Date: 2019-12-25 20:17:18 CET, cola version: 1.3.2
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All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 21168 rows and 58 columns.
#> Top rows are extracted by 'SD, CV, MAD, ATC' methods.
#> Subgroups are detected by 'hclust, kmeans, skmeans, pam, mclust, NMF' method.
#> Number of partitions are tried for k = 2, 3, 4, 5, 6.
#> Performed in total 30000 partitions by row resampling.
#>
#> Following methods can be applied to this 'ConsensusPartitionList' object:
#> [1] "cola_report" "collect_classes" "collect_plots" "collect_stats"
#> [5] "colnames" "functional_enrichment" "get_anno_col" "get_anno"
#> [9] "get_classes" "get_matrix" "get_membership" "get_stats"
#> [13] "is_best_k" "is_stable_k" "ncol" "nrow"
#> [17] "rownames" "show" "suggest_best_k" "test_to_known_factors"
#> [21] "top_rows_heatmap" "top_rows_overlap"
#>
#> You can get result for a single method by, e.g. object["SD", "hclust"] or object["SD:hclust"]
#> or a subset of methods by object[c("SD", "CV")], c("hclust", "kmeans")]
The call of run_all_consensus_partition_methods() was:
#> run_all_consensus_partition_methods(data = mat, mc.cores = 4, anno = anno)
Dimension of the input matrix:
mat = get_matrix(res_list)
dim(mat)
#> [1] 21168 58
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| SD:kmeans | 2 | 1.000 | 0.999 | 0.998 | ** | |
| SD:mclust | 2 | 1.000 | 1.000 | 1.000 | ** | |
| SD:NMF | 2 | 1.000 | 0.998 | 0.999 | ** | |
| CV:kmeans | 2 | 1.000 | 0.991 | 0.995 | ** | |
| MAD:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| MAD:NMF | 2 | 1.000 | 0.990 | 0.995 | ** | |
| ATC:kmeans | 4 | 1.000 | 0.965 | 0.971 | ** | 2 |
| ATC:skmeans | 2 | 1.000 | 0.986 | 0.994 | ** | |
| ATC:pam | 4 | 1.000 | 0.962 | 0.985 | ** | 3 |
| MAD:pam | 6 | 0.981 | 0.918 | 0.965 | ** | 2,4,5 |
| ATC:mclust | 4 | 0.976 | 0.929 | 0.964 | ** | |
| CV:NMF | 6 | 0.964 | 0.936 | 0.966 | ** | 2,3 |
| CV:pam | 5 | 0.952 | 0.927 | 0.969 | ** | 2,4 |
| CV:skmeans | 6 | 0.947 | 0.946 | 0.941 | * | 2,3,4,5 |
| SD:skmeans | 6 | 0.938 | 0.933 | 0.926 | * | 2,4,5 |
| SD:pam | 6 | 0.933 | 0.907 | 0.960 | * | 2 |
| ATC:NMF | 2 | 0.928 | 0.938 | 0.976 | * | |
| MAD:skmeans | 6 | 0.927 | 0.951 | 0.925 | * | 2,4,5 |
| MAD:mclust | 6 | 0.919 | 0.885 | 0.935 | * | 2,5 |
| CV:mclust | 6 | 0.919 | 0.838 | 0.920 | * | 2 |
| CV:hclust | 4 | 0.631 | 0.896 | 0.879 | ||
| MAD:hclust | 3 | 0.534 | 0.832 | 0.895 | ||
| ATC:hclust | 2 | 0.496 | 0.886 | 0.903 | ||
| SD:hclust | 3 | 0.461 | 0.596 | 0.792 |
**: 1-PAC > 0.95, *: 1-PAC > 0.9
Cumulative distribution function curves of consensus matrix for all methods.
collect_plots(res_list, fun = plot_ecdf)
Consensus heatmaps for all methods. (What is a consensus heatmap?)
collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = consensus_heatmap, mc.cores = 4)
Membership heatmaps for all methods. (What is a membership heatmap?)
collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = membership_heatmap, mc.cores = 4)
Signature heatmaps for all methods. (What is a signature heatmap?)
Note in following heatmaps, rows are scaled.
collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 3, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 4, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 5, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 6, fun = get_signatures, mc.cores = 4)
The statistics used for measuring the stability of consensus partitioning. (How are they defined?)
get_stats(res_list, k = 2)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 2 1.000 0.998 0.999 0.422 0.578 0.578
#> CV:NMF 2 1.000 0.969 0.988 0.423 0.578 0.578
#> MAD:NMF 2 1.000 0.990 0.995 0.426 0.578 0.578
#> ATC:NMF 2 0.928 0.938 0.976 0.303 0.710 0.710
#> SD:skmeans 2 1.000 1.000 1.000 0.422 0.578 0.578
#> CV:skmeans 2 1.000 0.991 0.996 0.425 0.578 0.578
#> MAD:skmeans 2 0.900 0.983 0.991 0.428 0.578 0.578
#> ATC:skmeans 2 1.000 0.986 0.994 0.501 0.501 0.501
#> SD:mclust 2 1.000 1.000 1.000 0.422 0.578 0.578
#> CV:mclust 2 1.000 1.000 1.000 0.422 0.578 0.578
#> MAD:mclust 2 1.000 1.000 1.000 0.422 0.578 0.578
#> ATC:mclust 2 0.794 0.901 0.957 0.435 0.552 0.552
#> SD:kmeans 2 1.000 0.999 0.998 0.422 0.578 0.578
#> CV:kmeans 2 1.000 0.991 0.995 0.419 0.578 0.578
#> MAD:kmeans 2 1.000 1.000 1.000 0.422 0.578 0.578
#> ATC:kmeans 2 1.000 1.000 1.000 0.500 0.501 0.501
#> SD:pam 2 1.000 1.000 1.000 0.422 0.578 0.578
#> CV:pam 2 1.000 1.000 1.000 0.422 0.578 0.578
#> MAD:pam 2 1.000 1.000 1.000 0.422 0.578 0.578
#> ATC:pam 2 0.733 0.956 0.972 0.483 0.501 0.501
#> SD:hclust 2 0.805 0.863 0.943 0.356 0.610 0.610
#> CV:hclust 2 0.781 0.875 0.946 0.328 0.733 0.733
#> MAD:hclust 2 0.805 0.949 0.970 0.380 0.593 0.593
#> ATC:hclust 2 0.496 0.886 0.903 0.430 0.501 0.501
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.886 0.904 0.960 0.586 0.724 0.534
#> CV:NMF 3 0.974 0.945 0.978 0.588 0.724 0.534
#> MAD:NMF 3 0.834 0.872 0.938 0.561 0.724 0.534
#> ATC:NMF 3 0.744 0.793 0.922 1.023 0.628 0.494
#> SD:skmeans 3 0.780 0.887 0.924 0.543 0.750 0.567
#> CV:skmeans 3 0.991 0.950 0.966 0.568 0.747 0.563
#> MAD:skmeans 3 0.781 0.930 0.951 0.540 0.750 0.567
#> ATC:skmeans 3 0.849 0.910 0.938 0.261 0.861 0.722
#> SD:mclust 3 0.712 0.819 0.903 0.487 0.789 0.636
#> CV:mclust 3 0.663 0.684 0.855 0.492 0.789 0.636
#> MAD:mclust 3 0.752 0.783 0.891 0.523 0.789 0.636
#> ATC:mclust 3 0.490 0.795 0.860 0.404 0.726 0.531
#> SD:kmeans 3 0.624 0.835 0.830 0.455 0.753 0.573
#> CV:kmeans 3 0.632 0.850 0.866 0.500 0.726 0.537
#> MAD:kmeans 3 0.639 0.894 0.867 0.478 0.758 0.582
#> ATC:kmeans 3 0.557 0.774 0.878 0.267 0.624 0.393
#> SD:pam 3 0.750 0.815 0.845 0.467 0.780 0.619
#> CV:pam 3 0.734 0.933 0.915 0.473 0.789 0.636
#> MAD:pam 3 0.759 0.811 0.848 0.494 0.758 0.582
#> ATC:pam 3 0.916 0.928 0.959 0.352 0.742 0.529
#> SD:hclust 3 0.461 0.596 0.792 0.515 0.950 0.919
#> CV:hclust 3 0.563 0.770 0.789 0.626 0.681 0.564
#> MAD:hclust 3 0.534 0.832 0.895 0.693 0.734 0.551
#> ATC:hclust 3 0.757 0.819 0.926 0.346 0.940 0.879
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.877 0.873 0.929 0.1190 0.869 0.630
#> CV:NMF 4 0.820 0.908 0.925 0.1120 0.889 0.675
#> MAD:NMF 4 0.896 0.882 0.943 0.1344 0.903 0.711
#> ATC:NMF 4 0.633 0.681 0.856 0.1667 0.731 0.421
#> SD:skmeans 4 1.000 0.982 0.989 0.1562 0.903 0.712
#> CV:skmeans 4 1.000 0.946 0.978 0.1315 0.895 0.689
#> MAD:skmeans 4 1.000 0.976 0.987 0.1427 0.903 0.712
#> ATC:skmeans 4 0.792 0.832 0.847 0.1124 0.946 0.849
#> SD:mclust 4 0.720 0.768 0.860 0.1660 0.843 0.594
#> CV:mclust 4 0.823 0.807 0.909 0.1727 0.846 0.599
#> MAD:mclust 4 0.770 0.807 0.902 0.1458 0.858 0.622
#> ATC:mclust 4 0.976 0.929 0.964 0.1605 0.894 0.716
#> SD:kmeans 4 0.632 0.772 0.778 0.1593 0.923 0.766
#> CV:kmeans 4 0.630 0.406 0.625 0.1506 0.757 0.438
#> MAD:kmeans 4 0.683 0.893 0.830 0.1591 0.891 0.685
#> ATC:kmeans 4 1.000 0.965 0.971 0.1616 0.761 0.443
#> SD:pam 4 0.888 0.913 0.959 0.2013 0.891 0.696
#> CV:pam 4 0.970 0.947 0.977 0.1978 0.891 0.704
#> MAD:pam 4 0.982 0.959 0.984 0.1957 0.891 0.685
#> ATC:pam 4 1.000 0.962 0.985 0.1292 0.861 0.623
#> SD:hclust 4 0.635 0.479 0.788 0.2159 0.716 0.506
#> CV:hclust 4 0.631 0.896 0.879 0.2677 0.879 0.708
#> MAD:hclust 4 0.639 0.747 0.874 0.0566 0.989 0.965
#> ATC:hclust 4 0.737 0.714 0.858 0.1994 0.890 0.750
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.853 0.727 0.867 0.0503 0.936 0.755
#> CV:NMF 5 0.884 0.900 0.936 0.0622 0.939 0.761
#> MAD:NMF 5 0.778 0.706 0.826 0.0468 0.974 0.899
#> ATC:NMF 5 0.671 0.741 0.862 0.0652 0.833 0.506
#> SD:skmeans 5 1.000 0.959 0.971 0.0593 0.943 0.775
#> CV:skmeans 5 0.911 0.948 0.958 0.0587 0.946 0.783
#> MAD:skmeans 5 1.000 0.973 0.977 0.0609 0.943 0.775
#> ATC:skmeans 5 0.828 0.889 0.918 0.1002 0.897 0.669
#> SD:mclust 5 0.880 0.863 0.904 0.0807 0.909 0.667
#> CV:mclust 5 0.892 0.872 0.934 0.0727 0.943 0.773
#> MAD:mclust 5 0.932 0.890 0.946 0.0710 0.906 0.655
#> ATC:mclust 5 0.780 0.700 0.844 0.1044 0.849 0.542
#> SD:kmeans 5 0.714 0.623 0.763 0.0837 0.964 0.862
#> CV:kmeans 5 0.774 0.817 0.780 0.0752 0.829 0.485
#> MAD:kmeans 5 0.775 0.688 0.733 0.0756 0.956 0.831
#> ATC:kmeans 5 0.811 0.856 0.876 0.0585 1.000 1.000
#> SD:pam 5 0.857 0.899 0.938 0.0551 0.960 0.840
#> CV:pam 5 0.952 0.927 0.969 0.0502 0.964 0.860
#> MAD:pam 5 0.916 0.883 0.878 0.0534 0.938 0.758
#> ATC:pam 5 0.832 0.770 0.873 0.0448 0.980 0.925
#> SD:hclust 5 0.621 0.590 0.793 0.0690 0.984 0.949
#> CV:hclust 5 0.642 0.809 0.806 0.0920 0.989 0.963
#> MAD:hclust 5 0.603 0.742 0.840 0.0483 0.983 0.946
#> ATC:hclust 5 0.732 0.757 0.827 0.1077 0.791 0.456
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.873 0.882 0.921 0.0423 0.943 0.741
#> CV:NMF 6 0.964 0.936 0.966 0.0484 0.941 0.722
#> MAD:NMF 6 0.859 0.833 0.908 0.0412 0.920 0.676
#> ATC:NMF 6 0.655 0.613 0.754 0.0538 0.944 0.783
#> SD:skmeans 6 0.938 0.933 0.926 0.0460 0.956 0.783
#> CV:skmeans 6 0.947 0.946 0.941 0.0472 0.956 0.783
#> MAD:skmeans 6 0.927 0.951 0.925 0.0462 0.956 0.783
#> ATC:skmeans 6 0.878 0.854 0.898 0.0340 0.968 0.852
#> SD:mclust 6 0.831 0.793 0.887 0.0456 0.964 0.824
#> CV:mclust 6 0.919 0.838 0.920 0.0440 0.950 0.760
#> MAD:mclust 6 0.919 0.885 0.935 0.0361 0.954 0.791
#> ATC:mclust 6 0.727 0.697 0.793 0.0456 0.915 0.642
#> SD:kmeans 6 0.833 0.764 0.783 0.0530 0.907 0.621
#> CV:kmeans 6 0.827 0.851 0.849 0.0554 0.948 0.750
#> MAD:kmeans 6 0.863 0.895 0.854 0.0535 0.912 0.624
#> ATC:kmeans 6 0.787 0.742 0.781 0.0435 1.000 1.000
#> SD:pam 6 0.933 0.907 0.960 0.0533 0.948 0.760
#> CV:pam 6 0.890 0.815 0.895 0.0440 0.909 0.623
#> MAD:pam 6 0.981 0.918 0.965 0.0464 0.930 0.684
#> ATC:pam 6 0.781 0.608 0.831 0.0618 0.929 0.723
#> SD:hclust 6 0.690 0.611 0.754 0.1074 0.839 0.515
#> CV:hclust 6 0.704 0.760 0.835 0.0792 0.889 0.620
#> MAD:hclust 6 0.700 0.719 0.758 0.1018 0.868 0.573
#> ATC:hclust 6 0.857 0.785 0.915 0.0610 0.949 0.779
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n cell.type(p) agent(p) individual(p) k
#> SD:NMF 58 2.54e-13 0.00184 0.99993 2
#> CV:NMF 57 4.19e-13 0.00243 0.99985 2
#> MAD:NMF 58 2.54e-13 0.00184 0.99993 2
#> ATC:NMF 56 3.35e-04 0.51056 0.10865 2
#> SD:skmeans 58 2.54e-13 0.00184 0.99993 2
#> CV:skmeans 58 2.54e-13 0.00184 0.99993 2
#> MAD:skmeans 58 2.54e-13 0.00184 0.99993 2
#> ATC:skmeans 58 5.91e-02 0.33980 0.00642 2
#> SD:mclust 58 2.54e-13 0.00184 0.99993 2
#> CV:mclust 58 2.54e-13 0.00184 0.99993 2
#> MAD:mclust 58 2.54e-13 0.00184 0.99993 2
#> ATC:mclust 56 8.02e-07 0.06509 0.19943 2
#> SD:kmeans 58 2.54e-13 0.00184 0.99993 2
#> CV:kmeans 58 2.54e-13 0.00184 0.99993 2
#> MAD:kmeans 58 2.54e-13 0.00184 0.99993 2
#> ATC:kmeans 58 5.91e-02 0.33980 0.00642 2
#> SD:pam 58 2.54e-13 0.00184 0.99993 2
#> CV:pam 58 2.54e-13 0.00184 0.99993 2
#> MAD:pam 58 2.54e-13 0.00184 0.99993 2
#> ATC:pam 58 5.91e-02 0.33980 0.00642 2
#> SD:hclust 56 6.91e-13 0.00345 0.99856 2
#> CV:hclust 52 1.55e-09 0.03378 0.86209 2
#> MAD:hclust 57 4.70e-12 0.00409 0.99752 2
#> ATC:hclust 58 5.91e-02 0.33980 0.00642 2
test_to_known_factors(res_list, k = 3)
#> n cell.type(p) agent(p) individual(p) k
#> SD:NMF 55 2.68e-14 0.00255 0.2277 3
#> CV:NMF 56 3.19e-14 0.00495 0.2677 3
#> MAD:NMF 53 7.72e-14 0.00271 0.2899 3
#> ATC:NMF 51 6.23e-04 0.15262 0.0664 3
#> SD:skmeans 57 1.37e-14 0.00234 0.2223 3
#> CV:skmeans 57 1.75e-14 0.00372 0.3072 3
#> MAD:skmeans 57 1.37e-14 0.00234 0.2223 3
#> ATC:skmeans 57 4.38e-02 0.41724 0.0557 3
#> SD:mclust 56 2.73e-23 0.00295 0.9396 3
#> CV:mclust 45 1.32e-18 0.00297 0.8445 3
#> MAD:mclust 47 7.26e-17 0.00603 0.8139 3
#> ATC:mclust 54 1.09e-04 0.13428 0.1806 3
#> SD:kmeans 57 2.67e-14 0.00370 0.1374 3
#> CV:kmeans 55 6.77e-14 0.00411 0.2105 3
#> MAD:kmeans 58 2.30e-14 0.00274 0.1144 3
#> ATC:kmeans 58 2.57e-02 0.23343 0.0134 3
#> SD:pam 57 2.40e-13 0.00357 0.2393 3
#> CV:pam 58 1.80e-13 0.00263 0.3207 3
#> MAD:pam 57 4.94e-14 0.00233 0.1301 3
#> ATC:pam 57 3.34e-02 0.25912 0.0479 3
#> SD:hclust 52 1.38e-10 0.01802 0.8287 3
#> CV:hclust 50 2.48e-12 0.03334 0.0329 3
#> MAD:hclust 57 5.24e-15 0.00507 0.4768 3
#> ATC:hclust 53 6.30e-02 0.72788 0.0949 3
test_to_known_factors(res_list, k = 4)
#> n cell.type(p) agent(p) individual(p) k
#> SD:NMF 55 2.04e-21 0.00750 0.2875 4
#> CV:NMF 57 2.96e-22 0.01039 0.4111 4
#> MAD:NMF 54 5.34e-21 0.00970 0.2271 4
#> ATC:NMF 49 2.76e-05 0.27571 0.4019 4
#> SD:skmeans 58 1.13e-22 0.00789 0.3966 4
#> CV:skmeans 56 7.77e-22 0.00848 0.4694 4
#> MAD:skmeans 58 1.13e-22 0.00789 0.3966 4
#> ATC:skmeans 56 1.57e-01 0.10805 0.2212 4
#> SD:mclust 52 3.67e-20 0.00382 0.5380 4
#> CV:mclust 52 3.67e-20 0.00980 0.7079 4
#> MAD:mclust 54 1.46e-19 0.00898 0.7409 4
#> ATC:mclust 56 1.35e-06 0.09194 0.5035 4
#> SD:kmeans 55 2.04e-21 0.00458 0.3619 4
#> CV:kmeans 32 4.18e-13 0.00408 0.3553 4
#> MAD:kmeans 57 2.96e-22 0.00688 0.3154 4
#> ATC:kmeans 57 1.01e-02 0.58199 0.0721 4
#> SD:pam 58 1.13e-22 0.00808 0.3426 4
#> CV:pam 57 2.96e-22 0.01024 0.5266 4
#> MAD:pam 57 2.96e-22 0.00689 0.3545 4
#> ATC:pam 57 1.01e-02 0.58199 0.0721 4
#> SD:hclust 28 2.01e-11 0.44224 0.1255 4
#> CV:hclust 58 4.14e-13 0.00812 0.1188 4
#> MAD:hclust 56 7.83e-16 0.00380 0.5580 4
#> ATC:hclust 44 6.42e-02 0.18127 0.2243 4
test_to_known_factors(res_list, k = 5)
#> n cell.type(p) agent(p) individual(p) k
#> SD:NMF 47 4.46e-18 0.0225 0.17018 5
#> CV:NMF 57 5.72e-21 0.0230 0.40472 5
#> MAD:NMF 53 1.40e-20 0.0281 0.28353 5
#> ATC:NMF 51 1.81e-08 0.0181 0.67272 5
#> SD:skmeans 56 1.48e-20 0.0135 0.08347 5
#> CV:skmeans 58 2.22e-21 0.0173 0.11456 5
#> MAD:skmeans 58 2.22e-21 0.0173 0.11456 5
#> ATC:skmeans 56 3.61e-05 0.0699 0.65266 5
#> SD:mclust 55 3.81e-20 0.0134 0.18580 5
#> CV:mclust 55 3.81e-20 0.0213 0.20129 5
#> MAD:mclust 55 3.81e-20 0.0134 0.18580 5
#> ATC:mclust 45 2.43e-03 0.2226 0.56158 5
#> SD:kmeans 40 2.06e-09 0.9822 0.01974 5
#> CV:kmeans 56 1.48e-20 0.0307 0.34266 5
#> MAD:kmeans 50 4.27e-18 0.1032 0.15893 5
#> ATC:kmeans 57 1.01e-02 0.5820 0.07213 5
#> SD:pam 58 2.22e-21 0.0189 0.29260 5
#> CV:pam 56 1.48e-20 0.0299 0.42907 5
#> MAD:pam 55 3.81e-20 0.0275 0.26823 5
#> ATC:pam 52 2.60e-02 0.5425 0.17726 5
#> SD:hclust 38 3.11e-13 0.2440 0.02242 5
#> CV:hclust 57 5.73e-12 0.0244 0.12480 5
#> MAD:hclust 56 1.55e-14 0.0110 0.45100 5
#> ATC:hclust 53 4.48e-02 0.5947 0.00981 5
test_to_known_factors(res_list, k = 6)
#> n cell.type(p) agent(p) individual(p) k
#> SD:NMF 56 2.11e-19 0.04069 0.0681 6
#> CV:NMF 57 8.31e-20 0.04734 0.0885 6
#> MAD:NMF 54 1.35e-18 0.04270 0.0824 6
#> ATC:NMF 47 1.10e-06 0.00664 0.5833 6
#> SD:skmeans 57 8.31e-20 0.03200 0.0855 6
#> CV:skmeans 58 3.27e-20 0.03468 0.1104 6
#> MAD:skmeans 58 3.27e-20 0.03468 0.1104 6
#> ATC:skmeans 56 1.91e-06 0.03043 0.5551 6
#> SD:mclust 53 3.41e-18 0.06407 0.1956 6
#> CV:mclust 53 3.41e-18 0.06575 0.1830 6
#> MAD:mclust 58 3.27e-20 0.03077 0.2427 6
#> ATC:mclust 50 1.05e-04 0.25993 0.4595 6
#> SD:kmeans 47 8.59e-16 0.33939 0.0375 6
#> CV:kmeans 57 8.31e-20 0.03753 0.0534 6
#> MAD:kmeans 58 3.27e-20 0.03468 0.1104 6
#> ATC:kmeans 56 9.11e-03 0.67331 0.0861 6
#> SD:pam 56 2.11e-19 0.02434 0.0380 6
#> CV:pam 54 1.35e-18 0.04299 0.0587 6
#> MAD:pam 56 2.11e-19 0.02434 0.0380 6
#> ATC:pam 46 1.36e-03 0.57771 0.2149 6
#> SD:hclust 48 2.80e-17 0.20637 0.1519 6
#> CV:hclust 52 8.60e-18 0.02694 0.1381 6
#> MAD:hclust 53 2.52e-19 0.03434 0.0472 6
#> ATC:hclust 52 4.83e-02 0.10594 0.0699 6
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "hclust"]
# you can also extract it by
# res = res_list["SD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 58 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)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.805 0.863 0.943 0.356 0.610 0.610
#> 3 3 0.461 0.596 0.792 0.515 0.950 0.919
#> 4 4 0.635 0.479 0.788 0.216 0.716 0.506
#> 5 5 0.621 0.590 0.793 0.069 0.984 0.949
#> 6 6 0.690 0.611 0.754 0.107 0.839 0.515
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
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.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM78539 1 0.000 0.9722 1.000 0.000
#> GSM78545 1 0.000 0.9722 1.000 0.000
#> GSM78550 1 0.000 0.9722 1.000 0.000
#> GSM78554 1 0.000 0.9722 1.000 0.000
#> GSM78562 1 0.000 0.9722 1.000 0.000
#> GSM78540 1 0.000 0.9722 1.000 0.000
#> GSM78546 1 0.000 0.9722 1.000 0.000
#> GSM78551 1 0.000 0.9722 1.000 0.000
#> GSM78555 1 0.000 0.9722 1.000 0.000
#> GSM78563 1 0.000 0.9722 1.000 0.000
#> GSM43005 1 0.000 0.9722 1.000 0.000
#> GSM43008 1 0.000 0.9722 1.000 0.000
#> GSM43011 1 0.000 0.9722 1.000 0.000
#> GSM78523 1 0.000 0.9722 1.000 0.000
#> GSM78526 1 0.000 0.9722 1.000 0.000
#> GSM78529 1 0.000 0.9722 1.000 0.000
#> GSM78532 1 0.000 0.9722 1.000 0.000
#> GSM78534 1 0.000 0.9722 1.000 0.000
#> GSM78537 1 0.000 0.9722 1.000 0.000
#> GSM78543 1 0.000 0.9722 1.000 0.000
#> GSM78548 1 0.000 0.9722 1.000 0.000
#> GSM78557 1 0.000 0.9722 1.000 0.000
#> GSM78560 1 0.000 0.9722 1.000 0.000
#> GSM78565 1 0.000 0.9722 1.000 0.000
#> GSM43000 1 0.000 0.9722 1.000 0.000
#> GSM43002 1 0.000 0.9722 1.000 0.000
#> GSM43004 1 0.000 0.9722 1.000 0.000
#> GSM43007 1 0.000 0.9722 1.000 0.000
#> GSM43010 1 0.000 0.9722 1.000 0.000
#> GSM78522 1 0.000 0.9722 1.000 0.000
#> GSM78525 1 0.000 0.9722 1.000 0.000
#> GSM78528 1 0.000 0.9722 1.000 0.000
#> GSM78531 1 0.000 0.9722 1.000 0.000
#> GSM78533 1 0.000 0.9722 1.000 0.000
#> GSM78536 1 0.000 0.9722 1.000 0.000
#> GSM78541 1 0.000 0.9722 1.000 0.000
#> GSM78547 1 0.000 0.9722 1.000 0.000
#> GSM78552 1 0.000 0.9722 1.000 0.000
#> GSM78556 1 0.000 0.9722 1.000 0.000
#> GSM78559 1 0.000 0.9722 1.000 0.000
#> GSM78564 1 0.000 0.9722 1.000 0.000
#> GSM42999 2 0.000 0.8119 0.000 1.000
#> GSM43001 2 0.000 0.8119 0.000 1.000
#> GSM43003 2 0.000 0.8119 0.000 1.000
#> GSM43006 2 0.000 0.8119 0.000 1.000
#> GSM43009 2 0.000 0.8119 0.000 1.000
#> GSM43012 2 0.000 0.8119 0.000 1.000
#> GSM78524 1 1.000 -0.3236 0.500 0.500
#> GSM78527 2 0.000 0.8119 0.000 1.000
#> GSM78530 2 0.971 0.5501 0.400 0.600
#> GSM78535 1 0.987 -0.0761 0.568 0.432
#> GSM78538 2 0.971 0.5501 0.400 0.600
#> GSM78542 2 0.971 0.5501 0.400 0.600
#> GSM78544 2 0.971 0.5501 0.400 0.600
#> GSM78549 2 0.000 0.8119 0.000 1.000
#> GSM78553 2 0.971 0.5501 0.400 0.600
#> GSM78558 2 0.971 0.5501 0.400 0.600
#> GSM78561 2 0.000 0.8119 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM78539 1 0.470 0.504 0.788 0.000 0.212
#> GSM78545 1 0.608 0.575 0.612 0.000 0.388
#> GSM78550 1 0.601 0.574 0.628 0.000 0.372
#> GSM78554 1 0.465 0.508 0.792 0.000 0.208
#> GSM78562 1 0.470 0.504 0.788 0.000 0.212
#> GSM78540 1 0.470 0.504 0.788 0.000 0.212
#> GSM78546 1 0.470 0.504 0.788 0.000 0.212
#> GSM78551 1 0.601 0.574 0.628 0.000 0.372
#> GSM78555 1 0.470 0.504 0.788 0.000 0.212
#> GSM78563 1 0.470 0.504 0.788 0.000 0.212
#> GSM43005 1 0.573 0.748 0.676 0.000 0.324
#> GSM43008 1 0.573 0.748 0.676 0.000 0.324
#> GSM43011 1 0.573 0.748 0.676 0.000 0.324
#> GSM78523 1 0.573 0.748 0.676 0.000 0.324
#> GSM78526 1 0.573 0.748 0.676 0.000 0.324
#> GSM78529 1 0.573 0.748 0.676 0.000 0.324
#> GSM78532 1 0.000 0.693 1.000 0.000 0.000
#> GSM78534 1 0.573 0.748 0.676 0.000 0.324
#> GSM78537 1 0.000 0.693 1.000 0.000 0.000
#> GSM78543 1 0.000 0.693 1.000 0.000 0.000
#> GSM78548 1 0.556 0.749 0.700 0.000 0.300
#> GSM78557 1 0.341 0.731 0.876 0.000 0.124
#> GSM78560 1 0.000 0.693 1.000 0.000 0.000
#> GSM78565 1 0.000 0.693 1.000 0.000 0.000
#> GSM43000 1 0.573 0.748 0.676 0.000 0.324
#> GSM43002 1 0.573 0.748 0.676 0.000 0.324
#> GSM43004 1 0.573 0.748 0.676 0.000 0.324
#> GSM43007 1 0.573 0.748 0.676 0.000 0.324
#> GSM43010 1 0.573 0.748 0.676 0.000 0.324
#> GSM78522 1 0.573 0.748 0.676 0.000 0.324
#> GSM78525 1 0.573 0.748 0.676 0.000 0.324
#> GSM78528 1 0.573 0.748 0.676 0.000 0.324
#> GSM78531 1 0.000 0.693 1.000 0.000 0.000
#> GSM78533 1 0.573 0.748 0.676 0.000 0.324
#> GSM78536 1 0.000 0.693 1.000 0.000 0.000
#> GSM78541 1 0.000 0.693 1.000 0.000 0.000
#> GSM78547 1 0.341 0.731 0.876 0.000 0.124
#> GSM78552 1 0.341 0.731 0.876 0.000 0.124
#> GSM78556 1 0.341 0.731 0.876 0.000 0.124
#> GSM78559 1 0.000 0.693 1.000 0.000 0.000
#> GSM78564 1 0.341 0.731 0.876 0.000 0.124
#> GSM42999 2 0.000 0.659 0.000 1.000 0.000
#> GSM43001 2 0.000 0.659 0.000 1.000 0.000
#> GSM43003 2 0.000 0.659 0.000 1.000 0.000
#> GSM43006 2 0.000 0.659 0.000 1.000 0.000
#> GSM43009 2 0.000 0.659 0.000 1.000 0.000
#> GSM43012 2 0.000 0.659 0.000 1.000 0.000
#> GSM78524 3 0.985 0.774 0.292 0.288 0.420
#> GSM78527 2 0.000 0.659 0.000 1.000 0.000
#> GSM78530 2 0.911 -0.138 0.292 0.532 0.176
#> GSM78535 3 0.926 0.807 0.324 0.176 0.500
#> GSM78538 2 0.911 -0.138 0.292 0.532 0.176
#> GSM78542 2 0.911 -0.138 0.292 0.532 0.176
#> GSM78544 2 0.911 -0.138 0.292 0.532 0.176
#> GSM78549 2 0.000 0.659 0.000 1.000 0.000
#> GSM78553 2 0.911 -0.138 0.292 0.532 0.176
#> GSM78558 2 0.911 -0.138 0.292 0.532 0.176
#> GSM78561 2 0.000 0.659 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM78539 4 0.215 0.656 0.000 0.000 0.088 0.912
#> GSM78545 4 0.470 0.422 0.000 0.000 0.356 0.644
#> GSM78550 4 0.436 0.507 0.000 0.000 0.292 0.708
#> GSM78554 4 0.228 0.656 0.000 0.000 0.096 0.904
#> GSM78562 4 0.208 0.656 0.000 0.000 0.084 0.916
#> GSM78540 4 0.208 0.656 0.000 0.000 0.084 0.916
#> GSM78546 4 0.208 0.656 0.000 0.000 0.084 0.916
#> GSM78551 4 0.430 0.508 0.000 0.000 0.284 0.716
#> GSM78555 4 0.208 0.656 0.000 0.000 0.084 0.916
#> GSM78563 4 0.208 0.656 0.000 0.000 0.084 0.916
#> GSM43005 3 0.000 0.881 0.000 0.000 1.000 0.000
#> GSM43008 3 0.000 0.881 0.000 0.000 1.000 0.000
#> GSM43011 3 0.000 0.881 0.000 0.000 1.000 0.000
#> GSM78523 3 0.000 0.881 0.000 0.000 1.000 0.000
#> GSM78526 3 0.000 0.881 0.000 0.000 1.000 0.000
#> GSM78529 3 0.000 0.881 0.000 0.000 1.000 0.000
#> GSM78532 4 0.499 0.462 0.000 0.000 0.480 0.520
#> GSM78534 3 0.000 0.881 0.000 0.000 1.000 0.000
#> GSM78537 4 0.499 0.462 0.000 0.000 0.480 0.520
#> GSM78543 4 0.499 0.462 0.000 0.000 0.480 0.520
#> GSM78548 3 0.102 0.846 0.000 0.000 0.968 0.032
#> GSM78557 3 0.436 0.419 0.000 0.000 0.708 0.292
#> GSM78560 4 0.499 0.462 0.000 0.000 0.480 0.520
#> GSM78565 4 0.499 0.462 0.000 0.000 0.480 0.520
#> GSM43000 3 0.000 0.881 0.000 0.000 1.000 0.000
#> GSM43002 3 0.000 0.881 0.000 0.000 1.000 0.000
#> GSM43004 3 0.000 0.881 0.000 0.000 1.000 0.000
#> GSM43007 3 0.000 0.881 0.000 0.000 1.000 0.000
#> GSM43010 3 0.000 0.881 0.000 0.000 1.000 0.000
#> GSM78522 3 0.000 0.881 0.000 0.000 1.000 0.000
#> GSM78525 3 0.000 0.881 0.000 0.000 1.000 0.000
#> GSM78528 3 0.000 0.881 0.000 0.000 1.000 0.000
#> GSM78531 4 0.499 0.462 0.000 0.000 0.480 0.520
#> GSM78533 3 0.000 0.881 0.000 0.000 1.000 0.000
#> GSM78536 4 0.499 0.462 0.000 0.000 0.480 0.520
#> GSM78541 4 0.499 0.462 0.000 0.000 0.480 0.520
#> GSM78547 3 0.436 0.419 0.000 0.000 0.708 0.292
#> GSM78552 3 0.436 0.419 0.000 0.000 0.708 0.292
#> GSM78556 3 0.436 0.419 0.000 0.000 0.708 0.292
#> GSM78559 4 0.499 0.462 0.000 0.000 0.480 0.520
#> GSM78564 3 0.436 0.419 0.000 0.000 0.708 0.292
#> GSM42999 2 0.499 -0.605 0.468 0.532 0.000 0.000
#> GSM43001 1 0.564 1.000 0.552 0.424 0.000 0.024
#> GSM43003 2 0.499 -0.605 0.468 0.532 0.000 0.000
#> GSM43006 2 0.499 -0.633 0.476 0.524 0.000 0.000
#> GSM43009 2 0.499 -0.605 0.468 0.532 0.000 0.000
#> GSM43012 2 0.499 -0.605 0.468 0.532 0.000 0.000
#> GSM78524 2 0.543 0.247 0.232 0.708 0.000 0.060
#> GSM78527 2 0.499 -0.605 0.468 0.532 0.000 0.000
#> GSM78530 2 0.000 0.405 0.000 1.000 0.000 0.000
#> GSM78535 2 0.683 0.140 0.424 0.476 0.000 0.100
#> GSM78538 2 0.000 0.405 0.000 1.000 0.000 0.000
#> GSM78542 2 0.000 0.405 0.000 1.000 0.000 0.000
#> GSM78544 2 0.000 0.405 0.000 1.000 0.000 0.000
#> GSM78549 2 0.499 -0.605 0.468 0.532 0.000 0.000
#> GSM78553 2 0.000 0.405 0.000 1.000 0.000 0.000
#> GSM78558 2 0.000 0.405 0.000 1.000 0.000 0.000
#> GSM78561 1 0.564 1.000 0.552 0.424 0.000 0.024
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM78539 4 0.0162 0.599 0.000 0.000 0.004 0.996 0.000
#> GSM78545 4 0.4883 0.335 0.200 0.000 0.092 0.708 0.000
#> GSM78550 4 0.3388 0.433 0.200 0.000 0.008 0.792 0.000
#> GSM78554 4 0.0404 0.602 0.000 0.000 0.012 0.988 0.000
#> GSM78562 4 0.0000 0.597 0.000 0.000 0.000 1.000 0.000
#> GSM78540 4 0.0000 0.597 0.000 0.000 0.000 1.000 0.000
#> GSM78546 4 0.0000 0.597 0.000 0.000 0.000 1.000 0.000
#> GSM78551 4 0.3109 0.426 0.200 0.000 0.000 0.800 0.000
#> GSM78555 4 0.0000 0.597 0.000 0.000 0.000 1.000 0.000
#> GSM78563 4 0.0000 0.597 0.000 0.000 0.000 1.000 0.000
#> GSM43005 3 0.3109 0.803 0.200 0.000 0.800 0.000 0.000
#> GSM43008 3 0.3109 0.803 0.200 0.000 0.800 0.000 0.000
#> GSM43011 3 0.0000 0.798 0.000 0.000 1.000 0.000 0.000
#> GSM78523 3 0.0000 0.798 0.000 0.000 1.000 0.000 0.000
#> GSM78526 3 0.0000 0.798 0.000 0.000 1.000 0.000 0.000
#> GSM78529 3 0.3109 0.803 0.200 0.000 0.800 0.000 0.000
#> GSM78532 4 0.5173 0.474 0.016 0.000 0.396 0.568 0.020
#> GSM78534 3 0.0000 0.798 0.000 0.000 1.000 0.000 0.000
#> GSM78537 4 0.5173 0.474 0.016 0.000 0.396 0.568 0.020
#> GSM78543 4 0.5173 0.474 0.016 0.000 0.396 0.568 0.020
#> GSM78548 3 0.4021 0.779 0.200 0.000 0.764 0.036 0.000
#> GSM78557 3 0.4009 0.510 0.004 0.000 0.684 0.312 0.000
#> GSM78560 4 0.5173 0.474 0.016 0.000 0.396 0.568 0.020
#> GSM78565 4 0.5173 0.474 0.016 0.000 0.396 0.568 0.020
#> GSM43000 3 0.3109 0.803 0.200 0.000 0.800 0.000 0.000
#> GSM43002 3 0.3109 0.803 0.200 0.000 0.800 0.000 0.000
#> GSM43004 3 0.0000 0.798 0.000 0.000 1.000 0.000 0.000
#> GSM43007 3 0.3109 0.803 0.200 0.000 0.800 0.000 0.000
#> GSM43010 3 0.0000 0.798 0.000 0.000 1.000 0.000 0.000
#> GSM78522 3 0.0000 0.798 0.000 0.000 1.000 0.000 0.000
#> GSM78525 3 0.3109 0.803 0.200 0.000 0.800 0.000 0.000
#> GSM78528 3 0.3109 0.803 0.200 0.000 0.800 0.000 0.000
#> GSM78531 4 0.5173 0.474 0.016 0.000 0.396 0.568 0.020
#> GSM78533 3 0.0000 0.798 0.000 0.000 1.000 0.000 0.000
#> GSM78536 4 0.5173 0.474 0.016 0.000 0.396 0.568 0.020
#> GSM78541 4 0.5173 0.474 0.016 0.000 0.396 0.568 0.020
#> GSM78547 3 0.4009 0.510 0.004 0.000 0.684 0.312 0.000
#> GSM78552 3 0.4009 0.510 0.004 0.000 0.684 0.312 0.000
#> GSM78556 3 0.4009 0.510 0.004 0.000 0.684 0.312 0.000
#> GSM78559 4 0.5173 0.474 0.016 0.000 0.396 0.568 0.020
#> GSM78564 3 0.4009 0.510 0.004 0.000 0.684 0.312 0.000
#> GSM42999 2 0.0000 0.608 0.000 1.000 0.000 0.000 0.000
#> GSM43001 5 0.3274 1.000 0.000 0.220 0.000 0.000 0.780
#> GSM43003 2 0.0000 0.608 0.000 1.000 0.000 0.000 0.000
#> GSM43006 2 0.3177 0.216 0.000 0.792 0.000 0.000 0.208
#> GSM43009 2 0.0000 0.608 0.000 1.000 0.000 0.000 0.000
#> GSM43012 2 0.0000 0.608 0.000 1.000 0.000 0.000 0.000
#> GSM78524 1 0.6357 0.393 0.512 0.288 0.000 0.000 0.200
#> GSM78527 2 0.0000 0.608 0.000 1.000 0.000 0.000 0.000
#> GSM78530 2 0.6279 0.267 0.268 0.532 0.000 0.000 0.200
#> GSM78535 1 0.3109 0.561 0.800 0.000 0.000 0.000 0.200
#> GSM78538 2 0.6279 0.267 0.268 0.532 0.000 0.000 0.200
#> GSM78542 2 0.6279 0.267 0.268 0.532 0.000 0.000 0.200
#> GSM78544 2 0.6279 0.267 0.268 0.532 0.000 0.000 0.200
#> GSM78549 2 0.0000 0.608 0.000 1.000 0.000 0.000 0.000
#> GSM78553 2 0.6279 0.267 0.268 0.532 0.000 0.000 0.200
#> GSM78558 2 0.6279 0.267 0.268 0.532 0.000 0.000 0.200
#> GSM78561 5 0.3274 1.000 0.000 0.220 0.000 0.000 0.780
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM78539 4 0.2969 0.874 0.224 0.000 0.000 0.776 0.000 0.000
#> GSM78545 4 0.1858 0.594 0.012 0.000 0.000 0.912 0.000 0.076
#> GSM78550 4 0.0777 0.695 0.024 0.000 0.000 0.972 0.000 0.004
#> GSM78554 4 0.3136 0.869 0.228 0.000 0.000 0.768 0.000 0.004
#> GSM78562 4 0.2941 0.876 0.220 0.000 0.000 0.780 0.000 0.000
#> GSM78540 4 0.2941 0.876 0.220 0.000 0.000 0.780 0.000 0.000
#> GSM78546 4 0.2941 0.876 0.220 0.000 0.000 0.780 0.000 0.000
#> GSM78551 4 0.0547 0.697 0.020 0.000 0.000 0.980 0.000 0.000
#> GSM78555 4 0.2941 0.876 0.220 0.000 0.000 0.780 0.000 0.000
#> GSM78563 4 0.2941 0.876 0.220 0.000 0.000 0.780 0.000 0.000
#> GSM43005 6 0.5985 0.638 0.272 0.000 0.000 0.220 0.008 0.500
#> GSM43008 6 0.5985 0.638 0.272 0.000 0.000 0.220 0.008 0.500
#> GSM43011 6 0.0790 0.665 0.032 0.000 0.000 0.000 0.000 0.968
#> GSM78523 6 0.0790 0.665 0.032 0.000 0.000 0.000 0.000 0.968
#> GSM78526 6 0.0146 0.652 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM78529 6 0.5985 0.638 0.272 0.000 0.000 0.220 0.008 0.500
#> GSM78532 1 0.1387 0.781 0.932 0.000 0.000 0.068 0.000 0.000
#> GSM78534 6 0.0146 0.652 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM78537 1 0.1531 0.780 0.928 0.000 0.000 0.068 0.000 0.004
#> GSM78543 1 0.1387 0.781 0.932 0.000 0.000 0.068 0.000 0.000
#> GSM78548 1 0.6081 -0.176 0.472 0.000 0.000 0.228 0.008 0.292
#> GSM78557 1 0.3161 0.634 0.776 0.000 0.000 0.000 0.008 0.216
#> GSM78560 1 0.1387 0.781 0.932 0.000 0.000 0.068 0.000 0.000
#> GSM78565 1 0.1531 0.780 0.928 0.000 0.000 0.068 0.000 0.004
#> GSM43000 6 0.5785 0.654 0.224 0.000 0.000 0.220 0.008 0.548
#> GSM43002 6 0.5985 0.638 0.272 0.000 0.000 0.220 0.008 0.500
#> GSM43004 6 0.0146 0.652 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM43007 6 0.5985 0.638 0.272 0.000 0.000 0.220 0.008 0.500
#> GSM43010 6 0.0146 0.652 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM78522 6 0.0146 0.652 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM78525 6 0.5985 0.638 0.272 0.000 0.000 0.220 0.008 0.500
#> GSM78528 6 0.5985 0.638 0.272 0.000 0.000 0.220 0.008 0.500
#> GSM78531 1 0.1387 0.781 0.932 0.000 0.000 0.068 0.000 0.000
#> GSM78533 6 0.1814 0.673 0.100 0.000 0.000 0.000 0.000 0.900
#> GSM78536 1 0.1531 0.780 0.928 0.000 0.000 0.068 0.000 0.004
#> GSM78541 1 0.1531 0.780 0.928 0.000 0.000 0.068 0.000 0.004
#> GSM78547 1 0.3161 0.634 0.776 0.000 0.000 0.000 0.008 0.216
#> GSM78552 1 0.3161 0.634 0.776 0.000 0.000 0.000 0.008 0.216
#> GSM78556 1 0.3161 0.634 0.776 0.000 0.000 0.000 0.008 0.216
#> GSM78559 1 0.1531 0.780 0.928 0.000 0.000 0.068 0.000 0.004
#> GSM78564 1 0.3161 0.634 0.776 0.000 0.000 0.000 0.008 0.216
#> GSM42999 2 0.3857 0.404 0.000 0.532 0.000 0.000 0.468 0.000
#> GSM43001 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM43003 2 0.3857 0.404 0.000 0.532 0.000 0.000 0.468 0.000
#> GSM43006 5 0.5844 -0.403 0.000 0.324 0.208 0.000 0.468 0.000
#> GSM43009 2 0.3857 0.404 0.000 0.532 0.000 0.000 0.468 0.000
#> GSM43012 2 0.3857 0.404 0.000 0.532 0.000 0.000 0.468 0.000
#> GSM78524 2 0.3371 -0.013 0.000 0.708 0.000 0.000 0.292 0.000
#> GSM78527 2 0.3857 0.404 0.000 0.532 0.000 0.000 0.468 0.000
#> GSM78530 2 0.0000 0.509 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78535 5 0.4089 -0.126 0.008 0.468 0.000 0.000 0.524 0.000
#> GSM78538 2 0.0000 0.509 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78542 2 0.0000 0.509 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78544 2 0.0000 0.509 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78549 2 0.3857 0.404 0.000 0.532 0.000 0.000 0.468 0.000
#> GSM78553 2 0.0000 0.509 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78558 2 0.0000 0.509 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78561 3 0.0000 1.000 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.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) agent(p) individual(p) k
#> SD:hclust 56 6.91e-13 0.00345 0.9986 2
#> SD:hclust 52 1.38e-10 0.01802 0.8287 3
#> SD:hclust 28 2.01e-11 0.44224 0.1255 4
#> SD:hclust 38 3.11e-13 0.24395 0.0224 5
#> SD:hclust 48 2.80e-17 0.20637 0.1519 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "kmeans"]
# you can also extract it by
# res = res_list["SD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 58 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.999 0.998 0.4218 0.578 0.578
#> 3 3 0.624 0.835 0.830 0.4545 0.753 0.573
#> 4 4 0.632 0.772 0.778 0.1593 0.923 0.766
#> 5 5 0.714 0.623 0.763 0.0837 0.964 0.862
#> 6 6 0.833 0.764 0.783 0.0530 0.907 0.621
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM78539 1 0.0376 0.997 0.996 0.004
#> GSM78545 1 0.0376 0.997 0.996 0.004
#> GSM78550 1 0.0376 0.997 0.996 0.004
#> GSM78554 1 0.0376 0.997 0.996 0.004
#> GSM78562 1 0.0376 0.997 0.996 0.004
#> GSM78540 1 0.0376 0.997 0.996 0.004
#> GSM78546 1 0.0376 0.997 0.996 0.004
#> GSM78551 1 0.0376 0.997 0.996 0.004
#> GSM78555 1 0.0376 0.997 0.996 0.004
#> GSM78563 1 0.0376 0.997 0.996 0.004
#> GSM43005 1 0.0000 0.999 1.000 0.000
#> GSM43008 1 0.0000 0.999 1.000 0.000
#> GSM43011 1 0.0000 0.999 1.000 0.000
#> GSM78523 1 0.0000 0.999 1.000 0.000
#> GSM78526 1 0.0000 0.999 1.000 0.000
#> GSM78529 1 0.0000 0.999 1.000 0.000
#> GSM78532 1 0.0000 0.999 1.000 0.000
#> GSM78534 1 0.0000 0.999 1.000 0.000
#> GSM78537 1 0.0000 0.999 1.000 0.000
#> GSM78543 1 0.0000 0.999 1.000 0.000
#> GSM78548 1 0.0000 0.999 1.000 0.000
#> GSM78557 1 0.0000 0.999 1.000 0.000
#> GSM78560 1 0.0000 0.999 1.000 0.000
#> GSM78565 1 0.0000 0.999 1.000 0.000
#> GSM43000 1 0.0000 0.999 1.000 0.000
#> GSM43002 1 0.0000 0.999 1.000 0.000
#> GSM43004 1 0.0000 0.999 1.000 0.000
#> GSM43007 1 0.0000 0.999 1.000 0.000
#> GSM43010 1 0.0000 0.999 1.000 0.000
#> GSM78522 1 0.0000 0.999 1.000 0.000
#> GSM78525 1 0.0000 0.999 1.000 0.000
#> GSM78528 1 0.0000 0.999 1.000 0.000
#> GSM78531 1 0.0000 0.999 1.000 0.000
#> GSM78533 1 0.0000 0.999 1.000 0.000
#> GSM78536 1 0.0000 0.999 1.000 0.000
#> GSM78541 1 0.0000 0.999 1.000 0.000
#> GSM78547 1 0.0000 0.999 1.000 0.000
#> GSM78552 1 0.0000 0.999 1.000 0.000
#> GSM78556 1 0.0000 0.999 1.000 0.000
#> GSM78559 1 0.0000 0.999 1.000 0.000
#> GSM78564 1 0.0000 0.999 1.000 0.000
#> GSM42999 2 0.0376 1.000 0.004 0.996
#> GSM43001 2 0.0376 1.000 0.004 0.996
#> GSM43003 2 0.0376 1.000 0.004 0.996
#> GSM43006 2 0.0376 1.000 0.004 0.996
#> GSM43009 2 0.0376 1.000 0.004 0.996
#> GSM43012 2 0.0376 1.000 0.004 0.996
#> GSM78524 2 0.0376 1.000 0.004 0.996
#> GSM78527 2 0.0376 1.000 0.004 0.996
#> GSM78530 2 0.0376 1.000 0.004 0.996
#> GSM78535 2 0.0376 1.000 0.004 0.996
#> GSM78538 2 0.0376 1.000 0.004 0.996
#> GSM78542 2 0.0376 1.000 0.004 0.996
#> GSM78544 2 0.0376 1.000 0.004 0.996
#> GSM78549 2 0.0376 1.000 0.004 0.996
#> GSM78553 2 0.0376 1.000 0.004 0.996
#> GSM78558 2 0.0376 1.000 0.004 0.996
#> GSM78561 2 0.0376 1.000 0.004 0.996
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM78539 1 0.0237 0.736 0.996 0.000 0.004
#> GSM78545 1 0.0237 0.736 0.996 0.000 0.004
#> GSM78550 1 0.0237 0.736 0.996 0.000 0.004
#> GSM78554 1 0.0237 0.736 0.996 0.000 0.004
#> GSM78562 1 0.0237 0.736 0.996 0.000 0.004
#> GSM78540 1 0.0237 0.736 0.996 0.000 0.004
#> GSM78546 1 0.0237 0.736 0.996 0.000 0.004
#> GSM78551 1 0.0237 0.736 0.996 0.000 0.004
#> GSM78555 1 0.0237 0.736 0.996 0.000 0.004
#> GSM78563 1 0.0237 0.736 0.996 0.000 0.004
#> GSM43005 3 0.4555 0.931 0.200 0.000 0.800
#> GSM43008 3 0.4702 0.922 0.212 0.000 0.788
#> GSM43011 3 0.4062 0.940 0.164 0.000 0.836
#> GSM78523 3 0.4062 0.940 0.164 0.000 0.836
#> GSM78526 3 0.4062 0.940 0.164 0.000 0.836
#> GSM78529 3 0.4654 0.924 0.208 0.000 0.792
#> GSM78532 1 0.5363 0.756 0.724 0.000 0.276
#> GSM78534 3 0.4062 0.940 0.164 0.000 0.836
#> GSM78537 1 0.5363 0.756 0.724 0.000 0.276
#> GSM78543 1 0.5363 0.756 0.724 0.000 0.276
#> GSM78548 3 0.6286 0.160 0.464 0.000 0.536
#> GSM78557 1 0.5363 0.756 0.724 0.000 0.276
#> GSM78560 1 0.5363 0.756 0.724 0.000 0.276
#> GSM78565 1 0.5363 0.756 0.724 0.000 0.276
#> GSM43000 3 0.4062 0.940 0.164 0.000 0.836
#> GSM43002 3 0.4555 0.931 0.200 0.000 0.800
#> GSM43004 3 0.4121 0.938 0.168 0.000 0.832
#> GSM43007 3 0.4654 0.924 0.208 0.000 0.792
#> GSM43010 3 0.4062 0.940 0.164 0.000 0.836
#> GSM78522 3 0.4062 0.940 0.164 0.000 0.836
#> GSM78525 3 0.4399 0.936 0.188 0.000 0.812
#> GSM78528 3 0.4654 0.924 0.208 0.000 0.792
#> GSM78531 1 0.5363 0.756 0.724 0.000 0.276
#> GSM78533 3 0.4062 0.940 0.164 0.000 0.836
#> GSM78536 1 0.5363 0.756 0.724 0.000 0.276
#> GSM78541 1 0.5363 0.756 0.724 0.000 0.276
#> GSM78547 1 0.5363 0.756 0.724 0.000 0.276
#> GSM78552 1 0.5948 0.566 0.640 0.000 0.360
#> GSM78556 1 0.5363 0.756 0.724 0.000 0.276
#> GSM78559 1 0.5363 0.756 0.724 0.000 0.276
#> GSM78564 1 0.5363 0.756 0.724 0.000 0.276
#> GSM42999 2 0.0000 0.936 0.000 1.000 0.000
#> GSM43001 2 0.1964 0.922 0.000 0.944 0.056
#> GSM43003 2 0.0237 0.935 0.000 0.996 0.004
#> GSM43006 2 0.1964 0.922 0.000 0.944 0.056
#> GSM43009 2 0.2356 0.938 0.000 0.928 0.072
#> GSM43012 2 0.1964 0.922 0.000 0.944 0.056
#> GSM78524 2 0.3116 0.937 0.000 0.892 0.108
#> GSM78527 2 0.0237 0.935 0.000 0.996 0.004
#> GSM78530 2 0.3116 0.937 0.000 0.892 0.108
#> GSM78535 2 0.7949 0.632 0.252 0.640 0.108
#> GSM78538 2 0.3116 0.937 0.000 0.892 0.108
#> GSM78542 2 0.3116 0.937 0.000 0.892 0.108
#> GSM78544 2 0.3116 0.937 0.000 0.892 0.108
#> GSM78549 2 0.0000 0.936 0.000 1.000 0.000
#> GSM78553 2 0.3116 0.937 0.000 0.892 0.108
#> GSM78558 2 0.3116 0.937 0.000 0.892 0.108
#> GSM78561 2 0.1964 0.922 0.000 0.944 0.056
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM78539 4 0.4999 0.959 0.492 0.000 0.000 0.508
#> GSM78545 4 0.6130 0.901 0.440 0.000 0.048 0.512
#> GSM78550 4 0.6130 0.901 0.440 0.000 0.048 0.512
#> GSM78554 4 0.4998 0.960 0.488 0.000 0.000 0.512
#> GSM78562 4 0.4999 0.959 0.492 0.000 0.000 0.508
#> GSM78540 4 0.5000 0.957 0.500 0.000 0.000 0.500
#> GSM78546 4 0.5000 0.960 0.496 0.000 0.000 0.504
#> GSM78551 4 0.5000 0.960 0.496 0.000 0.000 0.504
#> GSM78555 1 0.5000 -0.958 0.504 0.000 0.000 0.496
#> GSM78563 1 0.5000 -0.964 0.500 0.000 0.000 0.500
#> GSM43005 3 0.3300 0.818 0.144 0.000 0.848 0.008
#> GSM43008 3 0.3300 0.818 0.144 0.000 0.848 0.008
#> GSM43011 3 0.4105 0.841 0.032 0.000 0.812 0.156
#> GSM78523 3 0.4105 0.841 0.032 0.000 0.812 0.156
#> GSM78526 3 0.4105 0.841 0.032 0.000 0.812 0.156
#> GSM78529 3 0.3300 0.818 0.144 0.000 0.848 0.008
#> GSM78532 1 0.2647 0.837 0.880 0.000 0.120 0.000
#> GSM78534 3 0.4105 0.841 0.032 0.000 0.812 0.156
#> GSM78537 1 0.2647 0.837 0.880 0.000 0.120 0.000
#> GSM78543 1 0.2647 0.837 0.880 0.000 0.120 0.000
#> GSM78548 3 0.4897 0.452 0.332 0.000 0.660 0.008
#> GSM78557 1 0.2647 0.837 0.880 0.000 0.120 0.000
#> GSM78560 1 0.2647 0.837 0.880 0.000 0.120 0.000
#> GSM78565 1 0.2647 0.837 0.880 0.000 0.120 0.000
#> GSM43000 3 0.1022 0.832 0.032 0.000 0.968 0.000
#> GSM43002 3 0.3157 0.818 0.144 0.000 0.852 0.004
#> GSM43004 3 0.4105 0.841 0.032 0.000 0.812 0.156
#> GSM43007 3 0.3300 0.818 0.144 0.000 0.848 0.008
#> GSM43010 3 0.4105 0.841 0.032 0.000 0.812 0.156
#> GSM78522 3 0.4105 0.841 0.032 0.000 0.812 0.156
#> GSM78525 3 0.3157 0.818 0.144 0.000 0.852 0.004
#> GSM78528 3 0.3300 0.818 0.144 0.000 0.848 0.008
#> GSM78531 1 0.2647 0.837 0.880 0.000 0.120 0.000
#> GSM78533 3 0.4105 0.841 0.032 0.000 0.812 0.156
#> GSM78536 1 0.2647 0.837 0.880 0.000 0.120 0.000
#> GSM78541 1 0.2647 0.837 0.880 0.000 0.120 0.000
#> GSM78547 1 0.2647 0.837 0.880 0.000 0.120 0.000
#> GSM78552 1 0.4955 0.505 0.648 0.000 0.344 0.008
#> GSM78556 1 0.2647 0.837 0.880 0.000 0.120 0.000
#> GSM78559 1 0.2647 0.837 0.880 0.000 0.120 0.000
#> GSM78564 1 0.2814 0.820 0.868 0.000 0.132 0.000
#> GSM42999 2 0.0376 0.852 0.000 0.992 0.004 0.004
#> GSM43001 2 0.4234 0.801 0.068 0.844 0.020 0.068
#> GSM43003 2 0.0336 0.850 0.000 0.992 0.000 0.008
#> GSM43006 2 0.4234 0.801 0.068 0.844 0.020 0.068
#> GSM43009 2 0.3157 0.861 0.000 0.852 0.004 0.144
#> GSM43012 2 0.3975 0.809 0.064 0.856 0.016 0.064
#> GSM78524 2 0.4516 0.854 0.000 0.736 0.012 0.252
#> GSM78527 2 0.0336 0.850 0.000 0.992 0.000 0.008
#> GSM78530 2 0.4040 0.856 0.000 0.752 0.000 0.248
#> GSM78535 2 0.7627 0.599 0.240 0.504 0.004 0.252
#> GSM78538 2 0.4040 0.856 0.000 0.752 0.000 0.248
#> GSM78542 2 0.4040 0.856 0.000 0.752 0.000 0.248
#> GSM78544 2 0.4220 0.856 0.000 0.748 0.004 0.248
#> GSM78549 2 0.0000 0.852 0.000 1.000 0.000 0.000
#> GSM78553 2 0.4040 0.856 0.000 0.752 0.000 0.248
#> GSM78558 2 0.4040 0.856 0.000 0.752 0.000 0.248
#> GSM78561 2 0.4339 0.800 0.068 0.840 0.024 0.068
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM78539 4 0.3612 0.980 0.184 0.000 0.016 0.796 0.004
#> GSM78545 4 0.4151 0.957 0.156 0.000 0.044 0.788 0.012
#> GSM78550 4 0.4151 0.957 0.156 0.000 0.044 0.788 0.012
#> GSM78554 4 0.3843 0.978 0.184 0.000 0.016 0.788 0.012
#> GSM78562 4 0.3612 0.980 0.184 0.000 0.016 0.796 0.004
#> GSM78540 4 0.2966 0.981 0.184 0.000 0.000 0.816 0.000
#> GSM78546 4 0.2966 0.981 0.184 0.000 0.000 0.816 0.000
#> GSM78551 4 0.3123 0.981 0.184 0.000 0.000 0.812 0.004
#> GSM78555 4 0.3039 0.975 0.192 0.000 0.000 0.808 0.000
#> GSM78563 4 0.2966 0.981 0.184 0.000 0.000 0.816 0.000
#> GSM43005 3 0.3093 0.694 0.168 0.000 0.824 0.008 0.000
#> GSM43008 3 0.3132 0.692 0.172 0.000 0.820 0.008 0.000
#> GSM43011 3 0.6777 0.696 0.076 0.000 0.484 0.064 0.376
#> GSM78523 3 0.6777 0.696 0.076 0.000 0.484 0.064 0.376
#> GSM78526 3 0.6777 0.696 0.076 0.000 0.484 0.064 0.376
#> GSM78529 3 0.3132 0.692 0.172 0.000 0.820 0.008 0.000
#> GSM78532 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000
#> GSM78534 3 0.6869 0.695 0.076 0.000 0.480 0.072 0.372
#> GSM78537 1 0.0290 0.953 0.992 0.000 0.000 0.000 0.008
#> GSM78543 1 0.0290 0.953 0.992 0.000 0.000 0.000 0.008
#> GSM78548 3 0.3737 0.620 0.224 0.000 0.764 0.008 0.004
#> GSM78557 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000
#> GSM78560 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000
#> GSM78565 1 0.0290 0.953 0.992 0.000 0.000 0.000 0.008
#> GSM43000 3 0.1831 0.708 0.076 0.000 0.920 0.000 0.004
#> GSM43002 3 0.2813 0.696 0.168 0.000 0.832 0.000 0.000
#> GSM43004 3 0.6869 0.695 0.076 0.000 0.480 0.072 0.372
#> GSM43007 3 0.3132 0.692 0.172 0.000 0.820 0.008 0.000
#> GSM43010 3 0.6777 0.696 0.076 0.000 0.484 0.064 0.376
#> GSM78522 3 0.6869 0.695 0.076 0.000 0.480 0.072 0.372
#> GSM78525 3 0.2732 0.698 0.160 0.000 0.840 0.000 0.000
#> GSM78528 3 0.3132 0.692 0.172 0.000 0.820 0.008 0.000
#> GSM78531 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000
#> GSM78533 3 0.6777 0.696 0.076 0.000 0.484 0.064 0.376
#> GSM78536 1 0.0290 0.953 0.992 0.000 0.000 0.000 0.008
#> GSM78541 1 0.0290 0.953 0.992 0.000 0.000 0.000 0.008
#> GSM78547 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000
#> GSM78552 1 0.4664 0.149 0.552 0.000 0.436 0.008 0.004
#> GSM78556 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000
#> GSM78559 1 0.0290 0.953 0.992 0.000 0.000 0.000 0.008
#> GSM78564 1 0.0162 0.950 0.996 0.000 0.004 0.000 0.000
#> GSM42999 2 0.1525 0.435 0.000 0.948 0.012 0.004 0.036
#> GSM43001 2 0.4952 0.396 0.000 0.756 0.032 0.100 0.112
#> GSM43003 2 0.0000 0.449 0.000 1.000 0.000 0.000 0.000
#> GSM43006 2 0.4902 0.397 0.000 0.760 0.032 0.096 0.112
#> GSM43009 2 0.4181 0.178 0.000 0.732 0.020 0.004 0.244
#> GSM43012 2 0.4042 0.414 0.000 0.820 0.040 0.040 0.100
#> GSM78524 2 0.5084 -0.270 0.000 0.520 0.016 0.012 0.452
#> GSM78527 2 0.0000 0.449 0.000 1.000 0.000 0.000 0.000
#> GSM78530 2 0.4291 -0.203 0.000 0.536 0.000 0.000 0.464
#> GSM78535 5 0.6562 0.000 0.140 0.368 0.004 0.008 0.480
#> GSM78538 2 0.4262 -0.179 0.000 0.560 0.000 0.000 0.440
#> GSM78542 2 0.4262 -0.179 0.000 0.560 0.000 0.000 0.440
#> GSM78544 2 0.4576 -0.199 0.000 0.536 0.004 0.004 0.456
#> GSM78549 2 0.0771 0.444 0.000 0.976 0.004 0.000 0.020
#> GSM78553 2 0.4291 -0.203 0.000 0.536 0.000 0.000 0.464
#> GSM78558 2 0.4291 -0.203 0.000 0.536 0.000 0.000 0.464
#> GSM78561 2 0.4952 0.396 0.000 0.756 0.032 0.100 0.112
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM78539 4 0.1765 0.9601 0.096 0.000 0.000 0.904 0.000 0.000
#> GSM78545 4 0.3393 0.9435 0.088 0.000 0.012 0.844 0.036 0.020
#> GSM78550 4 0.3485 0.9436 0.088 0.000 0.016 0.840 0.036 0.020
#> GSM78554 4 0.3211 0.9484 0.096 0.000 0.004 0.848 0.032 0.020
#> GSM78562 4 0.1765 0.9601 0.096 0.000 0.000 0.904 0.000 0.000
#> GSM78540 4 0.3099 0.9603 0.096 0.000 0.012 0.848 0.044 0.000
#> GSM78546 4 0.3099 0.9603 0.096 0.000 0.012 0.848 0.044 0.000
#> GSM78551 4 0.3874 0.9582 0.096 0.000 0.020 0.812 0.060 0.012
#> GSM78555 4 0.3147 0.9586 0.100 0.000 0.012 0.844 0.044 0.000
#> GSM78563 4 0.3099 0.9603 0.096 0.000 0.012 0.848 0.044 0.000
#> GSM43005 3 0.1812 0.8840 0.080 0.000 0.912 0.008 0.000 0.000
#> GSM43008 3 0.1956 0.8841 0.080 0.000 0.908 0.004 0.008 0.000
#> GSM43011 6 0.3790 0.9586 0.024 0.000 0.216 0.004 0.004 0.752
#> GSM78523 6 0.3790 0.9586 0.024 0.000 0.216 0.004 0.004 0.752
#> GSM78526 6 0.3483 0.9619 0.024 0.000 0.212 0.000 0.000 0.764
#> GSM78529 3 0.2068 0.8825 0.080 0.000 0.904 0.008 0.008 0.000
#> GSM78532 1 0.0603 0.9526 0.980 0.000 0.000 0.000 0.016 0.004
#> GSM78534 6 0.5107 0.9408 0.024 0.000 0.212 0.008 0.076 0.680
#> GSM78537 1 0.1141 0.9504 0.948 0.000 0.000 0.000 0.052 0.000
#> GSM78543 1 0.1141 0.9504 0.948 0.000 0.000 0.000 0.052 0.000
#> GSM78548 3 0.4694 0.7335 0.184 0.000 0.716 0.004 0.080 0.016
#> GSM78557 1 0.1265 0.9438 0.948 0.000 0.000 0.000 0.044 0.008
#> GSM78560 1 0.1010 0.9484 0.960 0.000 0.000 0.000 0.036 0.004
#> GSM78565 1 0.1204 0.9494 0.944 0.000 0.000 0.000 0.056 0.000
#> GSM43000 3 0.2745 0.7830 0.024 0.000 0.880 0.004 0.020 0.072
#> GSM43002 3 0.2237 0.8797 0.080 0.000 0.896 0.000 0.020 0.004
#> GSM43004 6 0.5203 0.9378 0.024 0.000 0.212 0.008 0.084 0.672
#> GSM43007 3 0.1956 0.8841 0.080 0.000 0.908 0.004 0.008 0.000
#> GSM43010 6 0.3483 0.9619 0.024 0.000 0.212 0.000 0.000 0.764
#> GSM78522 6 0.5155 0.9398 0.024 0.000 0.212 0.008 0.080 0.676
#> GSM78525 3 0.2237 0.8797 0.080 0.000 0.896 0.000 0.020 0.004
#> GSM78528 3 0.1956 0.8834 0.080 0.000 0.908 0.004 0.008 0.000
#> GSM78531 1 0.0603 0.9526 0.980 0.000 0.000 0.000 0.016 0.004
#> GSM78533 6 0.3483 0.9619 0.024 0.000 0.212 0.000 0.000 0.764
#> GSM78536 1 0.1204 0.9494 0.944 0.000 0.000 0.000 0.056 0.000
#> GSM78541 1 0.1204 0.9494 0.944 0.000 0.000 0.000 0.056 0.000
#> GSM78547 1 0.1265 0.9438 0.948 0.000 0.000 0.000 0.044 0.008
#> GSM78552 3 0.5605 0.3467 0.404 0.000 0.496 0.004 0.080 0.016
#> GSM78556 1 0.1265 0.9438 0.948 0.000 0.000 0.000 0.044 0.008
#> GSM78559 1 0.1204 0.9494 0.944 0.000 0.000 0.000 0.056 0.000
#> GSM78564 1 0.0972 0.9485 0.964 0.000 0.000 0.000 0.028 0.008
#> GSM42999 2 0.1296 0.4528 0.000 0.948 0.004 0.004 0.044 0.000
#> GSM43001 2 0.6536 0.4726 0.000 0.584 0.044 0.040 0.136 0.196
#> GSM43003 2 0.0000 0.4957 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43006 2 0.6486 0.4753 0.000 0.592 0.044 0.040 0.136 0.188
#> GSM43009 2 0.3466 -0.0156 0.000 0.760 0.008 0.008 0.224 0.000
#> GSM43012 2 0.4450 0.5018 0.000 0.768 0.036 0.016 0.136 0.044
#> GSM78524 5 0.5086 0.7412 0.000 0.432 0.008 0.040 0.512 0.008
#> GSM78527 2 0.0000 0.4957 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78530 5 0.3866 0.8390 0.000 0.484 0.000 0.000 0.516 0.000
#> GSM78535 5 0.6251 0.5091 0.116 0.280 0.008 0.032 0.556 0.008
#> GSM78538 2 0.3864 -0.8211 0.000 0.520 0.000 0.000 0.480 0.000
#> GSM78542 2 0.3864 -0.8211 0.000 0.520 0.000 0.000 0.480 0.000
#> GSM78544 5 0.3864 0.8372 0.000 0.480 0.000 0.000 0.520 0.000
#> GSM78549 2 0.0865 0.4631 0.000 0.964 0.000 0.000 0.036 0.000
#> GSM78553 5 0.3866 0.8390 0.000 0.484 0.000 0.000 0.516 0.000
#> GSM78558 5 0.3866 0.8390 0.000 0.484 0.000 0.000 0.516 0.000
#> GSM78561 2 0.6536 0.4726 0.000 0.584 0.044 0.040 0.136 0.196
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) agent(p) individual(p) k
#> SD:kmeans 58 2.54e-13 0.00184 0.9999 2
#> SD:kmeans 57 2.67e-14 0.00370 0.1374 3
#> SD:kmeans 55 2.04e-21 0.00458 0.3619 4
#> SD:kmeans 40 2.06e-09 0.98224 0.0197 5
#> SD:kmeans 47 8.59e-16 0.33939 0.0375 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "skmeans"]
# you can also extract it by
# res = res_list["SD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 58 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4222 0.578 0.578
#> 3 3 0.780 0.887 0.924 0.5434 0.750 0.567
#> 4 4 1.000 0.982 0.989 0.1562 0.903 0.712
#> 5 5 1.000 0.959 0.971 0.0593 0.943 0.775
#> 6 6 0.938 0.933 0.926 0.0460 0.956 0.783
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 4 5
There is also optional best \(k\) = 2 4 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM78539 1 0 1 1 0
#> GSM78545 1 0 1 1 0
#> GSM78550 1 0 1 1 0
#> GSM78554 1 0 1 1 0
#> GSM78562 1 0 1 1 0
#> GSM78540 1 0 1 1 0
#> GSM78546 1 0 1 1 0
#> GSM78551 1 0 1 1 0
#> GSM78555 1 0 1 1 0
#> GSM78563 1 0 1 1 0
#> GSM43005 1 0 1 1 0
#> GSM43008 1 0 1 1 0
#> GSM43011 1 0 1 1 0
#> GSM78523 1 0 1 1 0
#> GSM78526 1 0 1 1 0
#> GSM78529 1 0 1 1 0
#> GSM78532 1 0 1 1 0
#> GSM78534 1 0 1 1 0
#> GSM78537 1 0 1 1 0
#> GSM78543 1 0 1 1 0
#> GSM78548 1 0 1 1 0
#> GSM78557 1 0 1 1 0
#> GSM78560 1 0 1 1 0
#> GSM78565 1 0 1 1 0
#> GSM43000 1 0 1 1 0
#> GSM43002 1 0 1 1 0
#> GSM43004 1 0 1 1 0
#> GSM43007 1 0 1 1 0
#> GSM43010 1 0 1 1 0
#> GSM78522 1 0 1 1 0
#> GSM78525 1 0 1 1 0
#> GSM78528 1 0 1 1 0
#> GSM78531 1 0 1 1 0
#> GSM78533 1 0 1 1 0
#> GSM78536 1 0 1 1 0
#> GSM78541 1 0 1 1 0
