cola Report for Hierarchical Partitioning - 'TCGA_KIRP_methylation'

Date: 2021-07-22 17:34:06 CEST, cola version: 1.9.4

Summary

First the variable is renamed to res_rh.

res_rh = rh

The partition hierarchy and all available functions which can be applied to res_rh object.

res_rh

#> A 'HierarchicalPartition' object with 4 combinations of top-value methods and partitioning methods.
#>   On a matrix with 376053 rows and 321 columns.
#>   Performed in total 75600 partitions.
#>   There are 37 groups under the following parameters:
#>     - min_samples: 6
#>     - mean_silhouette_cutoff: 0.9
#>     - min_n_signatures: 1000 (signatures are selected based on:)
#>       - fdr_cutoff: 0.05
#>       - group_diff: 0.25
#> 
#> Hierarchy of the partition:
#>   0, 321 cols
#>   |-- 01, 79 cols, 2544 signatures
#>   |   |-- 011, 33 cols, 424 signatures (c)
#>   |   |-- 012, 27 cols, 4789 signatures
#>   |   |   |-- 0121, 4 cols (b)
#>   |   |   |-- 0122, 10 cols (b)
#>   |   |   |-- 0123, 5 cols (b)
#>   |   |   `-- 0124, 8 cols (b)
#>   |   `-- 013, 19 cols, 3199 signatures
#>   |       |-- 0131, 14 cols, 1212 signatures
#>   |       |   |-- 01311, 12 cols, 139 signatures (c)
#>   |       |   `-- 01312, 2 cols (b)
#>   |       `-- 0132, 5 cols (b)
#>   |-- 02, 56 cols, 6551 signatures
#>   |   |-- 021, 31 cols, 454 signatures (c)
#>   |   |-- 022, 17 cols, 8085 signatures
#>   |   |   |-- 0221, 12 cols, 52 signatures (c)
#>   |   |   |-- 0222, 3 cols (b)
#>   |   |   `-- 0223, 2 cols (b)
#>   |   `-- 023, 8 cols (b)
#>   |-- 03, 59 cols, 26826 signatures
#>   |   |-- 031, 33 cols, 5590 signatures
#>   |   |   |-- 0311, 17 cols, 2840 signatures
#>   |   |   |   |-- 03111, 9 cols (b)
#>   |   |   |   |-- 03112, 3 cols (b)
#>   |   |   |   `-- 03113, 5 cols (b)
#>   |   |   |-- 0312, 4 cols (b)
#>   |   |   `-- 0313, 12 cols, 25 signatures (c)
#>   |   |-- 032, 22 cols, 2274 signatures
#>   |   |   |-- 0321, 12 cols, 1 signatures (c)
#>   |   |   `-- 0322, 10 cols (b)
#>   |   `-- 033, 4 cols (b)
#>   |-- 04, 44 cols, 36795 signatures
#>   |   |-- 041, 10 cols (b)
#>   |   |-- 042, 11 cols (b)
#>   |   |-- 043, 12 cols, 1141 signatures
#>   |   |   |-- 0431, 4 cols (b)
#>   |   |   |-- 0432, 4 cols (b)
#>   |   |   `-- 0433, 4 cols (b)
#>   |   `-- 044, 11 cols (b)
#>   `-- 05, 83 cols, 9931 signatures
#>       |-- 051, 32 cols, 1801 signatures
#>       |   |-- 0511, 15 cols, 9 signatures (c)
#>       |   |-- 0512, 7 cols (b)
#>       |   `-- 0513, 10 cols (b)
#>       |-- 052, 13 cols, 3659 signatures
#>       |   |-- 0521, 3 cols (b)
#>       |   |-- 0522, 8 cols (b)
#>       |   `-- 0523, 2 cols (b)
#>       |-- 053, 32 cols, 4193 signatures
#>       |   |-- 0531, 17 cols, 417 signatures (c)
#>       |   |-- 0532, 11 cols (b)
#>       |   `-- 0533, 4 cols (b)
#>       `-- 054, 6 cols (b)
#> Stop reason:
#>   b) Subgroup had too few columns.
#>   c) There were too few signatures.
#> 
#> Following methods can be applied to this 'HierarchicalPartition' object:
#>  [1] "all_leaves"            "all_nodes"             "cola_report"           "collect_classes"      
#>  [5] "colnames"              "compare_signatures"    "dimension_reduction"   "functional_enrichment"
#>  [9] "get_anno_col"          "get_anno"              "get_children_nodes"    "get_classes"          
#> [13] "get_matrix"            "get_signatures"        "is_leaf_node"          "max_depth"            
#> [17] "merge_node"            "ncol"                  "node_info"             "node_level"           
#> [21] "nrow"                  "rownames"              "show"                  "split_node"           
#> [25] "suggest_best_k"        "test_to_known_factors" "top_rows_heatmap"      "top_rows_overlap"     
#> 
#> You can get result for a single node by e.g. object["01"]

The call of hierarchical_partition() was:

#> hierarchical_partition(data = mat, top_n = 1000, top_value_method = c("SD", "ATC"), 
#>     partition_method = c("kmeans", "skmeans"), subset = 500, group_diff = 0.25, min_n_signatures = 1000, 
#>     filter_fun = function(mat) {
#>         s = rowSds(mat)
#>         order(-s)[1:30000]
#>     }, max_k = 8, scale_rows = FALSE, cores = 4)

Dimension of the input matrix:

mat = get_matrix(res_rh)
dim(mat)

#> [1] 376053    321

All the methods that were tried:

res_rh@param$combination_method

#> [[1]]
#> [1] "SD"     "kmeans"
#> 
#> [[2]]
#> [1] "ATC"    "kmeans"
#> 
#> [[3]]
#> [1] "SD"      "skmeans"
#> 
#> [[4]]
#> [1] "ATC"     "skmeans"

Density distribution

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

library(ComplexHeatmap)
densityHeatmap(mat, ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
    mc.cores = 1)

plot of chunk density-heatmap

Some values about the hierarchy:

all_nodes(res_rh)

#>  [1] "0"     "01"    "011"   "012"   "0121"  "0122"  "0123"  "0124"  "013"   "0131"  "01311" "01312"
#> [13] "0132"  "02"    "021"   "022"   "0221"  "0222"  "0223"  "023"   "03"    "031"   "0311"  "03111"
#> [25] "03112" "03113" "0312"  "0313"  "032"   "0321"  "0322"  "033"   "04"    "041"   "042"   "043"  
#> [37] "0431"  "0432"  "0433"  "044"   "05"    "051"   "0511"  "0512"  "0513"  "052"   "0521"  "0522" 
#> [49] "0523"  "053"   "0531"  "0532"  "0533"  "054"

all_leaves(res_rh)

#>  [1] "011"   "0121"  "0122"  "0123"  "0124"  "01311" "01312" "0132"  "021"   "0221"  "0222"  "0223" 
#> [13] "023"   "03111" "03112" "03113" "0312"  "0313"  "0321"  "0322"  "033"   "041"   "042"   "0431" 
#> [25] "0432"  "0433"  "044"   "0511"  "0512"  "0513"  "0521"  "0522"  "0523"  "0531"  "0532"  "0533" 
#> [37] "054"

node_info(res_rh)

#>       id best_method depth best_k n_columns n_signatures p_signatures is_leaf
#> 1      0 ATC:skmeans     1      5       321        40190     1.07e-01   FALSE
#> 2     01  SD:skmeans     2      3        79         2544     6.77e-03   FALSE
#> 3    011 ATC:skmeans     3      2        33          424     1.13e-03    TRUE
#> 4    012  ATC:kmeans     3      4        27         4789     1.27e-02   FALSE
#> 5   0121 not applied     4     NA         4           NA           NA    TRUE
#> 6   0122 not applied     4     NA        10           NA           NA    TRUE
#> 7   0123 not applied     4     NA         5           NA           NA    TRUE
#> 8   0124 not applied     4     NA         8           NA           NA    TRUE
#> 9    013  ATC:kmeans     3      2        19         3199     8.51e-03   FALSE
#> 10  0131  ATC:kmeans     4      2        14         1212     3.22e-03   FALSE
#> 11 01311  ATC:kmeans     5      2        12          139     3.70e-04    TRUE
#> 12 01312 not applied     5     NA         2           NA           NA    TRUE
#> 13  0132 not applied     4     NA         5           NA           NA    TRUE
#> 14    02  SD:skmeans     2      3        56         6551     1.74e-02   FALSE
#> 15   021 ATC:skmeans     3      4        31          454     1.21e-03    TRUE
#> 16   022   SD:kmeans     3      3        17         8085     2.15e-02   FALSE
#> 17  0221  ATC:kmeans     4      3        12           52     1.38e-04    TRUE
#> 18  0222 not applied     4     NA         3           NA           NA    TRUE
#> 19  0223 not applied     4     NA         2           NA           NA    TRUE
#> 20   023 not applied     3     NA         8           NA           NA    TRUE
#> 21    03  ATC:kmeans     2      3        59        26826     7.13e-02   FALSE
#> 22   031  ATC:kmeans     3      3        33         5590     1.49e-02   FALSE
#> 23  0311   SD:kmeans     4      3        17         2840     7.55e-03   FALSE
#> 24 03111 not applied     5     NA         9           NA           NA    TRUE
#> 25 03112 not applied     5     NA         3           NA           NA    TRUE
#> 26 03113 not applied     5     NA         5           NA           NA    TRUE
#> 27  0312 not applied     4     NA         4           NA           NA    TRUE
#> 28  0313 ATC:skmeans     4      3        12           25     6.65e-05    TRUE
#> 29   032   SD:kmeans     3      2        22         2274     6.05e-03   FALSE
#> 30  0321  ATC:kmeans     4      3        12            1     2.66e-06    TRUE
#> 31  0322 not applied     4     NA        10           NA           NA    TRUE
#> 32   033 not applied     3     NA         4           NA           NA    TRUE
#> 33    04   SD:kmeans     2      4        44        36795     9.78e-02   FALSE
#> 34   041 not applied     3     NA        10           NA           NA    TRUE
#> 35   042 not applied     3     NA        11           NA           NA    TRUE
#> 36   043 ATC:skmeans     3      3        12         1141     3.03e-03   FALSE
#> 37  0431 not applied     4     NA         4           NA           NA    TRUE
#> 38  0432 not applied     4     NA         4           NA           NA    TRUE
#> 39  0433 not applied     4     NA         4           NA           NA    TRUE
#> 40   044 not applied     3     NA        11           NA           NA    TRUE
#> 41    05 ATC:skmeans     2      4        83         9931     2.64e-02   FALSE
#> 42   051  ATC:kmeans     3      3        32         1801     4.79e-03   FALSE
#> 43  0511  ATC:kmeans     4      2        15            9     2.39e-05    TRUE
#> 44  0512 not applied     4     NA         7           NA           NA    TRUE
#> 45  0513 not applied     4     NA        10           NA           NA    TRUE
#> 46   052 ATC:skmeans     3      3        13         3659     9.73e-03   FALSE
#> 47  0521 not applied     4     NA         3           NA           NA    TRUE
#> 48  0522 not applied     4     NA         8           NA           NA    TRUE
#> 49  0523 not applied     4     NA         2           NA           NA    TRUE
#> 50   053  ATC:kmeans     3      3        32         4193     1.12e-02   FALSE
#> 51  0531  ATC:kmeans     4      3        17          417     1.11e-03    TRUE
#> 52  0532 not applied     4     NA        11           NA           NA    TRUE
#> 53  0533 not applied     4     NA         4           NA           NA    TRUE
#> 54   054 not applied     3     NA         6           NA           NA    TRUE

In the output from node_info(), there are the following columns:

Labels of nodes are encoded in a special way. The number of digits correspond to the depth of the node in the hierarchy and the value of the digits correspond to the index of the subgroup in the current node, E.g. a label of “012” means the node is the second subgroup of the partition which is the first subgroup of the root node.

Suggest the best k

Following table shows the best k (number of partitions) for each node in the partition hierarchy. Clicking on the node name in the table goes to the corresponding section for the partitioning on that node.

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

suggest_best_k(res_rh)
Node Best method Is leaf Best k 1-PAC Mean silhouette Concordance #samples
Node0 ATC:skmeans 7 0.95 0.89 0.95 321 *
Node01 SD:skmeans 3 1.00 0.96 0.98 79 **
Node011-leaf ATC:skmeans ✓ (c) 6 0.59 0.46 0.78 33
Node012 ATC:kmeans 8 0.92 0.77 0.88 27 *
Node0121-leaf not applied ✓ (b) 4
Node0122-leaf not applied ✓ (b) 10
Node0123-leaf not applied ✓ (b) 5
Node0124-leaf not applied ✓ (b) 8
Node013 ATC:kmeans 2 1.00 1.00 1.00 19 **
Node0131 ATC:kmeans 8 1.00 0.55 0.98 14 **
Node01311-leaf ATC:kmeans ✓ (c) 8 0.95 0.43 0.97 12 **
Node01312-leaf not applied ✓ (b) 2
Node0132-leaf not applied ✓ (b) 5
Node02 SD:skmeans 3 1.00 0.97 0.99 56 **
Node021-leaf ATC:skmeans ✓ (c) 7 0.97 0.91 0.96 31 **
Node022 SD:kmeans 4 0.84 0.85 0.96 17
Node0221-leaf ATC:kmeans ✓ (c) 8 0.92 0.44 0.88 12 *
Node0222-leaf not applied ✓ (b) 3
Node0223-leaf not applied ✓ (b) 2
Node023-leaf not applied ✓ (b) 8
Node03 ATC:kmeans 3 1.00 0.99 0.98 59 **
Node031 ATC:kmeans 3 1.00 0.96 0.99 33 **
Node0311 SD:kmeans 7 0.90 0.79 0.89 17 *
Node03111-leaf not applied ✓ (b) 9
Node03112-leaf not applied ✓ (b) 3
Node03113-leaf not applied ✓ (b) 5
Node0312-leaf not applied ✓ (b) 4
Node0313-leaf ATC:skmeans ✓ (c) 8 0.94 0.60 0.97 12 *
Node032 SD:kmeans 2 1.00 0.98 0.98 22 **
Node0321-leaf ATC:kmeans ✓ (c) 7 1.00 0.66 1.00 12 **
Node0322-leaf not applied ✓ (b) 10
Node033-leaf not applied ✓ (b) 4
Node04 SD:kmeans 6 0.90 0.84 0.88 44 *
Node041-leaf not applied ✓ (b) 10
Node042-leaf not applied ✓ (b) 11
Node043 ATC:skmeans 7 0.92 0.64 0.94 12 *
Node0431-leaf not applied ✓ (b) 4
Node0432-leaf not applied ✓ (b) 4
Node0433-leaf not applied ✓ (b) 4
Node044-leaf not applied ✓ (b) 11
Node05 ATC:skmeans 8 0.91 0.88 0.92 83 *
Node051 ATC:kmeans 3 1.00 1.00 1.00 32 **
Node0511-leaf ATC:kmeans ✓ (c) 2 1.00 1.00 1.00 15 **
Node0512-leaf not applied ✓ (b) 7
Node0513-leaf not applied ✓ (b) 10
Node052 ATC:skmeans 4 1.00 0.91 0.99 13 **
Node0521-leaf not applied ✓ (b) 3
Node0522-leaf not applied ✓ (b) 8
Node0523-leaf not applied ✓ (b) 2
Node053 ATC:kmeans 3 1.00 1.00 1.00 32 **
Node0531-leaf ATC:kmeans ✓ (c) 3 1.00 1.00 1.00 17 **
Node0532-leaf not applied ✓ (b) 11
Node0533-leaf not applied ✓ (b) 4
Node054-leaf not applied ✓ (b) 6

Stop reason: b) Subgroup had too few columns. c) There were too few signatures.

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

Partition hierarchy

The nodes of the hierarchy can be merged by setting the merge_node parameters. Here we control the hierarchy with the min_n_signatures parameter. The value of min_n_signatures is from node_info().

collect_classes(res_rh, merge_node = merge_node_param(min_n_signatures = 1141))

plot of chunk tab-collect-classes-from-hierarchical-partition-1

Following shows the table of the partitions (You need to click the show/hide code output link to see it).

show/hide code output

get_classes(res_rh, merge_node = merge_node_param(min_n_signatures = 1141))

