 0.000 0.176 0.220
#> SRR975563     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975564     1  0.6316      0.549 0.660 0.000 0.184 0.156
#> SRR975565     1  0.6689      0.574 0.620 0.000 0.184 0.196
#> SRR975566     4  0.6511      0.738 0.188 0.000 0.172 0.640
#> SRR975567     3  0.0188      0.621 0.000 0.000 0.996 0.004
#> SRR975568     1  0.6689      0.574 0.620 0.000 0.184 0.196
#> SRR975569     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975570     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975571     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975572     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975573     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975574     2  0.3024      0.794 0.000 0.852 0.148 0.000
#> SRR975575     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975576     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975577     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975578     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975579     3  0.3486      0.592 0.000 0.000 0.812 0.188
#> SRR975580     3  0.0188      0.622 0.000 0.004 0.996 0.000
#> SRR975581     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975582     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975583     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975584     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975585     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975586     3  0.1940      0.575 0.000 0.076 0.924 0.000
#> SRR975587     3  0.6666      0.493 0.404 0.000 0.508 0.088
#> SRR975588     2  0.0000      0.989 0.000 1.000 0.000 0.000
#> SRR975589     4  0.4888      0.636 0.412 0.000 0.000 0.588
#> SRR975590     1  0.2660      0.373 0.908 0.000 0.036 0.056
#> SRR975591     3  0.6417      0.530 0.388 0.000 0.540 0.072
#> SRR975592     1  0.6235     -0.425 0.524 0.000 0.420 0.056
#> SRR975593     4  0.4898      0.631 0.416 0.000 0.000 0.584
#> SRR975594     3  0.4988      0.605 0.236 0.000 0.728 0.036
#> SRR975595     1  0.0188      0.483 0.996 0.000 0.004 0.000
#> SRR975597     1  0.0376      0.480 0.992 0.000 0.004 0.004
#> SRR975596     4  0.6511      0.738 0.188 0.000 0.172 0.640
#> SRR975598     1  0.0188      0.483 0.996 0.000 0.004 0.000
#> SRR975599     3  0.6212      0.542 0.380 0.000 0.560 0.060
#> SRR975600     3  0.7701      0.289 0.388 0.000 0.392 0.220
#> SRR975601     3  0.6417      0.530 0.388 0.000 0.540 0.072
#> SRR975602     1  0.2222      0.402 0.924 0.000 0.060 0.016
#> SRR975603     3  0.6635      0.512 0.388 0.000 0.524 0.088
#> SRR975604     3  0.6417      0.530 0.388 0.000 0.540 0.072

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> SRR975551     1  0.1410     0.7166 0.940 0.000 0.000 0.000 0.060
#> SRR975552     1  0.1851     0.7082 0.912 0.000 0.000 0.000 0.088
#> SRR975554     1  0.6075     0.0631 0.476 0.000 0.428 0.012 0.084
#> SRR975553     2  0.0794     0.9578 0.000 0.972 0.000 0.000 0.028
#> SRR975555     1  0.1410     0.7166 0.940 0.000 0.000 0.000 0.060
#> SRR975556     5  0.4499     0.7861 0.004 0.136 0.000 0.096 0.764
#> SRR975557     4  0.2424     0.2698 0.000 0.000 0.000 0.868 0.132
#> SRR975558     5  0.5656     0.4167 0.008 0.000 0.064 0.376 0.552
#> SRR975559     3  0.3752     0.4495 0.200 0.000 0.780 0.004 0.016
#> SRR975560     5  0.4450     0.7841 0.004 0.080 0.000 0.152 0.764
#> SRR975561     5  0.4452     0.7592 0.004 0.164 0.000 0.072 0.760
#> SRR975562     1  0.6101     0.1938 0.520 0.000 0.380 0.016 0.084
#> SRR975563     2  0.0000     0.9799 0.000 1.000 0.000 0.000 0.000
#> SRR975564     1  0.2520     0.6963 0.896 0.000 0.056 0.000 0.048
#> SRR975565     1  0.1410     0.7166 0.940 0.000 0.000 0.000 0.060
#> SRR975566     3  0.3845     0.4371 0.224 0.000 0.760 0.004 0.012
#> SRR975567     5  0.5656     0.4167 0.008 0.000 0.064 0.376 0.552
#> SRR975568     1  0.1410     0.7166 0.940 0.000 0.000 0.000 0.060
#> SRR975569     2  0.0000     0.9799 0.000 1.000 0.000 0.000 0.000
#> SRR975570     2  0.0000     0.9799 0.000 1.000 0.000 0.000 0.000
#> SRR975571     2  0.0794     0.9578 0.000 0.972 0.000 0.000 0.028
#> SRR975572     2  0.0000     0.9799 0.000 1.000 0.000 0.000 0.000
#> SRR975573     2  0.0000     0.9799 0.000 1.000 0.000 0.000 0.000
#> SRR975574     2  0.3491     0.6515 0.004 0.768 0.000 0.000 0.228
#> SRR975575     2  0.0000     0.9799 0.000 1.000 0.000 0.000 0.000
#> SRR975576     2  0.0162     0.9777 0.000 0.996 0.000 0.000 0.004
#> SRR975577     2  0.0000     0.9799 0.000 1.000 0.000 0.000 0.000
#> SRR975578     2  0.0162     0.9777 0.000 0.996 0.000 0.000 0.004
#> SRR975579     4  0.2424     0.2698 0.000 0.000 0.000 0.868 0.132
#> SRR975580     5  0.4450     0.7841 0.004 0.080 0.000 0.152 0.764
#> SRR975581     2  0.0000     0.9799 0.000 1.000 0.000 0.000 0.000
#> SRR975582     2  0.0000     0.9799 0.000 1.000 0.000 0.000 0.000
#> SRR975583     2  0.0000     0.9799 0.000 1.000 0.000 0.000 0.000
#> SRR975584     2  0.0162     0.9774 0.000 0.996 0.000 0.000 0.004
#> SRR975585     2  0.0000     0.9799 0.000 1.000 0.000 0.000 0.000
#> SRR975586     5  0.4478     0.7815 0.004 0.144 0.000 0.088 0.764
#> SRR975587     3  0.7019    -0.1085 0.080 0.000 0.456 0.384 0.080
#> SRR975588     2  0.0000     0.9799 0.000 1.000 0.000 0.000 0.000
#> SRR975589     3  0.1478     0.4606 0.064 0.000 0.936 0.000 0.000
#> SRR975590     1  0.7104     0.1684 0.460 0.000 0.368 0.104 0.068
#> SRR975591     4  0.5146     0.3326 0.012 0.000 0.432 0.536 0.020
#> SRR975592     3  0.7810     0.0898 0.240 0.000 0.400 0.288 0.072
#> SRR975593     3  0.1478     0.4606 0.064 0.000 0.936 0.000 0.000
#> SRR975594     4  0.5968     0.3985 0.000 0.000 0.268 0.576 0.156
#> SRR975595     1  0.4985     0.6557 0.744 0.000 0.152 0.028 0.076
#> SRR975597     1  0.4985     0.6557 0.744 0.000 0.152 0.028 0.076
#> SRR975596     3  0.3652     0.4512 0.200 0.000 0.784 0.004 0.012
#> SRR975598     1  0.4985     0.6557 0.744 0.000 0.152 0.028 0.076
#> SRR975599     3  0.6361    -0.4363 0.004 0.000 0.428 0.428 0.140
#> SRR975600     3  0.4538    -0.1015 0.016 0.000 0.620 0.364 0.000
#> SRR975601     4  0.6109     0.3289 0.016 0.000 0.416 0.488 0.080
#> SRR975602     1  0.5631     0.5839 0.660 0.000 0.240 0.028 0.072
#> SRR975603     3  0.4747    -0.3408 0.016 0.000 0.500 0.484 0.000
#> SRR975604     4  0.5187     0.2660 0.016 0.000 0.484 0.484 0.016

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> SRR975551     1  0.1010      0.699 0.960 0.000 0.000 0.000 0.036 0.004
#> SRR975552     1  0.0692      0.709 0.976 0.000 0.000 0.000 0.020 0.004
#> SRR975554     5  0.4085      0.708 0.092 0.000 0.108 0.000 0.780 0.020
#> SRR975553     2  0.0790      0.957 0.000 0.968 0.000 0.000 0.000 0.032
#> SRR975555     1  0.0692      0.709 0.976 0.000 0.000 0.000 0.020 0.004
#> SRR975556     6  0.1863      0.724 0.000 0.104 0.000 0.000 0.000 0.896
#> SRR975557     4  0.4228      0.514 0.000 0.000 0.072 0.716 0.000 0.212
#> SRR975558     6  0.5812      0.352 0.004 0.000 0.072 0.164 0.116 0.644
#> SRR975559     5  0.1257      0.779 0.020 0.000 0.000 0.000 0.952 0.028
#> SRR975560     6  0.1575      0.707 0.000 0.032 0.000 0.032 0.000 0.936
#> SRR975561     6  0.2597      0.641 0.000 0.176 0.000 0.000 0.000 0.824
#> SRR975562     5  0.5458      0.566 0.216 0.000 0.124 0.004 0.636 0.020
#> SRR975563     2  0.0000      0.980 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975564     1  0.4935      0.109 0.556 0.000 0.044 0.000 0.388 0.012
#> SRR975565     1  0.0692      0.709 0.976 0.000 0.000 0.000 0.020 0.004
#> SRR975566     5  0.1078      0.780 0.016 0.000 0.012 0.000 0.964 0.008
#> SRR975567     6  0.5812      0.352 0.004 0.000 0.072 0.164 0.116 0.644
#> SRR975568     1  0.0692      0.709 0.976 0.000 0.000 0.000 0.020 0.004
#> SRR975569     2  0.0000      0.980 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975570     2  0.0000      0.980 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975571     2  0.0790      0.957 0.000 0.968 0.000 0.000 0.000 0.032
#> SRR975572     2  0.0000      0.980 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975573     2  0.0000      0.980 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975574     2  0.2823      0.713 0.000 0.796 0.000 0.000 0.000 0.204
#> SRR975575     2  0.0000      0.980 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975576     2  0.0146      0.978 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR975577     2  0.0000      0.980 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975578     2  0.0260      0.975 0.000 0.992 0.000 0.000 0.000 0.008
#> SRR975579     4  0.5348      0.479 0.000 0.056 0.068 0.652 0.000 0.224
#> SRR975580     6  0.0790      0.714 0.000 0.032 0.000 0.000 0.000 0.968
#> SRR975581     2  0.0000      0.980 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975582     2  0.0000      0.980 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975583     2  0.0000      0.980 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975584     2  0.0632      0.962 0.000 0.976 0.000 0.000 0.000 0.024
#> SRR975585     2  0.0000      0.980 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975586     6  0.1863      0.724 0.000 0.104 0.000 0.000 0.000 0.896
#> SRR975587     3  0.3638      0.487 0.040 0.000 0.836 0.044 0.068 0.012
#> SRR975588     2  0.0000      0.980 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975589     5  0.2994      0.623 0.004 0.000 0.208 0.000 0.788 0.000
#> SRR975590     3  0.5361      0.394 0.180 0.000 0.620 0.008 0.192 0.000
#> SRR975591     3  0.6218      0.456 0.000 0.000 0.592 0.168 0.144 0.096
#> SRR975592     3  0.4819      0.453 0.132 0.000 0.664 0.000 0.204 0.000
#> SRR975593     5  0.2883      0.619 0.000 0.000 0.212 0.000 0.788 0.000
#> SRR975594     4  0.4300     -0.152 0.000 0.000 0.444 0.540 0.008 0.008
#> SRR975595     1  0.5574      0.377 0.480 0.000 0.428 0.044 0.048 0.000
#> SRR975597     1  0.5519      0.380 0.484 0.000 0.428 0.040 0.048 0.000
#> SRR975596     5  0.1232      0.781 0.016 0.000 0.004 0.000 0.956 0.024
#> SRR975598     1  0.5578      0.368 0.472 0.000 0.436 0.044 0.048 0.000
#> SRR975599     3  0.3728      0.249 0.000 0.000 0.652 0.344 0.000 0.004
#> SRR975600     3  0.5447      0.472 0.000 0.000 0.580 0.076 0.316 0.028
#> SRR975601     3  0.4857      0.313 0.000 0.000 0.688 0.200 0.016 0.096
#> SRR975602     3  0.5491     -0.327 0.400 0.000 0.512 0.048 0.040 0.000
#> SRR975603     3  0.6161      0.482 0.000 0.000 0.576 0.112 0.232 0.080
#> SRR975604     3  0.6168      0.457 0.000 0.000 0.600 0.160 0.140 0.100

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

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 17171 rows and 54 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#>   Subgroups are detected by 'NMF' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 4.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk MAD-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           0.993       0.996         0.5043 0.497   0.497
#> 3 3 1.000           0.968       0.987         0.2443 0.867   0.734
#> 4 4 0.944           0.907       0.955         0.0548 0.956   0.884
#> 5 5 0.824           0.759       0.838         0.0935 0.898   0.714
#> 6 6 0.757           0.719       0.833         0.0724 0.928   0.743

