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#' Orthogonal Neighborhood Preserving Projections
#'
#' Orthogonal Neighborhood Preserving Projection (ONPP) is an unsupervised linear dimension reduction method.
#' It constructs a weighted data graph from LLE method. Also, it develops LPP method by preserving
#' the structure of local neighborhoods.
#'
#' @param X an \eqn{(n\times p)} matrix or data frame whose rows are observations
#' and columns represent independent variables.
#' @param ndim an integer-valued target dimension.
#' @param type a vector of neighborhood graph construction. Following types are supported;
#' \code{c("knn",k)}, \code{c("enn",radius)}, and \code{c("proportion",ratio)}.
#' Default is \code{c("proportion",0.1)}, connecting about 1/10 of nearest data points
#' among all data points. See also \code{\link{aux.graphnbd}} for more details.
#' @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
#' ## use 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])
#'
#' ## try different numbers for neighborhood size
#' out1 = do.onpp(X, type=c("proportion",0.10))
#' out2 = do.onpp(X, type=c("proportion",0.25))
#' out3 = do.onpp(X, type=c("proportion",0.50))
#'
#' ## visualize
#' opar <- par(no.readonly=TRUE)
#' par(mfrow=c(1,3))
#' plot(out1$Y, pch=19, col=label, main="ONPP::10% connectivity")
#' plot(out2$Y, pch=19, col=label, main="ONPP::25% connectivity")
#' plot(out3$Y, pch=19, col=label, main="ONPP::50% connectivity")
#' par(opar)
#'
#' @references
#' \insertRef{kokiopoulou_orthogonal_2007}{Rdimtools}
#'
#' @rdname linear_ONPP
#' @author Kisung You
#' @concept linear_methods
#' @export
do.onpp <- function(X, ndim=2, type=c("proportion",0.1),
preprocess=c("center","scale","cscale","decorrelate","whiten")){
#------------------------------------------------------------------------
## PREPROCESSING
# 1. data matrix
aux.typecheck(X)
n = nrow(X)
p = ncol(X)
# 2. ndim
ndim = as.integer(ndim)
if (!check_ndim(ndim,p)){
stop("* do.onpp : 'ndim' is a positive integer in [1,#(covariates)].")
}
# 3. type
nbdtype = type
nbdsymmetric = "union"
# 4. preprocess
if (missing(preprocess)){
algpreprocess = "center"
} else {
algpreprocess = match.arg(preprocess)
}
#------------------------------------------------------------------------
## COMPUTATION : PRELIMINARY and LLE step
# 1. preprocessing of data : note that output pX still has (n-by-p) format
tmplist = (X,type=algpreprocess,algtype="linear")
trfinfo = tmplist$info
pX = tmplist$pX
# 2. neighborhood information
nbdstruct = aux.graphnbd(pX,method="euclidean",
type=nbdtype,symmetric=nbdsymmetric)
# 3. LLE computation
regparam = 1.0
W = array(0,c(n,n))
for (i in 1:n){
# 3-1. separate target mask vector
tgtidx = which(nbdstruct$mask[i,])
# 3-2. select data
# For convenience, target matrix is transposed for Armadillo
vec_tgt = pX[i,]
mat_tgt = t(pX[tgtidx,])
k = ncol(mat_tgt)
# 3-3. no automatic regularization
W[i,tgtidx] = method_lleW(mat_tgt,vec_tgt,regparam);
}
#------------------------------------------------------------------------
## COMPUTATION : MAIN COMPUTATION FOR ONPP
# 1. cost function : Mtilde
diagN = diag(n)
Mtilde = (t(pX)%*%t(diagN-W)%*%(diagN-W)%*%pX)
# 2. use (ndim+1) lowest, except for the first one
if ((ndim+1)==p){
eigM = base::eigen(Mtilde)
projection = aux.adjprojection(eigM$vectors[,p:2])
} else {
projection = aux.adjprojection(RSpectra::eigs(Mtilde, ndim+1, which="SR")$vectors[,2:(ndim+1)])
}
#------------------------------------------------------------------------
## RETURN
result = list()
result$Y = pX%*%projection
result$trfinfo = trfinfo
result$projection = projection
return(result)
}
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