#> TCGA.SX.A7SM.01 TCGA.IA.A83W.01 TCGA.B1.A656.01 TCGA.4A.A93X.01 TCGA.G7.A8LC.01 TCGA.SX.A7SS.01 
#>           "042"          "0512"          "0312"           "042"          "0533"           "011" 
#> TCGA.B9.A69E.01 TCGA.BQ.5878.01 TCGA.DW.5561.01 TCGA.PJ.A8JU.01 TCGA.EV.5901.01 TCGA.SX.A7SR.01 
#>          "0313"           "011"         "01312"          "0322"           "054"          "0511" 
#> TCGA.BQ.5894.01 TCGA.KV.A6GE.01 TCGA.BQ.5882.01 TCGA.SX.A7SQ.01 TCGA.F9.A7Q0.01 TCGA.IZ.A6M8.01 
#>           "041"           "011"          "0432"         "01311"          "0321"          "0531" 
#> TCGA.B1.A654.01 TCGA.B3.8121.01 TCGA.MH.A856.01 TCGA.G7.A4TM.01 TCGA.IZ.8196.01 TCGA.B9.A5W7.01 
#>          "0132"         "03112"          "0512"         "01311"          "0123"         "01311" 
#> TCGA.B9.5156.01 TCGA.A4.A7UZ.01 TCGA.Y8.A897.01 TCGA.SX.A7SP.01 TCGA.Y8.A8RZ.01 TCGA.A4.A5XZ.01 
#>          "0513"          "0321"          "0511"          "0522"          "0523"          "0532" 
#> TCGA.Y8.A898.01 TCGA.BQ.5893.01 TCGA.SX.A7SU.01 TCGA.IZ.8195.01 TCGA.GL.8500.01 TCGA.EV.5902.01 
#>          "0511"           "041"         "01311"           "044"          "0124"          "0123" 
#> TCGA.J7.A8I2.01 TCGA.A4.8516.01 TCGA.A4.8312.01 TCGA.BQ.5880.01 TCGA.Y8.A8RY.01 TCGA.SX.A7SN.01 
#>           "033"          "0122"           "023"          "0321"          "0511"          "0513" 
#> TCGA.MH.A854.01 TCGA.A4.8517.01 TCGA.GL.A9DD.01 TCGA.A4.8630.01 TCGA.4A.A93W.01 TCGA.SX.A7SO.01 
#>          "0121"          "0531"         "03111"           "011"          "0132"          "0521" 
#> TCGA.GL.A9DC.01 TCGA.A4.8515.01 TCGA.IZ.A6M9.01 TCGA.BQ.5880.11 TCGA.B1.A657.01 TCGA.G7.A8LD.01 
#>          "0121"           "011"           "011"           "021"          "0511"          "0433" 
#> TCGA.Y8.A8S1.01 TCGA.IA.A83S.01 TCGA.Y8.A8S0.01 TCGA.BQ.5884.11 TCGA.B1.A655.01 TCGA.BQ.5877.11 
#>          "0313"         "03111"           "011"          "0221"          "0322"           "021" 
#> TCGA.EV.5903.01 TCGA.J7.8537.01 TCGA.A4.A6HP.01 TCGA.BQ.5890.01 TCGA.Y8.A896.01 TCGA.BQ.5888.01 
#>          "0513"          "0432"          "0513"           "042"          "0321"          "0322" 
#> TCGA.BQ.5879.01 TCGA.GL.A9DE.01 TCGA.G7.A8LB.01 TCGA.IA.A83T.01 TCGA.IA.A83V.01 TCGA.BQ.5876.11 
#>           "041"           "042"           "011"          "0313"          "0321"           "021" 
#> TCGA.BQ.5885.11 TCGA.KV.A6GD.01 TCGA.SX.A7SL.01 TCGA.B9.A8YI.01 TCGA.B9.A8YH.01 TCGA.4A.A93Y.01 
#>           "021"         "03111"           "011"           "044"          "0122"          "0322" 
#> TCGA.BQ.5886.01 TCGA.A4.A5Y0.01 TCGA.A4.8098.01 TCGA.MH.A857.01 TCGA.BQ.5889.11 TCGA.DW.5560.01 
#>          "0531"          "0522"          "0533"           "023"           "021"           "054" 
#> TCGA.F9.A8NY.01 TCGA.BQ.5894.11 TCGA.BQ.5891.11 TCGA.G7.A8LE.01 TCGA.SX.A71W.01 TCGA.Y8.A894.01 
#>           "041"           "021"          "0221"         "01311"           "011"          "0121" 
#> TCGA.WN.A9G9.01 TCGA.A4.8310.01 TCGA.A4.8518.01 TCGA.BQ.5881.11 TCGA.BQ.5893.11 TCGA.A4.8311.01 
#>          "0313"          "0532"          "0321"           "021"           "021"           "011" 
#> TCGA.BQ.5891.01 TCGA.Y8.A895.01 TCGA.BQ.5876.01 TCGA.MH.A855.01 TCGA.P4.AAVO.01 TCGA.BQ.5886.11 
#>          "0431"           "011"          "0312"          "0322"           "044"           "021" 
#> TCGA.2Z.A9JS.01 TCGA.BQ.5888.11 TCGA.2Z.A9J8.01 TCGA.KV.A74V.01 TCGA.A4.A5Y1.01 TCGA.BQ.5875.01 
#>           "011"          "0221"          "0523"           "011"          "0431"           "042" 
#> TCGA.UZ.A9PZ.01 TCGA.Q2.A5QZ.01 TCGA.P4.A5E8.01 TCGA.B9.5155.01 TCGA.B9.A5W9.01 TCGA.5P.A9K4.01 
#>          "0122"           "044"           "041"           "011"           "044"           "011" 
#> TCGA.P4.A5E7.01 TCGA.PJ.A5Z9.01 TCGA.5P.A9K8.01 TCGA.5P.A9KF.01 TCGA.P4.AAVK.01 TCGA.2Z.A9JM.01 
#>           "054"           "011"          "0223"          "0122"           "042"          "0513" 
#> TCGA.A4.A48D.01 TCGA.BQ.5889.01 TCGA.2Z.A9JD.01 TCGA.5P.A9K2.01 TCGA.2Z.A9JO.01 TCGA.5P.A9K9.01 
#>          "0313"         "03113"          "0531"           "011"          "0322"          "0433" 
#> TCGA.UZ.A9PV.01 TCGA.SX.A71V.01 TCGA.BQ.5892.11 TCGA.UZ.A9Q0.01 TCGA.UZ.A9PX.01 TCGA.UZ.A9PR.01 
#>           "011"          "0532"           "021"           "011"          "0122"          "0122" 
#> TCGA.IA.A40X.01 TCGA.5P.A9JW.01 TCGA.IA.A40Y.01 TCGA.BQ.5883.11 TCGA.BQ.5878.11 TCGA.P4.A5EA.01 
#>          "0522"          "0313"          "0431"          "0221"          "0221"           "041" 
#> TCGA.5P.A9KE.01 TCGA.5P.A9K3.01 TCGA.B1.A47N.01 TCGA.5P.A9KA.01 TCGA.BQ.5879.11 TCGA.P4.A5ED.01 
#>          "0531"           "042"         "01311"          "0512"          "0221"           "023" 
#> TCGA.A4.A772.01 TCGA.B1.A47O.01 TCGA.IA.A40U.01 TCGA.2Z.A9JE.01 TCGA.B9.A44B.01 TCGA.AT.A5NU.01 
#>          "0511"         "03112"          "0532"          "0123"           "042"           "011" 
#> TCGA.BQ.5882.11 TCGA.BQ.5877.01 TCGA.DW.7963.01 TCGA.2Z.A9JL.01 TCGA.2Z.A9JQ.01 TCGA.2Z.A9JK.01 
#>           "021"          "0431"          "0531"          "0512"          "0123"          "0321" 
#> TCGA.UZ.A9PU.01 TCGA.P4.A5EB.01 TCGA.BQ.5892.01 TCGA.B1.A47M.11 TCGA.2Z.A9J9.01 TCGA.UZ.A9PS.05 
#>          "0122"          "0124"          "0321"           "023"           "023"          "0312" 
#> TCGA.P4.AAVM.01 TCGA.PJ.A5Z8.01 TCGA.5P.A9JZ.01 TCGA.2Z.A9JG.01 TCGA.BQ.5884.01 TCGA.2Z.A9JI.01 
#>          "0531"          "0313"           "054"           "044"          "0322"          "0432" 
#> TCGA.BQ.5890.11 TCGA.BQ.5881.01 TCGA.UZ.A9PP.01 TCGA.5P.A9JU.01 TCGA.2Z.A9JN.01 TCGA.UZ.A9PS.01 
#>           "021"          "0531"         "01311"           "042"          "0222"          "0522" 
#> TCGA.BQ.5875.11 TCGA.5P.A9JY.01 TCGA.B9.A5W8.01 TCGA.F9.A4JJ.01 TCGA.BQ.5883.01 TCGA.5P.A9K0.01 
#>          "0221"           "011"         "03111"           "041"          "0222"          "0531" 
#> TCGA.P4.AAVL.01 TCGA.B1.5398.01 TCGA.5P.A9K6.01 TCGA.UZ.A9PQ.01 TCGA.P4.A5E6.01 TCGA.BQ.5885.01 
#>          "0124"          "0313"          "0531"           "044"          "0532"          "0532" 
#> TCGA.UZ.A9Q1.01 TCGA.2Z.A9JP.01 TCGA.5P.A9KC.01 TCGA.5P.A9KH.01 TCGA.2Z.A9JR.01 TCGA.GL.A59T.01 
#>           "044"          "0531"          "0322"           "023"          "0511"          "0511" 
#> TCGA.5P.A9JV.01 TCGA.WN.AB4C.01 TCGA.SX.A71R.01 TCGA.A4.A5DU.01 TCGA.B1.A47M.01 TCGA.2Z.A9JJ.01 
#>           "023"          "0322"          "0122"          "0132"          "0511"           "054" 
#> TCGA.2Z.A9JT.01 TCGA.GL.A4EM.01 TCGA.HE.7129.01 TCGA.HE.7128.01 TCGA.HE.A5NL.01 TCGA.G7.7502.01 
#>          "0531"          "0313"           "011"         "03111"          "0513"          "0532" 
#> TCGA.BQ.7059.01 TCGA.DZ.6134.11 TCGA.HE.A5NJ.01 TCGA.BQ.7053.11 TCGA.GL.6846.11 TCGA.GL.6846.01 
#>         "03111"           "021"           "011"          "0221"           "021"           "044" 
#> TCGA.DW.7839.01 TCGA.DW.7841.01 TCGA.BQ.7049.01 TCGA.G7.6793.01 TCGA.BQ.7051.01 TCGA.BQ.7045.01 
#>          "0132"          "0513"         "03113"           "041"           "011"          "0531" 
#> TCGA.HE.A5NF.01 TCGA.A4.7996.01 TCGA.BQ.7046.01 TCGA.DZ.6132.11 TCGA.G7.7501.01 TCGA.O9.A75Z.01 
#>         "03111"          "0532"          "0531"           "021"          "0521"         "01311" 
#> TCGA.DW.7834.01 TCGA.DZ.6133.01 TCGA.A4.A4ZT.01 TCGA.BQ.7060.01 TCGA.G7.6792.01 TCGA.HE.7130.01 
#>          "0511"          "0122"           "011"          "0531"          "0512"           "033" 
#> TCGA.GL.7773.01 TCGA.DZ.6133.11 TCGA.B1.7332.01 TCGA.BQ.7053.01 TCGA.DZ.6131.01 TCGA.BQ.7062.01 
#>           "054"          "0221"           "011"          "0522"           "033"          "0532" 
#> TCGA.BQ.7046.11 TCGA.A4.7288.01 TCGA.DZ.6131.11 TCGA.BQ.7062.11 TCGA.BQ.7061.01 TCGA.A4.7286.01 
#>           "021"          "0522"           "021"           "021"           "042"          "0532" 
#> TCGA.G7.6797.01 TCGA.BQ.7058.01 TCGA.G7.6795.01 TCGA.HE.A5NH.01 TCGA.MH.A55W.01 TCGA.G7.6790.01 
#>           "011"           "042"          "0511"          "0124"          "0532"          "0531" 
#> TCGA.MH.A560.01 TCGA.A4.7997.01 TCGA.MH.A561.01 TCGA.BQ.7056.11 TCGA.B9.7268.01 TCGA.BQ.7055.11 
#>          "0312"          "0512"          "0511"          "0221"           "011"           "021" 
#> TCGA.HE.A5NI.01 TCGA.GL.7966.01 TCGA.BQ.7059.11 TCGA.A4.A57E.01 TCGA.A4.7288.11 TCGA.AL.A5DJ.01 
#>           "011"           "041"           "021"          "0521"          "0221"          "0433" 
#> TCGA.G7.6796.01 TCGA.DW.7837.01 TCGA.BQ.7051.11 TCGA.BQ.7048.01 TCGA.F9.A7VF.01 TCGA.BQ.7049.11 
#>          "0321"          "0513"           "021"           "044"           "011"           "021" 
#> TCGA.DZ.6134.01 TCGA.BQ.5887.01 TCGA.DZ.6135.01 TCGA.MH.A55Z.01 TCGA.A4.7915.01 TCGA.BQ.7048.11 
#>          "0313"          "0432"          "0124"          "0122"           "041"           "021" 
#> TCGA.HE.A5NK.01 TCGA.G7.6789.01 TCGA.AL.7173.01 TCGA.SX.A71S.01 TCGA.BQ.7061.11 TCGA.DW.7840.01 
#>         "03111"          "0433"         "03112"          "0121"          "0223"          "0124" 
#> TCGA.GL.A59R.01 TCGA.BQ.7050.11 TCGA.BQ.7058.11 TCGA.DW.7838.01 TCGA.SX.A71U.01 TCGA.DZ.6135.11 
#>          "0123"          "0221"           "021"         "03113"          "0511"           "021" 
#> TCGA.BQ.7044.11 TCGA.V9.A7HT.01 TCGA.DW.7842.01 TCGA.BQ.7050.01 TCGA.BQ.7055.01 TCGA.J7.6720.01 
#>           "021"         "03111"         "01311"          "0522"           "023"          "0511" 
#> TCGA.BQ.7060.11 TCGA.BQ.7044.01 TCGA.DZ.6132.01 TCGA.DW.7836.01 TCGA.A4.7828.01 TCGA.BQ.5887.11 
#>           "021"           "044"         "03113"         "01311"          "0222"           "021" 
#> TCGA.B3.A6W5.01 TCGA.MH.A562.01 TCGA.A4.7734.01 TCGA.BQ.7045.11 TCGA.A4.7584.01 TCGA.BQ.7056.01 
#>           "011"          "0513"          "0132"           "021"          "0531"          "0522" 
#> TCGA.A4.7287.01 TCGA.UZ.A9PJ.01 TCGA.2Z.A9J1.01 TCGA.UN.AAZ9.01 TCGA.UZ.A9PO.01 TCGA.UZ.A9PL.01 
#>           "033"         "01311"          "0512"          "0533"          "0313"          "0124" 
#> TCGA.A4.7732.11 TCGA.A4.7732.01 TCGA.2Z.A9J2.01 TCGA.2Z.A9J3.01 TCGA.2Z.A9J6.01 TCGA.F9.A97G.01 
#>           "021"         "01311"          "0322"          "0124"          "0513"          "0313" 
#> TCGA.UZ.A9PM.01 TCGA.A4.7585.11 TCGA.2K.A9WE.01 TCGA.A4.7583.01 TCGA.UZ.A9PK.01 TCGA.UZ.A9PN.01 
#>          "0321"           "021"         "03113"          "0533"           "011"          "0321" 
#> TCGA.2Z.A9J7.01 TCGA.2Z.A9J5.01 TCGA.A4.7585.01 
#>         "01312"          "0511"          "0321"

Top rows heatmap

Heatmaps of the top rows:

top_rows_heatmap(res_rh)

plot of chunk top-rows-heatmap

#> Error in h(simpleError(msg, call)) : 
#>   error in evaluating the argument 'object' in selecting a method for function 'draw': no applicable method for 'height' applied to an object of class "list"

Top rows on each node:

top_rows_overlap(res_rh, method = "upset")

plot of chunk top-rows-overlap

UMAP plot

UMAP plot which shows how samples are separated.

par(mfrow = c(1, 2))
dimension_reduction(res_rh, merge_node = merge_node_param(min_n_signatures = 1141),
    method = "UMAP", top_value_method = "SD", top_n = 40000, scale_rows = FALSE)
dimension_reduction(res_rh, merge_node = merge_node_param(min_n_signatures = 1141),
    method = "UMAP", top_value_method = "ATC", top_n = 40000, scale_rows = TRUE)

plot of chunk tab-dimension-reduction-by-depth-1

Signature heatmap

Signatures on the heatmap are the union of all signatures found on every node on the hierarchy. The number of k-means on rows are automatically selected by the function.

get_signatures(res_rh, merge_node = merge_node_param(min_n_signatures = 1141))

plot of chunk tab-get-signatures-from-hierarchical-partition-1

Compare signatures from different nodes:

compare_signatures(res_rh, verbose = FALSE)

plot of chunk unnamed-chunk-24

If there are too many signatures, top_signatures = ... can be set to only show the signatures with the highest FDRs. Note it only works on every node and the final signatures are the union of all signatures of all nodes.

# code only for demonstration
# e.g. to show the top 500 most significant rows on each node.
tb = get_signature(res_rh, top_signatures = 500)

Results for each node

Node0

Child nodes: Node01 , Node02 , Node03 , Node04 , Node05 .

The object with results only for a single top-value method and a single partitioning method can be extracted as:

res = res_rh["0"]

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, 7, 8.
#>   On a matrix with 30000 rows and 321 columns.
#>   Top rows (1000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'skmeans' method.
#>   Performed in total 350 partitions by row resampling.
#>   Best k for subgroups seems to be 7.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_partitions"     
#>  [7] "compare_signatures"      "consensus_heatmap"       "dimension_reduction"    
#> [10] "functional_enrichment"   "get_anno_col"            "get_anno"               
#> [13] "get_classes"             "get_consensus"           "get_matrix"             
#> [16] "get_membership"          "get_param"               "get_signatures"         
#> [19] "get_stats"               "is_best_k"               "is_stable_k"            
#> [22] "membership_heatmap"      "ncol"                    "nrow"                   
#> [25] "plot_ecdf"               "predict_classes"         "rownames"               
#> [28] "select_partition_number" "show"                    "suggest_best_k"         
#> [31] "test_to_known_factors"   "top_rows_heatmap"

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

collect_plots(res)

plot of chunk node-0-collect-plots

The plots are:

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:

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

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

select_partition_number(res)

plot of chunk node-0-select-partition-number

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.993       0.997         0.5020 0.498   0.498
#> 3 3 1.000           0.993       0.997         0.3154 0.740   0.526
#> 4 4 1.000           0.971       0.987         0.1092 0.838   0.579
#> 5 5 1.000           0.988       0.995         0.0820 0.842   0.502
#> 6 6 0.913           0.836       0.925         0.0454 0.946   0.751
#> 7 7 0.948           0.887       0.946         0.0314 0.943   0.695
#> 8 8 0.895           0.785       0.895         0.0144 0.971   0.811

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

suggest_best_k(res)

#> [1] 7
#> attr(,"optional")
#> [1] 2 3 4 5 6

There is also optional best \(k\) = 2 3 4 5 6 that is worth to check.

Following is 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 subgroup 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.