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 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
#> SRR975551     1   0.000      0.993 1.000 0.000
#> SRR975552     1   0.000      0.993 1.000 0.000
#> SRR975554     1   0.000      0.993 1.000 0.000
#> SRR975553     2   0.000      1.000 0.000 1.000
#> SRR975555     1   0.000      0.993 1.000 0.000
#> SRR975556     2   0.000      1.000 0.000 1.000
#> SRR975557     1   0.184      0.969 0.972 0.028
#> SRR975558     1   0.552      0.857 0.872 0.128
#> SRR975559     1   0.000      0.993 1.000 0.000
#> SRR975560     2   0.000      1.000 0.000 1.000
#> SRR975561     2   0.000      1.000 0.000 1.000
#> SRR975562     1   0.000      0.993 1.000 0.000
#> SRR975563     2   0.000      1.000 0.000 1.000
#> SRR975564     1   0.000      0.993 1.000 0.000
#> SRR975565     1   0.000      0.993 1.000 0.000
#> SRR975566     1   0.000      0.993 1.000 0.000
#> SRR975567     1   0.242      0.957 0.960 0.040
#> SRR975568     1   0.000      0.993 1.000 0.000
#> SRR975569     2   0.000      1.000 0.000 1.000
#> SRR975570     2   0.000      1.000 0.000 1.000
#> SRR975571     2   0.000      1.000 0.000 1.000
#> SRR975572     2   0.000      1.000 0.000 1.000
#> SRR975573     2   0.000      1.000 0.000 1.000
#> SRR975574     2   0.000      1.000 0.000 1.000
#> SRR975575     2   0.000      1.000 0.000 1.000
#> SRR975576     2   0.000      1.000 0.000 1.000
#> SRR975577     2   0.000      1.000 0.000 1.000
#> SRR975578     2   0.000      1.000 0.000 1.000
#> SRR975579     2   0.000      1.000 0.000 1.000
#> SRR975580     2   0.000      1.000 0.000 1.000
#> SRR975581     2   0.000      1.000 0.000 1.000
#> SRR975582     2   0.000      1.000 0.000 1.000
#> SRR975583     2   0.000      1.000 0.000 1.000
#> SRR975584     2   0.000      1.000 0.000 1.000
#> SRR975585     2   0.000      1.000 0.000 1.000
#> SRR975586     2   0.000      1.000 0.000 1.000
#> SRR975587     1   0.000      0.993 1.000 0.000
#> SRR975588     2   0.000      1.000 0.000 1.000
#> SRR975589     1   0.000      0.993 1.000 0.000
#> SRR975590     1   0.000      0.993 1.000 0.000
#> SRR975591     1   0.000      0.993 1.000 0.000
#> SRR975592     1   0.000      0.993 1.000 0.000
#> SRR975593     1   0.000      0.993 1.000 0.000
#> SRR975594     1   0.000      0.993 1.000 0.000
#> SRR975595     1   0.000      0.993 1.000 0.000
#> SRR975597     1   0.000      0.993 1.000 0.000
#> SRR975596     1   0.000      0.993 1.000 0.000
#> SRR975598     1   0.000      0.993 1.000 0.000
#> SRR975599     1   0.000      0.993 1.000 0.000
#> SRR975600     1   0.000      0.993 1.000 0.000
#> SRR975601     1   0.000      0.993 1.000 0.000
#> SRR975602     1   0.000      0.993 1.000 0.000
#> SRR975603     1   0.000      0.993 1.000 0.000
#> SRR975604     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
#> SRR975551     1  0.0000      0.980 1.000 0.000 0.000
#> SRR975552     1  0.0000      0.980 1.000 0.000 0.000
#> SRR975554     1  0.0000      0.980 1.000 0.000 0.000
#> SRR975553     2  0.0000      1.000 0.000 1.000 0.000
#> SRR975555     1  0.0000      0.980 1.000 0.000 0.000
#> SRR975556     2  0.0000      1.000 0.000 1.000 0.000
#> SRR975557     3  0.0000      0.955 0.000 0.000 1.000
#> SRR975558     1  0.2165      0.904 0.936 0.064 0.000
#> SRR975559     1  0.0000      0.980 1.000 0.000 0.000
#> SRR975560     2  0.0000      1.000 0.000 1.000 0.000
#> SRR975561     2  0.0000      1.000 0.000 1.000 0.000
#> SRR975562     1  0.0000      0.980 1.000 0.000 0.000
#> SRR975563     2  0.0000      1.000 0.000 1.000 0.000
#> SRR975564     1  0.0000      0.980 1.000 0.000 0.000
#> SRR975565     1  0.0000      0.980 1.000 0.000 0.000
#> SRR975566     1  0.0000      0.980 1.000 0.000 0.000
#> SRR975567     1  0.0000      0.980 1.000 0.000 0.000
#> SRR975568     1  0.0000      0.980 1.000 0.000 0.000
#> SRR975569     2  0.0000      1.000 0.000 1.000 0.000
#> SRR975570     2  0.0000      1.000 0.000 1.000 0.000
#> SRR975571     2  0.0000      1.000 0.000 1.000 0.000
#> SRR975572     2  0.0000      1.000 0.000 1.000 0.000
#> SRR975573     2  0.0000      1.000 0.000 1.000 0.000
#> SRR975574     2  0.0000      1.000 0.000 1.000 0.000
#> SRR975575     2  0.0000      1.000 0.000 1.000 0.000
#> SRR975576     2  0.0000      1.000 0.000 1.000 0.000
#> SRR975577     2  0.0000      1.000 0.000 1.000 0.000
#> SRR975578     2  0.0000      1.000 0.000 1.000 0.000
#> SRR975579     3  0.4504      0.751 0.000 0.196 0.804
#> SRR975580     2  0.0000      1.000 0.000 1.000 0.000
#> SRR975581     2  0.0000      1.000 0.000 1.000 0.000
#> SRR975582     2  0.0000      1.000 0.000 1.000 0.000
#> SRR975583     2  0.0000      1.000 0.000 1.000 0.000
#> SRR975584     2  0.0000      1.000 0.000 1.000 0.000
#> SRR975585     2  0.0000      1.000 0.000 1.000 0.000
#> SRR975586     2  0.0000      1.000 0.000 1.000 0.000
#> SRR975587     1  0.5905      0.454 0.648 0.000 0.352
#> SRR975588     2  0.0000      1.000 0.000 1.000 0.000
#> SRR975589     1  0.0000      0.980 1.000 0.000 0.000
#> SRR975590     1  0.0000      0.980 1.000 0.000 0.000
#> SRR975591     3  0.0000      0.955 0.000 0.000 1.000
#> SRR975592     1  0.0000      0.980 1.000 0.000 0.000
#> SRR975593     1  0.0424      0.973 0.992 0.000 0.008
#> SRR975594     3  0.0000      0.955 0.000 0.000 1.000
#> SRR975595     1  0.0000      0.980 1.000 0.000 0.000
#> SRR975597     1  0.0000      0.980 1.000 0.000 0.000
#> SRR975596     1  0.0000      0.980 1.000 0.000 0.000
#> SRR975598     1  0.0000      0.980 1.000 0.000 0.000
#> SRR975599     1  0.0000      0.980 1.000 0.000 0.000
#> SRR975600     3  0.2356      0.903 0.072 0.000 0.928
#> SRR975601     3  0.1289      0.938 0.032 0.000 0.968
#> SRR975602     1  0.0000      0.980 1.000 0.000 0.000
#> SRR975603     3  0.0000      0.955 0.000 0.000 1.000
#> SRR975604     3  0.0000      0.955 0.000 0.000 1.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> SRR975551     1  0.0817      0.936 0.976 0.000 0.000 0.024
#> SRR975552     1  0.0000      0.938 1.000 0.000 0.000 0.000
#> SRR975554     1  0.0336      0.937 0.992 0.000 0.000 0.008
#> SRR975553     2  0.0000      0.995 0.000 1.000 0.000 0.000
#> SRR975555     1  0.0336      0.938 0.992 0.000 0.000 0.008
#> SRR975556     2  0.0000      0.995 0.000 1.000 0.000 0.000
#> SRR975557     4  0.2469      0.556 0.000 0.000 0.108 0.892
#> SRR975558     4  0.7150      0.183 0.384 0.136 0.000 0.480
#> SRR975559     1  0.2973      0.839 0.856 0.000 0.000 0.144
#> SRR975560     2  0.1890      0.927 0.008 0.936 0.000 0.056
#> SRR975561     2  0.0000      0.995 0.000 1.000 0.000 0.000
#> SRR975562     1  0.1637      0.914 0.940 0.000 0.000 0.060
#> SRR975563     2  0.0000      0.995 0.000 1.000 0.000 0.000
#> SRR975564     1  0.0707      0.937 0.980 0.000 0.000 0.020
#> SRR975565     1  0.0188      0.938 0.996 0.000 0.000 0.004
#> SRR975566     1  0.0469      0.937 0.988 0.000 0.000 0.012
#> SRR975567     1  0.5300      0.483 0.664 0.028 0.000 0.308
#> SRR975568     1  0.0921      0.933 0.972 0.000 0.000 0.028
#> SRR975569     2  0.0000      0.995 0.000 1.000 0.000 0.000
#> SRR975570     2  0.0000      0.995 0.000 1.000 0.000 0.000
#> SRR975571     2  0.0000      0.995 0.000 1.000 0.000 0.000
#> SRR975572     2  0.0000      0.995 0.000 1.000 0.000 0.000
#> SRR975573     2  0.0000      0.995 0.000 1.000 0.000 0.000
#> SRR975574     2  0.0000      0.995 0.000 1.000 0.000 0.000
#> SRR975575     2  0.0000      0.995 0.000 1.000 0.000 0.000
#> SRR975576     2  0.0000      0.995 0.000 1.000 0.000 0.000
#> SRR975577     2  0.0000      0.995 0.000 1.000 0.000 0.000
#> SRR975578     2  0.0000      0.995 0.000 1.000 0.000 0.000
#> SRR975579     4  0.3435      0.569 0.000 0.036 0.100 0.864
#> SRR975580     2  0.1211      0.954 0.000 0.960 0.000 0.040
#> SRR975581     2  0.0000      0.995 0.000 1.000 0.000 0.000
#> SRR975582     2  0.0000      0.995 0.000 1.000 0.000 0.000
#> SRR975583     2  0.0000      0.995 0.000 1.000 0.000 0.000
#> SRR975584     2  0.0000      0.995 0.000 1.000 0.000 0.000
#> SRR975585     2  0.0000      0.995 0.000 1.000 0.000 0.000
#> SRR975586     2  0.0000      0.995 0.000 1.000 0.000 0.000
#> SRR975587     3  0.2546      0.858 0.060 0.000 0.912 0.028
#> SRR975588     2  0.0000      0.995 0.000 1.000 0.000 0.000
#> SRR975589     1  0.0804      0.937 0.980 0.000 0.008 0.012
#> SRR975590     1  0.1545      0.928 0.952 0.000 0.008 0.040
#> SRR975591     3  0.0188      0.910 0.000 0.000 0.996 0.004
#> SRR975592     1  0.1488      0.925 0.956 0.000 0.032 0.012
#> SRR975593     1  0.1888      0.919 0.940 0.000 0.044 0.016
#> SRR975594     3  0.0188      0.910 0.000 0.000 0.996 0.004
#> SRR975595     1  0.1398      0.933 0.956 0.000 0.004 0.040
#> SRR975597     1  0.0895      0.934 0.976 0.000 0.004 0.020
#> SRR975596     1  0.3311      0.803 0.828 0.000 0.000 0.172
#> SRR975598     1  0.1661      0.929 0.944 0.000 0.004 0.052
#> SRR975599     1  0.2053      0.916 0.924 0.000 0.004 0.072
#> SRR975600     3  0.4182      0.631 0.180 0.000 0.796 0.024
#> SRR975601     3  0.1510      0.895 0.028 0.000 0.956 0.016
#> SRR975602     1  0.0707      0.938 0.980 0.000 0.000 0.020
#> SRR975603     3  0.0000      0.911 0.000 0.000 1.000 0.000
#> SRR975604     3  0.0000      0.911 0.000 0.000 1.000 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
#> SRR975551     1  0.1908      0.629 0.908 0.000 0.000 0.000 0.092
#> SRR975552     1  0.1270      0.671 0.948 0.000 0.000 0.000 0.052
#> SRR975554     1  0.1544      0.694 0.932 0.000 0.000 0.000 0.068
#> SRR975553     2  0.0703      0.957 0.000 0.976 0.000 0.000 0.024
#> SRR975555     1  0.2648      0.620 0.848 0.000 0.000 0.000 0.152
#> SRR975556     2  0.1608      0.922 0.000 0.928 0.000 0.000 0.072
#> SRR975557     4  0.0000      0.733 0.000 0.000 0.000 1.000 0.000
#> SRR975558     4  0.6603      0.669 0.108 0.108 0.000 0.628 0.156
#> SRR975559     1  0.6275     -0.185 0.480 0.000 0.000 0.364 0.156
#> SRR975560     5  0.4974     -0.154 0.028 0.464 0.000 0.000 0.508
#> SRR975561     2  0.0880      0.951 0.000 0.968 0.000 0.000 0.032
#> SRR975562     5  0.4300      0.689 0.476 0.000 0.000 0.000 0.524
#> SRR975563     2  0.0794      0.953 0.000 0.972 0.000 0.000 0.028
#> SRR975564     1  0.3895      0.557 0.680 0.000 0.000 0.000 0.320
#> SRR975565     1  0.0880      0.688 0.968 0.000 0.000 0.000 0.032
#> SRR975566     1  0.2124      0.693 0.916 0.000 0.000 0.028 0.056
#> SRR975567     4  0.5654      0.513 0.288 0.080 0.000 0.620 0.012
#> SRR975568     1  0.3796      0.579 0.700 0.000 0.000 0.000 0.300
#> SRR975569     2  0.0290      0.960 0.000 0.992 0.000 0.000 0.008
#> SRR975570     2  0.0000      0.960 0.000 1.000 0.000 0.000 0.000
#> SRR975571     2  0.0703      0.957 0.000 0.976 0.000 0.000 0.024
#> SRR975572     2  0.0162      0.960 0.000 0.996 0.000 0.000 0.004
#> SRR975573     2  0.0703      0.957 0.000 0.976 0.000 0.000 0.024
#> SRR975574     2  0.0703      0.957 0.000 0.976 0.000 0.000 0.024
#> SRR975575     2  0.0162      0.960 0.000 0.996 0.000 0.000 0.004
#> SRR975576     2  0.0703      0.954 0.000 0.976 0.000 0.000 0.024
#> SRR975577     2  0.0609      0.958 0.000 0.980 0.000 0.000 0.020
#> SRR975578     2  0.0880      0.957 0.000 0.968 0.000 0.000 0.032
#> SRR975579     4  0.0451      0.736 0.000 0.004 0.000 0.988 0.008
#> SRR975580     2  0.4161      0.417 0.000 0.608 0.000 0.000 0.392
#> SRR975581     2  0.0510      0.957 0.000 0.984 0.000 0.000 0.016
#> SRR975582     2  0.0609      0.958 0.000 0.980 0.000 0.000 0.020
#> SRR975583     2  0.0162      0.960 0.000 0.996 0.000 0.000 0.004
#> SRR975584     2  0.0794      0.956 0.000 0.972 0.000 0.000 0.028
#> SRR975585     2  0.0290      0.959 0.000 0.992 0.000 0.000 0.008
#> SRR975586     2  0.1671      0.920 0.000 0.924 0.000 0.000 0.076
#> SRR975587     3  0.0609      0.966 0.020 0.000 0.980 0.000 0.000
#> SRR975588     2  0.0000      0.960 0.000 1.000 0.000 0.000 0.000
#> SRR975589     1  0.3452      0.610 0.756 0.000 0.000 0.000 0.244
#> SRR975590     1  0.1768      0.693 0.924 0.000 0.004 0.000 0.072
#> SRR975591     3  0.0000      0.981 0.000 0.000 1.000 0.000 0.000
#> SRR975592     1  0.2378      0.687 0.904 0.000 0.048 0.000 0.048
#> SRR975593     1  0.3386      0.588 0.832 0.000 0.000 0.040 0.128
#> SRR975594     3  0.0000      0.981 0.000 0.000 1.000 0.000 0.000
#> SRR975595     5  0.4306      0.672 0.492 0.000 0.000 0.000 0.508
#> SRR975597     1  0.2813      0.512 0.832 0.000 0.000 0.000 0.168
#> SRR975596     5  0.4902      0.677 0.468 0.000 0.000 0.024 0.508
#> SRR975598     5  0.4297      0.690 0.472 0.000 0.000 0.000 0.528
#> SRR975599     5  0.4300      0.690 0.476 0.000 0.000 0.000 0.524
#> SRR975600     1  0.6433      0.264 0.488 0.000 0.200 0.000 0.312
#> SRR975601     3  0.0000      0.981 0.000 0.000 1.000 0.000 0.000
#> SRR975602     1  0.2813      0.510 0.832 0.000 0.000 0.000 0.168
#> SRR975603     3  0.1469      0.932 0.036 0.000 0.948 0.000 0.016
#> SRR975604     3  0.0000      0.981 0.000 0.000 1.000 0.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> SRR975551     1  0.0692     0.7325 0.976 0.000 0.000 0.000 0.004 0.020
#> SRR975552     1  0.1713     0.7179 0.928 0.000 0.000 0.000 0.028 0.044
#> SRR975554     1  0.3707     0.4258 0.680 0.000 0.000 0.000 0.312 0.008
#> SRR975553     2  0.1418     0.9147 0.000 0.944 0.000 0.000 0.024 0.032
#> SRR975555     1  0.6077    -0.0898 0.400 0.000 0.000 0.000 0.304 0.296
#> SRR975556     2  0.4853     0.6985 0.012 0.692 0.000 0.000 0.124 0.172
#> SRR975557     4  0.0000     0.7665 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR975558     5  0.4849     0.4916 0.000 0.016 0.000 0.156 0.700 0.128
#> SRR975559     4  0.4955     0.3630 0.296 0.000 0.000 0.608 0.000 0.096
#> SRR975560     6  0.4105     0.4629 0.008 0.196 0.000 0.012 0.032 0.752
#> SRR975561     2  0.2882     0.8641 0.000 0.860 0.000 0.004 0.060 0.076
#> SRR975562     6  0.3617     0.7066 0.244 0.000 0.000 0.000 0.020 0.736
#> SRR975563     2  0.3458     0.8225 0.000 0.808 0.000 0.000 0.080 0.112
#> SRR975564     5  0.3253     0.7560 0.192 0.000 0.000 0.000 0.788 0.020
#> SRR975565     1  0.2066     0.7125 0.904 0.000 0.000 0.000 0.072 0.024
#> SRR975566     1  0.2848     0.6587 0.828 0.000 0.000 0.004 0.160 0.008
#> SRR975567     4  0.4226     0.6790 0.036 0.088 0.000 0.796 0.064 0.016
#> SRR975568     5  0.3259     0.7448 0.216 0.000 0.000 0.000 0.772 0.012
#> SRR975569     2  0.0146     0.9210 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR975570     2  0.1074     0.9173 0.000 0.960 0.000 0.000 0.028 0.012
#> SRR975571     2  0.1418     0.9147 0.000 0.944 0.000 0.000 0.024 0.032
#> SRR975572     2  0.0405     0.9211 0.000 0.988 0.000 0.000 0.004 0.008
#> SRR975573     2  0.1341     0.9158 0.000 0.948 0.000 0.000 0.024 0.028
#> SRR975574     2  0.1341     0.9158 0.000 0.948 0.000 0.000 0.024 0.028
#> SRR975575     2  0.0508     0.9208 0.000 0.984 0.000 0.000 0.004 0.012
#> SRR975576     2  0.1720     0.9035 0.000 0.928 0.000 0.000 0.040 0.032
#> SRR975577     2  0.1341     0.9158 0.000 0.948 0.000 0.000 0.024 0.028
#> SRR975578     2  0.1418     0.9160 0.000 0.944 0.000 0.000 0.024 0.032
#> SRR975579     4  0.0000     0.7665 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR975580     6  0.4004     0.3797 0.012 0.328 0.000 0.000 0.004 0.656
#> SRR975581     2  0.1245     0.9153 0.000 0.952 0.000 0.000 0.016 0.032
#> SRR975582     2  0.1341     0.9158 0.000 0.948 0.000 0.000 0.024 0.028
#> SRR975583     2  0.0914     0.9193 0.000 0.968 0.000 0.000 0.016 0.016
#> SRR975584     2  0.1492     0.9131 0.000 0.940 0.000 0.000 0.024 0.036
#> SRR975585     2  0.0622     0.9205 0.000 0.980 0.000 0.000 0.012 0.008
#> SRR975586     2  0.4865     0.6740 0.004 0.672 0.000 0.000 0.128 0.196
#> SRR975587     3  0.3409     0.5723 0.300 0.000 0.700 0.000 0.000 0.000
#> SRR975588     2  0.1245     0.9157 0.000 0.952 0.000 0.000 0.032 0.016
#> SRR975589     5  0.3320     0.7494 0.212 0.000 0.000 0.000 0.772 0.016
#> SRR975590     1  0.1151     0.7366 0.956 0.000 0.012 0.000 0.032 0.000
#> SRR975591     3  0.1267     0.8292 0.000 0.000 0.940 0.000 0.060 0.000
#> SRR975592     1  0.4993     0.1568 0.572 0.000 0.084 0.000 0.344 0.000
#> SRR975593     5  0.6235     0.1480 0.364 0.000 0.000 0.016 0.424 0.196
#> SRR975594     3  0.0000     0.8430 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975595     6  0.3866     0.3584 0.484 0.000 0.000 0.000 0.000 0.516
#> SRR975597     1  0.1584     0.7120 0.928 0.000 0.000 0.000 0.008 0.064
#> SRR975596     6  0.4568     0.6950 0.232 0.000 0.000 0.036 0.032 0.700
#> SRR975598     6  0.3729     0.6763 0.296 0.000 0.000 0.000 0.012 0.692
#> SRR975599     6  0.3582     0.7057 0.252 0.000 0.000 0.000 0.016 0.732
#> SRR975600     5  0.3551     0.7238 0.148 0.000 0.060 0.000 0.792 0.000
#> SRR975601     3  0.0000     0.8430 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975602     1  0.1524     0.7190 0.932 0.000 0.000 0.000 0.008 0.060
#> SRR975603     3  0.3198     0.6132 0.000 0.000 0.740 0.000 0.260 0.000
#> SRR975604     3  0.0405     0.8410 0.000 0.000 0.988 0.000 0.008 0.004

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

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

consensus_heatmap(res, k = 2)

plot of chunk tab-MAD-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

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 17171 rows and 54 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'hclust' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 3.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk ATC-hclust-collect-plots

The plots are:

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

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

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

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

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

select_partition_number(res)

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

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           1.000       1.000         0.5099 0.491   0.491
#> 3 3 1.000           0.987       0.994         0.0780 0.965   0.929
#> 4 4 0.821           0.761       0.857         0.1529 0.874   0.724
#> 5 5 0.846           0.893       0.951         0.0785 0.904   0.741
#> 6 6 0.746           0.752       0.871         0.0759 0.947   0.833

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

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

suggest_best_k(res)

