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#' Adaptive Dimension Reduction
#'
#' Adaptive Dimension Reduction \insertCite{ding_adaptive_2002}{Rdimtools} iteratively finds the best subspace to perform data clustering. It can be regarded as
#' one of remedies for clustering in high dimensional space. Eigenvectors of a between-cluster scatter matrix are used
#' as basis of projection.
#'
#' @param X an \eqn{(n\times p)} matrix or data frame whose rows are observations.
#' @param ndim an integer-valued target dimension.
#' @param ... extra parameters including \describe{
#' \item{maxiter}{maximum number of iterations (default: 100).}
#' \item{abstol}{absolute tolerance stopping criterion (default: 1e-8).}
#' }
#'
#' @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{trfinfo}{a list containing information for out-of-sample prediction.}
#' \item{algorithm}{name of the algorithm.}
#' }
#'
#' @examples
#' \donttest{
#' ## load iris data
#' data(iris)
#' set.seed(100)
#' subid = sample(1:150,50)
#' X = as.matrix(iris[subid,1:4])
#' label = as.factor(iris[subid,5])
#'
#' ## compare ADR with other methods
#' outADR = do.adr(X)
#' outPCA = do.pca(X)
#' outLDA = do.lda(X, label)
#'
#' ## visualize
#' opar <- par(no.readonly=TRUE)
#' par(mfrow=c(1,3))
#' plot(outADR$Y, col=label, pch=19, main="ADR")
#' plot(outPCA$Y, col=label, pch=19, main="PCA")
#' plot(outLDA$Y, col=label, pch=19, main="LDA")
#' par(opar)
#' }
#'
#' @references
#' \insertAllCited{}
#'
#' @seealso \code{\link{do.ldakm}}
#' @rdname linear_ADR
#' @concept linear_methods
#' @export
do.adr <- function(X, ndim=2, ...){
#------------------------------------------------------------------------
## PREPROCESSING
# 1. data matrix
aux.typecheck(X)
n = nrow(X)
p = ncol(X)
# 2. ndim as 'd' and 'k' the number of clusters
d = as.integer(ndim)
if (!check_ndim(d,p)){stop("* do.adr : 'ndim' is a positive integer in [1,#(covariates)).")}
k = as.integer(d+1)
# Extra parameters
params = list(...)
pnames = names(params)
if ("abstol"%in%pnames){
abstol = max(.Machine$double.eps, as.double(params$abstol))
} else {
abstol = 10^(-8)
}
if ("maxiter"%in%pnames){
maxiter = max(5, round(params$maxiter))
} else {
maxiter = 100
}
preprocess = "cscale" # this is used by the paper.
#------------------------------------------------------------------------
## COMPUTATION : PRELIMINARY
# 1. preprocessing
tmplist = (X, type=preprocess, algtype="linear")
trfinfo = tmplist$info
pX = tmplist$pX
# 2. initialize
Uold = ldakm_PCAbasis(pX, ndim)
# 3. iterate
incstop = 10.0
citer = 1
while (incstop > abstol){
# 3-1. LDA-KM(1) : k-means in projected space
projected = pX%*%Uold
pXkmeans = kmeans(projected, k)
# 3-2. LDA-KM(2) : learn again
# 1. build H
H = ldakm_BuildH(pXkmeans$cluster) # H : (n-times-k)
M = t(pX)%*%H%*%aux.pinv(t(H)%*%H) # M : (p-times-k)
# 2. build Sw (p-by-p)
# Swterm1 = t(pX)-(M%*%t(H))
# Sw = Swterm1%*%t(Swterm1)
# 3. build Sb (p-by-p)
Sb = M%*%t(H)%*%H%*%t(M)
# 3-3. BRANCHING :: Solve for Eigenvectors
Unew = aux.adjprojection(RSpectra::eigs(Sb,ndim)$vectors)
# 3-4. update
incstop = base::norm(Uold-Unew,"f")
citer = citer + 1
Uold = Unew
if (citer >= maxiter){
break
}
}
# 4. we finally have projection
projection = aux.adjprojection(Uold)
#------------------------------------------------------------------------
## RETURN
result = list()
result$Y = pX%*%projection
result$projection = projection
result$trfinfo = trfinfo
result$algorithm = "linear:ADR"
return(structure(result, class="Rdimtools"))
}
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