show/hide code output

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

#>                 class entropy silhouette   p1   p2
#> TCGA.SX.A7SM.01     2   0.000      0.998 0.00 1.00
#> TCGA.IA.A83W.01     1   0.000      0.996 1.00 0.00
#> TCGA.B1.A656.01     2   0.000      0.998 0.00 1.00
#> TCGA.4A.A93X.01     2   0.000      0.998 0.00 1.00
#> TCGA.G7.A8LC.01     1   0.722      0.752 0.80 0.20
#> TCGA.SX.A7SS.01     1   0.000      0.996 1.00 0.00
#> TCGA.B9.A69E.01     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.5878.01     1   0.000      0.996 1.00 0.00
#> TCGA.DW.5561.01     1   0.000      0.996 1.00 0.00
#> TCGA.PJ.A8JU.01     2   0.000      0.998 0.00 1.00
#> TCGA.EV.5901.01     1   0.000      0.996 1.00 0.00
#> TCGA.SX.A7SR.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.5894.01     2   0.000      0.998 0.00 1.00
#> TCGA.KV.A6GE.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.5882.01     2   0.000      0.998 0.00 1.00
#> TCGA.SX.A7SQ.01     1   0.000      0.996 1.00 0.00
#> TCGA.F9.A7Q0.01     2   0.000      0.998 0.00 1.00
#> TCGA.IZ.A6M8.01     1   0.855      0.615 0.72 0.28
#> TCGA.B1.A654.01     1   0.000      0.996 1.00 0.00
#> TCGA.B3.8121.01     2   0.000      0.998 0.00 1.00
#> TCGA.MH.A856.01     1   0.000      0.996 1.00 0.00
#> TCGA.G7.A4TM.01     1   0.000      0.996 1.00 0.00
#> TCGA.IZ.8196.01     1   0.000      0.996 1.00 0.00
#> TCGA.B9.A5W7.01     1   0.000      0.996 1.00 0.00
#> TCGA.B9.5156.01     1   0.000      0.996 1.00 0.00
#> TCGA.A4.A7UZ.01     2   0.000      0.998 0.00 1.00
#> TCGA.Y8.A897.01     1   0.000      0.996 1.00 0.00
#> TCGA.SX.A7SP.01     1   0.000      0.996 1.00 0.00
#> TCGA.Y8.A8RZ.01     1   0.000      0.996 1.00 0.00
#> TCGA.A4.A5XZ.01     1   0.000      0.996 1.00 0.00
#> TCGA.Y8.A898.01     1   0.402      0.913 0.92 0.08
#> TCGA.BQ.5893.01     2   0.000      0.998 0.00 1.00
#> TCGA.SX.A7SU.01     1   0.000      0.996 1.00 0.00
#> TCGA.IZ.8195.01     1   0.000      0.996 1.00 0.00
#> TCGA.GL.8500.01     1   0.000      0.996 1.00 0.00
#> TCGA.EV.5902.01     1   0.000      0.996 1.00 0.00
#> TCGA.J7.A8I2.01     2   0.000      0.998 0.00 1.00
#> TCGA.A4.8516.01     1   0.000      0.996 1.00 0.00
#> TCGA.A4.8312.01     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.5880.01     2   0.000      0.998 0.00 1.00
#> TCGA.Y8.A8RY.01     1   0.000      0.996 1.00 0.00
#> TCGA.SX.A7SN.01     1   0.000      0.996 1.00 0.00
#> TCGA.MH.A854.01     1   0.000      0.996 1.00 0.00
#> TCGA.A4.8517.01     1   0.000      0.996 1.00 0.00
#> TCGA.GL.A9DD.01     2   0.000      0.998 0.00 1.00
#> TCGA.A4.8630.01     1   0.000      0.996 1.00 0.00
#> TCGA.4A.A93W.01     1   0.000      0.996 1.00 0.00
#> TCGA.SX.A7SO.01     1   0.000      0.996 1.00 0.00
#> TCGA.GL.A9DC.01     1   0.000      0.996 1.00 0.00
#> TCGA.A4.8515.01     1   0.000      0.996 1.00 0.00
#> TCGA.IZ.A6M9.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.5880.11     2   0.000      0.998 0.00 1.00
#> TCGA.B1.A657.01     1   0.000      0.996 1.00 0.00
#> TCGA.G7.A8LD.01     2   0.881      0.568 0.30 0.70
#> TCGA.Y8.A8S1.01     2   0.000      0.998 0.00 1.00
#> TCGA.IA.A83S.01     2   0.000      0.998 0.00 1.00
#> TCGA.Y8.A8S0.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.5884.11     2   0.000      0.998 0.00 1.00
#> TCGA.B1.A655.01     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.5877.11     2   0.000      0.998 0.00 1.00
#> TCGA.EV.5903.01     2   0.000      0.998 0.00 1.00
#> TCGA.J7.8537.01     2   0.000      0.998 0.00 1.00
#> TCGA.A4.A6HP.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.5890.01     2   0.000      0.998 0.00 1.00
#> TCGA.Y8.A896.01     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.5888.01     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.5879.01     2   0.000      0.998 0.00 1.00
#> TCGA.GL.A9DE.01     2   0.000      0.998 0.00 1.00
#> TCGA.G7.A8LB.01     1   0.000      0.996 1.00 0.00
#> TCGA.IA.A83T.01     2   0.000      0.998 0.00 1.00
#> TCGA.IA.A83V.01     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.5876.11     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.5885.11     2   0.000      0.998 0.00 1.00
#> TCGA.KV.A6GD.01     2   0.000      0.998 0.00 1.00
#> TCGA.SX.A7SL.01     1   0.000      0.996 1.00 0.00
#> TCGA.B9.A8YI.01     2   0.000      0.998 0.00 1.00
#> TCGA.B9.A8YH.01     1   0.000      0.996 1.00 0.00
#> TCGA.4A.A93Y.01     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.5886.01     1   0.327      0.935 0.94 0.06
#> TCGA.A4.A5Y0.01     1   0.000      0.996 1.00 0.00
#> TCGA.A4.8098.01     1   0.000      0.996 1.00 0.00
#> TCGA.MH.A857.01     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.5889.11     2   0.000      0.998 0.00 1.00
#> TCGA.DW.5560.01     1   0.000      0.996 1.00 0.00
#> TCGA.F9.A8NY.01     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.5894.11     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.5891.11     2   0.000      0.998 0.00 1.00
#> TCGA.G7.A8LE.01     1   0.000      0.996 1.00 0.00
#> TCGA.SX.A71W.01     1   0.000      0.996 1.00 0.00
#> TCGA.Y8.A894.01     1   0.000      0.996 1.00 0.00
#> TCGA.WN.A9G9.01     2   0.000      0.998 0.00 1.00
#> TCGA.A4.8310.01     1   0.000      0.996 1.00 0.00
#> TCGA.A4.8518.01     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.5881.11     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.5893.11     2   0.000      0.998 0.00 1.00
#> TCGA.A4.8311.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.5891.01     2   0.000      0.998 0.00 1.00
#> TCGA.Y8.A895.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.5876.01     2   0.000      0.998 0.00 1.00
#> TCGA.MH.A855.01     2   0.000      0.998 0.00 1.00
#> TCGA.P4.AAVO.01     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.5886.11     2   0.000      0.998 0.00 1.00
#> TCGA.2Z.A9JS.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.5888.11     2   0.000      0.998 0.00 1.00
#> TCGA.2Z.A9J8.01     1   0.000      0.996 1.00 0.00
#> TCGA.KV.A74V.01     1   0.000      0.996 1.00 0.00
#> TCGA.A4.A5Y1.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.5875.01     2   0.000      0.998 0.00 1.00
#> TCGA.UZ.A9PZ.01     1   0.000      0.996 1.00 0.00
#> TCGA.Q2.A5QZ.01     2   0.000      0.998 0.00 1.00
#> TCGA.P4.A5E8.01     2   0.000      0.998 0.00 1.00
#> TCGA.B9.5155.01     1   0.000      0.996 1.00 0.00
#> TCGA.B9.A5W9.01     1   0.000      0.996 1.00 0.00
#> TCGA.5P.A9K4.01     1   0.000      0.996 1.00 0.00
#> TCGA.P4.A5E7.01     1   0.000      0.996 1.00 0.00
#> TCGA.PJ.A5Z9.01     1   0.000      0.996 1.00 0.00
#> TCGA.5P.A9K8.01     2   0.000      0.998 0.00 1.00
#> TCGA.5P.A9KF.01     1   0.000      0.996 1.00 0.00
#> TCGA.P4.AAVK.01     2   0.000      0.998 0.00 1.00
#> TCGA.2Z.A9JM.01     1   0.000      0.996 1.00 0.00
#> TCGA.A4.A48D.01     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.5889.01     2   0.000      0.998 0.00 1.00
#> TCGA.2Z.A9JD.01     1   0.000      0.996 1.00 0.00
#> TCGA.5P.A9K2.01     1   0.000      0.996 1.00 0.00
#> TCGA.2Z.A9JO.01     2   0.000      0.998 0.00 1.00
#> TCGA.5P.A9K9.01     2   0.000      0.998 0.00 1.00
#> TCGA.UZ.A9PV.01     1   0.000      0.996 1.00 0.00
#> TCGA.SX.A71V.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.5892.11     2   0.000      0.998 0.00 1.00
#> TCGA.UZ.A9Q0.01     1   0.000      0.996 1.00 0.00
#> TCGA.UZ.A9PX.01     1   0.000      0.996 1.00 0.00
#> TCGA.UZ.A9PR.01     1   0.000      0.996 1.00 0.00
#> TCGA.IA.A40X.01     1   0.000      0.996 1.00 0.00
#> TCGA.5P.A9JW.01     2   0.000      0.998 0.00 1.00
#> TCGA.IA.A40Y.01     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.5883.11     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.5878.11     2   0.000      0.998 0.00 1.00
#> TCGA.P4.A5EA.01     2   0.000      0.998 0.00 1.00
#> TCGA.5P.A9KE.01     2   0.000      0.998 0.00 1.00
#> TCGA.5P.A9K3.01     2   0.000      0.998 0.00 1.00
#> TCGA.B1.A47N.01     1   0.000      0.996 1.00 0.00
#> TCGA.5P.A9KA.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.5879.11     2   0.000      0.998 0.00 1.00
#> TCGA.P4.A5ED.01     2   0.000      0.998 0.00 1.00
#> TCGA.A4.A772.01     1   0.000      0.996 1.00 0.00
#> TCGA.B1.A47O.01     2   0.000      0.998 0.00 1.00
#> TCGA.IA.A40U.01     1   0.000      0.996 1.00 0.00
#> TCGA.2Z.A9JE.01     1   0.000      0.996 1.00 0.00
#> TCGA.B9.A44B.01     2   0.000      0.998 0.00 1.00
#> TCGA.AT.A5NU.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.5882.11     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.5877.01     2   0.000      0.998 0.00 1.00
#> TCGA.DW.7963.01     2   0.000      0.998 0.00 1.00
#> TCGA.2Z.A9JL.01     1   0.000      0.996 1.00 0.00
#> TCGA.2Z.A9JQ.01     1   0.000      0.996 1.00 0.00
#> TCGA.2Z.A9JK.01     2   0.000      0.998 0.00 1.00
#> TCGA.UZ.A9PU.01     1   0.000      0.996 1.00 0.00
#> TCGA.P4.A5EB.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.5892.01     2   0.000      0.998 0.00 1.00
#> TCGA.B1.A47M.11     2   0.000      0.998 0.00 1.00
#> TCGA.2Z.A9J9.01     2   0.000      0.998 0.00 1.00
#> TCGA.UZ.A9PS.05     2   0.000      0.998 0.00 1.00
#> TCGA.P4.AAVM.01     1   0.000      0.996 1.00 0.00
#> TCGA.PJ.A5Z8.01     2   0.000      0.998 0.00 1.00
#> TCGA.5P.A9JZ.01     1   0.000      0.996 1.00 0.00
#> TCGA.2Z.A9JG.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.5884.01     2   0.000      0.998 0.00 1.00
#> TCGA.2Z.A9JI.01     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.5890.11     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.5881.01     2   0.000      0.998 0.00 1.00
#> TCGA.UZ.A9PP.01     1   0.000      0.996 1.00 0.00
#> TCGA.5P.A9JU.01     2   0.000      0.998 0.00 1.00
#> TCGA.2Z.A9JN.01     2   0.000      0.998 0.00 1.00
#> TCGA.UZ.A9PS.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.5875.11     2   0.000      0.998 0.00 1.00
#> TCGA.5P.A9JY.01     1   0.000      0.996 1.00 0.00
#> TCGA.B9.A5W8.01     2   0.000      0.998 0.00 1.00
#> TCGA.F9.A4JJ.01     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.5883.01     2   0.000      0.998 0.00 1.00
#> TCGA.5P.A9K0.01     1   0.000      0.996 1.00 0.00
#> TCGA.P4.AAVL.01     1   0.000      0.996 1.00 0.00
#> TCGA.B1.5398.01     2   0.000      0.998 0.00 1.00
#> TCGA.5P.A9K6.01     1   0.000      0.996 1.00 0.00
#> TCGA.UZ.A9PQ.01     2   0.000      0.998 0.00 1.00
#> TCGA.P4.A5E6.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.5885.01     1   0.000      0.996 1.00 0.00
#> TCGA.UZ.A9Q1.01     2   0.000      0.998 0.00 1.00
#> TCGA.2Z.A9JP.01     1   0.000      0.996 1.00 0.00
#> TCGA.5P.A9KC.01     2   0.000      0.998 0.00 1.00
#> TCGA.5P.A9KH.01     2   0.000      0.998 0.00 1.00
#> TCGA.2Z.A9JR.01     1   0.000      0.996 1.00 0.00
#> TCGA.GL.A59T.01     1   0.000      0.996 1.00 0.00
#> TCGA.5P.A9JV.01     2   0.000      0.998 0.00 1.00
#> TCGA.WN.AB4C.01     2   0.000      0.998 0.00 1.00
#> TCGA.SX.A71R.01     1   0.000      0.996 1.00 0.00
#> TCGA.A4.A5DU.01     1   0.000      0.996 1.00 0.00
#> TCGA.B1.A47M.01     1   0.000      0.996 1.00 0.00
#> TCGA.2Z.A9JJ.01     2   0.000      0.998 0.00 1.00
#> TCGA.2Z.A9JT.01     2   0.242      0.957 0.04 0.96
#> TCGA.GL.A4EM.01     2   0.000      0.998 0.00 1.00
#> TCGA.HE.7129.01     1   0.000      0.996 1.00 0.00
#> TCGA.HE.7128.01     2   0.000      0.998 0.00 1.00
#> TCGA.HE.A5NL.01     1   0.000      0.996 1.00 0.00
#> TCGA.G7.7502.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.7059.01     2   0.000      0.998 0.00 1.00
#> TCGA.DZ.6134.11     2   0.000      0.998 0.00 1.00
#> TCGA.HE.A5NJ.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.7053.11     2   0.000      0.998 0.00 1.00
#> TCGA.GL.6846.11     2   0.000      0.998 0.00 1.00
#> TCGA.GL.6846.01     1   0.141      0.976 0.98 0.02
#> TCGA.DW.7839.01     1   0.000      0.996 1.00 0.00
#> TCGA.DW.7841.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.7049.01     2   0.000      0.998 0.00 1.00
#> TCGA.G7.6793.01     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.7051.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.7045.01     1   0.000      0.996 1.00 0.00
#> TCGA.HE.A5NF.01     2   0.000      0.998 0.00 1.00
#> TCGA.A4.7996.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.7046.01     1   0.000      0.996 1.00 0.00
#> TCGA.DZ.6132.11     2   0.000      0.998 0.00 1.00
#> TCGA.G7.7501.01     1   0.000      0.996 1.00 0.00
#> TCGA.O9.A75Z.01     1   0.000      0.996 1.00 0.00
#> TCGA.DW.7834.01     1   0.000      0.996 1.00 0.00
#> TCGA.DZ.6133.01     1   0.000      0.996 1.00 0.00
#> TCGA.A4.A4ZT.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.7060.01     1   0.242      0.956 0.96 0.04
#> TCGA.G7.6792.01     1   0.000      0.996 1.00 0.00
#> TCGA.HE.7130.01     2   0.000      0.998 0.00 1.00
#> TCGA.GL.7773.01     1   0.000      0.996 1.00 0.00
#> TCGA.DZ.6133.11     2   0.000      0.998 0.00 1.00
#> TCGA.B1.7332.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.7053.01     2   0.000      0.998 0.00 1.00
#> TCGA.DZ.6131.01     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.7062.01     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.7046.11     2   0.000      0.998 0.00 1.00
#> TCGA.A4.7288.01     1   0.000      0.996 1.00 0.00
#> TCGA.DZ.6131.11     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.7062.11     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.7061.01     2   0.000      0.998 0.00 1.00
#> TCGA.A4.7286.01     1   0.000      0.996 1.00 0.00
#> TCGA.G7.6797.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.7058.01     2   0.000      0.998 0.00 1.00
#> TCGA.G7.6795.01     1   0.000      0.996 1.00 0.00
#> TCGA.HE.A5NH.01     1   0.000      0.996 1.00 0.00
#> TCGA.MH.A55W.01     1   0.000      0.996 1.00 0.00
#> TCGA.G7.6790.01     1   0.000      0.996 1.00 0.00
#> TCGA.MH.A560.01     2   0.000      0.998 0.00 1.00
#> TCGA.A4.7997.01     1   0.000      0.996 1.00 0.00
#> TCGA.MH.A561.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.7056.11     2   0.000      0.998 0.00 1.00
#> TCGA.B9.7268.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.7055.11     2   0.000      0.998 0.00 1.00
#> TCGA.HE.A5NI.01     1   0.000      0.996 1.00 0.00
#> TCGA.GL.7966.01     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.7059.11     2   0.000      0.998 0.00 1.00
#> TCGA.A4.A57E.01     1   0.000      0.996 1.00 0.00
#> TCGA.A4.7288.11     2   0.000      0.998 0.00 1.00
#> TCGA.AL.A5DJ.01     2   0.000      0.998 0.00 1.00
#> TCGA.G7.6796.01     2   0.000      0.998 0.00 1.00
#> TCGA.DW.7837.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.7051.11     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.7048.01     2   0.000      0.998 0.00 1.00
#> TCGA.F9.A7VF.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.7049.11     2   0.000      0.998 0.00 1.00
#> TCGA.DZ.6134.01     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.5887.01     2   0.000      0.998 0.00 1.00
#> TCGA.DZ.6135.01     1   0.000      0.996 1.00 0.00
#> TCGA.MH.A55Z.01     1   0.000      0.996 1.00 0.00
#> TCGA.A4.7915.01     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.7048.11     2   0.000      0.998 0.00 1.00
#> TCGA.HE.A5NK.01     2   0.000      0.998 0.00 1.00
#> TCGA.G7.6789.01     2   0.000      0.998 0.00 1.00
#> TCGA.AL.7173.01     2   0.000      0.998 0.00 1.00
#> TCGA.SX.A71S.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.7061.11     2   0.000      0.998 0.00 1.00
#> TCGA.DW.7840.01     1   0.000      0.996 1.00 0.00
#> TCGA.GL.A59R.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.7050.11     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.7058.11     2   0.000      0.998 0.00 1.00
#> TCGA.DW.7838.01     2   0.000      0.998 0.00 1.00
#> TCGA.SX.A71U.01     1   0.000      0.996 1.00 0.00
#> TCGA.DZ.6135.11     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.7044.11     2   0.000      0.998 0.00 1.00
#> TCGA.V9.A7HT.01     2   0.000      0.998 0.00 1.00
#> TCGA.DW.7842.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.7050.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.7055.01     2   0.000      0.998 0.00 1.00
#> TCGA.J7.6720.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.7060.11     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.7044.01     1   0.000      0.996 1.00 0.00
#> TCGA.DZ.6132.01     2   0.000      0.998 0.00 1.00
#> TCGA.DW.7836.01     1   0.000      0.996 1.00 0.00
#> TCGA.A4.7828.01     2   0.000      0.998 0.00 1.00
#> TCGA.BQ.5887.11     2   0.000      0.998 0.00 1.00
#> TCGA.B3.A6W5.01     1   0.000      0.996 1.00 0.00
#> TCGA.MH.A562.01     1   0.000      0.996 1.00 0.00
#> TCGA.A4.7734.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.7045.11     2   0.000      0.998 0.00 1.00
#> TCGA.A4.7584.01     1   0.000      0.996 1.00 0.00
#> TCGA.BQ.7056.01     1   0.000      0.996 1.00 0.00
#> TCGA.A4.7287.01     2   0.000      0.998 0.00 1.00
#> TCGA.UZ.A9PJ.01     1   0.000      0.996 1.00 0.00
#> TCGA.2Z.A9J1.01     1   0.000      0.996 1.00 0.00
#> TCGA.UN.AAZ9.01     1   0.000      0.996 1.00 0.00
#> TCGA.UZ.A9PO.01     2   0.000      0.998 0.00 1.00
#> TCGA.UZ.A9PL.01     1   0.000      0.996 1.00 0.00
#> TCGA.A4.7732.11     2   0.000      0.998 0.00 1.00
#> TCGA.A4.7732.01     1   0.000      0.996 1.00 0.00
#> TCGA.2Z.A9J2.01     2   0.000      0.998 0.00 1.00
#> TCGA.2Z.A9J3.01     1   0.000      0.996 1.00 0.00
#> TCGA.2Z.A9J6.01     1   0.000      0.996 1.00 0.00
#> TCGA.F9.A97G.01     2   0.000      0.998 0.00 1.00
#> TCGA.UZ.A9PM.01     2   0.000      0.998 0.00 1.00
#> TCGA.A4.7585.11     2   0.000      0.998 0.00 1.00
#> TCGA.2K.A9WE.01     2   0.000      0.998 0.00 1.00
#> TCGA.A4.7583.01     1   0.000      0.996 1.00 0.00
#> TCGA.UZ.A9PK.01     1   0.000      0.996 1.00 0.00
#> TCGA.UZ.A9PN.01     2   0.000      0.998 0.00 1.00
#> TCGA.2Z.A9J7.01     1   0.000      0.996 1.00 0.00
#> TCGA.2Z.A9J5.01     1   0.000      0.996 1.00 0.00
#> TCGA.A4.7585.01     2   0.000      0.998 0.00 1.00

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

consensus_heatmap(res, k = 2)

plot of chunk tab-node-0-consensus-heatmap-1

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

membership_heatmap(res, k = 2)

plot of chunk tab-node-0-membership-heatmap-1

As soon as the classes for columns are determined, the signatures that are significantly different between subgroups can be looked for. Following are the heatmaps for signatures.

get_signatures(res, k = 2)

plot of chunk tab-node-0-get-signatures-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk node-0-signature_compare

get_signature() returns a data frame invisibly. To get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

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

An example of the output of tb is:

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

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows (which is done by automatically selecting number of clusters).

If there are too many signatures, top_signatures = ... can be set to only show the signatures with the highest FDRs:

# code only for demonstration
# e.g. to show the top 500 most significant rows
tb = get_signature(res, k = ..., top_signatures = 500)

If the signatures are defined as these which are uniquely high in current group, diff_method argument can be set to "uniquely_high_in_one_group":

# code only for demonstration
tb = get_signature(res, k = ..., diff_method = "uniquely_high_in_one_group")

UMAP plot which shows how samples are separated.

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

plot of chunk tab-node-0-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk node-0-collect-classes

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

Node01

Parent node: Node0. Child nodes: Node011-leaf , Node012 , Node013 , Node021-leaf , Node022 , Node023-leaf , Node031 , Node032 , Node033-leaf , Node041-leaf , Node042-leaf , Node043 , Node044-leaf , Node051 , Node052 , Node053 , Node054-leaf .