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

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

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

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

show/hide code output

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

#>           class entropy silhouette p1 p2
#> SRR975551     1       0          1  1  0
#> SRR975552     1       0          1  1  0
#> SRR975554     1       0          1  1  0
#> SRR975553     2       0          1  0  1
#> SRR975555     1       0          1  1  0
#> SRR975556     2       0          1  0  1
#> SRR975557     2       0          1  0  1
#> SRR975558     1       0          1  1  0
#> SRR975559     1       0          1  1  0
#> SRR975560     2       0          1  0  1
#> SRR975561     2       0          1  0  1
#> SRR975562     1       0          1  1  0
#> SRR975563     2       0          1  0  1
#> SRR975564     1       0          1  1  0
#> SRR975565     1       0          1  1  0
#> SRR975566     1       0          1  1  0
#> SRR975567     1       0          1  1  0
#> SRR975568     1       0          1  1  0
#> SRR975569     2       0          1  0  1
#> SRR975570     2       0          1  0  1
#> SRR975571     2       0          1  0  1
#> SRR975572     2       0          1  0  1
#> SRR975573     2       0          1  0  1
#> SRR975574     2       0          1  0  1
#> SRR975575     2       0          1  0  1
#> SRR975576     2       0          1  0  1
#> SRR975577     2       0          1  0  1
#> SRR975578     2       0          1  0  1
#> SRR975579     2       0          1  0  1
#> SRR975580     2       0          1  0  1
#> SRR975581     2       0          1  0  1
#> SRR975582     2       0          1  0  1
#> SRR975583     2       0          1  0  1
#> SRR975584     2       0          1  0  1
#> SRR975585     2       0          1  0  1
#> SRR975586     2       0          1  0  1
#> SRR975587     1       0          1  1  0
#> SRR975588     2       0          1  0  1
#> SRR975589     1       0          1  1  0
#> SRR975590     1       0          1  1  0
#> SRR975591     1       0          1  1  0
#> SRR975592     1       0          1  1  0
#> SRR975593     1       0          1  1  0
#> SRR975594     2       0          1  0  1
#> SRR975595     1       0          1  1  0
#> SRR975597     1       0          1  1  0
#> SRR975596     1       0          1  1  0
#> SRR975598     1       0          1  1  0
#> SRR975599     2       0          1  0  1
#> SRR975600     1       0          1  1  0
#> SRR975601     1       0          1  1  0
#> SRR975602     1       0          1  1  0
#> SRR975603     1       0          1  1  0
#> SRR975604     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
#> SRR975551     1   0.000      1.000  1 0.000 0.000
#> SRR975552     1   0.000      1.000  1 0.000 0.000
#> SRR975554     1   0.000      1.000  1 0.000 0.000
#> SRR975553     2   0.000      0.986  0 1.000 0.000
#> SRR975555     1   0.000      1.000  1 0.000 0.000
#> SRR975556     2   0.000      0.986  0 1.000 0.000
#> SRR975557     2   0.510      0.679  0 0.752 0.248
#> SRR975558     1   0.000      1.000  1 0.000 0.000
#> SRR975559     1   0.000      1.000  1 0.000 0.000
#> SRR975560     2   0.000      0.986  0 1.000 0.000
#> SRR975561     2   0.000      0.986  0 1.000 0.000
#> SRR975562     1   0.000      1.000  1 0.000 0.000
#> SRR975563     2   0.000      0.986  0 1.000 0.000
#> SRR975564     1   0.000      1.000  1 0.000 0.000
#> SRR975565     1   0.000      1.000  1 0.000 0.000
#> SRR975566     1   0.000      1.000  1 0.000 0.000
#> SRR975567     1   0.000      1.000  1 0.000 0.000
#> SRR975568     1   0.000      1.000  1 0.000 0.000
#> SRR975569     2   0.000      0.986  0 1.000 0.000
#> SRR975570     2   0.000      0.986  0 1.000 0.000
#> SRR975571     2   0.000      0.986  0 1.000 0.000
#> SRR975572     2   0.000      0.986  0 1.000 0.000
#> SRR975573     2   0.000      0.986  0 1.000 0.000
#> SRR975574     2   0.000      0.986  0 1.000 0.000
#> SRR975575     2   0.000      0.986  0 1.000 0.000
#> SRR975576     2   0.000      0.986  0 1.000 0.000
#> SRR975577     2   0.000      0.986  0 1.000 0.000
#> SRR975578     2   0.000      0.986  0 1.000 0.000
#> SRR975579     2   0.245      0.912  0 0.924 0.076
#> SRR975580     2   0.000      0.986  0 1.000 0.000
#> SRR975581     2   0.000      0.986  0 1.000 0.000
#> SRR975582     2   0.000      0.986  0 1.000 0.000
#> SRR975583     2   0.000      0.986  0 1.000 0.000
#> SRR975584     2   0.000      0.986  0 1.000 0.000
#> SRR975585     2   0.000      0.986  0 1.000 0.000
#> SRR975586     2   0.000      0.986  0 1.000 0.000
#> SRR975587     1   0.000      1.000  1 0.000 0.000
#> SRR975588     2   0.000      0.986  0 1.000 0.000
#> SRR975589     1   0.000      1.000  1 0.000 0.000
#> SRR975590     1   0.000      1.000  1 0.000 0.000
#> SRR975591     1   0.000      1.000  1 0.000 0.000
#> SRR975592     1   0.000      1.000  1 0.000 0.000
#> SRR975593     1   0.000      1.000  1 0.000 0.000
#> SRR975594     3   0.000      1.000  0 0.000 1.000
#> SRR975595     1   0.000      1.000  1 0.000 0.000
#> SRR975597     1   0.000      1.000  1 0.000 0.000
#> SRR975596     1   0.000      1.000  1 0.000 0.000
#> SRR975598     1   0.000      1.000  1 0.000 0.000
#> SRR975599     3   0.000      1.000  0 0.000 1.000
#> SRR975600     1   0.000      1.000  1 0.000 0.000
#> SRR975601     1   0.000      1.000  1 0.000 0.000
#> SRR975602     1   0.000      1.000  1 0.000 0.000
#> SRR975603     1   0.000      1.000  1 0.000 0.000
#> SRR975604     1   0.000      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
#> SRR975551     1   0.464      0.944 0.656 0.000 0.344 0.000
#> SRR975552     1   0.464      0.944 0.656 0.000 0.344 0.000
#> SRR975554     1   0.464      0.944 0.656 0.000 0.344 0.000
#> SRR975553     2   0.000      0.958 0.000 1.000 0.000 0.000
#> SRR975555     3   0.499     -0.539 0.476 0.000 0.524 0.000
#> SRR975556     2   0.000      0.958 0.000 1.000 0.000 0.000
#> SRR975557     2   0.778     -0.133 0.344 0.408 0.000 0.248
#> SRR975558     3   0.000      0.693 0.000 0.000 1.000 0.000
#> SRR975559     1   0.476      0.911 0.628 0.000 0.372 0.000
#> SRR975560     2   0.000      0.958 0.000 1.000 0.000 0.000
#> SRR975561     2   0.000      0.958 0.000 1.000 0.000 0.000
#> SRR975562     3   0.130      0.668 0.044 0.000 0.956 0.000
#> SRR975563     2   0.000      0.958 0.000 1.000 0.000 0.000
#> SRR975564     3   0.498     -0.502 0.464 0.000 0.536 0.000
#> SRR975565     1   0.464      0.944 0.656 0.000 0.344 0.000
#> SRR975566     1   0.464      0.944 0.656 0.000 0.344 0.000
#> SRR975567     3   0.000      0.693 0.000 0.000 1.000 0.000
#> SRR975568     3   0.499     -0.515 0.468 0.000 0.532 0.000
#> SRR975569     2   0.000      0.958 0.000 1.000 0.000 0.000
#> SRR975570     2   0.000      0.958 0.000 1.000 0.000 0.000
#> SRR975571     2   0.000      0.958 0.000 1.000 0.000 0.000
#> SRR975572     2   0.000      0.958 0.000 1.000 0.000 0.000
#> SRR975573     2   0.000      0.958 0.000 1.000 0.000 0.000
#> SRR975574     2   0.000      0.958 0.000 1.000 0.000 0.000
#> SRR975575     2   0.000      0.958 0.000 1.000 0.000 0.000
#> SRR975576     2   0.000      0.958 0.000 1.000 0.000 0.000
#> SRR975577     2   0.000      0.958 0.000 1.000 0.000 0.000
#> SRR975578     2   0.000      0.958 0.000 1.000 0.000 0.000
#> SRR975579     2   0.634      0.371 0.344 0.580 0.000 0.076
#> SRR975580     2   0.000      0.958 0.000 1.000 0.000 0.000
#> SRR975581     2   0.000      0.958 0.000 1.000 0.000 0.000
#> SRR975582     2   0.000      0.958 0.000 1.000 0.000 0.000
#> SRR975583     2   0.000      0.958 0.000 1.000 0.000 0.000
#> SRR975584     2   0.000      0.958 0.000 1.000 0.000 0.000
#> SRR975585     2   0.000      0.958 0.000 1.000 0.000 0.000
#> SRR975586     2   0.000      0.958 0.000 1.000 0.000 0.000
#> SRR975587     1   0.464      0.944 0.656 0.000 0.344 0.000
#> SRR975588     2   0.000      0.958 0.000 1.000 0.000 0.000
#> SRR975589     1   0.500      0.596 0.508 0.000 0.492 0.000
#> SRR975590     1   0.464      0.944 0.656 0.000 0.344 0.000
#> SRR975591     3   0.000      0.693 0.000 0.000 1.000 0.000
#> SRR975592     1   0.464      0.944 0.656 0.000 0.344 0.000
#> SRR975593     1   0.500      0.596 0.508 0.000 0.492 0.000
#> SRR975594     4   0.000      1.000 0.000 0.000 0.000 1.000
#> SRR975595     1   0.476      0.911 0.628 0.000 0.372 0.000
#> SRR975597     1   0.464      0.944 0.656 0.000 0.344 0.000
#> SRR975596     3   0.130      0.668 0.044 0.000 0.956 0.000
#> SRR975598     1   0.468      0.934 0.648 0.000 0.352 0.000
#> SRR975599     4   0.000      1.000 0.000 0.000 0.000 1.000
#> SRR975600     3   0.498     -0.502 0.464 0.000 0.536 0.000
#> SRR975601     3   0.000      0.693 0.000 0.000 1.000 0.000
#> SRR975602     1   0.464      0.944 0.656 0.000 0.344 0.000
#> SRR975603     3   0.000      0.693 0.000 0.000 1.000 0.000
#> SRR975604     3   0.000      0.693 0.000 0.000 1.000 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
#> SRR975551     1   0.000      0.874 1.000 0.00 0.000 0.00  0
#> SRR975552     1   0.000      0.874 1.000 0.00 0.000 0.00  0
#> SRR975554     1   0.000      0.874 1.000 0.00 0.000 0.00  0
#> SRR975553     2   0.000      1.000 0.000 1.00 0.000 0.00  0
#> SRR975555     1   0.377      0.680 0.704 0.00 0.296 0.00  0
#> SRR975556     2   0.000      1.000 0.000 1.00 0.000 0.00  0
#> SRR975557     4   0.000      0.530 0.000 0.00 0.000 1.00  0
#> SRR975558     3   0.000      0.892 0.000 0.00 1.000 0.00  0
#> SRR975559     1   0.265      0.806 0.848 0.00 0.152 0.00  0
#> SRR975560     2   0.000      1.000 0.000 1.00 0.000 0.00  0
#> SRR975561     2   0.000      1.000 0.000 1.00 0.000 0.00  0
#> SRR975562     3   0.337      0.672 0.232 0.00 0.768 0.00  0
#> SRR975563     2   0.000      1.000 0.000 1.00 0.000 0.00  0
#> SRR975564     1   0.386      0.660 0.688 0.00 0.312 0.00  0
#> SRR975565     1   0.000      0.874 1.000 0.00 0.000 0.00  0
#> SRR975566     1   0.000      0.874 1.000 0.00 0.000 0.00  0
#> SRR975567     3   0.000      0.892 0.000 0.00 1.000 0.00  0
#> SRR975568     1   0.384      0.666 0.692 0.00 0.308 0.00  0
#> SRR975569     2   0.000      1.000 0.000 1.00 0.000 0.00  0
#> SRR975570     2   0.000      1.000 0.000 1.00 0.000 0.00  0
#> SRR975571     2   0.000      1.000 0.000 1.00 0.000 0.00  0
#> SRR975572     2   0.000      1.000 0.000 1.00 0.000 0.00  0
#> SRR975573     2   0.000      1.000 0.000 1.00 0.000 0.00  0
#> SRR975574     2   0.000      1.000 0.000 1.00 0.000 0.00  0
#> SRR975575     2   0.000      1.000 0.000 1.00 0.000 0.00  0
#> SRR975576     2   0.000      1.000 0.000 1.00 0.000 0.00  0
#> SRR975577     2   0.000      1.000 0.000 1.00 0.000 0.00  0
#> SRR975578     2   0.000      1.000 0.000 1.00 0.000 0.00  0
#> SRR975579     4   0.293      0.572 0.000 0.18 0.000 0.82  0
#> SRR975580     2   0.000      1.000 0.000 1.00 0.000 0.00  0
#> SRR975581     2   0.000      1.000 0.000 1.00 0.000 0.00  0
#> SRR975582     2   0.000      1.000 0.000 1.00 0.000 0.00  0
#> SRR975583     2   0.000      1.000 0.000 1.00 0.000 0.00  0
#> SRR975584     2   0.000      1.000 0.000 1.00 0.000 0.00  0
#> SRR975585     2   0.000      1.000 0.000 1.00 0.000 0.00  0
#> SRR975586     2   0.000      1.000 0.000 1.00 0.000 0.00  0
#> SRR975587     1   0.000      0.874 1.000 0.00 0.000 0.00  0
#> SRR975588     2   0.000      1.000 0.000 1.00 0.000 0.00  0
#> SRR975589     1   0.307      0.775 0.804 0.00 0.196 0.00  0
#> SRR975590     1   0.000      0.874 1.000 0.00 0.000 0.00  0
#> SRR975591     3   0.000      0.892 0.000 0.00 1.000 0.00  0
#> SRR975592     1   0.000      0.874 1.000 0.00 0.000 0.00  0
#> SRR975593     1   0.307      0.775 0.804 0.00 0.196 0.00  0
#> SRR975594     5   0.000      1.000 0.000 0.00 0.000 0.00  1
#> SRR975595     1   0.265      0.806 0.848 0.00 0.152 0.00  0
#> SRR975597     1   0.000      0.874 1.000 0.00 0.000 0.00  0
#> SRR975596     3   0.337      0.672 0.232 0.00 0.768 0.00  0
#> SRR975598     1   0.154      0.851 0.932 0.00 0.068 0.00  0
#> SRR975599     5   0.000      1.000 0.000 0.00 0.000 0.00  1
#> SRR975600     1   0.386      0.660 0.688 0.00 0.312 0.00  0
#> SRR975601     3   0.000      0.892 0.000 0.00 1.000 0.00  0
#> SRR975602     1   0.000      0.874 1.000 0.00 0.000 0.00  0
#> SRR975603     3   0.000      0.892 0.000 0.00 1.000 0.00  0
#> SRR975604     3   0.000      0.892 0.000 0.00 1.000 0.00  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
#> SRR975551     1  0.2048      0.789 0.880 0.000 0.000 0.00  0 0.120
#> SRR975552     1  0.2048      0.789 0.880 0.000 0.000 0.00  0 0.120
#> SRR975554     1  0.2048      0.789 0.880 0.000 0.000 0.00  0 0.120
#> SRR975553     2  0.0000      0.885 0.000 1.000 0.000 0.00  0 0.000
#> SRR975555     1  0.4281      0.668 0.704 0.000 0.228 0.00  0 0.068
#> SRR975556     6  0.3851      0.991 0.000 0.460 0.000 0.00  0 0.540
#> SRR975557     4  0.0000      0.530 0.000 0.000 0.000 1.00  0 0.000
#> SRR975558     3  0.3244      0.706 0.000 0.000 0.732 0.00  0 0.268
#> SRR975559     1  0.3626      0.736 0.788 0.000 0.144 0.00  0 0.068
#> SRR975560     6  0.3847      0.997 0.000 0.456 0.000 0.00  0 0.544
#> SRR975561     2  0.3620     -0.390 0.000 0.648 0.000 0.00  0 0.352
#> SRR975562     3  0.3874      0.685 0.172 0.000 0.760 0.00  0 0.068
#> SRR975563     2  0.0000      0.885 0.000 1.000 0.000 0.00  0 0.000
#> SRR975564     1  0.4377      0.650 0.688 0.000 0.244 0.00  0 0.068
#> SRR975565     1  0.2048      0.789 0.880 0.000 0.000 0.00  0 0.120
#> SRR975566     1  0.0865      0.820 0.964 0.000 0.000 0.00  0 0.036
#> SRR975567     3  0.3244      0.706 0.000 0.000 0.732 0.00  0 0.268
#> SRR975568     1  0.4354      0.655 0.692 0.000 0.240 0.00  0 0.068
#> SRR975569     2  0.0000      0.885 0.000 1.000 0.000 0.00  0 0.000
#> SRR975570     2  0.0000      0.885 0.000 1.000 0.000 0.00  0 0.000
#> SRR975571     2  0.0000      0.885 0.000 1.000 0.000 0.00  0 0.000
#> SRR975572     2  0.0000      0.885 0.000 1.000 0.000 0.00  0 0.000
#> SRR975573     2  0.0000      0.885 0.000 1.000 0.000 0.00  0 0.000
#> SRR975574     2  0.0000      0.885 0.000 1.000 0.000 0.00  0 0.000
#> SRR975575     2  0.0000      0.885 0.000 1.000 0.000 0.00  0 0.000
#> SRR975576     2  0.0000      0.885 0.000 1.000 0.000 0.00  0 0.000
#> SRR975577     2  0.3620     -0.390 0.000 0.648 0.000 0.00  0 0.352
#> SRR975578     2  0.3620     -0.390 0.000 0.648 0.000 0.00  0 0.352
#> SRR975579     4  0.2631      0.572 0.000 0.180 0.000 0.82  0 0.000
#> SRR975580     6  0.3847      0.997 0.000 0.456 0.000 0.00  0 0.544
#> SRR975581     2  0.0000      0.885 0.000 1.000 0.000 0.00  0 0.000
#> SRR975582     2  0.0000      0.885 0.000 1.000 0.000 0.00  0 0.000
#> SRR975583     2  0.0000      0.885 0.000 1.000 0.000 0.00  0 0.000
#> SRR975584     2  0.0000      0.885 0.000 1.000 0.000 0.00  0 0.000
#> SRR975585     2  0.0000      0.885 0.000 1.000 0.000 0.00  0 0.000
#> SRR975586     6  0.3847      0.997 0.000 0.456 0.000 0.00  0 0.544
#> SRR975587     1  0.0000      0.823 1.000 0.000 0.000 0.00  0 0.000
#> SRR975588     2  0.0000      0.885 0.000 1.000 0.000 0.00  0 0.000
#> SRR975589     1  0.3283      0.748 0.804 0.000 0.160 0.00  0 0.036
#> SRR975590     1  0.2048      0.789 0.880 0.000 0.000 0.00  0 0.120
#> SRR975591     3  0.0000      0.829 0.000 0.000 1.000 0.00  0 0.000
#> SRR975592     1  0.0000      0.823 1.000 0.000 0.000 0.00  0 0.000
#> SRR975593     1  0.3283      0.748 0.804 0.000 0.160 0.00  0 0.036
#> SRR975594     5  0.0000      1.000 0.000 0.000 0.000 0.00  1 0.000
#> SRR975595     1  0.3626      0.736 0.788 0.000 0.144 0.00  0 0.068
#> SRR975597     1  0.0363      0.822 0.988 0.000 0.000 0.00  0 0.012
#> SRR975596     3  0.3874      0.685 0.172 0.000 0.760 0.00  0 0.068
#> SRR975598     1  0.2629      0.796 0.872 0.000 0.060 0.00  0 0.068
#> SRR975599     5  0.0000      1.000 0.000 0.000 0.000 0.00  1 0.000
#> SRR975600     1  0.4377      0.650 0.688 0.000 0.244 0.00  0 0.068
#> SRR975601     3  0.0000      0.829 0.000 0.000 1.000 0.00  0 0.000
#> SRR975602     1  0.0865      0.820 0.964 0.000 0.000 0.00  0 0.036
#> SRR975603     3  0.0000      0.829 0.000 0.000 1.000 0.00  0 0.000
#> SRR975604     3  0.0000      0.829 0.000 0.000 1.000 0.00  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

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 17171 rows and 54 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'kmeans' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 3.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk ATC-kmeans-collect-plots

The plots are:

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

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

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

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

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

select_partition_number(res)

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

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           1.000       1.000         0.5099 0.491   0.491
#> 3 3 0.904           0.932       0.968         0.1661 0.929   0.857
#> 4 4 0.815           0.846       0.892         0.1281 0.874   0.707
#> 5 5 0.689           0.747       0.834         0.0824 0.954   0.854
#> 6 6 0.731           0.710       0.813         0.0506 0.979   0.924

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

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

suggest_best_k(res)

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

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

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

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

show/hide code output

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

#>           class entropy silhouette p1 p2
#> SRR975551     1       0          1  1  0
#> SRR975552     1       0          1  1  0
#> SRR975554     1       0          1  1  0
#> SRR975553     2       0          1  0  1
#> SRR975555     1       0          1  1  0
#> SRR975556     2       0          1  0  1
#> SRR975557     2       0          1  0  1
#> SRR975558     1       0          1  1  0
#> SRR975559     1       0          1  1  0
#> SRR975560     2       0          1  0  1
#> SRR975561     2       0          1  0  1
#> SRR975562     1       0          1  1  0
#> SRR975563     2       0          1  0  1
#> SRR975564     1       0          1  1  0
#> SRR975565     1       0          1  1  0
#> SRR975566     1       0          1  1  0
#> SRR975567     1       0          1  1  0
#> SRR975568     1       0          1  1  0
#> SRR975569     2       0          1  0  1
#> SRR975570     2       0          1  0  1
#> SRR975571     2       0          1  0  1
#> SRR975572     2       0          1  0  1
#> SRR975573     2       0          1  0  1
#> SRR975574     2       0          1  0  1
#> SRR975575     2       0          1  0  1
#> SRR975576     2       0          1  0  1
#> SRR975577     2       0          1  0  1
#> SRR975578     2       0          1  0  1
#> SRR975579     2       0          1  0  1
#> SRR975580     2       0          1  0  1
#> SRR975581     2       0          1  0  1
#> SRR975582     2       0          1  0  1
#> SRR975583     2       0          1  0  1
#> SRR975584     2       0          1  0  1
#> SRR975585     2       0          1  0  1
#> SRR975586     2       0          1  0  1
#> SRR975587     1       0          1  1  0
#> SRR975588     2       0          1  0  1
#> SRR975589     1       0          1  1  0
#> SRR975590     1       0          1  1  0
#> SRR975591     1       0          1  1  0
#> SRR975592     1       0          1  1  0
#> SRR975593     1       0          1  1  0
#> SRR975594     2       0          1  0  1
#> SRR975595     1       0          1  1  0
#> SRR975597     1       0          1  1  0
#> SRR975596     1       0          1  1  0
#> SRR975598     1       0          1  1  0
#> SRR975599     2       0          1  0  1
#> SRR975600     1       0          1  1  0
#> SRR975601     1       0          1  1  0
#> SRR975602     1       0          1  1  0
#> SRR975603     1       0          1  1  0
#> SRR975604     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
#> SRR975551     1  0.0000      0.947 1.000 0.000 0.000
#> SRR975552     1  0.0000      0.947 1.000 0.000 0.000
#> SRR975554     1  0.0000      0.947 1.000 0.000 0.000
#> SRR975553     2  0.0000      0.985 0.000 1.000 0.000
#> SRR975555     1  0.0000      0.947 1.000 0.000 0.000
#> SRR975556     2  0.0000      0.985 0.000 1.000 0.000
#> SRR975557     3  0.0424      0.959 0.000 0.008 0.992
#> SRR975558     1  0.4002      0.819 0.840 0.000 0.160
#> SRR975559     1  0.0000      0.947 1.000 0.000 0.000
#> SRR975560     2  0.3551      0.863 0.000 0.868 0.132
#> SRR975561     2  0.1529      0.955 0.000 0.960 0.040
#> SRR975562     1  0.3340      0.859 0.880 0.000 0.120
#> SRR975563     2  0.0000      0.985 0.000 1.000 0.000
#> SRR975564     1  0.0000      0.947 1.000 0.000 0.000
#> SRR975565     1  0.0000      0.947 1.000 0.000 0.000
#> SRR975566     1  0.0000      0.947 1.000 0.000 0.000
#> SRR975567     1  0.0424      0.942 0.992 0.000 0.008
#> SRR975568     1  0.0000      0.947 1.000 0.000 0.000
#> SRR975569     2  0.0000      0.985 0.000 1.000 0.000
#> SRR975570     2  0.0000      0.985 0.000 1.000 0.000
#> SRR975571     2  0.0000      0.985 0.000 1.000 0.000
#> SRR975572     2  0.0000      0.985 0.000 1.000 0.000
#> SRR975573     2  0.0000      0.985 0.000 1.000 0.000
#> SRR975574     2  0.0000      0.985 0.000 1.000 0.000
#> SRR975575     2  0.0000      0.985 0.000 1.000 0.000
#> SRR975576     2  0.0000      0.985 0.000 1.000 0.000
#> SRR975577     2  0.0000      0.985 0.000 1.000 0.000
#> SRR975578     2  0.0000      0.985 0.000 1.000 0.000
#> SRR975579     2  0.3879      0.841 0.000 0.848 0.152
#> SRR975580     2  0.1529      0.955 0.000 0.960 0.040
#> SRR975581     2  0.0000      0.985 0.000 1.000 0.000
#> SRR975582     2  0.0000      0.985 0.000 1.000 0.000
#> SRR975583     2  0.0000      0.985 0.000 1.000 0.000
#> SRR975584     2  0.0000      0.985 0.000 1.000 0.000
#> SRR975585     2  0.0000      0.985 0.000 1.000 0.000
#> SRR975586     2  0.0000      0.985 0.000 1.000 0.000
#> SRR975587     1  0.0000      0.947 1.000 0.000 0.000
#> SRR975588     2  0.0000      0.985 0.000 1.000 0.000
#> SRR975589     1  0.0000      0.947 1.000 0.000 0.000
#> SRR975590     1  0.0000      0.947 1.000 0.000 0.000
#> SRR975591     1  0.6008      0.475 0.628 0.000 0.372
#> SRR975592     1  0.0000      0.947 1.000 0.000 0.000
#> SRR975593     1  0.0000      0.947 1.000 0.000 0.000
#> SRR975594     3  0.0237      0.961 0.000 0.004 0.996
#> SRR975595     1  0.0000      0.947 1.000 0.000 0.000
#> SRR975597     1  0.0000      0.947 1.000 0.000 0.000
#> SRR975596     1  0.3340      0.859 0.880 0.000 0.120
#> SRR975598     1  0.0000      0.947 1.000 0.000 0.000
#> SRR975599     3  0.0000      0.960 0.000 0.000 1.000
#> SRR975600     1  0.0000      0.947 1.000 0.000 0.000
#> SRR975601     1  0.5988      0.483 0.632 0.000 0.368
#> SRR975602     1  0.0000      0.947 1.000 0.000 0.000
#> SRR975603     1  0.3340      0.859 0.880 0.000 0.120
#> SRR975604     3  0.2796      0.881 0.092 0.000 0.908

