partition

partition is a fast and flexible framework for agglomerative partitioning. partition uses an approach called Direct-Measure-Reduce to create new variables that maintain the user-specified minimum level of information. Each reduced variable is also interpretable: the original variables map to one and only one variable in the reduced data set. partition is flexible, as well: how variables are selected to reduce, how information loss is measured, and the way data is reduced can all be customized.

Installation

You can install the development version of partition2 GitHub with:

# install.packages("remotes)
remotes::install_github("USCbiostats/partition")

Example

library(partition)
set.seed(1234)
df <- simulate_block_data(c(3, 4, 5), lower_corr = .4, upper_corr = .6, n = 100)

#  don't accept reductions where information < .6
prt <- partition(df, threshold = .6)
prt
#> Partitioner:
#>    Director: Minimum Distance (Pearson) 
#>    Metric: Intraclass Correlation 
#>    Reducer: Scaled Mean
#> 
#> Reduced Variables:
#> 1 reduced variables created from 2 observed variables
#> 
#> Mappings:
#> reduced_var_1 = {block2_x3, block2_x4}
#> 
#> Minimum information:
#> 0.602

# return reduced data
partition_scores(prt)
#> # A tibble: 100 x 11
#>    block1_x1 block1_x2 block1_x3 block2_x1 block2_x2 block3_x1 block3_x2
#>        <dbl>     <dbl>     <dbl>     <dbl>     <dbl>     <dbl>     <dbl>
#>  1   -1.00     -0.344      1.35     -0.526    -1.25      1.13     0.357 
#>  2    0.518    -0.434     -0.361    -1.48     -1.53     -0.317    0.290 
#>  3   -1.77     -0.913     -0.722     0.122     0.224    -0.529    0.114 
#>  4   -1.49     -0.998      0.189     0.149    -0.994    -0.433    0.0120
#>  5    0.616     0.0211     0.895     1.09     -1.25      0.440   -0.550 
#>  6    0.0765    0.522      1.20     -0.152    -0.419    -0.912   -0.362 
#>  7    1.74      0.0993    -0.654    -1.26     -0.502    -0.792   -1.03  
#>  8    1.05      2.19       0.913     0.254     0.328    -1.07    -0.976 
#>  9   -1.07     -0.292     -0.763     0.437     0.739     0.899   -0.342 
#> 10   -1.02     -0.959     -1.33     -1.57     -1.11      0.618    0.153 
#> # … with 90 more rows, and 4 more variables: block3_x3 <dbl>,
#> #   block3_x4 <dbl>, block3_x5 <dbl>, reduced_var_1 <dbl>

# access mapping keys
mapping_key(prt)
#> # A tibble: 11 x 4
#>    variable      mapping   information indices  
#>    <chr>         <list>          <dbl> <list>   
#>  1 block1_x1     <chr [1]>       1     <int [1]>
#>  2 block1_x2     <chr [1]>       1     <int [1]>
#>  3 block1_x3     <chr [1]>       1     <int [1]>
#>  4 block2_x1     <chr [1]>       1     <int [1]>
#>  5 block2_x2     <chr [1]>       1     <int [1]>
#>  6 block3_x1     <chr [1]>       1     <int [1]>
#>  7 block3_x2     <chr [1]>       1     <int [1]>
#>  8 block3_x3     <chr [1]>       1     <int [1]>
#>  9 block3_x4     <chr [1]>       1     <int [1]>
#> 10 block3_x5     <chr [1]>       1     <int [1]>
#> 11 reduced_var_1 <chr [2]>       0.602 <int [2]>

unnest_mappings(prt)
#> # A tibble: 12 x 4
#>    variable      information mapping   indices
#>    <chr>               <dbl> <chr>       <int>
#>  1 block1_x1           1     block1_x1       1
#>  2 block1_x2           1     block1_x2       2
#>  3 block1_x3           1     block1_x3       3
#>  4 block2_x1           1     block2_x1       4
#>  5 block2_x2           1     block2_x2       5
#>  6 block3_x1           1     block3_x1       8
#>  7 block3_x2           1     block3_x2       9
#>  8 block3_x3           1     block3_x3      10
#>  9 block3_x4           1     block3_x4      11
#> 10 block3_x5           1     block3_x5      12
#> 11 reduced_var_1       0.602 block2_x3       6
#> 12 reduced_var_1       0.602 block2_x4       7

# use a lower threshold of information loss
partition(df, threshold = .5, partitioner = part_kmeans())
#> Partitioner:
#>    Director: K-Means Clusters 
#>    Metric: Minimum Intraclass Correlation 
#>    Reducer: Scaled Mean
#> 
#> Reduced Variables:
#> 2 reduced variables created from 7 observed variables
#> 
#> Mappings:
#> reduced_var_1 = {block3_x1, block3_x2, block3_x5}
#> reduced_var_2 = {block2_x1, block2_x2, block2_x3, block2_x4}
#> 
#> Minimum information:
#> 0.508

# use a custom partitioner
part_icc_rowmeans <- replace_partitioner(
  part_icc, 
  reduce = as_reducer(rowMeans)
)
partition(df, threshold = .6, partitioner = part_icc_rowmeans) 
#> Partitioner:
#>    Director: Minimum Distance (Pearson) 
#>    Metric: Intraclass Correlation 
#>    Reducer: <custom reducer>
#> 
#> Reduced Variables:
#> 1 reduced variables created from 2 observed variables
#> 
#> Mappings:
#> reduced_var_1 = {block2_x3, block2_x4}
#> 
#> Minimum information:
#> 0.602

partition also supports a number of ways to visualize partitions and permutation tests; these functions all start with plot_*(). These functions all return ggplots and can thus be extended using ggplot2.

plot_stacked_area_clusters(df) +
  ggplot2::theme_minimal(14)