The object with results only for a single top-value method and a single partitioning method can be extracted as:

res = res_rh["01"]

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, 7, 8.
#>   On a matrix with 30000 rows and 79 columns.
#>   Top rows (1000) are extracted by 'SD' method.
#>   Subgroups are detected by 'skmeans' method.
#>   Performed in total 350 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_partitions"     
#>  [7] "compare_signatures"      "consensus_heatmap"       "dimension_reduction"    
#> [10] "functional_enrichment"   "get_anno_col"            "get_anno"               
#> [13] "get_classes"             "get_consensus"           "get_matrix"             
#> [16] "get_membership"          "get_param"               "get_signatures"         
#> [19] "get_stats"               "is_best_k"               "is_stable_k"            
#> [22] "membership_heatmap"      "ncol"                    "nrow"                   
#> [25] "plot_ecdf"               "predict_classes"         "rownames"               
#> [28] "select_partition_number" "show"                    "suggest_best_k"         
#> [31] "test_to_known_factors"   "top_rows_heatmap"

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

collect_plots(res)

plot of chunk node-01-collect-plots

The plots are:

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:

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

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

select_partition_number(res)

plot of chunk node-01-select-partition-number

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.968       0.987         0.5015 0.498   0.498
#> 3 3 1.000           0.961       0.981         0.3149 0.763   0.559
#> 4 4 0.619           0.653       0.807         0.1153 0.919   0.768
#> 5 5 0.572           0.389       0.638         0.0609 0.890   0.640
#> 6 6 0.573           0.446       0.665         0.0376 0.902   0.630
#> 7 7 0.550           0.387       0.614         0.0252 0.931   0.717
#> 8 8 0.571           0.248       0.583         0.0180 0.935   0.714

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

suggest_best_k(res)

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

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

Following is 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 subgroup 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.

show/hide code output

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

#>                 class entropy silhouette   p1   p2
#> TCGA.SX.A7SS.01     1   0.000      0.978 1.00 0.00
#> TCGA.BQ.5878.01     1   0.000      0.978 1.00 0.00
#> TCGA.DW.5561.01     2   0.000      0.994 0.00 1.00
#> TCGA.KV.A6GE.01     1   0.000      0.978 1.00 0.00
#> TCGA.SX.A7SQ.01     2   0.000      0.994 0.00 1.00
#> TCGA.B1.A654.01     2   0.000      0.994 0.00 1.00
#> TCGA.G7.A4TM.01     2   0.000      0.994 0.00 1.00
#> TCGA.IZ.8196.01     2   0.000      0.994 0.00 1.00
#> TCGA.B9.A5W7.01     2   0.000      0.994 0.00 1.00
#> TCGA.SX.A7SU.01     2   0.000      0.994 0.00 1.00
#> TCGA.GL.8500.01     2   0.000      0.994 0.00 1.00
#> TCGA.EV.5902.01     1   0.855      0.613 0.72 0.28
#> TCGA.A4.8516.01     2   0.000      0.994 0.00 1.00
#> TCGA.MH.A854.01     2   0.000      0.994 0.00 1.00
#> TCGA.A4.8630.01     1   0.000      0.978 1.00 0.00
#> TCGA.4A.A93W.01     2   0.000      0.994 0.00 1.00
#> TCGA.GL.A9DC.01     2   0.000      0.994 0.00 1.00
#> TCGA.A4.8515.01     1   0.000      0.978 1.00 0.00
#> TCGA.IZ.A6M9.01     1   0.000      0.978 1.00 0.00
#> TCGA.Y8.A8S0.01     1   0.000      0.978 1.00 0.00
#> TCGA.G7.A8LB.01     1   0.000      0.978 1.00 0.00
#> TCGA.SX.A7SL.01     1   0.000      0.978 1.00 0.00
#> TCGA.B9.A8YH.01     2   0.000      0.994 0.00 1.00
#> TCGA.G7.A8LE.01     2   0.000      0.994 0.00 1.00
#> TCGA.SX.A71W.01     1   0.000      0.978 1.00 0.00
#> TCGA.Y8.A894.01     2   0.000      0.994 0.00 1.00
#> TCGA.A4.8311.01     1   0.000      0.978 1.00 0.00
#> TCGA.Y8.A895.01     1   0.000      0.978 1.00 0.00
#> TCGA.2Z.A9JS.01     1   0.000      0.978 1.00 0.00
#> TCGA.KV.A74V.01     1   0.000      0.978 1.00 0.00
#> TCGA.UZ.A9PZ.01     2   0.000      0.994 0.00 1.00
#> TCGA.B9.5155.01     1   0.000      0.978 1.00 0.00
#> TCGA.5P.A9K4.01     1   0.000      0.978 1.00 0.00
#> TCGA.PJ.A5Z9.01     1   0.000      0.978 1.00 0.00
#> TCGA.5P.A9KF.01     1   0.141      0.960 0.98 0.02
#> TCGA.5P.A9K2.01     1   0.000      0.978 1.00 0.00
#> TCGA.UZ.A9PV.01     1   0.000      0.978 1.00 0.00
#> TCGA.UZ.A9Q0.01     1   0.000      0.978 1.00 0.00
#> TCGA.UZ.A9PX.01     2   0.000      0.994 0.00 1.00
#> TCGA.UZ.A9PR.01     2   0.000      0.994 0.00 1.00
#> TCGA.B1.A47N.01     2   0.000      0.994 0.00 1.00
#> TCGA.2Z.A9JE.01     2   0.000      0.994 0.00 1.00
#> TCGA.AT.A5NU.01     1   0.000      0.978 1.00 0.00
#> TCGA.2Z.A9JQ.01     2   0.000      0.994 0.00 1.00
#> TCGA.UZ.A9PU.01     1   0.995      0.160 0.54 0.46
#> TCGA.P4.A5EB.01     1   0.000      0.978 1.00 0.00
#> TCGA.UZ.A9PP.01     2   0.000      0.994 0.00 1.00
#> TCGA.5P.A9JY.01     1   0.000      0.978 1.00 0.00
#> TCGA.P4.AAVL.01     2   0.000      0.994 0.00 1.00
#> TCGA.SX.A71R.01     2   0.000      0.994 0.00 1.00
#> TCGA.A4.A5DU.01     2   0.000      0.994 0.00 1.00
#> TCGA.HE.7129.01     1   0.000      0.978 1.00 0.00
#> TCGA.HE.A5NJ.01     1   0.000      0.978 1.00 0.00
#> TCGA.DW.7839.01     2   0.000      0.994 0.00 1.00
#> TCGA.BQ.7051.01     1   0.000      0.978 1.00 0.00
#> TCGA.O9.A75Z.01     2   0.000      0.994 0.00 1.00
#> TCGA.DZ.6133.01     2   0.000      0.994 0.00 1.00
#> TCGA.A4.A4ZT.01     1   0.000      0.978 1.00 0.00
#> TCGA.B1.7332.01     1   0.000      0.978 1.00 0.00
#> TCGA.G7.6797.01     1   0.000      0.978 1.00 0.00
#> TCGA.HE.A5NH.01     2   0.000      0.994 0.00 1.00
#> TCGA.B9.7268.01     1   0.000      0.978 1.00 0.00
#> TCGA.HE.A5NI.01     1   0.000      0.978 1.00 0.00
#> TCGA.F9.A7VF.01     1   0.000      0.978 1.00 0.00
#> TCGA.DZ.6135.01     2   0.000      0.994 0.00 1.00
#> TCGA.MH.A55Z.01     2   0.000      0.994 0.00 1.00
#> TCGA.SX.A71S.01     2   0.000      0.994 0.00 1.00
#> TCGA.DW.7840.01     2   0.000      0.994 0.00 1.00
#> TCGA.GL.A59R.01     2   0.000      0.994 0.00 1.00
#> TCGA.DW.7842.01     2   0.000      0.994 0.00 1.00
#> TCGA.DW.7836.01     2   0.000      0.994 0.00 1.00
#> TCGA.B3.A6W5.01     2   0.680      0.778 0.18 0.82
#> TCGA.A4.7734.01     2   0.000      0.994 0.00 1.00
#> TCGA.UZ.A9PJ.01     2   0.000      0.994 0.00 1.00
#> TCGA.UZ.A9PL.01     2   0.000      0.994 0.00 1.00
#> TCGA.A4.7732.01     2   0.000      0.994 0.00 1.00
#> TCGA.2Z.A9J3.01     2   0.000      0.994 0.00 1.00
#> TCGA.UZ.A9PK.01     1   0.000      0.978 1.00 0.00
#> TCGA.2Z.A9J7.01     2   0.327      0.933 0.06 0.94

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

consensus_heatmap(res, k = 2)

plot of chunk tab-node-01-consensus-heatmap-1

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

membership_heatmap(res, k = 2)

plot of chunk tab-node-01-membership-heatmap-1

As soon as the classes for columns are determined, the signatures that are significantly different between subgroups can be looked for. Following are the heatmaps for signatures.

get_signatures(res, k = 2)

plot of chunk tab-node-01-get-signatures-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk node-01-signature_compare

get_signature() returns a data frame invisibly. To get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

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

An example of the output of tb is:

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

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows (which is done by automatically selecting number of clusters).

If there are too many signatures, top_signatures = ... can be set to only show the signatures with the highest FDRs:

# code only for demonstration
# e.g. to show the top 500 most significant rows
tb = get_signature(res, k = ..., top_signatures = 500)

If the signatures are defined as these which are uniquely high in current group, diff_method argument can be set to "uniquely_high_in_one_group":

# code only for demonstration
tb = get_signature(res, k = ..., diff_method = "uniquely_high_in_one_group")

UMAP plot which shows how samples are separated.

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

plot of chunk tab-node-01-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk node-01-collect-classes

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

Node012

Parent node: Node01. Child nodes: Node0121-leaf , Node0122-leaf , Node0123-leaf , Node0124-leaf , Node0131 , Node0132-leaf , Node0221-leaf , Node0222-leaf , Node0223-leaf , Node0311 , Node0312-leaf , Node0313-leaf , Node0321-leaf , Node0322-leaf , Node0431-leaf , Node0432-leaf , Node0433-leaf , Node0511-leaf , Node0512-leaf , Node0513-leaf , Node0521-leaf , Node0522-leaf , Node0523-leaf , Node0531-leaf , Node0532-leaf , Node0533-leaf .

The object with results only for a single top-value method and a single partitioning method can be extracted as:

res = res_rh["012"]

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, 7, 8.
#>   On a matrix with 30000 rows and 27 columns.
#>   Top rows (1000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'kmeans' method.
#>   Performed in total 350 partitions by row resampling.
#>   Best k for subgroups seems to be 8.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_partitions"     
#>  [7] "compare_signatures"      "consensus_heatmap"       "dimension_reduction"    
#> [10] "functional_enrichment"   "get_anno_col"            "get_anno"               
#> [13] "get_classes"             "get_consensus"           "get_matrix"             
#> [16] "get_membership"          "get_param"               "get_signatures"         
#> [19] "get_stats"               "is_best_k"               "is_stable_k"            
#> [22] "membership_heatmap"      "ncol"                    "nrow"                   
#> [25] "plot_ecdf"               "predict_classes"         "rownames"               
#> [28] "select_partition_number" "show"                    "suggest_best_k"         
#> [31] "test_to_known_factors"   "top_rows_heatmap"

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

collect_plots(res)

plot of chunk node-012-collect-plots

The plots are:

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:

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

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

select_partition_number(res)

plot of chunk node-012-select-partition-number

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           1.000       1.000         0.2628 0.738   0.738
#> 3 3 0.628           0.775       0.893         1.1566 0.658   0.537
#> 4 4 0.687           0.966       0.919         0.2511 0.772   0.481
#> 5 5 0.812           0.865       0.813         0.0684 1.000   1.000
#> 6 6 0.893           0.841       0.901         0.0628 0.957   0.831
#> 7 7 0.930           0.813       0.880         0.0233 0.966   0.842
#> 8 8 0.923           0.774       0.881         0.0177 0.966   0.818

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

suggest_best_k(res)

#> [1] 8
#> attr(,"optional")
#> [1] 2 7

There is also optional best \(k\) = 2 7 that is worth to check.

Following is 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 subgroup 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.

show/hide code output

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

#>                 class entropy silhouette p1 p2
#> TCGA.IZ.8196.01     2       0          1  0  1
#> TCGA.GL.8500.01     2       0          1  0  1
#> TCGA.EV.5902.01     2       0          1  0  1
#> TCGA.A4.8516.01     2       0          1  0  1
#> TCGA.MH.A854.01     1       0          1  1  0
#> TCGA.GL.A9DC.01     1       0          1  1  0
#> TCGA.B9.A8YH.01     2       0          1  0  1
#> TCGA.Y8.A894.01     1       0          1  1  0
#> TCGA.UZ.A9PZ.01     2       0          1  0  1
#> TCGA.5P.A9KF.01     2       0          1  0  1
#> TCGA.UZ.A9PX.01     2       0          1  0  1
#> TCGA.UZ.A9PR.01     2       0          1  0  1
#> TCGA.2Z.A9JE.01     2       0          1  0  1
#> TCGA.2Z.A9JQ.01     2       0          1  0  1
#> TCGA.UZ.A9PU.01     2       0          1  0  1
#> TCGA.P4.A5EB.01     2       0          1  0  1
#> TCGA.P4.AAVL.01     2       0          1  0  1
#> TCGA.SX.A71R.01     2       0          1  0  1
#> TCGA.DZ.6133.01     2       0          1  0  1
#> TCGA.HE.A5NH.01     2       0          1  0  1
#> TCGA.DZ.6135.01     2       0          1  0  1
#> TCGA.MH.A55Z.01     2       0          1  0  1
#> TCGA.SX.A71S.01     1       0          1  1  0
#> TCGA.DW.7840.01     2       0          1  0  1
#> TCGA.GL.A59R.01     2       0          1  0  1
#> TCGA.UZ.A9PL.01     2       0          1  0  1
#> TCGA.2Z.A9J3.01     2       0          1  0  1

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

consensus_heatmap(res, k = 2)

plot of chunk tab-node-012-consensus-heatmap-1

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

membership_heatmap(res, k = 2)

plot of chunk tab-node-012-membership-heatmap-1

As soon as the classes for columns are determined, the signatures that are significantly different between subgroups can be looked for. Following are the heatmaps for signatures.

get_signatures(res, k = 2)

plot of chunk tab-node-012-get-signatures-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk node-012-signature_compare

get_signature() returns a data frame invisibly. To get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

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

An example of the output of tb is:

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

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows (which is done by automatically selecting number of clusters).

If there are too many signatures, top_signatures = ... can be set to only show the signatures with the highest FDRs:

# code only for demonstration
# e.g. to show the top 500 most significant rows
tb = get_signature(res, k = ..., top_signatures = 500)

If the signatures are defined as these which are uniquely high in current group, diff_method argument can be set to "uniquely_high_in_one_group":

# code only for demonstration
tb = get_signature(res, k = ..., diff_method = "uniquely_high_in_one_group")

UMAP plot which shows how samples are separated.

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

plot of chunk tab-node-012-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk node-012-collect-classes

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

Node013

Parent node: Node01. Child nodes: Node0121-leaf , Node0122-leaf , Node0123-leaf , Node0124-leaf , Node0131 , Node0132-leaf , Node0221-leaf , Node0222-leaf , Node0223-leaf , Node0311 , Node0312-leaf , Node0313-leaf , Node0321-leaf , Node0322-leaf , Node0431-leaf , Node0432-leaf , Node0433-leaf , Node0511-leaf , Node0512-leaf , Node0513-leaf , Node0521-leaf , Node0522-leaf , Node0523-leaf , Node0531-leaf , Node0532-leaf , Node0533-leaf .

The object with results only for a single top-value method and a single partitioning method can be extracted as:

res = res_rh["013"]

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, 7, 8.
#>   On a matrix with 30000 rows and 19 columns.
#>   Top rows (1000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'kmeans' method.
#>   Performed in total 350 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_partitions"     
#>  [7] "compare_signatures"      "consensus_heatmap"       "dimension_reduction"    
#> [10] "functional_enrichment"   "get_anno_col"            "get_anno"               
#> [13] "get_classes"             "get_consensus"           "get_matrix"             
#> [16] "get_membership"          "get_param"               "get_signatures"         
#> [19] "get_stats"               "is_best_k"               "is_stable_k"            
#> [22] "membership_heatmap"      "ncol"                    "nrow"                   
#> [25] "plot_ecdf"               "predict_classes"         "rownames"               
#> [28] "select_partition_number" "show"                    "suggest_best_k"         
#> [31] "test_to_known_factors"   "top_rows_heatmap"

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

collect_plots(res)

plot of chunk node-013-collect-plots

The plots are:

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:

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

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

select_partition_number(res)

plot of chunk node-013-select-partition-number

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           1.000       1.000         0.4099 0.591   0.591
#> 3 3 0.731           0.971       0.924         0.4540 0.766   0.604
#> 4 4 0.789           0.695       0.766         0.2035 0.977   0.934
#> 5 5 0.789           0.801       0.818         0.0758 0.836   0.525
#> 6 6 0.731           0.804       0.832         0.0532 0.965   0.818
#> 7 7 0.778           0.455       0.699         0.0468 0.906   0.543
#> 8 8 0.842           0.778       0.876         0.0303 0.930   0.586

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

suggest_best_k(res)

#> [1] 2

Following is 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 subgroup 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.

show/hide code output

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

#>                 class entropy silhouette p1 p2
#> TCGA.DW.5561.01     1       0          1  1  0
#> TCGA.SX.A7SQ.01     1       0          1  1  0
#> TCGA.B1.A654.01     2       0          1  0  1
#> TCGA.G7.A4TM.01     1       0          1  1  0
#> TCGA.B9.A5W7.01     1       0          1  1  0
#> TCGA.SX.A7SU.01     1       0          1  1  0
#> TCGA.4A.A93W.01     2       0          1  0  1
#> TCGA.G7.A8LE.01     1       0          1  1  0
#> TCGA.B1.A47N.01     1       0          1  1  0
#> TCGA.UZ.A9PP.01     1       0          1  1  0
#> TCGA.A4.A5DU.01     2       0          1  0  1
#> TCGA.DW.7839.01     2       0          1  0  1
#> TCGA.O9.A75Z.01     1       0          1  1  0
#> TCGA.DW.7842.01     1       0          1  1  0
#> TCGA.DW.7836.01     1       0          1  1  0
#> TCGA.A4.7734.01     2       0          1  0  1
#> TCGA.UZ.A9PJ.01     1       0          1  1  0
#> TCGA.A4.7732.01     1       0          1  1  0
#> TCGA.2Z.A9J7.01     1       0          1  1  0

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

consensus_heatmap(res, k = 2)

plot of chunk tab-node-013-consensus-heatmap-1

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

membership_heatmap(res, k = 2)

plot of chunk tab-node-013-membership-heatmap-1

As soon as the classes for columns are determined, the signatures that are significantly different between subgroups can be looked for. Following are the heatmaps for signatures.

get_signatures(res, k = 2)

plot of chunk tab-node-013-get-signatures-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk node-013-signature_compare

get_signature() returns a data frame invisibly. To get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

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

An example of the output of tb is:

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

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows (which is done by automatically selecting number of clusters).

If there are too many signatures, top_signatures = ... can be set to only show the signatures with the highest FDRs:

# code only for demonstration
# e.g. to show the top 500 most significant rows
tb = get_signature(res, k = ..., top_signatures = 500)

If the signatures are defined as these which are uniquely high in current group, diff_method argument can be set to "uniquely_high_in_one_group":

# code only for demonstration
tb = get_signature(res, k = ..., diff_method = "uniquely_high_in_one_group")

UMAP plot which shows how samples are separated.

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

plot of chunk tab-node-013-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk node-013-collect-classes

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

Node0131

Parent node: Node013. Child nodes: Node01311-leaf , Node01312-leaf , Node03111-leaf , Node03112-leaf , Node03113-leaf .

The object with results only for a single top-value method and a single partitioning method can be extracted as:

res = res_rh["0131"]

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, 7, 8.
#>   On a matrix with 30000 rows and 14 columns.
#>   Top rows (1000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'kmeans' method.
#>   Performed in total 350 partitions by row resampling.
#>   Best k for subgroups seems to be 8.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_partitions"     
#>  [7] "compare_signatures"      "consensus_heatmap"       "dimension_reduction"    
#> [10] "functional_enrichment"   "get_anno_col"            "get_anno"               
#> [13] "get_classes"             "get_consensus"           "get_matrix"             
#> [16] "get_membership"          "get_param"               "get_signatures"         
#> [19] "get_stats"               "is_best_k"               "is_stable_k"            
#> [22] "membership_heatmap"      "ncol"                    "nrow"                   
#> [25] "plot_ecdf"               "predict_classes"         "rownames"               
#> [28] "select_partition_number" "show"                    "suggest_best_k"         
#> [31] "test_to_known_factors"   "top_rows_heatmap"

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

collect_plots(res)

plot of chunk node-0131-collect-plots

The plots are:

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:

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

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

select_partition_number(res)

plot of chunk node-0131-select-partition-number

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           1.000       1.000         0.2645 0.736   0.736
#> 3 3 0.923           0.867       0.959         0.5273 0.857   0.809
#> 4 4 0.615           0.796       0.924         0.5457 0.593   0.403
#> 5 5 0.692           0.756       0.971         0.1411 0.934   0.806
#> 6 6 1.000           0.705       0.991         0.0926 0.945   0.800
#> 7 7 0.912           0.626       0.983         0.0590 0.956   0.800
#> 8 8 1.000           0.553       0.980         0.0514 0.956   0.750

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

suggest_best_k(res)

#> [1] 8
#> attr(,"optional")
#> [1] 2 3 6 7

There is also optional best \(k\) = 2 3 6 7 that is worth to check.

