R/linear_MMC.R

In kisungyou/Rdimtools: Dimension Reduction and Estimation Methods

#' Maximum Margin Criterion
#'
#' Maximum Margin Criterion (MMC) is a linear supervised dimension reduction method that
#' maximizes average margin between classes. The cost function is defined as
#' \deqn{trace(S_b - S_w)}
#' where \eqn{S_b} is an overall variance of class mean vectors, and \eqn{S_w} refers to
#' spread of every class. Note that Principal Component Analysis (PCA) maximizes
#' total scatter, \eqn{S_t = S_b + S_w}.
#'
#'
#' @param X an \eqn{(n\times p)} matrix 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.
#'
#' @return a named \code{Rdimtools} S3 object containing
#' \describe{
#' \item{Y}{an \eqn{(n\times ndim)} matrix whose rows are embedded observations.}
#' \item{projection}{a \eqn{(p\times ndim)} whose columns are basis for projection.}
#' \item{algorithm}{name of the algorithm.}
#' }
#'
#' @examples
#' \donttest{
#' ## use iris data
#' data(iris, package="Rdimtools")
#' subid = sample(1:150, 50)
#' X     = as.matrix(iris[subid,1:4])
#' label = as.factor(iris[subid,5])
#'
#' ## compare MMC with other methods
#' outMMC = do.mmc(X, label)
#' outMVP = do.mvp(X, label)
#' outPCA = do.pca(X)
#'
#' ## visualize
#' opar <- par(no.readonly=TRUE)
#' par(mfrow=c(1,3))
#' plot(outMMC$Y, pch=19, col=label, main="MMC")
#' plot(outMVP$Y, pch=19, col=label, main="MVP")
#' plot(outPCA$Y, pch=19, col=label, main="PCA")
#' par(opar)
#' }
#'
#' @references
#' \insertRef{li_efficient_2006}{Rdimtools}
#'
#' @author Kisung You
#' @rdname linear_MMC
#' @concept linear_methods
#' @export
do.mmc <- function(X, label, ndim=2){
  #------------------------------------------------------------------------
  ## PREPROCESSING
  #   1. data matrix
  aux.typecheck(X)
  n = nrow(X)
  p = ncol(X)
  #   2. label : check and return a de-factored vector
  #   For this example, there should be no degenerate class of size 1.
  label  = check_label(label, n)
  ulabel = unique(label)
  for (i in 1:length(ulabel)){
    if (sum(label==ulabel[i])==1){
      stop("* do.mmc : no degerate class of size 1 is allowed.")
    }
  }
  N = length(ulabel)
  if (any(is.na(label))||(any(is.infinite(label)))){
    stop("* Supervised Learning : any element of 'label' as NA or Inf will simply be considered as a class, not missing entries.")
  }
  #   3. ndim
  ndim = as.integer(ndim)
  if (!check_ndim(ndim,p)){stop("* do.mmc : 'ndim' is a positive integer in [1,#(covariates)).")}
  # #   4. preprocess
  # if (missing(preprocess)){
  #   algpreprocess = "center"
  # } else {
  #   algpreprocess = match.arg(preprocess)
  # }
  #------------------------------------------------------------------------
  ## COMPUTATION : PRELIMINARY
  # #   1. preprocess of data
  # tmplist = aux.preprocess.hidden(X,type=algpreprocess,algtype="linear")
  # trfinfo = tmplist$info
  # pX      = tmplist$pX

  #   2. vector of proportion : pi
  nlabel = length(ulabel) # number of classes
  proportion = rep(0,nlabel)
  for (i in 1:nlabel){
    proportion[i] = (length(which(label==ulabel[i]))/n)
  }
  #   3. per-class and overall : mean vectors
  mean_PerClass = array(0,c(nlabel,p))
  for (i in 1:nlabel){
    idxlabel = which(label==ulabel[i])
    mean_PerClass[i,] = as.vector(colMeans(X[idxlabel,]) )
  }
  mean_Overall = as.vector(colMeans(X))
  #   4. per-class and overall : scatter
  scatter_PerClass = list()
  for (i in 1:nlabel){
    idxlabel = which(label==ulabel[i])
    scatter_PerClass[[i]] = mmc_scatter(X[idxlabel,])
  }
  #   5. compute Sw
  Sw = array(0,c(p,p))
  for (i in 1:nlabel){
    Sw = Sw + ((proportion[i])*(scatter_PerClass[[i]]))
  }
  #   6. compute Sb
  Sb = array(0,c(p,p))
  for (i in 1:nlabel){
    vecdiff = as.vector(mean_PerClass[i,])-as.vector(mean_Overall)
    Sb = Sb + ((proportion[i])*outer(vecdiff,vecdiff))
  }
  #------------------------------------------------------------------------
  ## COMPUTATION : MAIN COMPUTATION
  costS = Sb-Sw
  projection = aux.adjprojection(RSpectra::eigs(costS, ndim)$vectors)

  #------------------------------------------------------------------------
  ## RETURN THE RESULTS
  result = list()
  result$Y = X%*%projection
  result$projection = projection
  result$algorithm  = "linear:MMC"
  return(structure(result, class="Rdimtools"))
}


#  ------------------------------------------------------------------------
#' @keywords internal
#' @noRd
mmc_scatter <- function(tgtmat){
  N      = nrow(tgtmat)
  onesN  = rep(1,N)
  Cn     = diag(N)-(outer(onesN,onesN)/N)
  output = t(tgtmat)%*%Cn%*%tgtmat
  return(output)
}