#' Uncorrelated Worst-Case Discriminative Feature Selection
#'
#' Built upon \code{do.wdfs}, this method selects features step-by-step to opt out the redundant sets
#' by iteratively update feature scores via scaling by the correlation between target and previously chosen variables.
#'
#' @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 preprocess an additional option for preprocessing the data.
#' Default is "null". See also \code{\link{aux.preprocess}} for more details.
#'
#' @return a named list 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{trfinfo}{a list containing information for out-of-sample prediction.}
#' \item{projection}{a \eqn{(p\times ndim)} whose columns are basis for projection.}
#' }
#'
#' @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 with other algorithms
#' out1 = do.lda(iris.dat, iris.lab)
#' out2 = do.wdfs(iris.dat, iris.lab)
#' out3 = do.uwdfs(iris.dat, iris.lab)
#'
#' ## visualize
#' opar <- par(no.readonly=TRUE)
#' par(mfrow=c(1,3))
#' plot(out1$Y, pch=19, col=iris.lab, main="LDA")
#' plot(out2$Y, pch=19, col=iris.lab, main="WDFS")
#' plot(out3$Y, pch=19, col=iris.lab, main="UWDFS")
#' par(opar)
#' }
#'
#' @references
#' \insertRef{liao_worstcase_2019}{Rdimtools}
#'
#'
#' @seealso \code{\link{do.wdfs}}
#' @rdname feature_UWDFS
#' @author Kisung You
#' @concept feature_methods
#' @export
do.uwdfs <- function(X, label, ndim=2, preprocess=c("null","center","scale","cscale","decorrelate","whiten")){
#------------------------------------------------------------------------
## PREPROCESSING
# 1. data matrix
aux.typecheck(X)
n = nrow(X)
p = ncol(X)
# 2. label vector
label = check_label(label, n)
ulabel = unique(label)
C = length(ulabel)
if (C==1){
stop("* do.uwdfs : 'label' should have at least 2 unique labelings.")
}
if (C==n){
stop("* do.uwdfs : given 'label' has all unique elements.")
}
if (any(is.na(label))||(any(is.infinite(label)))){
stop("* Supervised Learning : any element of 'label' as NA or Inf will simply be considered as a class, not missing entries.")
}
# 3. ndim
ndim = as.integer(ndim)
if (!check_ndim(ndim,p)){
stop("* do.uwdfs : 'ndim' is a positive integer in [1,#(covariates)].")
}
# 4. preprocess
if (missing(preprocess)){
algpreprocess = "null"
} else {
algpreprocess = match.arg(preprocess)
}
#------------------------------------------------------------------------
## COMPUTATION : PREPROCESSING OF THE DATA
tmplist = (X,type=algpreprocess,algtype="linear")
trfinfo = tmplist$info
pX = tmplist$pX
#------------------------------------------------------------------------
## COMPUTATION : main part from WDFS
# 1. class-mean and within-class scatter
prepBC <- array(0,c(C,p))
prepWC <- array(0,c(p,p,C))
for (i in 1:C){
idi = which(label==i)
idn = length(idi)
if (idn>1){
prepBC[i,] = as.vector(base::colMeans(pX[idi,]))
} else {
prepBC[i,] = as.vector(pX[idi,])
}
prepWC[,,i] = stats::cov(pX[idi,])*(idn-1)/idn
}
# 2. compute scores
wscore = rep(0,p)
for (i in 1:p){
wrvec = rep(0,p); wrvec[i] = 1
wscore[i] = WDFS.score(wrvec, prepBC, prepWC)
}
#------------------------------------------------------------------------
## COMPUTATION : iterative update
id.chosen = c()
id.left = (1:p)
vec.score = wscore
# main iteration
for (i in 1:ndim){
# select the one with the largest
posmax = which.max(vec.score)
idmax = id.left[posmax]
fmax = as.vector(pX[,idmax])
# update indices
id.chosen = c(id.chosen, idmax)
id.left = id.left[-posmax]
vec.score = vec.score[-posmax]
# update scores : we only use Pearson
for (j in 1:length(vec.score)){
fj = pX[,id.left[j]]
vec.score[j] = (1-base::abs(stats::cor(x=fmax, y=fj)))*vec.score[j]
}
}
# convert to conventional format and compute projection
idxvec = id.chosen
projection = aux.featureindicator(p,ndim,idxvec)
#------------------------------------------------------------------------
## RETURN
result = list()
result$Y = pX%*%projection
result$featidx = idxvec
result$trfinfo = trfinfo
result$projection = projection
return(result)
}
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