Following is 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 subgroup 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.

show/hide code output

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

#>                 class entropy silhouette p1 p2
#> TCGA.DW.5561.01     2       0          1  0  1
#> TCGA.SX.A7SQ.01     1       0          1  1  0
#> TCGA.G7.A4TM.01     1       0          1  1  0
#> TCGA.B9.A5W7.01     1       0          1  1  0
#> TCGA.SX.A7SU.01     1       0          1  1  0
#> TCGA.G7.A8LE.01     1       0          1  1  0
#> TCGA.B1.A47N.01     1       0          1  1  0
#> TCGA.UZ.A9PP.01     1       0          1  1  0
#> TCGA.O9.A75Z.01     1       0          1  1  0
#> TCGA.DW.7842.01     1       0          1  1  0
#> TCGA.DW.7836.01     1       0          1  1  0
#> TCGA.UZ.A9PJ.01     1       0          1  1  0
#> TCGA.A4.7732.01     1       0          1  1  0
#> TCGA.2Z.A9J7.01     2       0          1  0  1

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

consensus_heatmap(res, k = 2)

plot of chunk tab-node-0131-consensus-heatmap-1

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

membership_heatmap(res, k = 2)

plot of chunk tab-node-0131-membership-heatmap-1

As soon as the classes for columns are determined, the signatures that are significantly different between subgroups can be looked for. Following are the heatmaps for signatures.

get_signatures(res, k = 2)

plot of chunk tab-node-0131-get-signatures-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk node-0131-signature_compare

get_signature() returns a data frame invisibly. To get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

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

An example of the output of tb is:

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

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows (which is done by automatically selecting number of clusters).

If there are too many signatures, top_signatures = ... can be set to only show the signatures with the highest FDRs:

# code only for demonstration
# e.g. to show the top 500 most significant rows
tb = get_signature(res, k = ..., top_signatures = 500)

If the signatures are defined as these which are uniquely high in current group, diff_method argument can be set to "uniquely_high_in_one_group":

# code only for demonstration
tb = get_signature(res, k = ..., diff_method = "uniquely_high_in_one_group")

UMAP plot which shows how samples are separated.

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

plot of chunk tab-node-0131-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk node-0131-collect-classes

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

Node02

Parent node: Node0. Child nodes: Node011-leaf , Node012 , Node013 , Node021-leaf , Node022 , Node023-leaf , Node031 , Node032 , Node033-leaf , Node041-leaf , Node042-leaf , Node043 , Node044-leaf , Node051 , Node052 , Node053 , Node054-leaf .

The object with results only for a single top-value method and a single partitioning method can be extracted as:

res = res_rh["02"]

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, 7, 8.
#>   On a matrix with 30000 rows and 56 columns.
#>   Top rows (1000) are extracted by 'SD' method.
#>   Subgroups are detected by 'skmeans' method.
#>   Performed in total 350 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_partitions"     
#>  [7] "compare_signatures"      "consensus_heatmap"       "dimension_reduction"    
#> [10] "functional_enrichment"   "get_anno_col"            "get_anno"               
#> [13] "get_classes"             "get_consensus"           "get_matrix"             
#> [16] "get_membership"          "get_param"               "get_signatures"         
#> [19] "get_stats"               "is_best_k"               "is_stable_k"            
#> [22] "membership_heatmap"      "ncol"                    "nrow"                   
#> [25] "plot_ecdf"               "predict_classes"         "rownames"               
#> [28] "select_partition_number" "show"                    "suggest_best_k"         
#> [31] "test_to_known_factors"   "top_rows_heatmap"

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

collect_plots(res)

plot of chunk node-02-collect-plots

The plots are:

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:

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

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

select_partition_number(res)

plot of chunk node-02-select-partition-number

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           1.000       1.000        0.43109 0.569   0.569
#> 3 3 1.000           0.970       0.990        0.36191 0.839   0.717
#> 4 4 0.856           0.723       0.872        0.08140 0.968   0.921
#> 5 5 0.790           0.829       0.898        0.05735 0.919   0.795
#> 6 6 0.689           0.831       0.890        0.04112 0.977   0.930
#> 7 7 0.636           0.769       0.846        0.06272 0.997   0.991
#> 8 8 0.635           0.779       0.854        0.00397 0.997   0.991

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

suggest_best_k(res)

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

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

Following is 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 subgroup 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.

show/hide code output

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

#>                 class entropy silhouette p1 p2
#> TCGA.A4.8312.01     1       0          1  1  0
#> TCGA.BQ.5880.11     1       0          1  1  0
#> TCGA.BQ.5884.11     2       0          1  0  1
#> TCGA.BQ.5877.11     1       0          1  1  0
#> TCGA.BQ.5876.11     1       0          1  1  0
#> TCGA.BQ.5885.11     1       0          1  1  0
#> TCGA.MH.A857.01     1       0          1  1  0
#> TCGA.BQ.5889.11     1       0          1  1  0
#> TCGA.BQ.5894.11     1       0          1  1  0
#> TCGA.BQ.5891.11     2       0          1  0  1
#> TCGA.BQ.5881.11     1       0          1  1  0
#> TCGA.BQ.5893.11     1       0          1  1  0
#> TCGA.BQ.5886.11     1       0          1  1  0
#> TCGA.BQ.5888.11     2       0          1  0  1
#> TCGA.5P.A9K8.01     2       0          1  0  1
#> TCGA.BQ.5892.11     1       0          1  1  0
#> TCGA.BQ.5883.11     2       0          1  0  1
#> TCGA.BQ.5878.11     2       0          1  0  1
#> TCGA.BQ.5879.11     2       0          1  0  1
#> TCGA.P4.A5ED.01     1       0          1  1  0
#> TCGA.BQ.5882.11     1       0          1  1  0
#> TCGA.B1.A47M.11     1       0          1  1  0
#> TCGA.2Z.A9J9.01     1       0          1  1  0
#> TCGA.BQ.5890.11     1       0          1  1  0
#> TCGA.2Z.A9JN.01     2       0          1  0  1
#> TCGA.BQ.5875.11     2       0          1  0  1
#> TCGA.BQ.5883.01     2       0          1  0  1
#> TCGA.5P.A9KH.01     1       0          1  1  0
#> TCGA.5P.A9JV.01     1       0          1  1  0
#> TCGA.DZ.6134.11     1       0          1  1  0
#> TCGA.BQ.7053.11     2       0          1  0  1
#> TCGA.GL.6846.11     1       0          1  1  0
#> TCGA.DZ.6132.11     1       0          1  1  0
#> TCGA.DZ.6133.11     2       0          1  0  1
#> TCGA.BQ.7046.11     1       0          1  1  0
#> TCGA.DZ.6131.11     1       0          1  1  0
#> TCGA.BQ.7062.11     1       0          1  1  0
#> TCGA.BQ.7056.11     2       0          1  0  1
#> TCGA.BQ.7055.11     1       0          1  1  0
#> TCGA.BQ.7059.11     1       0          1  1  0
#> TCGA.A4.7288.11     2       0          1  0  1
#> TCGA.BQ.7051.11     1       0          1  1  0
#> TCGA.BQ.7049.11     1       0          1  1  0
#> TCGA.BQ.7048.11     1       0          1  1  0
#> TCGA.BQ.7061.11     2       0          1  0  1
#> TCGA.BQ.7050.11     2       0          1  0  1
#> TCGA.BQ.7058.11     1       0          1  1  0
#> TCGA.DZ.6135.11     1       0          1  1  0
#> TCGA.BQ.7044.11     1       0          1  1  0
#> TCGA.BQ.7055.01     1       0          1  1  0
#> TCGA.BQ.7060.11     1       0          1  1  0
#> TCGA.A4.7828.01     2       0          1  0  1
#> TCGA.BQ.5887.11     1       0          1  1  0
#> TCGA.BQ.7045.11     1       0          1  1  0
#> TCGA.A4.7732.11     1       0          1  1  0
#> TCGA.A4.7585.11     1       0          1  1  0

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

consensus_heatmap(res, k = 2)

plot of chunk tab-node-02-consensus-heatmap-1

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

membership_heatmap(res, k = 2)

plot of chunk tab-node-02-membership-heatmap-1

As soon as the classes for columns are determined, the signatures that are significantly different between subgroups can be looked for. Following are the heatmaps for signatures.

get_signatures(res, k = 2)

plot of chunk tab-node-02-get-signatures-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk node-02-signature_compare

get_signature() returns a data frame invisibly. To get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

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

An example of the output of tb is:

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

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows (which is done by automatically selecting number of clusters).

If there are too many signatures, top_signatures = ... can be set to only show the signatures with the highest FDRs:

# code only for demonstration
# e.g. to show the top 500 most significant rows
tb = get_signature(res, k = ..., top_signatures = 500)

If the signatures are defined as these which are uniquely high in current group, diff_method argument can be set to "uniquely_high_in_one_group":

# code only for demonstration
tb = get_signature(res, k = ..., diff_method = "uniquely_high_in_one_group")

UMAP plot which shows how samples are separated.

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

plot of chunk tab-node-02-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk node-02-collect-classes

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

Node022

Parent node: Node02. Child nodes: Node0121-leaf , Node0122-leaf , Node0123-leaf , Node0124-leaf , Node0131 , Node0132-leaf , Node0221-leaf , Node0222-leaf , Node0223-leaf , Node0311 , Node0312-leaf , Node0313-leaf , Node0321-leaf , Node0322-leaf , Node0431-leaf , Node0432-leaf , Node0433-leaf , Node0511-leaf , Node0512-leaf , Node0513-leaf , Node0521-leaf , Node0522-leaf , Node0523-leaf , Node0531-leaf , Node0532-leaf , Node0533-leaf .

The object with results only for a single top-value method and a single partitioning method can be extracted as:

res = res_rh["022"]

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, 7, 8.
#>   On a matrix with 30000 rows and 17 columns.
#>   Top rows (1000) are extracted by 'SD' method.
#>   Subgroups are detected by 'kmeans' method.
#>   Performed in total 350 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_partitions"     
#>  [7] "compare_signatures"      "consensus_heatmap"       "dimension_reduction"    
#> [10] "functional_enrichment"   "get_anno_col"            "get_anno"               
#> [13] "get_classes"             "get_consensus"           "get_matrix"             
#> [16] "get_membership"          "get_param"               "get_signatures"         
#> [19] "get_stats"               "is_best_k"               "is_stable_k"            
#> [22] "membership_heatmap"      "ncol"                    "nrow"                   
#> [25] "plot_ecdf"               "predict_classes"         "rownames"               
#> [28] "select_partition_number" "show"                    "suggest_best_k"         
#> [31] "test_to_known_factors"   "top_rows_heatmap"

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

collect_plots(res)

plot of chunk node-022-collect-plots

The plots are:

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:

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

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

select_partition_number(res)

plot of chunk node-022-select-partition-number

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.779           0.897       0.951         0.3862 0.559   0.559
#> 3 3 0.904           0.979       0.985         0.2888 0.956   0.921
#> 4 4 0.838           0.855       0.959         0.2872 0.772   0.575
#> 5 5 0.721           0.766       0.938         0.1629 0.743   0.386
#> 6 6 0.743           0.612       0.835         0.0752 0.853   0.474
#> 7 7 0.838           0.670       0.868         0.0625 0.941   0.704
#> 8 8 0.831           0.607       0.852         0.0463 0.919   0.542

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

suggest_best_k(res)

#> [1] 4

Following is 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 subgroup 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.

show/hide code output

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

#>                 class entropy silhouette   p1   p2
#> TCGA.BQ.5884.11     1   0.000      1.000 1.00 0.00
#> TCGA.BQ.5891.11     1   0.000      1.000 1.00 0.00
#> TCGA.BQ.5888.11     1   0.000      1.000 1.00 0.00
#> TCGA.5P.A9K8.01     2   0.981      0.457 0.42 0.58
#> TCGA.BQ.5883.11     1   0.000      1.000 1.00 0.00
#> TCGA.BQ.5878.11     1   0.000      1.000 1.00 0.00
#> TCGA.BQ.5879.11     1   0.000      1.000 1.00 0.00
#> TCGA.2Z.A9JN.01     2   0.000      0.777 0.00 1.00
#> TCGA.BQ.5875.11     1   0.000      1.000 1.00 0.00
#> TCGA.BQ.5883.01     2   0.000      0.777 0.00 1.00
#> TCGA.BQ.7053.11     1   0.000      1.000 1.00 0.00
#> TCGA.DZ.6133.11     1   0.000      1.000 1.00 0.00
#> TCGA.BQ.7056.11     1   0.000      1.000 1.00 0.00
#> TCGA.A4.7288.11     1   0.000      1.000 1.00 0.00
#> TCGA.BQ.7061.11     2   0.981      0.457 0.42 0.58
#> TCGA.BQ.7050.11     1   0.000      1.000 1.00 0.00
#> TCGA.A4.7828.01     2   0.000      0.777 0.00 1.00

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

consensus_heatmap(res, k = 2)

plot of chunk tab-node-022-consensus-heatmap-1

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

membership_heatmap(res, k = 2)

plot of chunk tab-node-022-membership-heatmap-1

As soon as the classes for columns are determined, the signatures that are significantly different between subgroups can be looked for. Following are the heatmaps for signatures.

get_signatures(res, k = 2)

plot of chunk tab-node-022-get-signatures-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk node-022-signature_compare

get_signature() returns a data frame invisibly. To get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

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

An example of the output of tb is:

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

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows (which is done by automatically selecting number of clusters).

If there are too many signatures, top_signatures = ... can be set to only show the signatures with the highest FDRs:

# code only for demonstration
# e.g. to show the top 500 most significant rows
tb = get_signature(res, k = ..., top_signatures = 500)

If the signatures are defined as these which are uniquely high in current group, diff_method argument can be set to "uniquely_high_in_one_group":

# code only for demonstration
tb = get_signature(res, k = ..., diff_method = "uniquely_high_in_one_group")

UMAP plot which shows how samples are separated.

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

plot of chunk tab-node-022-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk node-022-collect-classes

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

Node03

Parent node: Node0. Child nodes: Node011-leaf , Node012 , Node013 , Node021-leaf , Node022 , Node023-leaf , Node031 , Node032 , Node033-leaf , Node041-leaf , Node042-leaf , Node043 , Node044-leaf , Node051 , Node052 , Node053 , Node054-leaf .

The object with results only for a single top-value method and a single partitioning method can be extracted as:

res = res_rh["03"]

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, 7, 8.
#>   On a matrix with 30000 rows and 59 columns.
#>   Top rows (1000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'kmeans' method.
#>   Performed in total 350 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_partitions"     
#>  [7] "compare_signatures"      "consensus_heatmap"       "dimension_reduction"    
#> [10] "functional_enrichment"   "get_anno_col"            "get_anno"               
#> [13] "get_classes"             "get_consensus"           "get_matrix"             
#> [16] "get_membership"          "get_param"               "get_signatures"         
#> [19] "get_stats"               "is_best_k"               "is_stable_k"            
#> [22] "membership_heatmap"      "ncol"                    "nrow"                   
#> [25] "plot_ecdf"               "predict_classes"         "rownames"               
#> [28] "select_partition_number" "show"                    "suggest_best_k"         
#> [31] "test_to_known_factors"   "top_rows_heatmap"

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

collect_plots(res)

plot of chunk node-03-collect-plots

The plots are:

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:

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

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

select_partition_number(res)

plot of chunk node-03-select-partition-number

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.758           0.931       0.940         0.2495 0.670   0.670
#> 3 3 1.000           0.990       0.976         1.1196 0.646   0.519
#> 4 4 0.884           0.890       0.948         0.1773 0.944   0.875
#> 5 5 0.598           0.678       0.756         0.1572 0.841   0.593
#> 6 6 0.645           0.530       0.784         0.0909 0.893   0.618
#> 7 7 0.673           0.601       0.813         0.0278 0.911   0.635
#> 8 8 0.761           0.656       0.832         0.0382 0.948   0.731

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

suggest_best_k(res)

#> [1] 3

Following is 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 subgroup 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.

show/hide code output

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

#>                 class entropy silhouette   p1   p2
#> TCGA.B1.A656.01     1   0.000      0.994 1.00 0.00
#> TCGA.B9.A69E.01     1   0.000      0.994 1.00 0.00
#> TCGA.PJ.A8JU.01     1   0.000      0.994 1.00 0.00
#> TCGA.F9.A7Q0.01     2   0.981      0.733 0.42 0.58
#> TCGA.B3.8121.01     1   0.000      0.994 1.00 0.00
#> TCGA.A4.A7UZ.01     2   0.981      0.733 0.42 0.58
#> TCGA.J7.A8I2.01     2   0.000      0.669 0.00 1.00
#> TCGA.BQ.5880.01     2   0.981      0.733 0.42 0.58
#> TCGA.GL.A9DD.01     1   0.000      0.994 1.00 0.00
#> TCGA.Y8.A8S1.01     1   0.000      0.994 1.00 0.00
#> TCGA.IA.A83S.01     1   0.000      0.994 1.00 0.00
#> TCGA.B1.A655.01     1   0.000      0.994 1.00 0.00
#> TCGA.Y8.A896.01     1   0.000      0.994 1.00 0.00
#> TCGA.BQ.5888.01     2   0.981      0.733 0.42 0.58
#> TCGA.IA.A83T.01     1   0.000      0.994 1.00 0.00
#> TCGA.IA.A83V.01     1   0.000      0.994 1.00 0.00
#> TCGA.KV.A6GD.01     1   0.000      0.994 1.00 0.00
#> TCGA.4A.A93Y.01     1   0.000      0.994 1.00 0.00
#> TCGA.WN.A9G9.01     1   0.000      0.994 1.00 0.00
#> TCGA.A4.8518.01     1   0.000      0.994 1.00 0.00
#> TCGA.BQ.5876.01     1   0.000      0.994 1.00 0.00
#> TCGA.MH.A855.01     1   0.000      0.994 1.00 0.00
#> TCGA.A4.A48D.01     1   0.000      0.994 1.00 0.00
#> TCGA.BQ.5889.01     1   0.000      0.994 1.00 0.00
#> TCGA.2Z.A9JO.01     2   0.981      0.733 0.42 0.58
#> TCGA.5P.A9JW.01     1   0.000      0.994 1.00 0.00
#> TCGA.B1.A47O.01     1   0.000      0.994 1.00 0.00
#> TCGA.2Z.A9JK.01     1   0.000      0.994 1.00 0.00
#> TCGA.BQ.5892.01     1   0.000      0.994 1.00 0.00
#> TCGA.UZ.A9PS.05     1   0.000      0.994 1.00 0.00
#> TCGA.PJ.A5Z8.01     1   0.000      0.994 1.00 0.00
#> TCGA.BQ.5884.01     1   0.000      0.994 1.00 0.00
#> TCGA.B9.A5W8.01     1   0.000      0.994 1.00 0.00
#> TCGA.B1.5398.01     1   0.000      0.994 1.00 0.00
#> TCGA.5P.A9KC.01     1   0.000      0.994 1.00 0.00
#> TCGA.WN.AB4C.01     2   0.981      0.733 0.42 0.58
#> TCGA.GL.A4EM.01     1   0.000      0.994 1.00 0.00
#> TCGA.HE.7128.01     1   0.000      0.994 1.00 0.00
#> TCGA.BQ.7059.01     1   0.000      0.994 1.00 0.00
#> TCGA.BQ.7049.01     1   0.000      0.994 1.00 0.00
#> TCGA.HE.A5NF.01     1   0.000      0.994 1.00 0.00
#> TCGA.HE.7130.01     2   0.000      0.669 0.00 1.00
#> TCGA.DZ.6131.01     2   0.000      0.669 0.00 1.00
#> TCGA.MH.A560.01     1   0.000      0.994 1.00 0.00
#> TCGA.G7.6796.01     1   0.000      0.994 1.00 0.00
#> TCGA.DZ.6134.01     1   0.000      0.994 1.00 0.00
#> TCGA.HE.A5NK.01     1   0.000      0.994 1.00 0.00
#> TCGA.AL.7173.01     1   0.000      0.994 1.00 0.00
#> TCGA.DW.7838.01     1   0.000      0.994 1.00 0.00
#> TCGA.V9.A7HT.01     1   0.000      0.994 1.00 0.00
#> TCGA.DZ.6132.01     1   0.000      0.994 1.00 0.00
#> TCGA.A4.7287.01     2   0.000      0.669 0.00 1.00
#> TCGA.UZ.A9PO.01     1   0.000      0.994 1.00 0.00
#> TCGA.2Z.A9J2.01     2   0.981      0.733 0.42 0.58
#> TCGA.F9.A97G.01     1   0.000      0.994 1.00 0.00
#> TCGA.UZ.A9PM.01     1   0.000      0.994 1.00 0.00
#> TCGA.2K.A9WE.01     1   0.000      0.994 1.00 0.00
#> TCGA.UZ.A9PN.01     1   0.680      0.654 0.82 0.18
#> TCGA.A4.7585.01     2   0.981      0.733 0.42 0.58

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

consensus_heatmap(res, k = 2)

plot of chunk tab-node-03-consensus-heatmap-1

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

membership_heatmap(res, k = 2)

plot of chunk tab-node-03-membership-heatmap-1

As soon as the classes for columns are determined, the signatures that are significantly different between subgroups can be looked for. Following are the heatmaps for signatures.

get_signatures(res, k = 2)

plot of chunk tab-node-03-get-signatures-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk node-03-signature_compare

get_signature() returns a data frame invisibly. To get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

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

An example of the output of tb is:

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

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows (which is done by automatically selecting number of clusters).