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> SRR975551     1  0.0188      0.948 0.996 0.000 0.000 0.004
#> SRR975552     1  0.0188      0.948 0.996 0.000 0.000 0.004
#> SRR975554     1  0.0188      0.948 0.996 0.000 0.000 0.004
#> SRR975553     2  0.0000      0.931 0.000 1.000 0.000 0.000
#> SRR975555     1  0.0188      0.947 0.996 0.000 0.004 0.000
#> SRR975556     2  0.3616      0.821 0.000 0.852 0.036 0.112
#> SRR975557     4  0.1398      0.723 0.000 0.004 0.040 0.956
#> SRR975558     3  0.4741      0.885 0.328 0.000 0.668 0.004
#> SRR975559     1  0.0524      0.944 0.988 0.000 0.008 0.004
#> SRR975560     2  0.5383      0.605 0.000 0.672 0.036 0.292
#> SRR975561     2  0.4621      0.651 0.000 0.708 0.008 0.284
#> SRR975562     3  0.4855      0.896 0.352 0.000 0.644 0.004
#> SRR975563     2  0.0000      0.931 0.000 1.000 0.000 0.000
#> SRR975564     1  0.0188      0.947 0.996 0.000 0.004 0.000
#> SRR975565     1  0.0188      0.948 0.996 0.000 0.000 0.004
#> SRR975566     1  0.0000      0.949 1.000 0.000 0.000 0.000
#> SRR975567     3  0.4713      0.893 0.360 0.000 0.640 0.000
#> SRR975568     1  0.0188      0.947 0.996 0.000 0.004 0.000
#> SRR975569     2  0.0000      0.931 0.000 1.000 0.000 0.000
#> SRR975570     2  0.0000      0.931 0.000 1.000 0.000 0.000
#> SRR975571     2  0.0000      0.931 0.000 1.000 0.000 0.000
#> SRR975572     2  0.0000      0.931 0.000 1.000 0.000 0.000
#> SRR975573     2  0.0000      0.931 0.000 1.000 0.000 0.000
#> SRR975574     2  0.0000      0.931 0.000 1.000 0.000 0.000
#> SRR975575     2  0.0000      0.931 0.000 1.000 0.000 0.000
#> SRR975576     2  0.0524      0.926 0.000 0.988 0.004 0.008
#> SRR975577     2  0.0524      0.926 0.000 0.988 0.004 0.008
#> SRR975578     2  0.0524      0.926 0.000 0.988 0.004 0.008
#> SRR975579     4  0.4193      0.460 0.000 0.268 0.000 0.732
#> SRR975580     2  0.5383      0.605 0.000 0.672 0.036 0.292
#> SRR975581     2  0.0524      0.926 0.000 0.988 0.004 0.008
#> SRR975582     2  0.0000      0.931 0.000 1.000 0.000 0.000
#> SRR975583     2  0.0000      0.931 0.000 1.000 0.000 0.000
#> SRR975584     2  0.0000      0.931 0.000 1.000 0.000 0.000
#> SRR975585     2  0.0000      0.931 0.000 1.000 0.000 0.000
#> SRR975586     2  0.5052      0.677 0.000 0.720 0.036 0.244
#> SRR975587     1  0.0000      0.949 1.000 0.000 0.000 0.000
#> SRR975588     2  0.0000      0.931 0.000 1.000 0.000 0.000
#> SRR975589     1  0.0817      0.924 0.976 0.000 0.024 0.000
#> SRR975590     1  0.0188      0.948 0.996 0.000 0.000 0.004
#> SRR975591     3  0.4836      0.890 0.320 0.000 0.672 0.008
#> SRR975592     1  0.0000      0.949 1.000 0.000 0.000 0.000
#> SRR975593     1  0.4994     -0.590 0.520 0.000 0.480 0.000
#> SRR975594     4  0.4677      0.749 0.000 0.004 0.316 0.680
#> SRR975595     1  0.0524      0.944 0.988 0.000 0.008 0.004
#> SRR975597     1  0.0000      0.949 1.000 0.000 0.000 0.000
#> SRR975596     3  0.4855      0.896 0.352 0.000 0.644 0.004
#> SRR975598     1  0.0524      0.944 0.988 0.000 0.008 0.004
#> SRR975599     4  0.4677      0.749 0.000 0.004 0.316 0.680
#> SRR975600     3  0.4817      0.856 0.388 0.000 0.612 0.000
#> SRR975601     3  0.4836      0.890 0.320 0.000 0.672 0.008
#> SRR975602     1  0.0524      0.944 0.988 0.000 0.008 0.004
#> SRR975603     3  0.4697      0.896 0.356 0.000 0.644 0.000
#> SRR975604     3  0.1820      0.326 0.020 0.000 0.944 0.036

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> SRR975551     1  0.3039     0.7996 0.808 0.000 0.000 0.000 0.192
#> SRR975552     1  0.3039     0.7996 0.808 0.000 0.000 0.000 0.192
#> SRR975554     1  0.3039     0.7996 0.808 0.000 0.000 0.000 0.192
#> SRR975553     2  0.0290     0.8861 0.000 0.992 0.008 0.000 0.000
#> SRR975555     1  0.2233     0.8163 0.904 0.000 0.016 0.000 0.080
#> SRR975556     2  0.4575     0.4695 0.000 0.736 0.040 0.012 0.212
#> SRR975557     4  0.5646     0.3859 0.000 0.000 0.076 0.480 0.444
#> SRR975558     3  0.4503     0.8272 0.124 0.000 0.756 0.000 0.120
#> SRR975559     1  0.2818     0.7926 0.856 0.000 0.012 0.000 0.132
#> SRR975560     5  0.4781     0.7583 0.000 0.428 0.000 0.020 0.552
#> SRR975561     2  0.5179    -0.7076 0.000 0.496 0.012 0.020 0.472
#> SRR975562     3  0.5109     0.7936 0.172 0.000 0.696 0.000 0.132
#> SRR975563     2  0.0880     0.8836 0.000 0.968 0.032 0.000 0.000
#> SRR975564     1  0.1872     0.8210 0.928 0.000 0.020 0.000 0.052
#> SRR975565     1  0.3039     0.7996 0.808 0.000 0.000 0.000 0.192
#> SRR975566     1  0.0609     0.8417 0.980 0.000 0.000 0.000 0.020
#> SRR975567     3  0.4469     0.8386 0.148 0.000 0.756 0.000 0.096
#> SRR975568     1  0.1800     0.8227 0.932 0.000 0.020 0.000 0.048
#> SRR975569     2  0.0609     0.8840 0.000 0.980 0.020 0.000 0.000
#> SRR975570     2  0.0609     0.8840 0.000 0.980 0.020 0.000 0.000
#> SRR975571     2  0.0290     0.8861 0.000 0.992 0.008 0.000 0.000
#> SRR975572     2  0.0609     0.8840 0.000 0.980 0.020 0.000 0.000
#> SRR975573     2  0.0000     0.8867 0.000 1.000 0.000 0.000 0.000
#> SRR975574     2  0.1168     0.8715 0.000 0.960 0.032 0.008 0.000
#> SRR975575     2  0.0404     0.8874 0.000 0.988 0.012 0.000 0.000
#> SRR975576     2  0.2584     0.8222 0.000 0.900 0.040 0.008 0.052
#> SRR975577     2  0.2584     0.8222 0.000 0.900 0.040 0.008 0.052
#> SRR975578     2  0.2584     0.8222 0.000 0.900 0.040 0.008 0.052
#> SRR975579     5  0.7686     0.0902 0.000 0.208 0.076 0.272 0.444
#> SRR975580     5  0.4781     0.7583 0.000 0.428 0.000 0.020 0.552
#> SRR975581     2  0.2584     0.8222 0.000 0.900 0.040 0.008 0.052
#> SRR975582     2  0.1168     0.8715 0.000 0.960 0.032 0.008 0.000
#> SRR975583     2  0.0404     0.8861 0.000 0.988 0.012 0.000 0.000
#> SRR975584     2  0.0000     0.8867 0.000 1.000 0.000 0.000 0.000
#> SRR975585     2  0.0404     0.8861 0.000 0.988 0.012 0.000 0.000
#> SRR975586     5  0.4443     0.6842 0.000 0.472 0.000 0.004 0.524
#> SRR975587     1  0.1197     0.8414 0.952 0.000 0.000 0.000 0.048
#> SRR975588     2  0.0609     0.8840 0.000 0.980 0.020 0.000 0.000
#> SRR975589     1  0.1399     0.8306 0.952 0.000 0.020 0.000 0.028
#> SRR975590     1  0.3039     0.7996 0.808 0.000 0.000 0.000 0.192
#> SRR975591     3  0.2865     0.8532 0.132 0.000 0.856 0.008 0.004
#> SRR975592     1  0.1965     0.8337 0.904 0.000 0.000 0.000 0.096
#> SRR975593     1  0.5631    -0.2939 0.500 0.000 0.424 0.000 0.076
#> SRR975594     4  0.0404     0.7701 0.000 0.000 0.012 0.988 0.000
#> SRR975595     1  0.2771     0.7951 0.860 0.000 0.012 0.000 0.128
#> SRR975597     1  0.0880     0.8429 0.968 0.000 0.000 0.000 0.032
#> SRR975596     3  0.5109     0.7936 0.172 0.000 0.696 0.000 0.132
#> SRR975598     1  0.2864     0.7962 0.852 0.000 0.012 0.000 0.136
#> SRR975599     4  0.0404     0.7701 0.000 0.000 0.012 0.988 0.000
#> SRR975600     3  0.5142     0.6387 0.348 0.000 0.600 0.000 0.052
#> SRR975601     3  0.2865     0.8532 0.132 0.000 0.856 0.008 0.004
#> SRR975602     1  0.2513     0.7967 0.876 0.000 0.008 0.000 0.116
#> SRR975603     3  0.2648     0.8544 0.152 0.000 0.848 0.000 0.000
#> SRR975604     3  0.3031     0.7046 0.020 0.000 0.856 0.120 0.004

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5 p6
#> SRR975551     1  0.3371      0.711 0.708 0.000 0.000 0.000 0.000 NA
#> SRR975552     1  0.3371      0.711 0.708 0.000 0.000 0.000 0.000 NA
#> SRR975554     1  0.3489      0.712 0.708 0.000 0.000 0.004 0.000 NA
#> SRR975553     2  0.0405      0.881 0.000 0.988 0.008 0.000 0.000 NA
#> SRR975555     1  0.3042      0.740 0.852 0.000 0.020 0.028 0.000 NA
#> SRR975556     2  0.5105     -0.115 0.000 0.488 0.000 0.432 0.000 NA
#> SRR975557     4  0.6906     -0.161 0.000 0.000 0.048 0.336 0.300 NA
#> SRR975558     3  0.4222      0.689 0.016 0.000 0.764 0.120 0.000 NA
#> SRR975559     1  0.4339      0.690 0.736 0.000 0.004 0.140 0.000 NA
#> SRR975560     4  0.3620      0.663 0.000 0.248 0.008 0.736 0.008 NA
#> SRR975561     4  0.5311      0.516 0.000 0.344 0.000 0.556 0.008 NA
#> SRR975562     3  0.5761      0.655 0.088 0.000 0.644 0.156 0.000 NA
#> SRR975563     2  0.1757      0.865 0.000 0.916 0.000 0.008 0.000 NA
#> SRR975564     1  0.2898      0.741 0.864 0.000 0.024 0.024 0.000 NA
#> SRR975565     1  0.3489      0.712 0.708 0.000 0.000 0.004 0.000 NA
#> SRR975566     1  0.0260      0.778 0.992 0.000 0.000 0.000 0.000 NA
#> SRR975567     3  0.4468      0.737 0.076 0.000 0.764 0.060 0.000 NA
#> SRR975568     1  0.2677      0.744 0.876 0.000 0.024 0.016 0.000 NA
#> SRR975569     2  0.0603      0.880 0.000 0.980 0.004 0.000 0.000 NA
#> SRR975570     2  0.0603      0.880 0.000 0.980 0.004 0.000 0.000 NA
#> SRR975571     2  0.0405      0.881 0.000 0.988 0.008 0.000 0.000 NA
#> SRR975572     2  0.0603      0.880 0.000 0.980 0.004 0.000 0.000 NA
#> SRR975573     2  0.0146      0.882 0.000 0.996 0.004 0.000 0.000 NA
#> SRR975574     2  0.2070      0.845 0.000 0.892 0.000 0.008 0.000 NA
#> SRR975575     2  0.0865      0.880 0.000 0.964 0.000 0.000 0.000 NA
#> SRR975576     2  0.3586      0.769 0.000 0.796 0.000 0.080 0.000 NA
#> SRR975577     2  0.3586      0.769 0.000 0.796 0.000 0.080 0.000 NA
#> SRR975578     2  0.3586      0.769 0.000 0.796 0.000 0.080 0.000 NA
#> SRR975579     4  0.7943      0.221 0.000 0.120 0.048 0.344 0.156 NA
#> SRR975580     4  0.3620      0.663 0.000 0.248 0.008 0.736 0.008 NA
#> SRR975581     2  0.3586      0.769 0.000 0.796 0.000 0.080 0.000 NA
#> SRR975582     2  0.1806      0.854 0.000 0.908 0.000 0.004 0.000 NA
#> SRR975583     2  0.0363      0.882 0.000 0.988 0.000 0.000 0.000 NA
#> SRR975584     2  0.0146      0.882 0.000 0.996 0.004 0.000 0.000 NA
#> SRR975585     2  0.0363      0.882 0.000 0.988 0.000 0.000 0.000 NA
#> SRR975586     4  0.3351      0.658 0.000 0.288 0.000 0.712 0.000 NA
#> SRR975587     1  0.1285      0.779 0.944 0.000 0.000 0.004 0.000 NA
#> SRR975588     2  0.0603      0.880 0.000 0.980 0.004 0.000 0.000 NA
#> SRR975589     1  0.2249      0.753 0.900 0.000 0.032 0.004 0.000 NA
#> SRR975590     1  0.3489      0.712 0.708 0.000 0.000 0.004 0.000 NA
#> SRR975591     3  0.1471      0.785 0.064 0.000 0.932 0.000 0.004 NA
#> SRR975592     1  0.2053      0.772 0.888 0.000 0.000 0.004 0.000 NA
#> SRR975593     1  0.5841     -0.039 0.516 0.000 0.364 0.056 0.000 NA
#> SRR975594     5  0.0458      0.998 0.000 0.000 0.016 0.000 0.984 NA
#> SRR975595     1  0.4339      0.690 0.736 0.000 0.004 0.140 0.000 NA
#> SRR975597     1  0.1297      0.781 0.948 0.000 0.000 0.012 0.000 NA
#> SRR975596     3  0.5761      0.655 0.088 0.000 0.644 0.156 0.000 NA
#> SRR975598     1  0.4563      0.687 0.712 0.000 0.004 0.152 0.000 NA
#> SRR975599     5  0.0603      0.998 0.000 0.000 0.016 0.000 0.980 NA
#> SRR975600     3  0.5652      0.393 0.372 0.000 0.516 0.024 0.000 NA
#> SRR975601     3  0.1615      0.785 0.064 0.000 0.928 0.000 0.004 NA
#> SRR975602     1  0.3660      0.705 0.800 0.000 0.004 0.096 0.000 NA
#> SRR975603     3  0.1556      0.785 0.080 0.000 0.920 0.000 0.000 NA
#> SRR975604     3  0.2187      0.725 0.004 0.000 0.908 0.012 0.064 NA

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

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

consensus_heatmap(res, k = 2)

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

consensus_heatmap(res, k = 3)

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

consensus_heatmap(res, k = 4)

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

consensus_heatmap(res, k = 5)

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

consensus_heatmap(res, k = 6)

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

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

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

membership_heatmap(res, k = 2)

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

membership_heatmap(res, k = 3)

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

membership_heatmap(res, k = 4)

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

membership_heatmap(res, k = 5)

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

membership_heatmap(res, k = 6)

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

Signature heatmaps where rows are scaled:

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

get_signatures(res, k = 2)

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

get_signatures(res, k = 3)

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

get_signatures(res, k = 4)

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

get_signatures(res, k = 5)

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

get_signatures(res, k = 6)

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

Signature heatmaps where rows are not scaled:

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

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

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

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

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

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

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

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

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

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

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

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk ATC-kmeans-signature_compare

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

An example of the output of tb is:

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

The columns in tb are:

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

UMAP plot which shows how samples are separated.

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

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

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

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

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

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

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

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

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

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

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

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk ATC-kmeans-collect-classes

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 17171 rows and 54 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'skmeans' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 3.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk ATC-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         0.5099 0.491   0.491
#> 3 3 1.000           0.958       0.983         0.1546 0.929   0.857
#> 4 4 0.898           0.845       0.929         0.1279 0.886   0.736
#> 5 5 0.858           0.850       0.897         0.0507 0.939   0.815
#> 6 6 0.889           0.865       0.932         0.0427 0.992   0.970

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

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

suggest_best_k(res)

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

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

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

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

show/hide code output

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

#>           class entropy silhouette p1 p2
#> SRR975551     1       0          1  1  0
#> SRR975552     1       0          1  1  0
#> SRR975554     1       0          1  1  0
#> SRR975553     2       0          1  0  1
#> SRR975555     1       0          1  1  0
#> SRR975556     2       0          1  0  1
#> SRR975557     2       0          1  0  1
#> SRR975558     1       0          1  1  0
#> SRR975559     1       0          1  1  0
#> SRR975560     2       0          1  0  1
#> SRR975561     2       0          1  0  1
#> SRR975562     1       0          1  1  0
#> SRR975563     2       0          1  0  1
#> SRR975564     1       0          1  1  0
#> SRR975565     1       0          1  1  0
#> SRR975566     1       0          1  1  0
#> SRR975567     1       0          1  1  0
#> SRR975568     1       0          1  1  0
#> SRR975569     2       0          1  0  1
#> SRR975570     2       0          1  0  1
#> SRR975571     2       0          1  0  1
#> SRR975572     2       0          1  0  1
#> SRR975573     2       0          1  0  1
#> SRR975574     2       0          1  0  1
#> SRR975575     2       0          1  0  1
#> SRR975576     2       0          1  0  1
#> SRR975577     2       0          1  0  1
#> SRR975578     2       0          1  0  1
#> SRR975579     2       0          1  0  1
#> SRR975580     2       0          1  0  1
#> SRR975581     2       0          1  0  1
#> SRR975582     2       0          1  0  1
#> SRR975583     2       0          1  0  1
#> SRR975584     2       0          1  0  1
#> SRR975585     2       0          1  0  1
#> SRR975586     2       0          1  0  1
#> SRR975587     1       0          1  1  0
#> SRR975588     2       0          1  0  1
#> SRR975589     1       0          1  1  0
#> SRR975590     1       0          1  1  0
#> SRR975591     1       0          1  1  0
#> SRR975592     1       0          1  1  0
#> SRR975593     1       0          1  1  0
#> SRR975594     2       0          1  0  1
#> SRR975595     1       0          1  1  0
#> SRR975597     1       0          1  1  0
#> SRR975596     1       0          1  1  0
#> SRR975598     1       0          1  1  0
#> SRR975599     2       0          1  0  1
#> SRR975600     1       0          1  1  0
#> SRR975601     1       0          1  1  0
#> SRR975602     1       0          1  1  0
#> SRR975603     1       0          1  1  0
#> SRR975604     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
#> SRR975551     1  0.0000      0.963 1.000 0.000 0.000
#> SRR975552     1  0.0000      0.963 1.000 0.000 0.000
#> SRR975554     1  0.0000      0.963 1.000 0.000 0.000
#> SRR975553     2  0.0000      0.999 0.000 1.000 0.000
#> SRR975555     1  0.0000      0.963 1.000 0.000 0.000
#> SRR975556     2  0.0000      0.999 0.000 1.000 0.000
#> SRR975557     3  0.0000      0.997 0.000 0.000 1.000
#> SRR975558     1  0.0000      0.963 1.000 0.000 0.000
#> SRR975559     1  0.0000      0.963 1.000 0.000 0.000
#> SRR975560     2  0.0424      0.993 0.000 0.992 0.008
#> SRR975561     2  0.0424      0.993 0.000 0.992 0.008
#> SRR975562     1  0.0000      0.963 1.000 0.000 0.000
#> SRR975563     2  0.0000      0.999 0.000 1.000 0.000
#> SRR975564     1  0.0000      0.963 1.000 0.000 0.000
#> SRR975565     1  0.0000      0.963 1.000 0.000 0.000
#> SRR975566     1  0.0000      0.963 1.000 0.000 0.000
#> SRR975567     1  0.0000      0.963 1.000 0.000 0.000
#> SRR975568     1  0.0000      0.963 1.000 0.000 0.000
#> SRR975569     2  0.0000      0.999 0.000 1.000 0.000
#> SRR975570     2  0.0000      0.999 0.000 1.000 0.000
#> SRR975571     2  0.0000      0.999 0.000 1.000 0.000
#> SRR975572     2  0.0000      0.999 0.000 1.000 0.000
#> SRR975573     2  0.0000      0.999 0.000 1.000 0.000
#> SRR975574     2  0.0000      0.999 0.000 1.000 0.000
#> SRR975575     2  0.0000      0.999 0.000 1.000 0.000
#> SRR975576     2  0.0000      0.999 0.000 1.000 0.000
#> SRR975577     2  0.0000      0.999 0.000 1.000 0.000
#> SRR975578     2  0.0000      0.999 0.000 1.000 0.000
#> SRR975579     2  0.0424      0.993 0.000 0.992 0.008
#> SRR975580     2  0.0424      0.993 0.000 0.992 0.008
#> SRR975581     2  0.0000      0.999 0.000 1.000 0.000
#> SRR975582     2  0.0000      0.999 0.000 1.000 0.000
#> SRR975583     2  0.0000      0.999 0.000 1.000 0.000
#> SRR975584     2  0.0000      0.999 0.000 1.000 0.000
#> SRR975585     2  0.0000      0.999 0.000 1.000 0.000
#> SRR975586     2  0.0000      0.999 0.000 1.000 0.000
#> SRR975587     1  0.0000      0.963 1.000 0.000 0.000
#> SRR975588     2  0.0000      0.999 0.000 1.000 0.000
#> SRR975589     1  0.0000      0.963 1.000 0.000 0.000
#> SRR975590     1  0.0000      0.963 1.000 0.000 0.000
#> SRR975591     1  0.6095      0.395 0.608 0.000 0.392
#> SRR975592     1  0.0000      0.963 1.000 0.000 0.000
#> SRR975593     1  0.0000      0.963 1.000 0.000 0.000
#> SRR975594     3  0.0000      0.997 0.000 0.000 1.000
#> SRR975595     1  0.0000      0.963 1.000 0.000 0.000
#> SRR975597     1  0.0000      0.963 1.000 0.000 0.000
#> SRR975596     1  0.0000      0.963 1.000 0.000 0.000
#> SRR975598     1  0.0000      0.963 1.000 0.000 0.000
#> SRR975599     3  0.0000      0.997 0.000 0.000 1.000
#> SRR975600     1  0.0000      0.963 1.000 0.000 0.000
#> SRR975601     1  0.6095      0.395 0.608 0.000 0.392
#> SRR975602     1  0.0000      0.963 1.000 0.000 0.000
#> SRR975603     1  0.3267      0.850 0.884 0.000 0.116
#> SRR975604     3  0.0424      0.991 0.008 0.000 0.992