#> GSM78547 1 0 1 1 0
#> GSM78552 1 0 1 1 0
#> GSM78556 1 0 1 1 0
#> GSM78559 1 0 1 1 0
#> GSM78564 1 0 1 1 0
#> GSM42999 2 0 1 0 1
#> GSM43001 2 0 1 0 1
#> GSM43003 2 0 1 0 1
#> GSM43006 2 0 1 0 1
#> GSM43009 2 0 1 0 1
#> GSM43012 2 0 1 0 1
#> GSM78524 2 0 1 0 1
#> GSM78527 2 0 1 0 1
#> GSM78530 2 0 1 0 1
#> GSM78535 2 0 1 0 1
#> GSM78538 2 0 1 0 1
#> GSM78542 2 0 1 0 1
#> GSM78544 2 0 1 0 1
#> GSM78549 2 0 1 0 1
#> GSM78553 2 0 1 0 1
#> GSM78558 2 0 1 0 1
#> GSM78561 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM78539 1 0.000 0.7803 1.000 0 0.000
#> GSM78545 1 0.000 0.7803 1.000 0 0.000
#> GSM78550 1 0.000 0.7803 1.000 0 0.000
#> GSM78554 1 0.000 0.7803 1.000 0 0.000
#> GSM78562 1 0.000 0.7803 1.000 0 0.000
#> GSM78540 1 0.000 0.7803 1.000 0 0.000
#> GSM78546 1 0.000 0.7803 1.000 0 0.000
#> GSM78551 1 0.000 0.7803 1.000 0 0.000
#> GSM78555 1 0.000 0.7803 1.000 0 0.000
#> GSM78563 1 0.000 0.7803 1.000 0 0.000
#> GSM43005 3 0.000 0.9654 0.000 0 1.000
#> GSM43008 3 0.000 0.9654 0.000 0 1.000
#> GSM43011 3 0.000 0.9654 0.000 0 1.000
#> GSM78523 3 0.000 0.9654 0.000 0 1.000
#> GSM78526 3 0.000 0.9654 0.000 0 1.000
#> GSM78529 3 0.000 0.9654 0.000 0 1.000
#> GSM78532 1 0.559 0.7910 0.696 0 0.304
#> GSM78534 3 0.000 0.9654 0.000 0 1.000
#> GSM78537 1 0.559 0.7910 0.696 0 0.304
#> GSM78543 1 0.559 0.7910 0.696 0 0.304
#> GSM78548 3 0.196 0.8969 0.056 0 0.944
#> GSM78557 1 0.559 0.7910 0.696 0 0.304
#> GSM78560 1 0.559 0.7910 0.696 0 0.304
#> GSM78565 1 0.559 0.7910 0.696 0 0.304
#> GSM43000 3 0.000 0.9654 0.000 0 1.000
#> GSM43002 3 0.000 0.9654 0.000 0 1.000
#> GSM43004 3 0.000 0.9654 0.000 0 1.000
#> GSM43007 3 0.000 0.9654 0.000 0 1.000
#> GSM43010 3 0.000 0.9654 0.000 0 1.000
#> GSM78522 3 0.000 0.9654 0.000 0 1.000
#> GSM78525 3 0.000 0.9654 0.000 0 1.000
#> GSM78528 3 0.000 0.9654 0.000 0 1.000
#> GSM78531 1 0.559 0.7910 0.696 0 0.304
#> GSM78533 3 0.000 0.9654 0.000 0 1.000
#> GSM78536 1 0.559 0.7910 0.696 0 0.304
#> GSM78541 1 0.559 0.7910 0.696 0 0.304
#> GSM78547 1 0.559 0.7910 0.696 0 0.304
#> GSM78552 3 0.608 0.0291 0.388 0 0.612
#> GSM78556 1 0.559 0.7910 0.696 0 0.304
#> GSM78559 1 0.559 0.7910 0.696 0 0.304
#> GSM78564 1 0.559 0.7910 0.696 0 0.304
#> GSM42999 2 0.000 1.0000 0.000 1 0.000
#> GSM43001 2 0.000 1.0000 0.000 1 0.000
#> GSM43003 2 0.000 1.0000 0.000 1 0.000
#> GSM43006 2 0.000 1.0000 0.000 1 0.000
#> GSM43009 2 0.000 1.0000 0.000 1 0.000
#> GSM43012 2 0.000 1.0000 0.000 1 0.000
#> GSM78524 2 0.000 1.0000 0.000 1 0.000
#> GSM78527 2 0.000 1.0000 0.000 1 0.000
#> GSM78530 2 0.000 1.0000 0.000 1 0.000
#> GSM78535 2 0.000 1.0000 0.000 1 0.000
#> GSM78538 2 0.000 1.0000 0.000 1 0.000
#> GSM78542 2 0.000 1.0000 0.000 1 0.000
#> GSM78544 2 0.000 1.0000 0.000 1 0.000
#> GSM78549 2 0.000 1.0000 0.000 1 0.000
#> GSM78553 2 0.000 1.0000 0.000 1 0.000
#> GSM78558 2 0.000 1.0000 0.000 1 0.000
#> GSM78561 2 0.000 1.0000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM78539 4 0.0336 0.999 0.008 0 0.000 0.992
#> GSM78545 4 0.0188 0.996 0.004 0 0.000 0.996
#> GSM78550 4 0.0188 0.996 0.004 0 0.000 0.996
#> GSM78554 4 0.0336 0.999 0.008 0 0.000 0.992
#> GSM78562 4 0.0336 0.999 0.008 0 0.000 0.992
#> GSM78540 4 0.0336 0.999 0.008 0 0.000 0.992
#> GSM78546 4 0.0336 0.999 0.008 0 0.000 0.992
#> GSM78551 4 0.0336 0.999 0.008 0 0.000 0.992
#> GSM78555 4 0.0336 0.999 0.008 0 0.000 0.992
#> GSM78563 4 0.0336 0.999 0.008 0 0.000 0.992
#> GSM43005 3 0.0376 0.967 0.004 0 0.992 0.004
#> GSM43008 3 0.1743 0.934 0.056 0 0.940 0.004
#> GSM43011 3 0.0188 0.968 0.000 0 0.996 0.004
#> GSM78523 3 0.0188 0.968 0.000 0 0.996 0.004
#> GSM78526 3 0.0188 0.968 0.000 0 0.996 0.004
#> GSM78529 3 0.0524 0.966 0.008 0 0.988 0.004
#> GSM78532 1 0.0000 0.997 1.000 0 0.000 0.000
#> GSM78534 3 0.0188 0.968 0.000 0 0.996 0.004
#> GSM78537 1 0.0000 0.997 1.000 0 0.000 0.000
#> GSM78543 1 0.0000 0.997 1.000 0 0.000 0.000
#> GSM78548 3 0.4088 0.716 0.232 0 0.764 0.004
#> GSM78557 1 0.0000 0.997 1.000 0 0.000 0.000
#> GSM78560 1 0.0000 0.997 1.000 0 0.000 0.000
#> GSM78565 1 0.0000 0.997 1.000 0 0.000 0.000
#> GSM43000 3 0.0000 0.968 0.000 0 1.000 0.000
#> GSM43002 3 0.0376 0.967 0.004 0 0.992 0.004
#> GSM43004 3 0.2197 0.907 0.080 0 0.916 0.004
#> GSM43007 3 0.1743 0.934 0.056 0 0.940 0.004
#> GSM43010 3 0.0188 0.968 0.000 0 0.996 0.004
#> GSM78522 3 0.0188 0.968 0.000 0 0.996 0.004
#> GSM78525 3 0.0188 0.967 0.000 0 0.996 0.004
#> GSM78528 3 0.0524 0.966 0.008 0 0.988 0.004
#> GSM78531 1 0.0000 0.997 1.000 0 0.000 0.000
#> GSM78533 3 0.0188 0.968 0.000 0 0.996 0.004
#> GSM78536 1 0.0000 0.997 1.000 0 0.000 0.000
#> GSM78541 1 0.0000 0.997 1.000 0 0.000 0.000
#> GSM78547 1 0.0000 0.997 1.000 0 0.000 0.000
#> GSM78552 1 0.1305 0.956 0.960 0 0.036 0.004
#> GSM78556 1 0.0000 0.997 1.000 0 0.000 0.000
#> GSM78559 1 0.0000 0.997 1.000 0 0.000 0.000
#> GSM78564 1 0.0000 0.997 1.000 0 0.000 0.000
#> GSM42999 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM43001 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM43003 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM43006 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM43009 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM43012 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78524 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78527 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78530 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78535 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78538 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78542 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78544 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78549 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78553 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78558 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78561 2 0.0000 1.000 0.000 1 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM78539 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78545 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78550 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78554 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78562 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78540 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78546 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78551 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78555 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78563 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM43005 3 0.1341 0.900 0.000 0.000 0.944 0 0.056
#> GSM43008 3 0.1341 0.900 0.000 0.000 0.944 0 0.056
#> GSM43011 5 0.0000 0.999 0.000 0.000 0.000 0 1.000
#> GSM78523 5 0.0000 0.999 0.000 0.000 0.000 0 1.000
#> GSM78526 5 0.0000 0.999 0.000 0.000 0.000 0 1.000
#> GSM78529 3 0.1341 0.900 0.000 0.000 0.944 0 0.056
#> GSM78532 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78534 5 0.0000 0.999 0.000 0.000 0.000 0 1.000
#> GSM78537 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78543 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78548 3 0.3043 0.843 0.080 0.000 0.864 0 0.056
#> GSM78557 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78560 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78565 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM43000 3 0.4150 0.457 0.000 0.000 0.612 0 0.388
#> GSM43002 3 0.1341 0.900 0.000 0.000 0.944 0 0.056
#> GSM43004 5 0.0162 0.994 0.004 0.000 0.000 0 0.996
#> GSM43007 3 0.1341 0.900 0.000 0.000 0.944 0 0.056
#> GSM43010 5 0.0000 0.999 0.000 0.000 0.000 0 1.000
#> GSM78522 5 0.0000 0.999 0.000 0.000 0.000 0 1.000
#> GSM78525 3 0.1341 0.900 0.000 0.000 0.944 0 0.056
#> GSM78528 3 0.1341 0.900 0.000 0.000 0.944 0 0.056
#> GSM78531 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78533 5 0.0000 0.999 0.000 0.000 0.000 0 1.000
#> GSM78536 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78541 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78547 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78552 3 0.4088 0.440 0.368 0.000 0.632 0 0.000
#> GSM78556 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78559 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78564 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM42999 2 0.0000 0.977 0.000 1.000 0.000 0 0.000
#> GSM43001 2 0.0162 0.976 0.000 0.996 0.004 0 0.000
#> GSM43003 2 0.0000 0.977 0.000 1.000 0.000 0 0.000
#> GSM43006 2 0.0162 0.976 0.000 0.996 0.004 0 0.000
#> GSM43009 2 0.0000 0.977 0.000 1.000 0.000 0 0.000
#> GSM43012 2 0.0162 0.976 0.000 0.996 0.004 0 0.000
#> GSM78524 2 0.1270 0.975 0.000 0.948 0.052 0 0.000
#> GSM78527 2 0.0000 0.977 0.000 1.000 0.000 0 0.000
#> GSM78530 2 0.1270 0.975 0.000 0.948 0.052 0 0.000
#> GSM78535 2 0.1270 0.975 0.000 0.948 0.052 0 0.000
#> GSM78538 2 0.1270 0.975 0.000 0.948 0.052 0 0.000
#> GSM78542 2 0.1270 0.975 0.000 0.948 0.052 0 0.000
#> GSM78544 2 0.1270 0.975 0.000 0.948 0.052 0 0.000
#> GSM78549 2 0.0000 0.977 0.000 1.000 0.000 0 0.000
#> GSM78553 2 0.1270 0.975 0.000 0.948 0.052 0 0.000
#> GSM78558 2 0.1270 0.975 0.000 0.948 0.052 0 0.000
#> GSM78561 2 0.0162 0.976 0.000 0.996 0.004 0 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM78539 4 0.0547 0.984 0.000 0.000 0.000 0.980 0.020 0.000
#> GSM78545 4 0.1219 0.973 0.000 0.000 0.004 0.948 0.048 0.000
#> GSM78550 4 0.1219 0.973 0.000 0.000 0.004 0.948 0.048 0.000
#> GSM78554 4 0.0865 0.980 0.000 0.000 0.000 0.964 0.036 0.000
#> GSM78562 4 0.0547 0.984 0.000 0.000 0.000 0.980 0.020 0.000
#> GSM78540 4 0.0000 0.986 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78546 4 0.0000 0.986 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78551 4 0.0000 0.986 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78555 4 0.0000 0.986 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78563 4 0.0000 0.986 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM43005 3 0.0603 0.885 0.000 0.000 0.980 0.000 0.016 0.004
#> GSM43008 3 0.0603 0.885 0.000 0.000 0.980 0.000 0.016 0.004
#> GSM43011 6 0.0000 0.992 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78523 6 0.0000 0.992 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78526 6 0.0000 0.992 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78529 3 0.0692 0.884 0.000 0.000 0.976 0.000 0.020 0.004
#> GSM78532 1 0.0547 0.973 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM78534 6 0.0547 0.987 0.000 0.000 0.000 0.000 0.020 0.980
#> GSM78537 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78543 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78548 3 0.3808 0.780 0.080 0.000 0.784 0.000 0.132 0.004
#> GSM78557 1 0.1501 0.952 0.924 0.000 0.000 0.000 0.076 0.000
#> GSM78560 1 0.0547 0.973 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM78565 1 0.0363 0.970 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM43000 3 0.4064 0.501 0.000 0.000 0.644 0.000 0.020 0.336
#> GSM43002 3 0.0935 0.883 0.000 0.000 0.964 0.000 0.032 0.004
#> GSM43004 6 0.0790 0.980 0.000 0.000 0.000 0.000 0.032 0.968
#> GSM43007 3 0.0603 0.885 0.000 0.000 0.980 0.000 0.016 0.004
#> GSM43010 6 0.0000 0.992 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78522 6 0.0547 0.987 0.000 0.000 0.000 0.000 0.020 0.980
#> GSM78525 3 0.0858 0.882 0.000 0.000 0.968 0.000 0.028 0.004
#> GSM78528 3 0.0692 0.884 0.000 0.000 0.976 0.000 0.020 0.004
#> GSM78531 1 0.0547 0.973 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM78533 6 0.0000 0.992 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78536 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78541 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78547 1 0.1501 0.952 0.924 0.000 0.000 0.000 0.076 0.000
#> GSM78552 3 0.5109 0.455 0.316 0.000 0.580 0.000 0.104 0.000
#> GSM78556 1 0.1501 0.952 0.924 0.000 0.000 0.000 0.076 0.000
#> GSM78559 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78564 1 0.1387 0.953 0.932 0.000 0.000 0.000 0.068 0.000
#> GSM42999 2 0.2300 0.877 0.000 0.856 0.000 0.000 0.144 0.000
#> GSM43001 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43003 2 0.2048 0.898 0.000 0.880 0.000 0.000 0.120 0.000
#> GSM43006 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43009 2 0.2378 0.867 0.000 0.848 0.000 0.000 0.152 0.000
#> GSM43012 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78524 5 0.2969 0.983 0.000 0.224 0.000 0.000 0.776 0.000
#> GSM78527 2 0.2048 0.898 0.000 0.880 0.000 0.000 0.120 0.000
#> GSM78530 5 0.2941 0.992 0.000 0.220 0.000 0.000 0.780 0.000
#> GSM78535 5 0.3253 0.955 0.020 0.192 0.000 0.000 0.788 0.000
#> GSM78538 5 0.2941 0.992 0.000 0.220 0.000 0.000 0.780 0.000
#> GSM78542 5 0.2941 0.992 0.000 0.220 0.000 0.000 0.780 0.000
#> GSM78544 5 0.2941 0.992 0.000 0.220 0.000 0.000 0.780 0.000
#> GSM78549 2 0.2048 0.898 0.000 0.880 0.000 0.000 0.120 0.000
#> GSM78553 5 0.2941 0.992 0.000 0.220 0.000 0.000 0.780 0.000
#> GSM78558 5 0.2941 0.992 0.000 0.220 0.000 0.000 0.780 0.000
#> GSM78561 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) agent(p) individual(p) k
#> SD:skmeans 58 2.54e-13 0.00184 0.9999 2
#> SD:skmeans 57 1.37e-14 0.00234 0.2223 3
#> SD:skmeans 58 1.13e-22 0.00789 0.3966 4
#> SD:skmeans 56 1.48e-20 0.01345 0.0835 5
#> SD:skmeans 57 8.31e-20 0.03200 0.0855 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "pam"]
# you can also extract it by
# res = res_list["SD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 58 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4222 0.578 0.578
#> 3 3 0.750 0.815 0.845 0.4671 0.780 0.619
#> 4 4 0.888 0.913 0.959 0.2013 0.891 0.696
#> 5 5 0.857 0.899 0.938 0.0551 0.960 0.840
#> 6 6 0.933 0.907 0.960 0.0533 0.948 0.760
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM78539 1 0 1 1 0
#> GSM78545 1 0 1 1 0
#> GSM78550 1 0 1 1 0
#> GSM78554 1 0 1 1 0
#> GSM78562 1 0 1 1 0
#> GSM78540 1 0 1 1 0
#> GSM78546 1 0 1 1 0
#> GSM78551 1 0 1 1 0
#> GSM78555 1 0 1 1 0
#> GSM78563 1 0 1 1 0
#> GSM43005 1 0 1 1 0
#> GSM43008 1 0 1 1 0
#> GSM43011 1 0 1 1 0
#> GSM78523 1 0 1 1 0
#> GSM78526 1 0 1 1 0
#> GSM78529 1 0 1 1 0
#> GSM78532 1 0 1 1 0
#> GSM78534 1 0 1 1 0
#> GSM78537 1 0 1 1 0
#> GSM78543 1 0 1 1 0
#> GSM78548 1 0 1 1 0
#> GSM78557 1 0 1 1 0
#> GSM78560 1 0 1 1 0
#> GSM78565 1 0 1 1 0
#> GSM43000 1 0 1 1 0
#> GSM43002 1 0 1 1 0
#> GSM43004 1 0 1 1 0
#> GSM43007 1 0 1 1 0
#> GSM43010 1 0 1 1 0
#> GSM78522 1 0 1 1 0
#> GSM78525 1 0 1 1 0
#> GSM78528 1 0 1 1 0
#> GSM78531 1 0 1 1 0
#> GSM78533 1 0 1 1 0
#> GSM78536 1 0 1 1 0
#> GSM78541 1 0 1 1 0
#> GSM78547 1 0 1 1 0
#> GSM78552 1 0 1 1 0
#> GSM78556 1 0 1 1 0
#> GSM78559 1 0 1 1 0
#> GSM78564 1 0 1 1 0
#> GSM42999 2 0 1 0 1
#> GSM43001 2 0 1 0 1
#> GSM43003 2 0 1 0 1
#> GSM43006 2 0 1 0 1
#> GSM43009 2 0 1 0 1
#> GSM43012 2 0 1 0 1
#> GSM78524 2 0 1 0 1
#> GSM78527 2 0 1 0 1
#> GSM78530 2 0 1 0 1
#> GSM78535 2 0 1 0 1
#> GSM78538 2 0 1 0 1
#> GSM78542 2 0 1 0 1
#> GSM78544 2 0 1 0 1
#> GSM78549 2 0 1 0 1
#> GSM78553 2 0 1 0 1
#> GSM78558 2 0 1 0 1
#> GSM78561 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM78539 1 0.0000 0.553 1.000 0 0.000
#> GSM78545 1 0.0000 0.553 1.000 0 0.000
#> GSM78550 1 0.0000 0.553 1.000 0 0.000
#> GSM78554 1 0.6225 0.698 0.568 0 0.432
#> GSM78562 1 0.0237 0.554 0.996 0 0.004
#> GSM78540 1 0.0000 0.553 1.000 0 0.000
#> GSM78546 1 0.0000 0.553 1.000 0 0.000
#> GSM78551 1 0.0000 0.553 1.000 0 0.000
#> GSM78555 1 0.0000 0.553 1.000 0 0.000
#> GSM78563 1 0.0000 0.553 1.000 0 0.000
#> GSM43005 3 0.0000 0.964 0.000 0 1.000
#> GSM43008 1 0.6267 0.707 0.548 0 0.452
#> GSM43011 3 0.0000 0.964 0.000 0 1.000
#> GSM78523 3 0.0000 0.964 0.000 0 1.000
#> GSM78526 3 0.0000 0.964 0.000 0 1.000
#> GSM78529 3 0.0000 0.964 0.000 0 1.000
#> GSM78532 1 0.6267 0.707 0.548 0 0.452
#> GSM78534 3 0.5098 0.351 0.248 0 0.752
#> GSM78537 1 0.6267 0.707 0.548 0 0.452
#> GSM78543 1 0.6267 0.707 0.548 0 0.452
#> GSM78548 1 0.6267 0.707 0.548 0 0.452
#> GSM78557 1 0.6267 0.707 0.548 0 0.452
#> GSM78560 1 0.6267 0.707 0.548 0 0.452
#> GSM78565 1 0.6267 0.707 0.548 0 0.452
#> GSM43000 3 0.0000 0.964 0.000 0 1.000
#> GSM43002 3 0.0237 0.960 0.004 0 0.996
#> GSM43004 1 0.6291 0.680 0.532 0 0.468
#> GSM43007 1 0.6295 0.672 0.528 0 0.472
#> GSM43010 3 0.0000 0.964 0.000 0 1.000
#> GSM78522 3 0.0000 0.964 0.000 0 1.000
#> GSM78525 3 0.0000 0.964 0.000 0 1.000
#> GSM78528 3 0.0237 0.960 0.004 0 0.996
#> GSM78531 1 0.6267 0.707 0.548 0 0.452
#> GSM78533 3 0.0000 0.964 0.000 0 1.000
#> GSM78536 1 0.6267 0.707 0.548 0 0.452
#> GSM78541 1 0.6267 0.707 0.548 0 0.452
#> GSM78547 1 0.6267 0.707 0.548 0 0.452
#> GSM78552 1 0.6267 0.707 0.548 0 0.452
#> GSM78556 1 0.6267 0.707 0.548 0 0.452
#> GSM78559 1 0.6267 0.707 0.548 0 0.452
#> GSM78564 1 0.6267 0.707 0.548 0 0.452
#> GSM42999 2 0.0000 1.000 0.000 1 0.000
#> GSM43001 2 0.0000 1.000 0.000 1 0.000
#> GSM43003 2 0.0000 1.000 0.000 1 0.000
#> GSM43006 2 0.0000 1.000 0.000 1 0.000
#> GSM43009 2 0.0000 1.000 0.000 1 0.000
#> GSM43012 2 0.0000 1.000 0.000 1 0.000
#> GSM78524 2 0.0000 1.000 0.000 1 0.000
#> GSM78527 2 0.0000 1.000 0.000 1 0.000
#> GSM78530 2 0.0000 1.000 0.000 1 0.000
#> GSM78535 2 0.0000 1.000 0.000 1 0.000
#> GSM78538 2 0.0000 1.000 0.000 1 0.000
#> GSM78542 2 0.0000 1.000 0.000 1 0.000
#> GSM78544 2 0.0000 1.000 0.000 1 0.000
#> GSM78549 2 0.0000 1.000 0.000 1 0.000
#> GSM78553 2 0.0000 1.000 0.000 1 0.000
#> GSM78558 2 0.0000 1.000 0.000 1 0.000
#> GSM78561 2 0.0000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM78539 4 0.0000 0.946 0.000 0 0.000 1.000
#> GSM78545 4 0.0000 0.946 0.000 0 0.000 1.000
#> GSM78550 4 0.0336 0.941 0.008 0 0.000 0.992
#> GSM78554 4 0.4477 0.540 0.312 0 0.000 0.688
#> GSM78562 4 0.2081 0.871 0.084 0 0.000 0.916
#> GSM78540 4 0.0000 0.946 0.000 0 0.000 1.000
#> GSM78546 4 0.0000 0.946 0.000 0 0.000 1.000
#> GSM78551 4 0.0000 0.946 0.000 0 0.000 1.000
#> GSM78555 4 0.0000 0.946 0.000 0 0.000 1.000
#> GSM78563 4 0.0000 0.946 0.000 0 0.000 1.000
#> GSM43005 3 0.3528 0.806 0.192 0 0.808 0.000
#> GSM43008 1 0.3311 0.774 0.828 0 0.172 0.000
#> GSM43011 3 0.0000 0.879 0.000 0 1.000 0.000
#> GSM78523 3 0.0000 0.879 0.000 0 1.000 0.000
#> GSM78526 3 0.0000 0.879 0.000 0 1.000 0.000
#> GSM78529 3 0.3610 0.799 0.200 0 0.800 0.000
#> GSM78532 1 0.0000 0.946 1.000 0 0.000 0.000
#> GSM78534 3 0.4164 0.608 0.264 0 0.736 0.000
#> GSM78537 1 0.0000 0.946 1.000 0 0.000 0.000
#> GSM78543 1 0.0000 0.946 1.000 0 0.000 0.000
#> GSM78548 1 0.3486 0.752 0.812 0 0.188 0.000
#> GSM78557 1 0.0000 0.946 1.000 0 0.000 0.000
#> GSM78560 1 0.0000 0.946 1.000 0 0.000 0.000
#> GSM78565 1 0.0000 0.946 1.000 0 0.000 0.000
#> GSM43000 3 0.1022 0.878 0.032 0 0.968 0.000
#> GSM43002 3 0.3649 0.796 0.204 0 0.796 0.000
#> GSM43004 1 0.3726 0.706 0.788 0 0.212 0.000
#> GSM43007 1 0.3649 0.728 0.796 0 0.204 0.000
#> GSM43010 3 0.0000 0.879 0.000 0 1.000 0.000
#> GSM78522 3 0.0000 0.879 0.000 0 1.000 0.000
#> GSM78525 3 0.1792 0.871 0.068 0 0.932 0.000
#> GSM78528 3 0.3801 0.776 0.220 0 0.780 0.000
#> GSM78531 1 0.0000 0.946 1.000 0 0.000 0.000
#> GSM78533 3 0.0000 0.879 0.000 0 1.000 0.000
#> GSM78536 1 0.0000 0.946 1.000 0 0.000 0.000
#> GSM78541 1 0.0000 0.946 1.000 0 0.000 0.000
#> GSM78547 1 0.0000 0.946 1.000 0 0.000 0.000
#> GSM78552 1 0.0000 0.946 1.000 0 0.000 0.000
#> GSM78556 1 0.0000 0.946 1.000 0 0.000 0.000
#> GSM78559 1 0.0000 0.946 1.000 0 0.000 0.000
#> GSM78564 1 0.0000 0.946 1.000 0 0.000 0.000
#> GSM42999 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM43001 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM43003 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM43006 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM43009 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM43012 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78524 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78527 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78530 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78535 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78538 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78542 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78544 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78549 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78553 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78558 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78561 2 0.0000 1.000 0.000 1 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM78539 4 0.0000 0.946 0.000 0.000 0.000 1.000 0.000
#> GSM78545 4 0.0000 0.946 0.000 0.000 0.000 1.000 0.000
#> GSM78550 4 0.0290 0.940 0.008 0.000 0.000 0.992 0.000
#> GSM78554 4 0.3837 0.555 0.308 0.000 0.000 0.692 0.000
#> GSM78562 4 0.1197 0.900 0.048 0.000 0.000 0.952 0.000
#> GSM78540 4 0.0000 0.946 0.000 0.000 0.000 1.000 0.000
#> GSM78546 4 0.0000 0.946 0.000 0.000 0.000 1.000 0.000
#> GSM78551 4 0.0000 0.946 0.000 0.000 0.000 1.000 0.000
#> GSM78555 4 0.0000 0.946 0.000 0.000 0.000 1.000 0.000
#> GSM78563 4 0.0000 0.946 0.000 0.000 0.000 1.000 0.000
#> GSM43005 3 0.4255 0.815 0.128 0.000 0.776 0.000 0.096
#> GSM43008 1 0.4509 0.700 0.752 0.000 0.152 0.000 0.096
#> GSM43011 3 0.0000 0.871 0.000 0.000 1.000 0.000 0.000
#> GSM78523 3 0.0000 0.871 0.000 0.000 1.000 0.000 0.000
#> GSM78526 3 0.0000 0.871 0.000 0.000 1.000 0.000 0.000
#> GSM78529 3 0.4300 0.812 0.132 0.000 0.772 0.000 0.096
#> GSM78532 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000
#> GSM78534 3 0.3586 0.589 0.264 0.000 0.736 0.000 0.000
#> GSM78537 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000
#> GSM78543 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000
#> GSM78548 1 0.3359 0.763 0.816 0.000 0.164 0.000 0.020
#> GSM78557 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000
#> GSM78560 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000
#> GSM78565 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000
#> GSM43000 3 0.1800 0.867 0.020 0.000 0.932 0.000 0.048
#> GSM43002 3 0.4386 0.807 0.140 0.000 0.764 0.000 0.096
#> GSM43004 1 0.3551 0.705 0.772 0.000 0.220 0.000 0.008
#> GSM43007 1 0.4768 0.653 0.724 0.000 0.180 0.000 0.096
#> GSM43010 3 0.0000 0.871 0.000 0.000 1.000 0.000 0.000
#> GSM78522 3 0.0000 0.871 0.000 0.000 1.000 0.000 0.000
#> GSM78525 3 0.2520 0.861 0.048 0.000 0.896 0.000 0.056
#> GSM78528 3 0.4469 0.799 0.148 0.000 0.756 0.000 0.096
#> GSM78531 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000
#> GSM78533 3 0.0000 0.871 0.000 0.000 1.000 0.000 0.000
#> GSM78536 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000
#> GSM78541 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000
#> GSM78547 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000
#> GSM78552 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000
#> GSM78556 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000
#> GSM78559 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000
#> GSM78564 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000
#> GSM42999 2 0.0609 0.983 0.000 0.980 0.000 0.000 0.020
#> GSM43001 5 0.1965 0.948 0.000 0.096 0.000 0.000 0.904
#> GSM43003 5 0.3508 0.830 0.000 0.252 0.000 0.000 0.748
#> GSM43006 5 0.1965 0.948 0.000 0.096 0.000 0.000 0.904
#> GSM43009 2 0.0703 0.980 0.000 0.976 0.000 0.000 0.024
#> GSM43012 5 0.1965 0.948 0.000 0.096 0.000 0.000 0.904
#> GSM78524 2 0.0609 0.983 0.000 0.980 0.000 0.000 0.020
#> GSM78527 5 0.3003 0.900 0.000 0.188 0.000 0.000 0.812
#> GSM78530 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000
#> GSM78535 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000
#> GSM78538 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000
#> GSM78542 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000
#> GSM78544 2 0.0609 0.983 0.000 0.980 0.000 0.000 0.020
#> GSM78549 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000
#> GSM78553 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000
#> GSM78558 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000
#> GSM78561 5 0.1965 0.948 0.000 0.096 0.000 0.000 0.904
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM78539 4 0.0000 0.952 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78545 4 0.0000 0.952 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78550 4 0.0146 0.950 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM78554 4 0.3390 0.582 0.296 0.000 0.000 0.704 0.000 0.000
#> GSM78562 4 0.0790 0.924 0.032 0.000 0.000 0.968 0.000 0.000
#> GSM78540 4 0.0000 0.952 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78546 4 0.0000 0.952 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78551 4 0.0000 0.952 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78555 4 0.0000 0.952 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78563 4 0.0000 0.952 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM43005 3 0.0000 0.879 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM43008 3 0.1814 0.821 0.100 0.000 0.900 0.000 0.000 0.000
#> GSM43011 6 0.1814 0.903 0.000 0.000 0.100 0.000 0.000 0.900
#> GSM78523 6 0.1814 0.903 0.000 0.000 0.100 0.000 0.000 0.900
#> GSM78526 6 0.0000 0.964 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78529 3 0.0000 0.879 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM78532 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78534 6 0.0000 0.964 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78537 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78543 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78548 1 0.1387 0.895 0.932 0.000 0.068 0.000 0.000 0.000
#> GSM78557 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78560 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78565 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM43000 3 0.3706 0.360 0.000 0.000 0.620 0.000 0.000 0.380
#> GSM43002 3 0.0000 0.879 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM43004 1 0.5885 0.100 0.476 0.000 0.248 0.000 0.000 0.276
#> GSM43007 3 0.1814 0.821 0.100 0.000 0.900 0.000 0.000 0.000
#> GSM43010 6 0.0000 0.964 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78522 6 0.0000 0.964 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78525 3 0.2257 0.801 0.008 0.000 0.876 0.000 0.000 0.116
#> GSM78528 3 0.0000 0.879 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM78531 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78533 6 0.0000 0.964 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78536 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78541 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78547 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78552 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78556 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78559 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78564 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM42999 2 0.0790 0.974 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM43001 5 0.0000 0.917 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM43003 5 0.2996 0.763 0.000 0.228 0.000 0.000 0.772 0.000
#> GSM43006 5 0.0000 0.917 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM43009 2 0.0865 0.972 0.000 0.964 0.000 0.000 0.036 0.000
#> GSM43012 5 0.0000 0.917 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM78524 2 0.0790 0.974 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM78527 5 0.2340 0.848 0.000 0.148 0.000 0.000 0.852 0.000
#> GSM78530 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78535 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78538 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78542 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78544 2 0.0790 0.974 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM78549 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78553 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78558 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78561 5 0.0000 0.917 0.000 0.000 0.000 0.000 1.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) agent(p) individual(p) k
#> SD:pam 58 2.54e-13 0.00184 1.000 2
#> SD:pam 57 2.40e-13 0.00357 0.239 3
#> SD:pam 58 1.13e-22 0.00808 0.343 4
#> SD:pam 58 2.22e-21 0.01885 0.293 5
#> SD:pam 56 2.11e-19 0.02434 0.038 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "mclust"]
# you can also extract it by
# res = res_list["SD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 58 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4222 0.578 0.578
#> 3 3 0.712 0.819 0.903 0.4871 0.789 0.636
#> 4 4 0.720 0.768 0.860 0.1660 0.843 0.594
#> 5 5 0.880 0.863 0.904 0.0807 0.909 0.667
#> 6 6 0.831 0.793 0.887 0.0456 0.964 0.824
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM78539 1 0 1 1 0
#> GSM78545 1 0 1 1 0
#> GSM78550 1 0 1 1 0
#> GSM78554 1 0 1 1 0
#> GSM78562 1 0 1 1 0
#> GSM78540 1 0 1 1 0
#> GSM78546 1 0 1 1 0
#> GSM78551 1 0 1 1 0
#> GSM78555 1 0 1 1 0
#> GSM78563 1 0 1 1 0
#> GSM43005 1 0 1 1 0
#> GSM43008 1 0 1 1 0
#> GSM43011 1 0 1 1 0
#> GSM78523 1 0 1 1 0
#> GSM78526 1 0 1 1 0
#> GSM78529 1 0 1 1 0
#> GSM78532 1 0 1 1 0
#> GSM78534 1 0 1 1 0
#> GSM78537 1 0 1 1 0
#> GSM78543 1 0 1 1 0
#> GSM78548 1 0 1 1 0
#> GSM78557 1 0 1 1 0
#> GSM78560 1 0 1 1 0
#> GSM78565 1 0 1 1 0
#> GSM43000 1 0 1 1 0
#> GSM43002 1 0 1 1 0
#> GSM43004 1 0 1 1 0
#> GSM43007 1 0 1 1 0
#> GSM43010 1 0 1 1 0
#> GSM78522 1 0 1 1 0
#> GSM78525 1 0 1 1 0
#> GSM78528 1 0 1 1 0
#> GSM78531 1 0 1 1 0
#> GSM78533 1 0 1 1 0
#> GSM78536 1 0 1 1 0
#> GSM78541 1 0 1 1 0
#> GSM78547 1 0 1 1 0
#> GSM78552 1 0 1 1 0
#> GSM78556 1 0 1 1 0
#> GSM78559 1 0 1 1 0
#> GSM78564 1 0 1 1 0
#> GSM42999 2 0 1 0 1
#> GSM43001 2 0 1 0 1
#> GSM43003 2 0 1 0 1
#> GSM43006 2 0 1 0 1
#> GSM43009 2 0 1 0 1
#> GSM43012 2 0 1 0 1
#> GSM78524 2 0 1 0 1
#> GSM78527 2 0 1 0 1
#> GSM78530 2 0 1 0 1
#> GSM78535 2 0 1 0 1
#> GSM78538 2 0 1 0 1
#> GSM78542 2 0 1 0 1
#> GSM78544 2 0 1 0 1
#> GSM78549 2 0 1 0 1
#> GSM78553 2 0 1 0 1
#> GSM78558 2 0 1 0 1
#> GSM78561 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM78539 1 0.000 0.857 1.000 0 0.000
#> GSM78545 1 0.164 0.836 0.956 0 0.044
#> GSM78550 1 0.164 0.836 0.956 0 0.044
#> GSM78554 1 0.510 0.566 0.752 0 0.248
#> GSM78562 1 0.000 0.857 1.000 0 0.000
#> GSM78540 1 0.000 0.857 1.000 0 0.000
#> GSM78546 1 0.000 0.857 1.000 0 0.000
#> GSM78551 1 0.000 0.857 1.000 0 0.000
#> GSM78555 1 0.000 0.857 1.000 0 0.000
#> GSM78563 1 0.000 0.857 1.000 0 0.000
#> GSM43005 3 0.579 0.672 0.332 0 0.668
#> GSM43008 3 0.550 0.706 0.292 0 0.708
#> GSM43011 3 0.581 0.669 0.336 0 0.664
#> GSM78523 3 0.573 0.685 0.324 0 0.676
#> GSM78526 3 0.394 0.806 0.156 0 0.844
#> GSM78529 1 0.599 0.245 0.632 0 0.368
#> GSM78532 3 0.000 0.809 0.000 0 1.000
#> GSM78534 3 0.394 0.806 0.156 0 0.844
#> GSM78537 3 0.000 0.809 0.000 0 1.000
#> GSM78543 3 0.000 0.809 0.000 0 1.000
#> GSM78548 3 0.553 0.703 0.296 0 0.704
#> GSM78557 3 0.000 0.809 0.000 0 1.000
#> GSM78560 3 0.312 0.812 0.108 0 0.892
#> GSM78565 3 0.000 0.809 0.000 0 1.000
#> GSM43000 3 0.583 0.663 0.340 0 0.660
#> GSM43002 3 0.543 0.718 0.284 0 0.716
#> GSM43004 3 0.394 0.806 0.156 0 0.844
#> GSM43007 3 0.571 0.685 0.320 0 0.680
#> GSM43010 3 0.394 0.806 0.156 0 0.844
#> GSM78522 3 0.394 0.806 0.156 0 0.844
#> GSM78525 3 0.583 0.663 0.340 0 0.660
#> GSM78528 1 0.630 -0.197 0.528 0 0.472
#> GSM78531 3 0.000 0.809 0.000 0 1.000
#> GSM78533 3 0.394 0.806 0.156 0 0.844
#> GSM78536 3 0.000 0.809 0.000 0 1.000
#> GSM78541 3 0.000 0.809 0.000 0 1.000
#> GSM78547 3 0.000 0.809 0.000 0 1.000
#> GSM78552 3 0.559 0.698 0.304 0 0.696
#> GSM78556 3 0.000 0.809 0.000 0 1.000
#> GSM78559 3 0.000 0.809 0.000 0 1.000
#> GSM78564 3 0.000 0.809 0.000 0 1.000
#> GSM42999 2 0.000 1.000 0.000 1 0.000
#> GSM43001 2 0.000 1.000 0.000 1 0.000
#> GSM43003 2 0.000 1.000 0.000 1 0.000
#> GSM43006 2 0.000 1.000 0.000 1 0.000
#> GSM43009 2 0.000 1.000 0.000 1 0.000
#> GSM43012 2 0.000 1.000 0.000 1 0.000
#> GSM78524 2 0.000 1.000 0.000 1 0.000
#> GSM78527 2 0.000 1.000 0.000 1 0.000
#> GSM78530 2 0.000 1.000 0.000 1 0.000
#> GSM78535 2 0.000 1.000 0.000 1 0.000
#> GSM78538 2 0.000 1.000 0.000 1 0.000
#> GSM78542 2 0.000 1.000 0.000 1 0.000
#> GSM78544 2 0.000 1.000 0.000 1 0.000
#> GSM78549 2 0.000 1.000 0.000 1 0.000
#> GSM78553 2 0.000 1.000 0.000 1 0.000
#> GSM78558 2 0.000 1.000 0.000 1 0.000
#> GSM78561 2 0.000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM78539 4 0.0000 0.8882 0.000 0 0.000 1.000
#> GSM78545 4 0.4564 0.5135 0.000 0 0.328 0.672
#> GSM78550 4 0.3610 0.7152 0.000 0 0.200 0.800
#> GSM78554 4 0.4431 0.5746 0.000 0 0.304 0.696
#> GSM78562 4 0.0000 0.8882 0.000 0 0.000 1.000
#> GSM78540 4 0.0000 0.8882 0.000 0 0.000 1.000
#> GSM78546 4 0.0000 0.8882 0.000 0 0.000 1.000
#> GSM78551 4 0.0000 0.8882 0.000 0 0.000 1.000
#> GSM78555 4 0.0000 0.8882 0.000 0 0.000 1.000
#> GSM78563 4 0.0000 0.8882 0.000 0 0.000 1.000
#> GSM43005 3 0.0707 0.7769 0.020 0 0.980 0.000
#> GSM43008 3 0.2408 0.7326 0.104 0 0.896 0.000
#> GSM43011 3 0.0000 0.7719 0.000 0 1.000 0.000
#> GSM78523 3 0.1389 0.7425 0.048 0 0.952 0.000
#> GSM78526 3 0.4304 0.5245 0.284 0 0.716 0.000
#> GSM78529 3 0.3907 0.5720 0.000 0 0.768 0.232
#> GSM78532 1 0.4605 0.5969 0.664 0 0.336 0.000
#> GSM78534 1 0.4888 0.3406 0.588 0 0.412 0.000
#> GSM78537 1 0.3942 0.7285 0.764 0 0.236 0.000
#> GSM78543 1 0.2216 0.7424 0.908 0 0.092 0.000
#> GSM78548 3 0.0921 0.7763 0.028 0 0.972 0.000
#> GSM78557 3 0.4193 0.5126 0.268 0 0.732 0.000
#> GSM78560 1 0.4134 0.7099 0.740 0 0.260 0.000
#> GSM78565 1 0.2216 0.7424 0.908 0 0.092 0.000
#> GSM43000 3 0.0188 0.7705 0.004 0 0.996 0.000
#> GSM43002 3 0.0817 0.7769 0.024 0 0.976 0.000
#> GSM43004 1 0.4830 0.3789 0.608 0 0.392 0.000
#> GSM43007 3 0.1022 0.7751 0.032 0 0.968 0.000
#> GSM43010 3 0.4817 0.2751 0.388 0 0.612 0.000
#> GSM78522 1 0.4888 0.3406 0.588 0 0.412 0.000
#> GSM78525 3 0.0469 0.7757 0.012 0 0.988 0.000
#> GSM78528 3 0.3172 0.6570 0.000 0 0.840 0.160
#> GSM78531 1 0.3801 0.7353 0.780 0 0.220 0.000
#> GSM78533 3 0.4250 0.5319 0.276 0 0.724 0.000
#> GSM78536 1 0.2216 0.7424 0.908 0 0.092 0.000
#> GSM78541 1 0.2216 0.7424 0.908 0 0.092 0.000
#> GSM78547 3 0.4948 0.0684 0.440 0 0.560 0.000
#> GSM78552 3 0.2704 0.7149 0.124 0 0.876 0.000
#> GSM78556 3 0.4277 0.4955 0.280 0 0.720 0.000
#> GSM78559 1 0.2216 0.7424 0.908 0 0.092 0.000
#> GSM78564 1 0.4072 0.7165 0.748 0 0.252 0.000
#> GSM42999 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM43001 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM43003 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM43006 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM43009 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM43012 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM78524 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM78527 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM78530 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM78535 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM78538 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM78542 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM78544 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM78549 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM78553 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM78558 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM78561 2 0.0000 1.0000 0.000 1 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM78539 4 0.0000 0.989 0.000 0.000 0.000 1.000 0.000
#> GSM78545 4 0.0000 0.989 0.000 0.000 0.000 1.000 0.000
#> GSM78550 4 0.0000 0.989 0.000 0.000 0.000 1.000 0.000
#> GSM78554 4 0.1300 0.957 0.028 0.000 0.016 0.956 0.000
#> GSM78562 4 0.0865 0.971 0.024 0.000 0.004 0.972 0.000
#> GSM78540 4 0.0000 0.989 0.000 0.000 0.000 1.000 0.000
#> GSM78546 4 0.0000 0.989 0.000 0.000 0.000 1.000 0.000
#> GSM78551 4 0.0000 0.989 0.000 0.000 0.000 1.000 0.000
#> GSM78555 4 0.0510 0.979 0.016 0.000 0.000 0.984 0.000
#> GSM78563 4 0.0000 0.989 0.000 0.000 0.000 1.000 0.000
#> GSM43005 3 0.2653 0.846 0.096 0.000 0.880 0.000 0.024
#> GSM43008 3 0.2516 0.805 0.140 0.000 0.860 0.000 0.000
#> GSM43011 3 0.1121 0.816 0.000 0.000 0.956 0.000 0.044
#> GSM78523 3 0.3534 0.523 0.000 0.000 0.744 0.000 0.256
#> GSM78526 5 0.3074 0.976 0.000 0.000 0.196 0.000 0.804
#> GSM78529 3 0.2153 0.808 0.000 0.000 0.916 0.044 0.040
#> GSM78532 1 0.1341 0.831 0.944 0.000 0.056 0.000 0.000
#> GSM78534 5 0.3196 0.976 0.004 0.000 0.192 0.000 0.804
#> GSM78537 1 0.0671 0.836 0.980 0.000 0.016 0.000 0.004
#> GSM78543 1 0.0880 0.834 0.968 0.000 0.000 0.000 0.032
#> GSM78548 3 0.2020 0.839 0.100 0.000 0.900 0.000 0.000
#> GSM78557 1 0.4268 0.250 0.556 0.000 0.444 0.000 0.000
#> GSM78560 1 0.1478 0.828 0.936 0.000 0.064 0.000 0.000
#> GSM78565 1 0.0880 0.834 0.968 0.000 0.000 0.000 0.032
#> GSM43000 3 0.1121 0.816 0.000 0.000 0.956 0.000 0.044
#> GSM43002 3 0.1965 0.841 0.096 0.000 0.904 0.000 0.000
#> GSM43004 5 0.3906 0.898 0.068 0.000 0.132 0.000 0.800
#> GSM43007 3 0.2179 0.830 0.112 0.000 0.888 0.000 0.000
#> GSM43010 5 0.3074 0.976 0.000 0.000 0.196 0.000 0.804
#> GSM78522 5 0.3196 0.976 0.004 0.000 0.192 0.000 0.804
#> GSM78525 3 0.1469 0.830 0.016 0.000 0.948 0.000 0.036
#> GSM78528 3 0.2153 0.808 0.000 0.000 0.916 0.044 0.040
#> GSM78531 1 0.1270 0.833 0.948 0.000 0.052 0.000 0.000
#> GSM78533 5 0.3074 0.976 0.000 0.000 0.196 0.000 0.804
#> GSM78536 1 0.0880 0.834 0.968 0.000 0.000 0.000 0.032
#> GSM78541 1 0.0880 0.834 0.968 0.000 0.000 0.000 0.032
#> GSM78547 1 0.4268 0.250 0.556 0.000 0.444 0.000 0.000
#> GSM78552 3 0.3612 0.607 0.268 0.000 0.732 0.000 0.000
#> GSM78556 1 0.4268 0.250 0.556 0.000 0.444 0.000 0.000
#> GSM78559 1 0.0880 0.834 0.968 0.000 0.000 0.000 0.032
#> GSM78564 1 0.1270 0.833 0.948 0.000 0.052 0.000 0.000
#> GSM42999 2 0.0000 0.958 0.000 1.000 0.000 0.000 0.000
#> GSM43001 2 0.0000 0.958 0.000 1.000 0.000 0.000 0.000
#> GSM43003 2 0.0000 0.958 0.000 1.000 0.000 0.000 0.000
#> GSM43006 2 0.0000 0.958 0.000 1.000 0.000 0.000 0.000
#> GSM43009 2 0.0162 0.958 0.000 0.996 0.000 0.000 0.004
#> GSM43012 2 0.0000 0.958 0.000 1.000 0.000 0.000 0.000
#> GSM78524 2 0.1544 0.937 0.000 0.932 0.000 0.000 0.068
#> GSM78527 2 0.0000 0.958 0.000 1.000 0.000 0.000 0.000
#> GSM78530 2 0.2773 0.891 0.000 0.836 0.000 0.000 0.164
#> GSM78535 2 0.2773 0.891 0.000 0.836 0.000 0.000 0.164
#> GSM78538 2 0.0000 0.958 0.000 1.000 0.000 0.000 0.000
#> GSM78542 2 0.0000 0.958 0.000 1.000 0.000 0.000 0.000
#> GSM78544 2 0.1544 0.937 0.000 0.932 0.000 0.000 0.068
#> GSM78549 2 0.0000 0.958 0.000 1.000 0.000 0.000 0.000
#> GSM78553 2 0.2773 0.891 0.000 0.836 0.000 0.000 0.164
#> GSM78558 2 0.2773 0.891 0.000 0.836 0.000 0.000 0.164
#> GSM78561 2 0.0162 0.958 0.000 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM78539 4 0.0000 0.97752 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78545 4 0.0000 0.97752 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78550 4 0.0146 0.97571 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM78554 4 0.2320 0.84116 0.000 0.000 0.132 0.864 0.000 0.004
#> GSM78562 4 0.1010 0.94917 0.000 0.000 0.036 0.960 0.000 0.004
#> GSM78540 4 0.0000 0.97752 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78546 4 0.0000 0.97752 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78551 4 0.0000 0.97752 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78555 4 0.0146 0.97596 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM78563 4 0.0000 0.97752 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM43005 3 0.1492 0.82138 0.036 0.000 0.940 0.000 0.000 0.024
#> GSM43008 3 0.1141 0.81460 0.052 0.000 0.948 0.000 0.000 0.000
#> GSM43011 3 0.2300 0.78642 0.000 0.000 0.856 0.000 0.000 0.144
#> GSM78523 3 0.3647 0.54391 0.000 0.000 0.640 0.000 0.000 0.360
#> GSM78526 6 0.0146 0.98240 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM78529 3 0.2798 0.78929 0.000 0.000 0.852 0.036 0.000 0.112
#> GSM78532 1 0.2003 0.88285 0.884 0.000 0.116 0.000 0.000 0.000
#> GSM78534 6 0.0146 0.98240 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM78537 1 0.0935 0.89100 0.964 0.000 0.032 0.000 0.004 0.000
#> GSM78543 1 0.0146 0.88655 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM78548 3 0.1082 0.81935 0.040 0.000 0.956 0.000 0.000 0.004
#> GSM78557 1 0.3244 0.74481 0.732 0.000 0.268 0.000 0.000 0.000
#> GSM78560 1 0.2340 0.86837 0.852 0.000 0.148 0.000 0.000 0.000
#> GSM78565 1 0.0146 0.88655 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM43000 3 0.3445 0.68974 0.008 0.000 0.732 0.000 0.000 0.260
#> GSM43002 3 0.1196 0.81997 0.040 0.000 0.952 0.000 0.000 0.008
#> GSM43004 6 0.0937 0.94093 0.040 0.000 0.000 0.000 0.000 0.960
#> GSM43007 3 0.0865 0.81639 0.036 0.000 0.964 0.000 0.000 0.000
#> GSM43010 6 0.0146 0.98240 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM78522 6 0.0146 0.98240 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM78525 3 0.2887 0.80838 0.036 0.000 0.844 0.000 0.000 0.120
#> GSM78528 3 0.2798 0.78929 0.000 0.000 0.852 0.036 0.000 0.112
#> GSM78531 1 0.1863 0.88393 0.896 0.000 0.104 0.000 0.000 0.000
#> GSM78533 6 0.0865 0.96063 0.000 0.000 0.036 0.000 0.000 0.964
#> GSM78536 1 0.0146 0.88655 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM78541 1 0.0405 0.88363 0.988 0.000 0.008 0.000 0.004 0.000
#> GSM78547 1 0.3288 0.73861 0.724 0.000 0.276 0.000 0.000 0.000
#> GSM78552 3 0.3804 -0.00803 0.424 0.000 0.576 0.000 0.000 0.000
#> GSM78556 1 0.3266 0.74246 0.728 0.000 0.272 0.000 0.000 0.000
#> GSM78559 1 0.0146 0.88655 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM78564 1 0.1663 0.88844 0.912 0.000 0.088 0.000 0.000 0.000
#> GSM42999 2 0.0000 0.83177 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43001 2 0.0000 0.83177 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43003 2 0.0000 0.83177 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43006 2 0.0000 0.83177 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43009 2 0.1610 0.75389 0.000 0.916 0.000 0.000 0.084 0.000
#> GSM43012 2 0.0260 0.82808 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM78524 5 0.3647 0.30885 0.000 0.360 0.000 0.000 0.640 0.000
#> GSM78527 2 0.0000 0.83177 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78530 5 0.2969 0.77345 0.000 0.224 0.000 0.000 0.776 0.000
#> GSM78535 5 0.0146 0.65148 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM78538 2 0.3737 0.16285 0.000 0.608 0.000 0.000 0.392 0.000
#> GSM78542 2 0.3737 0.16285 0.000 0.608 0.000 0.000 0.392 0.000
#> GSM78544 2 0.3797 -0.00478 0.000 0.580 0.000 0.000 0.420 0.000
#> GSM78549 2 0.0000 0.83177 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78553 5 0.2969 0.77345 0.000 0.224 0.000 0.000 0.776 0.000
#> GSM78558 5 0.2969 0.77345 0.000 0.224 0.000 0.000 0.776 0.000
#> GSM78561 2 0.0363 0.82537 0.000 0.988 0.000 0.000 0.012 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) agent(p) individual(p) k
#> SD:mclust 58 2.54e-13 0.00184 1.000 2
#> SD:mclust 56 2.73e-23 0.00295 0.940 3
#> SD:mclust 52 3.67e-20 0.00382 0.538 4
#> SD:mclust 55 3.81e-20 0.01336 0.186 5
#> SD:mclust 53 3.41e-18 0.06407 0.196 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "NMF"]
# you can also extract it by
# res = res_list["SD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 58 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.998 0.999 0.4225 0.578 0.578
#> 3 3 0.886 0.904 0.960 0.5857 0.724 0.534
#> 4 4 0.877 0.873 0.929 0.1190 0.869 0.630
#> 5 5 0.853 0.727 0.867 0.0503 0.936 0.755
#> 6 6 0.873 0.882 0.921 0.0423 0.943 0.741
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM78539 1 0.000 0.999 1.00 0.00
#> GSM78545 1 0.000 0.999 1.00 0.00
#> GSM78550 1 0.000 0.999 1.00 0.00
#> GSM78554 1 0.000 0.999 1.00 0.00
#> GSM78562 1 0.000 0.999 1.00 0.00
#> GSM78540 1 0.000 0.999 1.00 0.00
#> GSM78546 1 0.000 0.999 1.00 0.00
#> GSM78551 1 0.000 0.999 1.00 0.00
#> GSM78555 1 0.000 0.999 1.00 0.00
#> GSM78563 1 0.000 0.999 1.00 0.00
#> GSM43005 1 0.000 0.999 1.00 0.00
#> GSM43008 1 0.000 0.999 1.00 0.00
#> GSM43011 1 0.000 0.999 1.00 0.00
#> GSM78523 1 0.000 0.999 1.00 0.00
#> GSM78526 1 0.000 0.999 1.00 0.00
#> GSM78529 1 0.242 0.958 0.96 0.04
#> GSM78532 1 0.000 0.999 1.00 0.00
#> GSM78534 1 0.000 0.999 1.00 0.00
#> GSM78537 1 0.000 0.999 1.00 0.00
#> GSM78543 1 0.000 0.999 1.00 0.00
#> GSM78548 1 0.000 0.999 1.00 0.00
#> GSM78557 1 0.000 0.999 1.00 0.00
#> GSM78560 1 0.000 0.999 1.00 0.00
#> GSM78565 1 0.000 0.999 1.00 0.00
#> GSM43000 1 0.000 0.999 1.00 0.00
#> GSM43002 1 0.000 0.999 1.00 0.00
#> GSM43004 1 0.000 0.999 1.00 0.00
#> GSM43007 1 0.000 0.999 1.00 0.00
#> GSM43010 1 0.000 0.999 1.00 0.00
#> GSM78522 1 0.000 0.999 1.00 0.00
#> GSM78525 1 0.000 0.999 1.00 0.00
#> GSM78528 1 0.000 0.999 1.00 0.00
#> GSM78531 1 0.000 0.999 1.00 0.00
#> GSM78533 1 0.000 0.999 1.00 0.00
#> GSM78536 1 0.000 0.999 1.00 0.00
#> GSM78541 1 0.000 0.999 1.00 0.00
#> GSM78547 1 0.000 0.999 1.00 0.00
#> GSM78552 1 0.000 0.999 1.00 0.00
#> GSM78556 1 0.000 0.999 1.00 0.00
#> GSM78559 1 0.000 0.999 1.00 0.00
#> GSM78564 1 0.000 0.999 1.00 0.00
#> GSM42999 2 0.000 0.999 0.00 1.00
#> GSM43001 2 0.000 0.999 0.00 1.00
#> GSM43003 2 0.000 0.999 0.00 1.00
#> GSM43006 2 0.000 0.999 0.00 1.00
#> GSM43009 2 0.000 0.999 0.00 1.00
#> GSM43012 2 0.000 0.999 0.00 1.00
#> GSM78524 2 0.000 0.999 0.00 1.00
#> GSM78527 2 0.000 0.999 0.00 1.00
#> GSM78530 2 0.000 0.999 0.00 1.00
#> GSM78535 2 0.141 0.980 0.02 0.98
#> GSM78538 2 0.000 0.999 0.00 1.00
#> GSM78542 2 0.000 0.999 0.00 1.00
#> GSM78544 2 0.000 0.999 0.00 1.00
#> GSM78549 2 0.000 0.999 0.00 1.00
#> GSM78553 2 0.000 0.999 0.00 1.00
#> GSM78558 2 0.000 0.999 0.00 1.00
#> GSM78561 2 0.000 0.999 0.00 1.00
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM78539 1 0.0000 0.930 1.000 0.00 0.000
#> GSM78545 1 0.5254 0.618 0.736 0.00 0.264
#> GSM78550 1 0.0592 0.927 0.988 0.00 0.012
#> GSM78554 1 0.0000 0.930 1.000 0.00 0.000
#> GSM78562 1 0.0000 0.930 1.000 0.00 0.000
#> GSM78540 1 0.0000 0.930 1.000 0.00 0.000
#> GSM78546 1 0.0000 0.930 1.000 0.00 0.000
#> GSM78551 1 0.0000 0.930 1.000 0.00 0.000
#> GSM78555 1 0.0000 0.930 1.000 0.00 0.000
#> GSM78563 1 0.0000 0.930 1.000 0.00 0.000
#> GSM43005 3 0.0000 0.947 0.000 0.00 1.000
#> GSM43008 3 0.0237 0.945 0.004 0.00 0.996
#> GSM43011 3 0.0000 0.947 0.000 0.00 1.000
#> GSM78523 3 0.0000 0.947 0.000 0.00 1.000
#> GSM78526 3 0.0000 0.947 0.000 0.00 1.000
#> GSM78529 3 0.0000 0.947 0.000 0.00 1.000
#> GSM78532 1 0.3267 0.865 0.884 0.00 0.116
#> GSM78534 3 0.0000 0.947 0.000 0.00 1.000
#> GSM78537 1 0.0237 0.931 0.996 0.00 0.004
#> GSM78543 1 0.0592 0.929 0.988 0.00 0.012
#> GSM78548 3 0.0237 0.945 0.004 0.00 0.996
#> GSM78557 1 0.0592 0.929 0.988 0.00 0.012
#> GSM78560 1 0.3482 0.854 0.872 0.00 0.128
#> GSM78565 1 0.1031 0.925 0.976 0.00 0.024
#> GSM43000 3 0.0000 0.947 0.000 0.00 1.000
#> GSM43002 3 0.0000 0.947 0.000 0.00 1.000
#> GSM43004 3 0.0000 0.947 0.000 0.00 1.000
#> GSM43007 3 0.0237 0.945 0.004 0.00 0.996
#> GSM43010 3 0.0000 0.947 0.000 0.00 1.000
#> GSM78522 3 0.0000 0.947 0.000 0.00 1.000
#> GSM78525 3 0.0000 0.947 0.000 0.00 1.000
#> GSM78528 3 0.0000 0.947 0.000 0.00 1.000
#> GSM78531 1 0.3340 0.862 0.880 0.00 0.120
#> GSM78533 3 0.0000 0.947 0.000 0.00 1.000
#> GSM78536 1 0.0237 0.931 0.996 0.00 0.004
#> GSM78541 1 0.0237 0.931 0.996 0.00 0.004
#> GSM78547 1 0.2448 0.894 0.924 0.00 0.076
#> GSM78552 3 0.6168 0.253 0.412 0.00 0.588
#> GSM78556 1 0.4555 0.768 0.800 0.00 0.200
#> GSM78559 1 0.1163 0.923 0.972 0.00 0.028
#> GSM78564 3 0.6260 0.112 0.448 0.00 0.552
#> GSM42999 2 0.0000 1.000 0.000 1.00 0.000
#> GSM43001 2 0.0000 1.000 0.000 1.00 0.000
#> GSM43003 2 0.0000 1.000 0.000 1.00 0.000
#> GSM43006 2 0.0000 1.000 0.000 1.00 0.000
#> GSM43009 2 0.0000 1.000 0.000 1.00 0.000
#> GSM43012 2 0.0000 1.000 0.000 1.00 0.000
#> GSM78524 2 0.0000 1.000 0.000 1.00 0.000
#> GSM78527 2 0.0000 1.000 0.000 1.00 0.000
#> GSM78530 2 0.0000 1.000 0.000 1.00 0.000
#> GSM78535 1 0.6244 0.241 0.560 0.44 0.000
#> GSM78538 2 0.0000 1.000 0.000 1.00 0.000
#> GSM78542 2 0.0000 1.000 0.000 1.00 0.000
#> GSM78544 2 0.0000 1.000 0.000 1.00 0.000
#> GSM78549 2 0.0000 1.000 0.000 1.00 0.000
#> GSM78553 2 0.0000 1.000 0.000 1.00 0.000
#> GSM78558 2 0.0000 1.000 0.000 1.00 0.000
#> GSM78561 2 0.0000 1.000 0.000 1.00 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM78539 4 0.2081 0.9677 0.084 0.000 0.000 0.916
#> GSM78545 4 0.0779 0.9272 0.016 0.000 0.004 0.980
#> GSM78550 4 0.1022 0.9432 0.032 0.000 0.000 0.968
#> GSM78554 4 0.2081 0.9677 0.084 0.000 0.000 0.916
#> GSM78562 4 0.2704 0.9404 0.124 0.000 0.000 0.876
#> GSM78540 4 0.2081 0.9677 0.084 0.000 0.000 0.916
#> GSM78546 4 0.1716 0.9636 0.064 0.000 0.000 0.936
#> GSM78551 4 0.1716 0.9636 0.064 0.000 0.000 0.936
#> GSM78555 4 0.2921 0.9248 0.140 0.000 0.000 0.860
#> GSM78563 4 0.2149 0.9659 0.088 0.000 0.000 0.912