If there are too many signatures, top_signatures = ... can be set to only show the signatures with the highest FDRs:

# code only for demonstration
# e.g. to show the top 500 most significant rows
tb = get_signature(res, k = ..., top_signatures = 500)

If the signatures are defined as these which are uniquely high in current group, diff_method argument can be set to "uniquely_high_in_one_group":

# code only for demonstration
tb = get_signature(res, k = ..., diff_method = "uniquely_high_in_one_group")

UMAP plot which shows how samples are separated.

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

plot of chunk tab-node-03-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk node-03-collect-classes

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

Node031

Parent node: Node03. Child nodes: Node0121-leaf , Node0122-leaf , Node0123-leaf , Node0124-leaf , Node0131 , Node0132-leaf , Node0221-leaf , Node0222-leaf , Node0223-leaf , Node0311 , Node0312-leaf , Node0313-leaf , Node0321-leaf , Node0322-leaf , Node0431-leaf , Node0432-leaf , Node0433-leaf , Node0511-leaf , Node0512-leaf , Node0513-leaf , Node0521-leaf , Node0522-leaf , Node0523-leaf , Node0531-leaf , Node0532-leaf , Node0533-leaf .

The object with results only for a single top-value method and a single partitioning method can be extracted as:

res = res_rh["031"]

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, 7, 8.
#>   On a matrix with 30000 rows and 33 columns.
#>   Top rows (1000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'kmeans' method.
#>   Performed in total 350 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_partitions"     
#>  [7] "compare_signatures"      "consensus_heatmap"       "dimension_reduction"    
#> [10] "functional_enrichment"   "get_anno_col"            "get_anno"               
#> [13] "get_classes"             "get_consensus"           "get_matrix"             
#> [16] "get_membership"          "get_param"               "get_signatures"         
#> [19] "get_stats"               "is_best_k"               "is_stable_k"            
#> [22] "membership_heatmap"      "ncol"                    "nrow"                   
#> [25] "plot_ecdf"               "predict_classes"         "rownames"               
#> [28] "select_partition_number" "show"                    "suggest_best_k"         
#> [31] "test_to_known_factors"   "top_rows_heatmap"

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

collect_plots(res)

plot of chunk node-031-collect-plots

The plots are:

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:

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

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

select_partition_number(res)

plot of chunk node-031-select-partition-number

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.997       0.998         0.3066 0.693   0.693
#> 3 3 1.000           0.963       0.988         0.9634 0.625   0.487
#> 4 4 0.750           0.869       0.910         0.1731 0.850   0.644
#> 5 5 0.746           0.750       0.857         0.0971 0.894   0.665
#> 6 6 0.720           0.794       0.826         0.0514 0.879   0.519
#> 7 7 0.761           0.792       0.839         0.0373 1.000   1.000
#> 8 8 0.718           0.699       0.796         0.0167 0.989   0.926

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

suggest_best_k(res)

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

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

Following is 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 subgroup 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.

show/hide code output

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

#>                 class entropy silhouette   p1   p2
#> TCGA.B1.A656.01     2   0.000      0.992 0.00 1.00
#> TCGA.B9.A69E.01     1   0.141      0.979 0.98 0.02
#> TCGA.B3.8121.01     1   0.000      0.999 1.00 0.00
#> TCGA.GL.A9DD.01     1   0.000      0.999 1.00 0.00
#> TCGA.Y8.A8S1.01     1   0.000      0.999 1.00 0.00
#> TCGA.IA.A83S.01     1   0.000      0.999 1.00 0.00
#> TCGA.IA.A83T.01     1   0.000      0.999 1.00 0.00
#> TCGA.KV.A6GD.01     1   0.000      0.999 1.00 0.00
#> TCGA.WN.A9G9.01     1   0.000      0.999 1.00 0.00
#> TCGA.BQ.5876.01     2   0.000      0.992 0.00 1.00
#> TCGA.A4.A48D.01     1   0.000      0.999 1.00 0.00
#> TCGA.BQ.5889.01     1   0.000      0.999 1.00 0.00
#> TCGA.5P.A9JW.01     2   0.141      0.984 0.02 0.98
#> TCGA.B1.A47O.01     1   0.000      0.999 1.00 0.00
#> TCGA.UZ.A9PS.05     2   0.000      0.992 0.00 1.00
#> TCGA.PJ.A5Z8.01     1   0.000      0.999 1.00 0.00
#> TCGA.B9.A5W8.01     1   0.000      0.999 1.00 0.00
#> TCGA.B1.5398.01     1   0.000      0.999 1.00 0.00
#> TCGA.GL.A4EM.01     1   0.000      0.999 1.00 0.00
#> TCGA.HE.7128.01     1   0.000      0.999 1.00 0.00
#> TCGA.BQ.7059.01     1   0.000      0.999 1.00 0.00
#> TCGA.BQ.7049.01     1   0.000      0.999 1.00 0.00
#> TCGA.HE.A5NF.01     1   0.000      0.999 1.00 0.00
#> TCGA.MH.A560.01     2   0.000      0.992 0.00 1.00
#> TCGA.DZ.6134.01     1   0.000      0.999 1.00 0.00
#> TCGA.HE.A5NK.01     1   0.000      0.999 1.00 0.00
#> TCGA.AL.7173.01     1   0.000      0.999 1.00 0.00
#> TCGA.DW.7838.01     1   0.000      0.999 1.00 0.00
#> TCGA.V9.A7HT.01     1   0.000      0.999 1.00 0.00
#> TCGA.DZ.6132.01     1   0.000      0.999 1.00 0.00
#> TCGA.UZ.A9PO.01     2   0.141      0.984 0.02 0.98
#> TCGA.F9.A97G.01     1   0.000      0.999 1.00 0.00
#> TCGA.2K.A9WE.01     1   0.000      0.999 1.00 0.00

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

consensus_heatmap(res, k = 2)

plot of chunk tab-node-031-consensus-heatmap-1

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

membership_heatmap(res, k = 2)

plot of chunk tab-node-031-membership-heatmap-1

As soon as the classes for columns are determined, the signatures that are significantly different between subgroups can be looked for. Following are the heatmaps for signatures.

get_signatures(res, k = 2)

plot of chunk tab-node-031-get-signatures-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk node-031-signature_compare

get_signature() returns a data frame invisibly. To get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

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

An example of the output of tb is:

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

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows (which is done by automatically selecting number of clusters).

If there are too many signatures, top_signatures = ... can be set to only show the signatures with the highest FDRs:

# code only for demonstration
# e.g. to show the top 500 most significant rows
tb = get_signature(res, k = ..., top_signatures = 500)

If the signatures are defined as these which are uniquely high in current group, diff_method argument can be set to "uniquely_high_in_one_group":

# code only for demonstration
tb = get_signature(res, k = ..., diff_method = "uniquely_high_in_one_group")

UMAP plot which shows how samples are separated.

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

plot of chunk tab-node-031-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk node-031-collect-classes

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

Node0311

Parent node: Node031. Child nodes: Node01311-leaf , Node01312-leaf , Node03111-leaf , Node03112-leaf , Node03113-leaf .

The object with results only for a single top-value method and a single partitioning method can be extracted as:

res = res_rh["0311"]

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, 7, 8.
#>   On a matrix with 30000 rows and 17 columns.
#>   Top rows (1000) are extracted by 'SD' method.
#>   Subgroups are detected by 'kmeans' method.
#>   Performed in total 350 partitions by row resampling.
#>   Best k for subgroups seems to be 7.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_partitions"     
#>  [7] "compare_signatures"      "consensus_heatmap"       "dimension_reduction"    
#> [10] "functional_enrichment"   "get_anno_col"            "get_anno"               
#> [13] "get_classes"             "get_consensus"           "get_matrix"             
#> [16] "get_membership"          "get_param"               "get_signatures"         
#> [19] "get_stats"               "is_best_k"               "is_stable_k"            
#> [22] "membership_heatmap"      "ncol"                    "nrow"                   
#> [25] "plot_ecdf"               "predict_classes"         "rownames"               
#> [28] "select_partition_number" "show"                    "suggest_best_k"         
#> [31] "test_to_known_factors"   "top_rows_heatmap"

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

collect_plots(res)

plot of chunk node-0311-collect-plots

The plots are:

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:

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

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

select_partition_number(res)

plot of chunk node-0311-select-partition-number

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.559           0.814       0.900         0.3844 0.691   0.691
#> 3 3 0.640           0.960       0.927         0.5772 0.669   0.521
#> 4 4 0.779           0.841       0.868         0.2103 0.897   0.714
#> 5 5 0.794           0.916       0.913         0.0881 0.926   0.714
#> 6 6 0.838           0.845       0.900         0.0397 1.000   1.000
#> 7 7 0.904           0.793       0.886         0.0279 0.971   0.840
#> 8 8 0.868           0.635       0.836         0.0241 0.993   0.952

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

suggest_best_k(res)

#> [1] 7

Following is 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 subgroup 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.

show/hide code output

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

#>                 class entropy silhouette   p1   p2
#> TCGA.B3.8121.01     2   0.925      1.000 0.34 0.66
#> TCGA.GL.A9DD.01     1   0.925      0.848 0.66 0.34
#> TCGA.IA.A83S.01     1   0.925      0.848 0.66 0.34
#> TCGA.KV.A6GD.01     1   0.925      0.848 0.66 0.34
#> TCGA.BQ.5889.01     1   0.000      0.643 1.00 0.00
#> TCGA.B1.A47O.01     2   0.925      1.000 0.34 0.66
#> TCGA.B9.A5W8.01     1   0.925      0.848 0.66 0.34
#> TCGA.HE.7128.01     1   0.925      0.848 0.66 0.34
#> TCGA.BQ.7059.01     1   0.925      0.848 0.66 0.34
#> TCGA.BQ.7049.01     1   0.000      0.643 1.00 0.00
#> TCGA.HE.A5NF.01     1   0.925      0.848 0.66 0.34
#> TCGA.HE.A5NK.01     1   0.925      0.848 0.66 0.34
#> TCGA.AL.7173.01     2   0.925      1.000 0.34 0.66
#> TCGA.DW.7838.01     1   0.000      0.643 1.00 0.00
#> TCGA.V9.A7HT.01     1   0.925      0.848 0.66 0.34
#> TCGA.DZ.6132.01     1   0.000      0.643 1.00 0.00
#> TCGA.2K.A9WE.01     1   0.000      0.643 1.00 0.00

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

consensus_heatmap(res, k = 2)

plot of chunk tab-node-0311-consensus-heatmap-1

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

membership_heatmap(res, k = 2)

plot of chunk tab-node-0311-membership-heatmap-1

As soon as the classes for columns are determined, the signatures that are significantly different between subgroups can be looked for. Following are the heatmaps for signatures.

get_signatures(res, k = 2)

plot of chunk tab-node-0311-get-signatures-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk node-0311-signature_compare

get_signature() returns a data frame invisibly. To get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

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

An example of the output of tb is:

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

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows (which is done by automatically selecting number of clusters).

If there are too many signatures, top_signatures = ... can be set to only show the signatures with the highest FDRs:

# code only for demonstration
# e.g. to show the top 500 most significant rows
tb = get_signature(res, k = ..., top_signatures = 500)

If the signatures are defined as these which are uniquely high in current group, diff_method argument can be set to "uniquely_high_in_one_group":

# code only for demonstration
tb = get_signature(res, k = ..., diff_method = "uniquely_high_in_one_group")

UMAP plot which shows how samples are separated.

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

plot of chunk tab-node-0311-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk node-0311-collect-classes

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

Node032

Parent node: Node03. Child nodes: Node0121-leaf , Node0122-leaf , Node0123-leaf , Node0124-leaf , Node0131 , Node0132-leaf , Node0221-leaf , Node0222-leaf , Node0223-leaf , Node0311 , Node0312-leaf , Node0313-leaf , Node0321-leaf , Node0322-leaf , Node0431-leaf , Node0432-leaf , Node0433-leaf , Node0511-leaf , Node0512-leaf , Node0513-leaf , Node0521-leaf , Node0522-leaf , Node0523-leaf , Node0531-leaf , Node0532-leaf , Node0533-leaf .

The object with results only for a single top-value method and a single partitioning method can be extracted as:

res = res_rh["032"]

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, 7, 8.
#>   On a matrix with 30000 rows and 22 columns.
#>   Top rows (1000) are extracted by 'SD' method.
#>   Subgroups are detected by 'kmeans' method.
#>   Performed in total 350 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_partitions"     
#>  [7] "compare_signatures"      "consensus_heatmap"       "dimension_reduction"    
#> [10] "functional_enrichment"   "get_anno_col"            "get_anno"               
#> [13] "get_classes"             "get_consensus"           "get_matrix"             
#> [16] "get_membership"          "get_param"               "get_signatures"         
#> [19] "get_stats"               "is_best_k"               "is_stable_k"            
#> [22] "membership_heatmap"      "ncol"                    "nrow"                   
#> [25] "plot_ecdf"               "predict_classes"         "rownames"               
#> [28] "select_partition_number" "show"                    "suggest_best_k"         
#> [31] "test_to_known_factors"   "top_rows_heatmap"

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

collect_plots(res)

plot of chunk node-032-collect-plots

The plots are:

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:

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

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

select_partition_number(res)

plot of chunk node-032-select-partition-number

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.976       0.980         0.5128 0.481   0.481
#> 3 3 0.737           0.807       0.905         0.1936 0.952   0.901
#> 4 4 0.614           0.667       0.811         0.1316 0.931   0.840
#> 5 5 0.610           0.739       0.825         0.0987 0.870   0.643
#> 6 6 0.600           0.586       0.717         0.0578 0.948   0.778
#> 7 7 0.753           0.765       0.837         0.0573 0.900   0.521
#> 8 8 0.771           0.645       0.829         0.0211 0.983   0.871

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

suggest_best_k(res)

#> [1] 2

Following is 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 subgroup 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.

show/hide code output

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

#>                 class entropy silhouette   p1   p2
#> TCGA.PJ.A8JU.01     2   0.141      1.000 0.02 0.98
#> TCGA.F9.A7Q0.01     1   0.795      0.707 0.76 0.24
#> TCGA.A4.A7UZ.01     1   0.000      0.979 1.00 0.00
#> TCGA.BQ.5880.01     1   0.000      0.979 1.00 0.00
#> TCGA.B1.A655.01     2   0.141      1.000 0.02 0.98
#> TCGA.Y8.A896.01     1   0.000      0.979 1.00 0.00
#> TCGA.BQ.5888.01     2   0.141      1.000 0.02 0.98
#> TCGA.IA.A83V.01     1   0.000      0.979 1.00 0.00
#> TCGA.4A.A93Y.01     2   0.141      1.000 0.02 0.98
#> TCGA.A4.8518.01     1   0.000      0.979 1.00 0.00
#> TCGA.MH.A855.01     2   0.141      1.000 0.02 0.98
#> TCGA.2Z.A9JO.01     2   0.141      1.000 0.02 0.98
#> TCGA.2Z.A9JK.01     1   0.000      0.979 1.00 0.00
#> TCGA.BQ.5892.01     1   0.000      0.979 1.00 0.00
#> TCGA.BQ.5884.01     2   0.141      1.000 0.02 0.98
#> TCGA.5P.A9KC.01     2   0.141      1.000 0.02 0.98
#> TCGA.WN.AB4C.01     2   0.141      1.000 0.02 0.98
#> TCGA.G7.6796.01     1   0.000      0.979 1.00 0.00
#> TCGA.2Z.A9J2.01     2   0.141      1.000 0.02 0.98
#> TCGA.UZ.A9PM.01     1   0.000      0.979 1.00 0.00
#> TCGA.UZ.A9PN.01     1   0.000      0.979 1.00 0.00
#> TCGA.A4.7585.01     1   0.000      0.979 1.00 0.00

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

consensus_heatmap(res, k = 2)

plot of chunk tab-node-032-consensus-heatmap-1

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

membership_heatmap(res, k = 2)

plot of chunk tab-node-032-membership-heatmap-1

As soon as the classes for columns are determined, the signatures that are significantly different between subgroups can be looked for. Following are the heatmaps for signatures.

get_signatures(res, k = 2)

plot of chunk tab-node-032-get-signatures-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk node-032-signature_compare

get_signature() returns a data frame invisibly. To get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

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

An example of the output of tb is:

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

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows (which is done by automatically selecting number of clusters).

If there are too many signatures, top_signatures = ... can be set to only show the signatures with the highest FDRs:

# code only for demonstration
# e.g. to show the top 500 most significant rows
tb = get_signature(res, k = ..., top_signatures = 500)

If the signatures are defined as these which are uniquely high in current group, diff_method argument can be set to "uniquely_high_in_one_group":

# code only for demonstration
tb = get_signature(res, k = ..., diff_method = "uniquely_high_in_one_group")

UMAP plot which shows how samples are separated.

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

plot of chunk tab-node-032-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk node-032-collect-classes

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

Node04

Parent node: Node0. Child nodes: Node011-leaf , Node012 , Node013 , Node021-leaf , Node022 , Node023-leaf , Node031 , Node032 , Node033-leaf , Node041-leaf , Node042-leaf , Node043 , Node044-leaf , Node051 , Node052 , Node053 , Node054-leaf .

