Maximum information preservable by hierarchical lumping

Calculates the maximum amount of mutual information that can be preserved by lumping a nominal variable inherited from a hierarchy.

Usage

maximum_mutual_information_hierarchical(
  counts,
  threshold,
  clusters,
  verbose = FALSE,
  alternative_metric = c("mutual information", "bin count", "surplus")
)

Arguments

counts: Named numeric vector containing the number of times each level is observed.
threshold: Minimum number of samples each level must contain.
clusters: List of character vectors, each vector is the names of the levels that can be grouped together.
verbose: Whether to print diagnostic messages or not. Default: FALSE
alternative_metric: The metric that should be optimised for, if it is different from the default, the mutual information. For an explanation of the metrics see vignette("metrics").

Value

A list containing information about the optimal lumping:

mutual_information: Double representing the mutual information between the lumped and unlumped variable.
loss: Double representing the amount of entropy lost in the lumping process.
lumping: A list of character vectors, where each vector contains the names of the original levels that have been lumped together.

Details

This acts as a wrapper around maximum_mutual_information_nominal(). By passing the hierarchical structure via the clusters argument, the algorithm divides the problem into independent sub-problems, speeding up the execution time for large datasets.

Author

Daan Koning

Examples

maximum_mutual_information_hierarchical(
     c(A = 1, B = 1, C = 2, D = 4, E = 2, F = 2),
     4,
     list(c("A", "B", "C"), c("D", "E", "F"))
)
#> $mutual_information
#> [1] 1.098612
#> 
#> $loss
#> [1] 0.5776227
#> 
#> $lumping
#> $lumping[[1]]
#> [1] "A" "B" "C"
#> 
#> $lumping[[2]]
#> [1] "E" "F"
#> 
#> $lumping[[3]]
#> [1] "D"
#> 
#>