#> GSM43005 3 0.2412 0.8378 0.008 0.000 0.908 0.084
#> GSM43008 3 0.4564 0.6009 0.328 0.000 0.672 0.000
#> GSM43011 3 0.0188 0.8772 0.004 0.000 0.996 0.000
#> GSM78523 3 0.0336 0.8787 0.008 0.000 0.992 0.000
#> GSM78526 3 0.0336 0.8787 0.008 0.000 0.992 0.000
#> GSM78529 3 0.3032 0.8121 0.008 0.000 0.868 0.124
#> GSM78532 1 0.0469 0.9370 0.988 0.000 0.012 0.000
#> GSM78534 3 0.0707 0.8766 0.020 0.000 0.980 0.000
#> GSM78537 1 0.0336 0.9367 0.992 0.000 0.000 0.008
#> GSM78543 1 0.0188 0.9400 0.996 0.000 0.004 0.000
#> GSM78548 3 0.5007 0.7702 0.172 0.000 0.760 0.068
#> GSM78557 1 0.0336 0.9367 0.992 0.000 0.000 0.008
#> GSM78560 1 0.0336 0.9393 0.992 0.000 0.008 0.000
#> GSM78565 1 0.0188 0.9400 0.996 0.000 0.004 0.000
#> GSM43000 3 0.0336 0.8787 0.008 0.000 0.992 0.000
#> GSM43002 3 0.2814 0.8290 0.132 0.000 0.868 0.000
#> GSM43004 1 0.5000 -0.0519 0.504 0.000 0.496 0.000
#> GSM43007 3 0.3688 0.7669 0.208 0.000 0.792 0.000
#> GSM43010 3 0.0469 0.8785 0.012 0.000 0.988 0.000
#> GSM78522 3 0.0469 0.8785 0.012 0.000 0.988 0.000
#> GSM78525 3 0.1474 0.8684 0.052 0.000 0.948 0.000
#> GSM78528 3 0.5998 0.7225 0.200 0.000 0.684 0.116
#> GSM78531 1 0.0336 0.9393 0.992 0.000 0.008 0.000
#> GSM78533 3 0.0336 0.8787 0.008 0.000 0.992 0.000
#> GSM78536 1 0.0188 0.9383 0.996 0.000 0.000 0.004
#> GSM78541 1 0.0469 0.9325 0.988 0.000 0.000 0.012
#> GSM78547 1 0.0376 0.9390 0.992 0.000 0.004 0.004
#> GSM78552 3 0.6024 0.3599 0.416 0.000 0.540 0.044
#> GSM78556 1 0.1211 0.9129 0.960 0.000 0.040 0.000
#> GSM78559 1 0.0188 0.9400 0.996 0.000 0.004 0.000
#> GSM78564 1 0.2216 0.8539 0.908 0.000 0.092 0.000
#> GSM42999 2 0.0000 0.9633 0.000 1.000 0.000 0.000
#> GSM43001 2 0.1847 0.9208 0.004 0.940 0.004 0.052
#> GSM43003 2 0.0000 0.9633 0.000 1.000 0.000 0.000
#> GSM43006 2 0.0336 0.9589 0.000 0.992 0.000 0.008
#> GSM43009 2 0.0000 0.9633 0.000 1.000 0.000 0.000
#> GSM43012 2 0.0000 0.9633 0.000 1.000 0.000 0.000
#> GSM78524 2 0.0000 0.9633 0.000 1.000 0.000 0.000
#> GSM78527 2 0.0000 0.9633 0.000 1.000 0.000 0.000
#> GSM78530 2 0.0000 0.9633 0.000 1.000 0.000 0.000
#> GSM78535 2 0.5155 0.1287 0.468 0.528 0.000 0.004
#> GSM78538 2 0.0000 0.9633 0.000 1.000 0.000 0.000
#> GSM78542 2 0.0000 0.9633 0.000 1.000 0.000 0.000
#> GSM78544 2 0.0000 0.9633 0.000 1.000 0.000 0.000
#> GSM78549 2 0.0000 0.9633 0.000 1.000 0.000 0.000
#> GSM78553 2 0.0000 0.9633 0.000 1.000 0.000 0.000
#> GSM78558 2 0.0000 0.9633 0.000 1.000 0.000 0.000
#> GSM78561 2 0.0707 0.9515 0.000 0.980 0.000 0.020
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM78539 4 0.0290 0.971 0.000 0.000 0.000 0.992 0.008
#> GSM78545 4 0.1478 0.939 0.000 0.000 0.000 0.936 0.064
#> GSM78550 4 0.1792 0.922 0.000 0.000 0.000 0.916 0.084
#> GSM78554 4 0.1121 0.954 0.000 0.000 0.000 0.956 0.044
#> GSM78562 4 0.0290 0.970 0.008 0.000 0.000 0.992 0.000
#> GSM78540 4 0.0162 0.972 0.000 0.004 0.000 0.996 0.000
#> GSM78546 4 0.0000 0.973 0.000 0.000 0.000 1.000 0.000
#> GSM78551 4 0.0000 0.973 0.000 0.000 0.000 1.000 0.000
#> GSM78555 4 0.0451 0.968 0.004 0.008 0.000 0.988 0.000
#> GSM78563 4 0.0162 0.972 0.000 0.004 0.000 0.996 0.000
#> GSM43005 3 0.5411 0.415 0.044 0.000 0.552 0.008 0.396
#> GSM43008 3 0.6877 0.189 0.224 0.000 0.412 0.008 0.356
#> GSM43011 3 0.0290 0.720 0.008 0.000 0.992 0.000 0.000
#> GSM78523 3 0.0404 0.723 0.012 0.000 0.988 0.000 0.000
#> GSM78526 3 0.0404 0.723 0.012 0.000 0.988 0.000 0.000
#> GSM78529 5 0.3525 0.122 0.008 0.000 0.184 0.008 0.800
#> GSM78532 1 0.0579 0.972 0.984 0.000 0.008 0.000 0.008
#> GSM78534 3 0.0703 0.720 0.024 0.000 0.976 0.000 0.000
#> GSM78537 1 0.0865 0.970 0.972 0.000 0.004 0.000 0.024
#> GSM78543 1 0.0290 0.971 0.992 0.000 0.008 0.000 0.000
#> GSM78548 3 0.6441 0.453 0.124 0.000 0.568 0.028 0.280
#> GSM78557 1 0.1894 0.944 0.920 0.000 0.008 0.000 0.072
#> GSM78560 1 0.1331 0.965 0.952 0.000 0.008 0.000 0.040
#> GSM78565 1 0.0579 0.968 0.984 0.000 0.008 0.000 0.008
#> GSM43000 3 0.2305 0.697 0.012 0.000 0.896 0.000 0.092
#> GSM43002 3 0.4728 0.558 0.040 0.000 0.664 0.000 0.296
#> GSM43004 3 0.3752 0.404 0.292 0.000 0.708 0.000 0.000
#> GSM43007 3 0.6644 0.279 0.176 0.000 0.460 0.008 0.356
#> GSM43010 3 0.0510 0.724 0.016 0.000 0.984 0.000 0.000
#> GSM78522 3 0.0609 0.722 0.020 0.000 0.980 0.000 0.000
#> GSM78525 3 0.4352 0.605 0.036 0.000 0.720 0.000 0.244
#> GSM78528 5 0.5633 -0.331 0.056 0.000 0.424 0.008 0.512
#> GSM78531 1 0.0290 0.971 0.992 0.000 0.008 0.000 0.000
#> GSM78533 3 0.0510 0.724 0.016 0.000 0.984 0.000 0.000
#> GSM78536 1 0.0324 0.968 0.992 0.000 0.004 0.000 0.004
#> GSM78541 1 0.0162 0.965 0.996 0.000 0.004 0.000 0.000
#> GSM78547 1 0.1628 0.955 0.936 0.000 0.008 0.000 0.056
#> GSM78552 5 0.7321 -0.284 0.272 0.000 0.340 0.024 0.364
#> GSM78556 1 0.1740 0.953 0.932 0.000 0.012 0.000 0.056
#> GSM78559 1 0.0451 0.970 0.988 0.000 0.008 0.000 0.004
#> GSM78564 1 0.1281 0.966 0.956 0.000 0.012 0.000 0.032
#> GSM42999 2 0.0510 0.899 0.000 0.984 0.000 0.000 0.016
#> GSM43001 5 0.4283 -0.212 0.000 0.456 0.000 0.000 0.544
#> GSM43003 2 0.0609 0.898 0.000 0.980 0.000 0.000 0.020
#> GSM43006 2 0.4210 0.340 0.000 0.588 0.000 0.000 0.412
#> GSM43009 2 0.0290 0.901 0.000 0.992 0.000 0.000 0.008
#> GSM43012 2 0.1410 0.876 0.000 0.940 0.000 0.000 0.060
#> GSM78524 2 0.0963 0.878 0.036 0.964 0.000 0.000 0.000
#> GSM78527 2 0.3424 0.673 0.000 0.760 0.000 0.000 0.240
#> GSM78530 2 0.0290 0.901 0.000 0.992 0.000 0.000 0.008
#> GSM78535 2 0.4392 0.587 0.200 0.748 0.000 0.048 0.004
#> GSM78538 2 0.0162 0.900 0.000 0.996 0.000 0.004 0.000
#> GSM78542 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM78544 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM78549 2 0.1341 0.879 0.000 0.944 0.000 0.000 0.056
#> GSM78553 2 0.0510 0.894 0.000 0.984 0.000 0.016 0.000
#> GSM78558 2 0.0703 0.889 0.000 0.976 0.000 0.024 0.000
#> GSM78561 5 0.4304 -0.270 0.000 0.484 0.000 0.000 0.516
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM78539 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78545 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78550 4 0.0146 0.995 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM78554 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78562 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78540 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78546 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78551 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78555 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78563 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM43005 3 0.3259 0.888 0.012 0.000 0.772 0.000 0.000 0.216
#> GSM43008 3 0.3522 0.870 0.072 0.000 0.800 0.000 0.000 0.128
#> GSM43011 6 0.0405 0.908 0.004 0.000 0.008 0.000 0.000 0.988
#> GSM78523 6 0.0405 0.908 0.004 0.000 0.008 0.000 0.000 0.988
#> GSM78526 6 0.0291 0.910 0.004 0.000 0.004 0.000 0.000 0.992
#> GSM78529 3 0.3612 0.839 0.000 0.000 0.796 0.000 0.100 0.104
#> GSM78532 1 0.1462 0.915 0.936 0.000 0.056 0.000 0.008 0.000
#> GSM78534 6 0.0665 0.903 0.008 0.000 0.004 0.000 0.008 0.980
#> GSM78537 1 0.1387 0.910 0.932 0.000 0.068 0.000 0.000 0.000
#> GSM78543 1 0.0260 0.912 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM78548 3 0.3744 0.860 0.016 0.000 0.724 0.000 0.004 0.256
#> GSM78557 1 0.3795 0.529 0.632 0.000 0.364 0.000 0.000 0.004
#> GSM78560 1 0.1462 0.915 0.936 0.000 0.056 0.000 0.008 0.000
#> GSM78565 1 0.0405 0.903 0.988 0.000 0.008 0.000 0.004 0.000
#> GSM43000 6 0.3426 0.435 0.004 0.000 0.276 0.000 0.000 0.720
#> GSM43002 3 0.3373 0.869 0.008 0.000 0.744 0.000 0.000 0.248
#> GSM43004 6 0.2933 0.666 0.200 0.000 0.000 0.000 0.004 0.796
#> GSM43007 3 0.3385 0.893 0.032 0.000 0.788 0.000 0.000 0.180
#> GSM43010 6 0.0146 0.909 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM78522 6 0.0436 0.907 0.004 0.000 0.004 0.000 0.004 0.988
#> GSM78525 3 0.3725 0.782 0.008 0.000 0.676 0.000 0.000 0.316
#> GSM78528 3 0.2308 0.846 0.016 0.000 0.896 0.000 0.012 0.076
#> GSM78531 1 0.1285 0.915 0.944 0.000 0.052 0.000 0.004 0.000
#> GSM78533 6 0.0291 0.910 0.004 0.000 0.004 0.000 0.000 0.992
#> GSM78536 1 0.0000 0.909 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78541 1 0.0547 0.913 0.980 0.000 0.020 0.000 0.000 0.000
#> GSM78547 1 0.2632 0.843 0.832 0.000 0.164 0.000 0.000 0.004
#> GSM78552 3 0.3041 0.883 0.040 0.000 0.832 0.000 0.000 0.128
#> GSM78556 1 0.2805 0.823 0.812 0.000 0.184 0.000 0.000 0.004
#> GSM78559 1 0.0146 0.908 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM78564 1 0.0837 0.910 0.972 0.000 0.020 0.000 0.004 0.004
#> GSM42999 2 0.0146 0.927 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM43001 5 0.0547 0.916 0.000 0.020 0.000 0.000 0.980 0.000
#> GSM43003 2 0.0632 0.918 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM43006 5 0.2340 0.822 0.000 0.148 0.000 0.000 0.852 0.000
#> GSM43009 2 0.0146 0.927 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM43012 2 0.3737 0.356 0.000 0.608 0.000 0.000 0.392 0.000
#> GSM78524 2 0.0405 0.925 0.000 0.988 0.008 0.000 0.004 0.000
#> GSM78527 2 0.2793 0.745 0.000 0.800 0.000 0.000 0.200 0.000
#> GSM78530 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78535 2 0.0777 0.906 0.024 0.972 0.000 0.000 0.004 0.000
#> GSM78538 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78542 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78544 2 0.0146 0.927 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM78549 2 0.2762 0.751 0.000 0.804 0.000 0.000 0.196 0.000
#> GSM78553 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78558 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78561 5 0.0458 0.914 0.000 0.016 0.000 0.000 0.984 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) agent(p) individual(p) k
#> SD:NMF 58 2.54e-13 0.00184 0.9999 2
#> SD:NMF 55 2.68e-14 0.00255 0.2277 3
#> SD:NMF 55 2.04e-21 0.00750 0.2875 4
#> SD:NMF 47 4.46e-18 0.02248 0.1702 5
#> SD:NMF 56 2.11e-19 0.04069 0.0681 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "hclust"]
# you can also extract it by
# res = res_list["CV:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 58 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)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.781 0.875 0.946 0.3283 0.733 0.733
#> 3 3 0.563 0.770 0.789 0.6259 0.681 0.564
#> 4 4 0.631 0.896 0.879 0.2677 0.879 0.708
#> 5 5 0.642 0.809 0.806 0.0920 0.989 0.963
#> 6 6 0.704 0.760 0.835 0.0792 0.889 0.620
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM78539 1 0.000 0.930 1.000 0.000
#> GSM78545 1 0.000 0.930 1.000 0.000
#> GSM78550 1 0.000 0.930 1.000 0.000
#> GSM78554 1 0.000 0.930 1.000 0.000
#> GSM78562 1 0.000 0.930 1.000 0.000
#> GSM78540 1 0.000 0.930 1.000 0.000
#> GSM78546 1 0.000 0.930 1.000 0.000
#> GSM78551 1 0.000 0.930 1.000 0.000
#> GSM78555 1 0.000 0.930 1.000 0.000
#> GSM78563 1 0.000 0.930 1.000 0.000
#> GSM43005 1 0.000 0.930 1.000 0.000
#> GSM43008 1 0.000 0.930 1.000 0.000
#> GSM43011 1 0.000 0.930 1.000 0.000
#> GSM78523 1 0.000 0.930 1.000 0.000
#> GSM78526 1 0.000 0.930 1.000 0.000
#> GSM78529 1 0.000 0.930 1.000 0.000
#> GSM78532 1 0.000 0.930 1.000 0.000
#> GSM78534 1 0.000 0.930 1.000 0.000
#> GSM78537 1 0.000 0.930 1.000 0.000
#> GSM78543 1 0.000 0.930 1.000 0.000
#> GSM78548 1 0.000 0.930 1.000 0.000
#> GSM78557 1 0.000 0.930 1.000 0.000
#> GSM78560 1 0.000 0.930 1.000 0.000
#> GSM78565 1 0.000 0.930 1.000 0.000
#> GSM43000 1 0.000 0.930 1.000 0.000
#> GSM43002 1 0.000 0.930 1.000 0.000
#> GSM43004 1 0.000 0.930 1.000 0.000
#> GSM43007 1 0.000 0.930 1.000 0.000
#> GSM43010 1 0.000 0.930 1.000 0.000
#> GSM78522 1 0.000 0.930 1.000 0.000
#> GSM78525 1 0.000 0.930 1.000 0.000
#> GSM78528 1 0.000 0.930 1.000 0.000
#> GSM78531 1 0.000 0.930 1.000 0.000
#> GSM78533 1 0.000 0.930 1.000 0.000
#> GSM78536 1 0.000 0.930 1.000 0.000
#> GSM78541 1 0.000 0.930 1.000 0.000
#> GSM78547 1 0.000 0.930 1.000 0.000
#> GSM78552 1 0.000 0.930 1.000 0.000
#> GSM78556 1 0.000 0.930 1.000 0.000
#> GSM78559 1 0.000 0.930 1.000 0.000
#> GSM78564 1 0.000 0.930 1.000 0.000
#> GSM42999 2 0.000 1.000 0.000 1.000
#> GSM43001 2 0.000 1.000 0.000 1.000
#> GSM43003 2 0.000 1.000 0.000 1.000
#> GSM43006 2 0.000 1.000 0.000 1.000
#> GSM43009 2 0.000 1.000 0.000 1.000
#> GSM43012 2 0.000 1.000 0.000 1.000
#> GSM78524 1 0.943 0.505 0.640 0.360
#> GSM78527 2 0.000 1.000 0.000 1.000
#> GSM78530 1 0.971 0.431 0.600 0.400
#> GSM78535 1 0.943 0.505 0.640 0.360
#> GSM78538 1 0.971 0.431 0.600 0.400
#> GSM78542 1 0.971 0.431 0.600 0.400
#> GSM78544 1 0.975 0.413 0.592 0.408
#> GSM78549 2 0.000 1.000 0.000 1.000
#> GSM78553 1 0.971 0.431 0.600 0.400
#> GSM78558 1 0.971 0.431 0.600 0.400
#> GSM78561 2 0.000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM78539 1 0.0000 0.707 1.000 0.000 0.000
#> GSM78545 1 0.3192 0.575 0.888 0.000 0.112
#> GSM78550 1 0.2711 0.622 0.912 0.000 0.088
#> GSM78554 1 0.1753 0.667 0.952 0.000 0.048
#> GSM78562 1 0.0000 0.707 1.000 0.000 0.000
#> GSM78540 1 0.0000 0.707 1.000 0.000 0.000
#> GSM78546 1 0.2537 0.632 0.920 0.000 0.080
#> GSM78551 1 0.2711 0.622 0.912 0.000 0.088
#> GSM78555 1 0.0592 0.712 0.988 0.000 0.012
#> GSM78563 1 0.0000 0.707 1.000 0.000 0.000
#> GSM43005 3 0.6280 0.997 0.460 0.000 0.540
#> GSM43008 3 0.6295 0.979 0.472 0.000 0.528
#> GSM43011 3 0.6280 0.997 0.460 0.000 0.540
#> GSM78523 3 0.6280 0.997 0.460 0.000 0.540
#> GSM78526 3 0.6280 0.997 0.460 0.000 0.540
#> GSM78529 3 0.6280 0.997 0.460 0.000 0.540
#> GSM78532 1 0.0592 0.712 0.988 0.000 0.012
#> GSM78534 3 0.6280 0.997 0.460 0.000 0.540
#> GSM78537 1 0.0592 0.712 0.988 0.000 0.012
#> GSM78543 1 0.0592 0.712 0.988 0.000 0.012
#> GSM78548 1 0.3267 0.565 0.884 0.000 0.116
#> GSM78557 1 0.2796 0.616 0.908 0.000 0.092
#> GSM78560 1 0.0592 0.712 0.988 0.000 0.012
#> GSM78565 1 0.0592 0.712 0.988 0.000 0.012
#> GSM43000 3 0.6280 0.997 0.460 0.000 0.540
#> GSM43002 3 0.6280 0.997 0.460 0.000 0.540
#> GSM43004 3 0.6280 0.997 0.460 0.000 0.540
#> GSM43007 3 0.6295 0.979 0.472 0.000 0.528
#> GSM43010 3 0.6280 0.997 0.460 0.000 0.540
#> GSM78522 3 0.6280 0.997 0.460 0.000 0.540
#> GSM78525 3 0.6280 0.997 0.460 0.000 0.540
#> GSM78528 3 0.6280 0.997 0.460 0.000 0.540
#> GSM78531 1 0.0592 0.712 0.988 0.000 0.012
#> GSM78533 3 0.6280 0.997 0.460 0.000 0.540
#> GSM78536 1 0.0592 0.712 0.988 0.000 0.012
#> GSM78541 1 0.0592 0.712 0.988 0.000 0.012
#> GSM78547 1 0.2878 0.609 0.904 0.000 0.096
#> GSM78552 1 0.2878 0.609 0.904 0.000 0.096
#> GSM78556 1 0.2878 0.609 0.904 0.000 0.096
#> GSM78559 1 0.0592 0.712 0.988 0.000 0.012
#> GSM78564 1 0.2796 0.616 0.908 0.000 0.092
#> GSM42999 2 0.1964 0.978 0.000 0.944 0.056
#> GSM43001 2 0.0000 0.973 0.000 1.000 0.000
#> GSM43003 2 0.2066 0.977 0.000 0.940 0.060
#> GSM43006 2 0.0000 0.973 0.000 1.000 0.000
#> GSM43009 2 0.1964 0.978 0.000 0.944 0.056
#> GSM43012 2 0.0000 0.973 0.000 1.000 0.000
#> GSM78524 1 0.6280 0.420 0.540 0.000 0.460
#> GSM78527 2 0.2066 0.977 0.000 0.940 0.060
#> GSM78530 1 0.8270 0.406 0.540 0.084 0.376
#> GSM78535 1 0.6280 0.420 0.540 0.000 0.460
#> GSM78538 1 0.8270 0.406 0.540 0.084 0.376
#> GSM78542 1 0.8270 0.406 0.540 0.084 0.376
#> GSM78544 1 0.8808 0.378 0.536 0.132 0.332
#> GSM78549 2 0.2066 0.977 0.000 0.940 0.060
#> GSM78553 1 0.8270 0.406 0.540 0.084 0.376
#> GSM78558 1 0.8270 0.406 0.540 0.084 0.376
#> GSM78561 2 0.0000 0.973 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM78539 1 0.0469 0.835 0.988 0.000 0.012 0.000
#> GSM78545 1 0.4543 0.641 0.676 0.000 0.324 0.000
#> GSM78550 1 0.2868 0.842 0.864 0.000 0.136 0.000
#> GSM78554 1 0.2281 0.858 0.904 0.000 0.096 0.000
#> GSM78562 1 0.0469 0.835 0.988 0.000 0.012 0.000
#> GSM78540 1 0.0469 0.835 0.988 0.000 0.012 0.000
#> GSM78546 1 0.2216 0.838 0.908 0.000 0.092 0.000
#> GSM78551 1 0.2408 0.834 0.896 0.000 0.104 0.000
#> GSM78555 1 0.0000 0.829 1.000 0.000 0.000 0.000
#> GSM78563 1 0.0469 0.835 0.988 0.000 0.012 0.000
#> GSM43005 3 0.2216 0.992 0.092 0.000 0.908 0.000
#> GSM43008 3 0.2530 0.976 0.112 0.000 0.888 0.000
#> GSM43011 3 0.2216 0.992 0.092 0.000 0.908 0.000
#> GSM78523 3 0.2216 0.992 0.092 0.000 0.908 0.000
#> GSM78526 3 0.2216 0.992 0.092 0.000 0.908 0.000
#> GSM78529 3 0.2216 0.992 0.092 0.000 0.908 0.000
#> GSM78532 1 0.2530 0.872 0.888 0.000 0.112 0.000
#> GSM78534 3 0.2469 0.981 0.108 0.000 0.892 0.000
#> GSM78537 1 0.2530 0.872 0.888 0.000 0.112 0.000
#> GSM78543 1 0.2530 0.872 0.888 0.000 0.112 0.000
#> GSM78548 1 0.4888 0.523 0.588 0.000 0.412 0.000
#> GSM78557 1 0.3942 0.809 0.764 0.000 0.236 0.000
#> GSM78560 1 0.2647 0.869 0.880 0.000 0.120 0.000
#> GSM78565 1 0.2530 0.872 0.888 0.000 0.112 0.000
#> GSM43000 3 0.2216 0.992 0.092 0.000 0.908 0.000
#> GSM43002 3 0.2216 0.992 0.092 0.000 0.908 0.000
#> GSM43004 3 0.2469 0.981 0.108 0.000 0.892 0.000
#> GSM43007 3 0.2530 0.976 0.112 0.000 0.888 0.000
#> GSM43010 3 0.2216 0.992 0.092 0.000 0.908 0.000
#> GSM78522 3 0.2469 0.981 0.108 0.000 0.892 0.000
#> GSM78525 3 0.2216 0.992 0.092 0.000 0.908 0.000
#> GSM78528 3 0.2216 0.992 0.092 0.000 0.908 0.000
#> GSM78531 1 0.2530 0.872 0.888 0.000 0.112 0.000
#> GSM78533 3 0.2216 0.992 0.092 0.000 0.908 0.000
#> GSM78536 1 0.2530 0.872 0.888 0.000 0.112 0.000
#> GSM78541 1 0.2530 0.872 0.888 0.000 0.112 0.000
#> GSM78547 1 0.4040 0.799 0.752 0.000 0.248 0.000
#> GSM78552 1 0.4746 0.620 0.632 0.000 0.368 0.000
#> GSM78556 1 0.3975 0.806 0.760 0.000 0.240 0.000
#> GSM78559 1 0.2530 0.872 0.888 0.000 0.112 0.000
#> GSM78564 1 0.4454 0.725 0.692 0.000 0.308 0.000
#> GSM42999 2 0.2921 0.934 0.000 0.860 0.000 0.140
#> GSM43001 2 0.0000 0.898 0.000 1.000 0.000 0.000
#> GSM43003 2 0.2973 0.932 0.000 0.856 0.000 0.144
#> GSM43006 2 0.0000 0.898 0.000 1.000 0.000 0.000
#> GSM43009 2 0.2921 0.934 0.000 0.860 0.000 0.140
#> GSM43012 2 0.2081 0.925 0.000 0.916 0.000 0.084
#> GSM78524 4 0.2216 0.916 0.000 0.000 0.092 0.908
#> GSM78527 2 0.2973 0.932 0.000 0.856 0.000 0.144
#> GSM78530 4 0.0000 0.965 0.000 0.000 0.000 1.000
#> GSM78535 4 0.2216 0.916 0.000 0.000 0.092 0.908
#> GSM78538 4 0.0000 0.965 0.000 0.000 0.000 1.000
#> GSM78542 4 0.0000 0.965 0.000 0.000 0.000 1.000
#> GSM78544 4 0.1389 0.922 0.000 0.048 0.000 0.952
#> GSM78549 2 0.2973 0.932 0.000 0.856 0.000 0.144
#> GSM78553 4 0.0000 0.965 0.000 0.000 0.000 1.000
#> GSM78558 4 0.0000 0.965 0.000 0.000 0.000 1.000
#> GSM78561 2 0.0000 0.898 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM78539 1 0.0807 0.654 0.976 0.000 0.012 0.000 0.012
#> GSM78545 1 0.5275 0.528 0.640 0.000 0.276 0.000 0.084
#> GSM78550 1 0.3420 0.660 0.840 0.000 0.076 0.000 0.084
#> GSM78554 1 0.2830 0.676 0.876 0.000 0.080 0.000 0.044
#> GSM78562 1 0.0807 0.654 0.976 0.000 0.012 0.000 0.012
#> GSM78540 1 0.0290 0.646 0.992 0.000 0.008 0.000 0.000
#> GSM78546 1 0.2110 0.641 0.912 0.000 0.016 0.000 0.072
#> GSM78551 1 0.2293 0.637 0.900 0.000 0.016 0.000 0.084
#> GSM78555 1 0.0609 0.645 0.980 0.000 0.000 0.000 0.020
#> GSM78563 1 0.0290 0.646 0.992 0.000 0.008 0.000 0.000
#> GSM43005 3 0.1952 0.894 0.004 0.000 0.912 0.000 0.084
#> GSM43008 3 0.2561 0.880 0.020 0.000 0.884 0.000 0.096
#> GSM43011 3 0.1608 0.894 0.000 0.000 0.928 0.000 0.072
#> GSM78523 3 0.1608 0.894 0.000 0.000 0.928 0.000 0.072
#> GSM78526 3 0.1608 0.894 0.000 0.000 0.928 0.000 0.072
#> GSM78529 3 0.2011 0.894 0.004 0.000 0.908 0.000 0.088
#> GSM78532 1 0.5744 0.738 0.572 0.000 0.108 0.000 0.320
#> GSM78534 3 0.2304 0.878 0.008 0.000 0.892 0.000 0.100
#> GSM78537 1 0.5744 0.738 0.572 0.000 0.108 0.000 0.320
#> GSM78543 1 0.5744 0.738 0.572 0.000 0.108 0.000 0.320
#> GSM78548 1 0.5752 0.399 0.500 0.000 0.412 0.000 0.088
#> GSM78557 1 0.6425 0.688 0.476 0.000 0.188 0.000 0.336
#> GSM78560 1 0.5923 0.736 0.572 0.000 0.140 0.000 0.288
#> GSM78565 1 0.5744 0.738 0.572 0.000 0.108 0.000 0.320
#> GSM43000 3 0.2011 0.894 0.004 0.000 0.908 0.000 0.088
#> GSM43002 3 0.2011 0.894 0.004 0.000 0.908 0.000 0.088
#> GSM43004 3 0.2304 0.878 0.008 0.000 0.892 0.000 0.100
#> GSM43007 3 0.2561 0.880 0.020 0.000 0.884 0.000 0.096
#> GSM43010 3 0.1608 0.894 0.000 0.000 0.928 0.000 0.072
#> GSM78522 3 0.2304 0.878 0.008 0.000 0.892 0.000 0.100
#> GSM78525 3 0.2011 0.894 0.004 0.000 0.908 0.000 0.088
#> GSM78528 3 0.2011 0.894 0.004 0.000 0.908 0.000 0.088
#> GSM78531 1 0.5744 0.738 0.572 0.000 0.108 0.000 0.320
#> GSM78533 3 0.1608 0.894 0.000 0.000 0.928 0.000 0.072
#> GSM78536 1 0.5744 0.738 0.572 0.000 0.108 0.000 0.320
#> GSM78541 1 0.5744 0.738 0.572 0.000 0.108 0.000 0.320
#> GSM78547 1 0.6544 0.669 0.468 0.000 0.224 0.000 0.308
#> GSM78552 1 0.6619 0.513 0.420 0.000 0.360 0.000 0.220
#> GSM78556 1 0.6447 0.685 0.472 0.000 0.192 0.000 0.336
#> GSM78559 1 0.5744 0.738 0.572 0.000 0.108 0.000 0.320
#> GSM78564 1 0.6618 0.630 0.452 0.000 0.244 0.000 0.304
#> GSM42999 4 0.0000 0.970 0.000 0.000 0.000 1.000 0.000
#> GSM43001 5 0.4227 1.000 0.000 0.000 0.000 0.420 0.580
#> GSM43003 4 0.0162 0.970 0.000 0.004 0.000 0.996 0.000
#> GSM43006 5 0.4227 1.000 0.000 0.000 0.000 0.420 0.580
#> GSM43009 4 0.0000 0.970 0.000 0.000 0.000 1.000 0.000
#> GSM43012 4 0.1341 0.859 0.000 0.000 0.000 0.944 0.056
#> GSM78524 2 0.0162 0.857 0.000 0.996 0.000 0.000 0.004
#> GSM78527 4 0.0162 0.970 0.000 0.004 0.000 0.996 0.000
#> GSM78530 2 0.2516 0.946 0.000 0.860 0.000 0.140 0.000
#> GSM78535 2 0.0162 0.857 0.000 0.996 0.000 0.000 0.004
#> GSM78538 2 0.2516 0.946 0.000 0.860 0.000 0.140 0.000
#> GSM78542 2 0.2516 0.946 0.000 0.860 0.000 0.140 0.000
#> GSM78544 2 0.3003 0.903 0.000 0.812 0.000 0.188 0.000
#> GSM78549 4 0.0162 0.970 0.000 0.004 0.000 0.996 0.000
#> GSM78553 2 0.2516 0.946 0.000 0.860 0.000 0.140 0.000
#> GSM78558 2 0.2516 0.946 0.000 0.860 0.000 0.140 0.000
#> GSM78561 5 0.4227 1.000 0.000 0.000 0.000 0.420 0.580
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM78539 4 0.0692 0.795 0.020 0.000 0.004 0.976 0.000 0.000
#> GSM78545 4 0.3620 0.587 0.000 0.000 0.352 0.648 0.000 0.000
#> GSM78550 4 0.2378 0.777 0.000 0.000 0.152 0.848 0.000 0.000
#> GSM78554 4 0.2003 0.799 0.000 0.000 0.116 0.884 0.000 0.000
#> GSM78562 4 0.0692 0.795 0.020 0.000 0.004 0.976 0.000 0.000
#> GSM78540 4 0.0000 0.801 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78546 4 0.1556 0.809 0.000 0.000 0.080 0.920 0.000 0.000
#> GSM78551 4 0.1714 0.805 0.000 0.000 0.092 0.908 0.000 0.000
#> GSM78555 4 0.1714 0.703 0.092 0.000 0.000 0.908 0.000 0.000
#> GSM78563 4 0.0000 0.801 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM43005 3 0.0508 0.713 0.004 0.000 0.984 0.012 0.000 0.000
#> GSM43008 3 0.1528 0.704 0.048 0.000 0.936 0.016 0.000 0.000
#> GSM43011 3 0.4493 0.704 0.344 0.000 0.612 0.000 0.044 0.000
#> GSM78523 3 0.4493 0.704 0.344 0.000 0.612 0.000 0.044 0.000
#> GSM78526 3 0.4493 0.704 0.344 0.000 0.612 0.000 0.044 0.000
#> GSM78529 3 0.0363 0.712 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM78532 1 0.2730 0.819 0.808 0.000 0.000 0.192 0.000 0.000
#> GSM78534 3 0.4627 0.675 0.396 0.000 0.560 0.000 0.044 0.000
#> GSM78537 1 0.2730 0.819 0.808 0.000 0.000 0.192 0.000 0.000
#> GSM78543 1 0.2730 0.819 0.808 0.000 0.000 0.192 0.000 0.000
#> GSM78548 4 0.4467 0.358 0.028 0.000 0.464 0.508 0.000 0.000
#> GSM78557 1 0.5648 0.464 0.512 0.000 0.176 0.312 0.000 0.000
#> GSM78560 1 0.3807 0.782 0.756 0.000 0.052 0.192 0.000 0.000
#> GSM78565 1 0.2730 0.819 0.808 0.000 0.000 0.192 0.000 0.000
#> GSM43000 3 0.0363 0.712 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM43002 3 0.0363 0.712 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM43004 3 0.4634 0.671 0.400 0.000 0.556 0.000 0.044 0.000
#> GSM43007 3 0.1528 0.704 0.048 0.000 0.936 0.016 0.000 0.000
#> GSM43010 3 0.4493 0.704 0.344 0.000 0.612 0.000 0.044 0.000
#> GSM78522 3 0.4627 0.675 0.396 0.000 0.560 0.000 0.044 0.000
#> GSM78525 3 0.0363 0.712 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM78528 3 0.0363 0.712 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM78531 1 0.2730 0.819 0.808 0.000 0.000 0.192 0.000 0.000
#> GSM78533 3 0.4493 0.704 0.344 0.000 0.612 0.000 0.044 0.000
#> GSM78536 1 0.2730 0.819 0.808 0.000 0.000 0.192 0.000 0.000
#> GSM78541 1 0.2730 0.819 0.808 0.000 0.000 0.192 0.000 0.000
#> GSM78547 1 0.5953 0.366 0.448 0.000 0.244 0.308 0.000 0.000
#> GSM78552 3 0.6076 -0.329 0.292 0.000 0.400 0.308 0.000 0.000
#> GSM78556 1 0.5660 0.462 0.512 0.000 0.180 0.308 0.000 0.000
#> GSM78559 1 0.2730 0.819 0.808 0.000 0.000 0.192 0.000 0.000
#> GSM78564 1 0.5925 0.376 0.456 0.000 0.236 0.308 0.000 0.000
#> GSM42999 6 0.0146 0.981 0.000 0.000 0.000 0.000 0.004 0.996
#> GSM43001 5 0.1007 1.000 0.000 0.000 0.000 0.000 0.956 0.044
#> GSM43003 6 0.0000 0.982 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM43006 5 0.1007 1.000 0.000 0.000 0.000 0.000 0.956 0.044
#> GSM43009 6 0.0146 0.981 0.000 0.000 0.000 0.000 0.004 0.996
#> GSM43012 6 0.1267 0.917 0.000 0.000 0.000 0.000 0.060 0.940
#> GSM78524 2 0.0000 0.850 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78527 6 0.0000 0.982 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78530 2 0.2300 0.945 0.000 0.856 0.000 0.000 0.000 0.144
#> GSM78535 2 0.0000 0.850 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78538 2 0.2300 0.945 0.000 0.856 0.000 0.000 0.000 0.144
#> GSM78542 2 0.2300 0.945 0.000 0.856 0.000 0.000 0.000 0.144
#> GSM78544 2 0.2730 0.902 0.000 0.808 0.000 0.000 0.000 0.192
#> GSM78549 6 0.0000 0.982 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78553 2 0.2300 0.945 0.000 0.856 0.000 0.000 0.000 0.144
#> GSM78558 2 0.2300 0.945 0.000 0.856 0.000 0.000 0.000 0.144
#> GSM78561 5 0.1007 1.000 0.000 0.000 0.000 0.000 0.956 0.044
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) agent(p) individual(p) k
#> CV:hclust 52 1.55e-09 0.03378 0.8621 2
#> CV:hclust 50 2.48e-12 0.03334 0.0329 3
#> CV:hclust 58 4.14e-13 0.00812 0.1188 4
#> CV:hclust 57 5.73e-12 0.02441 0.1248 5
#> CV:hclust 52 8.60e-18 0.02694 0.1381 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "kmeans"]
# you can also extract it by
# res = res_list["CV:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 58 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.991 0.995 0.4188 0.578 0.578
#> 3 3 0.632 0.850 0.866 0.5004 0.726 0.537
#> 4 4 0.630 0.406 0.625 0.1506 0.757 0.438
#> 5 5 0.774 0.817 0.780 0.0752 0.829 0.485
#> 6 6 0.827 0.851 0.849 0.0554 0.948 0.750
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM78539 1 0.0376 0.997 0.996 0.004
#> GSM78545 1 0.0376 0.997 0.996 0.004
#> GSM78550 1 0.0376 0.997 0.996 0.004
#> GSM78554 1 0.0376 0.997 0.996 0.004
#> GSM78562 1 0.0376 0.997 0.996 0.004
#> GSM78540 1 0.0376 0.997 0.996 0.004
#> GSM78546 1 0.0376 0.997 0.996 0.004
#> GSM78551 1 0.0376 0.997 0.996 0.004
#> GSM78555 1 0.0376 0.997 0.996 0.004
#> GSM78563 1 0.0376 0.997 0.996 0.004
#> GSM43005 1 0.0000 0.999 1.000 0.000
#> GSM43008 1 0.0000 0.999 1.000 0.000
#> GSM43011 1 0.0000 0.999 1.000 0.000
#> GSM78523 1 0.0000 0.999 1.000 0.000
#> GSM78526 1 0.0000 0.999 1.000 0.000
#> GSM78529 1 0.0000 0.999 1.000 0.000
#> GSM78532 1 0.0000 0.999 1.000 0.000
#> GSM78534 1 0.0000 0.999 1.000 0.000
#> GSM78537 1 0.0000 0.999 1.000 0.000
#> GSM78543 1 0.0000 0.999 1.000 0.000
#> GSM78548 1 0.0000 0.999 1.000 0.000
#> GSM78557 1 0.0000 0.999 1.000 0.000
#> GSM78560 1 0.0000 0.999 1.000 0.000
#> GSM78565 1 0.0000 0.999 1.000 0.000
#> GSM43000 1 0.0000 0.999 1.000 0.000
#> GSM43002 1 0.0000 0.999 1.000 0.000
#> GSM43004 1 0.0000 0.999 1.000 0.000
#> GSM43007 1 0.0000 0.999 1.000 0.000
#> GSM43010 1 0.0000 0.999 1.000 0.000
#> GSM78522 1 0.0000 0.999 1.000 0.000
#> GSM78525 1 0.0000 0.999 1.000 0.000
#> GSM78528 1 0.0000 0.999 1.000 0.000
#> GSM78531 1 0.0000 0.999 1.000 0.000
#> GSM78533 1 0.0000 0.999 1.000 0.000
#> GSM78536 1 0.0000 0.999 1.000 0.000
#> GSM78541 1 0.0000 0.999 1.000 0.000
#> GSM78547 1 0.0000 0.999 1.000 0.000
#> GSM78552 1 0.0000 0.999 1.000 0.000
#> GSM78556 1 0.0000 0.999 1.000 0.000
#> GSM78559 1 0.0000 0.999 1.000 0.000
#> GSM78564 1 0.0000 0.999 1.000 0.000
#> GSM42999 2 0.0376 0.987 0.004 0.996
#> GSM43001 2 0.0376 0.987 0.004 0.996
#> GSM43003 2 0.0376 0.987 0.004 0.996
#> GSM43006 2 0.0376 0.987 0.004 0.996
#> GSM43009 2 0.0376 0.987 0.004 0.996
#> GSM43012 2 0.0376 0.987 0.004 0.996
#> GSM78524 2 0.0376 0.987 0.004 0.996
#> GSM78527 2 0.0376 0.987 0.004 0.996
#> GSM78530 2 0.0376 0.987 0.004 0.996
#> GSM78535 2 0.7299 0.749 0.204 0.796
#> GSM78538 2 0.0376 0.987 0.004 0.996
#> GSM78542 2 0.0376 0.987 0.004 0.996
#> GSM78544 2 0.0376 0.987 0.004 0.996
#> GSM78549 2 0.0376 0.987 0.004 0.996
#> GSM78553 2 0.0376 0.987 0.004 0.996
#> GSM78558 2 0.0376 0.987 0.004 0.996
#> GSM78561 2 0.0376 0.987 0.004 0.996
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM78539 1 0.4062 0.8109 0.836 0.000 0.164
#> GSM78545 3 0.6126 0.2365 0.400 0.000 0.600
#> GSM78550 1 0.4178 0.8103 0.828 0.000 0.172
#> GSM78554 1 0.4178 0.8103 0.828 0.000 0.172
#> GSM78562 1 0.3941 0.8106 0.844 0.000 0.156
#> GSM78540 1 0.4178 0.8103 0.828 0.000 0.172
#> GSM78546 1 0.4178 0.8103 0.828 0.000 0.172
#> GSM78551 1 0.4178 0.8103 0.828 0.000 0.172
#> GSM78555 1 0.3941 0.8106 0.844 0.000 0.156
#> GSM78563 1 0.4178 0.8103 0.828 0.000 0.172
#> GSM43005 3 0.5650 0.9644 0.312 0.000 0.688
#> GSM43008 3 0.5678 0.9636 0.316 0.000 0.684
#> GSM43011 3 0.5650 0.9644 0.312 0.000 0.688
#> GSM78523 3 0.5678 0.9636 0.316 0.000 0.684
#> GSM78526 3 0.5678 0.9636 0.316 0.000 0.684
#> GSM78529 3 0.5650 0.9644 0.312 0.000 0.688
#> GSM78532 1 0.0000 0.8405 1.000 0.000 0.000
#> GSM78534 3 0.5785 0.9489 0.332 0.000 0.668
#> GSM78537 1 0.0000 0.8405 1.000 0.000 0.000
#> GSM78543 1 0.0000 0.8405 1.000 0.000 0.000
#> GSM78548 3 0.5650 0.9644 0.312 0.000 0.688
#> GSM78557 1 0.0000 0.8405 1.000 0.000 0.000
#> GSM78560 1 0.0000 0.8405 1.000 0.000 0.000
#> GSM78565 1 0.0000 0.8405 1.000 0.000 0.000
#> GSM43000 3 0.5650 0.9644 0.312 0.000 0.688
#> GSM43002 3 0.5650 0.9644 0.312 0.000 0.688
#> GSM43004 3 0.5859 0.9366 0.344 0.000 0.656
#> GSM43007 3 0.5650 0.9644 0.312 0.000 0.688
#> GSM43010 3 0.5678 0.9636 0.316 0.000 0.684
#> GSM78522 3 0.5785 0.9489 0.332 0.000 0.668
#> GSM78525 3 0.5650 0.9644 0.312 0.000 0.688
#> GSM78528 3 0.5650 0.9644 0.312 0.000 0.688
#> GSM78531 1 0.0000 0.8405 1.000 0.000 0.000
#> GSM78533 3 0.5678 0.9636 0.316 0.000 0.684
#> GSM78536 1 0.0000 0.8405 1.000 0.000 0.000
#> GSM78541 1 0.0000 0.8405 1.000 0.000 0.000
#> GSM78547 1 0.0000 0.8405 1.000 0.000 0.000
#> GSM78552 1 0.6309 -0.6525 0.500 0.000 0.500
#> GSM78556 1 0.0000 0.8405 1.000 0.000 0.000
#> GSM78559 1 0.0000 0.8405 1.000 0.000 0.000
#> GSM78564 1 0.0000 0.8405 1.000 0.000 0.000
#> GSM42999 2 0.0000 0.9467 0.000 1.000 0.000
#> GSM43001 2 0.0892 0.9434 0.000 0.980 0.020
#> GSM43003 2 0.0000 0.9467 0.000 1.000 0.000
#> GSM43006 2 0.0892 0.9434 0.000 0.980 0.020
#> GSM43009 2 0.2066 0.9466 0.000 0.940 0.060
#> GSM43012 2 0.0892 0.9434 0.000 0.980 0.020
#> GSM78524 2 0.3686 0.9406 0.000 0.860 0.140
#> GSM78527 2 0.0892 0.9434 0.000 0.980 0.020
#> GSM78530 2 0.3686 0.9406 0.000 0.860 0.140
#> GSM78535 1 0.9367 0.0648 0.476 0.344 0.180
#> GSM78538 2 0.3686 0.9406 0.000 0.860 0.140
#> GSM78542 2 0.3686 0.9406 0.000 0.860 0.140
#> GSM78544 2 0.3686 0.9406 0.000 0.860 0.140
#> GSM78549 2 0.0000 0.9467 0.000 1.000 0.000
#> GSM78553 2 0.3686 0.9406 0.000 0.860 0.140
#> GSM78558 2 0.3686 0.9406 0.000 0.860 0.140
#> GSM78561 2 0.0892 0.9434 0.000 0.980 0.020
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM78539 4 0.0921 0.8861 0.028 0.000 0.000 0.972
#> GSM78545 4 0.4605 0.4955 0.336 0.000 0.000 0.664
#> GSM78550 4 0.3764 0.6957 0.216 0.000 0.000 0.784
#> GSM78554 4 0.1557 0.8811 0.056 0.000 0.000 0.944
#> GSM78562 4 0.1557 0.8590 0.056 0.000 0.000 0.944
#> GSM78540 4 0.0921 0.8861 0.028 0.000 0.000 0.972
#> GSM78546 4 0.1389 0.8850 0.048 0.000 0.000 0.952
#> GSM78551 4 0.1389 0.8850 0.048 0.000 0.000 0.952
#> GSM78555 4 0.1557 0.8590 0.056 0.000 0.000 0.944
#> GSM78563 4 0.0921 0.8861 0.028 0.000 0.000 0.972
#> GSM43005 1 0.5671 -0.6995 0.572 0.000 0.400 0.028
#> GSM43008 1 0.5510 -0.6919 0.600 0.000 0.376 0.024
#> GSM43011 3 0.5060 0.9544 0.412 0.000 0.584 0.004
#> GSM78523 3 0.5060 0.9544 0.412 0.000 0.584 0.004
#> GSM78526 3 0.5004 0.9663 0.392 0.000 0.604 0.004
#> GSM78529 1 0.5671 -0.6995 0.572 0.000 0.400 0.028
#> GSM78532 1 0.4989 0.1802 0.528 0.000 0.000 0.472
#> GSM78534 3 0.4985 0.8547 0.468 0.000 0.532 0.000
#> GSM78537 1 0.4989 0.1802 0.528 0.000 0.000 0.472
#> GSM78543 1 0.4989 0.1802 0.528 0.000 0.000 0.472
#> GSM78548 1 0.5649 -0.6955 0.580 0.000 0.392 0.028
#> GSM78557 1 0.4981 0.1816 0.536 0.000 0.000 0.464
#> GSM78560 1 0.4981 0.1816 0.536 0.000 0.000 0.464
#> GSM78565 1 0.4989 0.1802 0.528 0.000 0.000 0.472
#> GSM43000 1 0.5126 -0.7577 0.552 0.000 0.444 0.004
#> GSM43002 1 0.5088 -0.7285 0.572 0.000 0.424 0.004
#> GSM43004 1 0.3881 -0.0861 0.812 0.000 0.172 0.016
#> GSM43007 1 0.5649 -0.6955 0.580 0.000 0.392 0.028
#> GSM43010 3 0.5004 0.9663 0.392 0.000 0.604 0.004
#> GSM78522 3 0.4843 0.9629 0.396 0.000 0.604 0.000
#> GSM78525 1 0.5088 -0.7285 0.572 0.000 0.424 0.004
#> GSM78528 1 0.5671 -0.6995 0.572 0.000 0.400 0.028
#> GSM78531 1 0.4989 0.1802 0.528 0.000 0.000 0.472
#> GSM78533 3 0.5004 0.9663 0.392 0.000 0.604 0.004
#> GSM78536 1 0.4989 0.1802 0.528 0.000 0.000 0.472
#> GSM78541 1 0.4989 0.1802 0.528 0.000 0.000 0.472
#> GSM78547 1 0.4981 0.1816 0.536 0.000 0.000 0.464
#> GSM78552 1 0.6209 -0.3708 0.656 0.000 0.232 0.112
#> GSM78556 1 0.4981 0.1816 0.536 0.000 0.000 0.464
#> GSM78559 1 0.4989 0.1802 0.528 0.000 0.000 0.472
#> GSM78564 1 0.4981 0.1816 0.536 0.000 0.000 0.464
#> GSM42999 2 0.3074 0.8204 0.000 0.848 0.152 0.000
#> GSM43001 2 0.4406 0.8031 0.000 0.780 0.192 0.028
#> GSM43003 2 0.3074 0.8204 0.000 0.848 0.152 0.000
#> GSM43006 2 0.4406 0.8031 0.000 0.780 0.192 0.028
#> GSM43009 2 0.0707 0.8245 0.000 0.980 0.020 0.000
#> GSM43012 2 0.3831 0.8066 0.000 0.792 0.204 0.004
#> GSM78524 2 0.3400 0.8119 0.000 0.820 0.180 0.000
#> GSM78527 2 0.3610 0.8092 0.000 0.800 0.200 0.000
#> GSM78530 2 0.3356 0.8126 0.000 0.824 0.176 0.000
#> GSM78535 2 0.9459 0.2324 0.220 0.424 0.180 0.176
#> GSM78538 2 0.3444 0.8124 0.000 0.816 0.184 0.000
#> GSM78542 2 0.3444 0.8124 0.000 0.816 0.184 0.000
#> GSM78544 2 0.3356 0.8126 0.000 0.824 0.176 0.000
#> GSM78549 2 0.3074 0.8204 0.000 0.848 0.152 0.000
#> GSM78553 2 0.3400 0.8119 0.000 0.820 0.180 0.000
#> GSM78558 2 0.3400 0.8119 0.000 0.820 0.180 0.000
#> GSM78561 2 0.4406 0.8031 0.000 0.780 0.192 0.028
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM78539 4 0.3937 0.932 0.252 0.000 0.008 0.736 0.004
#> GSM78545 4 0.5056 0.768 0.084 0.000 0.176 0.724 0.016
#> GSM78550 4 0.5158 0.826 0.124 0.000 0.136 0.724 0.016
#> GSM78554 4 0.4537 0.930 0.236 0.000 0.024 0.724 0.016
#> GSM78562 4 0.3766 0.917 0.268 0.000 0.000 0.728 0.004
#> GSM78540 4 0.3783 0.932 0.252 0.000 0.008 0.740 0.000
#> GSM78546 4 0.4212 0.932 0.236 0.000 0.024 0.736 0.004
#> GSM78551 4 0.4212 0.932 0.236 0.000 0.024 0.736 0.004
#> GSM78555 4 0.3612 0.917 0.268 0.000 0.000 0.732 0.000
#> GSM78563 4 0.3783 0.932 0.252 0.000 0.008 0.740 0.000
#> GSM43005 3 0.0579 0.807 0.008 0.000 0.984 0.008 0.000
#> GSM43008 3 0.1893 0.794 0.024 0.000 0.936 0.012 0.028
#> GSM43011 3 0.5672 0.749 0.008 0.000 0.632 0.104 0.256
#> GSM78523 3 0.5672 0.749 0.008 0.000 0.632 0.104 0.256
#> GSM78526 3 0.5960 0.732 0.008 0.000 0.588 0.116 0.288
#> GSM78529 3 0.0579 0.807 0.008 0.000 0.984 0.008 0.000
#> GSM78532 1 0.0963 0.956 0.964 0.000 0.036 0.000 0.000
#> GSM78534 3 0.7881 0.584 0.140 0.000 0.424 0.132 0.304
#> GSM78537 1 0.0963 0.956 0.964 0.000 0.036 0.000 0.000
#> GSM78543 1 0.0963 0.956 0.964 0.000 0.036 0.000 0.000
#> GSM78548 3 0.1455 0.801 0.008 0.000 0.952 0.008 0.032
#> GSM78557 1 0.1661 0.946 0.940 0.000 0.036 0.000 0.024
#> GSM78560 1 0.1124 0.955 0.960 0.000 0.036 0.000 0.004
#> GSM78565 1 0.0963 0.956 0.964 0.000 0.036 0.000 0.000
#> GSM43000 3 0.1200 0.809 0.008 0.000 0.964 0.016 0.012
#> GSM43002 3 0.0290 0.809 0.008 0.000 0.992 0.000 0.000
#> GSM43004 1 0.6558 0.515 0.632 0.000 0.148 0.128 0.092
#> GSM43007 3 0.1483 0.801 0.008 0.000 0.952 0.012 0.028
#> GSM43010 3 0.5960 0.732 0.008 0.000 0.588 0.116 0.288
#> GSM78522 3 0.6369 0.719 0.016 0.000 0.548 0.132 0.304
#> GSM78525 3 0.0290 0.809 0.008 0.000 0.992 0.000 0.000
#> GSM78528 3 0.0579 0.807 0.008 0.000 0.984 0.008 0.000
#> GSM78531 1 0.0963 0.956 0.964 0.000 0.036 0.000 0.000
#> GSM78533 3 0.5960 0.732 0.008 0.000 0.588 0.116 0.288
#> GSM78536 1 0.0963 0.956 0.964 0.000 0.036 0.000 0.000
#> GSM78541 1 0.0963 0.956 0.964 0.000 0.036 0.000 0.000
#> GSM78547 1 0.1661 0.946 0.940 0.000 0.036 0.000 0.024
#> GSM78552 3 0.4159 0.639 0.172 0.000 0.780 0.012 0.036
#> GSM78556 1 0.1661 0.946 0.940 0.000 0.036 0.000 0.024
#> GSM78559 1 0.0963 0.956 0.964 0.000 0.036 0.000 0.000
#> GSM78564 1 0.1911 0.940 0.932 0.000 0.036 0.004 0.028
#> GSM42999 5 0.4256 0.835 0.000 0.436 0.000 0.000 0.564
#> GSM43001 5 0.6448 0.790 0.028 0.336 0.000 0.104 0.532
#> GSM43003 5 0.4256 0.835 0.000 0.436 0.000 0.000 0.564
#> GSM43006 5 0.6448 0.790 0.028 0.336 0.000 0.104 0.532
#> GSM43009 2 0.4118 -0.238 0.000 0.660 0.004 0.000 0.336
#> GSM43012 5 0.4438 0.843 0.000 0.384 0.004 0.004 0.608
#> GSM78524 2 0.1404 0.807 0.008 0.956 0.004 0.028 0.004
#> GSM78527 5 0.4219 0.844 0.000 0.416 0.000 0.000 0.584
#> GSM78530 2 0.0000 0.835 0.000 1.000 0.000 0.000 0.000
#> GSM78535 2 0.4501 0.447 0.256 0.712 0.004 0.024 0.004
#> GSM78538 2 0.0162 0.834 0.000 0.996 0.000 0.000 0.004
#> GSM78542 2 0.0162 0.834 0.000 0.996 0.000 0.000 0.004
#> GSM78544 2 0.0162 0.833 0.000 0.996 0.004 0.000 0.000
#> GSM78549 5 0.4256 0.835 0.000 0.436 0.000 0.000 0.564
#> GSM78553 2 0.0324 0.834 0.004 0.992 0.000 0.004 0.000
#> GSM78558 2 0.0324 0.834 0.004 0.992 0.000 0.004 0.000
#> GSM78561 5 0.6448 0.790 0.028 0.336 0.000 0.104 0.532
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM78539 4 0.2468 0.9555 0.096 0.000 0.008 0.880 0.016 0.000
#> GSM78545 4 0.3536 0.9005 0.036 0.000 0.104 0.828 0.028 0.004
#> GSM78550 4 0.3463 0.9054 0.040 0.000 0.104 0.828 0.028 0.000
#> GSM78554 4 0.3414 0.9431 0.084 0.000 0.052 0.836 0.028 0.000
#> GSM78562 4 0.2565 0.9515 0.104 0.000 0.008 0.872 0.016 0.000
#> GSM78540 4 0.2020 0.9551 0.096 0.000 0.000 0.896 0.008 0.000
#> GSM78546 4 0.2309 0.9546 0.084 0.000 0.028 0.888 0.000 0.000
#> GSM78551 4 0.2600 0.9529 0.084 0.000 0.036 0.876 0.004 0.000
#> GSM78555 4 0.2118 0.9504 0.104 0.000 0.000 0.888 0.008 0.000
#> GSM78563 4 0.2020 0.9551 0.096 0.000 0.000 0.896 0.008 0.000
#> GSM43005 3 0.3789 0.8851 0.000 0.000 0.660 0.008 0.000 0.332
#> GSM43008 3 0.4554 0.8454 0.008 0.000 0.684 0.008 0.040 0.260
#> GSM43011 6 0.1285 0.8431 0.000 0.000 0.052 0.000 0.004 0.944
#> GSM78523 6 0.1285 0.8431 0.000 0.000 0.052 0.000 0.004 0.944
#> GSM78526 6 0.0000 0.8823 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78529 3 0.4289 0.8843 0.000 0.000 0.640 0.008 0.020 0.332
#> GSM78532 1 0.0146 0.9470 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM78534 6 0.4764 0.6824 0.100 0.000 0.068 0.020 0.052 0.760
#> GSM78537 1 0.0000 0.9472 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78543 1 0.0260 0.9467 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM78548 3 0.4668 0.8549 0.000 0.000 0.652 0.008 0.056 0.284
#> GSM78557 1 0.1720 0.9280 0.928 0.000 0.032 0.000 0.040 0.000
#> GSM78560 1 0.0713 0.9424 0.972 0.000 0.000 0.000 0.028 0.000
#> GSM78565 1 0.0363 0.9464 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM43000 3 0.4123 0.7887 0.000 0.000 0.568 0.000 0.012 0.420
#> GSM43002 3 0.3833 0.8804 0.000 0.000 0.648 0.000 0.008 0.344
#> GSM43004 1 0.5746 0.5940 0.660 0.000 0.068 0.020 0.068 0.184
#> GSM43007 3 0.4354 0.8507 0.000 0.000 0.684 0.008 0.040 0.268
#> GSM43010 6 0.0000 0.8823 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78522 6 0.3039 0.7951 0.000 0.000 0.068 0.020 0.052 0.860
#> GSM78525 3 0.3927 0.8795 0.000 0.000 0.644 0.000 0.012 0.344
#> GSM78528 3 0.4289 0.8843 0.000 0.000 0.640 0.008 0.020 0.332
#> GSM78531 1 0.0000 0.9472 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78533 6 0.0000 0.8823 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78536 1 0.0363 0.9464 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM78541 1 0.0363 0.9464 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM78547 1 0.1720 0.9280 0.928 0.000 0.032 0.000 0.040 0.000
#> GSM78552 3 0.5312 0.7086 0.084 0.000 0.692 0.008 0.052 0.164
#> GSM78556 1 0.1720 0.9280 0.928 0.000 0.032 0.000 0.040 0.000
#> GSM78559 1 0.0260 0.9467 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM78564 1 0.2308 0.9043 0.892 0.000 0.068 0.000 0.040 0.000
#> GSM42999 2 0.2378 0.7635 0.000 0.848 0.000 0.000 0.152 0.000
#> GSM43001 2 0.2907 0.7242 0.000 0.828 0.152 0.020 0.000 0.000
#> GSM43003 2 0.2378 0.7635 0.000 0.848 0.000 0.000 0.152 0.000
#> GSM43006 2 0.2907 0.7242 0.000 0.828 0.152 0.020 0.000 0.000
#> GSM43009 2 0.3961 0.0412 0.000 0.556 0.000 0.004 0.440 0.000
#> GSM43012 2 0.1793 0.7726 0.000 0.928 0.012 0.012 0.048 0.000
#> GSM78524 5 0.4695 0.7912 0.000 0.144 0.068 0.052 0.736 0.000
#> GSM78527 2 0.1910 0.7765 0.000 0.892 0.000 0.000 0.108 0.000
#> GSM78530 5 0.2697 0.9035 0.000 0.188 0.000 0.000 0.812 0.000
#> GSM78535 5 0.5910 0.6084 0.152 0.068 0.068 0.044 0.668 0.000
#> GSM78538 5 0.2697 0.9042 0.000 0.188 0.000 0.000 0.812 0.000
#> GSM78542 5 0.2697 0.9042 0.000 0.188 0.000 0.000 0.812 0.000
#> GSM78544 5 0.2838 0.9016 0.000 0.188 0.000 0.004 0.808 0.000
#> GSM78549 2 0.2520 0.7636 0.000 0.844 0.000 0.004 0.152 0.000
#> GSM78553 5 0.2597 0.9043 0.000 0.176 0.000 0.000 0.824 0.000
#> GSM78558 5 0.2597 0.9043 0.000 0.176 0.000 0.000 0.824 0.000
#> GSM78561 2 0.2907 0.7242 0.000 0.828 0.152 0.020 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) agent(p) individual(p) k
#> CV:kmeans 58 2.54e-13 0.00184 0.9999 2
#> CV:kmeans 55 6.77e-14 0.00411 0.2105 3
#> CV:kmeans 32 4.18e-13 0.00408 0.3553 4
#> CV:kmeans 56 1.48e-20 0.03066 0.3427 5
#> CV:kmeans 57 8.31e-20 0.03753 0.0534 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "skmeans"]
# you can also extract it by
# res = res_list["CV:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 58 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.991 0.996 0.4253 0.578 0.578
#> 3 3 0.991 0.950 0.966 0.5678 0.747 0.563
#> 4 4 1.000 0.946 0.978 0.1315 0.895 0.689
#> 5 5 0.911 0.948 0.958 0.0587 0.946 0.783
#> 6 6 0.947 0.946 0.941 0.0472 0.956 0.783
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 4 5
There is also optional best \(k\) = 2 3 4 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM78539 1 0.00 0.994 1.00 0.00
#> GSM78545 1 0.00 0.994 1.00 0.00
#> GSM78550 1 0.00 0.994 1.00 0.00
#> GSM78554 1 0.00 0.994 1.00 0.00
#> GSM78562 1 0.00 0.994 1.00 0.00
#> GSM78540 1 0.00 0.994 1.00 0.00
#> GSM78546 1 0.00 0.994 1.00 0.00
#> GSM78551 1 0.00 0.994 1.00 0.00
#> GSM78555 1 0.00 0.994 1.00 0.00
#> GSM78563 1 0.00 0.994 1.00 0.00
#> GSM43005 1 0.00 0.994 1.00 0.00
#> GSM43008 1 0.00 0.994 1.00 0.00
#> GSM43011 1 0.00 0.994 1.00 0.00
#> GSM78523 1 0.00 0.994 1.00 0.00
#> GSM78526 1 0.00 0.994 1.00 0.00
#> GSM78529 1 0.76 0.718 0.78 0.22
#> GSM78532 1 0.00 0.994 1.00 0.00
#> GSM78534 1 0.00 0.994 1.00 0.00
#> GSM78537 1 0.00 0.994 1.00 0.00
#> GSM78543 1 0.00 0.994 1.00 0.00
#> GSM78548 1 0.00 0.994 1.00 0.00
#> GSM78557 1 0.00 0.994 1.00 0.00
#> GSM78560 1 0.00 0.994 1.00 0.00
#> GSM78565 1 0.00 0.994 1.00 0.00
#> GSM43000 1 0.00 0.994 1.00 0.00
#> GSM43002 1 0.00 0.994 1.00 0.00
#> GSM43004 1 0.00 0.994 1.00 0.00
#> GSM43007 1 0.00 0.994 1.00 0.00
#> GSM43010 1 0.00 0.994 1.00 0.00
#> GSM78522 1 0.00 0.994 1.00 0.00
#> GSM78525 1 0.00 0.994 1.00 0.00
#> GSM78528 1 0.00 0.994 1.00 0.00
#> GSM78531 1 0.00 0.994 1.00 0.00
#> GSM78533 1 0.00 0.994 1.00 0.00
#> GSM78536 1 0.00 0.994 1.00 0.00
#> GSM78541 1 0.00 0.994 1.00 0.00
#> GSM78547 1 0.00 0.994 1.00 0.00
#> GSM78552 1 0.00 0.994 1.00 0.00
#> GSM78556 1 0.00 0.994 1.00 0.00
#> GSM78559 1 0.00 0.994 1.00 0.00
#> GSM78564 1 0.00 0.994 1.00 0.00
#> GSM42999 2 0.00 1.000 0.00 1.00
#> GSM43001 2 0.00 1.000 0.00 1.00
#> GSM43003 2 0.00 1.000 0.00 1.00
#> GSM43006 2 0.00 1.000 0.00 1.00
#> GSM43009 2 0.00 1.000 0.00 1.00
#> GSM43012 2 0.00 1.000 0.00 1.00
#> GSM78524 2 0.00 1.000 0.00 1.00
#> GSM78527 2 0.00 1.000 0.00 1.00
#> GSM78530 2 0.00 1.000 0.00 1.00
#> GSM78535 2 0.00 1.000 0.00 1.00
#> GSM78538 2 0.00 1.000 0.00 1.00
#> GSM78542 2 0.00 1.000 0.00 1.00
#> GSM78544 2 0.00 1.000 0.00 1.00
#> GSM78549 2 0.00 1.000 0.00 1.00
#> GSM78553 2 0.00 1.000 0.00 1.00
#> GSM78558 2 0.00 1.000 0.00 1.00
#> GSM78561 2 0.00 1.000 0.00 1.00
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM78539 1 0.0000 0.934 1.000 0.000 0.000
#> GSM78545 3 0.6111 0.428 0.396 0.000 0.604
#> GSM78550 1 0.0000 0.934 1.000 0.000 0.000
#> GSM78554 1 0.0000 0.934 1.000 0.000 0.000
#> GSM78562 1 0.0000 0.934 1.000 0.000 0.000
#> GSM78540 1 0.0000 0.934 1.000 0.000 0.000
#> GSM78546 1 0.0000 0.934 1.000 0.000 0.000
#> GSM78551 1 0.0000 0.934 1.000 0.000 0.000
#> GSM78555 1 0.0000 0.934 1.000 0.000 0.000
#> GSM78563 1 0.0000 0.934 1.000 0.000 0.000
#> GSM43005 3 0.0000 0.972 0.000 0.000 1.000
#> GSM43008 3 0.0000 0.972 0.000 0.000 1.000
#> GSM43011 3 0.0000 0.972 0.000 0.000 1.000
#> GSM78523 3 0.0000 0.972 0.000 0.000 1.000
#> GSM78526 3 0.0000 0.972 0.000 0.000 1.000
#> GSM78529 3 0.0000 0.972 0.000 0.000 1.000
#> GSM78532 1 0.2878 0.953 0.904 0.000 0.096
#> GSM78534 3 0.0000 0.972 0.000 0.000 1.000
#> GSM78537 1 0.2878 0.953 0.904 0.000 0.096
#> GSM78543 1 0.2878 0.953 0.904 0.000 0.096
#> GSM78548 3 0.0000 0.972 0.000 0.000 1.000
#> GSM78557 1 0.2878 0.953 0.904 0.000 0.096
#> GSM78560 1 0.2878 0.953 0.904 0.000 0.096
#> GSM78565 1 0.2878 0.953 0.904 0.000 0.096
#> GSM43000 3 0.0000 0.972 0.000 0.000 1.000
#> GSM43002 3 0.0000 0.972 0.000 0.000 1.000
#> GSM43004 3 0.0747 0.959 0.016 0.000 0.984
#> GSM43007 3 0.0000 0.972 0.000 0.000 1.000
#> GSM43010 3 0.0000 0.972 0.000 0.000 1.000
#> GSM78522 3 0.0000 0.972 0.000 0.000 1.000
#> GSM78525 3 0.0000 0.972 0.000 0.000 1.000
#> GSM78528 3 0.0000 0.972 0.000 0.000 1.000
#> GSM78531 1 0.2878 0.953 0.904 0.000 0.096
#> GSM78533 3 0.0000 0.972 0.000 0.000 1.000
#> GSM78536 1 0.2878 0.953 0.904 0.000 0.096
#> GSM78541 1 0.2878 0.953 0.904 0.000 0.096
#> GSM78547 1 0.2878 0.953 0.904 0.000 0.096
#> GSM78552 3 0.2796 0.878 0.092 0.000 0.908
#> GSM78556 1 0.2878 0.953 0.904 0.000 0.096
#> GSM78559 1 0.2878 0.953 0.904 0.000 0.096
#> GSM78564 1 0.2878 0.953 0.904 0.000 0.096
#> GSM42999 2 0.0000 0.986 0.000 1.000 0.000
#> GSM43001 2 0.0000 0.986 0.000 1.000 0.000
#> GSM43003 2 0.0000 0.986 0.000 1.000 0.000
#> GSM43006 2 0.0000 0.986 0.000 1.000 0.000
#> GSM43009 2 0.0000 0.986 0.000 1.000 0.000
#> GSM43012 2 0.0000 0.986 0.000 1.000 0.000
#> GSM78524 2 0.0000 0.986 0.000 1.000 0.000
#> GSM78527 2 0.0000 0.986 0.000 1.000 0.000
#> GSM78530 2 0.0000 0.986 0.000 1.000 0.000
#> GSM78535 2 0.4702 0.724 0.212 0.788 0.000
#> GSM78538 2 0.0000 0.986 0.000 1.000 0.000
#> GSM78542 2 0.0000 0.986 0.000 1.000 0.000
#> GSM78544 2 0.0000 0.986 0.000 1.000 0.000
#> GSM78549 2 0.0000 0.986 0.000 1.000 0.000
#> GSM78553 2 0.0000 0.986 0.000 1.000 0.000
#> GSM78558 2 0.0000 0.986 0.000 1.000 0.000
#> GSM78561 2 0.0000 0.986 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM78539 4 0.0336 0.9979 0.008 0.000 0.000 0.992
#> GSM78545 4 0.0000 0.9918 0.000 0.000 0.000 1.000
#> GSM78550 4 0.0000 0.9918 0.000 0.000 0.000 1.000
#> GSM78554 4 0.0336 0.9979 0.008 0.000 0.000 0.992
#> GSM78562 4 0.0336 0.9979 0.008 0.000 0.000 0.992
#> GSM78540 4 0.0336 0.9979 0.008 0.000 0.000 0.992
#> GSM78546 4 0.0336 0.9979 0.008 0.000 0.000 0.992
#> GSM78551 4 0.0336 0.9979 0.008 0.000 0.000 0.992
#> GSM78555 4 0.0336 0.9979 0.008 0.000 0.000 0.992
#> GSM78563 4 0.0336 0.9979 0.008 0.000 0.000 0.992
#> GSM43005 3 0.0336 0.9339 0.000 0.000 0.992 0.008
#> GSM43008 3 0.1545 0.9035 0.040 0.000 0.952 0.008
#> GSM43011 3 0.0000 0.9339 0.000 0.000 1.000 0.000
#> GSM78523 3 0.0000 0.9339 0.000 0.000 1.000 0.000
#> GSM78526 3 0.0000 0.9339 0.000 0.000 1.000 0.000
#> GSM78529 3 0.0336 0.9339 0.000 0.000 0.992 0.008
#> GSM78532 1 0.0000 0.9993 1.000 0.000 0.000 0.000
#> GSM78534 3 0.5000 0.0245 0.496 0.000 0.504 0.000
#> GSM78537 1 0.0000 0.9993 1.000 0.000 0.000 0.000
#> GSM78543 1 0.0000 0.9993 1.000 0.000 0.000 0.000
#> GSM78548 3 0.0336 0.9339 0.000 0.000 0.992 0.008
#> GSM78557 1 0.0000 0.9993 1.000 0.000 0.000 0.000
#> GSM78560 1 0.0000 0.9993 1.000 0.000 0.000 0.000
#> GSM78565 1 0.0000 0.9993 1.000 0.000 0.000 0.000
#> GSM43000 3 0.0000 0.9339 0.000 0.000 1.000 0.000
#> GSM43002 3 0.0336 0.9339 0.000 0.000 0.992 0.008
#> GSM43004 1 0.0336 0.9911 0.992 0.000 0.008 0.000