The object with results only for a single top-value method and a single partitioning method can be extracted as:

res = res_rh["04"]

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, 7, 8.
#>   On a matrix with 30000 rows and 44 columns.
#>   Top rows (1000) are extracted by 'SD' method.
#>   Subgroups are detected by 'kmeans' method.
#>   Performed in total 350 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_partitions"     
#>  [7] "compare_signatures"      "consensus_heatmap"       "dimension_reduction"    
#> [10] "functional_enrichment"   "get_anno_col"            "get_anno"               
#> [13] "get_classes"             "get_consensus"           "get_matrix"             
#> [16] "get_membership"          "get_param"               "get_signatures"         
#> [19] "get_stats"               "is_best_k"               "is_stable_k"            
#> [22] "membership_heatmap"      "ncol"                    "nrow"                   
#> [25] "plot_ecdf"               "predict_classes"         "rownames"               
#> [28] "select_partition_number" "show"                    "suggest_best_k"         
#> [31] "test_to_known_factors"   "top_rows_heatmap"

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

collect_plots(res)

plot of chunk node-04-collect-plots

The plots are:

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:

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

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

select_partition_number(res)

plot of chunk node-04-select-partition-number

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.976       0.976         0.4466 0.556   0.556
#> 3 3 0.598           0.685       0.801         0.4754 0.738   0.556
#> 4 4 1.000           0.980       0.973         0.1552 0.872   0.646
#> 5 5 0.894           0.913       0.932         0.0627 0.916   0.667
#> 6 6 0.900           0.842       0.882         0.0329 0.982   0.907
#> 7 7 0.878           0.789       0.862         0.0177 0.962   0.805
#> 8 8 0.867           0.780       0.836         0.0212 0.964   0.796

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

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

Following is 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 subgroup 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.

show/hide code output

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

#>                 class entropy silhouette   p1   p2
#> TCGA.SX.A7SM.01     2   0.141      0.978 0.02 0.98
#> TCGA.4A.A93X.01     2   0.141      0.978 0.02 0.98
#> TCGA.BQ.5894.01     1   0.141      0.993 0.98 0.02
#> TCGA.BQ.5882.01     2   0.242      0.974 0.04 0.96
#> TCGA.BQ.5893.01     1   0.141      0.993 0.98 0.02
#> TCGA.IZ.8195.01     2   0.000      0.975 0.00 1.00
#> TCGA.G7.A8LD.01     2   0.584      0.884 0.14 0.86
#> TCGA.J7.8537.01     1   0.000      0.984 1.00 0.00
#> TCGA.BQ.5890.01     2   0.141      0.978 0.02 0.98
#> TCGA.BQ.5879.01     1   0.141      0.993 0.98 0.02
#> TCGA.GL.A9DE.01     2   0.141      0.978 0.02 0.98
#> TCGA.B9.A8YI.01     2   0.000      0.975 0.00 1.00
#> TCGA.F9.A8NY.01     1   0.141      0.993 0.98 0.02
#> TCGA.BQ.5891.01     2   0.242      0.974 0.04 0.96
#> TCGA.P4.AAVO.01     2   0.000      0.975 0.00 1.00
#> TCGA.A4.A5Y1.01     2   0.242      0.974 0.04 0.96
#> TCGA.BQ.5875.01     2   0.141      0.978 0.02 0.98
#> TCGA.Q2.A5QZ.01     2   0.141      0.978 0.02 0.98
#> TCGA.P4.A5E8.01     1   0.141      0.993 0.98 0.02
#> TCGA.B9.A5W9.01     2   0.141      0.969 0.02 0.98
#> TCGA.P4.AAVK.01     2   0.242      0.974 0.04 0.96
#> TCGA.5P.A9K9.01     2   0.242      0.974 0.04 0.96
#> TCGA.IA.A40Y.01     2   0.584      0.884 0.14 0.86
#> TCGA.P4.A5EA.01     1   0.141      0.993 0.98 0.02
#> TCGA.5P.A9K3.01     2   0.141      0.978 0.02 0.98
#> TCGA.B9.A44B.01     2   0.141      0.978 0.02 0.98
#> TCGA.BQ.5877.01     2   0.242      0.974 0.04 0.96
#> TCGA.2Z.A9JG.01     2   0.141      0.969 0.02 0.98
#> TCGA.2Z.A9JI.01     1   0.000      0.984 1.00 0.00
#> TCGA.5P.A9JU.01     2   0.141      0.978 0.02 0.98
#> TCGA.F9.A4JJ.01     1   0.141      0.993 0.98 0.02
#> TCGA.UZ.A9PQ.01     2   0.000      0.975 0.00 1.00
#> TCGA.UZ.A9Q1.01     2   0.000      0.975 0.00 1.00
#> TCGA.GL.6846.01     2   0.000      0.975 0.00 1.00
#> TCGA.G7.6793.01     1   0.141      0.993 0.98 0.02
#> TCGA.BQ.7061.01     2   0.141      0.978 0.02 0.98
#> TCGA.BQ.7058.01     2   0.141      0.978 0.02 0.98
#> TCGA.GL.7966.01     1   0.141      0.993 0.98 0.02
#> TCGA.AL.A5DJ.01     1   0.000      0.984 1.00 0.00
#> TCGA.BQ.7048.01     2   0.000      0.975 0.00 1.00
#> TCGA.BQ.5887.01     2   0.402      0.946 0.08 0.92
#> TCGA.A4.7915.01     1   0.141      0.993 0.98 0.02
#> TCGA.G7.6789.01     1   0.000      0.984 1.00 0.00
#> TCGA.BQ.7044.01     2   0.000      0.975 0.00 1.00

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

consensus_heatmap(res, k = 2)

plot of chunk tab-node-04-consensus-heatmap-1

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

membership_heatmap(res, k = 2)

plot of chunk tab-node-04-membership-heatmap-1

As soon as the classes for columns are determined, the signatures that are significantly different between subgroups can be looked for. Following are the heatmaps for signatures.

get_signatures(res, k = 2)

plot of chunk tab-node-04-get-signatures-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk node-04-signature_compare

get_signature() returns a data frame invisibly. To get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

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

An example of the output of tb is:

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

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows (which is done by automatically selecting number of clusters).

If there are too many signatures, top_signatures = ... can be set to only show the signatures with the highest FDRs:

# code only for demonstration
# e.g. to show the top 500 most significant rows
tb = get_signature(res, k = ..., top_signatures = 500)

If the signatures are defined as these which are uniquely high in current group, diff_method argument can be set to "uniquely_high_in_one_group":

# code only for demonstration
tb = get_signature(res, k = ..., diff_method = "uniquely_high_in_one_group")

UMAP plot which shows how samples are separated.

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

plot of chunk tab-node-04-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk node-04-collect-classes

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

Node043

Parent node: Node04. Child nodes: Node0121-leaf , Node0122-leaf , Node0123-leaf , Node0124-leaf , Node0131 , Node0132-leaf , Node0221-leaf , Node0222-leaf , Node0223-leaf , Node0311 , Node0312-leaf , Node0313-leaf , Node0321-leaf , Node0322-leaf , Node0431-leaf , Node0432-leaf , Node0433-leaf , Node0511-leaf , Node0512-leaf , Node0513-leaf , Node0521-leaf , Node0522-leaf , Node0523-leaf , Node0531-leaf , Node0532-leaf , Node0533-leaf .

The object with results only for a single top-value method and a single partitioning method can be extracted as:

res = res_rh["043"]

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, 7, 8.
#>   On a matrix with 30000 rows and 12 columns.
#>   Top rows (1000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'skmeans' method.
#>   Performed in total 350 partitions by row resampling.
#>   Best k for subgroups seems to be 7.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_partitions"     
#>  [7] "compare_signatures"      "consensus_heatmap"       "dimension_reduction"    
#> [10] "functional_enrichment"   "get_anno_col"            "get_anno"               
#> [13] "get_classes"             "get_consensus"           "get_matrix"             
#> [16] "get_membership"          "get_param"               "get_signatures"         
#> [19] "get_stats"               "is_best_k"               "is_stable_k"            
#> [22] "membership_heatmap"      "ncol"                    "nrow"                   
#> [25] "plot_ecdf"               "predict_classes"         "rownames"               
#> [28] "select_partition_number" "show"                    "suggest_best_k"         
#> [31] "test_to_known_factors"   "top_rows_heatmap"

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

collect_plots(res)

plot of chunk node-043-collect-plots

The plots are:

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:

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

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

select_partition_number(res)

plot of chunk node-043-select-partition-number

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.993       0.997         0.4871 0.515   0.515
#> 3 3 1.000           1.000       1.000         0.4935 0.758   0.529
#> 4 4 1.000           0.909       0.990         0.0632 0.955   0.833
#> 5 5 0.894           0.898       0.968         0.0755 0.939   0.733
#> 6 6 0.924           0.776       0.963         0.0572 0.955   0.727
#> 7 7 0.924           0.636       0.942         0.0316 0.939   0.556
#> 8 8 0.970           0.519       0.970         0.0191 0.985   0.833

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

suggest_best_k(res)

#> [1] 7
#> attr(,"optional")
#> [1] 2 3 6

There is also optional best \(k\) = 2 3 6 that is worth to check.

Following is 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 subgroup 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.

show/hide code output

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

#>                 class entropy silhouette   p1   p2
#> TCGA.BQ.5882.01     2   0.242      0.958 0.04 0.96
#> TCGA.G7.A8LD.01     2   0.000      0.994 0.00 1.00
#> TCGA.J7.8537.01     2   0.000      0.994 0.00 1.00
#> TCGA.BQ.5891.01     1   0.000      1.000 1.00 0.00
#> TCGA.A4.A5Y1.01     1   0.000      1.000 1.00 0.00
#> TCGA.5P.A9K9.01     2   0.000      0.994 0.00 1.00
#> TCGA.IA.A40Y.01     1   0.000      1.000 1.00 0.00
#> TCGA.BQ.5877.01     1   0.000      1.000 1.00 0.00
#> TCGA.2Z.A9JI.01     2   0.000      0.994 0.00 1.00
#> TCGA.AL.A5DJ.01     2   0.000      0.994 0.00 1.00
#> TCGA.BQ.5887.01     2   0.000      0.994 0.00 1.00
#> TCGA.G7.6789.01     2   0.000      0.994 0.00 1.00

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

consensus_heatmap(res, k = 2)

plot of chunk tab-node-043-consensus-heatmap-1

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

membership_heatmap(res, k = 2)

plot of chunk tab-node-043-membership-heatmap-1

As soon as the classes for columns are determined, the signatures that are significantly different between subgroups can be looked for. Following are the heatmaps for signatures.

get_signatures(res, k = 2)

plot of chunk tab-node-043-get-signatures-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk node-043-signature_compare

get_signature() returns a data frame invisibly. To get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

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

An example of the output of tb is:

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

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows (which is done by automatically selecting number of clusters).

If there are too many signatures, top_signatures = ... can be set to only show the signatures with the highest FDRs:

# code only for demonstration
# e.g. to show the top 500 most significant rows
tb = get_signature(res, k = ..., top_signatures = 500)

If the signatures are defined as these which are uniquely high in current group, diff_method argument can be set to "uniquely_high_in_one_group":

# code only for demonstration
tb = get_signature(res, k = ..., diff_method = "uniquely_high_in_one_group")

UMAP plot which shows how samples are separated.

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

plot of chunk tab-node-043-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk node-043-collect-classes

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

Node05

Parent node: Node0. Child nodes: Node011-leaf , Node012 , Node013 , Node021-leaf , Node022 , Node023-leaf , Node031 , Node032 , Node033-leaf , Node041-leaf , Node042-leaf , Node043 , Node044-leaf , Node051 , Node052 , Node053 , Node054-leaf .

The object with results only for a single top-value method and a single partitioning method can be extracted as:

res = res_rh["05"]

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, 7, 8.
#>   On a matrix with 30000 rows and 83 columns.
#>   Top rows (1000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'skmeans' method.
#>   Performed in total 350 partitions by row resampling.
#>   Best k for subgroups seems to be 8.
#> 
#> Following methods can be applied to this 'ConsensusPartition' object:
#>  [1] "cola_report"             "collect_classes"         "collect_plots"          
#>  [4] "collect_stats"           "colnames"                "compare_partitions"     
#>  [7] "compare_signatures"      "consensus_heatmap"       "dimension_reduction"    
#> [10] "functional_enrichment"   "get_anno_col"            "get_anno"               
#> [13] "get_classes"             "get_consensus"           "get_matrix"             
#> [16] "get_membership"          "get_param"               "get_signatures"         
#> [19] "get_stats"               "is_best_k"               "is_stable_k"            
#> [22] "membership_heatmap"      "ncol"                    "nrow"                   
#> [25] "plot_ecdf"               "predict_classes"         "rownames"               
#> [28] "select_partition_number" "show"                    "suggest_best_k"         
#> [31] "test_to_known_factors"   "top_rows_heatmap"

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

collect_plots(res)

plot of chunk node-05-collect-plots

The plots are:

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:

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

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

select_partition_number(res)

plot of chunk node-05-select-partition-number

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           0.996       0.998         0.3844 0.617   0.617
#> 3 3 1.000           0.982       0.993         0.6634 0.658   0.482
#> 4 4 0.988           0.971       0.987         0.0669 0.855   0.650
#> 5 5 0.858           0.895       0.909         0.0939 0.872   0.625
#> 6 6 0.853           0.835       0.889         0.0551 0.980   0.915
#> 7 7 0.892           0.818       0.892         0.0490 0.922   0.661
#> 8 8 0.915           0.883       0.923         0.0247 0.980   0.880

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

suggest_best_k(res)

#> [1] 8
#> attr(,"optional")
#> [1] 2 3 4

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

Following is 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 subgroup 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.

show/hide code output

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

#>                 class entropy silhouette   p1   p2
#> TCGA.IA.A83W.01     1   0.000      0.998 1.00 0.00
#> TCGA.G7.A8LC.01     1   0.000      0.998 1.00 0.00
#> TCGA.EV.5901.01     2   0.000      0.999 0.00 1.00
#> TCGA.SX.A7SR.01     1   0.000      0.998 1.00 0.00
#> TCGA.IZ.A6M8.01     1   0.000      0.998 1.00 0.00
#> TCGA.MH.A856.01     1   0.000      0.998 1.00 0.00
#> TCGA.B9.5156.01     1   0.000      0.998 1.00 0.00
#> TCGA.Y8.A897.01     1   0.000      0.998 1.00 0.00
#> TCGA.SX.A7SP.01     2   0.000      0.999 0.00 1.00
#> TCGA.Y8.A8RZ.01     2   0.000      0.999 0.00 1.00
#> TCGA.A4.A5XZ.01     2   0.141      0.979 0.02 0.98
#> TCGA.Y8.A898.01     1   0.000      0.998 1.00 0.00
#> TCGA.Y8.A8RY.01     1   0.000      0.998 1.00 0.00
#> TCGA.SX.A7SN.01     1   0.000      0.998 1.00 0.00
#> TCGA.A4.8517.01     1   0.000      0.998 1.00 0.00
#> TCGA.SX.A7SO.01     2   0.000      0.999 0.00 1.00
#> TCGA.B1.A657.01     1   0.000      0.998 1.00 0.00
#> TCGA.EV.5903.01     1   0.000      0.998 1.00 0.00
#> TCGA.A4.A6HP.01     1   0.000      0.998 1.00 0.00
#> TCGA.BQ.5886.01     1   0.000      0.998 1.00 0.00
#> TCGA.A4.A5Y0.01     2   0.000      0.999 0.00 1.00
#> TCGA.A4.8098.01     1   0.000      0.998 1.00 0.00
#> TCGA.DW.5560.01     2   0.000      0.999 0.00 1.00
#> TCGA.A4.8310.01     1   0.000      0.998 1.00 0.00
#> TCGA.2Z.A9J8.01     2   0.000      0.999 0.00 1.00
#> TCGA.P4.A5E7.01     2   0.000      0.999 0.00 1.00
#> TCGA.2Z.A9JM.01     1   0.000      0.998 1.00 0.00
#> TCGA.2Z.A9JD.01     1   0.000      0.998 1.00 0.00
#> TCGA.SX.A71V.01     1   0.000      0.998 1.00 0.00
#> TCGA.IA.A40X.01     2   0.000      0.999 0.00 1.00
#> TCGA.5P.A9KE.01     1   0.000      0.998 1.00 0.00
#> TCGA.5P.A9KA.01     1   0.000      0.998 1.00 0.00
#> TCGA.A4.A772.01     1   0.000      0.998 1.00 0.00
#> TCGA.IA.A40U.01     1   0.000      0.998 1.00 0.00
#> TCGA.DW.7963.01     1   0.000      0.998 1.00 0.00
#> TCGA.2Z.A9JL.01     1   0.000      0.998 1.00 0.00
#> TCGA.P4.AAVM.01     1   0.000      0.998 1.00 0.00
#> TCGA.5P.A9JZ.01     2   0.000      0.999 0.00 1.00
#> TCGA.BQ.5881.01     1   0.000      0.998 1.00 0.00
#> TCGA.UZ.A9PS.01     2   0.000      0.999 0.00 1.00
#> TCGA.5P.A9K0.01     1   0.000      0.998 1.00 0.00
#> TCGA.5P.A9K6.01     1   0.000      0.998 1.00 0.00
#> TCGA.P4.A5E6.01     1   0.000      0.998 1.00 0.00
#> TCGA.BQ.5885.01     1   0.000      0.998 1.00 0.00
#> TCGA.2Z.A9JP.01     1   0.000      0.998 1.00 0.00
#> TCGA.2Z.A9JR.01     1   0.000      0.998 1.00 0.00
#> TCGA.GL.A59T.01     1   0.000      0.998 1.00 0.00
#> TCGA.B1.A47M.01     1   0.000      0.998 1.00 0.00
#> TCGA.2Z.A9JJ.01     2   0.000      0.999 0.00 1.00
#> TCGA.2Z.A9JT.01     1   0.000      0.998 1.00 0.00
#> TCGA.HE.A5NL.01     1   0.000      0.998 1.00 0.00
#> TCGA.G7.7502.01     1   0.000      0.998 1.00 0.00
#> TCGA.DW.7841.01     1   0.000      0.998 1.00 0.00
#> TCGA.BQ.7045.01     1   0.000      0.998 1.00 0.00
#> TCGA.A4.7996.01     2   0.000      0.999 0.00 1.00
#> TCGA.BQ.7046.01     1   0.000      0.998 1.00 0.00
#> TCGA.G7.7501.01     2   0.000      0.999 0.00 1.00
#> TCGA.DW.7834.01     1   0.000      0.998 1.00 0.00
#> TCGA.BQ.7060.01     1   0.000      0.998 1.00 0.00
#> TCGA.G7.6792.01     1   0.000      0.998 1.00 0.00
#> TCGA.GL.7773.01     2   0.000      0.999 0.00 1.00
#> TCGA.BQ.7053.01     2   0.000      0.999 0.00 1.00
#> TCGA.BQ.7062.01     1   0.000      0.998 1.00 0.00
#> TCGA.A4.7288.01     2   0.000      0.999 0.00 1.00
#> TCGA.A4.7286.01     1   0.000      0.998 1.00 0.00
#> TCGA.G7.6795.01     1   0.000      0.998 1.00 0.00
#> TCGA.MH.A55W.01     1   0.000      0.998 1.00 0.00
#> TCGA.G7.6790.01     1   0.000      0.998 1.00 0.00
#> TCGA.A4.7997.01     1   0.000      0.998 1.00 0.00
#> TCGA.MH.A561.01     1   0.000      0.998 1.00 0.00
#> TCGA.A4.A57E.01     2   0.000      0.999 0.00 1.00
#> TCGA.DW.7837.01     1   0.000      0.998 1.00 0.00
#> TCGA.SX.A71U.01     1   0.000      0.998 1.00 0.00
#> TCGA.BQ.7050.01     2   0.000      0.999 0.00 1.00
#> TCGA.J7.6720.01     1   0.000      0.998 1.00 0.00
#> TCGA.MH.A562.01     1   0.000      0.998 1.00 0.00
#> TCGA.A4.7584.01     1   0.000      0.998 1.00 0.00
#> TCGA.BQ.7056.01     2   0.000      0.999 0.00 1.00
#> TCGA.2Z.A9J1.01     1   0.000      0.998 1.00 0.00
#> TCGA.UN.AAZ9.01     1   0.529      0.863 0.88 0.12
#> TCGA.2Z.A9J6.01     1   0.000      0.998 1.00 0.00
#> TCGA.A4.7583.01     1   0.000      0.998 1.00 0.00
#> TCGA.2Z.A9J5.01     1   0.000      0.998 1.00 0.00

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

consensus_heatmap(res, k = 2)

plot of chunk tab-node-05-consensus-heatmap-1

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

membership_heatmap(res, k = 2)

plot of chunk tab-node-05-membership-heatmap-1

As soon as the classes for columns are determined, the signatures that are significantly different between subgroups can be looked for. Following are the heatmaps for signatures.

get_signatures(res, k = 2)

plot of chunk tab-node-05-get-signatures-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk node-05-signature_compare

get_signature() returns a data frame invisibly. To get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

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

An example of the output of tb is:

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

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows (which is done by automatically selecting number of clusters).

If there are too many signatures, top_signatures = ... can be set to only show the signatures with the highest FDRs:

# code only for demonstration
# e.g. to show the top 500 most significant rows
tb = get_signature(res, k = ..., top_signatures = 500)

If the signatures are defined as these which are uniquely high in current group, diff_method argument can be set to "uniquely_high_in_one_group":

# code only for demonstration
tb = get_signature(res, k = ..., diff_method = "uniquely_high_in_one_group")

UMAP plot which shows how samples are separated.

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

plot of chunk tab-node-05-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk node-05-collect-classes

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

Node051

Parent node: Node05. Child nodes: Node0121-leaf , Node0122-leaf , Node0123-leaf , Node0124-leaf , Node0131 , Node0132-leaf , Node0221-leaf , Node0222-leaf , Node0223-leaf , Node0311 , Node0312-leaf , Node0313-leaf , Node0321-leaf , Node0322-leaf , Node0431-leaf , Node0432-leaf , Node0433-leaf , Node0511-leaf , Node0512-leaf , Node0513-leaf , Node0521-leaf , Node0522-leaf , Node0523-leaf , Node0531-leaf , Node0532-leaf , Node0533-leaf .

