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#' Extended Locality Preserving Projection
#'
#' Extended Locality Preserving Projection (EXTLPP) is an unsupervised
#' dimension reduction algorithm with a bit of flavor in adopting
#' discriminative idea by nature. It raises a question on the data points
#' at \emph{moderate} distance in that a Z-shaped function is introduced in
#' defining similarity derived from Euclidean distance.
#'
#' @param X an \eqn{(n\times p)} matrix or data frame whose rows are observations.
#' @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
#' set.seed(100)
#' X <- aux.gensamples(n=75)
#'
#' ## run Extended LPP with different neighborhood graph
#' out1 <- do.extlpp(X, numk=5)
#' out2 <- do.extlpp(X, numk=10)
#' out3 <- do.extlpp(X, numk=25)
#'
#' ## Visualize three different projections
#' opar <- par(no.readonly=TRUE)
#' par(mfrow=c(1,3))
#' plot(out1$Y, main="EXTLPP::k=5")
#' plot(out2$Y, main="EXTLPP::k=10")
#' plot(out3$Y, main="EXTLPP::k=25")
#' par(opar)
#'
#' @references
#' \insertRef{shikkenawis_improving_2012}{Rdimtools}
#'
#' @seealso \code{\link{do.lpp}}
#' @author Kisung You
#' @rdname linear_EXTLPP
#' @concept linear_methods
#' @export
do.extlpp <- function(X, ndim=2, numk=max(ceiling(nrow(X)/10),2),
preprocess=c("center","scale","cscale","decorrelate","whiten")){
#------------------------------------------------------------------------
## PREPROCESSING
# 1. data matrix
aux.typecheck(X)
n = nrow(X)
p = ncol(X)
# 2. ndim
ndim = as.integer(ndim)
if (!check_ndim(ndim,p)){stop("* do.extlpp : 'ndim' is a positive integer in [1,#(covariates)).")}
# 3. numk
numk = as.integer(numk)
if (!check_NumMM(numk,1,n/2,compact=FALSE)){stop("* do.extlpp : 'numk' should be an integer in [2,nrow(X)/2).")}
# 4. preprocess
if (missing(preprocess)){ algpreprocess = "center" }
else { algpreprocess = match.arg(preprocess) }
#------------------------------------------------------------------------
## MAIN COMPUTATION
# 1. preprocessing
tmplist = (X,type=algpreprocess,algtype="linear")
trfinfo = tmplist$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
S = array(0,c(n,n))
for (i in 1:numk){
tgtidx = clustidx[[i]]
tgtmat = as.matrix(PD[tgtidx,tgtidx],nrow=length(tgtidx))
S[tgtidx,tgtidx] = method_trfextlpp(tgtmat,as.double(veca[i]),as.double(vecb[i]))
}
diag(S) = 0.0
# 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 : use 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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