#> GSM43007 3 0.0336 0.9339 0.000 0.000 0.992 0.008
#> GSM43010 3 0.0000 0.9339 0.000 0.000 1.000 0.000
#> GSM78522 3 0.0000 0.9339 0.000 0.000 1.000 0.000
#> GSM78525 3 0.0336 0.9339 0.000 0.000 0.992 0.008
#> GSM78528 3 0.0336 0.9339 0.000 0.000 0.992 0.008
#> GSM78531 1 0.0000 0.9993 1.000 0.000 0.000 0.000
#> GSM78533 3 0.0000 0.9339 0.000 0.000 1.000 0.000
#> GSM78536 1 0.0000 0.9993 1.000 0.000 0.000 0.000
#> GSM78541 1 0.0000 0.9993 1.000 0.000 0.000 0.000
#> GSM78547 1 0.0000 0.9993 1.000 0.000 0.000 0.000
#> GSM78552 3 0.5085 0.4101 0.376 0.000 0.616 0.008
#> GSM78556 1 0.0000 0.9993 1.000 0.000 0.000 0.000
#> GSM78559 1 0.0000 0.9993 1.000 0.000 0.000 0.000
#> GSM78564 1 0.0000 0.9993 1.000 0.000 0.000 0.000
#> GSM42999 2 0.0000 0.9855 0.000 1.000 0.000 0.000
#> GSM43001 2 0.0000 0.9855 0.000 1.000 0.000 0.000
#> GSM43003 2 0.0000 0.9855 0.000 1.000 0.000 0.000
#> GSM43006 2 0.0000 0.9855 0.000 1.000 0.000 0.000
#> GSM43009 2 0.0000 0.9855 0.000 1.000 0.000 0.000
#> GSM43012 2 0.0000 0.9855 0.000 1.000 0.000 0.000
#> GSM78524 2 0.0000 0.9855 0.000 1.000 0.000 0.000
#> GSM78527 2 0.0000 0.9855 0.000 1.000 0.000 0.000
#> GSM78530 2 0.0000 0.9855 0.000 1.000 0.000 0.000
#> GSM78535 2 0.3726 0.7281 0.212 0.788 0.000 0.000
#> GSM78538 2 0.0000 0.9855 0.000 1.000 0.000 0.000
#> GSM78542 2 0.0000 0.9855 0.000 1.000 0.000 0.000
#> GSM78544 2 0.0000 0.9855 0.000 1.000 0.000 0.000
#> GSM78549 2 0.0000 0.9855 0.000 1.000 0.000 0.000
#> GSM78553 2 0.0000 0.9855 0.000 1.000 0.000 0.000
#> GSM78558 2 0.0000 0.9855 0.000 1.000 0.000 0.000
#> GSM78561 2 0.0000 0.9855 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM78539 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78545 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78550 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78554 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78562 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78540 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78546 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78551 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78555 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78563 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM43005 3 0.0000 0.962 0.000 0.000 1.000 0 0.000
#> GSM43008 3 0.0000 0.962 0.000 0.000 1.000 0 0.000
#> GSM43011 5 0.2179 0.925 0.000 0.000 0.112 0 0.888
#> GSM78523 5 0.2127 0.928 0.000 0.000 0.108 0 0.892
#> GSM78526 5 0.2074 0.930 0.000 0.000 0.104 0 0.896
#> GSM78529 3 0.0000 0.962 0.000 0.000 1.000 0 0.000
#> GSM78532 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78534 5 0.2520 0.889 0.048 0.000 0.056 0 0.896
#> GSM78537 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78543 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78548 3 0.0000 0.962 0.000 0.000 1.000 0 0.000
#> GSM78557 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78560 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78565 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM43000 3 0.3003 0.745 0.000 0.000 0.812 0 0.188
#> GSM43002 3 0.0000 0.962 0.000 0.000 1.000 0 0.000
#> GSM43004 5 0.3816 0.562 0.304 0.000 0.000 0 0.696
#> GSM43007 3 0.0000 0.962 0.000 0.000 1.000 0 0.000
#> GSM43010 5 0.2074 0.930 0.000 0.000 0.104 0 0.896
#> GSM78522 5 0.2074 0.930 0.000 0.000 0.104 0 0.896
#> GSM78525 3 0.0000 0.962 0.000 0.000 1.000 0 0.000
#> GSM78528 3 0.0000 0.962 0.000 0.000 1.000 0 0.000
#> GSM78531 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78533 5 0.2074 0.930 0.000 0.000 0.104 0 0.896
#> GSM78536 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78541 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78547 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78552 3 0.2020 0.853 0.100 0.000 0.900 0 0.000
#> GSM78556 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78559 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78564 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM42999 2 0.0000 0.941 0.000 1.000 0.000 0 0.000
#> GSM43001 2 0.0162 0.941 0.000 0.996 0.000 0 0.004
#> GSM43003 2 0.0000 0.941 0.000 1.000 0.000 0 0.000
#> GSM43006 2 0.0162 0.941 0.000 0.996 0.000 0 0.004
#> GSM43009 2 0.0000 0.941 0.000 1.000 0.000 0 0.000
#> GSM43012 2 0.0162 0.941 0.000 0.996 0.000 0 0.004
#> GSM78524 2 0.2020 0.932 0.000 0.900 0.000 0 0.100
#> GSM78527 2 0.0000 0.941 0.000 1.000 0.000 0 0.000
#> GSM78530 2 0.2020 0.932 0.000 0.900 0.000 0 0.100
#> GSM78535 2 0.5312 0.642 0.248 0.652 0.000 0 0.100
#> GSM78538 2 0.2020 0.932 0.000 0.900 0.000 0 0.100
#> GSM78542 2 0.2020 0.932 0.000 0.900 0.000 0 0.100
#> GSM78544 2 0.2020 0.932 0.000 0.900 0.000 0 0.100
#> GSM78549 2 0.0000 0.941 0.000 1.000 0.000 0 0.000
#> GSM78553 2 0.2020 0.932 0.000 0.900 0.000 0 0.100
#> GSM78558 2 0.2020 0.932 0.000 0.900 0.000 0 0.100
#> GSM78561 2 0.0162 0.941 0.000 0.996 0.000 0 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM78539 4 0.0000 0.990 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78545 4 0.0937 0.977 0.000 0.000 0.000 0.960 0.040 0.000
#> GSM78550 4 0.0937 0.977 0.000 0.000 0.000 0.960 0.040 0.000
#> GSM78554 4 0.0713 0.982 0.000 0.000 0.000 0.972 0.028 0.000
#> GSM78562 4 0.0000 0.990 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78540 4 0.0000 0.990 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78546 4 0.0260 0.989 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM78551 4 0.0260 0.989 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM78555 4 0.0000 0.990 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78563 4 0.0000 0.990 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM43005 3 0.0291 0.929 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM43008 3 0.0858 0.927 0.000 0.000 0.968 0.000 0.028 0.004
#> GSM43011 6 0.1265 0.910 0.000 0.000 0.044 0.000 0.008 0.948
#> GSM78523 6 0.1196 0.913 0.000 0.000 0.040 0.000 0.008 0.952
#> GSM78526 6 0.0000 0.934 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78529 3 0.0777 0.929 0.000 0.000 0.972 0.000 0.024 0.004
#> GSM78532 1 0.0260 0.980 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM78534 6 0.0858 0.927 0.004 0.000 0.000 0.000 0.028 0.968
#> GSM78537 1 0.0146 0.980 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM78543 1 0.0260 0.980 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM78548 3 0.1644 0.902 0.000 0.000 0.920 0.000 0.076 0.004
#> GSM78557 1 0.1349 0.961 0.940 0.000 0.004 0.000 0.056 0.000
#> GSM78560 1 0.0000 0.980 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78565 1 0.0363 0.979 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM43000 3 0.3934 0.650 0.000 0.000 0.708 0.000 0.032 0.260
#> GSM43002 3 0.0622 0.929 0.000 0.000 0.980 0.000 0.012 0.008
#> GSM43004 6 0.3909 0.651 0.244 0.000 0.000 0.000 0.036 0.720
#> GSM43007 3 0.0858 0.927 0.000 0.000 0.968 0.000 0.028 0.004
#> GSM43010 6 0.0000 0.934 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78522 6 0.0713 0.929 0.000 0.000 0.000 0.000 0.028 0.972
#> GSM78525 3 0.1049 0.927 0.000 0.000 0.960 0.000 0.032 0.008
#> GSM78528 3 0.0777 0.929 0.000 0.000 0.972 0.000 0.024 0.004
#> GSM78531 1 0.0260 0.980 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM78533 6 0.0000 0.934 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78536 1 0.0260 0.980 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM78541 1 0.0363 0.980 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM78547 1 0.1285 0.963 0.944 0.000 0.004 0.000 0.052 0.000
#> GSM78552 3 0.3361 0.804 0.108 0.000 0.816 0.000 0.076 0.000
#> GSM78556 1 0.1349 0.961 0.940 0.000 0.004 0.000 0.056 0.000
#> GSM78559 1 0.0260 0.980 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM78564 1 0.1285 0.965 0.944 0.000 0.004 0.000 0.052 0.000
#> GSM42999 2 0.0865 0.967 0.000 0.964 0.000 0.000 0.036 0.000
#> GSM43001 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43003 2 0.0865 0.967 0.000 0.964 0.000 0.000 0.036 0.000
#> GSM43006 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43009 2 0.1075 0.957 0.000 0.952 0.000 0.000 0.048 0.000
#> GSM43012 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78524 5 0.2664 0.960 0.000 0.184 0.000 0.000 0.816 0.000
#> GSM78527 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78530 5 0.3023 0.947 0.000 0.232 0.000 0.000 0.768 0.000
#> GSM78535 5 0.3293 0.905 0.048 0.140 0.000 0.000 0.812 0.000
#> GSM78538 5 0.2793 0.969 0.000 0.200 0.000 0.000 0.800 0.000
#> GSM78542 5 0.2793 0.969 0.000 0.200 0.000 0.000 0.800 0.000
#> GSM78544 5 0.3101 0.935 0.000 0.244 0.000 0.000 0.756 0.000
#> GSM78549 2 0.0937 0.965 0.000 0.960 0.000 0.000 0.040 0.000
#> GSM78553 5 0.2793 0.969 0.000 0.200 0.000 0.000 0.800 0.000
#> GSM78558 5 0.2762 0.968 0.000 0.196 0.000 0.000 0.804 0.000
#> GSM78561 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) agent(p) individual(p) k
#> CV:skmeans 58 2.54e-13 0.00184 1.000 2
#> CV:skmeans 57 1.75e-14 0.00372 0.307 3
#> CV:skmeans 56 7.77e-22 0.00848 0.469 4
#> CV:skmeans 58 2.22e-21 0.01729 0.115 5
#> CV:skmeans 58 3.27e-20 0.03468 0.110 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "pam"]
# you can also extract it by
# res = res_list["CV:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 58 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 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)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4222 0.578 0.578
#> 3 3 0.734 0.933 0.915 0.4730 0.789 0.636
#> 4 4 0.970 0.947 0.977 0.1978 0.891 0.704
#> 5 5 0.952 0.927 0.969 0.0502 0.964 0.860
#> 6 6 0.890 0.815 0.895 0.0440 0.909 0.623
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2 4
There is also optional best \(k\) = 2 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM78539 1 0 1 1 0
#> GSM78545 1 0 1 1 0
#> GSM78550 1 0 1 1 0
#> GSM78554 1 0 1 1 0
#> GSM78562 1 0 1 1 0
#> GSM78540 1 0 1 1 0
#> GSM78546 1 0 1 1 0
#> GSM78551 1 0 1 1 0
#> GSM78555 1 0 1 1 0
#> GSM78563 1 0 1 1 0
#> GSM43005 1 0 1 1 0
#> GSM43008 1 0 1 1 0
#> GSM43011 1 0 1 1 0
#> GSM78523 1 0 1 1 0
#> GSM78526 1 0 1 1 0
#> GSM78529 1 0 1 1 0
#> GSM78532 1 0 1 1 0
#> GSM78534 1 0 1 1 0
#> GSM78537 1 0 1 1 0
#> GSM78543 1 0 1 1 0
#> GSM78548 1 0 1 1 0
#> GSM78557 1 0 1 1 0
#> GSM78560 1 0 1 1 0
#> GSM78565 1 0 1 1 0
#> GSM43000 1 0 1 1 0
#> GSM43002 1 0 1 1 0
#> GSM43004 1 0 1 1 0
#> GSM43007 1 0 1 1 0
#> GSM43010 1 0 1 1 0
#> GSM78522 1 0 1 1 0
#> GSM78525 1 0 1 1 0
#> GSM78528 1 0 1 1 0
#> GSM78531 1 0 1 1 0
#> GSM78533 1 0 1 1 0
#> GSM78536 1 0 1 1 0
#> GSM78541 1 0 1 1 0
#> GSM78547 1 0 1 1 0
#> GSM78552 1 0 1 1 0
#> GSM78556 1 0 1 1 0
#> GSM78559 1 0 1 1 0
#> GSM78564 1 0 1 1 0
#> GSM42999 2 0 1 0 1
#> GSM43001 2 0 1 0 1
#> GSM43003 2 0 1 0 1
#> GSM43006 2 0 1 0 1
#> GSM43009 2 0 1 0 1
#> GSM43012 2 0 1 0 1
#> GSM78524 2 0 1 0 1
#> GSM78527 2 0 1 0 1
#> GSM78530 2 0 1 0 1
#> GSM78535 2 0 1 0 1
#> GSM78538 2 0 1 0 1
#> GSM78542 2 0 1 0 1
#> GSM78544 2 0 1 0 1
#> GSM78549 2 0 1 0 1
#> GSM78553 2 0 1 0 1
#> GSM78558 2 0 1 0 1
#> GSM78561 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM78539 1 0.5058 0.778 0.756 0 0.244
#> GSM78545 1 0.5058 0.778 0.756 0 0.244
#> GSM78550 1 0.5058 0.778 0.756 0 0.244
#> GSM78554 1 0.1031 0.893 0.976 0 0.024
#> GSM78562 1 0.2959 0.854 0.900 0 0.100
#> GSM78540 1 0.5058 0.778 0.756 0 0.244
#> GSM78546 1 0.5058 0.778 0.756 0 0.244
#> GSM78551 1 0.5058 0.778 0.756 0 0.244
#> GSM78555 1 0.5058 0.778 0.756 0 0.244
#> GSM78563 1 0.5058 0.778 0.756 0 0.244
#> GSM43005 3 0.5058 1.000 0.244 0 0.756
#> GSM43008 1 0.0000 0.903 1.000 0 0.000
#> GSM43011 3 0.5058 1.000 0.244 0 0.756
#> GSM78523 3 0.5058 1.000 0.244 0 0.756
#> GSM78526 3 0.5058 1.000 0.244 0 0.756
#> GSM78529 3 0.5058 1.000 0.244 0 0.756
#> GSM78532 1 0.0000 0.903 1.000 0 0.000
#> GSM78534 1 0.0237 0.899 0.996 0 0.004
#> GSM78537 1 0.0000 0.903 1.000 0 0.000
#> GSM78543 1 0.0000 0.903 1.000 0 0.000
#> GSM78548 1 0.0000 0.903 1.000 0 0.000
#> GSM78557 1 0.0000 0.903 1.000 0 0.000
#> GSM78560 1 0.0000 0.903 1.000 0 0.000
#> GSM78565 1 0.0000 0.903 1.000 0 0.000
#> GSM43000 3 0.5058 1.000 0.244 0 0.756
#> GSM43002 3 0.5058 1.000 0.244 0 0.756
#> GSM43004 1 0.0000 0.903 1.000 0 0.000
#> GSM43007 1 0.0000 0.903 1.000 0 0.000
#> GSM43010 3 0.5058 1.000 0.244 0 0.756
#> GSM78522 3 0.5058 1.000 0.244 0 0.756
#> GSM78525 3 0.5058 1.000 0.244 0 0.756
#> GSM78528 3 0.5098 0.995 0.248 0 0.752
#> GSM78531 1 0.0000 0.903 1.000 0 0.000
#> GSM78533 3 0.5058 1.000 0.244 0 0.756
#> GSM78536 1 0.0000 0.903 1.000 0 0.000
#> GSM78541 1 0.0000 0.903 1.000 0 0.000
#> GSM78547 1 0.0000 0.903 1.000 0 0.000
#> GSM78552 1 0.0000 0.903 1.000 0 0.000
#> GSM78556 1 0.0000 0.903 1.000 0 0.000
#> GSM78559 1 0.0000 0.903 1.000 0 0.000
#> GSM78564 1 0.0000 0.903 1.000 0 0.000
#> GSM42999 2 0.0000 1.000 0.000 1 0.000
#> GSM43001 2 0.0000 1.000 0.000 1 0.000
#> GSM43003 2 0.0000 1.000 0.000 1 0.000
#> GSM43006 2 0.0000 1.000 0.000 1 0.000
#> GSM43009 2 0.0000 1.000 0.000 1 0.000
#> GSM43012 2 0.0000 1.000 0.000 1 0.000
#> GSM78524 2 0.0000 1.000 0.000 1 0.000
#> GSM78527 2 0.0000 1.000 0.000 1 0.000
#> GSM78530 2 0.0000 1.000 0.000 1 0.000
#> GSM78535 2 0.0000 1.000 0.000 1 0.000
#> GSM78538 2 0.0000 1.000 0.000 1 0.000
#> GSM78542 2 0.0000 1.000 0.000 1 0.000
#> GSM78544 2 0.0000 1.000 0.000 1 0.000
#> GSM78549 2 0.0000 1.000 0.000 1 0.000
#> GSM78553 2 0.0000 1.000 0.000 1 0.000
#> GSM78558 2 0.0000 1.000 0.000 1 0.000
#> GSM78561 2 0.0000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM78539 4 0.0000 0.987 0.000 0.00 0.000 1.000
#> GSM78545 4 0.0000 0.987 0.000 0.00 0.000 1.000
#> GSM78550 4 0.0000 0.987 0.000 0.00 0.000 1.000
#> GSM78554 4 0.2149 0.895 0.088 0.00 0.000 0.912
#> GSM78562 1 0.4948 0.225 0.560 0.00 0.000 0.440
#> GSM78540 4 0.0000 0.987 0.000 0.00 0.000 1.000
#> GSM78546 4 0.0000 0.987 0.000 0.00 0.000 1.000
#> GSM78551 4 0.0000 0.987 0.000 0.00 0.000 1.000
#> GSM78555 4 0.0000 0.987 0.000 0.00 0.000 1.000
#> GSM78563 4 0.0000 0.987 0.000 0.00 0.000 1.000
#> GSM43005 3 0.0188 0.988 0.004 0.00 0.996 0.000
#> GSM43008 1 0.0000 0.944 1.000 0.00 0.000 0.000
#> GSM43011 3 0.0000 0.988 0.000 0.00 1.000 0.000
#> GSM78523 3 0.0000 0.988 0.000 0.00 1.000 0.000
#> GSM78526 3 0.0000 0.988 0.000 0.00 1.000 0.000
#> GSM78529 3 0.0336 0.986 0.008 0.00 0.992 0.000
#> GSM78532 1 0.0000 0.944 1.000 0.00 0.000 0.000
#> GSM78534 1 0.3219 0.798 0.836 0.00 0.164 0.000
#> GSM78537 1 0.0000 0.944 1.000 0.00 0.000 0.000
#> GSM78543 1 0.0000 0.944 1.000 0.00 0.000 0.000
#> GSM78548 1 0.4406 0.591 0.700 0.00 0.300 0.000
#> GSM78557 1 0.0000 0.944 1.000 0.00 0.000 0.000
#> GSM78560 1 0.0000 0.944 1.000 0.00 0.000 0.000
#> GSM78565 1 0.0000 0.944 1.000 0.00 0.000 0.000
#> GSM43000 3 0.0000 0.988 0.000 0.00 1.000 0.000
#> GSM43002 3 0.0592 0.980 0.016 0.00 0.984 0.000
#> GSM43004 1 0.0000 0.944 1.000 0.00 0.000 0.000
#> GSM43007 1 0.2469 0.857 0.892 0.00 0.108 0.000
#> GSM43010 3 0.0000 0.988 0.000 0.00 1.000 0.000
#> GSM78522 3 0.1211 0.954 0.040 0.00 0.960 0.000
#> GSM78525 3 0.0000 0.988 0.000 0.00 1.000 0.000
#> GSM78528 3 0.1022 0.965 0.032 0.00 0.968 0.000
#> GSM78531 1 0.0000 0.944 1.000 0.00 0.000 0.000
#> GSM78533 3 0.0188 0.987 0.004 0.00 0.996 0.000
#> GSM78536 1 0.0000 0.944 1.000 0.00 0.000 0.000
#> GSM78541 1 0.0000 0.944 1.000 0.00 0.000 0.000
#> GSM78547 1 0.0000 0.944 1.000 0.00 0.000 0.000
#> GSM78552 1 0.0000 0.944 1.000 0.00 0.000 0.000
#> GSM78556 1 0.0000 0.944 1.000 0.00 0.000 0.000
#> GSM78559 1 0.0000 0.944 1.000 0.00 0.000 0.000
#> GSM78564 1 0.0000 0.944 1.000 0.00 0.000 0.000
#> GSM42999 2 0.0000 0.993 0.000 1.00 0.000 0.000
#> GSM43001 2 0.0000 0.993 0.000 1.00 0.000 0.000
#> GSM43003 2 0.0000 0.993 0.000 1.00 0.000 0.000
#> GSM43006 2 0.0000 0.993 0.000 1.00 0.000 0.000
#> GSM43009 2 0.0000 0.993 0.000 1.00 0.000 0.000
#> GSM43012 2 0.0000 0.993 0.000 1.00 0.000 0.000
#> GSM78524 2 0.0000 0.993 0.000 1.00 0.000 0.000
#> GSM78527 2 0.0000 0.993 0.000 1.00 0.000 0.000
#> GSM78530 2 0.0000 0.993 0.000 1.00 0.000 0.000
#> GSM78535 2 0.3247 0.873 0.060 0.88 0.000 0.060
#> GSM78538 2 0.0000 0.993 0.000 1.00 0.000 0.000
#> GSM78542 2 0.0000 0.993 0.000 1.00 0.000 0.000
#> GSM78544 2 0.0000 0.993 0.000 1.00 0.000 0.000
#> GSM78549 2 0.0000 0.993 0.000 1.00 0.000 0.000
#> GSM78553 2 0.0000 0.993 0.000 1.00 0.000 0.000
#> GSM78558 2 0.0000 0.993 0.000 1.00 0.000 0.000
#> GSM78561 2 0.0000 0.993 0.000 1.00 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM78539 4 0.0000 0.987 0.000 0.000 0.000 1.000 0.000
#> GSM78545 4 0.0000 0.987 0.000 0.000 0.000 1.000 0.000
#> GSM78550 4 0.0000 0.987 0.000 0.000 0.000 1.000 0.000
#> GSM78554 4 0.1671 0.890 0.076 0.000 0.000 0.924 0.000
#> GSM78562 1 0.4219 0.300 0.584 0.000 0.000 0.416 0.000
#> GSM78540 4 0.0000 0.987 0.000 0.000 0.000 1.000 0.000
#> GSM78546 4 0.0000 0.987 0.000 0.000 0.000 1.000 0.000
#> GSM78551 4 0.0000 0.987 0.000 0.000 0.000 1.000 0.000
#> GSM78555 4 0.0000 0.987 0.000 0.000 0.000 1.000 0.000
#> GSM78563 4 0.0000 0.987 0.000 0.000 0.000 1.000 0.000
#> GSM43005 3 0.0162 0.988 0.004 0.000 0.996 0.000 0.000
#> GSM43008 1 0.0000 0.942 1.000 0.000 0.000 0.000 0.000
#> GSM43011 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000
#> GSM78523 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000
#> GSM78526 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000
#> GSM78529 3 0.0290 0.985 0.008 0.000 0.992 0.000 0.000
#> GSM78532 1 0.0000 0.942 1.000 0.000 0.000 0.000 0.000
#> GSM78534 1 0.2732 0.795 0.840 0.000 0.160 0.000 0.000
#> GSM78537 1 0.0000 0.942 1.000 0.000 0.000 0.000 0.000
#> GSM78543 1 0.0000 0.942 1.000 0.000 0.000 0.000 0.000
#> GSM78548 1 0.3837 0.578 0.692 0.000 0.308 0.000 0.000
#> GSM78557 1 0.0000 0.942 1.000 0.000 0.000 0.000 0.000
#> GSM78560 1 0.0000 0.942 1.000 0.000 0.000 0.000 0.000
#> GSM78565 1 0.0000 0.942 1.000 0.000 0.000 0.000 0.000
#> GSM43000 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000
#> GSM43002 3 0.0404 0.982 0.012 0.000 0.988 0.000 0.000
#> GSM43004 1 0.0000 0.942 1.000 0.000 0.000 0.000 0.000
#> GSM43007 1 0.2179 0.845 0.888 0.000 0.112 0.000 0.000
#> GSM43010 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000
#> GSM78522 3 0.0963 0.954 0.036 0.000 0.964 0.000 0.000
#> GSM78525 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000
#> GSM78528 3 0.0794 0.966 0.028 0.000 0.972 0.000 0.000
#> GSM78531 1 0.0000 0.942 1.000 0.000 0.000 0.000 0.000
#> GSM78533 3 0.0162 0.987 0.004 0.000 0.996 0.000 0.000
#> GSM78536 1 0.0000 0.942 1.000 0.000 0.000 0.000 0.000
#> GSM78541 1 0.0000 0.942 1.000 0.000 0.000 0.000 0.000
#> GSM78547 1 0.0000 0.942 1.000 0.000 0.000 0.000 0.000
#> GSM78552 1 0.0000 0.942 1.000 0.000 0.000 0.000 0.000
#> GSM78556 1 0.0000 0.942 1.000 0.000 0.000 0.000 0.000
#> GSM78559 1 0.0000 0.942 1.000 0.000 0.000 0.000 0.000
#> GSM78564 1 0.0000 0.942 1.000 0.000 0.000 0.000 0.000
#> GSM42999 2 0.4114 0.429 0.000 0.624 0.000 0.000 0.376
#> GSM43001 5 0.0000 0.992 0.000 0.000 0.000 0.000 1.000
#> GSM43003 2 0.2074 0.867 0.000 0.896 0.000 0.000 0.104
#> GSM43006 5 0.0000 0.992 0.000 0.000 0.000 0.000 1.000
#> GSM43009 2 0.0963 0.924 0.000 0.964 0.000 0.000 0.036
#> GSM43012 5 0.0000 0.992 0.000 0.000 0.000 0.000 1.000
#> GSM78524 2 0.0000 0.944 0.000 1.000 0.000 0.000 0.000
#> GSM78527 5 0.0794 0.968 0.000 0.028 0.000 0.000 0.972
#> GSM78530 2 0.0000 0.944 0.000 1.000 0.000 0.000 0.000
#> GSM78535 2 0.1697 0.879 0.060 0.932 0.000 0.008 0.000
#> GSM78538 2 0.0000 0.944 0.000 1.000 0.000 0.000 0.000
#> GSM78542 2 0.0000 0.944 0.000 1.000 0.000 0.000 0.000
#> GSM78544 2 0.0000 0.944 0.000 1.000 0.000 0.000 0.000
#> GSM78549 2 0.0162 0.942 0.000 0.996 0.000 0.000 0.004
#> GSM78553 2 0.0000 0.944 0.000 1.000 0.000 0.000 0.000
#> GSM78558 2 0.0000 0.944 0.000 1.000 0.000 0.000 0.000
#> GSM78561 5 0.0000 0.992 0.000 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM78539 4 0.0000 0.920 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78545 4 0.0363 0.915 0.000 0.000 0.012 0.988 0.000 0.000
#> GSM78550 4 0.0363 0.915 0.000 0.000 0.012 0.988 0.000 0.000
#> GSM78554 4 0.1218 0.889 0.028 0.000 0.012 0.956 0.000 0.004
#> GSM78562 4 0.4296 0.145 0.440 0.000 0.008 0.544 0.000 0.008
#> GSM78540 4 0.0000 0.920 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78546 4 0.0000 0.920 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78551 4 0.0000 0.920 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78555 4 0.0000 0.920 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78563 4 0.0000 0.920 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM43005 3 0.0260 0.621 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM43008 3 0.4091 0.213 0.472 0.000 0.520 0.000 0.000 0.008
#> GSM43011 6 0.3659 0.745 0.000 0.000 0.364 0.000 0.000 0.636
#> GSM78523 6 0.3817 0.660 0.000 0.000 0.432 0.000 0.000 0.568
#> GSM78526 6 0.2854 0.851 0.000 0.000 0.208 0.000 0.000 0.792
#> GSM78529 3 0.0260 0.621 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM78532 1 0.0146 0.984 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM78534 6 0.2793 0.564 0.200 0.000 0.000 0.000 0.000 0.800
#> GSM78537 1 0.0146 0.984 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM78543 1 0.0146 0.984 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM78548 3 0.4229 0.311 0.436 0.000 0.548 0.000 0.000 0.016
#> GSM78557 1 0.0405 0.981 0.988 0.000 0.008 0.000 0.000 0.004
#> GSM78560 1 0.0146 0.984 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM78565 1 0.0260 0.984 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM43000 3 0.2003 0.505 0.000 0.000 0.884 0.000 0.000 0.116
#> GSM43002 3 0.0260 0.621 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM43004 1 0.0260 0.984 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM43007 3 0.4039 0.334 0.424 0.000 0.568 0.000 0.000 0.008
#> GSM43010 6 0.2854 0.851 0.000 0.000 0.208 0.000 0.000 0.792
#> GSM78522 6 0.3078 0.844 0.012 0.000 0.192 0.000 0.000 0.796
#> GSM78525 3 0.1957 0.512 0.000 0.000 0.888 0.000 0.000 0.112
#> GSM78528 3 0.0000 0.621 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM78531 1 0.0000 0.985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78533 6 0.2964 0.851 0.004 0.000 0.204 0.000 0.000 0.792
#> GSM78536 1 0.0146 0.984 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM78541 1 0.0405 0.984 0.988 0.000 0.008 0.000 0.000 0.004
#> GSM78547 1 0.0806 0.970 0.972 0.000 0.020 0.000 0.000 0.008
#> GSM78552 1 0.1812 0.896 0.912 0.000 0.080 0.000 0.000 0.008
#> GSM78556 1 0.0520 0.980 0.984 0.000 0.008 0.000 0.000 0.008
#> GSM78559 1 0.0146 0.984 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM78564 1 0.0520 0.980 0.984 0.000 0.008 0.000 0.000 0.008
#> GSM42999 2 0.4653 0.650 0.000 0.684 0.000 0.000 0.120 0.196
#> GSM43001 5 0.0000 0.912 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM43003 2 0.3269 0.779 0.000 0.792 0.000 0.000 0.024 0.184
#> GSM43006 5 0.0000 0.912 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM43009 2 0.2762 0.792 0.000 0.804 0.000 0.000 0.000 0.196
#> GSM43012 5 0.2762 0.863 0.000 0.000 0.000 0.000 0.804 0.196
#> GSM78524 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78527 5 0.3345 0.852 0.000 0.028 0.000 0.000 0.788 0.184
#> GSM78530 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78535 2 0.3349 0.604 0.244 0.748 0.000 0.008 0.000 0.000
#> GSM78538 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78542 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78544 2 0.0363 0.900 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM78549 2 0.0260 0.901 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM78553 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78558 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78561 5 0.0000 0.912 0.000 0.000 0.000 0.000 1.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) agent(p) individual(p) k
#> CV:pam 58 2.54e-13 0.00184 0.9999 2
#> CV:pam 58 1.80e-13 0.00263 0.3207 3
#> CV:pam 57 2.96e-22 0.01024 0.5266 4
#> CV:pam 56 1.48e-20 0.02988 0.4291 5
#> CV:pam 54 1.35e-18 0.04299 0.0587 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "mclust"]
# you can also extract it by
# res = res_list["CV:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 58 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4222 0.578 0.578
#> 3 3 0.663 0.684 0.855 0.4923 0.789 0.636
#> 4 4 0.823 0.807 0.909 0.1727 0.846 0.599
#> 5 5 0.892 0.872 0.934 0.0727 0.943 0.773
#> 6 6 0.919 0.838 0.920 0.0440 0.950 0.760
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM78539 1 0 1 1 0
#> GSM78545 1 0 1 1 0
#> GSM78550 1 0 1 1 0
#> GSM78554 1 0 1 1 0
#> GSM78562 1 0 1 1 0
#> GSM78540 1 0 1 1 0
#> GSM78546 1 0 1 1 0
#> GSM78551 1 0 1 1 0
#> GSM78555 1 0 1 1 0
#> GSM78563 1 0 1 1 0
#> GSM43005 1 0 1 1 0
#> GSM43008 1 0 1 1 0
#> GSM43011 1 0 1 1 0
#> GSM78523 1 0 1 1 0
#> GSM78526 1 0 1 1 0
#> GSM78529 1 0 1 1 0
#> GSM78532 1 0 1 1 0
#> GSM78534 1 0 1 1 0
#> GSM78537 1 0 1 1 0
#> GSM78543 1 0 1 1 0
#> GSM78548 1 0 1 1 0
#> GSM78557 1 0 1 1 0
#> GSM78560 1 0 1 1 0
#> GSM78565 1 0 1 1 0
#> GSM43000 1 0 1 1 0
#> GSM43002 1 0 1 1 0
#> GSM43004 1 0 1 1 0
#> GSM43007 1 0 1 1 0
#> GSM43010 1 0 1 1 0
#> GSM78522 1 0 1 1 0
#> GSM78525 1 0 1 1 0
#> GSM78528 1 0 1 1 0
#> GSM78531 1 0 1 1 0
#> GSM78533 1 0 1 1 0
#> GSM78536 1 0 1 1 0
#> GSM78541 1 0 1 1 0
#> GSM78547 1 0 1 1 0
#> GSM78552 1 0 1 1 0
#> GSM78556 1 0 1 1 0
#> GSM78559 1 0 1 1 0
#> GSM78564 1 0 1 1 0
#> GSM42999 2 0 1 0 1
#> GSM43001 2 0 1 0 1
#> GSM43003 2 0 1 0 1
#> GSM43006 2 0 1 0 1
#> GSM43009 2 0 1 0 1
#> GSM43012 2 0 1 0 1
#> GSM78524 2 0 1 0 1
#> GSM78527 2 0 1 0 1
#> GSM78530 2 0 1 0 1
#> GSM78535 2 0 1 0 1
#> GSM78538 2 0 1 0 1
#> GSM78542 2 0 1 0 1
#> GSM78544 2 0 1 0 1
#> GSM78549 2 0 1 0 1
#> GSM78553 2 0 1 0 1
#> GSM78558 2 0 1 0 1
#> GSM78561 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM78539 1 0.3192 0.80755 0.888 0.000 0.112
#> GSM78545 1 0.2448 0.80027 0.924 0.000 0.076
#> GSM78550 1 0.2711 0.80839 0.912 0.000 0.088
#> GSM78554 1 0.4121 0.73047 0.832 0.000 0.168
#> GSM78562 1 0.3340 0.80394 0.880 0.000 0.120
#> GSM78540 1 0.3192 0.80755 0.888 0.000 0.112
#> GSM78546 1 0.2711 0.80839 0.912 0.000 0.088
#> GSM78551 1 0.2711 0.80839 0.912 0.000 0.088
#> GSM78555 1 0.6235 0.23679 0.564 0.000 0.436
#> GSM78563 1 0.3192 0.80755 0.888 0.000 0.112
#> GSM43005 3 0.6291 0.20834 0.468 0.000 0.532
#> GSM43008 3 0.6286 0.20872 0.464 0.000 0.536
#> GSM43011 3 0.6291 0.20834 0.468 0.000 0.532
#> GSM78523 3 0.6291 0.20834 0.468 0.000 0.532
#> GSM78526 3 0.3412 0.66749 0.124 0.000 0.876
#> GSM78529 1 0.6267 0.00866 0.548 0.000 0.452
#> GSM78532 3 0.1643 0.71029 0.044 0.000 0.956
#> GSM78534 3 0.1163 0.70312 0.028 0.000 0.972
#> GSM78537 3 0.1643 0.71029 0.044 0.000 0.956
#> GSM78543 3 0.1643 0.71029 0.044 0.000 0.956
#> GSM78548 3 0.6305 0.19667 0.484 0.000 0.516
#> GSM78557 3 0.2796 0.70845 0.092 0.000 0.908
#> GSM78560 3 0.1964 0.71097 0.056 0.000 0.944
#> GSM78565 3 0.1643 0.71029 0.044 0.000 0.956
#> GSM43000 3 0.6291 0.20834 0.468 0.000 0.532
#> GSM43002 3 0.6291 0.20834 0.468 0.000 0.532
#> GSM43004 3 0.0747 0.70692 0.016 0.000 0.984
#> GSM43007 3 0.6286 0.20872 0.464 0.000 0.536
#> GSM43010 3 0.2537 0.69326 0.080 0.000 0.920
#> GSM78522 3 0.1411 0.69977 0.036 0.000 0.964
#> GSM78525 3 0.6291 0.20834 0.468 0.000 0.532
#> GSM78528 1 0.6267 0.00866 0.548 0.000 0.452
#> GSM78531 3 0.1643 0.71029 0.044 0.000 0.956
#> GSM78533 3 0.2537 0.69326 0.080 0.000 0.920
#> GSM78536 3 0.1643 0.71029 0.044 0.000 0.956
#> GSM78541 3 0.1860 0.71102 0.052 0.000 0.948
#> GSM78547 3 0.2796 0.70845 0.092 0.000 0.908
#> GSM78552 3 0.6309 0.16414 0.496 0.000 0.504
#> GSM78556 3 0.2796 0.70845 0.092 0.000 0.908
#> GSM78559 3 0.1643 0.71029 0.044 0.000 0.956
#> GSM78564 3 0.1643 0.71029 0.044 0.000 0.956
#> GSM42999 2 0.0000 0.99292 0.000 1.000 0.000
#> GSM43001 2 0.0000 0.99292 0.000 1.000 0.000
#> GSM43003 2 0.0000 0.99292 0.000 1.000 0.000
#> GSM43006 2 0.0000 0.99292 0.000 1.000 0.000
#> GSM43009 2 0.0000 0.99292 0.000 1.000 0.000
#> GSM43012 2 0.0000 0.99292 0.000 1.000 0.000
#> GSM78524 2 0.2356 0.94855 0.072 0.928 0.000
#> GSM78527 2 0.0000 0.99292 0.000 1.000 0.000
#> GSM78530 2 0.0000 0.99292 0.000 1.000 0.000
#> GSM78535 2 0.2356 0.94855 0.072 0.928 0.000
#> GSM78538 2 0.0000 0.99292 0.000 1.000 0.000
#> GSM78542 2 0.0000 0.99292 0.000 1.000 0.000
#> GSM78544 2 0.0000 0.99292 0.000 1.000 0.000
#> GSM78549 2 0.0000 0.99292 0.000 1.000 0.000
#> GSM78553 2 0.0424 0.98867 0.008 0.992 0.000
#> GSM78558 2 0.0000 0.99292 0.000 1.000 0.000
#> GSM78561 2 0.0000 0.99292 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM78539 4 0.0188 0.862 0.004 0.000 0.000 0.996
#> GSM78545 4 0.4989 0.195 0.000 0.000 0.472 0.528
#> GSM78550 4 0.3942 0.715 0.000 0.000 0.236 0.764
#> GSM78554 4 0.4867 0.692 0.032 0.000 0.232 0.736
#> GSM78562 4 0.2480 0.827 0.088 0.000 0.008 0.904
#> GSM78540 4 0.0188 0.862 0.004 0.000 0.000 0.996
#> GSM78546 4 0.0779 0.863 0.004 0.000 0.016 0.980
#> GSM78551 4 0.0779 0.863 0.004 0.000 0.016 0.980
#> GSM78555 4 0.2011 0.836 0.080 0.000 0.000 0.920
#> GSM78563 4 0.0188 0.862 0.004 0.000 0.000 0.996
#> GSM43005 3 0.1118 0.871 0.036 0.000 0.964 0.000
#> GSM43008 3 0.1474 0.867 0.052 0.000 0.948 0.000
#> GSM43011 3 0.1118 0.871 0.036 0.000 0.964 0.000
#> GSM78523 3 0.1118 0.871 0.036 0.000 0.964 0.000
#> GSM78526 3 0.4790 0.343 0.380 0.000 0.620 0.000
#> GSM78529 3 0.2281 0.783 0.000 0.000 0.904 0.096
#> GSM78532 1 0.0592 0.831 0.984 0.000 0.016 0.000
#> GSM78534 1 0.4500 0.511 0.684 0.000 0.316 0.000
#> GSM78537 1 0.0469 0.831 0.988 0.000 0.012 0.000
#> GSM78543 1 0.0524 0.831 0.988 0.000 0.008 0.004
#> GSM78548 3 0.1389 0.868 0.048 0.000 0.952 0.000
#> GSM78557 1 0.4898 0.275 0.584 0.000 0.416 0.000
#> GSM78560 1 0.0524 0.831 0.988 0.000 0.008 0.004
#> GSM78565 1 0.0524 0.831 0.988 0.000 0.008 0.004
#> GSM43000 3 0.1151 0.849 0.008 0.000 0.968 0.024
#> GSM43002 3 0.1118 0.871 0.036 0.000 0.964 0.000
#> GSM43004 1 0.4500 0.511 0.684 0.000 0.316 0.000
#> GSM43007 3 0.1474 0.867 0.052 0.000 0.948 0.000
#> GSM43010 3 0.4804 0.332 0.384 0.000 0.616 0.000
#> GSM78522 1 0.4500 0.511 0.684 0.000 0.316 0.000
#> GSM78525 3 0.1118 0.871 0.036 0.000 0.964 0.000
#> GSM78528 3 0.2281 0.783 0.000 0.000 0.904 0.096
#> GSM78531 1 0.0592 0.831 0.984 0.000 0.016 0.000
#> GSM78533 3 0.4804 0.332 0.384 0.000 0.616 0.000
#> GSM78536 1 0.0524 0.831 0.988 0.000 0.008 0.004
#> GSM78541 1 0.0524 0.831 0.988 0.000 0.008 0.004
#> GSM78547 1 0.4454 0.514 0.692 0.000 0.308 0.000
#> GSM78552 3 0.1557 0.865 0.056 0.000 0.944 0.000
#> GSM78556 1 0.4500 0.498 0.684 0.000 0.316 0.000
#> GSM78559 1 0.0524 0.831 0.988 0.000 0.008 0.004
#> GSM78564 1 0.0592 0.831 0.984 0.000 0.016 0.000
#> GSM42999 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM43001 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM43003 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM43006 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM43009 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM43012 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM78524 2 0.1674 0.963 0.012 0.952 0.032 0.004
#> GSM78527 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM78530 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM78535 2 0.1674 0.963 0.012 0.952 0.032 0.004
#> GSM78538 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM78542 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM78544 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM78549 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM78553 2 0.0376 0.990 0.004 0.992 0.000 0.004
#> GSM78558 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM78561 2 0.0000 0.995 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM78539 4 0.0404 0.9352 0.000 0.000 0.012 0.988 0.000
#> GSM78545 4 0.2516 0.8565 0.000 0.000 0.140 0.860 0.000
#> GSM78550 4 0.2516 0.8565 0.000 0.000 0.140 0.860 0.000
#> GSM78554 4 0.2929 0.8205 0.000 0.000 0.180 0.820 0.000
#> GSM78562 4 0.0510 0.9333 0.000 0.000 0.016 0.984 0.000
#> GSM78540 4 0.0000 0.9354 0.000 0.000 0.000 1.000 0.000
#> GSM78546 4 0.0000 0.9354 0.000 0.000 0.000 1.000 0.000
#> GSM78551 4 0.0000 0.9354 0.000 0.000 0.000 1.000 0.000
#> GSM78555 4 0.0404 0.9352 0.000 0.000 0.012 0.988 0.000
#> GSM78563 4 0.0000 0.9354 0.000 0.000 0.000 1.000 0.000
#> GSM43005 3 0.0404 0.8610 0.012 0.000 0.988 0.000 0.000
#> GSM43008 3 0.0963 0.8512 0.036 0.000 0.964 0.000 0.000
#> GSM43011 3 0.4268 -0.0117 0.000 0.000 0.556 0.000 0.444
#> GSM78523 5 0.4283 0.1896 0.000 0.000 0.456 0.000 0.544
#> GSM78526 5 0.2890 0.8014 0.004 0.000 0.160 0.000 0.836
#> GSM78529 3 0.1522 0.8351 0.012 0.000 0.944 0.044 0.000
#> GSM78532 1 0.0000 0.9817 1.000 0.000 0.000 0.000 0.000
#> GSM78534 5 0.3238 0.8060 0.136 0.000 0.028 0.000 0.836
#> GSM78537 1 0.0000 0.9817 1.000 0.000 0.000 0.000 0.000
#> GSM78543 1 0.0000 0.9817 1.000 0.000 0.000 0.000 0.000
#> GSM78548 3 0.0510 0.8612 0.016 0.000 0.984 0.000 0.000
#> GSM78557 1 0.1270 0.9460 0.948 0.000 0.052 0.000 0.000
#> GSM78560 1 0.0000 0.9817 1.000 0.000 0.000 0.000 0.000
#> GSM78565 1 0.0000 0.9817 1.000 0.000 0.000 0.000 0.000
#> GSM43000 3 0.4273 -0.0274 0.000 0.000 0.552 0.000 0.448
#> GSM43002 3 0.0404 0.8610 0.012 0.000 0.988 0.000 0.000
#> GSM43004 5 0.2971 0.7856 0.156 0.000 0.008 0.000 0.836
#> GSM43007 3 0.0609 0.8603 0.020 0.000 0.980 0.000 0.000
#> GSM43010 5 0.3151 0.8093 0.020 0.000 0.144 0.000 0.836
#> GSM78522 5 0.3238 0.8060 0.136 0.000 0.028 0.000 0.836
#> GSM78525 3 0.0451 0.8562 0.004 0.000 0.988 0.000 0.008
#> GSM78528 3 0.1522 0.8351 0.012 0.000 0.944 0.044 0.000
#> GSM78531 1 0.0000 0.9817 1.000 0.000 0.000 0.000 0.000
#> GSM78533 5 0.2890 0.8014 0.004 0.000 0.160 0.000 0.836
#> GSM78536 1 0.0000 0.9817 1.000 0.000 0.000 0.000 0.000
#> GSM78541 1 0.0000 0.9817 1.000 0.000 0.000 0.000 0.000
#> GSM78547 1 0.1478 0.9330 0.936 0.000 0.064 0.000 0.000
#> GSM78552 3 0.0963 0.8510 0.036 0.000 0.964 0.000 0.000
#> GSM78556 1 0.1341 0.9420 0.944 0.000 0.056 0.000 0.000
#> GSM78559 1 0.0000 0.9817 1.000 0.000 0.000 0.000 0.000
#> GSM78564 1 0.0404 0.9750 0.988 0.000 0.012 0.000 0.000
#> GSM42999 2 0.0000 0.9727 0.000 1.000 0.000 0.000 0.000
#> GSM43001 2 0.0000 0.9727 0.000 1.000 0.000 0.000 0.000
#> GSM43003 2 0.0000 0.9727 0.000 1.000 0.000 0.000 0.000
#> GSM43006 2 0.0000 0.9727 0.000 1.000 0.000 0.000 0.000
#> GSM43009 2 0.0404 0.9697 0.000 0.988 0.000 0.000 0.012
#> GSM43012 2 0.0000 0.9727 0.000 1.000 0.000 0.000 0.000
#> GSM78524 2 0.3163 0.8654 0.000 0.824 0.012 0.000 0.164
#> GSM78527 2 0.0000 0.9727 0.000 1.000 0.000 0.000 0.000
#> GSM78530 2 0.0703 0.9656 0.000 0.976 0.000 0.000 0.024
#> GSM78535 2 0.3163 0.8654 0.000 0.824 0.012 0.000 0.164
#> GSM78538 2 0.0000 0.9727 0.000 1.000 0.000 0.000 0.000
#> GSM78542 2 0.0000 0.9727 0.000 1.000 0.000 0.000 0.000
#> GSM78544 2 0.0510 0.9685 0.000 0.984 0.000 0.000 0.016
#> GSM78549 2 0.0000 0.9727 0.000 1.000 0.000 0.000 0.000
#> GSM78553 2 0.2074 0.9192 0.000 0.896 0.000 0.000 0.104
#> GSM78558 2 0.0963 0.9603 0.000 0.964 0.000 0.000 0.036
#> GSM78561 2 0.0000 0.9727 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM78539 4 0.0260 0.991 0.000 0.000 0.008 0.992 0.000 0.000
#> GSM78545 4 0.0260 0.991 0.000 0.000 0.008 0.992 0.000 0.000
#> GSM78550 4 0.0260 0.991 0.000 0.000 0.008 0.992 0.000 0.000
#> GSM78554 4 0.0458 0.987 0.000 0.000 0.016 0.984 0.000 0.000
#> GSM78562 4 0.0291 0.991 0.000 0.000 0.004 0.992 0.000 0.004
#> GSM78540 4 0.0000 0.993 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78546 4 0.0000 0.993 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78551 4 0.0000 0.993 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78555 4 0.0551 0.985 0.008 0.000 0.004 0.984 0.000 0.004
#> GSM78563 4 0.0000 0.993 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM43005 3 0.0260 0.855 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM43008 3 0.1753 0.803 0.084 0.000 0.912 0.000 0.000 0.004
#> GSM43011 3 0.3266 0.623 0.000 0.000 0.728 0.000 0.000 0.272
#> GSM78523 3 0.3804 0.346 0.000 0.000 0.576 0.000 0.000 0.424
#> GSM78526 6 0.1501 0.898 0.000 0.000 0.076 0.000 0.000 0.924
#> GSM78529 3 0.0881 0.850 0.000 0.000 0.972 0.012 0.008 0.008
#> GSM78532 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78534 6 0.2258 0.898 0.060 0.000 0.000 0.000 0.044 0.896
#> GSM78537 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78543 1 0.0146 0.996 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM78548 3 0.0260 0.855 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM78557 1 0.0260 0.992 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM78560 1 0.0146 0.994 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM78565 1 0.0146 0.996 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM43000 3 0.3717 0.437 0.000 0.000 0.616 0.000 0.000 0.384
#> GSM43002 3 0.0260 0.855 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM43004 6 0.2747 0.874 0.096 0.000 0.000 0.000 0.044 0.860
#> GSM43007 3 0.0363 0.854 0.012 0.000 0.988 0.000 0.000 0.000
#> GSM43010 6 0.1411 0.905 0.004 0.000 0.060 0.000 0.000 0.936
#> GSM78522 6 0.2471 0.909 0.040 0.000 0.020 0.000 0.044 0.896
#> GSM78525 3 0.0260 0.853 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM78528 3 0.0881 0.850 0.000 0.000 0.972 0.012 0.008 0.008
#> GSM78531 1 0.0146 0.996 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM78533 6 0.2048 0.857 0.000 0.000 0.120 0.000 0.000 0.880
#> GSM78536 1 0.0146 0.996 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM78541 1 0.0146 0.996 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM78547 1 0.0291 0.991 0.992 0.000 0.004 0.000 0.000 0.004
#> GSM78552 3 0.2454 0.732 0.160 0.000 0.840 0.000 0.000 0.000
#> GSM78556 1 0.0260 0.992 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM78559 1 0.0146 0.996 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM78564 1 0.0260 0.995 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM42999 2 0.0000 0.874 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43001 2 0.0000 0.874 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43003 2 0.0000 0.874 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43006 2 0.0000 0.874 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43009 2 0.0146 0.871 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM43012 2 0.0000 0.874 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78524 5 0.2451 0.665 0.000 0.060 0.000 0.000 0.884 0.056
#> GSM78527 2 0.0000 0.874 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78530 5 0.3592 0.693 0.000 0.344 0.000 0.000 0.656 0.000
#> GSM78535 5 0.2583 0.660 0.000 0.052 0.008 0.000 0.884 0.056
#> GSM78538 2 0.3797 -0.148 0.000 0.580 0.000 0.000 0.420 0.000
#> GSM78542 2 0.3797 -0.148 0.000 0.580 0.000 0.000 0.420 0.000
#> GSM78544 5 0.3847 0.474 0.000 0.456 0.000 0.000 0.544 0.000
#> GSM78549 2 0.0000 0.874 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78553 5 0.3266 0.736 0.000 0.272 0.000 0.000 0.728 0.000
#> GSM78558 5 0.3446 0.726 0.000 0.308 0.000 0.000 0.692 0.000
#> GSM78561 2 0.0146 0.871 0.000 0.996 0.000 0.000 0.004 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) agent(p) individual(p) k
#> CV:mclust 58 2.54e-13 0.00184 1.000 2
#> CV:mclust 45 1.32e-18 0.00297 0.845 3
#> CV:mclust 52 3.67e-20 0.00980 0.708 4
#> CV:mclust 55 3.81e-20 0.02134 0.201 5
#> CV:mclust 53 3.41e-18 0.06575 0.183 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "NMF"]
# you can also extract it by
# res = res_list["CV:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 58 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.969 0.988 0.4230 0.578 0.578
#> 3 3 0.974 0.945 0.978 0.5878 0.724 0.534
#> 4 4 0.820 0.908 0.925 0.1120 0.889 0.675
#> 5 5 0.884 0.900 0.936 0.0622 0.939 0.761
#> 6 6 0.964 0.936 0.966 0.0484 0.941 0.722
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM78539 1 0.000 0.990 1.000 0.000
#> GSM78545 1 0.000 0.990 1.000 0.000
#> GSM78550 1 0.000 0.990 1.000 0.000
#> GSM78554 1 0.000 0.990 1.000 0.000
#> GSM78562 1 0.000 0.990 1.000 0.000
#> GSM78540 1 0.000 0.990 1.000 0.000
#> GSM78546 1 0.000 0.990 1.000 0.000
#> GSM78551 1 0.000 0.990 1.000 0.000
#> GSM78555 1 0.000 0.990 1.000 0.000
#> GSM78563 1 0.000 0.990 1.000 0.000
#> GSM43005 1 0.000 0.990 1.000 0.000
#> GSM43008 1 0.000 0.990 1.000 0.000
#> GSM43011 1 0.000 0.990 1.000 0.000
#> GSM78523 1 0.000 0.990 1.000 0.000
#> GSM78526 1 0.000 0.990 1.000 0.000
#> GSM78529 1 0.952 0.394 0.628 0.372
#> GSM78532 1 0.000 0.990 1.000 0.000
#> GSM78534 1 0.000 0.990 1.000 0.000
#> GSM78537 1 0.000 0.990 1.000 0.000
#> GSM78543 1 0.000 0.990 1.000 0.000
#> GSM78548 1 0.000 0.990 1.000 0.000
#> GSM78557 1 0.000 0.990 1.000 0.000
#> GSM78560 1 0.000 0.990 1.000 0.000
#> GSM78565 1 0.000 0.990 1.000 0.000
#> GSM43000 1 0.000 0.990 1.000 0.000
#> GSM43002 1 0.000 0.990 1.000 0.000
#> GSM43004 1 0.000 0.990 1.000 0.000
#> GSM43007 1 0.000 0.990 1.000 0.000
#> GSM43010 1 0.000 0.990 1.000 0.000
#> GSM78522 1 0.000 0.990 1.000 0.000
#> GSM78525 1 0.000 0.990 1.000 0.000
#> GSM78528 1 0.000 0.990 1.000 0.000
#> GSM78531 1 0.000 0.990 1.000 0.000
#> GSM78533 1 0.000 0.990 1.000 0.000
#> GSM78536 1 0.000 0.990 1.000 0.000
#> GSM78541 1 0.000 0.990 1.000 0.000
#> GSM78547 1 0.000 0.990 1.000 0.000
#> GSM78552 1 0.000 0.990 1.000 0.000
#> GSM78556 1 0.000 0.990 1.000 0.000
#> GSM78559 1 0.000 0.990 1.000 0.000
#> GSM78564 1 0.000 0.990 1.000 0.000
#> GSM42999 2 0.000 0.980 0.000 1.000
#> GSM43001 2 0.000 0.980 0.000 1.000
#> GSM43003 2 0.000 0.980 0.000 1.000
#> GSM43006 2 0.000 0.980 0.000 1.000
#> GSM43009 2 0.000 0.980 0.000 1.000
#> GSM43012 2 0.000 0.980 0.000 1.000
#> GSM78524 2 0.000 0.980 0.000 1.000
#> GSM78527 2 0.000 0.980 0.000 1.000
#> GSM78530 2 0.000 0.980 0.000 1.000
#> GSM78535 2 0.900 0.532 0.316 0.684
#> GSM78538 2 0.000 0.980 0.000 1.000
#> GSM78542 2 0.000 0.980 0.000 1.000
#> GSM78544 2 0.000 0.980 0.000 1.000
#> GSM78549 2 0.000 0.980 0.000 1.000
#> GSM78553 2 0.000 0.980 0.000 1.000
#> GSM78558 2 0.000 0.980 0.000 1.000
#> GSM78561 2 0.000 0.980 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM78539 1 0.0000 0.966 1.000 0.000 0.000
#> GSM78545 3 0.6140 0.327 0.404 0.000 0.596
#> GSM78550 1 0.4702 0.709 0.788 0.000 0.212
#> GSM78554 1 0.0000 0.966 1.000 0.000 0.000
#> GSM78562 1 0.0000 0.966 1.000 0.000 0.000
#> GSM78540 1 0.0000 0.966 1.000 0.000 0.000
#> GSM78546 1 0.0000 0.966 1.000 0.000 0.000
#> GSM78551 1 0.0000 0.966 1.000 0.000 0.000
#> GSM78555 1 0.0000 0.966 1.000 0.000 0.000
#> GSM78563 1 0.0000 0.966 1.000 0.000 0.000
#> GSM43005 3 0.0000 0.967 0.000 0.000 1.000
#> GSM43008 3 0.0424 0.962 0.008 0.000 0.992
#> GSM43011 3 0.0000 0.967 0.000 0.000 1.000
#> GSM78523 3 0.0000 0.967 0.000 0.000 1.000
#> GSM78526 3 0.0000 0.967 0.000 0.000 1.000
#> GSM78529 3 0.0000 0.967 0.000 0.000 1.000
#> GSM78532 1 0.0000 0.966 1.000 0.000 0.000
#> GSM78534 3 0.0000 0.967 0.000 0.000 1.000
#> GSM78537 1 0.0000 0.966 1.000 0.000 0.000
#> GSM78543 1 0.0000 0.966 1.000 0.000 0.000
#> GSM78548 3 0.0000 0.967 0.000 0.000 1.000
#> GSM78557 1 0.0000 0.966 1.000 0.000 0.000
#> GSM78560 1 0.0237 0.963 0.996 0.000 0.004
#> GSM78565 1 0.0000 0.966 1.000 0.000 0.000
#> GSM43000 3 0.0000 0.967 0.000 0.000 1.000
#> GSM43002 3 0.0000 0.967 0.000 0.000 1.000
#> GSM43004 3 0.2165 0.912 0.064 0.000 0.936
#> GSM43007 3 0.0424 0.962 0.008 0.000 0.992
#> GSM43010 3 0.0000 0.967 0.000 0.000 1.000
#> GSM78522 3 0.0000 0.967 0.000 0.000 1.000
#> GSM78525 3 0.0000 0.967 0.000 0.000 1.000
#> GSM78528 3 0.0000 0.967 0.000 0.000 1.000
#> GSM78531 1 0.0000 0.966 1.000 0.000 0.000
#> GSM78533 3 0.0000 0.967 0.000 0.000 1.000
#> GSM78536 1 0.0000 0.966 1.000 0.000 0.000
#> GSM78541 1 0.0000 0.966 1.000 0.000 0.000
#> GSM78547 1 0.0000 0.966 1.000 0.000 0.000
#> GSM78552 3 0.2356 0.906 0.072 0.000 0.928
#> GSM78556 1 0.0237 0.963 0.996 0.000 0.004
#> GSM78559 1 0.0000 0.966 1.000 0.000 0.000
#> GSM78564 1 0.3412 0.841 0.876 0.000 0.124
#> GSM42999 2 0.0000 0.998 0.000 1.000 0.000
#> GSM43001 2 0.0000 0.998 0.000 1.000 0.000
#> GSM43003 2 0.0000 0.998 0.000 1.000 0.000
#> GSM43006 2 0.0000 0.998 0.000 1.000 0.000
#> GSM43009 2 0.0000 0.998 0.000 1.000 0.000
#> GSM43012 2 0.0000 0.998 0.000 1.000 0.000
#> GSM78524 2 0.1163 0.970 0.028 0.972 0.000
#> GSM78527 2 0.0000 0.998 0.000 1.000 0.000
#> GSM78530 2 0.0000 0.998 0.000 1.000 0.000
#> GSM78535 1 0.5988 0.413 0.632 0.368 0.000
#> GSM78538 2 0.0000 0.998 0.000 1.000 0.000
#> GSM78542 2 0.0000 0.998 0.000 1.000 0.000
#> GSM78544 2 0.0000 0.998 0.000 1.000 0.000
#> GSM78549 2 0.0000 0.998 0.000 1.000 0.000
#> GSM78553 2 0.0000 0.998 0.000 1.000 0.000
#> GSM78558 2 0.0000 0.998 0.000 1.000 0.000
#> GSM78561 2 0.0000 0.998 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM78539 4 0.3486 0.96924 0.188 0.000 0.000 0.812
#> GSM78545 4 0.4362 0.86456 0.096 0.000 0.088 0.816
#> GSM78550 4 0.4010 0.94212 0.156 0.000 0.028 0.816
#> GSM78554 4 0.3486 0.96924 0.188 0.000 0.000 0.812
#> GSM78562 4 0.3610 0.96087 0.200 0.000 0.000 0.800
#> GSM78540 4 0.3486 0.96924 0.188 0.000 0.000 0.812
#> GSM78546 4 0.3486 0.96924 0.188 0.000 0.000 0.812
#> GSM78551 4 0.3444 0.96728 0.184 0.000 0.000 0.816
#> GSM78555 4 0.4008 0.91214 0.244 0.000 0.000 0.756
#> GSM78563 4 0.3486 0.96924 0.188 0.000 0.000 0.812
#> GSM43005 3 0.0188 0.95564 0.000 0.000 0.996 0.004
#> GSM43008 3 0.3266 0.81600 0.168 0.000 0.832 0.000
#> GSM43011 3 0.0188 0.95705 0.000 0.000 0.996 0.004
#> GSM78523 3 0.0188 0.95705 0.000 0.000 0.996 0.004
#> GSM78526 3 0.0188 0.95705 0.000 0.000 0.996 0.004
#> GSM78529 3 0.2469 0.88395 0.000 0.000 0.892 0.108
#> GSM78532 1 0.0000 0.93012 1.000 0.000 0.000 0.000
#> GSM78534 3 0.2831 0.85834 0.120 0.000 0.876 0.004
#> GSM78537 1 0.0000 0.93012 1.000 0.000 0.000 0.000
#> GSM78543 1 0.0000 0.93012 1.000 0.000 0.000 0.000
#> GSM78548 3 0.0524 0.95421 0.004 0.000 0.988 0.008
#> GSM78557 1 0.0000 0.93012 1.000 0.000 0.000 0.000
#> GSM78560 1 0.0000 0.93012 1.000 0.000 0.000 0.000
#> GSM78565 1 0.0000 0.93012 1.000 0.000 0.000 0.000
#> GSM43000 3 0.0000 0.95665 0.000 0.000 1.000 0.000
#> GSM43002 3 0.0000 0.95665 0.000 0.000 1.000 0.000
#> GSM43004 1 0.3539 0.70572 0.820 0.000 0.176 0.004
#> GSM43007 3 0.1118 0.93806 0.036 0.000 0.964 0.000
#> GSM43010 3 0.0188 0.95705 0.000 0.000 0.996 0.004
#> GSM78522 3 0.0188 0.95705 0.000 0.000 0.996 0.004
#> GSM78525 3 0.0000 0.95665 0.000 0.000 1.000 0.000
#> GSM78528 3 0.0707 0.94907 0.000 0.000 0.980 0.020
#> GSM78531 1 0.0000 0.93012 1.000 0.000 0.000 0.000
#> GSM78533 3 0.0188 0.95705 0.000 0.000 0.996 0.004
#> GSM78536 1 0.0000 0.93012 1.000 0.000 0.000 0.000
#> GSM78541 1 0.0000 0.93012 1.000 0.000 0.000 0.000
#> GSM78547 1 0.0000 0.93012 1.000 0.000 0.000 0.000
#> GSM78552 3 0.3402 0.81952 0.164 0.000 0.832 0.004
#> GSM78556 1 0.0000 0.93012 1.000 0.000 0.000 0.000
#> GSM78559 1 0.0000 0.93012 1.000 0.000 0.000 0.000
#> GSM78564 1 0.0779 0.90981 0.980 0.000 0.016 0.004
#> GSM42999 2 0.0817 0.93456 0.000 0.976 0.000 0.024
#> GSM43001 2 0.3400 0.88303 0.000 0.820 0.000 0.180
#> GSM43003 2 0.0000 0.93879 0.000 1.000 0.000 0.000
#> GSM43006 2 0.3400 0.88303 0.000 0.820 0.000 0.180
#> GSM43009 2 0.0000 0.93879 0.000 1.000 0.000 0.000
#> GSM43012 2 0.3172 0.89136 0.000 0.840 0.000 0.160
#> GSM78524 2 0.3074 0.78831 0.152 0.848 0.000 0.000
#> GSM78527 2 0.3356 0.88490 0.000 0.824 0.000 0.176
#> GSM78530 2 0.0000 0.93879 0.000 1.000 0.000 0.000
#> GSM78535 1 0.5000 0.00235 0.500 0.500 0.000 0.000
#> GSM78538 2 0.0000 0.93879 0.000 1.000 0.000 0.000
#> GSM78542 2 0.0000 0.93879 0.000 1.000 0.000 0.000
#> GSM78544 2 0.0000 0.93879 0.000 1.000 0.000 0.000
#> GSM78549 2 0.0336 0.93786 0.000 0.992 0.000 0.008
#> GSM78553 2 0.0000 0.93879 0.000 1.000 0.000 0.000
#> GSM78558 2 0.0000 0.93879 0.000 1.000 0.000 0.000
#> GSM78561 2 0.3400 0.88303 0.000 0.820 0.000 0.180
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM78539 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM78545 4 0.0510 0.973 0.000 0.000 0.000 0.984 0.016
#> GSM78550 4 0.0510 0.973 0.000 0.000 0.000 0.984 0.016
#> GSM78554 4 0.0404 0.974 0.000 0.000 0.000 0.988 0.012
#> GSM78562 4 0.0703 0.963 0.024 0.000 0.000 0.976 0.000
#> GSM78540 4 0.0404 0.972 0.000 0.012 0.000 0.988 0.000
#> GSM78546 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM78551 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM78555 4 0.1608 0.910 0.072 0.000 0.000 0.928 0.000
#> GSM78563 4 0.0290 0.975 0.000 0.008 0.000 0.992 0.000
#> GSM43005 3 0.2723 0.882 0.000 0.000 0.864 0.012 0.124
#> GSM43008 3 0.5367 0.738 0.168 0.000 0.696 0.012 0.124
#> GSM43011 3 0.0000 0.904 0.000 0.000 1.000 0.000 0.000
#> GSM78523 3 0.0000 0.904 0.000 0.000 1.000 0.000 0.000
#> GSM78526 3 0.0000 0.904 0.000 0.000 1.000 0.000 0.000
#> GSM78529 5 0.4249 0.238 0.000 0.000 0.296 0.016 0.688