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> SRR975551     1  0.0000      0.988 1.000 0.000 0.000 0.000
#> SRR975552     1  0.0000      0.988 1.000 0.000 0.000 0.000
#> SRR975554     1  0.0000      0.988 1.000 0.000 0.000 0.000
#> SRR975553     2  0.0000      0.941 0.000 1.000 0.000 0.000
#> SRR975555     1  0.0000      0.988 1.000 0.000 0.000 0.000
#> SRR975556     2  0.0000      0.941 0.000 1.000 0.000 0.000
#> SRR975557     4  0.1118      0.529 0.000 0.000 0.036 0.964
#> SRR975558     1  0.2402      0.892 0.912 0.000 0.076 0.012
#> SRR975559     1  0.0000      0.988 1.000 0.000 0.000 0.000
#> SRR975560     4  0.4955      0.106 0.000 0.444 0.000 0.556
#> SRR975561     2  0.4746      0.361 0.000 0.632 0.000 0.368
#> SRR975562     3  0.4817      0.634 0.388 0.000 0.612 0.000
#> SRR975563     2  0.0000      0.941 0.000 1.000 0.000 0.000
#> SRR975564     1  0.0000      0.988 1.000 0.000 0.000 0.000
#> SRR975565     1  0.0000      0.988 1.000 0.000 0.000 0.000
#> SRR975566     1  0.0000      0.988 1.000 0.000 0.000 0.000
#> SRR975567     1  0.2402      0.892 0.912 0.000 0.076 0.012
#> SRR975568     1  0.0000      0.988 1.000 0.000 0.000 0.000
#> SRR975569     2  0.0000      0.941 0.000 1.000 0.000 0.000
#> SRR975570     2  0.0000      0.941 0.000 1.000 0.000 0.000
#> SRR975571     2  0.0000      0.941 0.000 1.000 0.000 0.000
#> SRR975572     2  0.0000      0.941 0.000 1.000 0.000 0.000
#> SRR975573     2  0.0000      0.941 0.000 1.000 0.000 0.000
#> SRR975574     2  0.0000      0.941 0.000 1.000 0.000 0.000
#> SRR975575     2  0.0000      0.941 0.000 1.000 0.000 0.000
#> SRR975576     2  0.0000      0.941 0.000 1.000 0.000 0.000
#> SRR975577     2  0.0000      0.941 0.000 1.000 0.000 0.000
#> SRR975578     2  0.0188      0.937 0.000 0.996 0.000 0.004
#> SRR975579     4  0.4103      0.526 0.000 0.256 0.000 0.744
#> SRR975580     2  0.4817      0.311 0.000 0.612 0.000 0.388
#> SRR975581     2  0.0000      0.941 0.000 1.000 0.000 0.000
#> SRR975582     2  0.0000      0.941 0.000 1.000 0.000 0.000
#> SRR975583     2  0.0000      0.941 0.000 1.000 0.000 0.000
#> SRR975584     2  0.0000      0.941 0.000 1.000 0.000 0.000
#> SRR975585     2  0.0000      0.941 0.000 1.000 0.000 0.000
#> SRR975586     2  0.4193      0.588 0.000 0.732 0.000 0.268
#> SRR975587     1  0.0000      0.988 1.000 0.000 0.000 0.000
#> SRR975588     2  0.0000      0.941 0.000 1.000 0.000 0.000
#> SRR975589     1  0.0188      0.985 0.996 0.000 0.004 0.000
#> SRR975590     1  0.0000      0.988 1.000 0.000 0.000 0.000
#> SRR975591     3  0.2216      0.679 0.092 0.000 0.908 0.000
#> SRR975592     1  0.0000      0.988 1.000 0.000 0.000 0.000
#> SRR975593     1  0.0188      0.985 0.996 0.000 0.004 0.000
#> SRR975594     4  0.4356      0.460 0.000 0.000 0.292 0.708
#> SRR975595     1  0.0000      0.988 1.000 0.000 0.000 0.000
#> SRR975597     1  0.0000      0.988 1.000 0.000 0.000 0.000
#> SRR975596     3  0.4817      0.634 0.388 0.000 0.612 0.000
#> SRR975598     1  0.0000      0.988 1.000 0.000 0.000 0.000
#> SRR975599     4  0.4356      0.460 0.000 0.000 0.292 0.708
#> SRR975600     1  0.0592      0.973 0.984 0.000 0.016 0.000
#> SRR975601     3  0.2281      0.681 0.096 0.000 0.904 0.000
#> SRR975602     1  0.0000      0.988 1.000 0.000 0.000 0.000
#> SRR975603     3  0.3975      0.708 0.240 0.000 0.760 0.000
#> SRR975604     3  0.1978      0.525 0.004 0.000 0.928 0.068

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> SRR975551     1  0.0162      0.977 0.996 0.000 0.000 0.000 0.004
#> SRR975552     1  0.0162      0.977 0.996 0.000 0.000 0.000 0.004
#> SRR975554     1  0.0162      0.977 0.996 0.000 0.000 0.000 0.004
#> SRR975553     2  0.0000      0.974 0.000 1.000 0.000 0.000 0.000
#> SRR975555     1  0.0290      0.976 0.992 0.000 0.000 0.000 0.008
#> SRR975556     2  0.0609      0.954 0.000 0.980 0.000 0.020 0.000
#> SRR975557     4  0.5448      0.422 0.000 0.000 0.076 0.584 0.340
#> SRR975558     5  0.4060      0.992 0.360 0.000 0.000 0.000 0.640
#> SRR975559     1  0.0510      0.969 0.984 0.000 0.000 0.000 0.016
#> SRR975560     4  0.3561      0.499 0.000 0.260 0.000 0.740 0.000
#> SRR975561     2  0.3999      0.325 0.000 0.656 0.000 0.344 0.000
#> SRR975562     3  0.4384      0.566 0.324 0.000 0.660 0.000 0.016
#> SRR975563     2  0.0000      0.974 0.000 1.000 0.000 0.000 0.000
#> SRR975564     1  0.0162      0.976 0.996 0.000 0.000 0.000 0.004
#> SRR975565     1  0.0162      0.977 0.996 0.000 0.000 0.000 0.004
#> SRR975566     1  0.0000      0.977 1.000 0.000 0.000 0.000 0.000
#> SRR975567     5  0.4074      0.992 0.364 0.000 0.000 0.000 0.636
#> SRR975568     1  0.0162      0.977 0.996 0.000 0.000 0.000 0.004
#> SRR975569     2  0.0000      0.974 0.000 1.000 0.000 0.000 0.000
#> SRR975570     2  0.0000      0.974 0.000 1.000 0.000 0.000 0.000
#> SRR975571     2  0.0000      0.974 0.000 1.000 0.000 0.000 0.000
#> SRR975572     2  0.0000      0.974 0.000 1.000 0.000 0.000 0.000
#> SRR975573     2  0.0000      0.974 0.000 1.000 0.000 0.000 0.000
#> SRR975574     2  0.0000      0.974 0.000 1.000 0.000 0.000 0.000
#> SRR975575     2  0.0000      0.974 0.000 1.000 0.000 0.000 0.000
#> SRR975576     2  0.0000      0.974 0.000 1.000 0.000 0.000 0.000
#> SRR975577     2  0.0000      0.974 0.000 1.000 0.000 0.000 0.000
#> SRR975578     2  0.0880      0.941 0.000 0.968 0.000 0.032 0.000
#> SRR975579     4  0.6564      0.508 0.000 0.236 0.000 0.468 0.296
#> SRR975580     4  0.3966      0.452 0.000 0.336 0.000 0.664 0.000
#> SRR975581     2  0.0000      0.974 0.000 1.000 0.000 0.000 0.000
#> SRR975582     2  0.0000      0.974 0.000 1.000 0.000 0.000 0.000
#> SRR975583     2  0.0000      0.974 0.000 1.000 0.000 0.000 0.000
#> SRR975584     2  0.0000      0.974 0.000 1.000 0.000 0.000 0.000
#> SRR975585     2  0.0000      0.974 0.000 1.000 0.000 0.000 0.000
#> SRR975586     4  0.4262      0.232 0.000 0.440 0.000 0.560 0.000
#> SRR975587     1  0.0404      0.970 0.988 0.000 0.012 0.000 0.000
#> SRR975588     2  0.0000      0.974 0.000 1.000 0.000 0.000 0.000
#> SRR975589     1  0.0794      0.948 0.972 0.000 0.000 0.000 0.028
#> SRR975590     1  0.0162      0.977 0.996 0.000 0.000 0.000 0.004
#> SRR975591     3  0.2260      0.748 0.064 0.000 0.908 0.000 0.028
#> SRR975592     1  0.0000      0.977 1.000 0.000 0.000 0.000 0.000
#> SRR975593     1  0.0955      0.946 0.968 0.000 0.028 0.000 0.004
#> SRR975594     4  0.6691      0.343 0.000 0.000 0.260 0.428 0.312
#> SRR975595     1  0.0510      0.969 0.984 0.000 0.000 0.000 0.016
#> SRR975597     1  0.0000      0.977 1.000 0.000 0.000 0.000 0.000
#> SRR975596     3  0.4384      0.566 0.324 0.000 0.660 0.000 0.016
#> SRR975598     1  0.0510      0.969 0.984 0.000 0.000 0.000 0.016
#> SRR975599     4  0.6691      0.343 0.000 0.000 0.260 0.428 0.312
#> SRR975600     1  0.2193      0.851 0.912 0.000 0.060 0.000 0.028
#> SRR975601     3  0.1502      0.743 0.056 0.000 0.940 0.000 0.004
#> SRR975602     1  0.0566      0.970 0.984 0.000 0.004 0.000 0.012
#> SRR975603     3  0.3452      0.731 0.148 0.000 0.820 0.000 0.032
#> SRR975604     3  0.0290      0.657 0.000 0.000 0.992 0.000 0.008

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> SRR975551     1  0.0146      0.964 0.996 0.000 0.000 0.004 0.000 0.000
#> SRR975552     1  0.0260      0.964 0.992 0.000 0.000 0.008 0.000 0.000
#> SRR975554     1  0.0146      0.964 0.996 0.000 0.000 0.004 0.000 0.000
#> SRR975553     2  0.0000      0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975555     1  0.0547      0.963 0.980 0.000 0.000 0.020 0.000 0.000
#> SRR975556     2  0.1908      0.876 0.000 0.900 0.000 0.004 0.000 0.096
#> SRR975557     5  0.1411      0.649 0.000 0.000 0.004 0.000 0.936 0.060
#> SRR975558     4  0.1663      0.956 0.088 0.000 0.000 0.912 0.000 0.000
#> SRR975559     1  0.1936      0.934 0.928 0.000 0.028 0.028 0.008 0.008
#> SRR975560     6  0.0820      0.760 0.000 0.012 0.000 0.000 0.016 0.972
#> SRR975561     2  0.4187      0.367 0.000 0.624 0.000 0.004 0.016 0.356
#> SRR975562     3  0.5107      0.564 0.288 0.000 0.636 0.044 0.012 0.020
#> SRR975563     2  0.0000      0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975564     1  0.0692      0.959 0.976 0.000 0.004 0.020 0.000 0.000
#> SRR975565     1  0.0146      0.964 0.996 0.000 0.000 0.004 0.000 0.000
#> SRR975566     1  0.0458      0.962 0.984 0.000 0.016 0.000 0.000 0.000
#> SRR975567     4  0.1957      0.956 0.112 0.000 0.000 0.888 0.000 0.000
#> SRR975568     1  0.0363      0.963 0.988 0.000 0.000 0.012 0.000 0.000
#> SRR975569     2  0.0000      0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975570     2  0.0000      0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975571     2  0.0000      0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975572     2  0.0000      0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975573     2  0.0000      0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975574     2  0.0146      0.958 0.000 0.996 0.000 0.004 0.000 0.000
#> SRR975575     2  0.0000      0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975576     2  0.1010      0.933 0.000 0.960 0.000 0.004 0.000 0.036
#> SRR975577     2  0.0508      0.951 0.000 0.984 0.000 0.004 0.000 0.012
#> SRR975578     2  0.2442      0.818 0.000 0.852 0.000 0.004 0.000 0.144
#> SRR975579     5  0.4836      0.328 0.000 0.196 0.000 0.000 0.664 0.140
#> SRR975580     6  0.0806      0.770 0.000 0.020 0.000 0.000 0.008 0.972
#> SRR975581     2  0.0508      0.951 0.000 0.984 0.000 0.004 0.000 0.012
#> SRR975582     2  0.0000      0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975583     2  0.0000      0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975584     2  0.0000      0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975585     2  0.0000      0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975586     6  0.3052      0.574 0.000 0.216 0.000 0.004 0.000 0.780
#> SRR975587     1  0.0790      0.958 0.968 0.000 0.032 0.000 0.000 0.000
#> SRR975588     2  0.0000      0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975589     1  0.0993      0.955 0.964 0.000 0.024 0.012 0.000 0.000
#> SRR975590     1  0.0146      0.964 0.996 0.000 0.000 0.004 0.000 0.000
#> SRR975591     3  0.1313      0.717 0.028 0.000 0.952 0.016 0.004 0.000
#> SRR975592     1  0.0458      0.962 0.984 0.000 0.016 0.000 0.000 0.000
#> SRR975593     1  0.1615      0.930 0.928 0.000 0.064 0.004 0.000 0.004
#> SRR975594     5  0.4147      0.703 0.000 0.000 0.136 0.044 0.776 0.044
#> SRR975595     1  0.1590      0.942 0.944 0.000 0.012 0.028 0.008 0.008
#> SRR975597     1  0.0260      0.964 0.992 0.000 0.000 0.008 0.000 0.000
#> SRR975596     3  0.5089      0.569 0.284 0.000 0.640 0.044 0.012 0.020
#> SRR975598     1  0.2202      0.921 0.916 0.000 0.016 0.040 0.012 0.016
#> SRR975599     5  0.4147      0.703 0.000 0.000 0.136 0.044 0.776 0.044
#> SRR975600     1  0.2487      0.862 0.876 0.000 0.092 0.032 0.000 0.000
#> SRR975601     3  0.1552      0.700 0.020 0.000 0.940 0.004 0.036 0.000
#> SRR975602     1  0.1503      0.945 0.944 0.000 0.016 0.032 0.008 0.000
#> SRR975603     3  0.2492      0.710 0.100 0.000 0.876 0.020 0.000 0.004
#> SRR975604     3  0.1297      0.662 0.000 0.000 0.948 0.012 0.040 0.000

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

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

consensus_heatmap(res, k = 2)

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

consensus_heatmap(res, k = 3)

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

consensus_heatmap(res, k = 4)

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

consensus_heatmap(res, k = 5)

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

consensus_heatmap(res, k = 6)

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

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

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

membership_heatmap(res, k = 2)

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

membership_heatmap(res, k = 3)

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

membership_heatmap(res, k = 4)

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

membership_heatmap(res, k = 5)

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

membership_heatmap(res, k = 6)

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

Signature heatmaps where rows are scaled:

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

get_signatures(res, k = 2)

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

get_signatures(res, k = 3)

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

get_signatures(res, k = 4)

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

get_signatures(res, k = 5)

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

get_signatures(res, k = 6)

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

Signature heatmaps where rows are not scaled:

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

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

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

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

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

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

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

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

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

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

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

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk ATC-skmeans-signature_compare

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

An example of the output of tb is:

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

The columns in tb are:

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

UMAP plot which shows how samples are separated.

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

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

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

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

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

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

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

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

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

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

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

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk ATC-skmeans-collect-classes

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 17171 rows and 54 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'pam' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 5.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk ATC-pam-collect-plots

The plots are:

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

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

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

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

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

select_partition_number(res)

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

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           1.000       1.000         0.5099 0.491   0.491
#> 3 3 0.856           0.829       0.917         0.1602 0.965   0.929
#> 4 4 0.981           0.936       0.977         0.1346 0.877   0.730
#> 5 5 0.921           0.919       0.966         0.0490 0.968   0.903
#> 6 6 0.893           0.912       0.928         0.0542 0.958   0.860