The object with results only for a single top-value method and a single partitioning method can be extracted as:

res = res_rh["051"]

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, 7, 8.
#>   On a matrix with 30000 rows and 32 columns.
#>   Top rows (1000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'kmeans' method.
#>   Performed in total 350 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_partitions"     
#>  [7] "compare_signatures"      "consensus_heatmap"       "dimension_reduction"    
#> [10] "functional_enrichment"   "get_anno_col"            "get_anno"               
#> [13] "get_classes"             "get_consensus"           "get_matrix"             
#> [16] "get_membership"          "get_param"               "get_signatures"         
#> [19] "get_stats"               "is_best_k"               "is_stable_k"            
#> [22] "membership_heatmap"      "ncol"                    "nrow"                   
#> [25] "plot_ecdf"               "predict_classes"         "rownames"               
#> [28] "select_partition_number" "show"                    "suggest_best_k"         
#> [31] "test_to_known_factors"   "top_rows_heatmap"

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

collect_plots(res)

plot of chunk node-051-collect-plots

The plots are:

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:

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

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

select_partition_number(res)

plot of chunk node-051-select-partition-number

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.685           0.805       0.914         0.4623 0.583   0.583
#> 3 3 1.000           1.000       1.000         0.4182 0.698   0.508
#> 4 4 0.752           0.689       0.863         0.1301 0.883   0.672
#> 5 5 0.703           0.691       0.829         0.0725 0.903   0.644
#> 6 6 0.713           0.493       0.686         0.0355 0.909   0.609
#> 7 7 0.789           0.667       0.784         0.0388 0.940   0.688
#> 8 8 0.821           0.646       0.810         0.0208 0.944   0.659

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

suggest_best_k(res)

#> [1] 3

Following is 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 subgroup 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.

show/hide code output

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

#>                 class entropy silhouette   p1   p2
#> TCGA.IA.A83W.01     2   0.000      1.000 0.00 1.00
#> TCGA.SX.A7SR.01     1   0.000      0.862 1.00 0.00
#> TCGA.MH.A856.01     2   0.000      1.000 0.00 1.00
#> TCGA.B9.5156.01     1   0.000      0.862 1.00 0.00
#> TCGA.Y8.A897.01     1   0.000      0.862 1.00 0.00
#> TCGA.Y8.A898.01     1   0.000      0.862 1.00 0.00
#> TCGA.Y8.A8RY.01     1   0.000      0.862 1.00 0.00
#> TCGA.SX.A7SN.01     1   0.995      0.342 0.54 0.46
#> TCGA.B1.A657.01     1   0.000      0.862 1.00 0.00
#> TCGA.EV.5903.01     2   0.000      1.000 0.00 1.00
#> TCGA.A4.A6HP.01     1   0.995      0.342 0.54 0.46
#> TCGA.2Z.A9JM.01     2   0.000      1.000 0.00 1.00
#> TCGA.5P.A9KA.01     2   0.000      1.000 0.00 1.00
#> TCGA.A4.A772.01     1   0.000      0.862 1.00 0.00
#> TCGA.2Z.A9JL.01     2   0.000      1.000 0.00 1.00
#> TCGA.2Z.A9JR.01     1   0.000      0.862 1.00 0.00
#> TCGA.GL.A59T.01     1   0.000      0.862 1.00 0.00
#> TCGA.B1.A47M.01     1   0.000      0.862 1.00 0.00
#> TCGA.HE.A5NL.01     1   0.990      0.378 0.56 0.44
#> TCGA.DW.7841.01     1   0.995      0.342 0.54 0.46
#> TCGA.DW.7834.01     1   0.000      0.862 1.00 0.00
#> TCGA.G7.6792.01     2   0.000      1.000 0.00 1.00
#> TCGA.G7.6795.01     1   0.000      0.862 1.00 0.00
#> TCGA.A4.7997.01     2   0.000      1.000 0.00 1.00
#> TCGA.MH.A561.01     1   0.000      0.862 1.00 0.00
#> TCGA.DW.7837.01     1   0.995      0.342 0.54 0.46
#> TCGA.SX.A71U.01     1   0.000      0.862 1.00 0.00
#> TCGA.J7.6720.01     1   0.000      0.862 1.00 0.00
#> TCGA.MH.A562.01     1   0.000      0.862 1.00 0.00
#> TCGA.2Z.A9J1.01     2   0.000      1.000 0.00 1.00
#> TCGA.2Z.A9J6.01     1   0.995      0.342 0.54 0.46
#> TCGA.2Z.A9J5.01     1   0.000      0.862 1.00 0.00

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

consensus_heatmap(res, k = 2)

plot of chunk tab-node-051-consensus-heatmap-1

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

membership_heatmap(res, k = 2)

plot of chunk tab-node-051-membership-heatmap-1

As soon as the classes for columns are determined, the signatures that are significantly different between subgroups can be looked for. Following are the heatmaps for signatures.

get_signatures(res, k = 2)

plot of chunk tab-node-051-get-signatures-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk node-051-signature_compare

get_signature() returns a data frame invisibly. To get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

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

An example of the output of tb is:

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

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows (which is done by automatically selecting number of clusters).

If there are too many signatures, top_signatures = ... can be set to only show the signatures with the highest FDRs:

# code only for demonstration
# e.g. to show the top 500 most significant rows
tb = get_signature(res, k = ..., top_signatures = 500)

If the signatures are defined as these which are uniquely high in current group, diff_method argument can be set to "uniquely_high_in_one_group":

# code only for demonstration
tb = get_signature(res, k = ..., diff_method = "uniquely_high_in_one_group")

UMAP plot which shows how samples are separated.

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

plot of chunk tab-node-051-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk node-051-collect-classes

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

Node052

Parent node: Node05. Child nodes: Node0121-leaf , Node0122-leaf , Node0123-leaf , Node0124-leaf , Node0131 , Node0132-leaf , Node0221-leaf , Node0222-leaf , Node0223-leaf , Node0311 , Node0312-leaf , Node0313-leaf , Node0321-leaf , Node0322-leaf , Node0431-leaf , Node0432-leaf , Node0433-leaf , Node0511-leaf , Node0512-leaf , Node0513-leaf , Node0521-leaf , Node0522-leaf , Node0523-leaf , Node0531-leaf , Node0532-leaf , Node0533-leaf .

The object with results only for a single top-value method and a single partitioning method can be extracted as:

res = res_rh["052"]

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, 7, 8.
#>   On a matrix with 30000 rows and 13 columns.
#>   Top rows (1000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'skmeans' method.
#>   Performed in total 350 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_partitions"     
#>  [7] "compare_signatures"      "consensus_heatmap"       "dimension_reduction"    
#> [10] "functional_enrichment"   "get_anno_col"            "get_anno"               
#> [13] "get_classes"             "get_consensus"           "get_matrix"             
#> [16] "get_membership"          "get_param"               "get_signatures"         
#> [19] "get_stats"               "is_best_k"               "is_stable_k"            
#> [22] "membership_heatmap"      "ncol"                    "nrow"                   
#> [25] "plot_ecdf"               "predict_classes"         "rownames"               
#> [28] "select_partition_number" "show"                    "suggest_best_k"         
#> [31] "test_to_known_factors"   "top_rows_heatmap"

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

collect_plots(res)

plot of chunk node-052-collect-plots

The plots are:

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:

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

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

select_partition_number(res)

plot of chunk node-052-select-partition-number

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 1.000           1.000       1.000         0.5133 0.487   0.487
#> 3 3 1.000           0.997       0.998         0.1488 0.923   0.842
#> 4 4 1.000           0.911       0.991         0.1562 0.910   0.781
#> 5 5 0.833           0.690       0.920         0.0627 0.987   0.960
#> 6 6 0.808           0.663       0.862         0.0974 0.846   0.500
#> 7 7 0.846           0.649       0.965         0.0861 0.974   0.833
#> 8 8 0.897           0.497       0.922         0.0493 0.962   0.700

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 is 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 subgroup 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.

show/hide code output

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

#>                 class entropy silhouette p1 p2
#> TCGA.SX.A7SP.01     2       0          1  0  1
#> TCGA.Y8.A8RZ.01     1       0          1  1  0
#> TCGA.SX.A7SO.01     1       0          1  1  0
#> TCGA.A4.A5Y0.01     2       0          1  0  1
#> TCGA.2Z.A9J8.01     1       0          1  1  0
#> TCGA.IA.A40X.01     2       0          1  0  1
#> TCGA.UZ.A9PS.01     2       0          1  0  1
#> TCGA.G7.7501.01     1       0          1  1  0
#> TCGA.BQ.7053.01     2       0          1  0  1
#> TCGA.A4.7288.01     2       0          1  0  1
#> TCGA.A4.A57E.01     1       0          1  1  0
#> TCGA.BQ.7050.01     2       0          1  0  1
#> TCGA.BQ.7056.01     2       0          1  0  1

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

consensus_heatmap(res, k = 2)

plot of chunk tab-node-052-consensus-heatmap-1

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

membership_heatmap(res, k = 2)

plot of chunk tab-node-052-membership-heatmap-1

As soon as the classes for columns are determined, the signatures that are significantly different between subgroups can be looked for. Following are the heatmaps for signatures.

get_signatures(res, k = 2)

plot of chunk tab-node-052-get-signatures-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk node-052-signature_compare

get_signature() returns a data frame invisibly. To get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

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

An example of the output of tb is:

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

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows (which is done by automatically selecting number of clusters).

If there are too many signatures, top_signatures = ... can be set to only show the signatures with the highest FDRs:

# code only for demonstration
# e.g. to show the top 500 most significant rows
tb = get_signature(res, k = ..., top_signatures = 500)

If the signatures are defined as these which are uniquely high in current group, diff_method argument can be set to "uniquely_high_in_one_group":

# code only for demonstration
tb = get_signature(res, k = ..., diff_method = "uniquely_high_in_one_group")

UMAP plot which shows how samples are separated.

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

plot of chunk tab-node-052-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk node-052-collect-classes

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

Node053

Parent node: Node05. Child nodes: Node0121-leaf , Node0122-leaf , Node0123-leaf , Node0124-leaf , Node0131 , Node0132-leaf , Node0221-leaf , Node0222-leaf , Node0223-leaf , Node0311 , Node0312-leaf , Node0313-leaf , Node0321-leaf , Node0322-leaf , Node0431-leaf , Node0432-leaf , Node0433-leaf , Node0511-leaf , Node0512-leaf , Node0513-leaf , Node0521-leaf , Node0522-leaf , Node0523-leaf , Node0531-leaf , Node0532-leaf , Node0533-leaf .

The object with results only for a single top-value method and a single partitioning method can be extracted as:

res = res_rh["053"]

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, 7, 8.
#>   On a matrix with 30000 rows and 32 columns.
#>   Top rows (1000) are extracted by 'ATC' method.
#>   Subgroups are detected by 'kmeans' method.
#>   Performed in total 350 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_partitions"     
#>  [7] "compare_signatures"      "consensus_heatmap"       "dimension_reduction"    
#> [10] "functional_enrichment"   "get_anno_col"            "get_anno"               
#> [13] "get_classes"             "get_consensus"           "get_matrix"             
#> [16] "get_membership"          "get_param"               "get_signatures"         
#> [19] "get_stats"               "is_best_k"               "is_stable_k"            
#> [22] "membership_heatmap"      "ncol"                    "nrow"                   
#> [25] "plot_ecdf"               "predict_classes"         "rownames"               
#> [28] "select_partition_number" "show"                    "suggest_best_k"         
#> [31] "test_to_known_factors"   "top_rows_heatmap"

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

collect_plots(res)

plot of chunk node-053-collect-plots

The plots are:

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:

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

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

select_partition_number(res)

plot of chunk node-053-select-partition-number

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

get_stats(res)

#>   k 1-PAC mean_silhouette concordance area_increased  Rand Jaccard
#> 2 2 0.557           0.920       0.931         0.4560 0.492   0.492
#> 3 3 1.000           1.000       1.000         0.3228 0.865   0.736
#> 4 4 0.743           0.562       0.807         0.1600 0.915   0.787
#> 5 5 0.715           0.697       0.721         0.0997 0.847   0.558
#> 6 6 0.724           0.828       0.853         0.0663 0.909   0.628
#> 7 7 0.687           0.789       0.811         0.0164 1.000   1.000
#> 8 8 0.844           0.725       0.781         0.0451 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] 3

Following is 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 subgroup 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.

show/hide code output

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

#>                 class entropy silhouette   p1   p2
#> TCGA.G7.A8LC.01     2   0.000      0.823 0.00 1.00
#> TCGA.IZ.A6M8.01     1   0.000      0.993 1.00 0.00
#> TCGA.A4.A5XZ.01     2   0.990      0.476 0.44 0.56
#> TCGA.A4.8517.01     1   0.000      0.993 1.00 0.00
#> TCGA.BQ.5886.01     1   0.000      0.993 1.00 0.00
#> TCGA.A4.8098.01     2   0.000      0.823 0.00 1.00
#> TCGA.A4.8310.01     2   0.722      0.887 0.20 0.80
#> TCGA.2Z.A9JD.01     1   0.000      0.993 1.00 0.00
#> TCGA.SX.A71V.01     2   0.722      0.887 0.20 0.80
#> TCGA.5P.A9KE.01     1   0.000      0.993 1.00 0.00
#> TCGA.IA.A40U.01     2   0.402      0.854 0.08 0.92
#> TCGA.DW.7963.01     1   0.000      0.993 1.00 0.00
#> TCGA.P4.AAVM.01     1   0.000      0.993 1.00 0.00
#> TCGA.BQ.5881.01     1   0.000      0.993 1.00 0.00
#> TCGA.5P.A9K0.01     1   0.000      0.993 1.00 0.00
#> TCGA.5P.A9K6.01     1   0.000      0.993 1.00 0.00
#> TCGA.P4.A5E6.01     1   0.469      0.859 0.90 0.10
#> TCGA.BQ.5885.01     2   0.722      0.887 0.20 0.80
#> TCGA.2Z.A9JP.01     1   0.000      0.993 1.00 0.00
#> TCGA.2Z.A9JT.01     1   0.000      0.993 1.00 0.00
#> TCGA.G7.7502.01     2   0.722      0.887 0.20 0.80
#> TCGA.BQ.7045.01     1   0.000      0.993 1.00 0.00
#> TCGA.A4.7996.01     2   0.722      0.887 0.20 0.80
#> TCGA.BQ.7046.01     1   0.000      0.993 1.00 0.00
#> TCGA.BQ.7060.01     1   0.000      0.993 1.00 0.00
#> TCGA.BQ.7062.01     2   0.722      0.887 0.20 0.80
#> TCGA.A4.7286.01     2   0.722      0.887 0.20 0.80
#> TCGA.MH.A55W.01     2   0.722      0.887 0.20 0.80
#> TCGA.G7.6790.01     1   0.000      0.993 1.00 0.00
#> TCGA.A4.7584.01     1   0.000      0.993 1.00 0.00
#> TCGA.UN.AAZ9.01     2   0.000      0.823 0.00 1.00
#> TCGA.A4.7583.01     2   0.000      0.823 0.00 1.00

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

consensus_heatmap(res, k = 2)

plot of chunk tab-node-053-consensus-heatmap-1

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

membership_heatmap(res, k = 2)

plot of chunk tab-node-053-membership-heatmap-1

As soon as the classes for columns are determined, the signatures that are significantly different between subgroups can be looked for. Following are the heatmaps for signatures.

get_signatures(res, k = 2)

plot of chunk tab-node-053-get-signatures-1

Compare the overlap of signatures from different k:

compare_signatures(res)

plot of chunk node-053-signature_compare

get_signature() returns a data frame invisibly. To get the list of signatures, the function call should be assigned to a variable explicitly. In following code, if plot argument is set to FALSE, no heatmap is plotted while only the differential analysis is performed.

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

An example of the output of tb is:

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

The columns in tb are:

  1. which_row: row indices corresponding to the input matrix.
  2. fdr: FDR for the differential test.
  3. mean_x: The mean value in group x.
  4. scaled_mean_x: The mean value in group x after rows are scaled.
  5. km: Row groups if k-means clustering is applied to rows (which is done by automatically selecting number of clusters).

If there are too many signatures, top_signatures = ... can be set to only show the signatures with the highest FDRs:

# code only for demonstration
# e.g. to show the top 500 most significant rows
tb = get_signature(res, k = ..., top_signatures = 500)

If the signatures are defined as these which are uniquely high in current group, diff_method argument can be set to "uniquely_high_in_one_group":

# code only for demonstration
tb = get_signature(res, k = ..., diff_method = "uniquely_high_in_one_group")

UMAP plot which shows how samples are separated.

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

plot of chunk tab-node-053-dimension-reduction-1

Following heatmap shows how subgroups are split when increasing k:

collect_classes(res)

plot of chunk node-053-collect-classes

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

Session info

sessionInfo()

#> R version 4.1.0 (2021-05-18)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: CentOS Linux 7 (Core)
#> 
#> Matrix products: default
#> BLAS/LAPACK: /usr/lib64/libopenblas-r0.3.3.so
#> 
#> locale:
#>  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C               LC_TIME=en_US.UTF-8       
#>  [4] LC_COLLATE=en_US.UTF-8     LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
#>  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                  LC_ADDRESS=C              
#> [10] LC_TELEPHONE=C             LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
#> 
#> attached base packages:
#> [1] grid      stats     graphics  grDevices utils     datasets  methods   base     
#> 
#> other attached packages:
#> [1] genefilter_1.74.0    ComplexHeatmap_2.8.0 markdown_1.1         knitr_1.33          
#> [5] matrixStats_0.59.0   cola_1.9.4          
#> 
#> loaded via a namespace (and not attached):
#>   [1] bitops_1.0-7           bit64_4.0.5            doParallel_1.0.16      RColorBrewer_1.1-2    
#>   [5] httr_1.4.2             GenomeInfoDb_1.28.1    data.tree_1.0.0        tools_4.1.0           
#>   [9] utf8_1.2.1             R6_2.5.0               irlba_2.3.3            DBI_1.1.1             
#>  [13] BiocGenerics_0.38.0    colorspace_2.0-2       GetoptLong_1.0.5       gridExtra_2.3         
#>  [17] tidyselect_1.1.1       bit_4.0.4              compiler_4.1.0         Biobase_2.52.0        
#>  [21] Cairo_1.5-12.2         xml2_1.3.2             microbenchmark_1.4-7   slam_0.1-48           
#>  [25] scales_1.1.1           askpass_1.1            stringr_1.4.0          digest_0.6.27         
#>  [29] XVector_0.32.0         pkgconfig_2.0.3        umap_0.2.7.0           fastmap_1.1.0         
#>  [33] highr_0.9              rlang_0.4.11           GlobalOptions_0.1.2    rstudioapi_0.13       
#>  [37] RSQLite_2.2.7          impute_1.66.0          generics_0.1.0         shape_1.4.6           
#>  [41] jsonlite_1.7.2         mclust_5.4.7           dplyr_1.0.7            dendextend_1.15.1     
#>  [45] RCurl_1.98-1.3         magrittr_2.0.1         GenomeInfoDbData_1.2.6 Matrix_1.3-4          
#>  [49] fansi_0.5.0            Rcpp_1.0.7             munsell_0.5.0          S4Vectors_0.30.0      
#>  [53] viridis_0.6.1          reticulate_1.20        lifecycle_1.0.0        scatterplot3d_0.3-41  
#>  [57] stringi_1.7.3          zlibbioc_1.38.0        blob_1.2.1             parallel_4.1.0        
#>  [61] crayon_1.4.1           lattice_0.20-44        Biostrings_2.60.1      splines_4.1.0         
#>  [65] annotate_1.70.0        circlize_0.4.13        KEGGREST_1.32.0        polylabelr_0.2.0      
#>  [69] pillar_1.6.1           rjson_0.2.20           codetools_0.2-18       stats4_4.1.0          
#>  [73] XML_3.99-0.6           glue_1.4.2             evaluate_0.14          png_0.1-7             
#>  [77] vctrs_0.3.8            foreach_1.5.1          polyclip_1.10-0        purrr_0.3.4           
#>  [81] gtable_0.3.0           openssl_1.4.4          assertthat_0.2.1       clue_0.3-59           
#>  [85] cachem_1.0.5           ggplot2_3.3.5          xfun_0.24              eulerr_6.1.0          
#>  [89] xtable_1.8-4           skmeans_0.2-13         RSpectra_0.16-0        viridisLite_0.4.0     
#>  [93] survival_3.2-11        tibble_3.1.2           Polychrome_1.3.1       iterators_1.0.13      
#>  [97] AnnotationDbi_1.54.1   memoise_2.0.0          IRanges_2.26.0         cluster_2.1.2         
#> [101] ellipsis_0.3.2         brew_1.0-6