#' 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$preprocess)
} else {
par_preprocess = "null"
}
# transform
tmplist = (X, type=par_preprocess, algtype="linear")
trfinfo = tmplist$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)
}
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