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
#> SRR975551     1       0          1  1  0
#> SRR975552     1       0          1  1  0
#> SRR975554     1       0          1  1  0
#> SRR975553     2       0          1  0  1
#> SRR975555     1       0          1  1  0
#> SRR975556     2       0          1  0  1
#> SRR975557     2       0          1  0  1
#> SRR975558     1       0          1  1  0
#> SRR975559     1       0          1  1  0
#> SRR975560     2       0          1  0  1
#> SRR975561     2       0          1  0  1
#> SRR975562     1       0          1  1  0
#> SRR975563     2       0          1  0  1
#> SRR975564     1       0          1  1  0
#> SRR975565     1       0          1  1  0
#> SRR975566     1       0          1  1  0
#> SRR975567     1       0          1  1  0
#> SRR975568     1       0          1  1  0
#> SRR975569     2       0          1  0  1
#> SRR975570     2       0          1  0  1
#> SRR975571     2       0          1  0  1
#> SRR975572     2       0          1  0  1
#> SRR975573     2       0          1  0  1
#> SRR975574     2       0          1  0  1
#> SRR975575     2       0          1  0  1
#> SRR975576     2       0          1  0  1
#> SRR975577     2       0          1  0  1
#> SRR975578     2       0          1  0  1
#> SRR975579     2       0          1  0  1
#> SRR975580     2       0          1  0  1
#> SRR975581     2       0          1  0  1
#> SRR975582     2       0          1  0  1
#> SRR975583     2       0          1  0  1
#> SRR975584     2       0          1  0  1
#> SRR975585     2       0          1  0  1
#> SRR975586     2       0          1  0  1
#> SRR975587     1       0          1  1  0
#> SRR975588     2       0          1  0  1
#> SRR975589     1       0          1  1  0
#> SRR975590     1       0          1  1  0
#> SRR975591     1       0          1  1  0
#> SRR975592     1       0          1  1  0
#> SRR975593     1       0          1  1  0
#> SRR975594     2       0          1  0  1
#> SRR975595     1       0          1  1  0
#> SRR975597     1       0          1  1  0
#> SRR975596     1       0          1  1  0
#> SRR975598     1       0          1  1  0
#> SRR975599     2       0          1  0  1
#> SRR975600     1       0          1  1  0
#> SRR975601     1       0          1  1  0
#> SRR975602     1       0          1  1  0
#> SRR975603     1       0          1  1  0
#> SRR975604     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
#> SRR975551     1   0.000      0.810 1.000 0.000 0.000
#> SRR975552     1   0.000      0.810 1.000 0.000 0.000
#> SRR975554     1   0.000      0.810 1.000 0.000 0.000
#> SRR975553     2   0.000      0.980 0.000 1.000 0.000
#> SRR975555     1   0.000      0.810 1.000 0.000 0.000
#> SRR975556     2   0.000      0.980 0.000 1.000 0.000
#> SRR975557     2   0.621      0.138 0.000 0.572 0.428
#> SRR975558     1   0.618      0.526 0.584 0.000 0.416
#> SRR975559     1   0.000      0.810 1.000 0.000 0.000
#> SRR975560     2   0.000      0.980 0.000 1.000 0.000
#> SRR975561     2   0.000      0.980 0.000 1.000 0.000
#> SRR975562     1   0.618      0.526 0.584 0.000 0.416
#> SRR975563     2   0.000      0.980 0.000 1.000 0.000
#> SRR975564     1   0.000      0.810 1.000 0.000 0.000
#> SRR975565     1   0.000      0.810 1.000 0.000 0.000
#> SRR975566     1   0.000      0.810 1.000 0.000 0.000
#> SRR975567     1   0.618      0.526 0.584 0.000 0.416
#> SRR975568     1   0.000      0.810 1.000 0.000 0.000
#> SRR975569     2   0.000      0.980 0.000 1.000 0.000
#> SRR975570     2   0.000      0.980 0.000 1.000 0.000
#> SRR975571     2   0.000      0.980 0.000 1.000 0.000
#> SRR975572     2   0.000      0.980 0.000 1.000 0.000
#> SRR975573     2   0.000      0.980 0.000 1.000 0.000
#> SRR975574     2   0.000      0.980 0.000 1.000 0.000
#> SRR975575     2   0.000      0.980 0.000 1.000 0.000
#> SRR975576     2   0.000      0.980 0.000 1.000 0.000
#> SRR975577     2   0.000      0.980 0.000 1.000 0.000
#> SRR975578     2   0.000      0.980 0.000 1.000 0.000
#> SRR975579     2   0.000      0.980 0.000 1.000 0.000
#> SRR975580     2   0.000      0.980 0.000 1.000 0.000
#> SRR975581     2   0.000      0.980 0.000 1.000 0.000
#> SRR975582     2   0.000      0.980 0.000 1.000 0.000
#> SRR975583     2   0.000      0.980 0.000 1.000 0.000
#> SRR975584     2   0.000      0.980 0.000 1.000 0.000
#> SRR975585     2   0.000      0.980 0.000 1.000 0.000
#> SRR975586     2   0.000      0.980 0.000 1.000 0.000
#> SRR975587     1   0.000      0.810 1.000 0.000 0.000
#> SRR975588     2   0.000      0.980 0.000 1.000 0.000
#> SRR975589     1   0.000      0.810 1.000 0.000 0.000
#> SRR975590     1   0.000      0.810 1.000 0.000 0.000
#> SRR975591     1   0.618      0.526 0.584 0.000 0.416
#> SRR975592     1   0.000      0.810 1.000 0.000 0.000
#> SRR975593     1   0.568      0.612 0.684 0.000 0.316
#> SRR975594     3   0.000      1.000 0.000 0.000 1.000
#> SRR975595     1   0.000      0.810 1.000 0.000 0.000
#> SRR975597     1   0.000      0.810 1.000 0.000 0.000
#> SRR975596     1   0.618      0.526 0.584 0.000 0.416
#> SRR975598     1   0.000      0.810 1.000 0.000 0.000
#> SRR975599     3   0.000      1.000 0.000 0.000 1.000
#> SRR975600     1   0.613      0.541 0.600 0.000 0.400
#> SRR975601     1   0.618      0.526 0.584 0.000 0.416
#> SRR975602     1   0.000      0.810 1.000 0.000 0.000
#> SRR975603     1   0.618      0.526 0.584 0.000 0.416
#> SRR975604     1   0.618      0.526 0.584 0.000 0.416

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> SRR975551     1  0.0000      0.971 1.000 0.000 0.000 0.000
#> SRR975552     1  0.0000      0.971 1.000 0.000 0.000 0.000
#> SRR975554     1  0.0000      0.971 1.000 0.000 0.000 0.000
#> SRR975553     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975555     1  0.0000      0.971 1.000 0.000 0.000 0.000
#> SRR975556     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975557     2  0.6816      0.371 0.000 0.604 0.212 0.184
#> SRR975558     3  0.0000      0.927 0.000 0.000 1.000 0.000
#> SRR975559     1  0.0000      0.971 1.000 0.000 0.000 0.000
#> SRR975560     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975561     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975562     3  0.0000      0.927 0.000 0.000 1.000 0.000
#> SRR975563     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975564     1  0.0000      0.971 1.000 0.000 0.000 0.000
#> SRR975565     1  0.0000      0.971 1.000 0.000 0.000 0.000
#> SRR975566     1  0.1022      0.939 0.968 0.000 0.032 0.000
#> SRR975567     3  0.0000      0.927 0.000 0.000 1.000 0.000
#> SRR975568     1  0.0000      0.971 1.000 0.000 0.000 0.000
#> SRR975569     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975570     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975571     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975572     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975573     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975574     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975575     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975576     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975577     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975578     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975579     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975580     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975581     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975582     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975583     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975584     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975585     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975586     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975587     1  0.4500      0.497 0.684 0.000 0.316 0.000
#> SRR975588     2  0.0000      0.983 0.000 1.000 0.000 0.000
#> SRR975589     3  0.4790      0.377 0.380 0.000 0.620 0.000
#> SRR975590     1  0.0000      0.971 1.000 0.000 0.000 0.000
#> SRR975591     3  0.0000      0.927 0.000 0.000 1.000 0.000
#> SRR975592     1  0.0000      0.971 1.000 0.000 0.000 0.000
#> SRR975593     3  0.2345      0.819 0.100 0.000 0.900 0.000
#> SRR975594     4  0.0000      1.000 0.000 0.000 0.000 1.000
#> SRR975595     1  0.0000      0.971 1.000 0.000 0.000 0.000
#> SRR975597     1  0.0000      0.971 1.000 0.000 0.000 0.000
#> SRR975596     3  0.0000      0.927 0.000 0.000 1.000 0.000
#> SRR975598     1  0.0000      0.971 1.000 0.000 0.000 0.000
#> SRR975599     4  0.0000      1.000 0.000 0.000 0.000 1.000
#> SRR975600     3  0.0592      0.914 0.016 0.000 0.984 0.000
#> SRR975601     3  0.0000      0.927 0.000 0.000 1.000 0.000
#> SRR975602     1  0.0000      0.971 1.000 0.000 0.000 0.000
#> SRR975603     3  0.0000      0.927 0.000 0.000 1.000 0.000
#> SRR975604     3  0.0000      0.927 0.000 0.000 1.000 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
#> SRR975551     1  0.0794      0.955 0.972 0.000 0.000 0.028 0.000
#> SRR975552     1  0.0794      0.955 0.972 0.000 0.000 0.028 0.000
#> SRR975554     1  0.0794      0.955 0.972 0.000 0.000 0.028 0.000
#> SRR975553     2  0.0000      0.975 0.000 1.000 0.000 0.000 0.000
#> SRR975555     1  0.0000      0.957 1.000 0.000 0.000 0.000 0.000
#> SRR975556     2  0.0000      0.975 0.000 1.000 0.000 0.000 0.000
#> SRR975557     4  0.3183      0.444 0.000 0.000 0.016 0.828 0.156
#> SRR975558     3  0.0000      0.941 0.000 0.000 1.000 0.000 0.000
#> SRR975559     1  0.0000      0.957 1.000 0.000 0.000 0.000 0.000
#> SRR975560     2  0.2773      0.814 0.000 0.836 0.000 0.164 0.000
#> SRR975561     2  0.0000      0.975 0.000 1.000 0.000 0.000 0.000
#> SRR975562     3  0.0000      0.941 0.000 0.000 1.000 0.000 0.000
#> SRR975563     2  0.0000      0.975 0.000 1.000 0.000 0.000 0.000
#> SRR975564     1  0.0000      0.957 1.000 0.000 0.000 0.000 0.000
#> SRR975565     1  0.0794      0.955 0.972 0.000 0.000 0.028 0.000
#> SRR975566     1  0.0880      0.931 0.968 0.000 0.032 0.000 0.000
#> SRR975567     3  0.0000      0.941 0.000 0.000 1.000 0.000 0.000
#> SRR975568     1  0.0000      0.957 1.000 0.000 0.000 0.000 0.000
#> SRR975569     2  0.0000      0.975 0.000 1.000 0.000 0.000 0.000
#> SRR975570     2  0.0000      0.975 0.000 1.000 0.000 0.000 0.000
#> SRR975571     2  0.0000      0.975 0.000 1.000 0.000 0.000 0.000
#> SRR975572     2  0.0000      0.975 0.000 1.000 0.000 0.000 0.000
#> SRR975573     2  0.0000      0.975 0.000 1.000 0.000 0.000 0.000
#> SRR975574     2  0.0000      0.975 0.000 1.000 0.000 0.000 0.000
#> SRR975575     2  0.0000      0.975 0.000 1.000 0.000 0.000 0.000
#> SRR975576     2  0.0000      0.975 0.000 1.000 0.000 0.000 0.000
#> SRR975577     2  0.0000      0.975 0.000 1.000 0.000 0.000 0.000
#> SRR975578     2  0.0000      0.975 0.000 1.000 0.000 0.000 0.000
#> SRR975579     4  0.3039      0.545 0.000 0.192 0.000 0.808 0.000
#> SRR975580     2  0.2773      0.814 0.000 0.836 0.000 0.164 0.000
#> SRR975581     2  0.0000      0.975 0.000 1.000 0.000 0.000 0.000
#> SRR975582     2  0.0000      0.975 0.000 1.000 0.000 0.000 0.000
#> SRR975583     2  0.0000      0.975 0.000 1.000 0.000 0.000 0.000
#> SRR975584     2  0.0000      0.975 0.000 1.000 0.000 0.000 0.000
#> SRR975585     2  0.0000      0.975 0.000 1.000 0.000 0.000 0.000
#> SRR975586     2  0.2773      0.814 0.000 0.836 0.000 0.164 0.000
#> SRR975587     1  0.3895      0.483 0.680 0.000 0.320 0.000 0.000
#> SRR975588     2  0.0000      0.975 0.000 1.000 0.000 0.000 0.000
#> SRR975589     3  0.3561      0.619 0.260 0.000 0.740 0.000 0.000
#> SRR975590     1  0.0794      0.955 0.972 0.000 0.000 0.028 0.000
#> SRR975591     3  0.0000      0.941 0.000 0.000 1.000 0.000 0.000
#> SRR975592     1  0.0794      0.955 0.972 0.000 0.000 0.028 0.000
#> SRR975593     3  0.2280      0.827 0.120 0.000 0.880 0.000 0.000
#> SRR975594     5  0.0000      1.000 0.000 0.000 0.000 0.000 1.000
#> SRR975595     1  0.0000      0.957 1.000 0.000 0.000 0.000 0.000
#> SRR975597     1  0.0000      0.957 1.000 0.000 0.000 0.000 0.000
#> SRR975596     3  0.0000      0.941 0.000 0.000 1.000 0.000 0.000
#> SRR975598     1  0.0794      0.955 0.972 0.000 0.000 0.028 0.000
#> SRR975599     5  0.0000      1.000 0.000 0.000 0.000 0.000 1.000
#> SRR975600     3  0.1121      0.910 0.044 0.000 0.956 0.000 0.000
#> SRR975601     3  0.0000      0.941 0.000 0.000 1.000 0.000 0.000
#> SRR975602     1  0.0000      0.957 1.000 0.000 0.000 0.000 0.000
#> SRR975603     3  0.0000      0.941 0.000 0.000 1.000 0.000 0.000
#> SRR975604     3  0.0000      0.941 0.000 0.000 1.000 0.000 0.000

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5    p6
#> SRR975551     1  0.3929      0.800 0.700 0.000 0.000 0.028 0.000 0.272
#> SRR975552     1  0.2784      0.837 0.848 0.000 0.000 0.028 0.000 0.124
#> SRR975554     1  0.3929      0.800 0.700 0.000 0.000 0.028 0.000 0.272
#> SRR975553     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975555     1  0.0260      0.846 0.992 0.000 0.000 0.000 0.000 0.008
#> SRR975556     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975557     4  0.0713      0.929 0.000 0.000 0.000 0.972 0.028 0.000
#> SRR975558     3  0.2912      0.708 0.000 0.000 0.784 0.000 0.000 0.216
#> SRR975559     1  0.3244      0.808 0.732 0.000 0.000 0.000 0.000 0.268
#> SRR975560     6  0.3309      1.000 0.000 0.280 0.000 0.000 0.000 0.720
#> SRR975561     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975562     3  0.0405      0.913 0.004 0.000 0.988 0.000 0.000 0.008
#> SRR975563     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975564     1  0.0146      0.847 0.996 0.000 0.000 0.000 0.000 0.004
#> SRR975565     1  0.3929      0.800 0.700 0.000 0.000 0.028 0.000 0.272
#> SRR975566     1  0.3512      0.801 0.720 0.000 0.008 0.000 0.000 0.272
#> SRR975567     3  0.0000      0.915 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975568     1  0.0547      0.850 0.980 0.000 0.000 0.000 0.000 0.020
#> SRR975569     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975570     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975571     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975572     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975573     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975574     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975575     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975576     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975577     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975578     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975579     4  0.0713      0.931 0.000 0.028 0.000 0.972 0.000 0.000
#> SRR975580     6  0.3309      1.000 0.000 0.280 0.000 0.000 0.000 0.720
#> SRR975581     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975582     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975583     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975584     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975585     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975586     6  0.3309      1.000 0.000 0.280 0.000 0.000 0.000 0.720
#> SRR975587     1  0.3565      0.533 0.692 0.000 0.304 0.000 0.000 0.004
#> SRR975588     2  0.0000      1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975589     3  0.3373      0.628 0.248 0.000 0.744 0.000 0.000 0.008
#> SRR975590     1  0.3929      0.800 0.700 0.000 0.000 0.028 0.000 0.272
#> SRR975591     3  0.0000      0.915 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975592     1  0.0858      0.845 0.968 0.000 0.000 0.028 0.000 0.004
#> SRR975593     3  0.2234      0.813 0.124 0.000 0.872 0.000 0.000 0.004
#> SRR975594     5  0.0000      1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR975595     1  0.0260      0.846 0.992 0.000 0.000 0.000 0.000 0.008
#> SRR975597     1  0.0146      0.847 0.996 0.000 0.000 0.000 0.000 0.004
#> SRR975596     3  0.0291      0.914 0.004 0.000 0.992 0.000 0.000 0.004
#> SRR975598     1  0.0858      0.845 0.968 0.000 0.000 0.028 0.000 0.004
#> SRR975599     5  0.0000      1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR975600     3  0.1152      0.891 0.044 0.000 0.952 0.000 0.000 0.004
#> SRR975601     3  0.0000      0.915 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975602     1  0.0146      0.847 0.996 0.000 0.000 0.000 0.000 0.004
#> SRR975603     3  0.0000      0.915 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR975604     3  0.0000      0.915 0.000 0.000 1.000 0.000 0.000 0.000

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

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

consensus_heatmap(res, k = 2)

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

consensus_heatmap(res, k = 3)

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

consensus_heatmap(res, k = 4)

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

consensus_heatmap(res, k = 5)

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

consensus_heatmap(res, k = 6)

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

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

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

membership_heatmap(res, k = 2)

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

membership_heatmap(res, k = 3)

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

membership_heatmap(res, k = 4)

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

membership_heatmap(res, k = 5)

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

membership_heatmap(res, k = 6)

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

Signature heatmaps where rows are scaled:

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

get_signatures(res, k = 2)

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

get_signatures(res, k = 3)

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

get_signatures(res, k = 4)

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

get_signatures(res, k = 5)

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

get_signatures(res, k = 6)

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

Signature heatmaps where rows are not scaled:

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

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

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

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

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

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

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

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

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

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

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

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk ATC-pam-signature_compare

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

An example of the output of tb is:

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

The columns in tb are:

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

UMAP plot which shows how samples are separated.

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

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

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

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

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

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

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

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

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

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

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

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk ATC-pam-collect-classes

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 17171 rows and 54 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'mclust' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 3.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_signatures"     
#>  [7] "consensus_heatmap"       "dimension_reduction"     "functional_enrichment"  
#> [10] "get_anno_col"            "get_anno"                "get_classes"            
#> [13] "get_consensus"           "get_matrix"              "get_membership"         
#> [16] "get_param"               "get_signatures"          "get_stats"              
#> [19] "is_best_k"               "is_stable_k"             "membership_heatmap"     
#> [22] "ncol"                    "nrow"                    "plot_ecdf"              
#> [25] "rownames"                "select_partition_number" "show"                   
#> [28] "suggest_best_k"          "test_to_known_factors"

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

collect_plots(res)

plot of chunk ATC-mclust-collect-plots

The plots are:

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

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

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

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

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

select_partition_number(res)

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

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.829           0.898       0.957         0.4777 0.502   0.502
#> 3 3 1.000           0.994       0.997         0.3840 0.781   0.586
#> 4 4 0.857           0.778       0.895         0.0766 0.940   0.825
#> 5 5 0.860           0.818       0.893         0.0607 0.899   0.673
#> 6 6 0.778           0.652       0.814         0.0267 0.900   0.642

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

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

suggest_best_k(res)

#> [1] 3

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

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

show/hide code output

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

#>           class entropy silhouette    p1    p2
#> SRR975551     1   0.000      1.000 1.000 0.000
#> SRR975552     1   0.000      1.000 1.000 0.000
#> SRR975554     1   0.000      1.000 1.000 0.000
#> SRR975553     2   0.000      0.889 0.000 1.000
#> SRR975555     1   0.000      1.000 1.000 0.000
#> SRR975556     2   0.996      0.292 0.464 0.536
#> SRR975557     1   0.000      1.000 1.000 0.000
#> SRR975558     1   0.000      1.000 1.000 0.000
#> SRR975559     1   0.000      1.000 1.000 0.000
#> SRR975560     2   0.996      0.292 0.464 0.536
#> SRR975561     2   0.996      0.292 0.464 0.536
#> SRR975562     1   0.000      1.000 1.000 0.000
#> SRR975563     2   0.000      0.889 0.000 1.000
#> SRR975564     1   0.000      1.000 1.000 0.000
#> SRR975565     1   0.000      1.000 1.000 0.000
#> SRR975566     1   0.000      1.000 1.000 0.000
#> SRR975567     1   0.000      1.000 1.000 0.000
#> SRR975568     1   0.000      1.000 1.000 0.000
#> SRR975569     2   0.000      0.889 0.000 1.000
#> SRR975570     2   0.000      0.889 0.000 1.000
#> SRR975571     2   0.000      0.889 0.000 1.000
#> SRR975572     2   0.000      0.889 0.000 1.000
#> SRR975573     2   0.000      0.889 0.000 1.000
#> SRR975574     2   0.000      0.889 0.000 1.000
#> SRR975575     2   0.000      0.889 0.000 1.000
#> SRR975576     2   0.000      0.889 0.000 1.000
#> SRR975577     2   0.000      0.889 0.000 1.000
#> SRR975578     2   0.000      0.889 0.000 1.000
#> SRR975579     1   0.000      1.000 1.000 0.000
#> SRR975580     2   0.996      0.292 0.464 0.536
#> SRR975581     2   0.000      0.889 0.000 1.000
#> SRR975582     2   0.000      0.889 0.000 1.000
#> SRR975583     2   0.000      0.889 0.000 1.000
#> SRR975584     2   0.000      0.889 0.000 1.000
#> SRR975585     2   0.000      0.889 0.000 1.000
#> SRR975586     2   0.996      0.292 0.464 0.536
#> SRR975587     1   0.000      1.000 1.000 0.000
#> SRR975588     2   0.000      0.889 0.000 1.000
#> SRR975589     1   0.000      1.000 1.000 0.000
#> SRR975590     1   0.000      1.000 1.000 0.000
#> SRR975591     1   0.000      1.000 1.000 0.000
#> SRR975592     1   0.000      1.000 1.000 0.000
#> SRR975593     1   0.000      1.000 1.000 0.000
#> SRR975594     1   0.000      1.000 1.000 0.000
#> SRR975595     1   0.000      1.000 1.000 0.000
#> SRR975597     1   0.000      1.000 1.000 0.000
#> SRR975596     1   0.000      1.000 1.000 0.000
#> SRR975598     1   0.000      1.000 1.000 0.000
#> SRR975599     1   0.000      1.000 1.000 0.000
#> SRR975600     1   0.000      1.000 1.000 0.000
#> SRR975601     1   0.000      1.000 1.000 0.000
#> SRR975602     1   0.000      1.000 1.000 0.000
#> SRR975603     1   0.000      1.000 1.000 0.000
#> SRR975604     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
#> SRR975551     1  0.0000      0.999 1.000  0 0.000
#> SRR975552     1  0.0000      0.999 1.000  0 0.000
#> SRR975554     1  0.0000      0.999 1.000  0 0.000
#> SRR975553     2  0.0000      1.000 0.000  1 0.000
#> SRR975555     1  0.0000      0.999 1.000  0 0.000
#> SRR975556     3  0.0000      0.988 0.000  0 1.000
#> SRR975557     3  0.0000      0.988 0.000  0 1.000
#> SRR975558     3  0.0000      0.988 0.000  0 1.000
#> SRR975559     1  0.0000      0.999 1.000  0 0.000
#> SRR975560     3  0.0000      0.988 0.000  0 1.000
#> SRR975561     3  0.0000      0.988 0.000  0 1.000
#> SRR975562     1  0.0000      0.999 1.000  0 0.000
#> SRR975563     2  0.0000      1.000 0.000  1 0.000
#> SRR975564     1  0.0000      0.999 1.000  0 0.000
#> SRR975565     1  0.0000      0.999 1.000  0 0.000
#> SRR975566     1  0.0000      0.999 1.000  0 0.000
#> SRR975567     3  0.0000      0.988 0.000  0 1.000
#> SRR975568     1  0.0000      0.999 1.000  0 0.000
#> SRR975569     2  0.0000      1.000 0.000  1 0.000
#> SRR975570     2  0.0000      1.000 0.000  1 0.000
#> SRR975571     2  0.0000      1.000 0.000  1 0.000
#> SRR975572     2  0.0000      1.000 0.000  1 0.000
#> SRR975573     2  0.0000      1.000 0.000  1 0.000
#> SRR975574     2  0.0000      1.000 0.000  1 0.000
#> SRR975575     2  0.0000      1.000 0.000  1 0.000
#> SRR975576     2  0.0000      1.000 0.000  1 0.000
#> SRR975577     2  0.0000      1.000 0.000  1 0.000
#> SRR975578     2  0.0000      1.000 0.000  1 0.000
#> SRR975579     3  0.0000      0.988 0.000  0 1.000
#> SRR975580     3  0.0000      0.988 0.000  0 1.000
#> SRR975581     2  0.0000      1.000 0.000  1 0.000
#> SRR975582     2  0.0000      1.000 0.000  1 0.000
#> SRR975583     2  0.0000      1.000 0.000  1 0.000
#> SRR975584     2  0.0000      1.000 0.000  1 0.000
#> SRR975585     2  0.0000      1.000 0.000  1 0.000
#> SRR975586     3  0.0000      0.988 0.000  0 1.000
#> SRR975587     1  0.0000      0.999 1.000  0 0.000
#> SRR975588     2  0.0000      1.000 0.000  1 0.000
#> SRR975589     1  0.0000      0.999 1.000  0 0.000
#> SRR975590     1  0.0000      0.999 1.000  0 0.000
#> SRR975591     3  0.1860      0.945 0.052  0 0.948
#> SRR975592     1  0.0000      0.999 1.000  0 0.000
#> SRR975593     1  0.0000      0.999 1.000  0 0.000
#> SRR975594     3  0.0000      0.988 0.000  0 1.000
#> SRR975595     1  0.0000      0.999 1.000  0 0.000
#> SRR975597     1  0.0000      0.999 1.000  0 0.000
#> SRR975596     1  0.0000      0.999 1.000  0 0.000
#> SRR975598     1  0.0000      0.999 1.000  0 0.000
#> SRR975599     3  0.0000      0.988 0.000  0 1.000
#> SRR975600     1  0.0000      0.999 1.000  0 0.000
#> SRR975601     1  0.0892      0.979 0.980  0 0.020
#> SRR975602     1  0.0000      0.999 1.000  0 0.000
#> SRR975603     1  0.0000      0.999 1.000  0 0.000
#> SRR975604     3  0.2537      0.917 0.080  0 0.920