#> GSM78532 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000
#> GSM78534 3 0.0703 0.892 0.024 0.000 0.976 0.000 0.000
#> GSM78537 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000
#> GSM78543 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000
#> GSM78548 3 0.3741 0.856 0.000 0.000 0.816 0.076 0.108
#> GSM78557 1 0.0510 0.963 0.984 0.000 0.000 0.000 0.016
#> GSM78560 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000
#> GSM78565 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000
#> GSM43000 3 0.0794 0.905 0.000 0.000 0.972 0.000 0.028
#> GSM43002 3 0.2074 0.893 0.000 0.000 0.896 0.000 0.104
#> GSM43004 1 0.3586 0.641 0.736 0.000 0.264 0.000 0.000
#> GSM43007 3 0.3976 0.860 0.048 0.000 0.812 0.016 0.124
#> GSM43010 3 0.0000 0.904 0.000 0.000 1.000 0.000 0.000
#> GSM78522 3 0.0000 0.904 0.000 0.000 1.000 0.000 0.000
#> GSM78525 3 0.1965 0.895 0.000 0.000 0.904 0.000 0.096
#> GSM78528 3 0.3696 0.831 0.000 0.000 0.772 0.016 0.212
#> GSM78531 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000
#> GSM78533 3 0.0000 0.904 0.000 0.000 1.000 0.000 0.000
#> GSM78536 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000
#> GSM78541 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000
#> GSM78547 1 0.0510 0.963 0.984 0.000 0.000 0.000 0.016
#> GSM78552 3 0.5650 0.776 0.108 0.000 0.708 0.056 0.128
#> GSM78556 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000
#> GSM78559 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000
#> GSM78564 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000
#> GSM42999 2 0.1544 0.904 0.000 0.932 0.000 0.000 0.068
#> GSM43001 5 0.2648 0.810 0.000 0.152 0.000 0.000 0.848
#> GSM43003 2 0.0703 0.948 0.000 0.976 0.000 0.000 0.024
#> GSM43006 5 0.2852 0.812 0.000 0.172 0.000 0.000 0.828
#> GSM43009 2 0.0404 0.954 0.000 0.988 0.000 0.000 0.012
#> GSM43012 5 0.4015 0.623 0.000 0.348 0.000 0.000 0.652
#> GSM78524 2 0.0771 0.943 0.020 0.976 0.000 0.004 0.000
#> GSM78527 5 0.3508 0.763 0.000 0.252 0.000 0.000 0.748
#> GSM78530 2 0.0000 0.958 0.000 1.000 0.000 0.000 0.000
#> GSM78535 2 0.2674 0.791 0.120 0.868 0.000 0.012 0.000
#> GSM78538 2 0.0162 0.958 0.000 0.996 0.000 0.004 0.000
#> GSM78542 2 0.0162 0.958 0.000 0.996 0.000 0.004 0.000
#> GSM78544 2 0.0000 0.958 0.000 1.000 0.000 0.000 0.000
#> GSM78549 2 0.1043 0.936 0.000 0.960 0.000 0.000 0.040
#> GSM78553 2 0.0404 0.955 0.000 0.988 0.000 0.012 0.000
#> GSM78558 2 0.0404 0.955 0.000 0.988 0.000 0.012 0.000
#> GSM78561 5 0.2732 0.812 0.000 0.160 0.000 0.000 0.840
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM78539 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78545 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78550 4 0.0363 0.986 0.000 0.000 0.012 0.988 0.000 0.000
#> GSM78554 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78562 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78540 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78546 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78551 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78555 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78563 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM43005 3 0.1663 0.931 0.000 0.000 0.912 0.000 0.000 0.088
#> GSM43008 3 0.0937 0.934 0.000 0.000 0.960 0.000 0.000 0.040
#> GSM43011 6 0.0000 0.942 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78523 6 0.0000 0.942 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78526 6 0.0000 0.942 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78529 3 0.1074 0.926 0.000 0.000 0.960 0.000 0.012 0.028
#> GSM78532 1 0.0363 0.977 0.988 0.000 0.012 0.000 0.000 0.000
#> GSM78534 6 0.0000 0.942 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78537 1 0.0458 0.976 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM78543 1 0.0146 0.978 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM78548 3 0.2527 0.880 0.000 0.000 0.832 0.000 0.000 0.168
#> GSM78557 1 0.1765 0.911 0.904 0.000 0.096 0.000 0.000 0.000
#> GSM78560 1 0.0260 0.978 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM78565 1 0.0000 0.977 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM43000 6 0.1663 0.855 0.000 0.000 0.088 0.000 0.000 0.912
#> GSM43002 3 0.2048 0.918 0.000 0.000 0.880 0.000 0.000 0.120
#> GSM43004 6 0.3288 0.599 0.276 0.000 0.000 0.000 0.000 0.724
#> GSM43007 3 0.1141 0.936 0.000 0.000 0.948 0.000 0.000 0.052
#> GSM43010 6 0.0000 0.942 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78522 6 0.0000 0.942 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78525 3 0.2854 0.834 0.000 0.000 0.792 0.000 0.000 0.208
#> GSM78528 3 0.0603 0.919 0.000 0.000 0.980 0.000 0.004 0.016
#> GSM78531 1 0.0146 0.978 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM78533 6 0.0000 0.942 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78536 1 0.0000 0.977 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78541 1 0.0146 0.978 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM78547 1 0.1714 0.915 0.908 0.000 0.092 0.000 0.000 0.000
#> GSM78552 3 0.1082 0.934 0.004 0.000 0.956 0.000 0.000 0.040
#> GSM78556 1 0.0790 0.966 0.968 0.000 0.032 0.000 0.000 0.000
#> GSM78559 1 0.0000 0.977 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78564 1 0.0146 0.978 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM42999 2 0.1141 0.931 0.000 0.948 0.000 0.000 0.052 0.000
#> GSM43001 5 0.0000 0.879 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM43003 2 0.0000 0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43006 5 0.0146 0.880 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM43009 2 0.0000 0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43012 5 0.0713 0.872 0.000 0.028 0.000 0.000 0.972 0.000
#> GSM78524 2 0.0000 0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78527 5 0.3717 0.377 0.000 0.384 0.000 0.000 0.616 0.000
#> GSM78530 2 0.0000 0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78535 2 0.1910 0.843 0.108 0.892 0.000 0.000 0.000 0.000
#> GSM78538 2 0.0000 0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78542 2 0.0000 0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78544 2 0.0000 0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78549 2 0.0146 0.978 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM78553 2 0.0000 0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78558 2 0.0000 0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78561 5 0.0000 0.879 0.000 0.000 0.000 0.000 1.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) agent(p) individual(p) k
#> CV:NMF 57 4.19e-13 0.00243 0.9999 2
#> CV:NMF 56 3.19e-14 0.00495 0.2677 3
#> CV:NMF 57 2.96e-22 0.01039 0.4111 4
#> CV:NMF 57 5.72e-21 0.02302 0.4047 5
#> CV:NMF 57 8.31e-20 0.04734 0.0885 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "hclust"]
# you can also extract it by
# res = res_list["MAD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 58 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)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.805 0.949 0.970 0.3798 0.593 0.593
#> 3 3 0.534 0.832 0.895 0.6926 0.734 0.551
#> 4 4 0.639 0.747 0.874 0.0566 0.989 0.965
#> 5 5 0.603 0.742 0.840 0.0483 0.983 0.946
#> 6 6 0.700 0.719 0.758 0.1018 0.868 0.573
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
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.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM78539 1 0.000 0.995 1.000 0.000
#> GSM78545 1 0.000 0.995 1.000 0.000
#> GSM78550 1 0.000 0.995 1.000 0.000
#> GSM78554 1 0.000 0.995 1.000 0.000
#> GSM78562 1 0.000 0.995 1.000 0.000
#> GSM78540 1 0.000 0.995 1.000 0.000
#> GSM78546 1 0.000 0.995 1.000 0.000
#> GSM78551 1 0.000 0.995 1.000 0.000
#> GSM78555 1 0.000 0.995 1.000 0.000
#> GSM78563 1 0.000 0.995 1.000 0.000
#> GSM43005 1 0.000 0.995 1.000 0.000
#> GSM43008 1 0.000 0.995 1.000 0.000
#> GSM43011 1 0.000 0.995 1.000 0.000
#> GSM78523 1 0.000 0.995 1.000 0.000
#> GSM78526 1 0.000 0.995 1.000 0.000
#> GSM78529 1 0.000 0.995 1.000 0.000
#> GSM78532 1 0.000 0.995 1.000 0.000
#> GSM78534 1 0.000 0.995 1.000 0.000
#> GSM78537 1 0.000 0.995 1.000 0.000
#> GSM78543 1 0.000 0.995 1.000 0.000
#> GSM78548 1 0.000 0.995 1.000 0.000
#> GSM78557 1 0.000 0.995 1.000 0.000
#> GSM78560 1 0.000 0.995 1.000 0.000
#> GSM78565 1 0.000 0.995 1.000 0.000
#> GSM43000 1 0.000 0.995 1.000 0.000
#> GSM43002 1 0.000 0.995 1.000 0.000
#> GSM43004 1 0.000 0.995 1.000 0.000
#> GSM43007 1 0.000 0.995 1.000 0.000
#> GSM43010 1 0.000 0.995 1.000 0.000
#> GSM78522 1 0.000 0.995 1.000 0.000
#> GSM78525 1 0.000 0.995 1.000 0.000
#> GSM78528 1 0.000 0.995 1.000 0.000
#> GSM78531 1 0.000 0.995 1.000 0.000
#> GSM78533 1 0.000 0.995 1.000 0.000
#> GSM78536 1 0.000 0.995 1.000 0.000
#> GSM78541 1 0.000 0.995 1.000 0.000
#> GSM78547 1 0.000 0.995 1.000 0.000
#> GSM78552 1 0.000 0.995 1.000 0.000
#> GSM78556 1 0.000 0.995 1.000 0.000
#> GSM78559 1 0.000 0.995 1.000 0.000
#> GSM78564 1 0.000 0.995 1.000 0.000
#> GSM42999 2 0.000 0.893 0.000 1.000
#> GSM43001 2 0.000 0.893 0.000 1.000
#> GSM43003 2 0.000 0.893 0.000 1.000
#> GSM43006 2 0.000 0.893 0.000 1.000
#> GSM43009 2 0.000 0.893 0.000 1.000
#> GSM43012 2 0.000 0.893 0.000 1.000
#> GSM78524 2 0.981 0.420 0.420 0.580
#> GSM78527 2 0.000 0.893 0.000 1.000
#> GSM78530 2 0.697 0.839 0.188 0.812
#> GSM78535 1 0.671 0.750 0.824 0.176
#> GSM78538 2 0.697 0.839 0.188 0.812
#> GSM78542 2 0.697 0.839 0.188 0.812
#> GSM78544 2 0.697 0.839 0.188 0.812
#> GSM78549 2 0.000 0.893 0.000 1.000
#> GSM78553 2 0.697 0.839 0.188 0.812
#> GSM78558 2 0.697 0.839 0.188 0.812
#> GSM78561 2 0.000 0.893 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM78539 1 0.0892 0.820 0.980 0.000 0.020
#> GSM78545 1 0.4654 0.743 0.792 0.000 0.208
#> GSM78550 1 0.3551 0.809 0.868 0.000 0.132
#> GSM78554 1 0.3340 0.816 0.880 0.000 0.120
#> GSM78562 1 0.0892 0.820 0.980 0.000 0.020
#> GSM78540 1 0.0892 0.820 0.980 0.000 0.020
#> GSM78546 1 0.3116 0.820 0.892 0.000 0.108
#> GSM78551 1 0.3551 0.809 0.868 0.000 0.132
#> GSM78555 1 0.0892 0.820 0.980 0.000 0.020
#> GSM78563 1 0.0892 0.820 0.980 0.000 0.020
#> GSM43005 3 0.0000 0.913 0.000 0.000 1.000
#> GSM43008 3 0.0000 0.913 0.000 0.000 1.000
#> GSM43011 3 0.0000 0.913 0.000 0.000 1.000
#> GSM78523 3 0.0000 0.913 0.000 0.000 1.000
#> GSM78526 3 0.0000 0.913 0.000 0.000 1.000
#> GSM78529 3 0.0000 0.913 0.000 0.000 1.000
#> GSM78532 1 0.4796 0.819 0.780 0.000 0.220
#> GSM78534 3 0.0000 0.913 0.000 0.000 1.000
#> GSM78537 1 0.4750 0.822 0.784 0.000 0.216
#> GSM78543 1 0.5098 0.796 0.752 0.000 0.248
#> GSM78548 3 0.4178 0.760 0.172 0.000 0.828
#> GSM78557 3 0.5016 0.679 0.240 0.000 0.760
#> GSM78560 1 0.5529 0.736 0.704 0.000 0.296
#> GSM78565 1 0.4750 0.822 0.784 0.000 0.216
#> GSM43000 3 0.0000 0.913 0.000 0.000 1.000
#> GSM43002 3 0.0000 0.913 0.000 0.000 1.000
#> GSM43004 3 0.0000 0.913 0.000 0.000 1.000
#> GSM43007 3 0.0000 0.913 0.000 0.000 1.000
#> GSM43010 3 0.0000 0.913 0.000 0.000 1.000
#> GSM78522 3 0.0000 0.913 0.000 0.000 1.000
#> GSM78525 3 0.0000 0.913 0.000 0.000 1.000
#> GSM78528 3 0.0000 0.913 0.000 0.000 1.000
#> GSM78531 1 0.4796 0.819 0.780 0.000 0.220
#> GSM78533 3 0.0000 0.913 0.000 0.000 1.000
#> GSM78536 1 0.4750 0.822 0.784 0.000 0.216
#> GSM78541 1 0.4750 0.822 0.784 0.000 0.216
#> GSM78547 3 0.5016 0.679 0.240 0.000 0.760
#> GSM78552 3 0.5016 0.679 0.240 0.000 0.760
#> GSM78556 3 0.5016 0.679 0.240 0.000 0.760
#> GSM78559 1 0.4750 0.822 0.784 0.000 0.216
#> GSM78564 3 0.5178 0.648 0.256 0.000 0.744
#> GSM42999 2 0.0000 0.888 0.000 1.000 0.000
#> GSM43001 2 0.0000 0.888 0.000 1.000 0.000
#> GSM43003 2 0.0000 0.888 0.000 1.000 0.000
#> GSM43006 2 0.0000 0.888 0.000 1.000 0.000
#> GSM43009 2 0.0000 0.888 0.000 1.000 0.000
#> GSM43012 2 0.0000 0.888 0.000 1.000 0.000
#> GSM78524 2 0.6244 0.408 0.440 0.560 0.000
#> GSM78527 2 0.0000 0.888 0.000 1.000 0.000
#> GSM78530 2 0.4452 0.837 0.192 0.808 0.000
#> GSM78535 1 0.3941 0.694 0.844 0.156 0.000
#> GSM78538 2 0.4452 0.837 0.192 0.808 0.000
#> GSM78542 2 0.4452 0.837 0.192 0.808 0.000
#> GSM78544 2 0.4452 0.837 0.192 0.808 0.000
#> GSM78549 2 0.0237 0.887 0.004 0.996 0.000
#> GSM78553 2 0.4452 0.837 0.192 0.808 0.000
#> GSM78558 2 0.4452 0.837 0.192 0.808 0.000
#> GSM78561 2 0.0000 0.888 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM78539 4 0.0000 0.685 0.000 0.000 0.000 1.000
#> GSM78545 4 0.3528 0.586 0.000 0.000 0.192 0.808
#> GSM78550 4 0.2530 0.683 0.000 0.000 0.112 0.888
#> GSM78554 4 0.2408 0.688 0.000 0.000 0.104 0.896
#> GSM78562 4 0.0188 0.683 0.004 0.000 0.000 0.996
#> GSM78540 4 0.0000 0.685 0.000 0.000 0.000 1.000
#> GSM78546 4 0.2149 0.691 0.000 0.000 0.088 0.912
#> GSM78551 4 0.2530 0.683 0.000 0.000 0.112 0.888
#> GSM78555 4 0.0188 0.683 0.004 0.000 0.000 0.996
#> GSM78563 4 0.0188 0.683 0.004 0.000 0.000 0.996
#> GSM43005 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM43008 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM43011 3 0.1792 0.860 0.068 0.000 0.932 0.000
#> GSM78523 3 0.1792 0.860 0.068 0.000 0.932 0.000
#> GSM78526 3 0.1792 0.860 0.068 0.000 0.932 0.000
#> GSM78529 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM78532 4 0.3791 0.736 0.004 0.000 0.200 0.796
#> GSM78534 3 0.1792 0.860 0.068 0.000 0.932 0.000
#> GSM78537 4 0.4019 0.737 0.012 0.000 0.196 0.792
#> GSM78543 4 0.4194 0.719 0.008 0.000 0.228 0.764
#> GSM78548 3 0.3444 0.722 0.000 0.000 0.816 0.184
#> GSM78557 3 0.4103 0.633 0.000 0.000 0.744 0.256
#> GSM78560 4 0.4428 0.676 0.004 0.000 0.276 0.720
#> GSM78565 4 0.4019 0.737 0.012 0.000 0.196 0.792
#> GSM43000 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM43002 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM43004 3 0.1792 0.860 0.068 0.000 0.932 0.000
#> GSM43007 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM43010 3 0.1792 0.860 0.068 0.000 0.932 0.000
#> GSM78522 3 0.1792 0.860 0.068 0.000 0.932 0.000
#> GSM78525 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM78528 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM78531 4 0.3791 0.736 0.004 0.000 0.200 0.796
#> GSM78533 3 0.1792 0.860 0.068 0.000 0.932 0.000
#> GSM78536 4 0.4019 0.737 0.012 0.000 0.196 0.792
#> GSM78541 4 0.4019 0.737 0.012 0.000 0.196 0.792
#> GSM78547 3 0.4103 0.633 0.000 0.000 0.744 0.256
#> GSM78552 3 0.4103 0.633 0.000 0.000 0.744 0.256
#> GSM78556 3 0.4103 0.633 0.000 0.000 0.744 0.256
#> GSM78559 4 0.4019 0.737 0.012 0.000 0.196 0.792
#> GSM78564 3 0.4222 0.605 0.000 0.000 0.728 0.272
#> GSM42999 2 0.0000 0.839 0.000 1.000 0.000 0.000
#> GSM43001 2 0.4103 0.630 0.256 0.744 0.000 0.000
#> GSM43003 2 0.0000 0.839 0.000 1.000 0.000 0.000
#> GSM43006 2 0.0000 0.839 0.000 1.000 0.000 0.000
#> GSM43009 2 0.0000 0.839 0.000 1.000 0.000 0.000
#> GSM43012 2 0.0000 0.839 0.000 1.000 0.000 0.000
#> GSM78524 2 0.6757 0.385 0.376 0.524 0.000 0.100
#> GSM78527 2 0.0000 0.839 0.000 1.000 0.000 0.000
#> GSM78530 2 0.4482 0.802 0.128 0.804 0.000 0.068
#> GSM78535 1 0.4543 0.000 0.676 0.000 0.000 0.324
#> GSM78538 2 0.4482 0.802 0.128 0.804 0.000 0.068
#> GSM78542 2 0.4482 0.802 0.128 0.804 0.000 0.068
#> GSM78544 2 0.4482 0.802 0.128 0.804 0.000 0.068
#> GSM78549 2 0.0188 0.839 0.004 0.996 0.000 0.000
#> GSM78553 2 0.4482 0.802 0.128 0.804 0.000 0.068
#> GSM78558 2 0.4482 0.802 0.128 0.804 0.000 0.068
#> GSM78561 2 0.4103 0.630 0.256 0.744 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM78539 4 0.0162 0.708 0.000 0.000 0.000 0.996 0.004
#> GSM78545 4 0.3282 0.619 0.000 0.000 0.188 0.804 0.008
#> GSM78550 4 0.2338 0.689 0.000 0.000 0.112 0.884 0.004
#> GSM78554 4 0.2233 0.693 0.000 0.000 0.104 0.892 0.004
#> GSM78562 4 0.0162 0.708 0.000 0.000 0.000 0.996 0.004
#> GSM78540 4 0.0162 0.708 0.000 0.000 0.000 0.996 0.004
#> GSM78546 4 0.2011 0.698 0.000 0.000 0.088 0.908 0.004
#> GSM78551 4 0.2338 0.689 0.000 0.000 0.112 0.884 0.004
#> GSM78555 4 0.0162 0.708 0.000 0.000 0.000 0.996 0.004
#> GSM78563 4 0.0162 0.708 0.000 0.000 0.000 0.996 0.004
#> GSM43005 3 0.0162 0.823 0.000 0.000 0.996 0.000 0.004
#> GSM43008 3 0.0000 0.824 0.000 0.000 1.000 0.000 0.000
#> GSM43011 3 0.2813 0.792 0.000 0.000 0.832 0.000 0.168
#> GSM78523 3 0.2813 0.792 0.000 0.000 0.832 0.000 0.168
#> GSM78526 3 0.2813 0.792 0.000 0.000 0.832 0.000 0.168
#> GSM78529 3 0.0162 0.823 0.000 0.000 0.996 0.000 0.004
#> GSM78532 4 0.5399 0.721 0.000 0.000 0.188 0.664 0.148
#> GSM78534 3 0.2813 0.792 0.000 0.000 0.832 0.000 0.168
#> GSM78537 4 0.5440 0.722 0.000 0.000 0.184 0.660 0.156
#> GSM78543 4 0.5638 0.710 0.000 0.000 0.216 0.632 0.152
#> GSM78548 3 0.3513 0.669 0.000 0.000 0.800 0.180 0.020
#> GSM78557 3 0.4114 0.577 0.000 0.000 0.732 0.244 0.024
#> GSM78560 4 0.5882 0.679 0.000 0.000 0.264 0.588 0.148
#> GSM78565 4 0.5440 0.722 0.000 0.000 0.184 0.660 0.156
#> GSM43000 3 0.0000 0.824 0.000 0.000 1.000 0.000 0.000
#> GSM43002 3 0.0000 0.824 0.000 0.000 1.000 0.000 0.000
#> GSM43004 3 0.2773 0.792 0.000 0.000 0.836 0.000 0.164
#> GSM43007 3 0.0000 0.824 0.000 0.000 1.000 0.000 0.000
#> GSM43010 3 0.2813 0.792 0.000 0.000 0.832 0.000 0.168
#> GSM78522 3 0.2813 0.792 0.000 0.000 0.832 0.000 0.168
#> GSM78525 3 0.0000 0.824 0.000 0.000 1.000 0.000 0.000
#> GSM78528 3 0.0162 0.823 0.000 0.000 0.996 0.000 0.004
#> GSM78531 4 0.5399 0.721 0.000 0.000 0.188 0.664 0.148
#> GSM78533 3 0.2813 0.792 0.000 0.000 0.832 0.000 0.168
#> GSM78536 4 0.5440 0.722 0.000 0.000 0.184 0.660 0.156
#> GSM78541 4 0.5440 0.722 0.000 0.000 0.184 0.660 0.156
#> GSM78547 3 0.4114 0.577 0.000 0.000 0.732 0.244 0.024
#> GSM78552 3 0.4114 0.577 0.000 0.000 0.732 0.244 0.024
#> GSM78556 3 0.4114 0.577 0.000 0.000 0.732 0.244 0.024
#> GSM78559 4 0.5440 0.722 0.000 0.000 0.184 0.660 0.156
#> GSM78564 3 0.4276 0.551 0.000 0.000 0.716 0.256 0.028
#> GSM42999 2 0.3074 0.840 0.196 0.804 0.000 0.000 0.000
#> GSM43001 1 0.0404 1.000 0.988 0.012 0.000 0.000 0.000
#> GSM43003 2 0.3074 0.840 0.196 0.804 0.000 0.000 0.000
#> GSM43006 2 0.3336 0.812 0.228 0.772 0.000 0.000 0.000
#> GSM43009 2 0.3074 0.840 0.196 0.804 0.000 0.000 0.000
#> GSM43012 2 0.3074 0.840 0.196 0.804 0.000 0.000 0.000
#> GSM78524 2 0.4121 0.370 0.004 0.720 0.000 0.012 0.264
#> GSM78527 2 0.3074 0.840 0.196 0.804 0.000 0.000 0.000
#> GSM78530 2 0.0000 0.828 0.000 1.000 0.000 0.000 0.000
#> GSM78535 5 0.4042 0.000 0.012 0.196 0.000 0.020 0.772
#> GSM78538 2 0.0000 0.828 0.000 1.000 0.000 0.000 0.000
#> GSM78542 2 0.0000 0.828 0.000 1.000 0.000 0.000 0.000
#> GSM78544 2 0.0000 0.828 0.000 1.000 0.000 0.000 0.000
#> GSM78549 2 0.3039 0.840 0.192 0.808 0.000 0.000 0.000
#> GSM78553 2 0.0000 0.828 0.000 1.000 0.000 0.000 0.000
#> GSM78558 2 0.0000 0.828 0.000 1.000 0.000 0.000 0.000
#> GSM78561 1 0.0404 1.000 0.988 0.012 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM78539 4 0.3620 0.876 0.352 0.000 0.000 0.648 0.000 0.000
#> GSM78545 4 0.5392 0.777 0.224 0.000 0.192 0.584 0.000 0.000
#> GSM78550 4 0.4849 0.862 0.240 0.000 0.112 0.648 0.000 0.000
#> GSM78554 4 0.5019 0.838 0.292 0.000 0.104 0.604 0.000 0.000
#> GSM78562 4 0.3647 0.873 0.360 0.000 0.000 0.640 0.000 0.000
#> GSM78540 4 0.3620 0.876 0.352 0.000 0.000 0.648 0.000 0.000
#> GSM78546 4 0.4725 0.871 0.264 0.000 0.088 0.648 0.000 0.000
#> GSM78551 4 0.4849 0.862 0.240 0.000 0.112 0.648 0.000 0.000
#> GSM78555 4 0.3647 0.873 0.360 0.000 0.000 0.640 0.000 0.000
#> GSM78563 4 0.3647 0.873 0.360 0.000 0.000 0.640 0.000 0.000
#> GSM43005 3 0.0000 0.626 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM43008 3 0.0146 0.630 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM43011 6 0.3838 0.734 0.000 0.000 0.448 0.000 0.000 0.552
#> GSM78523 6 0.3838 0.734 0.000 0.000 0.448 0.000 0.000 0.552
#> GSM78526 6 0.3838 0.734 0.000 0.000 0.448 0.000 0.000 0.552
#> GSM78529 3 0.0000 0.626 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM78532 1 0.0291 0.966 0.992 0.000 0.004 0.004 0.000 0.000
#> GSM78534 6 0.3966 0.732 0.004 0.000 0.444 0.000 0.000 0.552
#> GSM78537 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78543 1 0.0935 0.931 0.964 0.000 0.032 0.004 0.000 0.000
#> GSM78548 3 0.3728 0.583 0.344 0.000 0.652 0.004 0.000 0.000
#> GSM78557 3 0.3930 0.511 0.420 0.000 0.576 0.004 0.000 0.000
#> GSM78560 1 0.1700 0.852 0.916 0.000 0.080 0.004 0.000 0.000
#> GSM78565 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM43000 3 0.0858 0.643 0.028 0.000 0.968 0.000 0.000 0.004
#> GSM43002 3 0.0713 0.645 0.028 0.000 0.972 0.000 0.000 0.000
#> GSM43004 6 0.4482 0.694 0.032 0.000 0.416 0.000 0.000 0.552
#> GSM43007 3 0.0146 0.630 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM43010 6 0.3838 0.734 0.000 0.000 0.448 0.000 0.000 0.552
#> GSM78522 6 0.3966 0.732 0.004 0.000 0.444 0.000 0.000 0.552
#> GSM78525 3 0.0713 0.645 0.028 0.000 0.972 0.000 0.000 0.000
#> GSM78528 3 0.0000 0.626 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM78531 1 0.0291 0.966 0.992 0.000 0.004 0.004 0.000 0.000
#> GSM78533 6 0.3838 0.734 0.000 0.000 0.448 0.000 0.000 0.552
#> GSM78536 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78541 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78547 3 0.3930 0.511 0.420 0.000 0.576 0.004 0.000 0.000
#> GSM78552 3 0.3930 0.511 0.420 0.000 0.576 0.004 0.000 0.000
#> GSM78556 3 0.3930 0.511 0.420 0.000 0.576 0.004 0.000 0.000
#> GSM78559 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78564 3 0.3955 0.478 0.436 0.000 0.560 0.004 0.000 0.000
#> GSM42999 2 0.0000 0.851 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43001 6 0.6628 -0.371 0.000 0.104 0.000 0.352 0.096 0.448
#> GSM43003 2 0.0000 0.851 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43006 2 0.0790 0.827 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM43009 2 0.0000 0.851 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43012 2 0.0000 0.851 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78524 2 0.3862 0.375 0.000 0.524 0.000 0.000 0.476 0.000
#> GSM78527 2 0.0000 0.851 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78530 2 0.2762 0.835 0.000 0.804 0.000 0.000 0.196 0.000
#> GSM78535 5 0.1765 0.000 0.096 0.000 0.000 0.000 0.904 0.000
#> GSM78538 2 0.2762 0.835 0.000 0.804 0.000 0.000 0.196 0.000
#> GSM78542 2 0.2762 0.835 0.000 0.804 0.000 0.000 0.196 0.000
#> GSM78544 2 0.2762 0.835 0.000 0.804 0.000 0.000 0.196 0.000
#> GSM78549 2 0.0146 0.851 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM78553 2 0.2762 0.835 0.000 0.804 0.000 0.000 0.196 0.000
#> GSM78558 2 0.2762 0.835 0.000 0.804 0.000 0.000 0.196 0.000
#> GSM78561 6 0.6628 -0.371 0.000 0.104 0.000 0.352 0.096 0.448
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) agent(p) individual(p) k
#> MAD:hclust 57 4.70e-12 0.00409 0.9975 2
#> MAD:hclust 57 5.24e-15 0.00507 0.4768 3
#> MAD:hclust 56 7.83e-16 0.00380 0.5580 4
#> MAD:hclust 56 1.55e-14 0.01096 0.4510 5
#> MAD:hclust 53 2.52e-19 0.03434 0.0472 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "kmeans"]
# you can also extract it by
# res = res_list["MAD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 58 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4222 0.578 0.578
#> 3 3 0.639 0.894 0.867 0.4783 0.758 0.582
#> 4 4 0.683 0.893 0.830 0.1591 0.891 0.685
#> 5 5 0.775 0.688 0.733 0.0756 0.956 0.831
#> 6 6 0.863 0.895 0.854 0.0535 0.912 0.624
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM78539 1 0 1 1 0
#> GSM78545 1 0 1 1 0
#> GSM78550 1 0 1 1 0
#> GSM78554 1 0 1 1 0
#> GSM78562 1 0 1 1 0
#> GSM78540 1 0 1 1 0
#> GSM78546 1 0 1 1 0
#> GSM78551 1 0 1 1 0
#> GSM78555 1 0 1 1 0
#> GSM78563 1 0 1 1 0
#> GSM43005 1 0 1 1 0
#> GSM43008 1 0 1 1 0
#> GSM43011 1 0 1 1 0
#> GSM78523 1 0 1 1 0
#> GSM78526 1 0 1 1 0
#> GSM78529 1 0 1 1 0
#> GSM78532 1 0 1 1 0
#> GSM78534 1 0 1 1 0
#> GSM78537 1 0 1 1 0
#> GSM78543 1 0 1 1 0
#> GSM78548 1 0 1 1 0
#> GSM78557 1 0 1 1 0
#> GSM78560 1 0 1 1 0
#> GSM78565 1 0 1 1 0
#> GSM43000 1 0 1 1 0
#> GSM43002 1 0 1 1 0
#> GSM43004 1 0 1 1 0
#> GSM43007 1 0 1 1 0
#> GSM43010 1 0 1 1 0
#> GSM78522 1 0 1 1 0
#> GSM78525 1 0 1 1 0
#> GSM78528 1 0 1 1 0
#> GSM78531 1 0 1 1 0
#> GSM78533 1 0 1 1 0
#> GSM78536 1 0 1 1 0
#> GSM78541 1 0 1 1 0
#> GSM78547 1 0 1 1 0
#> GSM78552 1 0 1 1 0
#> GSM78556 1 0 1 1 0
#> GSM78559 1 0 1 1 0
#> GSM78564 1 0 1 1 0
#> GSM42999 2 0 1 0 1
#> GSM43001 2 0 1 0 1
#> GSM43003 2 0 1 0 1
#> GSM43006 2 0 1 0 1
#> GSM43009 2 0 1 0 1
#> GSM43012 2 0 1 0 1
#> GSM78524 2 0 1 0 1
#> GSM78527 2 0 1 0 1
#> GSM78530 2 0 1 0 1
#> GSM78535 2 0 1 0 1
#> GSM78538 2 0 1 0 1
#> GSM78542 2 0 1 0 1
#> GSM78544 2 0 1 0 1
#> GSM78549 2 0 1 0 1
#> GSM78553 2 0 1 0 1
#> GSM78558 2 0 1 0 1
#> GSM78561 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM78539 1 0.4842 0.801 0.776 0.000 0.224
#> GSM78545 1 0.4842 0.801 0.776 0.000 0.224
#> GSM78550 1 0.4842 0.801 0.776 0.000 0.224
#> GSM78554 1 0.4842 0.801 0.776 0.000 0.224
#> GSM78562 1 0.4842 0.801 0.776 0.000 0.224
#> GSM78540 1 0.4842 0.801 0.776 0.000 0.224
#> GSM78546 1 0.4842 0.801 0.776 0.000 0.224
#> GSM78551 1 0.4842 0.801 0.776 0.000 0.224
#> GSM78555 1 0.4842 0.801 0.776 0.000 0.224
#> GSM78563 1 0.4842 0.801 0.776 0.000 0.224
#> GSM43005 3 0.5926 0.995 0.356 0.000 0.644
#> GSM43008 3 0.5926 0.995 0.356 0.000 0.644
#> GSM43011 3 0.5926 0.995 0.356 0.000 0.644
#> GSM78523 3 0.5926 0.995 0.356 0.000 0.644
#> GSM78526 3 0.5968 0.992 0.364 0.000 0.636
#> GSM78529 3 0.5926 0.995 0.356 0.000 0.644
#> GSM78532 1 0.0000 0.836 1.000 0.000 0.000
#> GSM78534 3 0.5968 0.992 0.364 0.000 0.636
#> GSM78537 1 0.0000 0.836 1.000 0.000 0.000
#> GSM78543 1 0.0000 0.836 1.000 0.000 0.000
#> GSM78548 1 0.4235 0.518 0.824 0.000 0.176
#> GSM78557 1 0.0000 0.836 1.000 0.000 0.000
#> GSM78560 1 0.0000 0.836 1.000 0.000 0.000
#> GSM78565 1 0.0000 0.836 1.000 0.000 0.000
#> GSM43000 3 0.5926 0.995 0.356 0.000 0.644
#> GSM43002 3 0.5926 0.995 0.356 0.000 0.644
#> GSM43004 3 0.5968 0.992 0.364 0.000 0.636
#> GSM43007 3 0.5926 0.995 0.356 0.000 0.644
#> GSM43010 3 0.5968 0.992 0.364 0.000 0.636
#> GSM78522 3 0.5968 0.992 0.364 0.000 0.636
#> GSM78525 3 0.5926 0.995 0.356 0.000 0.644
#> GSM78528 3 0.5926 0.995 0.356 0.000 0.644
#> GSM78531 1 0.0000 0.836 1.000 0.000 0.000
#> GSM78533 3 0.5968 0.992 0.364 0.000 0.636
#> GSM78536 1 0.0000 0.836 1.000 0.000 0.000
#> GSM78541 1 0.0000 0.836 1.000 0.000 0.000
#> GSM78547 1 0.0000 0.836 1.000 0.000 0.000
#> GSM78552 1 0.3267 0.662 0.884 0.000 0.116
#> GSM78556 1 0.0000 0.836 1.000 0.000 0.000
#> GSM78559 1 0.0000 0.836 1.000 0.000 0.000
#> GSM78564 1 0.0000 0.836 1.000 0.000 0.000
#> GSM42999 2 0.2878 0.950 0.000 0.904 0.096
#> GSM43001 2 0.3619 0.940 0.000 0.864 0.136
#> GSM43003 2 0.2878 0.950 0.000 0.904 0.096
#> GSM43006 2 0.3619 0.940 0.000 0.864 0.136
#> GSM43009 2 0.2878 0.950 0.000 0.904 0.096
#> GSM43012 2 0.3267 0.945 0.000 0.884 0.116
#> GSM78524 2 0.0237 0.944 0.000 0.996 0.004
#> GSM78527 2 0.2878 0.950 0.000 0.904 0.096
#> GSM78530 2 0.0000 0.945 0.000 1.000 0.000
#> GSM78535 2 0.4575 0.747 0.184 0.812 0.004
#> GSM78538 2 0.0000 0.945 0.000 1.000 0.000
#> GSM78542 2 0.0000 0.945 0.000 1.000 0.000
#> GSM78544 2 0.0000 0.945 0.000 1.000 0.000
#> GSM78549 2 0.2878 0.950 0.000 0.904 0.096
#> GSM78553 2 0.0000 0.945 0.000 1.000 0.000
#> GSM78558 2 0.0237 0.944 0.000 0.996 0.004
#> GSM78561 2 0.3619 0.940 0.000 0.864 0.136
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM78539 4 0.5510 0.971 0.376 0.000 0.024 0.600
#> GSM78545 4 0.5384 0.906 0.324 0.000 0.028 0.648
#> GSM78550 4 0.5311 0.912 0.328 0.000 0.024 0.648
#> GSM78554 4 0.5510 0.970 0.376 0.000 0.024 0.600
#> GSM78562 4 0.5510 0.971 0.376 0.000 0.024 0.600
#> GSM78540 4 0.5510 0.971 0.376 0.000 0.024 0.600
#> GSM78546 4 0.5496 0.971 0.372 0.000 0.024 0.604
#> GSM78551 4 0.5510 0.970 0.376 0.000 0.024 0.600
#> GSM78555 4 0.5548 0.953 0.388 0.000 0.024 0.588
#> GSM78563 4 0.5510 0.971 0.376 0.000 0.024 0.600
#> GSM43005 3 0.2053 0.913 0.004 0.000 0.924 0.072
#> GSM43008 3 0.2053 0.913 0.004 0.000 0.924 0.072
#> GSM43011 3 0.1743 0.913 0.004 0.000 0.940 0.056
#> GSM78523 3 0.1743 0.913 0.004 0.000 0.940 0.056
#> GSM78526 3 0.1890 0.913 0.008 0.000 0.936 0.056
#> GSM78529 3 0.2053 0.913 0.004 0.000 0.924 0.072
#> GSM78532 1 0.2469 0.955 0.892 0.000 0.108 0.000
#> GSM78534 3 0.1890 0.913 0.008 0.000 0.936 0.056
#> GSM78537 1 0.2593 0.953 0.892 0.000 0.104 0.004
#> GSM78543 1 0.2593 0.953 0.892 0.000 0.104 0.004
#> GSM78548 3 0.5464 0.552 0.228 0.000 0.708 0.064
#> GSM78557 1 0.2469 0.955 0.892 0.000 0.108 0.000
#> GSM78560 1 0.2469 0.955 0.892 0.000 0.108 0.000
#> GSM78565 1 0.2593 0.953 0.892 0.000 0.104 0.004
#> GSM43000 3 0.1576 0.917 0.004 0.000 0.948 0.048
#> GSM43002 3 0.1824 0.915 0.004 0.000 0.936 0.060
#> GSM43004 3 0.3533 0.856 0.080 0.000 0.864 0.056
#> GSM43007 3 0.2053 0.913 0.004 0.000 0.924 0.072
#> GSM43010 3 0.1890 0.913 0.008 0.000 0.936 0.056
#> GSM78522 3 0.1890 0.913 0.008 0.000 0.936 0.056
#> GSM78525 3 0.1824 0.915 0.004 0.000 0.936 0.060
#> GSM78528 3 0.2053 0.913 0.004 0.000 0.924 0.072
#> GSM78531 1 0.2469 0.955 0.892 0.000 0.108 0.000
#> GSM78533 3 0.1890 0.913 0.008 0.000 0.936 0.056
#> GSM78536 1 0.2593 0.953 0.892 0.000 0.104 0.004
#> GSM78541 1 0.2593 0.953 0.892 0.000 0.104 0.004
#> GSM78547 1 0.2469 0.955 0.892 0.000 0.108 0.000
#> GSM78552 1 0.6089 0.490 0.608 0.000 0.328 0.064
#> GSM78556 1 0.2469 0.955 0.892 0.000 0.108 0.000
#> GSM78559 1 0.2593 0.953 0.892 0.000 0.104 0.004
#> GSM78564 1 0.2469 0.955 0.892 0.000 0.108 0.000
#> GSM42999 2 0.5184 0.863 0.060 0.736 0.000 0.204
#> GSM43001 2 0.6248 0.833 0.100 0.640 0.000 0.260
#> GSM43003 2 0.5429 0.860 0.072 0.720 0.000 0.208
#> GSM43006 2 0.6124 0.834 0.084 0.640 0.000 0.276
#> GSM43009 2 0.5184 0.863 0.060 0.736 0.000 0.204
#> GSM43012 2 0.5820 0.850 0.084 0.684 0.000 0.232
#> GSM78524 2 0.0469 0.847 0.000 0.988 0.000 0.012
#> GSM78527 2 0.5429 0.860 0.072 0.720 0.000 0.208
#> GSM78530 2 0.0000 0.849 0.000 1.000 0.000 0.000
#> GSM78535 2 0.3933 0.648 0.200 0.792 0.000 0.008
#> GSM78538 2 0.0000 0.849 0.000 1.000 0.000 0.000
#> GSM78542 2 0.0000 0.849 0.000 1.000 0.000 0.000
#> GSM78544 2 0.0000 0.849 0.000 1.000 0.000 0.000
#> GSM78549 2 0.5325 0.862 0.068 0.728 0.000 0.204
#> GSM78553 2 0.0000 0.849 0.000 1.000 0.000 0.000
#> GSM78558 2 0.0336 0.846 0.000 0.992 0.000 0.008
#> GSM78561 2 0.6248 0.833 0.100 0.640 0.000 0.260
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM78539 4 0.3336 0.983 0.228 0.000 0.000 0.772 0.000
#> GSM78545 4 0.4338 0.943 0.192 0.000 0.036 0.760 0.012
#> GSM78550 4 0.4295 0.949 0.196 0.000 0.032 0.760 0.012
#> GSM78554 4 0.3720 0.978 0.228 0.000 0.000 0.760 0.012
#> GSM78562 4 0.3366 0.980 0.232 0.000 0.000 0.768 0.000
#> GSM78540 4 0.3336 0.983 0.228 0.000 0.000 0.772 0.000
#> GSM78546 4 0.3336 0.983 0.228 0.000 0.000 0.772 0.000
#> GSM78551 4 0.3336 0.983 0.228 0.000 0.000 0.772 0.000
#> GSM78555 4 0.3424 0.971 0.240 0.000 0.000 0.760 0.000
#> GSM78563 4 0.3336 0.983 0.228 0.000 0.000 0.772 0.000
#> GSM43005 3 0.1597 0.730 0.048 0.000 0.940 0.012 0.000
#> GSM43008 3 0.1597 0.730 0.048 0.000 0.940 0.012 0.000
#> GSM43011 3 0.6021 0.688 0.024 0.000 0.504 0.060 0.412
#> GSM78523 3 0.6021 0.688 0.024 0.000 0.504 0.060 0.412
#> GSM78526 3 0.6021 0.688 0.024 0.000 0.504 0.060 0.412
#> GSM78529 3 0.1597 0.730 0.048 0.000 0.940 0.012 0.000
#> GSM78532 1 0.0671 0.971 0.980 0.000 0.004 0.000 0.016
#> GSM78534 3 0.6118 0.687 0.024 0.000 0.500 0.068 0.408
#> GSM78537 1 0.0898 0.970 0.972 0.000 0.000 0.008 0.020
#> GSM78543 1 0.0898 0.970 0.972 0.000 0.000 0.008 0.020
#> GSM78548 3 0.3711 0.638 0.136 0.000 0.820 0.012 0.032
#> GSM78557 1 0.0671 0.971 0.980 0.000 0.004 0.000 0.016
#> GSM78560 1 0.0771 0.969 0.976 0.000 0.004 0.000 0.020
#> GSM78565 1 0.0992 0.969 0.968 0.000 0.000 0.008 0.024
#> GSM43000 3 0.0703 0.730 0.024 0.000 0.976 0.000 0.000
#> GSM43002 3 0.1197 0.731 0.048 0.000 0.952 0.000 0.000
#> GSM43004 3 0.6860 0.654 0.076 0.000 0.448 0.068 0.408
#> GSM43007 3 0.1597 0.730 0.048 0.000 0.940 0.012 0.000
#> GSM43010 3 0.6021 0.688 0.024 0.000 0.504 0.060 0.412
#> GSM78522 3 0.6118 0.687 0.024 0.000 0.500 0.068 0.408
#> GSM78525 3 0.1043 0.731 0.040 0.000 0.960 0.000 0.000
#> GSM78528 3 0.1597 0.730 0.048 0.000 0.940 0.012 0.000
#> GSM78531 1 0.0671 0.971 0.980 0.000 0.004 0.000 0.016
#> GSM78533 3 0.6021 0.688 0.024 0.000 0.504 0.060 0.412
#> GSM78536 1 0.0992 0.969 0.968 0.000 0.000 0.008 0.024
#> GSM78541 1 0.0992 0.969 0.968 0.000 0.000 0.008 0.024
#> GSM78547 1 0.0671 0.971 0.980 0.000 0.004 0.000 0.016
#> GSM78552 3 0.4985 0.178 0.392 0.000 0.580 0.012 0.016
#> GSM78556 1 0.0671 0.971 0.980 0.000 0.004 0.000 0.016
#> GSM78559 1 0.0992 0.969 0.968 0.000 0.000 0.008 0.024
#> GSM78564 1 0.0451 0.972 0.988 0.000 0.004 0.000 0.008
#> GSM42999 2 0.4264 -0.140 0.000 0.620 0.000 0.004 0.376
#> GSM43001 5 0.6474 0.921 0.000 0.424 0.012 0.128 0.436
#> GSM43003 2 0.4321 -0.215 0.000 0.600 0.000 0.004 0.396
#> GSM43006 5 0.5483 0.838 0.000 0.424 0.000 0.064 0.512
#> GSM43009 2 0.4264 -0.140 0.000 0.620 0.000 0.004 0.376
#> GSM43012 2 0.5436 -0.664 0.000 0.492 0.004 0.048 0.456
#> GSM78524 2 0.1682 0.544 0.000 0.944 0.012 0.032 0.012
#> GSM78527 2 0.4321 -0.215 0.000 0.600 0.000 0.004 0.396
#> GSM78530 2 0.0000 0.577 0.000 1.000 0.000 0.000 0.000
#> GSM78535 2 0.4059 0.324 0.148 0.804 0.008 0.020 0.020
#> GSM78538 2 0.0000 0.577 0.000 1.000 0.000 0.000 0.000
#> GSM78542 2 0.0000 0.577 0.000 1.000 0.000 0.000 0.000
#> GSM78544 2 0.0000 0.577 0.000 1.000 0.000 0.000 0.000
#> GSM78549 2 0.4150 -0.176 0.000 0.612 0.000 0.000 0.388
#> GSM78553 2 0.0000 0.577 0.000 1.000 0.000 0.000 0.000
#> GSM78558 2 0.0000 0.577 0.000 1.000 0.000 0.000 0.000
#> GSM78561 5 0.6474 0.921 0.000 0.424 0.012 0.128 0.436
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM78539 4 0.2121 0.980 0.096 0.012 0.000 0.892 0.000 0.000
#> GSM78545 4 0.3370 0.948 0.072 0.032 0.024 0.852 0.000 0.020
#> GSM78550 4 0.3343 0.952 0.076 0.032 0.020 0.852 0.000 0.020
#> GSM78554 4 0.2994 0.967 0.096 0.028 0.000 0.856 0.000 0.020
#> GSM78562 4 0.2121 0.980 0.096 0.012 0.000 0.892 0.000 0.000
#> GSM78540 4 0.1765 0.981 0.096 0.000 0.000 0.904 0.000 0.000
#> GSM78546 4 0.1765 0.981 0.096 0.000 0.000 0.904 0.000 0.000
#> GSM78551 4 0.1908 0.980 0.096 0.000 0.000 0.900 0.000 0.004
#> GSM78555 4 0.1765 0.981 0.096 0.000 0.000 0.904 0.000 0.000
#> GSM78563 4 0.1765 0.981 0.096 0.000 0.000 0.904 0.000 0.000
#> GSM43005 3 0.0291 0.908 0.004 0.004 0.992 0.000 0.000 0.000
#> GSM43008 3 0.0405 0.906 0.004 0.008 0.988 0.000 0.000 0.000
#> GSM43011 6 0.3567 0.966 0.004 0.004 0.252 0.004 0.000 0.736
#> GSM78523 6 0.3567 0.966 0.004 0.004 0.252 0.004 0.000 0.736
#> GSM78526 6 0.3429 0.967 0.004 0.000 0.252 0.004 0.000 0.740
#> GSM78529 3 0.0291 0.908 0.004 0.004 0.992 0.000 0.000 0.000
#> GSM78532 1 0.0458 0.950 0.984 0.016 0.000 0.000 0.000 0.000
#> GSM78534 6 0.4420 0.951 0.004 0.048 0.252 0.004 0.000 0.692
#> GSM78537 1 0.1225 0.950 0.952 0.036 0.000 0.000 0.000 0.012
#> GSM78543 1 0.1225 0.950 0.952 0.036 0.000 0.000 0.000 0.012
#> GSM78548 3 0.4041 0.736 0.108 0.076 0.788 0.000 0.000 0.028
#> GSM78557 1 0.1297 0.941 0.948 0.040 0.000 0.000 0.000 0.012
#> GSM78560 1 0.1010 0.946 0.960 0.036 0.000 0.000 0.000 0.004
#> GSM78565 1 0.1686 0.942 0.924 0.064 0.000 0.000 0.000 0.012
#> GSM43000 3 0.1363 0.882 0.004 0.012 0.952 0.004 0.000 0.028
#> GSM43002 3 0.0508 0.906 0.004 0.012 0.984 0.000 0.000 0.000
#> GSM43004 6 0.5217 0.892 0.048 0.060 0.216 0.004 0.000 0.672
#> GSM43007 3 0.0405 0.906 0.004 0.008 0.988 0.000 0.000 0.000
#> GSM43010 6 0.3290 0.968 0.004 0.000 0.252 0.000 0.000 0.744
#> GSM78522 6 0.4360 0.953 0.004 0.044 0.252 0.004 0.000 0.696
#> GSM78525 3 0.0508 0.906 0.004 0.012 0.984 0.000 0.000 0.000
#> GSM78528 3 0.0291 0.908 0.004 0.004 0.992 0.000 0.000 0.000
#> GSM78531 1 0.0458 0.950 0.984 0.016 0.000 0.000 0.000 0.000
#> GSM78533 6 0.3290 0.968 0.004 0.000 0.252 0.000 0.000 0.744
#> GSM78536 1 0.1625 0.943 0.928 0.060 0.000 0.000 0.000 0.012
#> GSM78541 1 0.1625 0.943 0.928 0.060 0.000 0.000 0.000 0.012
#> GSM78547 1 0.1297 0.941 0.948 0.040 0.000 0.000 0.000 0.012
#> GSM78552 3 0.5080 0.572 0.244 0.072 0.656 0.000 0.000 0.028
#> GSM78556 1 0.1297 0.941 0.948 0.040 0.000 0.000 0.000 0.012
#> GSM78559 1 0.1625 0.943 0.928 0.060 0.000 0.000 0.000 0.012
#> GSM78564 1 0.1528 0.939 0.936 0.048 0.000 0.000 0.000 0.016
#> GSM42999 2 0.4504 0.769 0.000 0.536 0.000 0.000 0.432 0.032
#> GSM43001 2 0.5463 0.687 0.000 0.652 0.004 0.064 0.220 0.060
#> GSM43003 2 0.4123 0.787 0.000 0.568 0.000 0.000 0.420 0.012
#> GSM43006 2 0.3426 0.739 0.000 0.764 0.000 0.004 0.220 0.012
#> GSM43009 2 0.4513 0.761 0.000 0.528 0.000 0.000 0.440 0.032
#> GSM43012 2 0.4522 0.771 0.000 0.648 0.000 0.004 0.300 0.048
#> GSM78524 5 0.3222 0.805 0.000 0.012 0.000 0.024 0.824 0.140
#> GSM78527 2 0.4123 0.787 0.000 0.568 0.000 0.000 0.420 0.012
#> GSM78530 5 0.0000 0.910 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM78535 5 0.4351 0.714 0.060 0.044 0.000 0.016 0.788 0.092
#> GSM78538 5 0.0748 0.901 0.000 0.004 0.000 0.004 0.976 0.016
#> GSM78542 5 0.0748 0.901 0.000 0.004 0.000 0.004 0.976 0.016
#> GSM78544 5 0.0935 0.902 0.000 0.000 0.000 0.004 0.964 0.032
#> GSM78549 2 0.4229 0.774 0.000 0.548 0.000 0.000 0.436 0.016
#> GSM78553 5 0.0405 0.911 0.000 0.000 0.000 0.004 0.988 0.008
#> GSM78558 5 0.0405 0.911 0.000 0.000 0.000 0.004 0.988 0.008
#> GSM78561 2 0.5463 0.687 0.000 0.652 0.004 0.064 0.220 0.060
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) agent(p) individual(p) k
#> MAD:kmeans 58 2.54e-13 0.00184 1.000 2
#> MAD:kmeans 58 2.30e-14 0.00274 0.114 3
#> MAD:kmeans 57 2.96e-22 0.00688 0.315 4
#> MAD:kmeans 50 4.27e-18 0.10324 0.159 5
#> MAD:kmeans 58 3.27e-20 0.03468 0.110 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "skmeans"]
# you can also extract it by
# res = res_list["MAD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 58 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.900 0.983 0.991 0.4281 0.578 0.578
#> 3 3 0.781 0.930 0.951 0.5398 0.750 0.567
#> 4 4 1.000 0.976 0.987 0.1427 0.903 0.712
#> 5 5 1.000 0.973 0.977 0.0609 0.943 0.775
#> 6 6 0.927 0.951 0.925 0.0462 0.956 0.783
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 4 5
There is also optional best \(k\) = 2 4 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM78539 1 0.000 0.987 1.000 0.000
#> GSM78545 1 0.000 0.987 1.000 0.000
#> GSM78550 1 0.000 0.987 1.000 0.000
#> GSM78554 1 0.000 0.987 1.000 0.000
#> GSM78562 1 0.000 0.987 1.000 0.000
#> GSM78540 1 0.494 0.891 0.892 0.108
#> GSM78546 1 0.482 0.895 0.896 0.104
#> GSM78551 1 0.482 0.895 0.896 0.104
#> GSM78555 1 0.456 0.903 0.904 0.096
#> GSM78563 1 0.482 0.895 0.896 0.104
#> GSM43005 1 0.000 0.987 1.000 0.000
#> GSM43008 1 0.000 0.987 1.000 0.000
#> GSM43011 1 0.000 0.987 1.000 0.000
#> GSM78523 1 0.000 0.987 1.000 0.000
#> GSM78526 1 0.000 0.987 1.000 0.000
#> GSM78529 1 0.000 0.987 1.000 0.000
#> GSM78532 1 0.000 0.987 1.000 0.000
#> GSM78534 1 0.000 0.987 1.000 0.000
#> GSM78537 1 0.000 0.987 1.000 0.000
#> GSM78543 1 0.000 0.987 1.000 0.000
#> GSM78548 1 0.000 0.987 1.000 0.000
#> GSM78557 1 0.000 0.987 1.000 0.000
#> GSM78560 1 0.000 0.987 1.000 0.000
#> GSM78565 1 0.000 0.987 1.000 0.000
#> GSM43000 1 0.000 0.987 1.000 0.000
#> GSM43002 1 0.000 0.987 1.000 0.000
#> GSM43004 1 0.000 0.987 1.000 0.000
#> GSM43007 1 0.000 0.987 1.000 0.000
#> GSM43010 1 0.000 0.987 1.000 0.000
#> GSM78522 1 0.000 0.987 1.000 0.000
#> GSM78525 1 0.000 0.987 1.000 0.000
#> GSM78528 1 0.000 0.987 1.000 0.000
#> GSM78531 1 0.000 0.987 1.000 0.000
#> GSM78533 1 0.000 0.987 1.000 0.000
#> GSM78536 1 0.000 0.987 1.000 0.000
#> GSM78541 1 0.000 0.987 1.000 0.000
#> GSM78547 1 0.000 0.987 1.000 0.000
#> GSM78552 1 0.000 0.987 1.000 0.000
#> GSM78556 1 0.000 0.987 1.000 0.000
#> GSM78559 1 0.000 0.987 1.000 0.000
#> GSM78564 1 0.000 0.987 1.000 0.000
#> GSM42999 2 0.000 1.000 0.000 1.000
#> GSM43001 2 0.000 1.000 0.000 1.000
#> GSM43003 2 0.000 1.000 0.000 1.000
#> GSM43006 2 0.000 1.000 0.000 1.000
#> GSM43009 2 0.000 1.000 0.000 1.000
#> GSM43012 2 0.000 1.000 0.000 1.000
#> GSM78524 2 0.000 1.000 0.000 1.000
#> GSM78527 2 0.000 1.000 0.000 1.000
#> GSM78530 2 0.000 1.000 0.000 1.000
#> GSM78535 2 0.000 1.000 0.000 1.000
#> GSM78538 2 0.000 1.000 0.000 1.000
#> GSM78542 2 0.000 1.000 0.000 1.000
#> GSM78544 2 0.000 1.000 0.000 1.000
#> GSM78549 2 0.000 1.000 0.000 1.000
#> GSM78553 2 0.000 1.000 0.000 1.000
#> GSM78558 2 0.000 1.000 0.000 1.000
#> GSM78561 2 0.000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM78539 1 0.000 0.876 1.000 0 0.000
#> GSM78545 1 0.000 0.876 1.000 0 0.000
#> GSM78550 1 0.000 0.876 1.000 0 0.000
#> GSM78554 1 0.000 0.876 1.000 0 0.000
#> GSM78562 1 0.000 0.876 1.000 0 0.000
#> GSM78540 1 0.000 0.876 1.000 0 0.000
#> GSM78546 1 0.000 0.876 1.000 0 0.000
#> GSM78551 1 0.000 0.876 1.000 0 0.000
#> GSM78555 1 0.000 0.876 1.000 0 0.000
#> GSM78563 1 0.000 0.876 1.000 0 0.000
#> GSM43005 3 0.000 0.966 0.000 0 1.000
#> GSM43008 3 0.000 0.966 0.000 0 1.000
#> GSM43011 3 0.000 0.966 0.000 0 1.000
#> GSM78523 3 0.000 0.966 0.000 0 1.000
#> GSM78526 3 0.000 0.966 0.000 0 1.000
#> GSM78529 3 0.000 0.966 0.000 0 1.000
#> GSM78532 1 0.429 0.895 0.820 0 0.180
#> GSM78534 3 0.000 0.966 0.000 0 1.000
#> GSM78537 1 0.429 0.895 0.820 0 0.180
#> GSM78543 1 0.429 0.895 0.820 0 0.180
#> GSM78548 3 0.319 0.836 0.112 0 0.888
#> GSM78557 1 0.429 0.895 0.820 0 0.180
#> GSM78560 1 0.429 0.895 0.820 0 0.180
#> GSM78565 1 0.429 0.895 0.820 0 0.180
#> GSM43000 3 0.000 0.966 0.000 0 1.000
#> GSM43002 3 0.000 0.966 0.000 0 1.000
#> GSM43004 3 0.000 0.966 0.000 0 1.000
#> GSM43007 3 0.000 0.966 0.000 0 1.000
#> GSM43010 3 0.000 0.966 0.000 0 1.000
#> GSM78522 3 0.000 0.966 0.000 0 1.000
#> GSM78525 3 0.000 0.966 0.000 0 1.000
#> GSM78528 3 0.000 0.966 0.000 0 1.000
#> GSM78531 1 0.429 0.895 0.820 0 0.180
#> GSM78533 3 0.000 0.966 0.000 0 1.000
#> GSM78536 1 0.429 0.895 0.820 0 0.180
#> GSM78541 1 0.429 0.895 0.820 0 0.180
#> GSM78547 1 0.429 0.895 0.820 0 0.180
#> GSM78552 3 0.603 0.245 0.376 0 0.624
#> GSM78556 1 0.429 0.895 0.820 0 0.180
#> GSM78559 1 0.429 0.895 0.820 0 0.180
#> GSM78564 1 0.429 0.895 0.820 0 0.180
#> GSM42999 2 0.000 1.000 0.000 1 0.000
#> GSM43001 2 0.000 1.000 0.000 1 0.000
#> GSM43003 2 0.000 1.000 0.000 1 0.000
#> GSM43006 2 0.000 1.000 0.000 1 0.000
#> GSM43009 2 0.000 1.000 0.000 1 0.000
#> GSM43012 2 0.000 1.000 0.000 1 0.000
#> GSM78524 2 0.000 1.000 0.000 1 0.000
#> GSM78527 2 0.000 1.000 0.000 1 0.000
#> GSM78530 2 0.000 1.000 0.000 1 0.000
#> GSM78535 2 0.000 1.000 0.000 1 0.000
#> GSM78538 2 0.000 1.000 0.000 1 0.000
#> GSM78542 2 0.000 1.000 0.000 1 0.000
#> GSM78544 2 0.000 1.000 0.000 1 0.000
#> GSM78549 2 0.000 1.000 0.000 1 0.000
#> GSM78553 2 0.000 1.000 0.000 1 0.000
#> GSM78558 2 0.000 1.000 0.000 1 0.000
#> GSM78561 2 0.000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM78539 4 0.0469 0.997 0.012 0 0.000 0.988
#> GSM78545 4 0.0000 0.987 0.000 0 0.000 1.000
#> GSM78550 4 0.0000 0.987 0.000 0 0.000 1.000
#> GSM78554 4 0.0469 0.997 0.012 0 0.000 0.988
#> GSM78562 4 0.0469 0.997 0.012 0 0.000 0.988
#> GSM78540 4 0.0469 0.997 0.012 0 0.000 0.988
#> GSM78546 4 0.0469 0.997 0.012 0 0.000 0.988
#> GSM78551 4 0.0469 0.997 0.012 0 0.000 0.988
#> GSM78555 4 0.0469 0.997 0.012 0 0.000 0.988
#> GSM78563 4 0.0469 0.997 0.012 0 0.000 0.988
#> GSM43005 3 0.0469 0.968 0.000 0 0.988 0.012
#> GSM43008 3 0.0469 0.968 0.000 0 0.988 0.012
#> GSM43011 3 0.0000 0.969 0.000 0 1.000 0.000
#> GSM78523 3 0.0000 0.969 0.000 0 1.000 0.000
#> GSM78526 3 0.0000 0.969 0.000 0 1.000 0.000
#> GSM78529 3 0.0469 0.968 0.000 0 0.988 0.012
#> GSM78532 1 0.0000 0.985 1.000 0 0.000 0.000
#> GSM78534 3 0.0000 0.969 0.000 0 1.000 0.000
#> GSM78537 1 0.0000 0.985 1.000 0 0.000 0.000
#> GSM78543 1 0.0000 0.985 1.000 0 0.000 0.000
#> GSM78548 3 0.4019 0.752 0.196 0 0.792 0.012
#> GSM78557 1 0.0000 0.985 1.000 0 0.000 0.000
#> GSM78560 1 0.0000 0.985 1.000 0 0.000 0.000
#> GSM78565 1 0.0000 0.985 1.000 0 0.000 0.000
#> GSM43000 3 0.0000 0.969 0.000 0 1.000 0.000
#> GSM43002 3 0.0469 0.968 0.000 0 0.988 0.012
#> GSM43004 3 0.3528 0.760 0.192 0 0.808 0.000
#> GSM43007 3 0.0469 0.968 0.000 0 0.988 0.012
#> GSM43010 3 0.0000 0.969 0.000 0 1.000 0.000
#> GSM78522 3 0.0000 0.969 0.000 0 1.000 0.000
#> GSM78525 3 0.0469 0.968 0.000 0 0.988 0.012
#> GSM78528 3 0.0469 0.968 0.000 0 0.988 0.012
#> GSM78531 1 0.0000 0.985 1.000 0 0.000 0.000
#> GSM78533 3 0.0000 0.969 0.000 0 1.000 0.000
#> GSM78536 1 0.0000 0.985 1.000 0 0.000 0.000
#> GSM78541 1 0.0000 0.985 1.000 0 0.000 0.000
#> GSM78547 1 0.0000 0.985 1.000 0 0.000 0.000
#> GSM78552 1 0.3625 0.786 0.828 0 0.160 0.012
#> GSM78556 1 0.0000 0.985 1.000 0 0.000 0.000
#> GSM78559 1 0.0000 0.985 1.000 0 0.000 0.000
#> GSM78564 1 0.0000 0.985 1.000 0 0.000 0.000
#> GSM42999 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM43001 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM43003 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM43006 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM43009 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM43012 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78524 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78527 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78530 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78535 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78538 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78542 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78544 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78549 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78553 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78558 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78561 2 0.0000 1.000 0.000 1 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM78539 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78545 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78550 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78554 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78562 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78540 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78546 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78551 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78555 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78563 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> GSM43005 3 0.1121 0.943 0.000 0.000 0.956 0 0.044
#> GSM43008 3 0.1121 0.943 0.000 0.000 0.956 0 0.044
#> GSM43011 5 0.0404 0.999 0.000 0.000 0.012 0 0.988
#> GSM78523 5 0.0404 0.999 0.000 0.000 0.012 0 0.988
#> GSM78526 5 0.0404 0.999 0.000 0.000 0.012 0 0.988
#> GSM78529 3 0.1121 0.943 0.000 0.000 0.956 0 0.044
#> GSM78532 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78534 5 0.0404 0.999 0.000 0.000 0.012 0 0.988
#> GSM78537 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78543 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78548 3 0.1281 0.933 0.012 0.000 0.956 0 0.032
#> GSM78557 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78560 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78565 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM43000 3 0.4060 0.501 0.000 0.000 0.640 0 0.360
#> GSM43002 3 0.1121 0.943 0.000 0.000 0.956 0 0.044
#> GSM43004 5 0.0451 0.994 0.004 0.000 0.008 0 0.988
#> GSM43007 3 0.1121 0.943 0.000 0.000 0.956 0 0.044
#> GSM43010 5 0.0404 0.999 0.000 0.000 0.012 0 0.988
#> GSM78522 5 0.0404 0.999 0.000 0.000 0.012 0 0.988
#> GSM78525 3 0.1121 0.943 0.000 0.000 0.956 0 0.044
#> GSM78528 3 0.1121 0.943 0.000 0.000 0.956 0 0.044
#> GSM78531 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78533 5 0.0404 0.999 0.000 0.000 0.012 0 0.988
#> GSM78536 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78541 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78547 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78552 3 0.2329 0.824 0.124 0.000 0.876 0 0.000
#> GSM78556 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78559 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM78564 1 0.0000 1.000 1.000 0.000 0.000 0 0.000
#> GSM42999 2 0.0000 0.977 0.000 1.000 0.000 0 0.000
#> GSM43001 2 0.0000 0.977 0.000 1.000 0.000 0 0.000
#> GSM43003 2 0.0000 0.977 0.000 1.000 0.000 0 0.000
#> GSM43006 2 0.0000 0.977 0.000 1.000 0.000 0 0.000
#> GSM43009 2 0.0000 0.977 0.000 1.000 0.000 0 0.000
#> GSM43012 2 0.0000 0.977 0.000 1.000 0.000 0 0.000
#> GSM78524 2 0.1522 0.974 0.000 0.944 0.044 0 0.012
#> GSM78527 2 0.0000 0.977 0.000 1.000 0.000 0 0.000
#> GSM78530 2 0.1522 0.974 0.000 0.944 0.044 0 0.012
#> GSM78535 2 0.1522 0.974 0.000 0.944 0.044 0 0.012
#> GSM78538 2 0.1522 0.974 0.000 0.944 0.044 0 0.012
