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#' Extended Supervised Locality Preserving Projection
#'
#' Extended LPP and Supervised LPP are two variants of the celebrated Locality Preserving Projection (LPP) algorithm for dimension
#' reduction. Their combination, Extended Supervised LPP, is a combination of two algorithmic novelties in one that
#' it reflects discriminant information with realistic distance measure via Z-score function.
#'
#' @param X an \eqn{(n\times p)} matrix or data frame whose rows are observations.
#' @param label a length-\eqn{n} vector of data class labels.
#' @param ndim an integer-valued target dimension.
#' @param numk the number of neighboring points for k-nn graph construction.
#' @param preprocess an additional option for preprocessing the data.
#' Default is "center". 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{trfinfo}{a list containing information for out-of-sample prediction.}
#' \item{projection}{a \eqn{(p\times ndim)} whose columns are basis for projection.}
#' }
#'
#'
#' @examples
#' ## generate data of 2 types with clear difference
#' set.seed(100)
#' diff = 50
#' dt1 = aux.gensamples(n=50)-diff;
#' dt2 = aux.gensamples(n=50)+diff;
#'
#' ## merge the data and create a label correspondingly
#' Y = rbind(dt1,dt2)
#' label = rep(1:2, each=50)
#'
#' ## compare LPP, SLPP and ESLPP
#' outLPP <- do.lpp(Y)
#' outSLPP <- do.slpp(Y, label)
#' outESLPP <- do.eslpp(Y, label)
#'
#' ## visualize
#' opar <- par(no.readonly=TRUE)
#' par(mfrow=c(1,3))
#' plot(outLPP$Y, col=label, pch=19, main="LPP")
#' plot(outSLPP$Y, col=label, pch=19, main="SLPP")
#' plot(outESLPP$Y, col=label, pch=19, main="ESLPP")
#' par(opar)
#'
#' @references
#' \insertRef{zheng_gabor_2007}{Rdimtools}
#'
#' \insertRef{shikkenawis_improving_2012}{Rdimtools}
#'
#' @seealso \code{\link{do.lpp}}, \code{\link{do.slpp}}, \code{\link{do.extlpp}}
#' @author Kisung You
#' @rdname linear_ESLPP
#' @concept linear_methods
#' @export
do.eslpp <- function(X, label, ndim=2, numk=max(ceiling(nrow(X)/10),2),
preprocess=c("center","scale","cscale","decorrelate","whiten")){
#------------------------------------------------------------------------
## PREPROCESSING
# 1. data matrix
aux.typecheck(X)
n = nrow(X)
p = ncol(X)
# 2. label : check and return a de-factored vector
# For this example, there should be no degenerate class of size 1.
label = check_label(label, n)
ulabel = unique(label)
for (i in 1:length(ulabel)){
if (sum(label==ulabel[i])==1){
stop("* do.eslpp : no degerate class of size 1 is allowed.")
}
}
if (any(is.na(label))||(any(is.infinite(label)))){stop("* Supervised Learning : any element of 'label' as NA or Inf will simply be considered as a class, not missing entries.") }
# 3. ndim
ndim = as.integer(ndim)
if (!check_ndim(ndim,p)){stop("* do.eslpp : 'ndim' is a positive integer in [1,#(covariates)).")}
# 4. numk
numk = as.integer(numk)
if (!check_NumMM(numk,1,n/2,compact=FALSE)){stop("* do.eslpp : 'numk' should be an integer in [2,nrow(X)/2).")}
# 5. preprocess
if (missing(preprocess)){ algpreprocess = "center" }
else { algpreprocess = match.arg(preprocess) }
#------------------------------------------------------------------------
## MAIN COMPUTATION
# 1. preprocessing
tmplist = (X,type=algpreprocess,algtype="linear")
trfinfo = tmplist$info
pX = tmplist$pX
# 2. K-Means Clustering
kclust = stats::kmeans(pX, numk)
clustlabel = kclust$cluster
clustidx = list() # for each label, find the corresponding # length-'numk' list
for (i in 1:numk){
clustidx[[i]] = which(clustlabel==unique(clustlabel)[i])
}
# 3. pairwise distance
PD = as.matrix(dist(pX))
vecb = rep(0,numk)
for (i in 1:numk){
tgtidx = clustidx[[i]]
vecb[i] = max(PD[tgtidx,tgtidx])
}
veca = rep(min(vecb)/20,numk)
# 4. compute S
Stmp = array(0,c(n,n))
for (i in 1:numk){
tgtidx = clustidx[[i]]
Stmp[tgtidx,tgtidx] = method_trfextlpp(PD[tgtidx,tgtidx],veca[i],vecb[i])
}
diag(Stmp) = 0.0
############# EXTENDED "SUPERVISED" SENSE
S = array(0,c(n,n))
for (i in 1:length(ulabel)){
tgtidx = which(label==ulabel[i])
S[tgtidx,tgtidx] = Stmp[tgtidx,tgtidx]
}
# 5. graph laplaciana and generalized eigenvalue problem
D = diag(rowSums(S))
L = D-S
LHS = t(pX)%*%L%*%pX
RHS = t(pX)%*%D%*%pX
# 6. compute Projection Matrix : Lowest Ones
projection = aux.geigen(LHS, RHS, ndim, maximal=FALSE)
#------------------------------------------------------------------------
## RETURN
result = list()
result$Y = pX%*%projection
result$trfinfo = trfinfo
result$projection = projection
return(result)
}
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