R/degenScore.R

In CMTFtoolbox: Create (Advanced) Coupled Matrix and Tensor Factorization Models

#' degenScore
#'
#' Computes the maximum absolute off-diagonal Tucker congruence coefficient
#' between subject-mode components in an ACMTF model. This metric serves as a
#' diagnostic tool to detect potential degeneracy in the subject-mode loadings.
#'
#' A high \code{degenScore} (e.g., > 0.85) indicates that two or more components
#' in the subject mode are highly similar, suggesting a possible degeneracy or
#' lack of uniqueness. A low value (e.g., < 0.3) indicates well-separated components.
#'
#' @param A A numeric matrix of subject-mode loadings (dimensions: subjects x components).
#'
#' @return A numeric scalar representing the maximum absolute off-diagonal
#' Tucker congruence between components.
#'
#' @examples
#' # Example: Compute degenScore for a random loading matrix
#' A <- matrix(rnorm(100), nrow = 10, ncol = 10)
#' degenScore(A)
#'
#' @export
degenScore = function(A){
  d = ncol(A)
  M = matrix(0L, nrow=d, ncol=d)

  for(i in 1:d){
    for(j in 1:d){
      M[i,j] = multiway::congru(A[,i],A[,j])
    }
  }
  return(max(abs(M-diag(d))))
}