#> GSM78542 2 0.1522 0.974 0.000 0.944 0.044 0 0.012
#> GSM78544 2 0.1522 0.974 0.000 0.944 0.044 0 0.012
#> GSM78549 2 0.0000 0.977 0.000 1.000 0.000 0 0.000
#> GSM78553 2 0.1522 0.974 0.000 0.944 0.044 0 0.012
#> GSM78558 2 0.1522 0.974 0.000 0.944 0.044 0 0.012
#> GSM78561 2 0.0000 0.977 0.000 1.000 0.000 0 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM78539 4 0.0000 0.989 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78545 4 0.1075 0.969 0.000 0.000 0.000 0.952 0.048 0.000
#> GSM78550 4 0.1075 0.969 0.000 0.000 0.000 0.952 0.048 0.000
#> GSM78554 4 0.0790 0.977 0.000 0.000 0.000 0.968 0.032 0.000
#> GSM78562 4 0.0000 0.989 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78540 4 0.0000 0.989 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78546 4 0.0000 0.989 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78551 4 0.0000 0.989 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78555 4 0.0000 0.989 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78563 4 0.0000 0.989 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM43005 3 0.0547 0.906 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM43008 3 0.0146 0.906 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM43011 6 0.0363 0.990 0.000 0.000 0.000 0.000 0.012 0.988
#> GSM78523 6 0.0363 0.990 0.000 0.000 0.000 0.000 0.012 0.988
#> GSM78526 6 0.0000 0.995 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78529 3 0.0547 0.906 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM78532 1 0.0632 0.959 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM78534 6 0.0000 0.995 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78537 1 0.0000 0.963 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78543 1 0.0000 0.963 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78548 3 0.3298 0.814 0.008 0.000 0.756 0.000 0.236 0.000
#> GSM78557 1 0.2003 0.922 0.884 0.000 0.000 0.000 0.116 0.000
#> GSM78560 1 0.0632 0.959 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM78565 1 0.0000 0.963 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM43000 3 0.4453 0.507 0.000 0.000 0.624 0.000 0.044 0.332
#> GSM43002 3 0.0937 0.902 0.000 0.000 0.960 0.000 0.040 0.000
#> GSM43004 6 0.0405 0.987 0.008 0.000 0.000 0.000 0.004 0.988
#> GSM43007 3 0.0146 0.906 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM43010 6 0.0000 0.995 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78522 6 0.0000 0.995 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78525 3 0.0937 0.902 0.000 0.000 0.960 0.000 0.040 0.000
#> GSM78528 3 0.0363 0.906 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM78531 1 0.0632 0.959 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM78533 6 0.0000 0.995 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78536 1 0.0000 0.963 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78541 1 0.0000 0.963 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78547 1 0.2003 0.922 0.884 0.000 0.000 0.000 0.116 0.000
#> GSM78552 3 0.4205 0.774 0.084 0.000 0.728 0.000 0.188 0.000
#> GSM78556 1 0.2003 0.922 0.884 0.000 0.000 0.000 0.116 0.000
#> GSM78559 1 0.0000 0.963 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78564 1 0.1863 0.926 0.896 0.000 0.000 0.000 0.104 0.000
#> GSM42999 2 0.1075 0.965 0.000 0.952 0.000 0.000 0.048 0.000
#> GSM43001 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43003 2 0.0865 0.973 0.000 0.964 0.000 0.000 0.036 0.000
#> GSM43006 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43009 2 0.1075 0.965 0.000 0.952 0.000 0.000 0.048 0.000
#> GSM43012 2 0.0458 0.970 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM78524 5 0.3309 0.965 0.000 0.280 0.000 0.000 0.720 0.000
#> GSM78527 2 0.0865 0.973 0.000 0.964 0.000 0.000 0.036 0.000
#> GSM78530 5 0.3198 0.992 0.000 0.260 0.000 0.000 0.740 0.000
#> GSM78535 5 0.3265 0.981 0.004 0.248 0.000 0.000 0.748 0.000
#> GSM78538 5 0.3198 0.992 0.000 0.260 0.000 0.000 0.740 0.000
#> GSM78542 5 0.3198 0.992 0.000 0.260 0.000 0.000 0.740 0.000
#> GSM78544 5 0.3198 0.992 0.000 0.260 0.000 0.000 0.740 0.000
#> GSM78549 2 0.0937 0.971 0.000 0.960 0.000 0.000 0.040 0.000
#> GSM78553 5 0.3198 0.992 0.000 0.260 0.000 0.000 0.740 0.000
#> GSM78558 5 0.3175 0.989 0.000 0.256 0.000 0.000 0.744 0.000
#> GSM78561 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) agent(p) individual(p) k
#> MAD:skmeans 58 2.54e-13 0.00184 1.000 2
#> MAD:skmeans 57 1.37e-14 0.00234 0.222 3
#> MAD:skmeans 58 1.13e-22 0.00789 0.397 4
#> MAD:skmeans 58 2.22e-21 0.01729 0.115 5
#> MAD:skmeans 58 3.27e-20 0.03468 0.110 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "pam"]
# you can also extract it by
# res = res_list["MAD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 58 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4222 0.578 0.578
#> 3 3 0.759 0.811 0.848 0.4938 0.758 0.582
#> 4 4 0.982 0.959 0.984 0.1957 0.891 0.685
#> 5 5 0.916 0.883 0.878 0.0534 0.938 0.758
#> 6 6 0.981 0.918 0.965 0.0464 0.930 0.684
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 4 5
There is also optional best \(k\) = 2 4 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM78539 1 0 1 1 0
#> GSM78545 1 0 1 1 0
#> GSM78550 1 0 1 1 0
#> GSM78554 1 0 1 1 0
#> GSM78562 1 0 1 1 0
#> GSM78540 1 0 1 1 0
#> GSM78546 1 0 1 1 0
#> GSM78551 1 0 1 1 0
#> GSM78555 1 0 1 1 0
#> GSM78563 1 0 1 1 0
#> GSM43005 1 0 1 1 0
#> GSM43008 1 0 1 1 0
#> GSM43011 1 0 1 1 0
#> GSM78523 1 0 1 1 0
#> GSM78526 1 0 1 1 0
#> GSM78529 1 0 1 1 0
#> GSM78532 1 0 1 1 0
#> GSM78534 1 0 1 1 0
#> GSM78537 1 0 1 1 0
#> GSM78543 1 0 1 1 0
#> GSM78548 1 0 1 1 0
#> GSM78557 1 0 1 1 0
#> GSM78560 1 0 1 1 0
#> GSM78565 1 0 1 1 0
#> GSM43000 1 0 1 1 0
#> GSM43002 1 0 1 1 0
#> GSM43004 1 0 1 1 0
#> GSM43007 1 0 1 1 0
#> GSM43010 1 0 1 1 0
#> GSM78522 1 0 1 1 0
#> GSM78525 1 0 1 1 0
#> GSM78528 1 0 1 1 0
#> GSM78531 1 0 1 1 0
#> GSM78533 1 0 1 1 0
#> GSM78536 1 0 1 1 0
#> GSM78541 1 0 1 1 0
#> GSM78547 1 0 1 1 0
#> GSM78552 1 0 1 1 0
#> GSM78556 1 0 1 1 0
#> GSM78559 1 0 1 1 0
#> GSM78564 1 0 1 1 0
#> GSM42999 2 0 1 0 1
#> GSM43001 2 0 1 0 1
#> GSM43003 2 0 1 0 1
#> GSM43006 2 0 1 0 1
#> GSM43009 2 0 1 0 1
#> GSM43012 2 0 1 0 1
#> GSM78524 2 0 1 0 1
#> GSM78527 2 0 1 0 1
#> GSM78530 2 0 1 0 1
#> GSM78535 2 0 1 0 1
#> GSM78538 2 0 1 0 1
#> GSM78542 2 0 1 0 1
#> GSM78544 2 0 1 0 1
#> GSM78549 2 0 1 0 1
#> GSM78553 2 0 1 0 1
#> GSM78558 2 0 1 0 1
#> GSM78561 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM78539 1 0.0000 0.585 1.000 0 0.000
#> GSM78545 1 0.0000 0.585 1.000 0 0.000
#> GSM78550 1 0.0000 0.585 1.000 0 0.000
#> GSM78554 1 0.6062 0.616 0.616 0 0.384
#> GSM78562 1 0.0237 0.585 0.996 0 0.004
#> GSM78540 1 0.0000 0.585 1.000 0 0.000
#> GSM78546 1 0.0000 0.585 1.000 0 0.000
#> GSM78551 1 0.0000 0.585 1.000 0 0.000
#> GSM78555 1 0.0000 0.585 1.000 0 0.000
#> GSM78563 1 0.0000 0.585 1.000 0 0.000
#> GSM43005 3 0.0000 0.962 0.000 0 1.000
#> GSM43008 3 0.0424 0.955 0.008 0 0.992
#> GSM43011 3 0.0000 0.962 0.000 0 1.000
#> GSM78523 3 0.0000 0.962 0.000 0 1.000
#> GSM78526 3 0.0000 0.962 0.000 0 1.000
#> GSM78529 3 0.0000 0.962 0.000 0 1.000
#> GSM78532 1 0.6299 0.634 0.524 0 0.476
#> GSM78534 3 0.2066 0.876 0.060 0 0.940
#> GSM78537 1 0.6299 0.634 0.524 0 0.476
#> GSM78543 1 0.6299 0.634 0.524 0 0.476
#> GSM78548 1 0.6299 0.634 0.524 0 0.476
#> GSM78557 1 0.6299 0.634 0.524 0 0.476
#> GSM78560 1 0.6299 0.634 0.524 0 0.476
#> GSM78565 1 0.6299 0.634 0.524 0 0.476
#> GSM43000 3 0.0000 0.962 0.000 0 1.000
#> GSM43002 3 0.0000 0.962 0.000 0 1.000
#> GSM43004 3 0.5291 0.309 0.268 0 0.732
#> GSM43007 3 0.0424 0.955 0.008 0 0.992
#> GSM43010 3 0.0000 0.962 0.000 0 1.000
#> GSM78522 3 0.0000 0.962 0.000 0 1.000
#> GSM78525 3 0.0000 0.962 0.000 0 1.000
#> GSM78528 3 0.0000 0.962 0.000 0 1.000
#> GSM78531 1 0.6299 0.634 0.524 0 0.476
#> GSM78533 3 0.0000 0.962 0.000 0 1.000
#> GSM78536 1 0.6299 0.634 0.524 0 0.476
#> GSM78541 1 0.6299 0.634 0.524 0 0.476
#> GSM78547 1 0.6299 0.634 0.524 0 0.476
#> GSM78552 1 0.6299 0.634 0.524 0 0.476
#> GSM78556 1 0.6299 0.634 0.524 0 0.476
#> GSM78559 1 0.6299 0.634 0.524 0 0.476
#> GSM78564 1 0.6299 0.634 0.524 0 0.476
#> GSM42999 2 0.0000 1.000 0.000 1 0.000
#> GSM43001 2 0.0000 1.000 0.000 1 0.000
#> GSM43003 2 0.0000 1.000 0.000 1 0.000
#> GSM43006 2 0.0000 1.000 0.000 1 0.000
#> GSM43009 2 0.0000 1.000 0.000 1 0.000
#> GSM43012 2 0.0000 1.000 0.000 1 0.000
#> GSM78524 2 0.0000 1.000 0.000 1 0.000
#> GSM78527 2 0.0000 1.000 0.000 1 0.000
#> GSM78530 2 0.0000 1.000 0.000 1 0.000
#> GSM78535 2 0.0000 1.000 0.000 1 0.000
#> GSM78538 2 0.0000 1.000 0.000 1 0.000
#> GSM78542 2 0.0000 1.000 0.000 1 0.000
#> GSM78544 2 0.0000 1.000 0.000 1 0.000
#> GSM78549 2 0.0000 1.000 0.000 1 0.000
#> GSM78553 2 0.0000 1.000 0.000 1 0.000
#> GSM78558 2 0.0000 1.000 0.000 1 0.000
#> GSM78561 2 0.0000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM78539 4 0.000 1.000 0.000 0 0.000 1
#> GSM78545 4 0.000 1.000 0.000 0 0.000 1
#> GSM78550 4 0.000 1.000 0.000 0 0.000 1
#> GSM78554 4 0.000 1.000 0.000 0 0.000 1
#> GSM78562 4 0.000 1.000 0.000 0 0.000 1
#> GSM78540 4 0.000 1.000 0.000 0 0.000 1
#> GSM78546 4 0.000 1.000 0.000 0 0.000 1
#> GSM78551 4 0.000 1.000 0.000 0 0.000 1
#> GSM78555 4 0.000 1.000 0.000 0 0.000 1
#> GSM78563 4 0.000 1.000 0.000 0 0.000 1
#> GSM43005 3 0.000 0.977 0.000 0 1.000 0
#> GSM43008 3 0.259 0.873 0.116 0 0.884 0
#> GSM43011 3 0.000 0.977 0.000 0 1.000 0
#> GSM78523 3 0.000 0.977 0.000 0 1.000 0
#> GSM78526 3 0.000 0.977 0.000 0 1.000 0
#> GSM78529 3 0.000 0.977 0.000 0 1.000 0
#> GSM78532 1 0.000 0.954 1.000 0 0.000 0
#> GSM78534 3 0.164 0.928 0.060 0 0.940 0
#> GSM78537 1 0.000 0.954 1.000 0 0.000 0
#> GSM78543 1 0.000 0.954 1.000 0 0.000 0
#> GSM78548 1 0.317 0.787 0.840 0 0.160 0
#> GSM78557 1 0.000 0.954 1.000 0 0.000 0
#> GSM78560 1 0.000 0.954 1.000 0 0.000 0
#> GSM78565 1 0.000 0.954 1.000 0 0.000 0
#> GSM43000 3 0.000 0.977 0.000 0 1.000 0
#> GSM43002 3 0.000 0.977 0.000 0 1.000 0
#> GSM43004 1 0.498 0.105 0.540 0 0.460 0
#> GSM43007 3 0.259 0.873 0.116 0 0.884 0
#> GSM43010 3 0.000 0.977 0.000 0 1.000 0
#> GSM78522 3 0.000 0.977 0.000 0 1.000 0
#> GSM78525 3 0.000 0.977 0.000 0 1.000 0
#> GSM78528 3 0.000 0.977 0.000 0 1.000 0
#> GSM78531 1 0.000 0.954 1.000 0 0.000 0
#> GSM78533 3 0.000 0.977 0.000 0 1.000 0
#> GSM78536 1 0.000 0.954 1.000 0 0.000 0
#> GSM78541 1 0.000 0.954 1.000 0 0.000 0
#> GSM78547 1 0.000 0.954 1.000 0 0.000 0
#> GSM78552 1 0.000 0.954 1.000 0 0.000 0
#> GSM78556 1 0.000 0.954 1.000 0 0.000 0
#> GSM78559 1 0.000 0.954 1.000 0 0.000 0
#> GSM78564 1 0.000 0.954 1.000 0 0.000 0
#> GSM42999 2 0.000 1.000 0.000 1 0.000 0
#> GSM43001 2 0.000 1.000 0.000 1 0.000 0
#> GSM43003 2 0.000 1.000 0.000 1 0.000 0
#> GSM43006 2 0.000 1.000 0.000 1 0.000 0
#> GSM43009 2 0.000 1.000 0.000 1 0.000 0
#> GSM43012 2 0.000 1.000 0.000 1 0.000 0
#> GSM78524 2 0.000 1.000 0.000 1 0.000 0
#> GSM78527 2 0.000 1.000 0.000 1 0.000 0
#> GSM78530 2 0.000 1.000 0.000 1 0.000 0
#> GSM78535 2 0.000 1.000 0.000 1 0.000 0
#> GSM78538 2 0.000 1.000 0.000 1 0.000 0
#> GSM78542 2 0.000 1.000 0.000 1 0.000 0
#> GSM78544 2 0.000 1.000 0.000 1 0.000 0
#> GSM78549 2 0.000 1.000 0.000 1 0.000 0
#> GSM78553 2 0.000 1.000 0.000 1 0.000 0
#> GSM78558 2 0.000 1.000 0.000 1 0.000 0
#> GSM78561 2 0.000 1.000 0.000 1 0.000 0
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM78539 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78545 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78550 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78554 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78562 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78540 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78546 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78551 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78555 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM78563 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM43005 3 0.411 0.788 0.000 0.376 0.624 0 0.000
#> GSM43008 3 0.459 0.781 0.016 0.380 0.604 0 0.000
#> GSM43011 3 0.000 0.812 0.000 0.000 1.000 0 0.000
#> GSM78523 3 0.000 0.812 0.000 0.000 1.000 0 0.000
#> GSM78526 3 0.000 0.812 0.000 0.000 1.000 0 0.000
#> GSM78529 3 0.413 0.787 0.000 0.380 0.620 0 0.000
#> GSM78532 1 0.000 0.995 1.000 0.000 0.000 0 0.000
#> GSM78534 3 0.141 0.776 0.060 0.000 0.940 0 0.000
#> GSM78537 1 0.000 0.995 1.000 0.000 0.000 0 0.000
#> GSM78543 1 0.000 0.995 1.000 0.000 0.000 0 0.000
#> GSM78548 1 0.201 0.918 0.920 0.020 0.060 0 0.000
#> GSM78557 1 0.000 0.995 1.000 0.000 0.000 0 0.000
#> GSM78560 1 0.000 0.995 1.000 0.000 0.000 0 0.000
#> GSM78565 1 0.000 0.995 1.000 0.000 0.000 0 0.000
#> GSM43000 3 0.247 0.816 0.000 0.136 0.864 0 0.000
#> GSM43002 3 0.413 0.787 0.000 0.380 0.620 0 0.000
#> GSM43004 3 0.539 0.272 0.400 0.060 0.540 0 0.000
#> GSM43007 3 0.468 0.779 0.020 0.380 0.600 0 0.000
#> GSM43010 3 0.000 0.812 0.000 0.000 1.000 0 0.000
#> GSM78522 3 0.000 0.812 0.000 0.000 1.000 0 0.000
#> GSM78525 3 0.356 0.808 0.000 0.260 0.740 0 0.000
#> GSM78528 3 0.413 0.787 0.000 0.380 0.620 0 0.000
#> GSM78531 1 0.000 0.995 1.000 0.000 0.000 0 0.000
#> GSM78533 3 0.000 0.812 0.000 0.000 1.000 0 0.000
#> GSM78536 1 0.000 0.995 1.000 0.000 0.000 0 0.000
#> GSM78541 1 0.000 0.995 1.000 0.000 0.000 0 0.000
#> GSM78547 1 0.000 0.995 1.000 0.000 0.000 0 0.000
#> GSM78552 1 0.000 0.995 1.000 0.000 0.000 0 0.000
#> GSM78556 1 0.000 0.995 1.000 0.000 0.000 0 0.000
#> GSM78559 1 0.000 0.995 1.000 0.000 0.000 0 0.000
#> GSM78564 1 0.000 0.995 1.000 0.000 0.000 0 0.000
#> GSM42999 5 0.386 0.115 0.000 0.312 0.000 0 0.688
#> GSM43001 5 0.000 0.832 0.000 0.000 0.000 0 1.000
#> GSM43003 5 0.120 0.789 0.000 0.048 0.000 0 0.952
#> GSM43006 5 0.000 0.832 0.000 0.000 0.000 0 1.000
#> GSM43009 5 0.384 0.136 0.000 0.308 0.000 0 0.692
#> GSM43012 5 0.000 0.832 0.000 0.000 0.000 0 1.000
#> GSM78524 2 0.416 0.980 0.000 0.608 0.000 0 0.392
#> GSM78527 5 0.029 0.827 0.000 0.008 0.000 0 0.992
#> GSM78530 2 0.413 0.994 0.000 0.620 0.000 0 0.380
#> GSM78535 2 0.413 0.994 0.000 0.620 0.000 0 0.380
#> GSM78538 2 0.413 0.994 0.000 0.620 0.000 0 0.380
#> GSM78542 2 0.413 0.994 0.000 0.620 0.000 0 0.380
#> GSM78544 2 0.416 0.980 0.000 0.608 0.000 0 0.392
#> GSM78549 2 0.413 0.994 0.000 0.620 0.000 0 0.380
#> GSM78553 2 0.413 0.994 0.000 0.620 0.000 0 0.380
#> GSM78558 2 0.413 0.994 0.000 0.620 0.000 0 0.380
#> GSM78561 5 0.000 0.832 0.000 0.000 0.000 0 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM78539 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM78545 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM78550 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM78554 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM78562 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM78540 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM78546 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM78551 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM78555 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM78563 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM43005 3 0.0146 0.971 0.000 0.000 0.996 0 0.000 0.004
#> GSM43008 3 0.0000 0.974 0.000 0.000 1.000 0 0.000 0.000
#> GSM43011 6 0.0937 0.906 0.000 0.000 0.040 0 0.000 0.960
#> GSM78523 6 0.0937 0.906 0.000 0.000 0.040 0 0.000 0.960
#> GSM78526 6 0.0000 0.922 0.000 0.000 0.000 0 0.000 1.000
#> GSM78529 3 0.0000 0.974 0.000 0.000 1.000 0 0.000 0.000
#> GSM78532 1 0.0000 0.969 1.000 0.000 0.000 0 0.000 0.000
#> GSM78534 6 0.0000 0.922 0.000 0.000 0.000 0 0.000 1.000
#> GSM78537 1 0.0000 0.969 1.000 0.000 0.000 0 0.000 0.000
#> GSM78543 1 0.0000 0.969 1.000 0.000 0.000 0 0.000 0.000
#> GSM78548 1 0.1549 0.915 0.936 0.000 0.020 0 0.000 0.044
#> GSM78557 1 0.0000 0.969 1.000 0.000 0.000 0 0.000 0.000
#> GSM78560 1 0.0000 0.969 1.000 0.000 0.000 0 0.000 0.000
#> GSM78565 1 0.0000 0.969 1.000 0.000 0.000 0 0.000 0.000
#> GSM43000 6 0.3817 0.228 0.000 0.000 0.432 0 0.000 0.568
#> GSM43002 3 0.0000 0.974 0.000 0.000 1.000 0 0.000 0.000
#> GSM43004 1 0.4900 0.375 0.592 0.000 0.080 0 0.000 0.328
#> GSM43007 3 0.0000 0.974 0.000 0.000 1.000 0 0.000 0.000
#> GSM43010 6 0.0000 0.922 0.000 0.000 0.000 0 0.000 1.000
#> GSM78522 6 0.0000 0.922 0.000 0.000 0.000 0 0.000 1.000
#> GSM78525 3 0.2178 0.828 0.000 0.000 0.868 0 0.000 0.132
#> GSM78528 3 0.0000 0.974 0.000 0.000 1.000 0 0.000 0.000
#> GSM78531 1 0.0000 0.969 1.000 0.000 0.000 0 0.000 0.000
#> GSM78533 6 0.0000 0.922 0.000 0.000 0.000 0 0.000 1.000
#> GSM78536 1 0.0000 0.969 1.000 0.000 0.000 0 0.000 0.000
#> GSM78541 1 0.0000 0.969 1.000 0.000 0.000 0 0.000 0.000
#> GSM78547 1 0.0000 0.969 1.000 0.000 0.000 0 0.000 0.000
#> GSM78552 1 0.0000 0.969 1.000 0.000 0.000 0 0.000 0.000
#> GSM78556 1 0.0000 0.969 1.000 0.000 0.000 0 0.000 0.000
#> GSM78559 1 0.0000 0.969 1.000 0.000 0.000 0 0.000 0.000
#> GSM78564 1 0.0000 0.969 1.000 0.000 0.000 0 0.000 0.000
#> GSM42999 2 0.3620 0.543 0.000 0.648 0.000 0 0.352 0.000
#> GSM43001 5 0.0000 0.980 0.000 0.000 0.000 0 1.000 0.000
#> GSM43003 5 0.1267 0.937 0.000 0.060 0.000 0 0.940 0.000
#> GSM43006 5 0.0000 0.980 0.000 0.000 0.000 0 1.000 0.000
#> GSM43009 2 0.3659 0.520 0.000 0.636 0.000 0 0.364 0.000
#> GSM43012 5 0.0000 0.980 0.000 0.000 0.000 0 1.000 0.000
#> GSM78524 2 0.1141 0.893 0.000 0.948 0.000 0 0.052 0.000
#> GSM78527 5 0.0790 0.962 0.000 0.032 0.000 0 0.968 0.000
#> GSM78530 2 0.0000 0.915 0.000 1.000 0.000 0 0.000 0.000
#> GSM78535 2 0.0000 0.915 0.000 1.000 0.000 0 0.000 0.000
#> GSM78538 2 0.0000 0.915 0.000 1.000 0.000 0 0.000 0.000
#> GSM78542 2 0.0000 0.915 0.000 1.000 0.000 0 0.000 0.000
#> GSM78544 2 0.1141 0.893 0.000 0.948 0.000 0 0.052 0.000
#> GSM78549 2 0.0000 0.915 0.000 1.000 0.000 0 0.000 0.000
#> GSM78553 2 0.0000 0.915 0.000 1.000 0.000 0 0.000 0.000
#> GSM78558 2 0.0000 0.915 0.000 1.000 0.000 0 0.000 0.000
#> GSM78561 5 0.0000 0.980 0.000 0.000 0.000 0 1.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) agent(p) individual(p) k
#> MAD:pam 58 2.54e-13 0.00184 1.000 2
#> MAD:pam 57 4.94e-14 0.00233 0.130 3
#> MAD:pam 57 2.96e-22 0.00689 0.354 4
#> MAD:pam 55 3.81e-20 0.02745 0.268 5
#> MAD:pam 56 2.11e-19 0.02434 0.038 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "mclust"]
# you can also extract it by
# res = res_list["MAD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 58 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4222 0.578 0.578
#> 3 3 0.752 0.783 0.891 0.5234 0.789 0.636
#> 4 4 0.770 0.807 0.902 0.1458 0.858 0.622
#> 5 5 0.932 0.890 0.946 0.0710 0.906 0.655
#> 6 6 0.919 0.885 0.935 0.0361 0.954 0.791
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 5
There is also optional best \(k\) = 2 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM78539 1 0 1 1 0
#> GSM78545 1 0 1 1 0
#> GSM78550 1 0 1 1 0
#> GSM78554 1 0 1 1 0
#> GSM78562 1 0 1 1 0
#> GSM78540 1 0 1 1 0
#> GSM78546 1 0 1 1 0
#> GSM78551 1 0 1 1 0
#> GSM78555 1 0 1 1 0
#> GSM78563 1 0 1 1 0
#> GSM43005 1 0 1 1 0
#> GSM43008 1 0 1 1 0
#> GSM43011 1 0 1 1 0
#> GSM78523 1 0 1 1 0
#> GSM78526 1 0 1 1 0
#> GSM78529 1 0 1 1 0
#> GSM78532 1 0 1 1 0
#> GSM78534 1 0 1 1 0
#> GSM78537 1 0 1 1 0
#> GSM78543 1 0 1 1 0
#> GSM78548 1 0 1 1 0
#> GSM78557 1 0 1 1 0
#> GSM78560 1 0 1 1 0
#> GSM78565 1 0 1 1 0
#> GSM43000 1 0 1 1 0
#> GSM43002 1 0 1 1 0
#> GSM43004 1 0 1 1 0
#> GSM43007 1 0 1 1 0
#> GSM43010 1 0 1 1 0
#> GSM78522 1 0 1 1 0
#> GSM78525 1 0 1 1 0
#> GSM78528 1 0 1 1 0
#> GSM78531 1 0 1 1 0
#> GSM78533 1 0 1 1 0
#> GSM78536 1 0 1 1 0
#> GSM78541 1 0 1 1 0
#> GSM78547 1 0 1 1 0
#> GSM78552 1 0 1 1 0
#> GSM78556 1 0 1 1 0
#> GSM78559 1 0 1 1 0
#> GSM78564 1 0 1 1 0
#> GSM42999 2 0 1 0 1
#> GSM43001 2 0 1 0 1
#> GSM43003 2 0 1 0 1
#> GSM43006 2 0 1 0 1
#> GSM43009 2 0 1 0 1
#> GSM43012 2 0 1 0 1
#> GSM78524 2 0 1 0 1
#> GSM78527 2 0 1 0 1
#> GSM78530 2 0 1 0 1
#> GSM78535 2 0 1 0 1
#> GSM78538 2 0 1 0 1
#> GSM78542 2 0 1 0 1
#> GSM78544 2 0 1 0 1
#> GSM78549 2 0 1 0 1
#> GSM78553 2 0 1 0 1
#> GSM78558 2 0 1 0 1
#> GSM78561 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM78539 1 0.0424 0.899 0.992 0 0.008
#> GSM78545 1 0.2959 0.854 0.900 0 0.100
#> GSM78550 1 0.2165 0.871 0.936 0 0.064
#> GSM78554 1 0.5810 0.289 0.664 0 0.336
#> GSM78562 1 0.0424 0.899 0.992 0 0.008
#> GSM78540 1 0.0424 0.899 0.992 0 0.008
#> GSM78546 1 0.0424 0.899 0.992 0 0.008
#> GSM78551 1 0.0237 0.898 0.996 0 0.004
#> GSM78555 1 0.0424 0.899 0.992 0 0.008
#> GSM78563 1 0.0424 0.899 0.992 0 0.008
#> GSM43005 3 0.6215 0.426 0.428 0 0.572
#> GSM43008 3 0.6192 0.434 0.420 0 0.580
#> GSM43011 3 0.6204 0.434 0.424 0 0.576
#> GSM78523 3 0.6204 0.434 0.424 0 0.576
#> GSM78526 3 0.1529 0.760 0.040 0 0.960
#> GSM78529 1 0.4178 0.787 0.828 0 0.172
#> GSM78532 3 0.1529 0.758 0.040 0 0.960
#> GSM78534 3 0.1289 0.762 0.032 0 0.968
#> GSM78537 3 0.1529 0.758 0.040 0 0.960
#> GSM78543 3 0.2448 0.740 0.076 0 0.924
#> GSM78548 3 0.6192 0.434 0.420 0 0.580
#> GSM78557 3 0.2356 0.761 0.072 0 0.928
#> GSM78560 3 0.5016 0.663 0.240 0 0.760
#> GSM78565 3 0.2448 0.740 0.076 0 0.924
#> GSM43000 3 0.6204 0.434 0.424 0 0.576
#> GSM43002 3 0.6192 0.434 0.420 0 0.580
#> GSM43004 3 0.1289 0.762 0.032 0 0.968
#> GSM43007 3 0.6204 0.426 0.424 0 0.576
#> GSM43010 3 0.1529 0.760 0.040 0 0.960
#> GSM78522 3 0.1289 0.762 0.032 0 0.968
#> GSM78525 3 0.6204 0.434 0.424 0 0.576
#> GSM78528 1 0.4235 0.781 0.824 0 0.176
#> GSM78531 3 0.1411 0.757 0.036 0 0.964
#> GSM78533 3 0.1529 0.760 0.040 0 0.960
#> GSM78536 3 0.2448 0.740 0.076 0 0.924
#> GSM78541 3 0.2448 0.740 0.076 0 0.924
#> GSM78547 3 0.2356 0.761 0.072 0 0.928
#> GSM78552 3 0.6260 0.421 0.448 0 0.552
#> GSM78556 3 0.2356 0.761 0.072 0 0.928
#> GSM78559 3 0.2448 0.740 0.076 0 0.924
#> GSM78564 3 0.1411 0.759 0.036 0 0.964
#> GSM42999 2 0.0000 1.000 0.000 1 0.000
#> GSM43001 2 0.0000 1.000 0.000 1 0.000
#> GSM43003 2 0.0000 1.000 0.000 1 0.000
#> GSM43006 2 0.0000 1.000 0.000 1 0.000
#> GSM43009 2 0.0000 1.000 0.000 1 0.000
#> GSM43012 2 0.0000 1.000 0.000 1 0.000
#> GSM78524 2 0.0000 1.000 0.000 1 0.000
#> GSM78527 2 0.0000 1.000 0.000 1 0.000
#> GSM78530 2 0.0000 1.000 0.000 1 0.000
#> GSM78535 2 0.0000 1.000 0.000 1 0.000
#> GSM78538 2 0.0000 1.000 0.000 1 0.000
#> GSM78542 2 0.0000 1.000 0.000 1 0.000
#> GSM78544 2 0.0000 1.000 0.000 1 0.000
#> GSM78549 2 0.0000 1.000 0.000 1 0.000
#> GSM78553 2 0.0000 1.000 0.000 1 0.000
#> GSM78558 2 0.0000 1.000 0.000 1 0.000
#> GSM78561 2 0.0000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM78539 4 0.0000 0.835 0.000 0 0.000 1.000
#> GSM78545 4 0.4072 0.655 0.000 0 0.252 0.748
#> GSM78550 4 0.4072 0.655 0.000 0 0.252 0.748
#> GSM78554 3 0.3837 0.615 0.000 0 0.776 0.224
#> GSM78562 4 0.0000 0.835 0.000 0 0.000 1.000
#> GSM78540 4 0.0000 0.835 0.000 0 0.000 1.000
#> GSM78546 4 0.0000 0.835 0.000 0 0.000 1.000
#> GSM78551 4 0.0000 0.835 0.000 0 0.000 1.000
#> GSM78555 4 0.0000 0.835 0.000 0 0.000 1.000
#> GSM78563 4 0.0000 0.835 0.000 0 0.000 1.000
#> GSM43005 3 0.0336 0.861 0.008 0 0.992 0.000
#> GSM43008 3 0.0336 0.861 0.008 0 0.992 0.000
#> GSM43011 3 0.0000 0.859 0.000 0 1.000 0.000
#> GSM78523 3 0.0188 0.856 0.004 0 0.996 0.000
#> GSM78526 3 0.4277 0.430 0.280 0 0.720 0.000
#> GSM78529 4 0.5285 0.298 0.008 0 0.468 0.524
#> GSM78532 1 0.3569 0.778 0.804 0 0.196 0.000
#> GSM78534 1 0.4817 0.597 0.612 0 0.388 0.000
#> GSM78537 1 0.3400 0.788 0.820 0 0.180 0.000
#> GSM78543 1 0.0188 0.759 0.996 0 0.004 0.000
#> GSM78548 3 0.0336 0.861 0.008 0 0.992 0.000
#> GSM78557 3 0.4331 0.580 0.288 0 0.712 0.000
#> GSM78560 1 0.3444 0.786 0.816 0 0.184 0.000
#> GSM78565 1 0.0188 0.759 0.996 0 0.004 0.000
#> GSM43000 3 0.0000 0.859 0.000 0 1.000 0.000
#> GSM43002 3 0.0336 0.861 0.008 0 0.992 0.000
#> GSM43004 1 0.3569 0.783 0.804 0 0.196 0.000
#> GSM43007 3 0.0336 0.861 0.008 0 0.992 0.000
#> GSM43010 1 0.4941 0.516 0.564 0 0.436 0.000
#> GSM78522 1 0.4817 0.597 0.612 0 0.388 0.000
#> GSM78525 3 0.0000 0.859 0.000 0 1.000 0.000
#> GSM78528 4 0.5285 0.298 0.008 0 0.468 0.524
#> GSM78531 1 0.2868 0.789 0.864 0 0.136 0.000
#> GSM78533 1 0.4967 0.481 0.548 0 0.452 0.000
#> GSM78536 1 0.0188 0.759 0.996 0 0.004 0.000
#> GSM78541 1 0.0188 0.759 0.996 0 0.004 0.000
#> GSM78547 3 0.4331 0.580 0.288 0 0.712 0.000
#> GSM78552 3 0.1557 0.834 0.056 0 0.944 0.000
#> GSM78556 3 0.4331 0.580 0.288 0 0.712 0.000
#> GSM78559 1 0.0188 0.759 0.996 0 0.004 0.000
#> GSM78564 1 0.3400 0.788 0.820 0 0.180 0.000
#> GSM42999 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM43001 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM43003 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM43006 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM43009 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM43012 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78524 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78527 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78530 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78535 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78538 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78542 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78544 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78549 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78553 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78558 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM78561 2 0.0000 1.000 0.000 1 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM78539 4 0.0000 0.9981 0.000 0.000 0.000 1.000 0.000
#> GSM78545 4 0.0162 0.9966 0.000 0.000 0.000 0.996 0.004
#> GSM78550 4 0.0162 0.9966 0.000 0.000 0.000 0.996 0.004
#> GSM78554 4 0.0451 0.9899 0.000 0.000 0.004 0.988 0.008
#> GSM78562 4 0.0000 0.9981 0.000 0.000 0.000 1.000 0.000
#> GSM78540 4 0.0000 0.9981 0.000 0.000 0.000 1.000 0.000
#> GSM78546 4 0.0000 0.9981 0.000 0.000 0.000 1.000 0.000
#> GSM78551 4 0.0000 0.9981 0.000 0.000 0.000 1.000 0.000
#> GSM78555 4 0.0000 0.9981 0.000 0.000 0.000 1.000 0.000
#> GSM78563 4 0.0000 0.9981 0.000 0.000 0.000 1.000 0.000
#> GSM43005 3 0.0000 0.8817 0.000 0.000 1.000 0.000 0.000
#> GSM43008 3 0.0000 0.8817 0.000 0.000 1.000 0.000 0.000
#> GSM43011 3 0.0000 0.8817 0.000 0.000 1.000 0.000 0.000
#> GSM78523 3 0.0290 0.8771 0.000 0.000 0.992 0.000 0.008
#> GSM78526 5 0.2852 0.9476 0.000 0.000 0.172 0.000 0.828
#> GSM78529 3 0.1041 0.8596 0.000 0.000 0.964 0.032 0.004
#> GSM78532 1 0.0000 0.9226 1.000 0.000 0.000 0.000 0.000
#> GSM78534 5 0.2890 0.9474 0.004 0.000 0.160 0.000 0.836
#> GSM78537 1 0.0000 0.9226 1.000 0.000 0.000 0.000 0.000
#> GSM78543 1 0.0794 0.9222 0.972 0.000 0.000 0.000 0.028
#> GSM78548 3 0.0290 0.8800 0.000 0.000 0.992 0.000 0.008
#> GSM78557 3 0.4562 0.0143 0.496 0.000 0.496 0.000 0.008
#> GSM78560 1 0.0000 0.9226 1.000 0.000 0.000 0.000 0.000
#> GSM78565 1 0.0794 0.9222 0.972 0.000 0.000 0.000 0.028
#> GSM43000 3 0.0000 0.8817 0.000 0.000 1.000 0.000 0.000
#> GSM43002 3 0.0290 0.8800 0.000 0.000 0.992 0.000 0.008
#> GSM43004 5 0.3284 0.7728 0.148 0.000 0.024 0.000 0.828
#> GSM43007 3 0.0000 0.8817 0.000 0.000 1.000 0.000 0.000
#> GSM43010 5 0.2852 0.9476 0.000 0.000 0.172 0.000 0.828
#> GSM78522 5 0.2890 0.9474 0.004 0.000 0.160 0.000 0.836
#> GSM78525 3 0.0000 0.8817 0.000 0.000 1.000 0.000 0.000
#> GSM78528 3 0.1041 0.8596 0.000 0.000 0.964 0.032 0.004
#> GSM78531 1 0.0000 0.9226 1.000 0.000 0.000 0.000 0.000
#> GSM78533 5 0.2966 0.9379 0.000 0.000 0.184 0.000 0.816
#> GSM78536 1 0.0794 0.9222 0.972 0.000 0.000 0.000 0.028
#> GSM78541 1 0.0794 0.9222 0.972 0.000 0.000 0.000 0.028
#> GSM78547 1 0.4562 -0.1679 0.496 0.000 0.496 0.000 0.008
#> GSM78552 3 0.1251 0.8541 0.036 0.000 0.956 0.000 0.008
#> GSM78556 3 0.4562 0.0143 0.496 0.000 0.496 0.000 0.008
#> GSM78559 1 0.0794 0.9222 0.972 0.000 0.000 0.000 0.028
#> GSM78564 1 0.0162 0.9204 0.996 0.000 0.004 0.000 0.000
#> GSM42999 2 0.0000 0.9860 0.000 1.000 0.000 0.000 0.000
#> GSM43001 2 0.0000 0.9860 0.000 1.000 0.000 0.000 0.000
#> GSM43003 2 0.0000 0.9860 0.000 1.000 0.000 0.000 0.000
#> GSM43006 2 0.0000 0.9860 0.000 1.000 0.000 0.000 0.000
#> GSM43009 2 0.0000 0.9860 0.000 1.000 0.000 0.000 0.000
#> GSM43012 2 0.0000 0.9860 0.000 1.000 0.000 0.000 0.000
#> GSM78524 2 0.2020 0.9183 0.000 0.900 0.000 0.000 0.100
#> GSM78527 2 0.0000 0.9860 0.000 1.000 0.000 0.000 0.000
#> GSM78530 2 0.0404 0.9821 0.000 0.988 0.000 0.000 0.012
#> GSM78535 2 0.2280 0.9015 0.000 0.880 0.000 0.000 0.120
#> GSM78538 2 0.0000 0.9860 0.000 1.000 0.000 0.000 0.000
#> GSM78542 2 0.0000 0.9860 0.000 1.000 0.000 0.000 0.000
#> GSM78544 2 0.0404 0.9821 0.000 0.988 0.000 0.000 0.012
#> GSM78549 2 0.0000 0.9860 0.000 1.000 0.000 0.000 0.000
#> GSM78553 2 0.0404 0.9821 0.000 0.988 0.000 0.000 0.012
#> GSM78558 2 0.0404 0.9821 0.000 0.988 0.000 0.000 0.012
#> GSM78561 2 0.0000 0.9860 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM78539 4 0.0000 0.994 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78545 4 0.0146 0.992 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM78550 4 0.0146 0.992 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM78554 4 0.0777 0.968 0.000 0.000 0.024 0.972 0.000 0.004
#> GSM78562 4 0.0260 0.988 0.000 0.000 0.008 0.992 0.000 0.000
#> GSM78540 4 0.0000 0.994 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78546 4 0.0000 0.994 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78551 4 0.0000 0.994 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78555 4 0.0000 0.994 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78563 4 0.0000 0.994 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM43005 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM43008 3 0.0146 0.915 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM43011 3 0.1327 0.886 0.000 0.000 0.936 0.000 0.000 0.064
#> GSM78523 3 0.2823 0.748 0.000 0.000 0.796 0.000 0.000 0.204
#> GSM78526 6 0.1910 0.928 0.000 0.000 0.108 0.000 0.000 0.892
#> GSM78529 3 0.0777 0.905 0.000 0.000 0.972 0.024 0.000 0.004
#> GSM78532 1 0.0000 0.952 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78534 6 0.1890 0.940 0.024 0.000 0.060 0.000 0.000 0.916
#> GSM78537 1 0.0000 0.952 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78543 1 0.1225 0.946 0.952 0.000 0.000 0.000 0.012 0.036
#> GSM78548 3 0.0653 0.907 0.012 0.000 0.980 0.000 0.004 0.004
#> GSM78557 1 0.1426 0.934 0.948 0.000 0.028 0.000 0.016 0.008
#> GSM78560 1 0.0458 0.948 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM78565 1 0.1951 0.933 0.908 0.000 0.000 0.000 0.016 0.076
#> GSM43000 3 0.2491 0.798 0.000 0.000 0.836 0.000 0.000 0.164
#> GSM43002 3 0.0146 0.913 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM43004 6 0.1531 0.853 0.068 0.000 0.004 0.000 0.000 0.928
#> GSM43007 3 0.0146 0.915 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM43010 6 0.1700 0.940 0.004 0.000 0.080 0.000 0.000 0.916
#> GSM78522 6 0.1890 0.940 0.024 0.000 0.060 0.000 0.000 0.916
#> GSM78525 3 0.0146 0.915 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM78528 3 0.0777 0.905 0.000 0.000 0.972 0.024 0.000 0.004
#> GSM78531 1 0.0363 0.952 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM78533 6 0.2048 0.917 0.000 0.000 0.120 0.000 0.000 0.880
#> GSM78536 1 0.1951 0.933 0.908 0.000 0.000 0.000 0.016 0.076
#> GSM78541 1 0.1951 0.933 0.908 0.000 0.000 0.000 0.016 0.076
#> GSM78547 1 0.1390 0.933 0.948 0.000 0.032 0.000 0.016 0.004
#> GSM78552 3 0.3448 0.595 0.280 0.000 0.716 0.000 0.004 0.000
#> GSM78556 1 0.1426 0.934 0.948 0.000 0.028 0.000 0.016 0.008
#> GSM78559 1 0.1951 0.933 0.908 0.000 0.000 0.000 0.016 0.076
#> GSM78564 1 0.0000 0.952 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM42999 2 0.0000 0.865 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43001 2 0.0000 0.865 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43003 2 0.0000 0.865 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43006 2 0.0000 0.865 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43009 2 0.0000 0.865 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43012 2 0.0632 0.846 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM78524 5 0.3446 0.604 0.000 0.308 0.000 0.000 0.692 0.000
#> GSM78527 2 0.0000 0.865 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78530 2 0.3330 0.700 0.000 0.716 0.000 0.000 0.284 0.000
#> GSM78535 5 0.0790 0.617 0.000 0.032 0.000 0.000 0.968 0.000
#> GSM78538 2 0.3221 0.718 0.000 0.736 0.000 0.000 0.264 0.000
#> GSM78542 2 0.3221 0.718 0.000 0.736 0.000 0.000 0.264 0.000
#> GSM78544 2 0.0865 0.850 0.000 0.964 0.000 0.000 0.036 0.000
#> GSM78549 2 0.0000 0.865 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78553 2 0.3330 0.700 0.000 0.716 0.000 0.000 0.284 0.000
#> GSM78558 2 0.3330 0.700 0.000 0.716 0.000 0.000 0.284 0.000
#> GSM78561 2 0.0000 0.865 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) agent(p) individual(p) k
#> MAD:mclust 58 2.54e-13 0.00184 1.000 2
#> MAD:mclust 47 7.26e-17 0.00603 0.814 3
#> MAD:mclust 54 1.46e-19 0.00898 0.741 4
#> MAD:mclust 55 3.81e-20 0.01336 0.186 5
#> MAD:mclust 58 3.27e-20 0.03077 0.243 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "NMF"]
# you can also extract it by
# res = res_list["MAD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 58 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.990 0.995 0.4262 0.578 0.578
#> 3 3 0.834 0.872 0.938 0.5612 0.724 0.534
#> 4 4 0.896 0.882 0.943 0.1344 0.903 0.711
#> 5 5 0.778 0.706 0.826 0.0468 0.974 0.899
#> 6 6 0.859 0.833 0.908 0.0412 0.920 0.676
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM78539 1 0.0000 0.993 1.000 0.000
#> GSM78545 1 0.0000 0.993 1.000 0.000
#> GSM78550 1 0.0000 0.993 1.000 0.000
#> GSM78554 1 0.0000 0.993 1.000 0.000
#> GSM78562 1 0.0000 0.993 1.000 0.000
#> GSM78540 1 0.5946 0.836 0.856 0.144
#> GSM78546 1 0.1843 0.968 0.972 0.028
#> GSM78551 1 0.0672 0.986 0.992 0.008
#> GSM78555 1 0.0000 0.993 1.000 0.000
#> GSM78563 1 0.0672 0.986 0.992 0.008
#> GSM43005 1 0.0000 0.993 1.000 0.000
#> GSM43008 1 0.0000 0.993 1.000 0.000
#> GSM43011 1 0.0000 0.993 1.000 0.000
#> GSM78523 1 0.0000 0.993 1.000 0.000
#> GSM78526 1 0.0000 0.993 1.000 0.000
#> GSM78529 1 0.4815 0.885 0.896 0.104
#> GSM78532 1 0.0000 0.993 1.000 0.000
#> GSM78534 1 0.0000 0.993 1.000 0.000
#> GSM78537 1 0.0000 0.993 1.000 0.000
#> GSM78543 1 0.0000 0.993 1.000 0.000
#> GSM78548 1 0.0000 0.993 1.000 0.000
#> GSM78557 1 0.0000 0.993 1.000 0.000
#> GSM78560 1 0.0000 0.993 1.000 0.000
#> GSM78565 1 0.0000 0.993 1.000 0.000
#> GSM43000 1 0.0000 0.993 1.000 0.000
#> GSM43002 1 0.0000 0.993 1.000 0.000
#> GSM43004 1 0.0000 0.993 1.000 0.000
#> GSM43007 1 0.0000 0.993 1.000 0.000
#> GSM43010 1 0.0000 0.993 1.000 0.000
#> GSM78522 1 0.0000 0.993 1.000 0.000
#> GSM78525 1 0.0000 0.993 1.000 0.000
#> GSM78528 1 0.0000 0.993 1.000 0.000
#> GSM78531 1 0.0000 0.993 1.000 0.000
#> GSM78533 1 0.0000 0.993 1.000 0.000
#> GSM78536 1 0.0000 0.993 1.000 0.000
#> GSM78541 1 0.0000 0.993 1.000 0.000
#> GSM78547 1 0.0000 0.993 1.000 0.000
#> GSM78552 1 0.0000 0.993 1.000 0.000
#> GSM78556 1 0.0000 0.993 1.000 0.000
#> GSM78559 1 0.0000 0.993 1.000 0.000
#> GSM78564 1 0.0000 0.993 1.000 0.000
#> GSM42999 2 0.0000 1.000 0.000 1.000
#> GSM43001 2 0.0000 1.000 0.000 1.000
#> GSM43003 2 0.0000 1.000 0.000 1.000
#> GSM43006 2 0.0000 1.000 0.000 1.000
#> GSM43009 2 0.0000 1.000 0.000 1.000
#> GSM43012 2 0.0000 1.000 0.000 1.000
#> GSM78524 2 0.0000 1.000 0.000 1.000
#> GSM78527 2 0.0000 1.000 0.000 1.000
#> GSM78530 2 0.0000 1.000 0.000 1.000
#> GSM78535 2 0.0000 1.000 0.000 1.000
#> GSM78538 2 0.0000 1.000 0.000 1.000
#> GSM78542 2 0.0000 1.000 0.000 1.000
#> GSM78544 2 0.0000 1.000 0.000 1.000
#> GSM78549 2 0.0000 1.000 0.000 1.000
#> GSM78553 2 0.0000 1.000 0.000 1.000
#> GSM78558 2 0.0000 1.000 0.000 1.000
#> GSM78561 2 0.0000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM78539 1 0.0237 0.888 0.996 0.000 0.004
#> GSM78545 1 0.6180 0.334 0.584 0.000 0.416
#> GSM78550 1 0.3038 0.860 0.896 0.000 0.104
#> GSM78554 1 0.0892 0.892 0.980 0.000 0.020
#> GSM78562 1 0.0424 0.889 0.992 0.000 0.008
#> GSM78540 1 0.1031 0.875 0.976 0.024 0.000
#> GSM78546 1 0.0592 0.882 0.988 0.012 0.000
#> GSM78551 1 0.0592 0.882 0.988 0.012 0.000
#> GSM78555 1 0.0424 0.884 0.992 0.008 0.000
#> GSM78563 1 0.0592 0.882 0.988 0.012 0.000
#> GSM43005 3 0.1163 0.932 0.028 0.000 0.972
#> GSM43008 3 0.1163 0.932 0.028 0.000 0.972
#> GSM43011 3 0.0424 0.932 0.008 0.000 0.992
#> GSM78523 3 0.0000 0.930 0.000 0.000 1.000
#> GSM78526 3 0.0000 0.930 0.000 0.000 1.000
#> GSM78529 3 0.0237 0.927 0.000 0.004 0.996
#> GSM78532 1 0.4654 0.762 0.792 0.000 0.208
#> GSM78534 3 0.0237 0.931 0.004 0.000 0.996
#> GSM78537 1 0.1411 0.891 0.964 0.000 0.036
#> GSM78543 1 0.1289 0.892 0.968 0.000 0.032
#> GSM78548 3 0.2066 0.905 0.060 0.000 0.940
#> GSM78557 1 0.3116 0.858 0.892 0.000 0.108
#> GSM78560 1 0.4062 0.812 0.836 0.000 0.164
#> GSM78565 1 0.1163 0.892 0.972 0.000 0.028
#> GSM43000 3 0.0000 0.930 0.000 0.000 1.000
#> GSM43002 3 0.1163 0.932 0.028 0.000 0.972
#> GSM43004 3 0.1163 0.932 0.028 0.000 0.972
#> GSM43007 3 0.1289 0.930 0.032 0.000 0.968
#> GSM43010 3 0.0000 0.930 0.000 0.000 1.000
#> GSM78522 3 0.0000 0.930 0.000 0.000 1.000
#> GSM78525 3 0.1163 0.932 0.028 0.000 0.972
#> GSM78528 3 0.0892 0.933 0.020 0.000 0.980
#> GSM78531 1 0.3482 0.845 0.872 0.000 0.128
#> GSM78533 3 0.1031 0.933 0.024 0.000 0.976
#> GSM78536 1 0.1031 0.892 0.976 0.000 0.024
#> GSM78541 1 0.0892 0.892 0.980 0.000 0.020
#> GSM78547 1 0.3686 0.835 0.860 0.000 0.140
#> GSM78552 3 0.6140 0.253 0.404 0.000 0.596
#> GSM78556 1 0.6026 0.452 0.624 0.000 0.376
#> GSM78559 1 0.1289 0.892 0.968 0.000 0.032
#> GSM78564 3 0.6154 0.239 0.408 0.000 0.592
#> GSM42999 2 0.0237 0.988 0.000 0.996 0.004
#> GSM43001 2 0.1163 0.979 0.000 0.972 0.028
#> GSM43003 2 0.0000 0.989 0.000 1.000 0.000
#> GSM43006 2 0.0747 0.985 0.000 0.984 0.016
#> GSM43009 2 0.0747 0.985 0.000 0.984 0.016
#> GSM43012 2 0.1163 0.979 0.000 0.972 0.028
#> GSM78524 2 0.0237 0.989 0.004 0.996 0.000
#> GSM78527 2 0.0000 0.989 0.000 1.000 0.000
#> GSM78530 2 0.0592 0.988 0.012 0.988 0.000
#> GSM78535 1 0.5988 0.357 0.632 0.368 0.000
#> GSM78538 2 0.0592 0.988 0.012 0.988 0.000
#> GSM78542 2 0.0592 0.988 0.012 0.988 0.000
#> GSM78544 2 0.0237 0.989 0.004 0.996 0.000
#> GSM78549 2 0.0424 0.988 0.008 0.992 0.000
#> GSM78553 2 0.0747 0.986 0.016 0.984 0.000
#> GSM78558 2 0.1031 0.981 0.024 0.976 0.000
#> GSM78561 2 0.1031 0.981 0.000 0.976 0.024
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM78539 4 0.0707 0.960 0.020 0.000 0.000 0.980
#> GSM78545 4 0.1584 0.933 0.012 0.000 0.036 0.952
#> GSM78550 4 0.1297 0.952 0.020 0.000 0.016 0.964
#> GSM78554 4 0.0895 0.959 0.020 0.000 0.004 0.976
#> GSM78562 4 0.2921 0.866 0.140 0.000 0.000 0.860
#> GSM78540 4 0.0707 0.960 0.020 0.000 0.000 0.980
#> GSM78546 4 0.0707 0.960 0.020 0.000 0.000 0.980
#> GSM78551 4 0.0707 0.960 0.020 0.000 0.000 0.980
#> GSM78555 4 0.3311 0.821 0.172 0.000 0.000 0.828
#> GSM78563 4 0.0707 0.960 0.020 0.000 0.000 0.980
#> GSM43005 3 0.1389 0.875 0.000 0.000 0.952 0.048
#> GSM43008 3 0.0921 0.887 0.028 0.000 0.972 0.000
#> GSM43011 3 0.0188 0.896 0.004 0.000 0.996 0.000
#> GSM78523 3 0.0188 0.896 0.004 0.000 0.996 0.000
#> GSM78526 3 0.0336 0.896 0.008 0.000 0.992 0.000
#> GSM78529 3 0.2760 0.815 0.000 0.000 0.872 0.128
#> GSM78532 1 0.0188 0.925 0.996 0.000 0.000 0.004
#> GSM78534 3 0.0592 0.894 0.016 0.000 0.984 0.000
#> GSM78537 1 0.0336 0.925 0.992 0.000 0.000 0.008
#> GSM78543 1 0.0188 0.926 0.996 0.000 0.000 0.004
#> GSM78548 3 0.5161 0.135 0.004 0.000 0.520 0.476
#> GSM78557 1 0.2773 0.839 0.880 0.000 0.004 0.116
#> GSM78560 1 0.0592 0.921 0.984 0.000 0.000 0.016
#> GSM78565 1 0.0188 0.926 0.996 0.000 0.000 0.004
#> GSM43000 3 0.0188 0.896 0.004 0.000 0.996 0.000
#> GSM43002 3 0.0336 0.896 0.008 0.000 0.992 0.000
#> GSM43004 3 0.4697 0.429 0.356 0.000 0.644 0.000
#> GSM43007 3 0.0779 0.893 0.016 0.000 0.980 0.004
#> GSM43010 3 0.0336 0.896 0.008 0.000 0.992 0.000
#> GSM78522 3 0.0524 0.895 0.008 0.004 0.988 0.000
#> GSM78525 3 0.0188 0.896 0.004 0.000 0.996 0.000
#> GSM78528 3 0.2408 0.835 0.000 0.000 0.896 0.104
#> GSM78531 1 0.0000 0.924 1.000 0.000 0.000 0.000
#> GSM78533 3 0.0469 0.896 0.012 0.000 0.988 0.000
#> GSM78536 1 0.0188 0.926 0.996 0.000 0.000 0.004
#> GSM78541 1 0.0188 0.926 0.996 0.000 0.000 0.004
#> GSM78547 1 0.1867 0.885 0.928 0.000 0.000 0.072
#> GSM78552 3 0.7220 0.138 0.144 0.000 0.472 0.384
#> GSM78556 1 0.3239 0.860 0.880 0.000 0.068 0.052
#> GSM78559 1 0.0188 0.926 0.996 0.000 0.000 0.004
#> GSM78564 1 0.3052 0.811 0.860 0.000 0.136 0.004
#> GSM42999 2 0.0188 0.990 0.000 0.996 0.000 0.004
#> GSM43001 2 0.0927 0.977 0.000 0.976 0.008 0.016
#> GSM43003 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM43006 2 0.0188 0.990 0.000 0.996 0.000 0.004
#> GSM43009 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM43012 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM78524 2 0.2053 0.922 0.072 0.924 0.000 0.004
#> GSM78527 2 0.0188 0.990 0.000 0.996 0.000 0.004
#> GSM78530 2 0.0188 0.990 0.000 0.996 0.000 0.004
#> GSM78535 1 0.5355 0.396 0.620 0.360 0.000 0.020
#> GSM78538 2 0.0336 0.989 0.000 0.992 0.000 0.008
#> GSM78542 2 0.0336 0.989 0.000 0.992 0.000 0.008
#> GSM78544 2 0.0188 0.990 0.000 0.996 0.000 0.004
#> GSM78549 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM78553 2 0.0336 0.989 0.000 0.992 0.000 0.008
#> GSM78558 2 0.0336 0.989 0.000 0.992 0.000 0.008
#> GSM78561 2 0.0336 0.988 0.000 0.992 0.000 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM78539 4 0.1410 0.922 0.000 0.000 0.060 0.940 0.000
#> GSM78545 4 0.2471 0.887 0.000 0.000 0.136 0.864 0.000
#> GSM78550 4 0.2732 0.869 0.000 0.000 0.160 0.840 0.000
#> GSM78554 4 0.2648 0.875 0.000 0.000 0.152 0.848 0.000
#> GSM78562 4 0.1205 0.910 0.040 0.000 0.004 0.956 0.000
#> GSM78540 4 0.0000 0.926 0.000 0.000 0.000 1.000 0.000
#> GSM78546 4 0.0404 0.930 0.000 0.000 0.012 0.988 0.000
#> GSM78551 4 0.0510 0.930 0.000 0.000 0.016 0.984 0.000
#> GSM78555 4 0.0794 0.916 0.028 0.000 0.000 0.972 0.000
#> GSM78563 4 0.0000 0.926 0.000 0.000 0.000 1.000 0.000
#> GSM43005 3 0.1498 0.700 0.016 0.000 0.952 0.008 0.024
#> GSM43008 3 0.1818 0.682 0.044 0.000 0.932 0.000 0.024
#> GSM43011 3 0.4242 0.730 0.000 0.000 0.572 0.000 0.428
#> GSM78523 3 0.4242 0.730 0.000 0.000 0.572 0.000 0.428
#> GSM78526 3 0.4504 0.729 0.008 0.000 0.564 0.000 0.428
#> GSM78529 3 0.5025 0.412 0.016 0.000 0.680 0.040 0.264
#> GSM78532 1 0.1121 0.910 0.956 0.000 0.044 0.000 0.000
#> GSM78534 3 0.5538 0.697 0.068 0.000 0.504 0.000 0.428
#> GSM78537 1 0.1662 0.907 0.936 0.000 0.056 0.004 0.004
#> GSM78543 1 0.0324 0.909 0.992 0.000 0.004 0.004 0.000
#> GSM78548 3 0.4462 0.532 0.000 0.000 0.740 0.196 0.064
#> GSM78557 1 0.5489 0.688 0.656 0.000 0.248 0.084 0.012
#> GSM78560 1 0.1952 0.900 0.912 0.000 0.084 0.004 0.000
#> GSM78565 1 0.0510 0.899 0.984 0.000 0.000 0.000 0.016
#> GSM43000 3 0.3774 0.739 0.000 0.000 0.704 0.000 0.296
#> GSM43002 3 0.1386 0.712 0.016 0.000 0.952 0.000 0.032
#> GSM43004 3 0.6420 0.629 0.176 0.000 0.448 0.000 0.376
#> GSM43007 3 0.1469 0.690 0.036 0.000 0.948 0.000 0.016
#> GSM43010 3 0.4604 0.728 0.012 0.000 0.560 0.000 0.428
#> GSM78522 3 0.4696 0.726 0.016 0.000 0.556 0.000 0.428
#> GSM78525 3 0.2806 0.733 0.004 0.000 0.844 0.000 0.152
#> GSM78528 3 0.2131 0.675 0.016 0.000 0.920 0.008 0.056
#> GSM78531 1 0.0510 0.910 0.984 0.000 0.016 0.000 0.000
#> GSM78533 3 0.4504 0.729 0.008 0.000 0.564 0.000 0.428
#> GSM78536 1 0.0162 0.906 0.996 0.000 0.000 0.000 0.004
#> GSM78541 1 0.0324 0.908 0.992 0.000 0.004 0.004 0.000
#> GSM78547 1 0.3111 0.864 0.840 0.000 0.144 0.012 0.004
#> GSM78552 3 0.2765 0.672 0.044 0.000 0.896 0.036 0.024
#> GSM78556 1 0.3883 0.763 0.744 0.000 0.244 0.008 0.004
#> GSM78559 1 0.0404 0.902 0.988 0.000 0.000 0.000 0.012
#> GSM78564 1 0.2471 0.869 0.864 0.000 0.136 0.000 0.000
#> GSM42999 2 0.0162 0.754 0.000 0.996 0.000 0.000 0.004
#> GSM43001 5 0.4307 0.000 0.000 0.500 0.000 0.000 0.500
#> GSM43003 2 0.0290 0.752 0.000 0.992 0.000 0.000 0.008
#> GSM43006 2 0.3895 -0.406 0.000 0.680 0.000 0.000 0.320
#> GSM43009 2 0.0000 0.755 0.000 1.000 0.000 0.000 0.000
#> GSM43012 2 0.1197 0.717 0.000 0.952 0.000 0.000 0.048
#> GSM78524 2 0.2522 0.685 0.056 0.904 0.000 0.028 0.012
#> GSM78527 2 0.0963 0.729 0.000 0.964 0.000 0.000 0.036
#> GSM78530 2 0.0290 0.758 0.000 0.992 0.000 0.008 0.000
#> GSM78535 2 0.6287 0.135 0.244 0.592 0.000 0.144 0.020
#> GSM78538 2 0.1341 0.743 0.000 0.944 0.000 0.056 0.000
#> GSM78542 2 0.0963 0.757 0.000 0.964 0.000 0.036 0.000
#> GSM78544 2 0.0963 0.757 0.000 0.964 0.000 0.036 0.000
#> GSM78549 2 0.1544 0.683 0.000 0.932 0.000 0.000 0.068
#> GSM78553 2 0.1121 0.752 0.000 0.956 0.000 0.044 0.000
#> GSM78558 2 0.2020 0.683 0.000 0.900 0.000 0.100 0.000
#> GSM78561 2 0.4306 -0.980 0.000 0.508 0.000 0.000 0.492
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM78539 4 0.0603 0.967 0.016 0.000 0.004 0.980 0.000 0.000
#> GSM78545 4 0.1296 0.955 0.000 0.000 0.032 0.952 0.004 0.012
#> GSM78550 4 0.1327 0.939 0.000 0.000 0.064 0.936 0.000 0.000
#> GSM78554 4 0.1327 0.940 0.000 0.000 0.064 0.936 0.000 0.000
#> GSM78562 4 0.0363 0.969 0.012 0.000 0.000 0.988 0.000 0.000
#> GSM78540 4 0.0146 0.972 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM78546 4 0.0000 0.972 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78551 4 0.0291 0.973 0.000 0.000 0.004 0.992 0.004 0.000
#> GSM78555 4 0.0260 0.972 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM78563 4 0.0260 0.972 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM43005 3 0.2773 0.824 0.004 0.000 0.828 0.000 0.004 0.164
#> GSM43008 3 0.2257 0.828 0.008 0.000 0.876 0.000 0.000 0.116
#> GSM43011 6 0.0363 0.951 0.000 0.000 0.012 0.000 0.000 0.988
#> GSM78523 6 0.0260 0.953 0.000 0.000 0.008 0.000 0.000 0.992
#> GSM78526 6 0.0000 0.956 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78529 3 0.1845 0.786 0.000 0.000 0.920 0.000 0.028 0.052
#> GSM78532 1 0.1349 0.896 0.940 0.000 0.056 0.004 0.000 0.000
#> GSM78534 6 0.0508 0.949 0.000 0.000 0.004 0.000 0.012 0.984
#> GSM78537 1 0.1644 0.891 0.920 0.004 0.076 0.000 0.000 0.000
#> GSM78543 1 0.0508 0.895 0.984 0.000 0.012 0.004 0.000 0.000
#> GSM78548 3 0.3728 0.782 0.004 0.000 0.748 0.012 0.008 0.228
#> GSM78557 3 0.3737 0.155 0.392 0.000 0.608 0.000 0.000 0.000
#> GSM78560 1 0.1908 0.880 0.900 0.000 0.096 0.004 0.000 0.000
#> GSM78565 1 0.0291 0.888 0.992 0.000 0.004 0.000 0.004 0.000
#> GSM43000 6 0.2838 0.696 0.000 0.000 0.188 0.000 0.004 0.808
#> GSM43002 3 0.3489 0.712 0.000 0.000 0.708 0.000 0.004 0.288
#> GSM43004 6 0.1152 0.911 0.044 0.000 0.000 0.000 0.004 0.952
#> GSM43007 3 0.2362 0.831 0.004 0.000 0.860 0.000 0.000 0.136
#> GSM43010 6 0.0000 0.956 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78522 6 0.0000 0.956 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78525 3 0.3955 0.431 0.000 0.000 0.560 0.000 0.004 0.436
#> GSM78528 3 0.0858 0.772 0.004 0.000 0.968 0.000 0.000 0.028
#> GSM78531 1 0.1010 0.897 0.960 0.000 0.036 0.004 0.000 0.000
#> GSM78533 6 0.0000 0.956 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78536 1 0.0146 0.890 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM78541 1 0.0508 0.893 0.984 0.000 0.012 0.000 0.004 0.000
#> GSM78547 1 0.3189 0.745 0.760 0.000 0.236 0.004 0.000 0.000
#> GSM78552 3 0.2442 0.830 0.004 0.000 0.852 0.000 0.000 0.144
#> GSM78556 1 0.3976 0.463 0.612 0.000 0.380 0.004 0.000 0.004
#> GSM78559 1 0.0291 0.888 0.992 0.000 0.004 0.000 0.004 0.000
#> GSM78564 1 0.2876 0.824 0.836 0.000 0.148 0.004 0.004 0.008
#> GSM42999 2 0.1010 0.881 0.000 0.960 0.004 0.000 0.036 0.000
#> GSM43001 5 0.1387 0.823 0.000 0.068 0.000 0.000 0.932 0.000
#> GSM43003 2 0.1444 0.862 0.000 0.928 0.000 0.000 0.072 0.000
#> GSM43006 5 0.3531 0.518 0.000 0.328 0.000 0.000 0.672 0.000
#> GSM43009 2 0.0508 0.890 0.000 0.984 0.000 0.000 0.012 0.004
#> GSM43012 2 0.3281 0.704 0.000 0.784 0.004 0.000 0.200 0.012
#> GSM78524 2 0.1223 0.882 0.012 0.960 0.008 0.004 0.016 0.000
#> GSM78527 2 0.2092 0.818 0.000 0.876 0.000 0.000 0.124 0.000
#> GSM78530 2 0.0146 0.891 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM78535 2 0.3316 0.723 0.124 0.828 0.000 0.024 0.024 0.000
#> GSM78538 2 0.0260 0.891 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM78542 2 0.0260 0.891 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM78544 2 0.0551 0.888 0.000 0.984 0.004 0.000 0.008 0.004
#> GSM78549 2 0.3804 0.139 0.000 0.576 0.000 0.000 0.424 0.000
#> GSM78553 2 0.0405 0.889 0.000 0.988 0.000 0.004 0.008 0.000
#> GSM78558 2 0.1088 0.872 0.000 0.960 0.000 0.024 0.016 0.000
