#' Discriminant Neighborhood Embedding
#'
#' Discriminant Neighborhood Embedding (DNE) is a supervised subspace learning method.
#' DNE tries to move multi-class data points in high-dimensional space in accordance with
#' local intra-class attraction and inter-class repulsion.
#'
#'
#' @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
#' ## 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])
#'
#' ## try different numbers for neighborhood size
#' out1 = do.dne(X, label, numk=5)
#' out2 = do.dne(X, label, numk=10)
#' out3 = do.dne(X, label, numk=20)
#'
#' ## visualize
#' opar <- par(no.readonly=TRUE)
#' par(mfrow=c(1,3))
#' plot(out1$Y, main="DNE::nbd size=5", col=label, pch=19)
#' plot(out2$Y, main="DNE::nbd size=10", col=label, pch=19)
#' plot(out3$Y, main="DNE::nbd size=20", col=label, pch=19)
#' par(opar)
#'
#' @references
#' \insertRef{zhang_discriminant_2006}{Rdimtools}
#'
#' @author Kisung You
#' @rdname linear_DNE
#' @concept linear_methods
#' @export
do.dne <- function(X, label, ndim=2, numk=max(ceiling(nrow(X)/10),2),
preprocess=c("center","scale","cscale","decorrelate","whiten")){
#------------------------------------------------------------------------
## PREPROCESSING
# 1. data matrix
aux.typecheck(X)
n = nrow(X)
p = ncol(X)
# 2. ndim
ndim = as.integer(ndim)
if (!check_ndim(ndim,p)){stop("* do.dne : 'ndim' is a positive integer in [1,#(covariates)).")}
# 3. numk
numk = as.integer(numk)
if (!check_NumMM(numk,1,n/2,compact=FALSE)){stop("* do.dne : 'numk' should be an integer in [2,nrow(X)/2).")}
# 4. preprocess
if (missing(preprocess)){ algpreprocess = "center" }
else { algpreprocess = match.arg(preprocess) }
# 5. label
# 2. label : check and return a de-factored vector
# For this example, there should be no degenerate class of size 1.
label = check_label(label, n)
ulabel = unique(label)
if (any(is.na(label))||(any(is.infinite(label)))){stop("* Supervised Learning : any element of 'label' as NA or Inf will simply be considered as a class, not missing entries.") }
#------------------------------------------------------------------------
## COMPUTATION : PRELIMINARY
# 1. preprocessing
tmplist = (X,type=algpreprocess,algtype="linear")
trfinfo = tmplist$info
pX = tmplist$pX
# 2. neighborhood creation
nbdtype = c("knn",numk)
nbdsymmetric = "union"
nbdstruct = aux.graphnbd(pX,method="euclidean",
type=nbdtype,symmetric=nbdsymmetric)
nbdmask = nbdstruct$mask
# 3. adjacency matrix F
matF = array(0,c(n,n))
for (i in 1:(n-1)){
for (j in (i+1):n){
# for non-zeros, it needs to be neighbors
if (nbdmask[i,j]==TRUE){
if (label[i]==label[j]){
matF[i,j] = 1.0
matF[j,i] = 1.0
} else {
matF[i,j] = -1.0
matF[j,i] = -1.0
}
}
}
}
#------------------------------------------------------------------------
## COMPUTATION : PRELIMINARY
# 1. cost function :S-F
# arbitrary regularization
# matS = diag(rowSums(matF))-matF
matS = diag(rowSums(matF))
costobj = t(pX)%*%(matS-matF)%*%pX
# 2. minimal eigenvectors
projection = aux.adjprojection(RSpectra::eigs(costobj, ndim, which="SR")$vectors)
#------------------------------------------------------------------------
## RETURN
result = list()
result$Y = pX%*%projection
result$trfinfo = trfinfo
result$projection = projection
return(result)
}
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