R/TuckerCongruence.R

In syuanuvt/CSSCA: ClusterSSCA: Cluster-wise Simultaneous Component Analysis

#' Calculate the Tucker Congruence of two matrices which allow for rotation freedom.
#' Note that the factor.congruence in the "psych" package would not allow for rotation freedom
#'
#' @param matrix1 the first matrix
#' @param matrix2 the second matrix
#' @return the congruence between the two matrices which is in theory
#' the maximum possible congruence taking into account all possible rotations
#' @examples
#'
TuckerCongruence <- function(matrix1, matrix2){
  ## note that two matrices should be in the same size
  # matrix1: reference matrix
  # matrix2: matrix to compare to the reference

  m <- nrow(matrix1)
  n <- ncol(matrix2)

  indic_perms <- permn(1:n)
  tuck <- vector("numeric")
  for (i in 1:length(indic_perms)){
    matrix2_perm <- matrix2[ ,indic_perms[[i]]]
    tuck[i] <- tr(abs(factor.congruence(matrix1, matrix2_perm))) / n
  }

  tuck_max <- max(tuck)
  return (tuck_max)
}