#> GSM78561 5 0.1141 0.817 0.000 0.052 0.000 0.000 0.948 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) agent(p) individual(p) k
#> MAD:NMF 58 2.54e-13 0.00184 0.9999 2
#> MAD:NMF 53 7.72e-14 0.00271 0.2899 3
#> MAD:NMF 54 5.34e-21 0.00970 0.2271 4
#> MAD:NMF 53 1.40e-20 0.02814 0.2835 5
#> MAD:NMF 54 1.35e-18 0.04270 0.0824 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "hclust"]
# you can also extract it by
# res = res_list["ATC:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 58 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 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.496 0.886 0.903 0.430 0.501 0.501
#> 3 3 0.757 0.819 0.926 0.346 0.940 0.879
#> 4 4 0.737 0.714 0.858 0.199 0.890 0.750
#> 5 5 0.732 0.757 0.827 0.108 0.791 0.456
#> 6 6 0.857 0.785 0.915 0.061 0.949 0.779
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM78539 1 0.4562 0.871 0.904 0.096
#> GSM78545 2 0.8608 0.853 0.284 0.716
#> GSM78550 1 0.0000 0.962 1.000 0.000
#> GSM78554 1 0.4562 0.871 0.904 0.096
#> GSM78562 1 0.0000 0.962 1.000 0.000
#> GSM78540 1 0.0000 0.962 1.000 0.000
#> GSM78546 2 0.8608 0.853 0.284 0.716
#> GSM78551 1 0.0000 0.962 1.000 0.000
#> GSM78555 1 0.0000 0.962 1.000 0.000
#> GSM78563 1 0.0000 0.962 1.000 0.000
#> GSM43005 2 0.8608 0.853 0.284 0.716
#> GSM43008 2 0.8608 0.853 0.284 0.716
#> GSM43011 2 0.8608 0.853 0.284 0.716
#> GSM78523 2 0.8144 0.851 0.252 0.748
#> GSM78526 1 0.0000 0.962 1.000 0.000
#> GSM78529 2 0.0000 0.763 0.000 1.000
#> GSM78532 1 0.0000 0.962 1.000 0.000
#> GSM78534 1 0.0000 0.962 1.000 0.000
#> GSM78537 1 0.0000 0.962 1.000 0.000
#> GSM78543 1 0.6343 0.783 0.840 0.160
#> GSM78548 1 0.0000 0.962 1.000 0.000
#> GSM78557 1 0.6343 0.783 0.840 0.160
#> GSM78560 1 0.6343 0.783 0.840 0.160
#> GSM78565 1 0.0000 0.962 1.000 0.000
#> GSM43000 2 0.8144 0.851 0.252 0.748
#> GSM43002 2 0.8608 0.853 0.284 0.716
#> GSM43004 1 0.0000 0.962 1.000 0.000
#> GSM43007 2 0.8608 0.853 0.284 0.716
#> GSM43010 1 0.0000 0.962 1.000 0.000
#> GSM78522 2 0.8608 0.853 0.284 0.716
#> GSM78525 2 0.8608 0.853 0.284 0.716
#> GSM78528 2 0.8327 0.854 0.264 0.736
#> GSM78531 1 0.0000 0.962 1.000 0.000
#> GSM78533 1 0.3879 0.893 0.924 0.076
#> GSM78536 1 0.0000 0.962 1.000 0.000
#> GSM78541 1 0.0000 0.962 1.000 0.000
#> GSM78547 1 0.0000 0.962 1.000 0.000
#> GSM78552 2 0.8608 0.853 0.284 0.716
#> GSM78556 1 0.0000 0.962 1.000 0.000
#> GSM78559 1 0.0000 0.962 1.000 0.000
#> GSM78564 1 0.6343 0.783 0.840 0.160
#> GSM42999 2 0.0000 0.763 0.000 1.000
#> GSM43001 2 0.0000 0.763 0.000 1.000
#> GSM43003 2 0.0000 0.763 0.000 1.000
#> GSM43006 2 0.0000 0.763 0.000 1.000
#> GSM43009 2 0.8443 0.854 0.272 0.728
#> GSM43012 2 0.0000 0.763 0.000 1.000
#> GSM78524 1 0.0000 0.962 1.000 0.000
#> GSM78527 2 0.0000 0.763 0.000 1.000
#> GSM78530 2 0.8608 0.853 0.284 0.716
#> GSM78535 1 0.0000 0.962 1.000 0.000
#> GSM78538 1 0.0000 0.962 1.000 0.000
#> GSM78542 1 0.0000 0.962 1.000 0.000
#> GSM78544 2 0.8608 0.853 0.284 0.716
#> GSM78549 2 0.8443 0.854 0.272 0.728
#> GSM78553 1 0.0000 0.962 1.000 0.000
#> GSM78558 1 0.0376 0.959 0.996 0.004
#> GSM78561 2 0.0000 0.763 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM78539 1 0.5859 0.554 0.656 0.000 0.344
#> GSM78545 3 0.0000 0.927 0.000 0.000 1.000
#> GSM78550 1 0.0000 0.896 1.000 0.000 0.000
#> GSM78554 1 0.5859 0.554 0.656 0.000 0.344
#> GSM78562 1 0.0000 0.896 1.000 0.000 0.000
#> GSM78540 1 0.0000 0.896 1.000 0.000 0.000
#> GSM78546 3 0.0000 0.927 0.000 0.000 1.000
#> GSM78551 1 0.0000 0.896 1.000 0.000 0.000
#> GSM78555 1 0.0000 0.896 1.000 0.000 0.000
#> GSM78563 1 0.0000 0.896 1.000 0.000 0.000
#> GSM43005 3 0.0000 0.927 0.000 0.000 1.000
#> GSM43008 3 0.0000 0.927 0.000 0.000 1.000
#> GSM43011 3 0.0000 0.927 0.000 0.000 1.000
#> GSM78523 3 0.1411 0.907 0.000 0.036 0.964
#> GSM78526 1 0.0000 0.896 1.000 0.000 0.000
#> GSM78529 2 0.5650 0.508 0.000 0.688 0.312
#> GSM78532 1 0.0000 0.896 1.000 0.000 0.000
#> GSM78534 1 0.0000 0.896 1.000 0.000 0.000
#> GSM78537 1 0.0000 0.896 1.000 0.000 0.000
#> GSM78543 1 0.6252 0.365 0.556 0.000 0.444
#> GSM78548 1 0.0000 0.896 1.000 0.000 0.000
#> GSM78557 1 0.6252 0.365 0.556 0.000 0.444
#> GSM78560 1 0.6252 0.365 0.556 0.000 0.444
#> GSM78565 1 0.0000 0.896 1.000 0.000 0.000
#> GSM43000 3 0.1289 0.910 0.000 0.032 0.968
#> GSM43002 3 0.0000 0.927 0.000 0.000 1.000
#> GSM43004 1 0.0000 0.896 1.000 0.000 0.000
#> GSM43007 3 0.0000 0.927 0.000 0.000 1.000
#> GSM43010 1 0.0000 0.896 1.000 0.000 0.000
#> GSM78522 3 0.0000 0.927 0.000 0.000 1.000
#> GSM78525 3 0.0000 0.927 0.000 0.000 1.000
#> GSM78528 3 0.0892 0.918 0.000 0.020 0.980
#> GSM78531 1 0.0000 0.896 1.000 0.000 0.000
#> GSM78533 1 0.5560 0.616 0.700 0.000 0.300
#> GSM78536 1 0.0000 0.896 1.000 0.000 0.000
#> GSM78541 1 0.0000 0.896 1.000 0.000 0.000
#> GSM78547 1 0.0000 0.896 1.000 0.000 0.000
#> GSM78552 3 0.0000 0.927 0.000 0.000 1.000
#> GSM78556 1 0.0000 0.896 1.000 0.000 0.000
#> GSM78559 1 0.0000 0.896 1.000 0.000 0.000
#> GSM78564 1 0.6244 0.373 0.560 0.000 0.440
#> GSM42999 2 0.1643 0.882 0.000 0.956 0.044
#> GSM43001 2 0.0000 0.901 0.000 1.000 0.000
#> GSM43003 3 0.5591 0.514 0.000 0.304 0.696
#> GSM43006 2 0.0000 0.901 0.000 1.000 0.000
#> GSM43009 3 0.0592 0.922 0.000 0.012 0.988
#> GSM43012 3 0.5591 0.514 0.000 0.304 0.696
#> GSM78524 1 0.0000 0.896 1.000 0.000 0.000
#> GSM78527 3 0.6244 0.183 0.000 0.440 0.560
#> GSM78530 3 0.0000 0.927 0.000 0.000 1.000
#> GSM78535 1 0.0000 0.896 1.000 0.000 0.000
#> GSM78538 1 0.0000 0.896 1.000 0.000 0.000
#> GSM78542 1 0.0000 0.896 1.000 0.000 0.000
#> GSM78544 3 0.0000 0.927 0.000 0.000 1.000
#> GSM78549 3 0.0592 0.922 0.000 0.012 0.988
#> GSM78553 1 0.0000 0.896 1.000 0.000 0.000
#> GSM78558 1 0.0592 0.887 0.988 0.000 0.012
#> GSM78561 2 0.0000 0.901 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM78539 4 0.2921 0.866 0.140 0.000 0.000 0.860
#> GSM78545 3 0.0336 0.896 0.000 0.000 0.992 0.008
#> GSM78550 1 0.4888 0.493 0.588 0.000 0.000 0.412
#> GSM78554 4 0.2921 0.866 0.140 0.000 0.000 0.860
#> GSM78562 1 0.0000 0.718 1.000 0.000 0.000 0.000
#> GSM78540 1 0.5000 0.287 0.504 0.000 0.000 0.496
#> GSM78546 3 0.0336 0.896 0.000 0.000 0.992 0.008
#> GSM78551 1 0.4888 0.493 0.588 0.000 0.000 0.412
#> GSM78555 1 0.0000 0.718 1.000 0.000 0.000 0.000
#> GSM78563 1 0.5000 0.287 0.504 0.000 0.000 0.496
#> GSM43005 3 0.0336 0.896 0.000 0.000 0.992 0.008
#> GSM43008 3 0.0336 0.896 0.000 0.000 0.992 0.008
#> GSM43011 3 0.0336 0.896 0.000 0.000 0.992 0.008
#> GSM78523 3 0.1867 0.856 0.000 0.072 0.928 0.000
#> GSM78526 1 0.4888 0.493 0.588 0.000 0.000 0.412
#> GSM78529 2 0.4250 0.524 0.000 0.724 0.276 0.000
#> GSM78532 1 0.0000 0.718 1.000 0.000 0.000 0.000
#> GSM78534 1 0.0000 0.718 1.000 0.000 0.000 0.000
#> GSM78537 1 0.0000 0.718 1.000 0.000 0.000 0.000
#> GSM78543 4 0.2111 0.907 0.044 0.000 0.024 0.932
#> GSM78548 1 0.4888 0.493 0.588 0.000 0.000 0.412
#> GSM78557 4 0.2111 0.907 0.044 0.000 0.024 0.932
#> GSM78560 4 0.2111 0.907 0.044 0.000 0.024 0.932
#> GSM78565 1 0.0000 0.718 1.000 0.000 0.000 0.000
#> GSM43000 3 0.1792 0.858 0.000 0.068 0.932 0.000
#> GSM43002 3 0.0336 0.896 0.000 0.000 0.992 0.008
#> GSM43004 1 0.0000 0.718 1.000 0.000 0.000 0.000
#> GSM43007 3 0.0336 0.896 0.000 0.000 0.992 0.008
#> GSM43010 1 0.4888 0.493 0.588 0.000 0.000 0.412
#> GSM78522 3 0.4907 0.394 0.000 0.000 0.580 0.420
#> GSM78525 3 0.0336 0.896 0.000 0.000 0.992 0.008
#> GSM78528 3 0.0921 0.881 0.000 0.028 0.972 0.000
#> GSM78531 1 0.0000 0.718 1.000 0.000 0.000 0.000
#> GSM78533 4 0.3528 0.777 0.192 0.000 0.000 0.808
#> GSM78536 1 0.0000 0.718 1.000 0.000 0.000 0.000
#> GSM78541 1 0.0000 0.718 1.000 0.000 0.000 0.000
#> GSM78547 1 0.0000 0.718 1.000 0.000 0.000 0.000
#> GSM78552 3 0.0336 0.896 0.000 0.000 0.992 0.008
#> GSM78556 1 0.5000 0.287 0.504 0.000 0.000 0.496
#> GSM78559 1 0.0000 0.718 1.000 0.000 0.000 0.000
#> GSM78564 4 0.2089 0.907 0.048 0.000 0.020 0.932
#> GSM42999 2 0.0000 0.873 0.000 1.000 0.000 0.000
#> GSM43001 2 0.1716 0.892 0.000 0.936 0.000 0.064
#> GSM43003 3 0.4624 0.522 0.000 0.340 0.660 0.000
#> GSM43006 2 0.1716 0.892 0.000 0.936 0.000 0.064
#> GSM43009 3 0.0188 0.891 0.000 0.004 0.996 0.000
#> GSM43012 3 0.4624 0.522 0.000 0.340 0.660 0.000
#> GSM78524 1 0.0000 0.718 1.000 0.000 0.000 0.000
#> GSM78527 3 0.4992 0.196 0.000 0.476 0.524 0.000
#> GSM78530 3 0.0336 0.896 0.000 0.000 0.992 0.008
#> GSM78535 1 0.0000 0.718 1.000 0.000 0.000 0.000
#> GSM78538 1 0.4888 0.493 0.588 0.000 0.000 0.412
#> GSM78542 1 0.4888 0.493 0.588 0.000 0.000 0.412
#> GSM78544 3 0.0336 0.896 0.000 0.000 0.992 0.008
#> GSM78549 3 0.1545 0.878 0.000 0.040 0.952 0.008
#> GSM78553 1 0.4888 0.493 0.588 0.000 0.000 0.412
#> GSM78558 1 0.4916 0.472 0.576 0.000 0.000 0.424
#> GSM78561 2 0.1716 0.892 0.000 0.936 0.000 0.064
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM78539 4 0.483 0.627 0.028 0.308 0.008 0.656 0.000
#> GSM78545 3 0.000 0.883 0.000 0.000 1.000 0.000 0.000
#> GSM78550 4 0.314 0.745 0.204 0.000 0.000 0.796 0.000
#> GSM78554 4 0.483 0.627 0.028 0.308 0.008 0.656 0.000
#> GSM78562 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM78540 4 0.321 0.701 0.212 0.000 0.000 0.788 0.000
#> GSM78546 3 0.000 0.883 0.000 0.000 1.000 0.000 0.000
#> GSM78551 4 0.314 0.745 0.204 0.000 0.000 0.796 0.000
#> GSM78555 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM78563 4 0.321 0.701 0.212 0.000 0.000 0.788 0.000
#> GSM43005 3 0.000 0.883 0.000 0.000 1.000 0.000 0.000
#> GSM43008 3 0.000 0.883 0.000 0.000 1.000 0.000 0.000
#> GSM43011 3 0.000 0.883 0.000 0.000 1.000 0.000 0.000
#> GSM78523 5 0.424 0.511 0.000 0.000 0.428 0.000 0.572
#> GSM78526 4 0.314 0.745 0.204 0.000 0.000 0.796 0.000
#> GSM78529 5 0.591 -0.318 0.000 0.348 0.116 0.000 0.536
#> GSM78532 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM78534 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM78537 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM78543 4 0.448 0.562 0.000 0.376 0.012 0.612 0.000
#> GSM78548 4 0.314 0.745 0.204 0.000 0.000 0.796 0.000
#> GSM78557 4 0.448 0.562 0.000 0.376 0.012 0.612 0.000
#> GSM78560 4 0.448 0.562 0.000 0.376 0.012 0.612 0.000
#> GSM78565 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM43000 5 0.425 0.505 0.000 0.000 0.432 0.000 0.568
#> GSM43002 3 0.000 0.883 0.000 0.000 1.000 0.000 0.000
#> GSM43004 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM43007 3 0.000 0.883 0.000 0.000 1.000 0.000 0.000
#> GSM43010 4 0.314 0.745 0.204 0.000 0.000 0.796 0.000
#> GSM78522 3 0.528 0.262 0.000 0.376 0.568 0.056 0.000
#> GSM78525 3 0.000 0.883 0.000 0.000 1.000 0.000 0.000
#> GSM78528 5 0.430 0.423 0.000 0.000 0.472 0.000 0.528
#> GSM78531 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM78533 4 0.482 0.650 0.040 0.264 0.008 0.688 0.000
#> GSM78536 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM78541 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM78547 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM78552 3 0.000 0.883 0.000 0.000 1.000 0.000 0.000
#> GSM78556 4 0.321 0.701 0.212 0.000 0.000 0.788 0.000
#> GSM78559 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM78564 4 0.463 0.565 0.004 0.376 0.012 0.608 0.000
#> GSM42999 2 0.430 0.868 0.000 0.520 0.000 0.000 0.480
#> GSM43001 2 0.411 0.959 0.000 0.624 0.000 0.000 0.376
#> GSM43003 5 0.265 0.579 0.000 0.000 0.152 0.000 0.848
#> GSM43006 2 0.411 0.959 0.000 0.624 0.000 0.000 0.376
#> GSM43009 3 0.415 -0.127 0.000 0.000 0.612 0.000 0.388
#> GSM43012 5 0.265 0.579 0.000 0.000 0.152 0.000 0.848
#> GSM78524 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM78527 5 0.445 0.414 0.000 0.112 0.128 0.000 0.760
#> GSM78530 3 0.029 0.875 0.000 0.000 0.992 0.000 0.008
#> GSM78535 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM78538 4 0.314 0.745 0.204 0.000 0.000 0.796 0.000
#> GSM78542 4 0.314 0.745 0.204 0.000 0.000 0.796 0.000
#> GSM78544 3 0.000 0.883 0.000 0.000 1.000 0.000 0.000
#> GSM78549 3 0.269 0.660 0.000 0.000 0.844 0.000 0.156
#> GSM78553 4 0.314 0.745 0.204 0.000 0.000 0.796 0.000
#> GSM78558 4 0.353 0.744 0.204 0.012 0.000 0.784 0.000
#> GSM78561 2 0.411 0.959 0.000 0.624 0.000 0.000 0.376
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM78539 6 0.2631 0.771386 0.000 0.000 0.000 0.180 0.000 0.820
#> GSM78545 3 0.0000 0.893041 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM78550 4 0.0000 0.859700 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78554 6 0.2631 0.771386 0.000 0.000 0.000 0.180 0.000 0.820
#> GSM78562 1 0.0000 0.999198 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78540 4 0.4693 0.614833 0.176 0.000 0.000 0.684 0.000 0.140
#> GSM78546 3 0.0000 0.893041 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM78551 4 0.0146 0.858214 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM78555 1 0.0000 0.999198 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78563 4 0.4693 0.614833 0.176 0.000 0.000 0.684 0.000 0.140
#> GSM43005 3 0.0000 0.893041 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM43008 3 0.0000 0.893041 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM43011 3 0.0000 0.893041 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM78523 5 0.3592 0.534062 0.000 0.000 0.344 0.000 0.656 0.000
#> GSM78526 4 0.0000 0.859700 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78529 5 0.3717 -0.131603 0.000 0.384 0.000 0.000 0.616 0.000
#> GSM78532 1 0.0000 0.999198 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78534 1 0.0146 0.995180 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM78537 1 0.0000 0.999198 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78543 6 0.0000 0.830668 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78548 4 0.0000 0.859700 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78557 6 0.0000 0.830668 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78560 6 0.0000 0.830668 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM78565 1 0.0000 0.999198 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM43000 5 0.3607 0.528814 0.000 0.000 0.348 0.000 0.652 0.000
#> GSM43002 3 0.0000 0.893041 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM43004 1 0.0000 0.999198 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM43007 3 0.0000 0.893041 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM43010 4 0.0000 0.859700 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78522 3 0.3833 0.186681 0.000 0.000 0.556 0.000 0.000 0.444
#> GSM78525 3 0.0000 0.893041 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM78528 5 0.3737 0.448739 0.000 0.000 0.392 0.000 0.608 0.000
#> GSM78531 1 0.0000 0.999198 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78533 6 0.3737 0.395323 0.000 0.000 0.000 0.392 0.000 0.608
#> GSM78536 1 0.0000 0.999198 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78541 1 0.0000 0.999198 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78547 1 0.0000 0.999198 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78552 3 0.0000 0.893041 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM78556 4 0.4693 0.614833 0.176 0.000 0.000 0.684 0.000 0.140
#> GSM78559 1 0.0000 0.999198 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78564 6 0.0146 0.831182 0.000 0.000 0.000 0.004 0.000 0.996
#> GSM42999 2 0.3288 0.642742 0.000 0.724 0.000 0.000 0.276 0.000
#> GSM43001 2 0.0000 0.901514 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43003 5 0.0000 0.570401 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM43006 2 0.0000 0.901514 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43009 3 0.3782 -0.000383 0.000 0.000 0.588 0.000 0.412 0.000
#> GSM43012 5 0.0000 0.570401 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM78524 1 0.0146 0.995180 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM78527 5 0.2219 0.453728 0.000 0.136 0.000 0.000 0.864 0.000
#> GSM78530 3 0.0260 0.886183 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM78535 1 0.0000 0.999198 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78538 4 0.0000 0.859700 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78542 4 0.0000 0.859700 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78544 3 0.0000 0.893041 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM78549 3 0.2631 0.669852 0.000 0.000 0.820 0.000 0.180 0.000
#> GSM78553 4 0.1204 0.820208 0.000 0.000 0.000 0.944 0.000 0.056
#> GSM78558 4 0.3050 0.586517 0.000 0.000 0.000 0.764 0.000 0.236
#> GSM78561 2 0.0000 0.901514 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) agent(p) individual(p) k
#> ATC:hclust 58 0.0591 0.340 0.00642 2
#> ATC:hclust 53 0.0630 0.728 0.09488 3
#> ATC:hclust 44 0.0642 0.181 0.22427 4
#> ATC:hclust 53 0.0448 0.595 0.00981 5
#> ATC:hclust 52 0.0483 0.106 0.06992 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "kmeans"]
# you can also extract it by
# res = res_list["ATC:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 58 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4996 0.501 0.501
#> 3 3 0.557 0.774 0.878 0.2670 0.624 0.393
#> 4 4 1.000 0.965 0.971 0.1616 0.761 0.443
#> 5 5 0.811 0.856 0.876 0.0585 1.000 1.000
#> 6 6 0.787 0.742 0.781 0.0435 1.000 1.000
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM78539 1 0 1 1 0
#> GSM78545 2 0 1 0 1
#> GSM78550 1 0 1 1 0
#> GSM78554 1 0 1 1 0
#> GSM78562 1 0 1 1 0
#> GSM78540 1 0 1 1 0
#> GSM78546 2 0 1 0 1
#> GSM78551 1 0 1 1 0
#> GSM78555 1 0 1 1 0
#> GSM78563 1 0 1 1 0
#> GSM43005 2 0 1 0 1
#> GSM43008 2 0 1 0 1
#> GSM43011 2 0 1 0 1
#> GSM78523 2 0 1 0 1
#> GSM78526 1 0 1 1 0
#> GSM78529 2 0 1 0 1
#> GSM78532 1 0 1 1 0
#> GSM78534 1 0 1 1 0
#> GSM78537 1 0 1 1 0
#> GSM78543 1 0 1 1 0
#> GSM78548 1 0 1 1 0
#> GSM78557 1 0 1 1 0
#> GSM78560 1 0 1 1 0
#> GSM78565 1 0 1 1 0
#> GSM43000 2 0 1 0 1
#> GSM43002 2 0 1 0 1
#> GSM43004 1 0 1 1 0
#> GSM43007 2 0 1 0 1
#> GSM43010 1 0 1 1 0
#> GSM78522 2 0 1 0 1
#> GSM78525 2 0 1 0 1
#> GSM78528 2 0 1 0 1
#> GSM78531 1 0 1 1 0
#> GSM78533 1 0 1 1 0
#> GSM78536 1 0 1 1 0
#> GSM78541 1 0 1 1 0
#> GSM78547 1 0 1 1 0
#> GSM78552 2 0 1 0 1
#> GSM78556 1 0 1 1 0
#> GSM78559 1 0 1 1 0
#> GSM78564 1 0 1 1 0
#> GSM42999 2 0 1 0 1
#> GSM43001 2 0 1 0 1
#> GSM43003 2 0 1 0 1
#> GSM43006 2 0 1 0 1
#> GSM43009 2 0 1 0 1
#> GSM43012 2 0 1 0 1
#> GSM78524 1 0 1 1 0
#> GSM78527 2 0 1 0 1
#> GSM78530 2 0 1 0 1
#> GSM78535 1 0 1 1 0
#> GSM78538 1 0 1 1 0
#> GSM78542 1 0 1 1 0
#> GSM78544 2 0 1 0 1
#> GSM78549 2 0 1 0 1
#> GSM78553 1 0 1 1 0
#> GSM78558 1 0 1 1 0
#> GSM78561 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM78539 3 0.4555 0.720 0.200 0.000 0.800
#> GSM78545 3 0.4842 0.637 0.000 0.224 0.776
#> GSM78550 3 0.4555 0.720 0.200 0.000 0.800
#> GSM78554 3 0.4555 0.720 0.200 0.000 0.800
#> GSM78562 1 0.0000 0.941 1.000 0.000 0.000
#> GSM78540 1 0.4842 0.763 0.776 0.000 0.224
#> GSM78546 3 0.2711 0.707 0.000 0.088 0.912
#> GSM78551 3 0.4654 0.710 0.208 0.000 0.792
#> GSM78555 1 0.0000 0.941 1.000 0.000 0.000
#> GSM78563 1 0.4842 0.763 0.776 0.000 0.224
#> GSM43005 3 0.0592 0.727 0.000 0.012 0.988
#> GSM43008 3 0.4605 0.653 0.000 0.204 0.796
#> GSM43011 3 0.4842 0.637 0.000 0.224 0.776
#> GSM78523 2 0.5591 0.643 0.000 0.696 0.304
#> GSM78526 3 0.4555 0.720 0.200 0.000 0.800
#> GSM78529 2 0.0000 0.872 0.000 1.000 0.000
#> GSM78532 1 0.0000 0.941 1.000 0.000 0.000
#> GSM78534 1 0.0000 0.941 1.000 0.000 0.000
#> GSM78537 1 0.0000 0.941 1.000 0.000 0.000
#> GSM78543 3 0.4555 0.720 0.200 0.000 0.800
#> GSM78548 3 0.0000 0.729 0.000 0.000 1.000
#> GSM78557 3 0.4555 0.720 0.200 0.000 0.800
#> GSM78560 3 0.0000 0.729 0.000 0.000 1.000
#> GSM78565 1 0.0000 0.941 1.000 0.000 0.000
#> GSM43000 2 0.6008 0.524 0.000 0.628 0.372
#> GSM43002 3 0.4842 0.637 0.000 0.224 0.776
#> GSM43004 1 0.0000 0.941 1.000 0.000 0.000
#> GSM43007 3 0.4605 0.653 0.000 0.204 0.796
#> GSM43010 3 0.4605 0.715 0.204 0.000 0.796
#> GSM78522 3 0.4842 0.637 0.000 0.224 0.776
#> GSM78525 3 0.4842 0.637 0.000 0.224 0.776
#> GSM78528 2 0.6008 0.524 0.000 0.628 0.372
#> GSM78531 1 0.0000 0.941 1.000 0.000 0.000
#> GSM78533 3 0.4555 0.720 0.200 0.000 0.800
#> GSM78536 1 0.0000 0.941 1.000 0.000 0.000
#> GSM78541 1 0.0000 0.941 1.000 0.000 0.000
#> GSM78547 1 0.0000 0.941 1.000 0.000 0.000
#> GSM78552 3 0.4842 0.637 0.000 0.224 0.776
#> GSM78556 1 0.4842 0.763 0.776 0.000 0.224
#> GSM78559 1 0.0000 0.941 1.000 0.000 0.000
#> GSM78564 3 0.4555 0.720 0.200 0.000 0.800
#> GSM42999 2 0.0000 0.872 0.000 1.000 0.000
#> GSM43001 2 0.0000 0.872 0.000 1.000 0.000
#> GSM43003 2 0.0000 0.872 0.000 1.000 0.000
#> GSM43006 2 0.0000 0.872 0.000 1.000 0.000
#> GSM43009 2 0.4702 0.746 0.000 0.788 0.212
#> GSM43012 2 0.0000 0.872 0.000 1.000 0.000
#> GSM78524 1 0.0000 0.941 1.000 0.000 0.000
#> GSM78527 2 0.0000 0.872 0.000 1.000 0.000
#> GSM78530 3 0.4842 0.637 0.000 0.224 0.776
#> GSM78535 1 0.0000 0.941 1.000 0.000 0.000
#> GSM78538 1 0.4842 0.763 0.776 0.000 0.224
#> GSM78542 3 0.4654 0.710 0.208 0.000 0.792
#> GSM78544 3 0.4605 0.653 0.000 0.204 0.796
#> GSM78549 3 0.4887 0.631 0.000 0.228 0.772
#> GSM78553 3 0.4555 0.720 0.200 0.000 0.800
#> GSM78558 3 0.0000 0.729 0.000 0.000 1.000
#> GSM78561 2 0.0000 0.872 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM78539 4 0.0376 0.990 0.000 0.004 0.004 0.992
#> GSM78545 3 0.0000 0.989 0.000 0.000 1.000 0.000
#> GSM78550 4 0.0188 0.991 0.000 0.000 0.004 0.996
#> GSM78554 4 0.0188 0.991 0.000 0.000 0.004 0.996
#> GSM78562 1 0.1837 0.987 0.944 0.028 0.000 0.028
#> GSM78540 4 0.0376 0.989 0.004 0.004 0.000 0.992
#> GSM78546 3 0.0817 0.965 0.000 0.000 0.976 0.024
#> GSM78551 4 0.0188 0.991 0.000 0.000 0.004 0.996
#> GSM78555 1 0.1256 0.989 0.964 0.008 0.000 0.028
#> GSM78563 4 0.0376 0.989 0.004 0.004 0.000 0.992
#> GSM43005 3 0.1118 0.950 0.000 0.000 0.964 0.036
#> GSM43008 3 0.0188 0.987 0.000 0.000 0.996 0.004
#> GSM43011 3 0.0000 0.989 0.000 0.000 1.000 0.000
#> GSM78523 3 0.0000 0.989 0.000 0.000 1.000 0.000
#> GSM78526 4 0.0188 0.991 0.000 0.000 0.004 0.996
#> GSM78529 2 0.1118 0.928 0.000 0.964 0.036 0.000
#> GSM78532 1 0.1510 0.989 0.956 0.016 0.000 0.028
#> GSM78534 1 0.1837 0.987 0.944 0.028 0.000 0.028
#> GSM78537 1 0.1388 0.990 0.960 0.012 0.000 0.028
#> GSM78543 4 0.0376 0.990 0.000 0.004 0.004 0.992
#> GSM78548 4 0.1022 0.964 0.000 0.000 0.032 0.968
#> GSM78557 4 0.0376 0.990 0.000 0.004 0.004 0.992
#> GSM78560 4 0.1209 0.964 0.000 0.004 0.032 0.964
#> GSM78565 1 0.1109 0.989 0.968 0.004 0.000 0.028
#> GSM43000 3 0.0000 0.989 0.000 0.000 1.000 0.000
#> GSM43002 3 0.0000 0.989 0.000 0.000 1.000 0.000
#> GSM43004 1 0.1837 0.987 0.944 0.028 0.000 0.028
#> GSM43007 3 0.0188 0.987 0.000 0.000 0.996 0.004
#> GSM43010 4 0.0188 0.991 0.000 0.000 0.004 0.996
#> GSM78522 3 0.0000 0.989 0.000 0.000 1.000 0.000
#> GSM78525 3 0.0000 0.989 0.000 0.000 1.000 0.000
#> GSM78528 3 0.0000 0.989 0.000 0.000 1.000 0.000
#> GSM78531 1 0.1510 0.989 0.956 0.016 0.000 0.028
#> GSM78533 4 0.0188 0.991 0.000 0.000 0.004 0.996
#> GSM78536 1 0.0921 0.990 0.972 0.000 0.000 0.028
#> GSM78541 1 0.0921 0.990 0.972 0.000 0.000 0.028
#> GSM78547 1 0.1837 0.987 0.944 0.028 0.000 0.028
#> GSM78552 3 0.0000 0.989 0.000 0.000 1.000 0.000
#> GSM78556 4 0.0376 0.989 0.004 0.004 0.000 0.992
#> GSM78559 1 0.1109 0.989 0.968 0.004 0.000 0.028
#> GSM78564 4 0.0376 0.990 0.000 0.004 0.004 0.992
#> GSM42999 2 0.1118 0.928 0.000 0.964 0.036 0.000
#> GSM43001 2 0.1452 0.928 0.008 0.956 0.036 0.000
#> GSM43003 2 0.5581 0.230 0.020 0.532 0.448 0.000
#> GSM43006 2 0.1452 0.928 0.008 0.956 0.036 0.000
#> GSM43009 3 0.1229 0.966 0.020 0.008 0.968 0.004
#> GSM43012 2 0.1913 0.922 0.020 0.940 0.040 0.000
#> GSM78524 1 0.1510 0.988 0.956 0.016 0.000 0.028
#> GSM78527 2 0.1820 0.923 0.020 0.944 0.036 0.000
#> GSM78530 3 0.0188 0.986 0.000 0.000 0.996 0.004
#> GSM78535 1 0.1109 0.989 0.968 0.004 0.000 0.028
#> GSM78538 4 0.0336 0.985 0.000 0.008 0.000 0.992
#> GSM78542 4 0.0000 0.989 0.000 0.000 0.000 1.000
#> GSM78544 3 0.0336 0.986 0.000 0.000 0.992 0.008
#> GSM78549 3 0.1229 0.966 0.020 0.008 0.968 0.004
#> GSM78553 4 0.0000 0.989 0.000 0.000 0.000 1.000
#> GSM78558 4 0.0921 0.965 0.000 0.000 0.028 0.972
#> GSM78561 2 0.1452 0.928 0.008 0.956 0.036 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM78539 4 0.3741 0.839 0.000 0.000 0.004 0.732 0.264
#> GSM78545 3 0.0162 0.903 0.000 0.000 0.996 0.000 0.004
#> GSM78550 4 0.0162 0.875 0.000 0.000 0.004 0.996 0.000
#> GSM78554 4 0.3366 0.859 0.000 0.000 0.004 0.784 0.212
#> GSM78562 1 0.3561 0.877 0.740 0.000 0.000 0.000 0.260
#> GSM78540 4 0.2536 0.875 0.004 0.000 0.000 0.868 0.128
#> GSM78546 3 0.2519 0.868 0.000 0.000 0.884 0.016 0.100
#> GSM78551 4 0.0162 0.875 0.000 0.000 0.004 0.996 0.000
#> GSM78555 1 0.1670 0.901 0.936 0.012 0.000 0.000 0.052
#> GSM78563 4 0.2536 0.875 0.004 0.000 0.000 0.868 0.128
#> GSM43005 3 0.0671 0.900 0.000 0.000 0.980 0.016 0.004
#> GSM43008 3 0.1851 0.883 0.000 0.000 0.912 0.000 0.088
#> GSM43011 3 0.0404 0.903 0.000 0.000 0.988 0.000 0.012
#> GSM78523 3 0.2806 0.853 0.000 0.004 0.844 0.000 0.152
#> GSM78526 4 0.0162 0.875 0.000 0.000 0.004 0.996 0.000
#> GSM78529 2 0.0912 0.880 0.000 0.972 0.016 0.000 0.012
#> GSM78532 1 0.2230 0.905 0.884 0.000 0.000 0.000 0.116
#> GSM78534 1 0.3715 0.874 0.736 0.004 0.000 0.000 0.260
#> GSM78537 1 0.2230 0.907 0.884 0.000 0.000 0.000 0.116
#> GSM78543 4 0.4359 0.740 0.000 0.000 0.004 0.584 0.412
#> GSM78548 4 0.1571 0.878 0.000 0.000 0.004 0.936 0.060
#> GSM78557 4 0.4066 0.808 0.000 0.000 0.004 0.672 0.324
#> GSM78560 4 0.4367 0.736 0.000 0.000 0.004 0.580 0.416
#> GSM78565 1 0.1364 0.902 0.952 0.012 0.000 0.000 0.036
#> GSM43000 3 0.2806 0.853 0.000 0.004 0.844 0.000 0.152
#> GSM43002 3 0.0609 0.903 0.000 0.000 0.980 0.000 0.020
#> GSM43004 1 0.3715 0.874 0.736 0.004 0.000 0.000 0.260
#> GSM43007 3 0.1851 0.883 0.000 0.000 0.912 0.000 0.088
#> GSM43010 4 0.0162 0.875 0.000 0.000 0.004 0.996 0.000
#> GSM78522 3 0.2690 0.840 0.000 0.000 0.844 0.000 0.156
#> GSM78525 3 0.0404 0.903 0.000 0.000 0.988 0.000 0.012
#> GSM78528 3 0.2806 0.853 0.000 0.004 0.844 0.000 0.152
#> GSM78531 1 0.2230 0.905 0.884 0.000 0.000 0.000 0.116
#> GSM78533 4 0.2719 0.877 0.000 0.000 0.004 0.852 0.144
#> GSM78536 1 0.0000 0.902 1.000 0.000 0.000 0.000 0.000
#> GSM78541 1 0.0000 0.902 1.000 0.000 0.000 0.000 0.000
#> GSM78547 1 0.3561 0.877 0.740 0.000 0.000 0.000 0.260
#> GSM78552 3 0.1851 0.883 0.000 0.000 0.912 0.000 0.088
#> GSM78556 4 0.2389 0.876 0.004 0.000 0.000 0.880 0.116
#> GSM78559 1 0.0290 0.900 0.992 0.000 0.000 0.000 0.008
#> GSM78564 4 0.4066 0.808 0.000 0.000 0.004 0.672 0.324
#> GSM42999 2 0.0912 0.880 0.000 0.972 0.016 0.000 0.012
#> GSM43001 2 0.0798 0.880 0.000 0.976 0.016 0.000 0.008
#> GSM43003 2 0.6676 0.191 0.000 0.416 0.344 0.000 0.240
#> GSM43006 2 0.0798 0.880 0.000 0.976 0.016 0.000 0.008
#> GSM43009 3 0.3662 0.771 0.000 0.004 0.744 0.000 0.252
#> GSM43012 2 0.3999 0.795 0.000 0.740 0.020 0.000 0.240
#> GSM78524 1 0.3343 0.883 0.812 0.016 0.000 0.000 0.172
#> GSM78527 2 0.3183 0.841 0.000 0.828 0.016 0.000 0.156
#> GSM78530 3 0.1768 0.891 0.000 0.000 0.924 0.004 0.072
#> GSM78535 1 0.0290 0.900 0.992 0.000 0.000 0.000 0.008
#> GSM78538 4 0.1410 0.852 0.000 0.000 0.000 0.940 0.060
#> GSM78542 4 0.0963 0.861 0.000 0.000 0.000 0.964 0.036
#> GSM78544 3 0.1430 0.896 0.000 0.000 0.944 0.004 0.052
#> GSM78549 3 0.3010 0.835 0.000 0.000 0.824 0.004 0.172
#> GSM78553 4 0.0963 0.861 0.000 0.000 0.000 0.964 0.036
#> GSM78558 4 0.2471 0.864 0.000 0.000 0.000 0.864 0.136
#> GSM78561 2 0.0798 0.880 0.000 0.976 0.016 0.000 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM78539 4 0.2048 0.697 0.000 0.000 0.000 0.880 NA 0.120
#> GSM78545 3 0.0146 0.824 0.000 0.000 0.996 0.000 NA 0.000
#> GSM78550 4 0.3774 0.755 0.000 0.000 0.000 0.664 NA 0.328
#> GSM78554 4 0.1075 0.727 0.000 0.000 0.000 0.952 NA 0.048
#> GSM78562 1 0.0622 0.744 0.980 0.000 0.000 0.000 NA 0.012
#> GSM78540 4 0.2709 0.755 0.000 0.000 0.000 0.848 NA 0.132
#> GSM78546 3 0.4299 0.742 0.000 0.000 0.720 0.000 NA 0.188
#> GSM78551 4 0.3578 0.755 0.000 0.000 0.000 0.660 NA 0.340
#> GSM78555 1 0.4488 0.785 0.548 0.000 0.000 0.000 NA 0.032
#> GSM78563 4 0.2709 0.755 0.000 0.000 0.000 0.848 NA 0.132
#> GSM43005 3 0.1257 0.822 0.000 0.000 0.952 0.000 NA 0.020
#> GSM43008 3 0.3978 0.765 0.000 0.000 0.756 0.000 NA 0.160
#> GSM43011 3 0.0291 0.824 0.000 0.000 0.992 0.000 NA 0.004
#> GSM78523 3 0.3412 0.763 0.000 0.000 0.808 0.000 NA 0.064
#> GSM78526 4 0.3804 0.754 0.000 0.000 0.000 0.656 NA 0.336
#> GSM78529 2 0.1082 0.830 0.000 0.956 0.000 0.000 NA 0.004
#> GSM78532 1 0.3512 0.799 0.772 0.000 0.000 0.000 NA 0.032
#> GSM78534 1 0.0717 0.747 0.976 0.000 0.000 0.000 NA 0.016
#> GSM78537 1 0.3511 0.802 0.760 0.000 0.000 0.000 NA 0.024
#> GSM78543 4 0.4580 0.502 0.000 0.000 0.000 0.612 NA 0.336
#> GSM78548 4 0.3217 0.757 0.000 0.000 0.000 0.768 NA 0.224
#> GSM78557 4 0.3457 0.622 0.000 0.000 0.000 0.752 NA 0.232
#> GSM78560 4 0.4575 0.484 0.000 0.000 0.000 0.600 NA 0.352
#> GSM78565 1 0.4499 0.784 0.540 0.000 0.000 0.000 NA 0.032
#> GSM43000 3 0.3370 0.764 0.000 0.000 0.812 0.000 NA 0.064
#> GSM43002 3 0.1757 0.816 0.000 0.000 0.916 0.000 NA 0.008
#> GSM43004 1 0.0717 0.747 0.976 0.000 0.000 0.000 NA 0.016
#> GSM43007 3 0.3978 0.765 0.000 0.000 0.756 0.000 NA 0.160
#> GSM43010 4 0.3592 0.754 0.000 0.000 0.000 0.656 NA 0.344
#> GSM78522 3 0.4871 0.696 0.000 0.000 0.660 0.000 NA 0.196
#> GSM78525 3 0.0146 0.824 0.000 0.000 0.996 0.000 NA 0.000
#> GSM78528 3 0.3370 0.764 0.000 0.000 0.812 0.000 NA 0.064
#> GSM78531 1 0.3512 0.799 0.772 0.000 0.000 0.000 NA 0.032
#> GSM78533 4 0.1007 0.753 0.000 0.000 0.000 0.956 NA 0.044
#> GSM78536 1 0.4509 0.792 0.532 0.000 0.000 0.000 NA 0.032
#> GSM78541 1 0.4509 0.792 0.532 0.000 0.000 0.000 NA 0.032
#> GSM78547 1 0.0622 0.744 0.980 0.000 0.000 0.000 NA 0.012
#> GSM78552 3 0.3978 0.765 0.000 0.000 0.756 0.000 NA 0.160
#> GSM78556 4 0.2581 0.757 0.000 0.000 0.000 0.860 NA 0.120
#> GSM78559 1 0.3867 0.785 0.512 0.000 0.000 0.000 NA 0.000
#> GSM78564 4 0.3457 0.622 0.000 0.000 0.000 0.752 NA 0.232
#> GSM42999 2 0.1082 0.830 0.000 0.956 0.000 0.000 NA 0.004
#> GSM43001 2 0.0713 0.826 0.000 0.972 0.000 0.000 NA 0.028
#> GSM43003 2 0.7187 0.177 0.000 0.332 0.288 0.000 NA 0.080
#> GSM43006 2 0.0713 0.826 0.000 0.972 0.000 0.000 NA 0.028
#> GSM43009 3 0.5201 0.594 0.000 0.012 0.616 0.000 NA 0.096
#> GSM43012 2 0.4916 0.706 0.000 0.620 0.004 0.000 NA 0.080
#> GSM78524 1 0.3651 0.763 0.772 0.000 0.000 0.000 NA 0.048
#> GSM78527 2 0.3920 0.769 0.000 0.736 0.000 0.000 NA 0.048
#> GSM78530 3 0.2499 0.803 0.000 0.000 0.880 0.000 NA 0.048
#> GSM78535 1 0.3867 0.785 0.512 0.000 0.000 0.000 NA 0.000
#> GSM78538 4 0.4586 0.724 0.004 0.000 0.000 0.564 NA 0.400
#> GSM78542 4 0.4076 0.732 0.000 0.000 0.000 0.592 NA 0.396
#> GSM78544 3 0.2070 0.815 0.000 0.000 0.908 0.000 NA 0.044
#> GSM78549 3 0.4841 0.672 0.000 0.012 0.684 0.000 NA 0.100
#> GSM78553 4 0.4121 0.733 0.000 0.000 0.000 0.604 NA 0.380
#> GSM78558 4 0.3725 0.731 0.000 0.000 0.000 0.676 NA 0.316
#> GSM78561 2 0.0713 0.826 0.000 0.972 0.000 0.000 NA 0.028
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) agent(p) individual(p) k
#> ATC:kmeans 58 0.05915 0.340 0.00642 2
#> ATC:kmeans 58 0.02569 0.233 0.01335 3
#> ATC:kmeans 57 0.01011 0.582 0.07213 4
#> ATC:kmeans 57 0.01011 0.582 0.07213 5
#> ATC:kmeans 56 0.00911 0.673 0.08608 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "skmeans"]
# you can also extract it by
# res = res_list["ATC:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 58 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.986 0.994 0.501 0.501 0.501
#> 3 3 0.849 0.910 0.938 0.261 0.861 0.722
#> 4 4 0.792 0.832 0.847 0.112 0.946 0.849
#> 5 5 0.828 0.889 0.918 0.100 0.897 0.669
#> 6 6 0.878 0.854 0.898 0.034 0.968 0.852
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM78539 1 0.000 0.988 1.000 0.000
#> GSM78545 2 0.000 1.000 0.000 1.000
#> GSM78550 1 0.000 0.988 1.000 0.000
#> GSM78554 1 0.000 0.988 1.000 0.000
#> GSM78562 1 0.000 0.988 1.000 0.000
#> GSM78540 1 0.000 0.988 1.000 0.000
#> GSM78546 2 0.000 1.000 0.000 1.000
#> GSM78551 1 0.000 0.988 1.000 0.000
#> GSM78555 1 0.000 0.988 1.000 0.000
#> GSM78563 1 0.000 0.988 1.000 0.000
#> GSM43005 2 0.000 1.000 0.000 1.000
#> GSM43008 2 0.000 1.000 0.000 1.000
#> GSM43011 2 0.000 1.000 0.000 1.000
#> GSM78523 2 0.000 1.000 0.000 1.000
#> GSM78526 1 0.000 0.988 1.000 0.000
#> GSM78529 2 0.000 1.000 0.000 1.000
#> GSM78532 1 0.000 0.988 1.000 0.000
#> GSM78534 1 0.000 0.988 1.000 0.000
#> GSM78537 1 0.000 0.988 1.000 0.000
#> GSM78543 1 0.000 0.988 1.000 0.000
#> GSM78548 1 0.653 0.803 0.832 0.168
#> GSM78557 1 0.000 0.988 1.000 0.000
#> GSM78560 1 0.722 0.758 0.800 0.200
#> GSM78565 1 0.000 0.988 1.000 0.000
#> GSM43000 2 0.000 1.000 0.000 1.000
#> GSM43002 2 0.000 1.000 0.000 1.000
#> GSM43004 1 0.000 0.988 1.000 0.000
#> GSM43007 2 0.000 1.000 0.000 1.000
#> GSM43010 1 0.000 0.988 1.000 0.000
#> GSM78522 2 0.000 1.000 0.000 1.000
#> GSM78525 2 0.000 1.000 0.000 1.000
#> GSM78528 2 0.000 1.000 0.000 1.000
#> GSM78531 1 0.000 0.988 1.000 0.000
#> GSM78533 1 0.000 0.988 1.000 0.000
#> GSM78536 1 0.000 0.988 1.000 0.000
#> GSM78541 1 0.000 0.988 1.000 0.000
#> GSM78547 1 0.000 0.988 1.000 0.000
#> GSM78552 2 0.000 1.000 0.000 1.000
#> GSM78556 1 0.000 0.988 1.000 0.000
#> GSM78559 1 0.000 0.988 1.000 0.000
#> GSM78564 1 0.000 0.988 1.000 0.000
#> GSM42999 2 0.000 1.000 0.000 1.000
#> GSM43001 2 0.000 1.000 0.000 1.000
#> GSM43003 2 0.000 1.000 0.000 1.000
#> GSM43006 2 0.000 1.000 0.000 1.000
#> GSM43009 2 0.000 1.000 0.000 1.000
#> GSM43012 2 0.000 1.000 0.000 1.000
#> GSM78524 1 0.000 0.988 1.000 0.000
#> GSM78527 2 0.000 1.000 0.000 1.000
#> GSM78530 2 0.000 1.000 0.000 1.000
#> GSM78535 1 0.000 0.988 1.000 0.000
#> GSM78538 1 0.000 0.988 1.000 0.000
#> GSM78542 1 0.000 0.988 1.000 0.000
#> GSM78544 2 0.000 1.000 0.000 1.000
#> GSM78549 2 0.000 1.000 0.000 1.000
#> GSM78553 1 0.000 0.988 1.000 0.000
#> GSM78558 1 0.000 0.988 1.000 0.000
#> GSM78561 2 0.000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM78539 1 0.4796 0.73733 0.780 0.220 0.000
#> GSM78545 3 0.0000 0.99209 0.000 0.000 1.000
#> GSM78550 2 0.4887 0.89728 0.228 0.772 0.000
#> GSM78554 2 0.3619 0.70568 0.136 0.864 0.000
#> GSM78562 1 0.0000 0.92188 1.000 0.000 0.000
#> GSM78540 1 0.0000 0.92188 1.000 0.000 0.000
#> GSM78546 3 0.0237 0.99098 0.000 0.004 0.996
#> GSM78551 2 0.5016 0.89839 0.240 0.760 0.000
#> GSM78555 1 0.0000 0.92188 1.000 0.000 0.000
#> GSM78563 1 0.0000 0.92188 1.000 0.000 0.000
#> GSM43005 3 0.0000 0.99209 0.000 0.000 1.000
#> GSM43008 3 0.0237 0.99098 0.000 0.004 0.996
#> GSM43011 3 0.0000 0.99209 0.000 0.000 1.000
#> GSM78523 3 0.0000 0.99209 0.000 0.000 1.000
#> GSM78526 2 0.4974 0.89898 0.236 0.764 0.000
#> GSM78529 3 0.0747 0.99194 0.000 0.016 0.984
#> GSM78532 1 0.0000 0.92188 1.000 0.000 0.000
#> GSM78534 1 0.0000 0.92188 1.000 0.000 0.000
#> GSM78537 1 0.0000 0.92188 1.000 0.000 0.000
#> GSM78543 1 0.4702 0.74551 0.788 0.212 0.000
#> GSM78548 2 0.5911 0.74683 0.060 0.784 0.156
#> GSM78557 1 0.4702 0.74495 0.788 0.212 0.000
#> GSM78560 1 0.5024 0.73342 0.776 0.220 0.004
#> GSM78565 1 0.0000 0.92188 1.000 0.000 0.000
#> GSM43000 3 0.0000 0.99209 0.000 0.000 1.000
#> GSM43002 3 0.0237 0.99098 0.000 0.004 0.996
#> GSM43004 1 0.0000 0.92188 1.000 0.000 0.000
#> GSM43007 3 0.0237 0.99098 0.000 0.004 0.996
#> GSM43010 2 0.5016 0.89839 0.240 0.760 0.000
#> GSM78522 3 0.0237 0.99098 0.000 0.004 0.996
#> GSM78525 3 0.0000 0.99209 0.000 0.000 1.000
#> GSM78528 3 0.0000 0.99209 0.000 0.000 1.000
#> GSM78531 1 0.0000 0.92188 1.000 0.000 0.000
#> GSM78533 1 0.6095 -0.00779 0.608 0.392 0.000
#> GSM78536 1 0.0000 0.92188 1.000 0.000 0.000
#> GSM78541 1 0.0000 0.92188 1.000 0.000 0.000
#> GSM78547 1 0.0000 0.92188 1.000 0.000 0.000
#> GSM78552 3 0.0237 0.99098 0.000 0.004 0.996
#> GSM78556 1 0.0000 0.92188 1.000 0.000 0.000
#> GSM78559 1 0.0000 0.92188 1.000 0.000 0.000
#> GSM78564 1 0.2537 0.86153 0.920 0.080 0.000
#> GSM42999 3 0.0747 0.99194 0.000 0.016 0.984
#> GSM43001 3 0.0747 0.99194 0.000 0.016 0.984
#> GSM43003 3 0.0747 0.99194 0.000 0.016 0.984
#> GSM43006 3 0.0747 0.99194 0.000 0.016 0.984
#> GSM43009 3 0.0747 0.99194 0.000 0.016 0.984
#> GSM43012 3 0.0747 0.99194 0.000 0.016 0.984
#> GSM78524 1 0.0000 0.92188 1.000 0.000 0.000
#> GSM78527 3 0.0747 0.99194 0.000 0.016 0.984
#> GSM78530 3 0.0747 0.99194 0.000 0.016 0.984
#> GSM78535 1 0.0000 0.92188 1.000 0.000 0.000
#> GSM78538 2 0.5016 0.89839 0.240 0.760 0.000
#> GSM78542 2 0.5016 0.89839 0.240 0.760 0.000
#> GSM78544 3 0.0747 0.99194 0.000 0.016 0.984
#> GSM78549 3 0.0747 0.99194 0.000 0.016 0.984
#> GSM78553 2 0.4931 0.89856 0.232 0.768 0.000
#> GSM78558 2 0.0892 0.75640 0.020 0.980 0.000
#> GSM78561 3 0.0747 0.99194 0.000 0.016 0.984
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM78539 4 0.5453 0.925 0.388 0.020 0.000 0.592
#> GSM78545 3 0.4624 0.814 0.000 0.000 0.660 0.340
#> GSM78550 2 0.0707 0.813 0.020 0.980 0.000 0.000
#> GSM78554 2 0.7286 -0.074 0.156 0.480 0.000 0.364
#> GSM78562 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM78540 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM78546 3 0.4866 0.788 0.000 0.000 0.596 0.404
#> GSM78551 2 0.3266 0.780 0.168 0.832 0.000 0.000
#> GSM78555 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM78563 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM43005 3 0.4624 0.814 0.000 0.000 0.660 0.340
#> GSM43008 3 0.4855 0.790 0.000 0.000 0.600 0.400
#> GSM43011 3 0.4605 0.815 0.000 0.000 0.664 0.336
#> GSM78523 3 0.4585 0.815 0.000 0.000 0.668 0.332
#> GSM78526 2 0.0707 0.813 0.020 0.980 0.000 0.000
#> GSM78529 3 0.0000 0.809 0.000 0.000 1.000 0.000
#> GSM78532 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM78534 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM78537 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM78543 4 0.5386 0.920 0.368 0.020 0.000 0.612
#> GSM78548 2 0.0779 0.811 0.016 0.980 0.000 0.004
#> GSM78557 4 0.5453 0.925 0.388 0.020 0.000 0.592
#> GSM78560 4 0.5193 0.872 0.324 0.020 0.000 0.656
#> GSM78565 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM43000 3 0.4585 0.815 0.000 0.000 0.668 0.332
#> GSM43002 3 0.4843 0.792 0.000 0.000 0.604 0.396
#> GSM43004 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM43007 3 0.4855 0.790 0.000 0.000 0.600 0.400
#> GSM43010 2 0.3837 0.733 0.224 0.776 0.000 0.000
#> GSM78522 3 0.4843 0.792 0.000 0.000 0.604 0.396
#> GSM78525 3 0.4624 0.814 0.000 0.000 0.660 0.340
#> GSM78528 3 0.4585 0.815 0.000 0.000 0.668 0.332
#> GSM78531 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM78533 1 0.4477 0.356 0.688 0.312 0.000 0.000
#> GSM78536 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM78541 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM78547 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM78552 3 0.4855 0.790 0.000 0.000 0.600 0.400
#> GSM78556 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM78559 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM78564 4 0.5506 0.798 0.472 0.016 0.000 0.512
#> GSM42999 3 0.0000 0.809 0.000 0.000 1.000 0.000
#> GSM43001 3 0.0000 0.809 0.000 0.000 1.000 0.000
#> GSM43003 3 0.0000 0.809 0.000 0.000 1.000 0.000
#> GSM43006 3 0.0000 0.809 0.000 0.000 1.000 0.000
#> GSM43009 3 0.0000 0.809 0.000 0.000 1.000 0.000
#> GSM43012 3 0.0000 0.809 0.000 0.000 1.000 0.000
#> GSM78524 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM78527 3 0.0000 0.809 0.000 0.000 1.000 0.000
#> GSM78530 3 0.0000 0.809 0.000 0.000 1.000 0.000
#> GSM78535 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM78538 2 0.4621 0.657 0.284 0.708 0.000 0.008
#> GSM78542 2 0.3591 0.780 0.168 0.824 0.000 0.008
#> GSM78544 3 0.0000 0.809 0.000 0.000 1.000 0.000
#> GSM78549 3 0.0000 0.809 0.000 0.000 1.000 0.000
#> GSM78553 2 0.1042 0.812 0.020 0.972 0.000 0.008
#> GSM78558 2 0.2125 0.774 0.004 0.920 0.000 0.076
#> GSM78561 3 0.0000 0.809 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM78539 4 0.2824 0.861 0.116 0.000 0.020 0.864 0.000
#> GSM78545 3 0.2813 0.903 0.000 0.168 0.832 0.000 0.000
#> GSM78550 5 0.0510 0.795 0.000 0.000 0.016 0.000 0.984
#> GSM78554 4 0.5265 0.301 0.004 0.000 0.040 0.544 0.412
#> GSM78562 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM78540 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM78546 3 0.1845 0.890 0.000 0.056 0.928 0.016 0.000
#> GSM78551 5 0.2690 0.768 0.156 0.000 0.000 0.000 0.844
#> GSM78555 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM78563 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM43005 3 0.2732 0.905 0.000 0.160 0.840 0.000 0.000
#> GSM43008 3 0.1809 0.894 0.000 0.060 0.928 0.012 0.000
#> GSM43011 3 0.2813 0.903 0.000 0.168 0.832 0.000 0.000
#> GSM78523 3 0.3452 0.848 0.000 0.244 0.756 0.000 0.000
#> GSM78526 5 0.0000 0.797 0.000 0.000 0.000 0.000 1.000
#> GSM78529 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM78532 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM78534 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM78537 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM78543 4 0.2305 0.862 0.092 0.000 0.012 0.896 0.000
#> GSM78548 5 0.0609 0.794 0.000 0.000 0.020 0.000 0.980
#> GSM78557 4 0.2179 0.864 0.112 0.000 0.000 0.888 0.000
#> GSM78560 4 0.2331 0.853 0.080 0.000 0.020 0.900 0.000
#> GSM78565 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM43000 3 0.3561 0.832 0.000 0.260 0.740 0.000 0.000
#> GSM43002 3 0.1478 0.896 0.000 0.064 0.936 0.000 0.000
#> GSM43004 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM43007 3 0.1809 0.894 0.000 0.060 0.928 0.012 0.000
#> GSM43010 5 0.3109 0.732 0.200 0.000 0.000 0.000 0.800
#> GSM78522 3 0.2006 0.895 0.000 0.072 0.916 0.012 0.000
#> GSM78525 3 0.2732 0.905 0.000 0.160 0.840 0.000 0.000
#> GSM78528 3 0.3561 0.832 0.000 0.260 0.740 0.000 0.000
#> GSM78531 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM78533 1 0.4415 0.236 0.604 0.000 0.000 0.008 0.388
#> GSM78536 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM78541 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM78547 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM78552 3 0.1809 0.894 0.000 0.060 0.928 0.012 0.000
#> GSM78556 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM78559 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM78564 4 0.3074 0.786 0.196 0.000 0.000 0.804 0.000
#> GSM42999 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM43001 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM43003 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM43006 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM43009 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM43012 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM78524 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM78527 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM78530 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM78535 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM78538 5 0.6036 0.615 0.280 0.000 0.020 0.100 0.600
#> GSM78542 5 0.5012 0.767 0.140 0.000 0.020 0.100 0.740
#> GSM78544 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM78549 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM78553 5 0.2616 0.780 0.000 0.000 0.020 0.100 0.880
#> GSM78558 5 0.3995 0.746 0.000 0.000 0.060 0.152 0.788
#> GSM78561 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM78539 4 0.2510 0.866 0.028 0.000 0.000 0.872 0.100 0.000
#> GSM78545 3 0.1814 0.820 0.000 0.100 0.900 0.000 0.000 0.000
#> GSM78550 6 0.2060 0.599 0.000 0.000 0.016 0.000 0.084 0.900
#> GSM78554 6 0.5486 0.360 0.000 0.000 0.000 0.208 0.224 0.568
#> GSM78562 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78540 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78546 3 0.4050 0.757 0.000 0.016 0.728 0.024 0.232 0.000
#> GSM78551 6 0.1788 0.584 0.076 0.000 0.000 0.004 0.004 0.916
#> GSM78555 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78563 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM43005 3 0.1556 0.821 0.000 0.080 0.920 0.000 0.000 0.000
#> GSM43008 3 0.3810 0.769 0.000 0.016 0.748 0.016 0.220 0.000
#> GSM43011 3 0.1863 0.818 0.000 0.104 0.896 0.000 0.000 0.000
#> GSM78523 3 0.2823 0.767 0.000 0.204 0.796 0.000 0.000 0.000
#> GSM78526 6 0.0146 0.581 0.000 0.000 0.000 0.000 0.004 0.996
#> GSM78529 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78532 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78534 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78537 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78543 4 0.0603 0.899 0.004 0.000 0.000 0.980 0.016 0.000
#> GSM78548 6 0.2581 0.587 0.000 0.000 0.020 0.000 0.120 0.860
#> GSM78557 4 0.1092 0.902 0.020 0.000 0.000 0.960 0.020 0.000
#> GSM78560 4 0.0458 0.897 0.000 0.000 0.000 0.984 0.016 0.000
#> GSM78565 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM43000 3 0.2883 0.757 0.000 0.212 0.788 0.000 0.000 0.000
#> GSM43002 3 0.0820 0.805 0.000 0.016 0.972 0.000 0.012 0.000
#> GSM43004 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM43007 3 0.3810 0.769 0.000 0.016 0.748 0.016 0.220 0.000
#> GSM43010 6 0.2006 0.559 0.104 0.000 0.000 0.000 0.004 0.892
#> GSM78522 3 0.4563 0.749 0.000 0.040 0.700 0.028 0.232 0.000
#> GSM78525 3 0.1663 0.821 0.000 0.088 0.912 0.000 0.000 0.000
#> GSM78528 3 0.2854 0.761 0.000 0.208 0.792 0.000 0.000 0.000
#> GSM78531 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78533 6 0.4266 0.267 0.348 0.000 0.000 0.008 0.016 0.628
#> GSM78536 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78541 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78547 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78552 3 0.3810 0.769 0.000 0.016 0.748 0.016 0.220 0.000
#> GSM78556 1 0.0146 0.995 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM78559 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78564 4 0.2260 0.774 0.140 0.000 0.000 0.860 0.000 0.000
#> GSM42999 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43001 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43003 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43006 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43009 2 0.0146 0.996 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM43012 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78524 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78527 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78530 2 0.0146 0.996 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM78535 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78538 5 0.5659 0.618 0.168 0.000 0.000 0.000 0.496 0.336
#> GSM78542 5 0.5162 0.700 0.088 0.000 0.000 0.000 0.504 0.408
#> GSM78544 2 0.0405 0.990 0.000 0.988 0.004 0.000 0.008 0.000
#> GSM78549 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM78553 5 0.3868 0.645 0.000 0.000 0.000 0.000 0.504 0.496
#> GSM78558 5 0.3670 0.563 0.000 0.000 0.000 0.024 0.736 0.240
#> GSM78561 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) agent(p) individual(p) k
#> ATC:skmeans 58 5.91e-02 0.3398 0.00642 2
#> ATC:skmeans 57 4.38e-02 0.4172 0.05569 3
#> ATC:skmeans 56 1.57e-01 0.1081 0.22123 4
#> ATC:skmeans 56 3.61e-05 0.0699 0.65266 5
#> ATC:skmeans 56 1.91e-06 0.0304 0.55514 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "pam"]
# you can also extract it by
# res = res_list["ATC:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 58 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.733 0.956 0.972 0.4833 0.501 0.501
#> 3 3 0.916 0.928 0.959 0.3516 0.742 0.529
#> 4 4 1.000 0.962 0.985 0.1292 0.861 0.623
#> 5 5 0.832 0.770 0.873 0.0448 0.980 0.925
#> 6 6 0.781 0.608 0.831 0.0618 0.929 0.723
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 3
There is also optional best \(k\) = 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM78539 1 0.000 1.000 1.000 0.000
#> GSM78545 2 0.706 0.838 0.192 0.808
#> GSM78550 1 0.000 1.000 1.000 0.000
#> GSM78554 1 0.000 1.000 1.000 0.000
#> GSM78562 1 0.000 1.000 1.000 0.000
#> GSM78540 1 0.000 1.000 1.000 0.000
#> GSM78546 2 0.706 0.838 0.192 0.808
#> GSM78551 1 0.000 1.000 1.000 0.000
#> GSM78555 1 0.000 1.000 1.000 0.000
#> GSM78563 1 0.000 1.000 1.000 0.000
#> GSM43005 2 0.706 0.838 0.192 0.808
#> GSM43008 2 0.706 0.838 0.192 0.808
#> GSM43011 2 0.000 0.929 0.000 1.000
#> GSM78523 2 0.000 0.929 0.000 1.000
#> GSM78526 1 0.000 1.000 1.000 0.000
#> GSM78529 2 0.000 0.929 0.000 1.000
#> GSM78532 1 0.000 1.000 1.000 0.000
#> GSM78534 1 0.000 1.000 1.000 0.000
#> GSM78537 1 0.000 1.000 1.000 0.000
#> GSM78543 1 0.000 1.000 1.000 0.000
#> GSM78548 1 0.000 1.000 1.000 0.000
#> GSM78557 1 0.000 1.000 1.000 0.000
