reduced_mutual_information: Reduced Mutual Information
In clustAnalytics: Cluster Evaluation on Graphs

View source: R/corrected_mutual_information.R

reduced_mutual_information

R Documentation

Reduced Mutual Information

Description

Computes the Newman's Reduced Mutual Information (RMI) as defined in \insertCitecorrected_MI_Newman2020clustAnalytics.

Usage

reduced_mutual_information(
  c1,
  c2,
  base = 2,
  normalized = FALSE,
  method = "approximation2",
  warning = TRUE
)

Arguments

`c1`, `c2`	membership vectors
`base`	base of the logarithms used in the calculations. Changing it only scales the final value. By default set to e=exp(1).
`normalized`	If true, computes the normalized version of the corrected mutual information.
`method`	Can be "hybrid" (default, combines Monte Carlo with analytical formula), "monte_carlo", approximation1" (appropriate for partitions into many very small clusters), or "approximation2" (for partitions into few larger clusters).
`warning`	set to false to ignore the warning.

Details

The implementation is based on equations 23 (25 for the normalized case) and 29 in \insertCitecorrected_MI_Newman2020clustAnalytics. The evaluations of the \Gamma functions can get too large and cause overflow issues in the intermediate steps, so the following term of equation 29:

\frac{1}{2} \log \frac{\Gamma(\mu R) \Gamma(\nu S)} {(\Gamma(\nu)\Gamma(R))^S (\Gamma(\mu)\Gamma(S))^R }

is rewritten as

\frac{1}{2} (\log\Gamma(\mu R) + \log\Gamma(\nu S) - S\log(\Gamma(\nu) - S\log(\Gamma(R) - R\log\Gamma(\mu) - R\log\Gamma(R) )

, and then the function lgamma is used instead of gamma.