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> SRR975551     1  0.0000      0.925 1.000 0.000 0.000 0.000
#> SRR975552     1  0.0000      0.925 1.000 0.000 0.000 0.000
#> SRR975554     1  0.0000      0.925 1.000 0.000 0.000 0.000
#> SRR975553     2  0.0000      0.953 0.000 1.000 0.000 0.000
#> SRR975555     1  0.0000      0.925 1.000 0.000 0.000 0.000
#> SRR975556     4  0.0000      0.717 0.000 0.000 0.000 1.000
#> SRR975557     4  0.4998      0.634 0.000 0.000 0.488 0.512
#> SRR975558     3  0.4245      0.345 0.020 0.000 0.784 0.196
#> SRR975559     1  0.0000      0.925 1.000 0.000 0.000 0.000
#> SRR975560     4  0.2469      0.737 0.000 0.000 0.108 0.892
#> SRR975561     4  0.1022      0.695 0.000 0.032 0.000 0.968
#> SRR975562     1  0.4804      0.191 0.616 0.000 0.384 0.000
#> SRR975563     2  0.0188      0.952 0.000 0.996 0.004 0.000
#> SRR975564     1  0.0000      0.925 1.000 0.000 0.000 0.000
#> SRR975565     1  0.0000      0.925 1.000 0.000 0.000 0.000
#> SRR975566     1  0.0000      0.925 1.000 0.000 0.000 0.000
#> SRR975567     3  0.4348      0.353 0.024 0.000 0.780 0.196
#> SRR975568     1  0.0000      0.925 1.000 0.000 0.000 0.000
#> SRR975569     2  0.0000      0.953 0.000 1.000 0.000 0.000
#> SRR975570     2  0.0000      0.953 0.000 1.000 0.000 0.000
#> SRR975571     2  0.0000      0.953 0.000 1.000 0.000 0.000
#> SRR975572     2  0.0000      0.953 0.000 1.000 0.000 0.000
#> SRR975573     2  0.0000      0.953 0.000 1.000 0.000 0.000
#> SRR975574     2  0.1902      0.916 0.000 0.932 0.004 0.064
#> SRR975575     2  0.0188      0.952 0.000 0.996 0.004 0.000
#> SRR975576     2  0.2197      0.904 0.000 0.916 0.004 0.080
#> SRR975577     2  0.2944      0.858 0.000 0.868 0.004 0.128
#> SRR975578     2  0.5167      0.139 0.000 0.508 0.004 0.488
#> SRR975579     4  0.4972      0.654 0.000 0.000 0.456 0.544
#> SRR975580     4  0.2469      0.737 0.000 0.000 0.108 0.892
#> SRR975581     2  0.1109      0.938 0.000 0.968 0.004 0.028
#> SRR975582     2  0.0188      0.952 0.000 0.996 0.004 0.000
#> SRR975583     2  0.0000      0.953 0.000 1.000 0.000 0.000
#> SRR975584     2  0.0000      0.953 0.000 1.000 0.000 0.000
#> SRR975585     2  0.0000      0.953 0.000 1.000 0.000 0.000
#> SRR975586     4  0.0000      0.717 0.000 0.000 0.000 1.000
#> SRR975587     1  0.0000      0.925 1.000 0.000 0.000 0.000
#> SRR975588     2  0.0000      0.953 0.000 1.000 0.000 0.000
#> SRR975589     1  0.0000      0.925 1.000 0.000 0.000 0.000
#> SRR975590     1  0.0000      0.925 1.000 0.000 0.000 0.000
#> SRR975591     3  0.3404      0.588 0.104 0.000 0.864 0.032
#> SRR975592     1  0.0000      0.925 1.000 0.000 0.000 0.000
#> SRR975593     1  0.0000      0.925 1.000 0.000 0.000 0.000
#> SRR975594     4  0.4972      0.637 0.000 0.000 0.456 0.544
#> SRR975595     1  0.0000      0.925 1.000 0.000 0.000 0.000
#> SRR975597     1  0.0000      0.925 1.000 0.000 0.000 0.000
#> SRR975596     1  0.4804      0.191 0.616 0.000 0.384 0.000
#> SRR975598     1  0.0000      0.925 1.000 0.000 0.000 0.000
#> SRR975599     4  0.4972      0.637 0.000 0.000 0.456 0.544
#> SRR975600     1  0.4855      0.171 0.600 0.000 0.400 0.000
#> SRR975601     3  0.5649      0.390 0.392 0.000 0.580 0.028
#> SRR975602     1  0.0000      0.925 1.000 0.000 0.000 0.000
#> SRR975603     3  0.4961      0.241 0.448 0.000 0.552 0.000
#> SRR975604     3  0.3149      0.576 0.088 0.000 0.880 0.032

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4    p5
#> SRR975551     1  0.0000      0.960 1.000 0.000 0.000 0.000 0.000
#> SRR975552     1  0.0000      0.960 1.000 0.000 0.000 0.000 0.000
#> SRR975554     1  0.1341      0.960 0.944 0.000 0.056 0.000 0.000
#> SRR975553     2  0.0290      0.961 0.000 0.992 0.000 0.000 0.008
#> SRR975555     1  0.0162      0.959 0.996 0.000 0.004 0.000 0.000
#> SRR975556     5  0.4074      0.136 0.000 0.000 0.000 0.364 0.636
#> SRR975557     4  0.0000      0.865 0.000 0.000 0.000 1.000 0.000
#> SRR975558     3  0.3934      0.478 0.008 0.000 0.716 0.276 0.000
#> SRR975559     1  0.1341      0.960 0.944 0.000 0.056 0.000 0.000
#> SRR975560     4  0.3975      0.892 0.000 0.000 0.144 0.792 0.064
#> SRR975561     5  0.0404      0.473 0.000 0.000 0.000 0.012 0.988
#> SRR975562     3  0.3636      0.680 0.272 0.000 0.728 0.000 0.000
#> SRR975563     2  0.0000      0.962 0.000 1.000 0.000 0.000 0.000
#> SRR975564     1  0.0000      0.960 1.000 0.000 0.000 0.000 0.000
#> SRR975565     1  0.0000      0.960 1.000 0.000 0.000 0.000 0.000
#> SRR975566     1  0.1341      0.960 0.944 0.000 0.056 0.000 0.000
#> SRR975567     3  0.3934      0.478 0.008 0.000 0.716 0.276 0.000
#> SRR975568     1  0.0000      0.960 1.000 0.000 0.000 0.000 0.000
#> SRR975569     2  0.0290      0.961 0.000 0.992 0.000 0.000 0.008
#> SRR975570     2  0.0162      0.962 0.000 0.996 0.000 0.000 0.004
#> SRR975571     2  0.0290      0.961 0.000 0.992 0.000 0.000 0.008
#> SRR975572     2  0.0290      0.961 0.000 0.992 0.000 0.000 0.008
#> SRR975573     2  0.0000      0.962 0.000 1.000 0.000 0.000 0.000
#> SRR975574     2  0.3774      0.430 0.000 0.704 0.000 0.000 0.296
#> SRR975575     2  0.0000      0.962 0.000 1.000 0.000 0.000 0.000
#> SRR975576     5  0.4015      0.535 0.000 0.348 0.000 0.000 0.652
#> SRR975577     5  0.4015      0.535 0.000 0.348 0.000 0.000 0.652
#> SRR975578     5  0.4201      0.554 0.000 0.328 0.000 0.008 0.664
#> SRR975579     4  0.0000      0.865 0.000 0.000 0.000 1.000 0.000
#> SRR975580     4  0.3975      0.892 0.000 0.000 0.144 0.792 0.064
#> SRR975581     2  0.1544      0.885 0.000 0.932 0.000 0.000 0.068
#> SRR975582     2  0.0000      0.962 0.000 1.000 0.000 0.000 0.000
#> SRR975583     2  0.0000      0.962 0.000 1.000 0.000 0.000 0.000
#> SRR975584     2  0.0000      0.962 0.000 1.000 0.000 0.000 0.000
#> SRR975585     2  0.0000      0.962 0.000 1.000 0.000 0.000 0.000
#> SRR975586     5  0.4101      0.116 0.000 0.000 0.000 0.372 0.628
#> SRR975587     1  0.1341      0.960 0.944 0.000 0.056 0.000 0.000
#> SRR975588     2  0.0290      0.961 0.000 0.992 0.000 0.000 0.008
#> SRR975589     1  0.1341      0.960 0.944 0.000 0.056 0.000 0.000
#> SRR975590     1  0.1341      0.960 0.944 0.000 0.056 0.000 0.000
#> SRR975591     3  0.1408      0.658 0.008 0.000 0.948 0.044 0.000
#> SRR975592     1  0.1341      0.960 0.944 0.000 0.056 0.000 0.000
#> SRR975593     1  0.1410      0.958 0.940 0.000 0.060 0.000 0.000
#> SRR975594     4  0.2280      0.904 0.000 0.000 0.120 0.880 0.000
#> SRR975595     1  0.0162      0.959 0.996 0.000 0.004 0.000 0.000
#> SRR975597     1  0.0162      0.959 0.996 0.000 0.004 0.000 0.000
#> SRR975596     3  0.3684      0.676 0.280 0.000 0.720 0.000 0.000
#> SRR975598     1  0.0963      0.941 0.964 0.000 0.036 0.000 0.000
#> SRR975599     4  0.2424      0.901 0.000 0.000 0.132 0.868 0.000
#> SRR975600     3  0.4161      0.493 0.392 0.000 0.608 0.000 0.000
#> SRR975601     3  0.1399      0.667 0.020 0.000 0.952 0.028 0.000
#> SRR975602     1  0.1851      0.936 0.912 0.000 0.088 0.000 0.000
#> SRR975603     3  0.4114      0.689 0.272 0.000 0.712 0.016 0.000
#> SRR975604     3  0.1408      0.658 0.008 0.000 0.948 0.044 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
#> SRR975551     1  0.0291      0.662 0.992 0.000 0.004 0.000 0.000 0.004
#> SRR975552     1  0.0291      0.662 0.992 0.000 0.004 0.000 0.000 0.004
#> SRR975554     1  0.2473      0.637 0.856 0.000 0.136 0.000 0.000 0.008
#> SRR975553     2  0.0865      0.886 0.000 0.964 0.000 0.000 0.000 0.036
#> SRR975555     1  0.1492      0.664 0.940 0.000 0.036 0.000 0.000 0.024
#> SRR975556     5  0.1151      0.896 0.000 0.012 0.000 0.032 0.956 0.000
#> SRR975557     4  0.0000      0.661 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR975558     3  0.5915      0.152 0.000 0.000 0.428 0.212 0.000 0.360
#> SRR975559     1  0.4286      0.319 0.728 0.000 0.108 0.000 0.000 0.164
#> SRR975560     4  0.7492      0.499 0.000 0.000 0.156 0.360 0.220 0.264
#> SRR975561     5  0.1663      0.818 0.000 0.088 0.000 0.000 0.912 0.000
#> SRR975562     1  0.4589      0.203 0.504 0.000 0.460 0.000 0.000 0.036
#> SRR975563     2  0.0146      0.894 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR975564     1  0.0291      0.667 0.992 0.000 0.004 0.000 0.000 0.004
#> SRR975565     1  0.0291      0.662 0.992 0.000 0.004 0.000 0.000 0.004
#> SRR975566     6  0.4407      0.995 0.480 0.000 0.024 0.000 0.000 0.496
#> SRR975567     3  0.5915      0.152 0.000 0.000 0.428 0.212 0.000 0.360
#> SRR975568     1  0.0291      0.667 0.992 0.000 0.004 0.000 0.000 0.004
#> SRR975569     2  0.1610      0.867 0.000 0.916 0.000 0.000 0.000 0.084
#> SRR975570     2  0.0146      0.894 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR975571     2  0.0865      0.886 0.000 0.964 0.000 0.000 0.000 0.036
#> SRR975572     2  0.0363      0.892 0.000 0.988 0.000 0.000 0.000 0.012
#> SRR975573     2  0.0000      0.894 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975574     2  0.3584      0.620 0.000 0.688 0.000 0.000 0.308 0.004
#> SRR975575     2  0.0146      0.894 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR975576     2  0.3578      0.590 0.000 0.660 0.000 0.000 0.340 0.000
#> SRR975577     2  0.3578      0.590 0.000 0.660 0.000 0.000 0.340 0.000
#> SRR975578     2  0.3672      0.542 0.000 0.632 0.000 0.000 0.368 0.000
#> SRR975579     4  0.0363      0.661 0.000 0.000 0.000 0.988 0.012 0.000
#> SRR975580     4  0.7492      0.499 0.000 0.000 0.156 0.360 0.220 0.264
#> SRR975581     2  0.1471      0.863 0.000 0.932 0.000 0.000 0.064 0.004
#> SRR975582     2  0.0146      0.894 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR975583     2  0.0000      0.894 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975584     2  0.0000      0.894 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975585     2  0.0000      0.894 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975586     5  0.0865      0.883 0.000 0.000 0.000 0.036 0.964 0.000
#> SRR975587     6  0.4407      0.990 0.484 0.000 0.024 0.000 0.000 0.492
#> SRR975588     2  0.1610      0.867 0.000 0.916 0.000 0.000 0.000 0.084
#> SRR975589     6  0.4407      0.995 0.480 0.000 0.024 0.000 0.000 0.496
#> SRR975590     1  0.2402      0.634 0.856 0.000 0.140 0.000 0.000 0.004
#> SRR975591     3  0.1814      0.582 0.000 0.000 0.900 0.100 0.000 0.000
#> SRR975592     1  0.2402      0.634 0.856 0.000 0.140 0.000 0.000 0.004
#> SRR975593     1  0.5313     -0.788 0.508 0.000 0.108 0.000 0.000 0.384
#> SRR975594     4  0.3027      0.671 0.000 0.000 0.148 0.824 0.000 0.028
#> SRR975595     1  0.1367      0.661 0.944 0.000 0.044 0.000 0.000 0.012
#> SRR975597     1  0.0363      0.669 0.988 0.000 0.012 0.000 0.000 0.000
#> SRR975596     1  0.4589      0.203 0.504 0.000 0.460 0.000 0.000 0.036
#> SRR975598     1  0.3168      0.614 0.804 0.000 0.172 0.000 0.000 0.024
#> SRR975599     4  0.3776      0.638 0.000 0.000 0.196 0.756 0.000 0.048
#> SRR975600     3  0.3742      0.083 0.348 0.000 0.648 0.000 0.000 0.004
#> SRR975601     3  0.0260      0.648 0.008 0.000 0.992 0.000 0.000 0.000
#> SRR975602     1  0.3261      0.578 0.780 0.000 0.204 0.000 0.000 0.016
#> SRR975603     3  0.0777      0.644 0.024 0.000 0.972 0.000 0.000 0.004
#> SRR975604     3  0.0405      0.646 0.004 0.000 0.988 0.008 0.000 0.000

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

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

consensus_heatmap(res, k = 2)

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

consensus_heatmap(res, k = 3)

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

consensus_heatmap(res, k = 4)

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

consensus_heatmap(res, k = 5)

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

consensus_heatmap(res, k = 6)

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

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

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

membership_heatmap(res, k = 2)

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

membership_heatmap(res, k = 3)

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

membership_heatmap(res, k = 4)

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

membership_heatmap(res, k = 5)

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

membership_heatmap(res, k = 6)

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

Signature heatmaps where rows are scaled:

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

get_signatures(res, k = 2)

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

get_signatures(res, k = 3)

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

get_signatures(res, k = 4)

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

get_signatures(res, k = 5)

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

get_signatures(res, k = 6)

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

Signature heatmaps where rows are not scaled:

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

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

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

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

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

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

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

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

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

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

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

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk ATC-mclust-signature_compare

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

An example of the output of tb is:

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

The columns in tb are:

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

UMAP plot which shows how samples are separated.