#> GSM78560 1 0.000 1.000 1.000 0.000
#> GSM78565 1 0.000 1.000 1.000 0.000
#> GSM43000 2 0.000 0.929 0.000 1.000
#> GSM43002 2 0.706 0.838 0.192 0.808
#> GSM43004 1 0.000 1.000 1.000 0.000
#> GSM43007 2 0.706 0.838 0.192 0.808
#> GSM43010 1 0.000 1.000 1.000 0.000
#> GSM78522 2 0.469 0.889 0.100 0.900
#> GSM78525 2 0.706 0.838 0.192 0.808
#> GSM78528 2 0.000 0.929 0.000 1.000
#> GSM78531 1 0.000 1.000 1.000 0.000
#> GSM78533 1 0.000 1.000 1.000 0.000
#> GSM78536 1 0.000 1.000 1.000 0.000
#> GSM78541 1 0.000 1.000 1.000 0.000
#> GSM78547 1 0.000 1.000 1.000 0.000
#> GSM78552 2 0.706 0.838 0.192 0.808
#> GSM78556 1 0.000 1.000 1.000 0.000
#> GSM78559 1 0.000 1.000 1.000 0.000
#> GSM78564 1 0.000 1.000 1.000 0.000
#> GSM42999 2 0.000 0.929 0.000 1.000
#> GSM43001 2 0.000 0.929 0.000 1.000
#> GSM43003 2 0.000 0.929 0.000 1.000
#> GSM43006 2 0.000 0.929 0.000 1.000
#> GSM43009 2 0.000 0.929 0.000 1.000
#> GSM43012 2 0.000 0.929 0.000 1.000
#> GSM78524 1 0.000 1.000 1.000 0.000
#> GSM78527 2 0.000 0.929 0.000 1.000
#> GSM78530 2 0.000 0.929 0.000 1.000
#> GSM78535 1 0.000 1.000 1.000 0.000
#> GSM78538 1 0.000 1.000 1.000 0.000
#> GSM78542 1 0.000 1.000 1.000 0.000
#> GSM78544 2 0.000 0.929 0.000 1.000
#> GSM78549 2 0.000 0.929 0.000 1.000
#> GSM78553 1 0.000 1.000 1.000 0.000
#> GSM78558 1 0.000 1.000 1.000 0.000
#> GSM78561 2 0.000 0.929 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM78539 3 0.0000 0.994 0.000 0.000 1.000
#> GSM78545 2 0.5098 0.767 0.000 0.752 0.248
#> GSM78550 3 0.0000 0.994 0.000 0.000 1.000
#> GSM78554 3 0.0000 0.994 0.000 0.000 1.000
#> GSM78562 1 0.0000 0.999 1.000 0.000 0.000
#> GSM78540 3 0.0000 0.994 0.000 0.000 1.000
#> GSM78546 3 0.0000 0.994 0.000 0.000 1.000
#> GSM78551 3 0.0000 0.994 0.000 0.000 1.000
#> GSM78555 1 0.0000 0.999 1.000 0.000 0.000
#> GSM78563 3 0.0000 0.994 0.000 0.000 1.000
#> GSM43005 3 0.0000 0.994 0.000 0.000 1.000
#> GSM43008 3 0.2711 0.887 0.000 0.088 0.912
#> GSM43011 2 0.2878 0.876 0.000 0.904 0.096
#> GSM78523 2 0.0592 0.878 0.000 0.988 0.012
#> GSM78526 3 0.0000 0.994 0.000 0.000 1.000
#> GSM78529 2 0.0000 0.876 0.000 1.000 0.000
#> GSM78532 1 0.0000 0.999 1.000 0.000 0.000
#> GSM78534 1 0.0000 0.999 1.000 0.000 0.000
#> GSM78537 1 0.0000 0.999 1.000 0.000 0.000
#> GSM78543 3 0.0000 0.994 0.000 0.000 1.000
#> GSM78548 3 0.0000 0.994 0.000 0.000 1.000
#> GSM78557 3 0.0000 0.994 0.000 0.000 1.000
#> GSM78560 3 0.0000 0.994 0.000 0.000 1.000
#> GSM78565 1 0.0000 0.999 1.000 0.000 0.000
#> GSM43000 2 0.2796 0.877 0.000 0.908 0.092
#> GSM43002 2 0.5098 0.767 0.000 0.752 0.248
#> GSM43004 1 0.0000 0.999 1.000 0.000 0.000
#> GSM43007 3 0.1289 0.960 0.000 0.032 0.968
#> GSM43010 3 0.0000 0.994 0.000 0.000 1.000
#> GSM78522 2 0.5431 0.719 0.000 0.716 0.284
#> GSM78525 2 0.4750 0.797 0.000 0.784 0.216
#> GSM78528 2 0.2796 0.877 0.000 0.908 0.092
#> GSM78531 1 0.0000 0.999 1.000 0.000 0.000
#> GSM78533 3 0.0000 0.994 0.000 0.000 1.000
#> GSM78536 1 0.0000 0.999 1.000 0.000 0.000
#> GSM78541 1 0.0000 0.999 1.000 0.000 0.000
#> GSM78547 1 0.0424 0.991 0.992 0.000 0.008
#> GSM78552 2 0.5178 0.757 0.000 0.744 0.256
#> GSM78556 3 0.0000 0.994 0.000 0.000 1.000
#> GSM78559 1 0.0000 0.999 1.000 0.000 0.000
#> GSM78564 3 0.0000 0.994 0.000 0.000 1.000
#> GSM42999 2 0.0000 0.876 0.000 1.000 0.000
#> GSM43001 2 0.0000 0.876 0.000 1.000 0.000
#> GSM43003 2 0.0000 0.876 0.000 1.000 0.000
#> GSM43006 2 0.0000 0.876 0.000 1.000 0.000
#> GSM43009 2 0.0000 0.876 0.000 1.000 0.000
#> GSM43012 2 0.0000 0.876 0.000 1.000 0.000
#> GSM78524 1 0.0000 0.999 1.000 0.000 0.000
#> GSM78527 2 0.0000 0.876 0.000 1.000 0.000
#> GSM78530 2 0.2878 0.876 0.000 0.904 0.096
#> GSM78535 1 0.0000 0.999 1.000 0.000 0.000
#> GSM78538 3 0.0000 0.994 0.000 0.000 1.000
#> GSM78542 3 0.0000 0.994 0.000 0.000 1.000
#> GSM78544 2 0.6308 0.172 0.000 0.508 0.492
#> GSM78549 2 0.2878 0.876 0.000 0.904 0.096
#> GSM78553 3 0.0000 0.994 0.000 0.000 1.000
#> GSM78558 3 0.0000 0.994 0.000 0.000 1.000
#> GSM78561 2 0.0000 0.876 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM78539 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM78545 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM78550 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM78554 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM78562 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM78540 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM78546 3 0.4304 0.601 0.000 0.000 0.716 0.284
#> GSM78551 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM78555 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM78563 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM43005 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM43008 3 0.1474 0.903 0.000 0.000 0.948 0.052
#> GSM43011 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM78523 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM78526 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM78529 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM78532 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM78534 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM78537 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM78543 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM78548 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM78557 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM78560 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM78565 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM43000 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM43002 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM43004 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM43007 3 0.0921 0.926 0.000 0.000 0.972 0.028
#> GSM43010 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM78522 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM78525 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM78528 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM78531 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM78533 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM78536 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM78541 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM78547 1 0.1474 0.932 0.948 0.000 0.000 0.052
#> GSM78552 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM78556 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM78559 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM78564 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM42999 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM43001 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM43003 3 0.4855 0.340 0.000 0.400 0.600 0.000
#> GSM43006 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM43009 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM43012 2 0.1474 0.941 0.000 0.948 0.052 0.000
#> GSM78524 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM78527 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM78530 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM78535 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM78538 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM78542 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM78544 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM78549 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM78553 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM78558 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM78561 2 0.0000 0.991 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM78539 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000
#> GSM78545 3 0.0000 0.855 0.000 0.000 1.000 0.000 0.000
#> GSM78550 4 0.2233 0.925 0.000 0.000 0.004 0.892 0.104
#> GSM78554 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000
#> GSM78562 1 0.3586 0.787 0.736 0.000 0.000 0.000 0.264
#> GSM78540 4 0.0703 0.935 0.000 0.000 0.000 0.976 0.024
#> GSM78546 3 0.3895 0.471 0.000 0.000 0.680 0.320 0.000
#> GSM78551 4 0.1908 0.929 0.000 0.000 0.000 0.908 0.092
#> GSM78555 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM78563 4 0.0703 0.935 0.000 0.000 0.000 0.976 0.024
#> GSM43005 3 0.0000 0.855 0.000 0.000 1.000 0.000 0.000
#> GSM43008 3 0.1270 0.828 0.000 0.000 0.948 0.052 0.000
#> GSM43011 3 0.0162 0.854 0.000 0.004 0.996 0.000 0.000
#> GSM78523 3 0.3857 0.634 0.000 0.312 0.688 0.000 0.000
#> GSM78526 4 0.2439 0.921 0.000 0.000 0.004 0.876 0.120
#> GSM78529 2 0.3895 -0.308 0.000 0.680 0.000 0.000 0.320
#> GSM78532 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM78534 1 0.3508 0.795 0.748 0.000 0.000 0.000 0.252
#> GSM78537 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM78543 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000
#> GSM78548 4 0.2423 0.921 0.000 0.000 0.024 0.896 0.080
#> GSM78557 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000
#> GSM78560 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000
#> GSM78565 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM43000 3 0.3857 0.634 0.000 0.312 0.688 0.000 0.000
#> GSM43002 3 0.0000 0.855 0.000 0.000 1.000 0.000 0.000
#> GSM43004 1 0.3508 0.795 0.748 0.000 0.000 0.000 0.252
#> GSM43007 3 0.0794 0.844 0.000 0.000 0.972 0.028 0.000
#> GSM43010 4 0.2280 0.922 0.000 0.000 0.000 0.880 0.120
#> GSM78522 3 0.0000 0.855 0.000 0.000 1.000 0.000 0.000
#> GSM78525 3 0.0000 0.855 0.000 0.000 1.000 0.000 0.000
#> GSM78528 3 0.3837 0.637 0.000 0.308 0.692 0.000 0.000
#> GSM78531 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM78533 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000
#> GSM78536 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM78541 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM78547 1 0.4777 0.731 0.680 0.000 0.000 0.052 0.268
#> GSM78552 3 0.0000 0.855 0.000 0.000 1.000 0.000 0.000
#> GSM78556 4 0.0703 0.935 0.000 0.000 0.000 0.976 0.024
#> GSM78559 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM78564 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000
#> GSM42999 2 0.4126 -0.467 0.000 0.620 0.000 0.000 0.380
#> GSM43001 5 0.4227 1.000 0.000 0.420 0.000 0.000 0.580
#> GSM43003 2 0.4639 -0.113 0.000 0.632 0.344 0.000 0.024
#> GSM43006 5 0.4227 1.000 0.000 0.420 0.000 0.000 0.580
#> GSM43009 3 0.4654 0.592 0.000 0.348 0.628 0.000 0.024
#> GSM43012 2 0.0693 0.148 0.000 0.980 0.008 0.000 0.012
#> GSM78524 1 0.1121 0.898 0.956 0.000 0.000 0.000 0.044
#> GSM78527 2 0.3857 -0.301 0.000 0.688 0.000 0.000 0.312
#> GSM78530 3 0.2036 0.833 0.000 0.056 0.920 0.000 0.024
#> GSM78535 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> GSM78538 4 0.4161 0.637 0.000 0.000 0.000 0.608 0.392
#> GSM78542 4 0.2561 0.910 0.000 0.000 0.000 0.856 0.144
#> GSM78544 3 0.2291 0.823 0.000 0.036 0.908 0.000 0.056
#> GSM78549 3 0.3055 0.796 0.000 0.072 0.864 0.000 0.064
#> GSM78553 4 0.2280 0.915 0.000 0.000 0.000 0.880 0.120
#> GSM78558 4 0.2280 0.915 0.000 0.000 0.000 0.880 0.120
#> GSM78561 5 0.4227 1.000 0.000 0.420 0.000 0.000 0.580
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM78539 4 0.0000 0.75815 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78545 3 0.0000 0.73846 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM78550 6 0.3866 0.32646 0.000 0.000 0.000 0.484 0.000 0.516
#> GSM78554 4 0.0000 0.75815 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78562 1 0.4942 0.72315 0.652 0.000 0.000 0.000 0.156 0.192
#> GSM78540 4 0.3351 0.53677 0.000 0.000 0.000 0.712 0.000 0.288
#> GSM78546 3 0.3857 0.09148 0.000 0.000 0.532 0.468 0.000 0.000
#> GSM78551 4 0.3867 -0.00612 0.000 0.000 0.000 0.512 0.000 0.488
#> GSM78555 1 0.0632 0.88404 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM78563 4 0.3351 0.53677 0.000 0.000 0.000 0.712 0.000 0.288
#> GSM43005 3 0.0000 0.73846 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM43008 3 0.1141 0.70731 0.000 0.000 0.948 0.052 0.000 0.000
#> GSM43011 3 0.0146 0.73679 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM78523 3 0.3828 -0.15702 0.000 0.000 0.560 0.000 0.440 0.000
#> GSM78526 6 0.3198 0.59766 0.000 0.000 0.000 0.260 0.000 0.740
#> GSM78529 2 0.3563 0.71029 0.000 0.664 0.000 0.000 0.336 0.000
#> GSM78532 1 0.0000 0.88790 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78534 1 0.4302 0.77946 0.728 0.000 0.000 0.000 0.156 0.116
#> GSM78537 1 0.0547 0.88447 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM78543 4 0.0000 0.75815 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78548 4 0.4972 0.07630 0.000 0.000 0.116 0.628 0.000 0.256
#> GSM78557 4 0.0000 0.75815 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78560 4 0.0000 0.75815 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78565 1 0.0000 0.88790 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM43000 3 0.3828 -0.15702 0.000 0.000 0.560 0.000 0.440 0.000
#> GSM43002 3 0.0000 0.73846 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM43004 1 0.4302 0.77946 0.728 0.000 0.000 0.000 0.156 0.116
#> GSM43007 3 0.0632 0.72836 0.000 0.000 0.976 0.024 0.000 0.000
#> GSM43010 6 0.3266 0.58239 0.000 0.000 0.000 0.272 0.000 0.728
#> GSM78522 3 0.0458 0.73364 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM78525 3 0.0000 0.73846 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM78528 3 0.3828 -0.15702 0.000 0.000 0.560 0.000 0.440 0.000
#> GSM78531 1 0.0000 0.88790 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78533 4 0.0000 0.75815 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM78536 1 0.0000 0.88790 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78541 1 0.0000 0.88790 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78547 1 0.5997 0.64904 0.588 0.000 0.000 0.048 0.156 0.208
#> GSM78552 3 0.0000 0.73846 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM78556 4 0.3351 0.53677 0.000 0.000 0.000 0.712 0.000 0.288
#> GSM78559 1 0.0000 0.88790 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78564 4 0.0000 0.75815 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM42999 2 0.3050 0.77871 0.000 0.764 0.000 0.000 0.236 0.000
#> GSM43001 2 0.0000 0.81185 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43003 5 0.2416 0.49854 0.000 0.000 0.156 0.000 0.844 0.000
#> GSM43006 2 0.0000 0.81185 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM43009 5 0.3864 -0.04823 0.000 0.000 0.480 0.000 0.520 0.000
#> GSM43012 5 0.3151 0.01003 0.000 0.252 0.000 0.000 0.748 0.000
#> GSM78524 1 0.4539 0.69289 0.688 0.000 0.000 0.000 0.096 0.216
#> GSM78527 2 0.3634 0.69797 0.000 0.644 0.000 0.000 0.356 0.000
#> GSM78530 3 0.1501 0.69597 0.000 0.000 0.924 0.000 0.076 0.000
#> GSM78535 1 0.0000 0.88790 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM78538 6 0.0458 0.58739 0.000 0.000 0.000 0.016 0.000 0.984
#> GSM78542 6 0.2048 0.64265 0.000 0.000 0.000 0.120 0.000 0.880
#> GSM78544 3 0.4305 0.48639 0.000 0.000 0.708 0.000 0.076 0.216
#> GSM78549 3 0.4855 0.42673 0.000 0.000 0.660 0.000 0.136 0.204
#> GSM78553 6 0.3765 0.52133 0.000 0.000 0.000 0.404 0.000 0.596
#> GSM78558 6 0.3774 0.51728 0.000 0.000 0.000 0.408 0.000 0.592
#> GSM78561 2 0.0000 0.81185 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) agent(p) individual(p) k
#> ATC:pam 58 0.05915 0.340 0.00642 2
#> ATC:pam 57 0.03338 0.259 0.04791 3
#> ATC:pam 57 0.01011 0.582 0.07213 4
#> ATC:pam 52 0.02597 0.543 0.17726 5
#> ATC:pam 46 0.00136 0.578 0.21493 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "mclust"]
# you can also extract it by
# res = res_list["ATC:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 58 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.794 0.901 0.957 0.4353 0.552 0.552
#> 3 3 0.490 0.795 0.860 0.4037 0.726 0.531
#> 4 4 0.976 0.929 0.964 0.1605 0.894 0.716
#> 5 5 0.780 0.700 0.844 0.1044 0.849 0.542
#> 6 6 0.727 0.697 0.793 0.0456 0.915 0.642
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM78539 1 0.0000 0.978 1.000 0.000
#> GSM78545 1 0.8813 0.519 0.700 0.300
#> GSM78550 1 0.0000 0.978 1.000 0.000
#> GSM78554 1 0.0000 0.978 1.000 0.000
#> GSM78562 1 0.0000 0.978 1.000 0.000
#> GSM78540 1 0.0000 0.978 1.000 0.000
#> GSM78546 1 0.0000 0.978 1.000 0.000
#> GSM78551 1 0.0000 0.978 1.000 0.000
#> GSM78555 1 0.0000 0.978 1.000 0.000
#> GSM78563 1 0.0000 0.978 1.000 0.000
#> GSM43005 1 0.0376 0.974 0.996 0.004
#> GSM43008 1 0.0000 0.978 1.000 0.000
#> GSM43011 2 0.9850 0.306 0.428 0.572
#> GSM78523 2 0.7674 0.710 0.224 0.776
#> GSM78526 1 0.0000 0.978 1.000 0.000
#> GSM78529 2 0.0000 0.896 0.000 1.000
#> GSM78532 1 0.0000 0.978 1.000 0.000
#> GSM78534 1 0.0000 0.978 1.000 0.000
#> GSM78537 1 0.0000 0.978 1.000 0.000
#> GSM78543 1 0.0000 0.978 1.000 0.000
#> GSM78548 1 0.0000 0.978 1.000 0.000
#> GSM78557 1 0.0000 0.978 1.000 0.000
#> GSM78560 1 0.0000 0.978 1.000 0.000
#> GSM78565 1 0.0000 0.978 1.000 0.000
#> GSM43000 2 0.5946 0.797 0.144 0.856
#> GSM43002 1 0.0000 0.978 1.000 0.000
#> GSM43004 1 0.0000 0.978 1.000 0.000
#> GSM43007 1 0.0000 0.978 1.000 0.000
#> GSM43010 1 0.0000 0.978 1.000 0.000
#> GSM78522 1 0.0000 0.978 1.000 0.000
#> GSM78525 1 0.6623 0.759 0.828 0.172
#> GSM78528 2 0.0672 0.893 0.008 0.992
#> GSM78531 1 0.0000 0.978 1.000 0.000
#> GSM78533 1 0.0000 0.978 1.000 0.000
#> GSM78536 1 0.0000 0.978 1.000 0.000
#> GSM78541 1 0.0000 0.978 1.000 0.000
#> GSM78547 1 0.0000 0.978 1.000 0.000
#> GSM78552 1 0.0000 0.978 1.000 0.000
#> GSM78556 1 0.0000 0.978 1.000 0.000
#> GSM78559 1 0.0000 0.978 1.000 0.000
#> GSM78564 1 0.0000 0.978 1.000 0.000
#> GSM42999 2 0.0000 0.896 0.000 1.000
#> GSM43001 2 0.0000 0.896 0.000 1.000
#> GSM43003 2 0.0000 0.896 0.000 1.000
#> GSM43006 2 0.0000 0.896 0.000 1.000
#> GSM43009 2 0.0000 0.896 0.000 1.000
#> GSM43012 2 0.0000 0.896 0.000 1.000
#> GSM78524 1 0.0000 0.978 1.000 0.000
#> GSM78527 2 0.0000 0.896 0.000 1.000
#> GSM78530 2 0.0000 0.896 0.000 1.000
#> GSM78535 1 0.0000 0.978 1.000 0.000
#> GSM78538 2 0.8443 0.655 0.272 0.728
#> GSM78542 2 0.8443 0.655 0.272 0.728
#> GSM78544 2 0.0000 0.896 0.000 1.000
#> GSM78549 2 0.0000 0.896 0.000 1.000
#> GSM78553 2 0.9732 0.395 0.404 0.596
#> GSM78558 1 0.8016 0.630 0.756 0.244
#> GSM78561 2 0.0000 0.896 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM78539 3 0.0892 0.912 0.020 0.000 0.980
#> GSM78545 3 0.6393 0.549 0.048 0.216 0.736
#> GSM78550 3 0.1411 0.910 0.036 0.000 0.964
#> GSM78554 3 0.0892 0.912 0.020 0.000 0.980
#> GSM78562 1 0.5431 0.772 0.716 0.000 0.284
#> GSM78540 3 0.5497 0.380 0.292 0.000 0.708
#> GSM78546 3 0.0000 0.910 0.000 0.000 1.000
#> GSM78551 3 0.1289 0.909 0.032 0.000 0.968
#> GSM78555 1 0.5216 0.797 0.740 0.000 0.260
#> GSM78563 3 0.1411 0.907 0.036 0.000 0.964
#> GSM43005 3 0.3456 0.849 0.036 0.060 0.904
#> GSM43008 3 0.0000 0.910 0.000 0.000 1.000
#> GSM43011 2 0.7755 0.384 0.048 0.492 0.460
#> GSM78523 2 0.7065 0.734 0.048 0.664 0.288
#> GSM78526 3 0.1529 0.909 0.040 0.000 0.960
#> GSM78529 2 0.6252 0.748 0.024 0.708 0.268
#> GSM78532 1 0.3752 0.866 0.856 0.000 0.144
#> GSM78534 1 0.3482 0.859 0.872 0.000 0.128
#> GSM78537 1 0.5016 0.812 0.760 0.000 0.240
#> GSM78543 3 0.3038 0.796 0.104 0.000 0.896
#> GSM78548 3 0.1411 0.910 0.036 0.000 0.964
#> GSM78557 3 0.0592 0.912 0.012 0.000 0.988
#> GSM78560 3 0.0237 0.910 0.004 0.000 0.996
#> GSM78565 1 0.3752 0.866 0.856 0.000 0.144
#> GSM43000 2 0.7034 0.738 0.048 0.668 0.284
#> GSM43002 3 0.0983 0.906 0.004 0.016 0.980
#> GSM43004 1 0.3879 0.864 0.848 0.000 0.152
#> GSM43007 3 0.0000 0.910 0.000 0.000 1.000
#> GSM43010 3 0.1289 0.909 0.032 0.000 0.968
#> GSM78522 3 0.0000 0.910 0.000 0.000 1.000
#> GSM78525 3 0.5268 0.635 0.012 0.212 0.776
#> GSM78528 2 0.7002 0.742 0.048 0.672 0.280
#> GSM78531 1 0.3752 0.866 0.856 0.000 0.144
#> GSM78533 3 0.1289 0.909 0.032 0.000 0.968
#> GSM78536 1 0.3412 0.858 0.876 0.000 0.124
#> GSM78541 1 0.3752 0.866 0.856 0.000 0.144
#> GSM78547 1 0.6168 0.554 0.588 0.000 0.412
#> GSM78552 3 0.0000 0.910 0.000 0.000 1.000
#> GSM78556 3 0.1289 0.909 0.032 0.000 0.968
#> GSM78559 1 0.3752 0.866 0.856 0.000 0.144
#> GSM78564 3 0.0747 0.912 0.016 0.000 0.984
#> GSM42999 2 0.0424 0.779 0.008 0.992 0.000
#> GSM43001 2 0.0747 0.778 0.016 0.984 0.000
#> GSM43003 2 0.0892 0.779 0.020 0.980 0.000
#> GSM43006 2 0.0747 0.778 0.016 0.984 0.000
#> GSM43009 2 0.6904 0.748 0.048 0.684 0.268
#> GSM43012 2 0.0592 0.779 0.012 0.988 0.000
#> GSM78524 1 0.4555 0.739 0.800 0.000 0.200
#> GSM78527 2 0.0592 0.778 0.012 0.988 0.000
#> GSM78530 2 0.6904 0.748 0.048 0.684 0.268
#> GSM78535 1 0.2796 0.835 0.908 0.000 0.092
#> GSM78538 1 0.7478 0.497 0.632 0.060 0.308
#> GSM78542 1 0.7801 0.487 0.616 0.076 0.308
#> GSM78544 2 0.6904 0.748 0.048 0.684 0.268
#> GSM78549 2 0.1529 0.776 0.040 0.960 0.000
#> GSM78553 3 0.7501 0.586 0.212 0.104 0.684
#> GSM78558 3 0.4339 0.810 0.048 0.084 0.868
#> GSM78561 2 0.0747 0.778 0.016 0.984 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM78539 3 0.0469 0.940 0.012 0.000 0.988 0.000
#> GSM78545 3 0.4679 0.502 0.000 0.352 0.648 0.000
#> GSM78550 3 0.0376 0.940 0.004 0.000 0.992 0.004
#> GSM78554 3 0.0469 0.940 0.012 0.000 0.988 0.000
#> GSM78562 1 0.0469 0.992 0.988 0.000 0.012 0.000
#> GSM78540 3 0.0657 0.940 0.012 0.000 0.984 0.004
#> GSM78546 3 0.0000 0.940 0.000 0.000 1.000 0.000
#> GSM78551 3 0.0657 0.940 0.012 0.000 0.984 0.004
#> GSM78555 1 0.0592 0.988 0.984 0.000 0.016 0.000
#> GSM78563 3 0.0657 0.940 0.012 0.000 0.984 0.004
#> GSM43005 3 0.4730 0.459 0.000 0.364 0.636 0.000
#> GSM43008 3 0.0000 0.940 0.000 0.000 1.000 0.000
#> GSM43011 3 0.1557 0.908 0.000 0.056 0.944 0.000
#> GSM78523 2 0.0524 0.955 0.000 0.988 0.008 0.004
#> GSM78526 3 0.0376 0.940 0.004 0.000 0.992 0.004
#> GSM78529 2 0.1557 0.922 0.000 0.944 0.000 0.056
#> GSM78532 1 0.0336 0.995 0.992 0.000 0.008 0.000
#> GSM78534 1 0.0336 0.995 0.992 0.000 0.008 0.000
#> GSM78537 1 0.0336 0.995 0.992 0.000 0.008 0.000
#> GSM78543 3 0.0524 0.940 0.008 0.000 0.988 0.004
#> GSM78548 3 0.0188 0.940 0.004 0.000 0.996 0.000
#> GSM78557 3 0.0336 0.940 0.008 0.000 0.992 0.000
#> GSM78560 3 0.0336 0.940 0.008 0.000 0.992 0.000
#> GSM78565 1 0.0524 0.993 0.988 0.000 0.008 0.004
#> GSM43000 2 0.0336 0.957 0.000 0.992 0.008 0.000
#> GSM43002 3 0.0707 0.932 0.000 0.020 0.980 0.000
#> GSM43004 1 0.0336 0.995 0.992 0.000 0.008 0.000
#> GSM43007 3 0.0188 0.939 0.000 0.000 0.996 0.004
#> GSM43010 3 0.2311 0.882 0.004 0.076 0.916 0.004
#> GSM78522 3 0.0188 0.939 0.000 0.000 0.996 0.004
#> GSM78525 3 0.0469 0.937 0.000 0.012 0.988 0.000
#> GSM78528 2 0.0336 0.957 0.000 0.992 0.008 0.000
#> GSM78531 1 0.0336 0.995 0.992 0.000 0.008 0.000
#> GSM78533 3 0.0469 0.940 0.012 0.000 0.988 0.000
#> GSM78536 1 0.0336 0.995 0.992 0.000 0.008 0.000
#> GSM78541 1 0.0336 0.995 0.992 0.000 0.008 0.000
#> GSM78547 1 0.0707 0.984 0.980 0.000 0.020 0.000
#> GSM78552 3 0.0000 0.940 0.000 0.000 1.000 0.000
#> GSM78556 3 0.0657 0.940 0.012 0.000 0.984 0.004
#> GSM78559 1 0.0336 0.995 0.992 0.000 0.008 0.000
#> GSM78564 3 0.0336 0.940 0.008 0.000 0.992 0.000
#> GSM42999 4 0.0592 0.994 0.000 0.016 0.000 0.984
#> GSM43001 4 0.0469 0.994 0.000 0.012 0.000 0.988
#> GSM43003 4 0.0707 0.993 0.000 0.020 0.000 0.980
#> GSM43006 4 0.0707 0.993 0.000 0.020 0.000 0.980
#> GSM43009 2 0.0336 0.957 0.000 0.992 0.000 0.008
#> GSM43012 4 0.0707 0.994 0.000 0.020 0.000 0.980
#> GSM78524 1 0.0524 0.980 0.988 0.008 0.000 0.004
#> GSM78527 4 0.0707 0.994 0.000 0.020 0.000 0.980
#> GSM78530 2 0.0188 0.957 0.000 0.996 0.000 0.004
#> GSM78535 1 0.0376 0.989 0.992 0.000 0.004 0.004
#> GSM78538 2 0.0927 0.951 0.016 0.976 0.008 0.000
#> GSM78542 2 0.0804 0.953 0.008 0.980 0.012 0.000
#> GSM78544 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM78549 2 0.0592 0.955 0.000 0.984 0.000 0.016
#> GSM78553 2 0.3710 0.724 0.004 0.804 0.192 0.000
#> GSM78558 3 0.5070 0.311 0.004 0.416 0.580 0.000
#> GSM78561 4 0.0469 0.994 0.000 0.012 0.000 0.988
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM78539 4 0.4173 0.568 0.012 0.000 0.000 0.688 0.300
#> GSM78545 3 0.3449 0.616 0.000 0.000 0.812 0.164 0.024
#> GSM78550 5 0.6672 -0.227 0.016 0.000 0.144 0.416 0.424
#> GSM78554 4 0.4367 0.489 0.008 0.000 0.000 0.620 0.372
#> GSM78562 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM78540 4 0.5077 0.450 0.016 0.000 0.016 0.576 0.392
#> GSM78546 4 0.1697 0.699 0.000 0.000 0.060 0.932 0.008
#> GSM78551 4 0.6326 0.150 0.016 0.000 0.100 0.444 0.440
#> GSM78555 1 0.1697 0.917 0.932 0.000 0.000 0.060 0.008
#> GSM78563 4 0.4994 0.450 0.016 0.000 0.012 0.576 0.396
#> GSM43005 3 0.4768 0.244 0.000 0.000 0.592 0.384 0.024
#> GSM43008 4 0.1410 0.699 0.000 0.000 0.060 0.940 0.000
#> GSM43011 3 0.3821 0.581 0.000 0.000 0.764 0.216 0.020
#> GSM78523 3 0.0162 0.679 0.000 0.000 0.996 0.004 0.000
#> GSM78526 5 0.4806 0.650 0.016 0.000 0.144 0.088 0.752
#> GSM78529 3 0.5628 0.486 0.000 0.220 0.632 0.000 0.148
#> GSM78532 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM78534 1 0.0162 0.983 0.996 0.000 0.000 0.000 0.004
#> GSM78537 1 0.0162 0.982 0.996 0.000 0.000 0.004 0.000
#> GSM78543 4 0.0290 0.694 0.000 0.000 0.000 0.992 0.008
#> GSM78548 4 0.6897 0.199 0.016 0.000 0.360 0.436 0.188
#> GSM78557 4 0.1331 0.697 0.008 0.000 0.000 0.952 0.040
#> GSM78560 4 0.0290 0.695 0.000 0.000 0.000 0.992 0.008
#> GSM78565 1 0.0404 0.980 0.988 0.000 0.000 0.000 0.012
#> GSM43000 3 0.0000 0.679 0.000 0.000 1.000 0.000 0.000
#> GSM43002 3 0.4718 0.317 0.008 0.000 0.580 0.404 0.008
#> GSM43004 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM43007 4 0.1410 0.699 0.000 0.000 0.060 0.940 0.000
#> GSM43010 5 0.3547 0.689 0.016 0.000 0.144 0.016 0.824
#> GSM78522 4 0.1430 0.700 0.000 0.000 0.052 0.944 0.004
#> GSM78525 3 0.4726 0.262 0.000 0.000 0.580 0.400 0.020
#> GSM78528 3 0.0510 0.680 0.000 0.000 0.984 0.000 0.016
#> GSM78531 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM78533 4 0.5077 0.451 0.016 0.000 0.016 0.576 0.392
#> GSM78536 1 0.0162 0.984 0.996 0.000 0.000 0.000 0.004
#> GSM78541 1 0.0162 0.984 0.996 0.000 0.000 0.000 0.004
#> GSM78547 1 0.1282 0.940 0.952 0.000 0.000 0.044 0.004
#> GSM78552 4 0.1697 0.699 0.000 0.000 0.060 0.932 0.008
#> GSM78556 4 0.4640 0.460 0.016 0.000 0.000 0.584 0.400
#> GSM78559 1 0.0162 0.984 0.996 0.000 0.000 0.000 0.004
#> GSM78564 4 0.1597 0.698 0.012 0.000 0.000 0.940 0.048
#> GSM42999 2 0.0324 0.987 0.000 0.992 0.004 0.000 0.004
#> GSM43001 2 0.0162 0.988 0.000 0.996 0.000 0.000 0.004
#> GSM43003 2 0.0880 0.964 0.000 0.968 0.032 0.000 0.000
#> GSM43006 2 0.0162 0.988 0.000 0.996 0.004 0.000 0.000
#> GSM43009 3 0.2605 0.657 0.000 0.000 0.852 0.000 0.148
#> GSM43012 2 0.0693 0.980 0.000 0.980 0.008 0.000 0.012
#> GSM78524 1 0.0794 0.970 0.972 0.000 0.000 0.000 0.028
#> GSM78527 2 0.0162 0.988 0.000 0.996 0.000 0.000 0.004
#> GSM78530 3 0.2561 0.656 0.000 0.000 0.856 0.000 0.144
#> GSM78535 1 0.0404 0.980 0.988 0.000 0.000 0.000 0.012
#> GSM78538 5 0.1731 0.712 0.004 0.004 0.060 0.000 0.932
#> GSM78542 5 0.1798 0.712 0.004 0.004 0.064 0.000 0.928
#> GSM78544 3 0.2605 0.655 0.000 0.000 0.852 0.000 0.148
#> GSM78549 3 0.6166 0.221 0.000 0.340 0.512 0.000 0.148
#> GSM78553 5 0.1341 0.718 0.000 0.000 0.056 0.000 0.944
#> GSM78558 5 0.4571 0.588 0.000 0.000 0.076 0.188 0.736
#> GSM78561 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM78539 4 0.2830 0.757 0.000 0.000 0.000 0.836 0.020 0.144
#> GSM78545 3 0.2182 0.718 0.000 0.000 0.904 0.020 0.008 0.068
#> GSM78550 4 0.1116 0.829 0.000 0.000 0.004 0.960 0.028 0.008
#> GSM78554 4 0.4454 0.382 0.004 0.000 0.000 0.616 0.032 0.348
#> GSM78562 1 0.3986 0.779 0.664 0.000 0.000 0.020 0.316 0.000
#> GSM78540 4 0.0777 0.828 0.000 0.000 0.000 0.972 0.024 0.004
#> GSM78546 6 0.5081 0.617 0.000 0.000 0.316 0.088 0.004 0.592
#> GSM78551 4 0.1010 0.828 0.000 0.000 0.004 0.960 0.036 0.000
#> GSM78555 1 0.2151 0.757 0.904 0.000 0.000 0.072 0.008 0.016
#> GSM78563 4 0.0603 0.828 0.000 0.000 0.000 0.980 0.016 0.004
#> GSM43005 3 0.3792 0.619 0.000 0.000 0.780 0.160 0.008 0.052
#> GSM43008 6 0.5317 0.623 0.000 0.000 0.316 0.112 0.004 0.568
#> GSM43011 3 0.2877 0.678 0.000 0.000 0.848 0.020 0.008 0.124
#> GSM78523 3 0.0260 0.734 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM78526 4 0.2234 0.775 0.000 0.000 0.004 0.872 0.124 0.000
#> GSM78529 3 0.4585 0.471 0.000 0.192 0.692 0.000 0.116 0.000
#> GSM78532 1 0.3758 0.798 0.700 0.000 0.000 0.016 0.284 0.000
#> GSM78534 1 0.4018 0.774 0.656 0.000 0.000 0.020 0.324 0.000
#> GSM78537 1 0.2892 0.817 0.840 0.000 0.000 0.020 0.136 0.004
#> GSM78543 6 0.2730 0.612 0.000 0.000 0.000 0.192 0.000 0.808
#> GSM78548 4 0.1346 0.827 0.000 0.000 0.016 0.952 0.024 0.008
#> GSM78557 6 0.3512 0.523 0.000 0.000 0.000 0.272 0.008 0.720
#> GSM78560 6 0.3244 0.576 0.000 0.000 0.000 0.268 0.000 0.732
#> GSM78565 1 0.1500 0.784 0.936 0.000 0.000 0.012 0.000 0.052
#> GSM43000 3 0.0000 0.735 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM43002 3 0.5705 0.449 0.000 0.000 0.608 0.028 0.172 0.192
#> GSM43004 1 0.3819 0.799 0.700 0.000 0.000 0.020 0.280 0.000
#> GSM43007 6 0.5454 0.618 0.000 0.000 0.316 0.128 0.004 0.552
#> GSM43010 4 0.2743 0.721 0.000 0.000 0.008 0.828 0.164 0.000
#> GSM78522 6 0.3822 0.665 0.000 0.000 0.096 0.128 0.000 0.776
#> GSM78525 3 0.4886 0.222 0.000 0.000 0.620 0.076 0.004 0.300
#> GSM78528 3 0.0000 0.735 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM78531 1 0.3738 0.800 0.704 0.000 0.000 0.016 0.280 0.000
#> GSM78533 4 0.0777 0.831 0.000 0.000 0.000 0.972 0.024 0.004
#> GSM78536 1 0.1364 0.792 0.944 0.000 0.000 0.004 0.004 0.048
#> GSM78541 1 0.0820 0.808 0.972 0.000 0.000 0.012 0.016 0.000
#> GSM78547 1 0.5058 0.752 0.604 0.000 0.004 0.056 0.324 0.012
#> GSM78552 6 0.4993 0.612 0.000 0.000 0.316 0.080 0.004 0.600
#> GSM78556 4 0.1757 0.820 0.012 0.000 0.000 0.928 0.008 0.052
#> GSM78559 1 0.1219 0.791 0.948 0.000 0.000 0.004 0.000 0.048
#> GSM78564 4 0.3953 0.402 0.000 0.000 0.000 0.656 0.016 0.328
#> GSM42999 2 0.1204 0.899 0.000 0.944 0.000 0.000 0.056 0.000
#> GSM43001 2 0.1556 0.917 0.000 0.920 0.000 0.000 0.080 0.000
#> GSM43003 2 0.1204 0.889 0.000 0.944 0.056 0.000 0.000 0.000
#> GSM43006 2 0.0790 0.910 0.000 0.968 0.032 0.000 0.000 0.000
#> GSM43009 3 0.2609 0.679 0.000 0.000 0.868 0.036 0.096 0.000
#> GSM43012 2 0.1814 0.905 0.000 0.900 0.000 0.000 0.100 0.000
#> GSM78524 1 0.3753 0.788 0.748 0.000 0.000 0.028 0.220 0.004
#> GSM78527 2 0.1556 0.917 0.000 0.920 0.000 0.000 0.080 0.000
#> GSM78530 3 0.3834 0.547 0.000 0.000 0.732 0.036 0.232 0.000
#> GSM78535 1 0.1075 0.790 0.952 0.000 0.000 0.000 0.000 0.048
#> GSM78538 5 0.2536 0.676 0.000 0.000 0.020 0.116 0.864 0.000
#> GSM78542 5 0.2830 0.664 0.000 0.000 0.020 0.144 0.836 0.000
#> GSM78544 3 0.4810 0.350 0.000 0.000 0.660 0.220 0.120 0.000
#> GSM78549 5 0.6071 0.154 0.000 0.276 0.328 0.000 0.396 0.000
#> GSM78553 4 0.4399 0.124 0.000 0.000 0.024 0.516 0.460 0.000
#> GSM78558 4 0.2094 0.817 0.000 0.000 0.008 0.908 0.068 0.016
#> GSM78561 2 0.0000 0.914 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) agent(p) individual(p) k
#> ATC:mclust 56 8.02e-07 0.0651 0.199 2
#> ATC:mclust 54 1.09e-04 0.1343 0.181 3
#> ATC:mclust 56 1.35e-06 0.0919 0.504 4
#> ATC:mclust 45 2.43e-03 0.2226 0.562 5
#> ATC:mclust 50 1.05e-04 0.2599 0.460 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "NMF"]
# you can also extract it by
# res = res_list["ATC:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 58 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.928 0.938 0.976 0.3035 0.710 0.710
#> 3 3 0.744 0.793 0.922 1.0230 0.628 0.494
#> 4 4 0.633 0.681 0.856 0.1667 0.731 0.421
#> 5 5 0.671 0.741 0.862 0.0652 0.833 0.506
#> 6 6 0.655 0.613 0.754 0.0538 0.944 0.783
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM78539 1 0.0000 0.9773 1.000 0.000
#> GSM78545 1 0.0000 0.9773 1.000 0.000
#> GSM78550 1 0.0000 0.9773 1.000 0.000
#> GSM78554 1 0.0000 0.9773 1.000 0.000
#> GSM78562 1 0.0000 0.9773 1.000 0.000
#> GSM78540 1 0.0000 0.9773 1.000 0.000
#> GSM78546 1 0.0000 0.9773 1.000 0.000
#> GSM78551 1 0.0000 0.9773 1.000 0.000
#> GSM78555 1 0.0000 0.9773 1.000 0.000
#> GSM78563 1 0.0000 0.9773 1.000 0.000
#> GSM43005 1 0.0000 0.9773 1.000 0.000
#> GSM43008 1 0.0000 0.9773 1.000 0.000
#> GSM43011 1 0.0000 0.9773 1.000 0.000
#> GSM78523 2 0.6887 0.7892 0.184 0.816
#> GSM78526 1 0.0000 0.9773 1.000 0.000
#> GSM78529 2 0.0000 0.9553 0.000 1.000
#> GSM78532 1 0.0000 0.9773 1.000 0.000
#> GSM78534 1 0.0000 0.9773 1.000 0.000
#> GSM78537 1 0.0000 0.9773 1.000 0.000
#> GSM78543 1 0.0000 0.9773 1.000 0.000
#> GSM78548 1 0.0000 0.9773 1.000 0.000
#> GSM78557 1 0.0000 0.9773 1.000 0.000
#> GSM78560 1 0.0000 0.9773 1.000 0.000
#> GSM78565 1 0.0000 0.9773 1.000 0.000
#> GSM43000 1 0.9608 0.3448 0.616 0.384
#> GSM43002 1 0.0000 0.9773 1.000 0.000
#> GSM43004 1 0.0000 0.9773 1.000 0.000
#> GSM43007 1 0.0000 0.9773 1.000 0.000
#> GSM43010 1 0.0000 0.9773 1.000 0.000
#> GSM78522 1 0.0000 0.9773 1.000 0.000
#> GSM78525 1 0.0000 0.9773 1.000 0.000
#> GSM78528 1 0.5408 0.8394 0.876 0.124
#> GSM78531 1 0.0000 0.9773 1.000 0.000
#> GSM78533 1 0.0000 0.9773 1.000 0.000
#> GSM78536 1 0.0000 0.9773 1.000 0.000
#> GSM78541 1 0.0000 0.9773 1.000 0.000
#> GSM78547 1 0.0000 0.9773 1.000 0.000
#> GSM78552 1 0.0000 0.9773 1.000 0.000
#> GSM78556 1 0.0000 0.9773 1.000 0.000
#> GSM78559 1 0.0000 0.9773 1.000 0.000
#> GSM78564 1 0.0000 0.9773 1.000 0.000
#> GSM42999 2 0.0000 0.9553 0.000 1.000
#> GSM43001 2 0.0000 0.9553 0.000 1.000
#> GSM43003 2 0.0672 0.9511 0.008 0.992
#> GSM43006 2 0.0000 0.9553 0.000 1.000
#> GSM43009 2 0.7056 0.7780 0.192 0.808
#> GSM43012 2 0.0000 0.9553 0.000 1.000
#> GSM78524 1 0.0000 0.9773 1.000 0.000
#> GSM78527 2 0.0000 0.9553 0.000 1.000
#> GSM78530 1 0.1184 0.9621 0.984 0.016
#> GSM78535 1 0.0000 0.9773 1.000 0.000
#> GSM78538 1 0.0000 0.9773 1.000 0.000
#> GSM78542 1 0.0000 0.9773 1.000 0.000
#> GSM78544 1 0.0000 0.9773 1.000 0.000
#> GSM78549 1 0.9988 0.0247 0.520 0.480
#> GSM78553 1 0.0000 0.9773 1.000 0.000
#> GSM78558 1 0.0000 0.9773 1.000 0.000
#> GSM78561 2 0.0000 0.9553 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM78539 1 0.0237 0.8968 0.996 0.000 0.004
#> GSM78545 3 0.0000 0.8704 0.000 0.000 1.000
#> GSM78550 3 0.0000 0.8704 0.000 0.000 1.000
#> GSM78554 1 0.5733 0.5280 0.676 0.000 0.324
#> GSM78562 1 0.0000 0.8992 1.000 0.000 0.000
#> GSM78540 1 0.0000 0.8992 1.000 0.000 0.000
#> GSM78546 1 0.6126 0.2448 0.600 0.000 0.400
#> GSM78551 1 0.6215 0.2764 0.572 0.000 0.428
#> GSM78555 1 0.0000 0.8992 1.000 0.000 0.000
#> GSM78563 1 0.0000 0.8992 1.000 0.000 0.000
#> GSM43005 3 0.0000 0.8704 0.000 0.000 1.000
#> GSM43008 3 0.5465 0.5668 0.288 0.000 0.712
#> GSM43011 3 0.0000 0.8704 0.000 0.000 1.000
#> GSM78523 3 0.0000 0.8704 0.000 0.000 1.000
#> GSM78526 3 0.0000 0.8704 0.000 0.000 1.000
#> GSM78529 2 0.0237 0.9632 0.000 0.996 0.004
#> GSM78532 1 0.0000 0.8992 1.000 0.000 0.000
#> GSM78534 1 0.0237 0.8968 0.996 0.000 0.004
#> GSM78537 1 0.0000 0.8992 1.000 0.000 0.000
#> GSM78543 1 0.0000 0.8992 1.000 0.000 0.000
#> GSM78548 3 0.0000 0.8704 0.000 0.000 1.000
#> GSM78557 1 0.0000 0.8992 1.000 0.000 0.000
#> GSM78560 1 0.0000 0.8992 1.000 0.000 0.000
#> GSM78565 1 0.0000 0.8992 1.000 0.000 0.000
#> GSM43000 3 0.0000 0.8704 0.000 0.000 1.000
#> GSM43002 3 0.0000 0.8704 0.000 0.000 1.000
#> GSM43004 1 0.0000 0.8992 1.000 0.000 0.000
#> GSM43007 1 0.6302 -0.0227 0.520 0.000 0.480
#> GSM43010 3 0.0592 0.8631 0.012 0.000 0.988
#> GSM78522 1 0.0000 0.8992 1.000 0.000 0.000
#> GSM78525 3 0.0000 0.8704 0.000 0.000 1.000
#> GSM78528 3 0.0000 0.8704 0.000 0.000 1.000
#> GSM78531 1 0.0000 0.8992 1.000 0.000 0.000
#> GSM78533 3 0.6215 0.2436 0.428 0.000 0.572
#> GSM78536 1 0.0000 0.8992 1.000 0.000 0.000
#> GSM78541 1 0.0000 0.8992 1.000 0.000 0.000
#> GSM78547 1 0.2537 0.8372 0.920 0.000 0.080
#> GSM78552 3 0.5988 0.4117 0.368 0.000 0.632
#> GSM78556 1 0.0000 0.8992 1.000 0.000 0.000
#> GSM78559 1 0.0000 0.8992 1.000 0.000 0.000
#> GSM78564 1 0.0000 0.8992 1.000 0.000 0.000
#> GSM42999 2 0.0000 0.9663 0.000 1.000 0.000
#> GSM43001 2 0.0000 0.9663 0.000 1.000 0.000
#> GSM43003 2 0.0000 0.9663 0.000 1.000 0.000
#> GSM43006 2 0.0000 0.9663 0.000 1.000 0.000
#> GSM43009 3 0.4399 0.6752 0.000 0.188 0.812
#> GSM43012 2 0.0000 0.9663 0.000 1.000 0.000
#> GSM78524 1 0.0000 0.8992 1.000 0.000 0.000
#> GSM78527 2 0.0000 0.9663 0.000 1.000 0.000
#> GSM78530 3 0.1163 0.8508 0.000 0.028 0.972
#> GSM78535 1 0.0000 0.8992 1.000 0.000 0.000
#> GSM78538 1 0.4605 0.7070 0.796 0.000 0.204
#> GSM78542 1 0.5810 0.4972 0.664 0.000 0.336
#> GSM78544 3 0.0237 0.8684 0.004 0.000 0.996
#> GSM78549 2 0.5058 0.6578 0.000 0.756 0.244
#> GSM78553 3 0.6274 0.0561 0.456 0.000 0.544
#> GSM78558 1 0.5178 0.6388 0.744 0.000 0.256
#> GSM78561 2 0.0000 0.9663 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM78539 4 0.5938 -0.0254 0.476 0.000 0.036 0.488
#> GSM78545 3 0.0188 0.8741 0.000 0.000 0.996 0.004
#> GSM78550 4 0.4431 0.5254 0.000 0.000 0.304 0.696
#> GSM78554 4 0.4019 0.6433 0.012 0.000 0.196 0.792
#> GSM78562 4 0.1557 0.7580 0.056 0.000 0.000 0.944
#> GSM78540 4 0.1637 0.7573 0.060 0.000 0.000 0.940
#> GSM78546 3 0.2814 0.7991 0.132 0.000 0.868 0.000
#> GSM78551 4 0.0469 0.7578 0.000 0.000 0.012 0.988
#> GSM78555 1 0.4948 0.5144 0.560 0.000 0.000 0.440
#> GSM78563 4 0.1474 0.7590 0.052 0.000 0.000 0.948
#> GSM43005 3 0.1022 0.8601 0.000 0.000 0.968 0.032
#> GSM43008 3 0.1211 0.8615 0.040 0.000 0.960 0.000
#> GSM43011 3 0.0000 0.8747 0.000 0.000 1.000 0.000
#> GSM78523 3 0.0336 0.8738 0.008 0.000 0.992 0.000
#> GSM78526 4 0.4981 0.1117 0.000 0.000 0.464 0.536
#> GSM78529 2 0.2760 0.8002 0.000 0.872 0.128 0.000
#> GSM78532 4 0.1716 0.7548 0.064 0.000 0.000 0.936
#> GSM78534 4 0.0817 0.7622 0.024 0.000 0.000 0.976
#> GSM78537 4 0.3123 0.6611 0.156 0.000 0.000 0.844
#> GSM78543 1 0.0469 0.6631 0.988 0.000 0.000 0.012
#> GSM78548 3 0.3726 0.6879 0.000 0.000 0.788 0.212
#> GSM78557 1 0.1867 0.7011 0.928 0.000 0.000 0.072
#> GSM78560 1 0.0000 0.6530 1.000 0.000 0.000 0.000
#> GSM78565 1 0.3688 0.7042 0.792 0.000 0.000 0.208
#> GSM43000 3 0.0000 0.8747 0.000 0.000 1.000 0.000
#> GSM43002 3 0.0336 0.8738 0.008 0.000 0.992 0.000
#> GSM43004 4 0.2081 0.7412 0.084 0.000 0.000 0.916
#> GSM43007 3 0.2149 0.8345 0.088 0.000 0.912 0.000
#> GSM43010 4 0.2704 0.7064 0.000 0.000 0.124 0.876
#> GSM78522 1 0.2530 0.5497 0.888 0.000 0.112 0.000
#> GSM78525 3 0.0336 0.8728 0.000 0.000 0.992 0.008
#> GSM78528 3 0.0000 0.8747 0.000 0.000 1.000 0.000
#> GSM78531 4 0.1716 0.7548 0.064 0.000 0.000 0.936
#> GSM78533 4 0.4456 0.5330 0.004 0.000 0.280 0.716
#> GSM78536 1 0.4955 0.5085 0.556 0.000 0.000 0.444
#> GSM78541 4 0.4585 0.2239 0.332 0.000 0.000 0.668
#> GSM78547 4 0.0188 0.7614 0.004 0.000 0.000 0.996
#> GSM78552 3 0.2081 0.8380 0.084 0.000 0.916 0.000
#> GSM78556 4 0.2081 0.7436 0.084 0.000 0.000 0.916
#> GSM78559 1 0.4977 0.4728 0.540 0.000 0.000 0.460
#> GSM78564 1 0.3801 0.7007 0.780 0.000 0.000 0.220
#> GSM42999 2 0.0000 0.8855 0.000 1.000 0.000 0.000
#> GSM43001 2 0.0000 0.8855 0.000 1.000 0.000 0.000
#> GSM43003 2 0.2919 0.8447 0.044 0.896 0.060 0.000
#> GSM43006 2 0.0000 0.8855 0.000 1.000 0.000 0.000
#> GSM43009 2 0.4985 0.1160 0.000 0.532 0.468 0.000
#> GSM43012 2 0.0000 0.8855 0.000 1.000 0.000 0.000
#> GSM78524 4 0.3311 0.6378 0.172 0.000 0.000 0.828
#> GSM78527 2 0.0000 0.8855 0.000 1.000 0.000 0.000
#> GSM78530 3 0.6650 0.4288 0.004 0.272 0.612 0.112
#> GSM78535 1 0.4948 0.4951 0.560 0.000 0.000 0.440
#> GSM78538 4 0.0000 0.7607 0.000 0.000 0.000 1.000
#> GSM78542 4 0.0188 0.7603 0.000 0.000 0.004 0.996
#> GSM78544 3 0.4994 0.0329 0.000 0.000 0.520 0.480
#> GSM78549 2 0.4050 0.7447 0.000 0.808 0.168 0.024
#> GSM78553 4 0.3123 0.6753 0.000 0.000 0.156 0.844
#> GSM78558 4 0.4699 0.4885 0.004 0.000 0.320 0.676
#> GSM78561 2 0.0000 0.8855 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM78539 4 0.6004 0.352 0.328 0.068 0.028 0.576 0.000
#> GSM78545 3 0.1410 0.882 0.000 0.060 0.940 0.000 0.000
#> GSM78550 4 0.6129 0.386 0.004 0.160 0.264 0.572 0.000
#> GSM78554 4 0.4733 0.642 0.008 0.116 0.124 0.752 0.000
#> GSM78562 4 0.0162 0.798 0.000 0.004 0.000 0.996 0.000
#> GSM78540 4 0.0703 0.798 0.000 0.024 0.000 0.976 0.000
#> GSM78546 3 0.4444 0.775 0.156 0.088 0.756 0.000 0.000
#> GSM78551 4 0.2177 0.769 0.004 0.080 0.008 0.908 0.000
#> GSM78555 4 0.3728 0.599 0.244 0.008 0.000 0.748 0.000
#> GSM78563 4 0.0404 0.799 0.000 0.012 0.000 0.988 0.000
#> GSM43005 3 0.1671 0.877 0.000 0.076 0.924 0.000 0.000
#> GSM43008 3 0.3586 0.827 0.096 0.076 0.828 0.000 0.000
#> GSM43011 3 0.0609 0.892 0.000 0.020 0.980 0.000 0.000
#> GSM78523 3 0.0324 0.889 0.004 0.000 0.992 0.000 0.004
#> GSM78526 3 0.5834 0.303 0.004 0.092 0.548 0.356 0.000
#> GSM78529 5 0.1043 0.890 0.000 0.000 0.040 0.000 0.960
#> GSM78532 4 0.0162 0.798 0.000 0.004 0.000 0.996 0.000
#> GSM78534 4 0.1205 0.792 0.004 0.040 0.000 0.956 0.000
#> GSM78537 4 0.1211 0.793 0.024 0.016 0.000 0.960 0.000
#> GSM78543 1 0.1331 0.718 0.952 0.008 0.000 0.040 0.000
#> GSM78548 3 0.3617 0.797 0.004 0.128 0.824 0.044 0.000
#> GSM78557 1 0.3304 0.716 0.816 0.016 0.000 0.168 0.000
#> GSM78560 1 0.1369 0.693 0.956 0.028 0.008 0.008 0.000
#> GSM78565 1 0.4235 0.531 0.656 0.008 0.000 0.336 0.000
#> GSM43000 3 0.0609 0.892 0.000 0.020 0.980 0.000 0.000
#> GSM43002 3 0.0324 0.889 0.004 0.004 0.992 0.000 0.000
#> GSM43004 4 0.0451 0.799 0.008 0.004 0.000 0.988 0.000
#> GSM43007 3 0.2208 0.867 0.072 0.020 0.908 0.000 0.000
#> GSM43010 4 0.3827 0.690 0.004 0.068 0.112 0.816 0.000
#> GSM78522 1 0.2300 0.657 0.904 0.024 0.072 0.000 0.000
#> GSM78525 3 0.0963 0.891 0.000 0.036 0.964 0.000 0.000
#> GSM78528 3 0.0880 0.892 0.000 0.032 0.968 0.000 0.000
#> GSM78531 4 0.0000 0.798 0.000 0.000 0.000 1.000 0.000
#> GSM78533 4 0.5245 0.461 0.016 0.044 0.292 0.648 0.000
#> GSM78536 4 0.3231 0.657 0.196 0.004 0.000 0.800 0.000
#> GSM78541 4 0.1478 0.776 0.064 0.000 0.000 0.936 0.000
#> GSM78547 4 0.0451 0.798 0.004 0.008 0.000 0.988 0.000
#> GSM78552 3 0.1557 0.871 0.052 0.008 0.940 0.000 0.000
#> GSM78556 4 0.0451 0.798 0.008 0.004 0.000 0.988 0.000
#> GSM78559 4 0.3003 0.668 0.188 0.000 0.000 0.812 0.000
#> GSM78564 1 0.4510 0.292 0.560 0.008 0.000 0.432 0.000
#> GSM42999 5 0.0000 0.913 0.000 0.000 0.000 0.000 1.000
#> GSM43001 5 0.0000 0.913 0.000 0.000 0.000 0.000 1.000
#> GSM43003 2 0.5433 0.560 0.060 0.676 0.028 0.000 0.236
#> GSM43006 5 0.0000 0.913 0.000 0.000 0.000 0.000 1.000
#> GSM43009 2 0.3650 0.819 0.000 0.796 0.176 0.000 0.028
#> GSM43012 5 0.3003 0.768 0.000 0.188 0.000 0.000 0.812
#> GSM78524 4 0.5816 0.366 0.132 0.280 0.000 0.588 0.000
#> GSM78527 5 0.3242 0.727 0.000 0.216 0.000 0.000 0.784
#> GSM78530 2 0.3283 0.838 0.028 0.832 0.140 0.000 0.000
#> GSM78535 4 0.4511 0.319 0.356 0.016 0.000 0.628 0.000
#> GSM78538 2 0.3128 0.740 0.004 0.824 0.004 0.168 0.000
#> GSM78542 2 0.2624 0.797 0.000 0.872 0.012 0.116 0.000
#> GSM78544 2 0.2439 0.852 0.004 0.876 0.120 0.000 0.000
#> GSM78549 2 0.3073 0.846 0.004 0.868 0.076 0.000 0.052
#> GSM78553 2 0.2843 0.851 0.000 0.876 0.076 0.048 0.000
#> GSM78558 2 0.2707 0.857 0.024 0.888 0.080 0.008 0.000
#> GSM78561 5 0.0510 0.909 0.000 0.016 0.000 0.000 0.984
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM78539 1 0.8752 -0.0202 0.268 0.124 0.220 0.144 NA 0.000
#> GSM78545 3 0.4131 0.6361 0.004 0.072 0.744 0.000 NA 0.000
#> GSM78550 3 0.7462 0.2825 0.000 0.156 0.360 0.200 NA 0.000
#> GSM78554 3 0.8227 0.1166 0.048 0.136 0.308 0.232 NA 0.000
#> GSM78562 4 0.1692 0.7322 0.012 0.008 0.000 0.932 NA 0.000
#> GSM78540 4 0.4146 0.6403 0.028 0.024 0.004 0.752 NA 0.000
#> GSM78546 3 0.7012 0.4008 0.192 0.088 0.464 0.004 NA 0.000
#> GSM78551 4 0.6945 0.1309 0.000 0.104 0.156 0.448 NA 0.000
#> GSM78555 4 0.4111 0.5780 0.244 0.012 0.000 0.716 NA 0.000
#> GSM78563 4 0.4478 0.6535 0.040 0.040 0.004 0.744 NA 0.000
#> GSM43005 3 0.3260 0.6692 0.000 0.072 0.832 0.004 NA 0.000
#> GSM43008 3 0.5060 0.5644 0.168 0.056 0.700 0.000 NA 0.000
#> GSM43011 3 0.3110 0.5944 0.000 0.012 0.792 0.000 NA 0.000
#> GSM78523 3 0.3240 0.5604 0.000 0.004 0.752 0.000 NA 0.000
#> GSM78526 3 0.7364 0.1279 0.000 0.112 0.336 0.304 NA 0.000
#> GSM78529 6 0.1327 0.8418 0.000 0.000 0.064 0.000 NA 0.936
#> GSM78532 4 0.1116 0.7339 0.008 0.004 0.000 0.960 NA 0.000
#> GSM78534 4 0.3840 0.6541 0.020 0.052 0.000 0.792 NA 0.000
#> GSM78537 4 0.2402 0.7226 0.060 0.012 0.000 0.896 NA 0.000
#> GSM78543 1 0.2510 0.5939 0.884 0.008 0.000 0.080 NA 0.000
#> GSM78548 3 0.5967 0.5479 0.000 0.124 0.584 0.052 NA 0.000
#> GSM78557 1 0.4010 0.5735 0.780 0.016 0.004 0.148 NA 0.000
#> GSM78560 1 0.2517 0.5399 0.888 0.016 0.008 0.008 NA 0.000
#> GSM78565 1 0.4387 0.1923 0.572 0.004 0.000 0.404 NA 0.000
#> GSM43000 3 0.3046 0.5993 0.000 0.012 0.800 0.000 NA 0.000
#> GSM43002 3 0.0458 0.6640 0.000 0.000 0.984 0.000 NA 0.000
#> GSM43004 4 0.2741 0.7005 0.032 0.008 0.000 0.868 NA 0.000
#> GSM43007 3 0.4868 0.6158 0.124 0.028 0.712 0.000 NA 0.000
#> GSM43010 4 0.5253 0.5601 0.000 0.076 0.068 0.684 NA 0.000
#> GSM78522 1 0.5592 0.2641 0.516 0.000 0.136 0.004 NA 0.000
#> GSM78525 3 0.2624 0.6462 0.000 0.020 0.856 0.000 NA 0.000
#> GSM78528 3 0.2795 0.6684 0.000 0.044 0.856 0.000 NA 0.000
#> GSM78531 4 0.0405 0.7325 0.000 0.004 0.000 0.988 NA 0.000
#> GSM78533 4 0.6165 0.4764 0.004 0.088 0.188 0.604 NA 0.000
#> GSM78536 4 0.2920 0.6680 0.168 0.004 0.000 0.820 NA 0.000
#> GSM78541 4 0.1812 0.7179 0.080 0.000 0.000 0.912 NA 0.000
#> GSM78547 4 0.2230 0.7199 0.000 0.024 0.000 0.892 NA 0.000
#> GSM78552 3 0.2866 0.6496 0.084 0.004 0.860 0.000 NA 0.000
#> GSM78556 4 0.3308 0.7067 0.064 0.012 0.000 0.836 NA 0.000
#> GSM78559 4 0.3359 0.6392 0.196 0.012 0.000 0.784 NA 0.000
#> GSM78564 1 0.4189 0.1533 0.552 0.008 0.000 0.436 NA 0.000
#> GSM42999 6 0.0000 0.8799 0.000 0.000 0.000 0.000 NA 1.000
#> GSM43001 6 0.0000 0.8799 0.000 0.000 0.000 0.000 NA 1.000
#> GSM43003 2 0.4538 0.6788 0.048 0.740 0.004 0.000 NA 0.172
#> GSM43006 6 0.0000 0.8799 0.000 0.000 0.000 0.000 NA 1.000
#> GSM43009 2 0.2865 0.8234 0.000 0.840 0.140 0.000 NA 0.012
#> GSM43012 6 0.3109 0.7046 0.000 0.224 0.000 0.000 NA 0.772
#> GSM78524 4 0.6775 0.3082 0.148 0.128 0.000 0.516 NA 0.000
#> GSM78527 6 0.3489 0.5954 0.000 0.288 0.000 0.000 NA 0.708
#> GSM78530 2 0.2375 0.8772 0.008 0.896 0.060 0.000 NA 0.000
#> GSM78535 4 0.4029 0.5064 0.288 0.012 0.000 0.688 NA 0.000
#> GSM78538 2 0.2727 0.8293 0.004 0.876 0.004 0.068 NA 0.000
#> GSM78542 2 0.1708 0.8738 0.004 0.932 0.000 0.024 NA 0.000
#> GSM78544 2 0.1480 0.8948 0.000 0.940 0.040 0.000 NA 0.000
#> GSM78549 2 0.1679 0.8938 0.000 0.936 0.036 0.000 NA 0.012
#> GSM78553 2 0.1542 0.8862 0.000 0.944 0.016 0.016 NA 0.000
#> GSM78558 2 0.1078 0.8941 0.012 0.964 0.016 0.000 NA 0.000
#> GSM78561 6 0.0820 0.8731 0.000 0.012 0.000 0.000 NA 0.972
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) agent(p) individual(p) k
#> ATC:NMF 56 3.35e-04 0.51056 0.1086 2
#> ATC:NMF 51 6.23e-04 0.15262 0.0664 3
#> ATC:NMF 49 2.76e-05 0.27571 0.4019 4
#> ATC:NMF 51 1.81e-08 0.01808 0.6727 5
#> ATC:NMF 47 1.10e-06 0.00664 0.5833 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
sessionInfo()
#> R version 3.6.0 (2019-04-26)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: CentOS Linux 7 (Core)
#>
#> Matrix products: default
#> BLAS: /usr/lib64/libblas.so.3.4.2
#> LAPACK: /usr/lib64/liblapack.so.3.4.2
#>
#> locale:
#> [1] LC_CTYPE=en_GB.UTF-8 LC_NUMERIC=C LC_TIME=en_GB.UTF-8
#> [4] LC_COLLATE=en_GB.UTF-8 LC_MONETARY=en_GB.UTF-8 LC_MESSAGES=en_GB.UTF-8
#> [7] LC_PAPER=en_GB.UTF-8 LC_NAME=C LC_ADDRESS=C
#> [10] LC_TELEPHONE=C LC_MEASUREMENT=en_GB.UTF-8 LC_IDENTIFICATION=C
#>
#> attached base packages:
#> [1] grid stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] genefilter_1.66.0 ComplexHeatmap_2.3.1 markdown_1.1 knitr_1.26
#> [5] GetoptLong_0.1.7 cola_1.3.2
#>
#> loaded via a namespace (and not attached):
#> [1] circlize_0.4.8 shape_1.4.4 xfun_0.11 slam_0.1-46
#> [5] lattice_0.20-38 splines_3.6.0 colorspace_1.4-1 vctrs_0.2.0
#> [9] stats4_3.6.0 blob_1.2.0 XML_3.98-1.20 survival_2.44-1.1
#> [13] rlang_0.4.2 pillar_1.4.2 DBI_1.0.0 BiocGenerics_0.30.0
#> [17] bit64_0.9-7 RColorBrewer_1.1-2 matrixStats_0.55.0 stringr_1.4.0
#> [21] GlobalOptions_0.1.1 evaluate_0.14 memoise_1.1.0 Biobase_2.44.0
#> [25] IRanges_2.18.3 parallel_3.6.0 AnnotationDbi_1.46.1 highr_0.8
#> [29] Rcpp_1.0.3 xtable_1.8-4 backports_1.1.5 S4Vectors_0.22.1
#> [33] annotate_1.62.0 skmeans_0.2-11 bit_1.1-14 microbenchmark_1.4-7
#> [37] brew_1.0-6 impute_1.58.0 rjson_0.2.20 png_0.1-7
#> [41] digest_0.6.23 stringi_1.4.3 polyclip_1.10-0 clue_0.3-57
#> [45] tools_3.6.0 bitops_1.0-6 magrittr_1.5 eulerr_6.0.0
#> [49] RCurl_1.95-4.12 RSQLite_2.1.4 tibble_2.1.3 cluster_2.1.0
#> [53] crayon_1.3.4 pkgconfig_2.0.3 zeallot_0.1.0 Matrix_1.2-17
#> [57] xml2_1.2.2 httr_1.4.1 R6_2.4.1 mclust_5.4.5
#> [61] compiler_3.6.0