R/v1_feature_FSCORE.R

In Rdimtools: Dimension Reduction and Estimation Methods

#' Fisher Score
#'
#' Fisher Score \insertCite{fisher_use_1936}{Rdimtools} is a supervised linear feature extraction method. For each
#' feature/variable, it computes Fisher score, a ratio of between-class variance to within-class variance.
#' The algorithm selects variables with largest Fisher scores and returns an indicator projection matrix.
#'
#' @param X an \eqn{(n\times p)} matrix or data frame whose rows are observations
#' and columns represent independent variables.
#' @param label a length-\eqn{n} vector of data class labels.
#' @param ndim an integer-valued target dimension.
#' @param ... extra parameters including \describe{
#' \item{preprocess}{an additional option for preprocessing the data.
#' Default is \code{"null"}. See also \code{\link{aux.preprocess}} for more details.}
#' }
#'
#' @return a named \code{Rdimtools} S3 object containing
#' \describe{
#' \item{Y}{an \eqn{(n\times ndim)} matrix whose rows are embedded observations.}
#' \item{featidx}{a length-\eqn{ndim} vector of indices with highest scores.}
#' \item{projection}{a \eqn{(p\times ndim)} whose columns are basis for projection.}
#' \item{trfinfo}{a list containing information for out-of-sample prediction.}
#' \item{algorithm}{name of the algorithm.}
#' }
#'
#' @examples
#' \donttest{
#' ## use iris data
#' ## it is known that feature 3 and 4 are more important.
#' data(iris)
#' set.seed(100)
#' subid    = sample(1:150,50)
#' iris.dat = as.matrix(iris[subid,1:4])
#' iris.lab = as.factor(iris[subid,5])
#'
#' ## compare Fisher score with LDA
#' out1 = do.lda(iris.dat, iris.lab)
#' out2 = do.fscore(iris.dat, iris.lab)
#'
#' ## visualize
#' opar <- par(no.readonly=TRUE)
#' par(mfrow=c(1,2))
#' plot(out1$Y, pch=19, col=iris.lab, main="LDA")
#' plot(out2$Y, pch=19, col=iris.lab, main="Fisher Score")
#' par(opar)
#' }
#'
#' @references
#' \insertAllCited{}
#'
#' @rdname feature_FSCORE
#' @concept feature_methods
#' @export
do.fscore <- function(X, label, ndim=2, ...){
  #------------------------------------------------------------------------
  ## PREPROCESSING
  #   1. data matrix
  aux.typecheck(X)
  n = nrow(X)
  p = ncol(X)
  #   2. label vector
  label  = check_label(label, n)
  ulabel = unique(label)
  C      = length(ulabel)
  if (C==1){
    stop("* do.fscore : 'label' should have at least 2 unique labelings.")
  }
  if (C==n){
    stop("* do.fscore : given 'label' has all unique elements.")
  }
  if (any(is.na(label))||(any(is.infinite(label)))){
    stop("* Supervised Learning : any element of 'label' as NA or Inf will simply be considered as a class, not missing entries.")
  }
  #   3. ndim
  ndim = as.integer(ndim)
  if (!check_ndim(ndim,p)){
    stop("* do.fscore : 'ndim' is a positive integer in [1,#(covariates)].")
  }

  #------------------------------------------------------------------------
  ## PREPROCESSING
  #   check
  params = list(...)
  pnames = names(params)
  if ("preprocess"%in%pnames){
    par_preprocess = tolower(params$preprocess)
  } else {
    par_preprocess = "null"
  }
  #   transform
  tmplist = aux.preprocess.hidden(X, type=par_preprocess, algtype="linear")
  trfinfo = tmplist$info
  pX      = tmplist$pX

  #------------------------------------------------------------------------
  ## COMPUTATION : MAIN COMPUTATION FOR LSDF
  #   1. compute Fisher score for each feature
  fscore = rep(0,p)
  for (i in 1:p){
    vecfr     = as.vector(pX[,i])
    fscore[i] = fscore_single(vecfr, label, ulabel, C)
  }
  #   2. select the largest ones
  idxvec = base::order(fscore, decreasing=TRUE)[1:ndim]
  #   3. find the projection matrix
  projection = aux.featureindicator(p,ndim,idxvec)

  #------------------------------------------------------------------------
  ## RETURN
  result = list()
  result$Y = pX%*%projection
  result$featidx = idxvec
  result$projection = projection
  result$algorithm = "linear:FSCORE"
  result$trfinfo   = trfinfo
  return(structure(result, class="Rdimtools"))
}





#  ------------------------------------------------------------------------
#' @keywords internal
#' @noRd
fscore_single <- function(vec, label, ulabel, C){
  if (length(vec)!=length(label)){
    stop("* fscore_single : vec and label.")
  }
  if (length(ulabel)!=C){
    stop("* fscore_single : ulabel and C.")
  }

  # 1. compute overall values
  all_mean = mean(vec)
  all_var  = var(vec)

  # 2. class-wise information
  term1 = 0.0 # numerator
  term2 = 0.0 # denominator
  for (i in 1:C){
    idxc = which(label==ulabel[i])
    vecc = vec[idxc]
    ni   = length(idxc)

    term1 = term1 + ni*((mean(vecc)-all_mean)^2)
    term2 = term2 + ni*(var(vecc))
  }
  output = term1/term2
  return(output)
}