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

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

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

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

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

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

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

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

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

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

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

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk ATC-mclust-collect-classes

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 17171 rows and 54 columns.
#>   Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'NMF' method.
#>   Performed in total 1250 partitions by row resampling.
#>   Best k for subgroups seems to be 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           0.974       0.991         0.5082 0.491   0.491
#> 3 3 0.807           0.782       0.894         0.1976 0.911   0.821
#> 4 4 0.799           0.828       0.902         0.1368 0.859   0.663
#> 5 5 0.758           0.693       0.831         0.0405 0.954   0.850
#> 6 6 0.729           0.676       0.826         0.0377 0.891   0.663

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
#> SRR975551     1   0.000      1.000 1.000 0.000
#> SRR975552     1   0.000      1.000 1.000 0.000
#> SRR975554     1   0.000      1.000 1.000 0.000
#> SRR975553     2   0.000      0.980 0.000 1.000
#> SRR975555     1   0.000      1.000 1.000 0.000
#> SRR975556     2   0.000      0.980 0.000 1.000
#> SRR975557     2   0.000      0.980 0.000 1.000
#> SRR975558     1   0.000      1.000 1.000 0.000
#> SRR975559     1   0.000      1.000 1.000 0.000
#> SRR975560     2   0.000      0.980 0.000 1.000
#> SRR975561     2   0.000      0.980 0.000 1.000
#> SRR975562     1   0.000      1.000 1.000 0.000
#> SRR975563     2   0.000      0.980 0.000 1.000
#> SRR975564     1   0.000      1.000 1.000 0.000
#> SRR975565     1   0.000      1.000 1.000 0.000
#> SRR975566     1   0.000      1.000 1.000 0.000
#> SRR975567     1   0.000      1.000 1.000 0.000
#> SRR975568     1   0.000      1.000 1.000 0.000
#> SRR975569     2   0.000      0.980 0.000 1.000
#> SRR975570     2   0.000      0.980 0.000 1.000
#> SRR975571     2   0.000      0.980 0.000 1.000
#> SRR975572     2   0.000      0.980 0.000 1.000
#> SRR975573     2   0.000      0.980 0.000 1.000
#> SRR975574     2   0.000      0.980 0.000 1.000
#> SRR975575     2   0.000      0.980 0.000 1.000
#> SRR975576     2   0.000      0.980 0.000 1.000
#> SRR975577     2   0.000      0.980 0.000 1.000
#> SRR975578     2   0.000      0.980 0.000 1.000
#> SRR975579     2   0.000      0.980 0.000 1.000
#> SRR975580     2   0.000      0.980 0.000 1.000
#> SRR975581     2   0.000      0.980 0.000 1.000
#> SRR975582     2   0.000      0.980 0.000 1.000
#> SRR975583     2   0.000      0.980 0.000 1.000
#> SRR975584     2   0.000      0.980 0.000 1.000
#> SRR975585     2   0.000      0.980 0.000 1.000
#> SRR975586     2   0.000      0.980 0.000 1.000
#> SRR975587     1   0.000      1.000 1.000 0.000
#> SRR975588     2   0.000      0.980 0.000 1.000
#> SRR975589     1   0.000      1.000 1.000 0.000
#> SRR975590     1   0.000      1.000 1.000 0.000
#> SRR975591     1   0.000      1.000 1.000 0.000
#> SRR975592     1   0.000      1.000 1.000 0.000
#> SRR975593     1   0.000      1.000 1.000 0.000
#> SRR975594     2   0.999      0.062 0.484 0.516
#> SRR975595     1   0.000      1.000 1.000 0.000
#> SRR975597     1   0.000      1.000 1.000 0.000
#> SRR975596     1   0.000      1.000 1.000 0.000
#> SRR975598     1   0.000      1.000 1.000 0.000
#> SRR975599     1   0.000      1.000 1.000 0.000
#> SRR975600     1   0.000      1.000 1.000 0.000
#> SRR975601     1   0.000      1.000 1.000 0.000
#> SRR975602     1   0.000      1.000 1.000 0.000
#> SRR975603     1   0.000      1.000 1.000 0.000
#> SRR975604     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
#> SRR975551     1  0.1289     0.8127 0.968 0.000 0.032
#> SRR975552     1  0.1289     0.8127 0.968 0.000 0.032
#> SRR975554     1  0.0747     0.8250 0.984 0.000 0.016
#> SRR975553     2  0.0000     0.9827 0.000 1.000 0.000
#> SRR975555     1  0.0892     0.8179 0.980 0.000 0.020
#> SRR975556     2  0.0000     0.9827 0.000 1.000 0.000
#> SRR975557     3  0.6421     0.2279 0.004 0.424 0.572
#> SRR975558     1  0.4887     0.7349 0.772 0.000 0.228
#> SRR975559     1  0.6154     0.5431 0.592 0.000 0.408
#> SRR975560     2  0.5899     0.5053 0.020 0.736 0.244
#> SRR975561     2  0.0000     0.9827 0.000 1.000 0.000
#> SRR975562     1  0.6260     0.4869 0.552 0.000 0.448
#> SRR975563     2  0.0000     0.9827 0.000 1.000 0.000
#> SRR975564     1  0.1031     0.8164 0.976 0.000 0.024
#> SRR975565     1  0.1289     0.8127 0.968 0.000 0.032
#> SRR975566     1  0.2356     0.8204 0.928 0.000 0.072
#> SRR975567     1  0.3038     0.8083 0.896 0.000 0.104
#> SRR975568     1  0.1163     0.8146 0.972 0.000 0.028
#> SRR975569     2  0.0000     0.9827 0.000 1.000 0.000
#> SRR975570     2  0.0000     0.9827 0.000 1.000 0.000
#> SRR975571     2  0.0000     0.9827 0.000 1.000 0.000
#> SRR975572     2  0.0000     0.9827 0.000 1.000 0.000
#> SRR975573     2  0.0000     0.9827 0.000 1.000 0.000
#> SRR975574     2  0.0000     0.9827 0.000 1.000 0.000
#> SRR975575     2  0.0000     0.9827 0.000 1.000 0.000
#> SRR975576     2  0.0000     0.9827 0.000 1.000 0.000
#> SRR975577     2  0.0000     0.9827 0.000 1.000 0.000
#> SRR975578     2  0.0000     0.9827 0.000 1.000 0.000
#> SRR975579     3  0.6309     0.0264 0.000 0.496 0.504
#> SRR975580     2  0.0592     0.9675 0.000 0.988 0.012
#> SRR975581     2  0.0000     0.9827 0.000 1.000 0.000
#> SRR975582     2  0.0000     0.9827 0.000 1.000 0.000
#> SRR975583     2  0.0000     0.9827 0.000 1.000 0.000
#> SRR975584     2  0.0000     0.9827 0.000 1.000 0.000
#> SRR975585     2  0.0000     0.9827 0.000 1.000 0.000
#> SRR975586     2  0.0000     0.9827 0.000 1.000 0.000
#> SRR975587     1  0.0237     0.8228 0.996 0.000 0.004
#> SRR975588     2  0.0000     0.9827 0.000 1.000 0.000
#> SRR975589     1  0.1964     0.8246 0.944 0.000 0.056
#> SRR975590     1  0.1289     0.8127 0.968 0.000 0.032
#> SRR975591     3  0.2625     0.4769 0.084 0.000 0.916
#> SRR975592     1  0.0892     0.8261 0.980 0.000 0.020
#> SRR975593     1  0.5988     0.5946 0.632 0.000 0.368
#> SRR975594     3  0.1647     0.5006 0.036 0.004 0.960
#> SRR975595     1  0.4399     0.7629 0.812 0.000 0.188
#> SRR975597     1  0.1289     0.8268 0.968 0.000 0.032
#> SRR975596     1  0.6267     0.4799 0.548 0.000 0.452
#> SRR975598     1  0.5363     0.6962 0.724 0.000 0.276
#> SRR975599     1  0.6280     0.4654 0.540 0.000 0.460
#> SRR975600     1  0.0424     0.8240 0.992 0.000 0.008
#> SRR975601     1  0.2165     0.8230 0.936 0.000 0.064
#> SRR975602     1  0.1753     0.8261 0.952 0.000 0.048
#> SRR975603     1  0.6267     0.4772 0.548 0.000 0.452
#> SRR975604     3  0.6154    -0.2976 0.408 0.000 0.592

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4
#> SRR975551     1  0.1109     0.8283 0.968 0.000 0.028 0.004
#> SRR975552     1  0.0657     0.8238 0.984 0.000 0.012 0.004
#> SRR975554     1  0.4992     0.0195 0.524 0.000 0.476 0.000
#> SRR975553     2  0.0000     0.9904 0.000 1.000 0.000 0.000
#> SRR975555     3  0.5055     0.4758 0.368 0.000 0.624 0.008
#> SRR975556     2  0.0188     0.9886 0.000 0.996 0.000 0.004
#> SRR975557     4  0.1114     0.8789 0.004 0.008 0.016 0.972
#> SRR975558     3  0.4304     0.6760 0.284 0.000 0.716 0.000
#> SRR975559     3  0.2530     0.8238 0.112 0.000 0.888 0.000
#> SRR975560     3  0.4875     0.4176 0.008 0.296 0.692 0.004
#> SRR975561     2  0.0336     0.9876 0.000 0.992 0.008 0.000
#> SRR975562     3  0.2081     0.8183 0.084 0.000 0.916 0.000
#> SRR975563     2  0.0000     0.9904 0.000 1.000 0.000 0.000
#> SRR975564     1  0.4920     0.4303 0.628 0.000 0.368 0.004
#> SRR975565     1  0.1004     0.8280 0.972 0.000 0.024 0.004
#> SRR975566     1  0.3356     0.7615 0.824 0.000 0.176 0.000
#> SRR975567     1  0.4222     0.6424 0.728 0.000 0.272 0.000
#> SRR975568     1  0.0336     0.8231 0.992 0.000 0.008 0.000
#> SRR975569     2  0.0000     0.9904 0.000 1.000 0.000 0.000
#> SRR975570     2  0.0000     0.9904 0.000 1.000 0.000 0.000
#> SRR975571     2  0.0000     0.9904 0.000 1.000 0.000 0.000
#> SRR975572     2  0.0000     0.9904 0.000 1.000 0.000 0.000
#> SRR975573     2  0.0000     0.9904 0.000 1.000 0.000 0.000
#> SRR975574     2  0.0000     0.9904 0.000 1.000 0.000 0.000
#> SRR975575     2  0.0000     0.9904 0.000 1.000 0.000 0.000
#> SRR975576     2  0.0336     0.9876 0.000 0.992 0.008 0.000
#> SRR975577     2  0.0336     0.9876 0.000 0.992 0.008 0.000
#> SRR975578     2  0.0336     0.9876 0.000 0.992 0.008 0.000
#> SRR975579     4  0.1406     0.8702 0.000 0.024 0.016 0.960
#> SRR975580     2  0.3128     0.8388 0.004 0.864 0.128 0.004
#> SRR975581     2  0.0336     0.9876 0.000 0.992 0.008 0.000
#> SRR975582     2  0.0000     0.9904 0.000 1.000 0.000 0.000
#> SRR975583     2  0.0000     0.9904 0.000 1.000 0.000 0.000
#> SRR975584     2  0.0000     0.9904 0.000 1.000 0.000 0.000
#> SRR975585     2  0.0000     0.9904 0.000 1.000 0.000 0.000
#> SRR975586     2  0.0524     0.9853 0.000 0.988 0.008 0.004
#> SRR975587     1  0.0921     0.8282 0.972 0.000 0.028 0.000
#> SRR975588     2  0.0188     0.9884 0.000 0.996 0.000 0.004
#> SRR975589     1  0.3219     0.7716 0.836 0.000 0.164 0.000
#> SRR975590     1  0.0000     0.8174 1.000 0.000 0.000 0.000
#> SRR975591     4  0.0817     0.8745 0.024 0.000 0.000 0.976
#> SRR975592     1  0.3837     0.7125 0.776 0.000 0.224 0.000
#> SRR975593     3  0.3764     0.7724 0.216 0.000 0.784 0.000
#> SRR975594     4  0.0672     0.8787 0.008 0.000 0.008 0.984
#> SRR975595     3  0.2921     0.8206 0.140 0.000 0.860 0.000
#> SRR975597     3  0.3668     0.7961 0.188 0.000 0.808 0.004
#> SRR975596     3  0.2149     0.8198 0.088 0.000 0.912 0.000
#> SRR975598     3  0.2216     0.8215 0.092 0.000 0.908 0.000
#> SRR975599     3  0.2011     0.8156 0.080 0.000 0.920 0.000
#> SRR975600     1  0.0376     0.8207 0.992 0.000 0.004 0.004
#> SRR975601     1  0.2494     0.8155 0.916 0.000 0.048 0.036
#> SRR975602     3  0.3219     0.8123 0.164 0.000 0.836 0.000
#> SRR975603     3  0.7236     0.4188 0.168 0.000 0.520 0.312
#> SRR975604     4  0.6116     0.3687 0.068 0.000 0.320 0.612

show/hide code output

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

#>           class entropy silhouette    p1    p2    p3    p4 p5
#> SRR975551     3  0.2144     0.7061 0.020 0.000 0.912 0.000 NA
#> SRR975552     3  0.1341     0.7043 0.000 0.000 0.944 0.000 NA
#> SRR975554     3  0.3790     0.4881 0.272 0.000 0.724 0.000 NA
#> SRR975553     2  0.0000     0.9618 0.000 1.000 0.000 0.000 NA
#> SRR975555     1  0.5798     0.4793 0.608 0.000 0.236 0.000 NA
#> SRR975556     2  0.0703     0.9516 0.000 0.976 0.000 0.000 NA
#> SRR975557     4  0.4291     0.6216 0.000 0.000 0.000 0.536 NA
#> SRR975558     1  0.5752     0.4894 0.620 0.000 0.208 0.000 NA
#> SRR975559     1  0.4138     0.4497 0.616 0.000 0.384 0.000 NA
#> SRR975560     1  0.2992     0.5718 0.872 0.092 0.012 0.000 NA
#> SRR975561     2  0.0162     0.9615 0.000 0.996 0.000 0.000 NA
#> SRR975562     1  0.1502     0.6674 0.940 0.000 0.056 0.000 NA
#> SRR975563     2  0.0000     0.9618 0.000 1.000 0.000 0.000 NA
#> SRR975564     3  0.5990     0.4033 0.296 0.000 0.560 0.000 NA
#> SRR975565     3  0.2293     0.6966 0.016 0.000 0.900 0.000 NA
#> SRR975566     3  0.2127     0.6910 0.108 0.000 0.892 0.000 NA
#> SRR975567     3  0.5384     0.5412 0.196 0.000 0.664 0.000 NA
#> SRR975568     3  0.3123     0.6624 0.012 0.000 0.828 0.000 NA
#> SRR975569     2  0.1671     0.9099 0.000 0.924 0.000 0.000 NA
#> SRR975570     2  0.0000     0.9618 0.000 1.000 0.000 0.000 NA
#> SRR975571     2  0.0000     0.9618 0.000 1.000 0.000 0.000 NA
#> SRR975572     2  0.0000     0.9618 0.000 1.000 0.000 0.000 NA
#> SRR975573     2  0.0000     0.9618 0.000 1.000 0.000 0.000 NA
#> SRR975574     2  0.0162     0.9615 0.000 0.996 0.000 0.000 NA
#> SRR975575     2  0.0000     0.9618 0.000 1.000 0.000 0.000 NA
#> SRR975576     2  0.0162     0.9615 0.000 0.996 0.000 0.000 NA
#> SRR975577     2  0.0162     0.9615 0.000 0.996 0.000 0.000 NA
#> SRR975578     2  0.0162     0.9615 0.000 0.996 0.000 0.000 NA
#> SRR975579     4  0.4291     0.6216 0.000 0.000 0.000 0.536 NA
#> SRR975580     2  0.4794     0.2163 0.464 0.520 0.004 0.000 NA
#> SRR975581     2  0.0162     0.9615 0.000 0.996 0.000 0.000 NA
#> SRR975582     2  0.0162     0.9615 0.000 0.996 0.000 0.000 NA
#> SRR975583     2  0.0000     0.9618 0.000 1.000 0.000 0.000 NA
#> SRR975584     2  0.0290     0.9582 0.000 0.992 0.000 0.000 NA
#> SRR975585     2  0.0000     0.9618 0.000 1.000 0.000 0.000 NA
#> SRR975586     2  0.2067     0.9051 0.032 0.920 0.000 0.000 NA
#> SRR975587     3  0.1901     0.7109 0.004 0.000 0.932 0.024 NA
#> SRR975588     2  0.2127     0.8825 0.000 0.892 0.000 0.000 NA
#> SRR975589     3  0.4057     0.6772 0.120 0.000 0.792 0.000 NA
#> SRR975590     3  0.1502     0.7032 0.004 0.000 0.940 0.000 NA
#> SRR975591     4  0.0290     0.6892 0.000 0.000 0.008 0.992 NA
#> SRR975592     3  0.2900     0.6891 0.108 0.000 0.864 0.000 NA
#> SRR975593     3  0.4827    -0.1968 0.476 0.000 0.504 0.000 NA
#> SRR975594     4  0.0000     0.6892 0.000 0.000 0.000 1.000 NA
#> SRR975595     1  0.4127     0.5571 0.680 0.000 0.312 0.000 NA
#> SRR975597     1  0.4542     0.2844 0.536 0.000 0.456 0.000 NA
#> SRR975596     1  0.1341     0.6690 0.944 0.000 0.056 0.000 NA
#> SRR975598     1  0.3562     0.6458 0.788 0.000 0.196 0.000 NA
#> SRR975599     1  0.0960     0.6465 0.972 0.000 0.016 0.008 NA
#> SRR975600     3  0.4729     0.6214 0.024 0.000 0.748 0.048 NA
#> SRR975601     4  0.6426     0.0365 0.012 0.000 0.372 0.488 NA
#> SRR975602     1  0.4415     0.3318 0.552 0.000 0.444 0.000 NA
#> SRR975603     3  0.7369     0.1368 0.260 0.000 0.448 0.252 NA
#> SRR975604     4  0.5579     0.5144 0.172 0.000 0.084 0.700 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
#> SRR975551     1  0.1881     0.5889 0.924 0.000 0.004 0.004 0.052 0.016
#> SRR975552     1  0.1364     0.5855 0.944 0.000 0.004 0.004 0.048 0.000
#> SRR975554     1  0.2667     0.6179 0.852 0.000 0.000 0.000 0.020 0.128
#> SRR975553     2  0.0260     0.9576 0.000 0.992 0.000 0.000 0.008 0.000
#> SRR975555     6  0.6268     0.3121 0.156 0.000 0.016 0.040 0.204 0.584
#> SRR975556     2  0.2730     0.9013 0.000 0.872 0.004 0.024 0.092 0.008
#> SRR975557     4  0.2932     0.9805 0.000 0.000 0.164 0.820 0.016 0.000
#> SRR975558     5  0.5491     0.2650 0.092 0.004 0.000 0.008 0.532 0.364
#> SRR975559     1  0.4253     0.4708 0.608 0.000 0.000 0.008 0.012 0.372
#> SRR975560     6  0.2078     0.6509 0.000 0.040 0.000 0.012 0.032 0.916
#> SRR975561     2  0.1297     0.9506 0.000 0.948 0.000 0.012 0.040 0.000
#> SRR975562     6  0.1908     0.6771 0.096 0.000 0.004 0.000 0.000 0.900
#> SRR975563     2  0.0363     0.9582 0.000 0.988 0.000 0.000 0.012 0.000
#> SRR975564     5  0.6000     0.5786 0.332 0.000 0.004 0.004 0.476 0.184
#> SRR975565     1  0.2840     0.5413 0.872 0.000 0.008 0.032 0.080 0.008
#> SRR975566     1  0.2999     0.5846 0.840 0.000 0.000 0.000 0.112 0.048
#> SRR975567     1  0.5984     0.1980 0.600 0.000 0.004 0.112 0.228 0.056
#> SRR975568     5  0.3907     0.5186 0.408 0.000 0.004 0.000 0.588 0.000
#> SRR975569     2  0.2765     0.8751 0.000 0.876 0.016 0.044 0.064 0.000
#> SRR975570     2  0.0260     0.9560 0.000 0.992 0.000 0.000 0.008 0.000
#> SRR975571     2  0.0260     0.9576 0.000 0.992 0.000 0.000 0.008 0.000
#> SRR975572     2  0.0000     0.9573 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975573     2  0.0000     0.9573 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975574     2  0.0603     0.9574 0.000 0.980 0.000 0.004 0.016 0.000
#> SRR975575     2  0.0000     0.9573 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975576     2  0.1124     0.9527 0.000 0.956 0.000 0.008 0.036 0.000
#> SRR975577     2  0.1124     0.9527 0.000 0.956 0.000 0.008 0.036 0.000
#> SRR975578     2  0.1124     0.9527 0.000 0.956 0.000 0.008 0.036 0.000
#> SRR975579     4  0.2491     0.9805 0.000 0.000 0.164 0.836 0.000 0.000
#> SRR975580     6  0.3837     0.4700 0.000 0.224 0.000 0.016 0.016 0.744
#> SRR975581     2  0.1124     0.9527 0.000 0.956 0.000 0.008 0.036 0.000
#> SRR975582     2  0.1049     0.9535 0.000 0.960 0.000 0.008 0.032 0.000
#> SRR975583     2  0.0000     0.9573 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR975584     2  0.0622     0.9545 0.000 0.980 0.000 0.008 0.012 0.000
#> SRR975585     2  0.0146     0.9578 0.000 0.996 0.000 0.000 0.004 0.000
#> SRR975586     2  0.3693     0.8066 0.000 0.800 0.000 0.016 0.136 0.048
#> SRR975587     1  0.0458     0.6010 0.984 0.000 0.016 0.000 0.000 0.000
#> SRR975588     2  0.3374     0.8345 0.000 0.836 0.024 0.048 0.092 0.000
#> SRR975589     1  0.5071    -0.1499 0.552 0.000 0.004 0.004 0.380 0.060
#> SRR975590     1  0.0972     0.6004 0.964 0.000 0.000 0.000 0.028 0.008
#> SRR975591     3  0.4225     0.6510 0.084 0.000 0.784 0.060 0.072 0.000
#> SRR975592     1  0.3062     0.5372 0.816 0.000 0.000 0.000 0.160 0.024
#> SRR975593     1  0.5408     0.4359 0.616 0.000 0.004 0.004 0.168 0.208
#> SRR975594     3  0.1204     0.5641 0.000 0.000 0.944 0.056 0.000 0.000
#> SRR975595     1  0.4227     0.1603 0.500 0.000 0.008 0.000 0.004 0.488
#> SRR975597     1  0.3895     0.5562 0.696 0.000 0.004 0.000 0.016 0.284
#> SRR975596     6  0.2211     0.6769 0.080 0.000 0.004 0.008 0.008 0.900
#> SRR975598     6  0.4118     0.0738 0.396 0.000 0.004 0.000 0.008 0.592
#> SRR975599     6  0.1862     0.6663 0.012 0.000 0.008 0.032 0.016 0.932
#> SRR975600     5  0.4273     0.5849 0.364 0.000 0.008 0.004 0.616 0.008
#> SRR975601     3  0.4000     0.5949 0.192 0.000 0.756 0.032 0.020 0.000
#> SRR975602     1  0.3738     0.5427 0.680 0.000 0.000 0.004 0.004 0.312
#> SRR975603     1  0.6950     0.1047 0.512 0.000 0.124 0.012 0.236 0.116
#> SRR975604     3  0.4668     0.6309 0.048 0.000 0.732 0.004 0.172 0.044

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

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