Nothing
#' Locality-Preserved Maximum Information Projection
#'
#' Locality-Preserved Maximum Information Projection (LPMIP) is an unsupervised linear dimension reduction method
#' to identify the underlying manifold structure by learning both the within- and between-locality information. The
#' parameter \code{alpha} is balancing the tradeoff between two and the flexibility of this model enables an interpretation
#' of it as a generalized extension of LPP.
#'
#' @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 "null". See also \code{\link{aux.preprocess}} for more details.
#' @param sigma bandwidth parameter for heat kernel in \eqn{(0,\infty)}.
#' @param alpha balancing parameter between two locality information in \eqn{[0,1]}.
#'
#' @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 dataset
#' data(iris)
#' set.seed(100)
#' subid <- sample(1:150, 50)
#' X <- as.matrix(iris[subid,1:4])
#' lab <- as.factor(iris[subid,5])
#'
#' ## try different neighborhood size
#' out1 <- do.lpmip(X, ndim=2, type=c("proportion",0.10))
#' out2 <- do.lpmip(X, ndim=2, type=c("proportion",0.25))
#' out3 <- do.lpmip(X, ndim=2, type=c("proportion",0.50))
#'
#' ## Visualize
#' opar <- par(no.readonly=TRUE)
#' par(mfrow=c(1,3))
#' plot(out1$Y, pch=19, col=lab, main="10% connected")
#' plot(out2$Y, pch=19, col=lab, main="25% connected")
#' plot(out3$Y, pch=19, col=lab, main="50% connected")
#' par(opar)
#'
#' @references
#' \insertRef{haixianwang_localitypreserved_2008}{Rdimtools}
#'
#' @author Kisung You
#' @rdname linear_LPMIP
#' @concept linear_methods
#' @export
do.lpmip <- function(X, ndim=2, type=c("proportion",0.1),
preprocess=c("null","center","scale","cscale","whiten","decorrelate"),
sigma=10, alpha=0.5){
#------------------------------------------------------------------------
## PREPROCESSING
# 1. data matrix
aux.typecheck(X)
n = nrow(X)
p = ncol(X)
# 2. ndim
ndim = as.integer(ndim)
if (!check_ndim(ndim,p)){stop("* do.lpmip : 'ndim' is a positive integer in [1,#(covariates)).")}
# 3. neighborhood information
nbdtype = type
nbdsymmetric = "union"
# 4. preprocess
if (missing(preprocess)){
algpreprocess = "null"
} else {
algpreprocess = match.arg(preprocess)
}
# 5. sigma
sigma = as.double(sigma)
if (!check_NumMM(sigma, 0, Inf, compact=FALSE)){stop("* do.lpmip : 'sigma' is a bandwidth parameter in (0,Inf).")}
# 6. alpha
alpha = as.double(alpha)
if (!check_NumMM(alpha,0,1,compact=TRUE)){stop(" do.lpmip : 'alpha' is a balancing parameter in [0,1].")}
#------------------------------------------------------------------------
## COMPUTATION : PRELIMINARY
# 1. preprocessing of data : note that output pX still has (n-by-p) format
tmplist = (X,type=algpreprocess,algtype="linear")
trfinfo = tmplist$info
pX = tmplist$pX
# 2. build neighborhood information
nbdstruct = aux.graphnbd(pX,method="euclidean",
type=nbdtype,symmetric=nbdsymmetric)
nbdmask = nbdstruct$mask
#------------------------------------------------------------------------
## COMPUTATION : MAIN PART FOR LPMIP
# 1. W : weight matrix & Ltilde
Dsqmat = (as.matrix(dist(pX))^2)
W = exp(-Dsqmat/sigma)
Ltilde = diag(rowSums(W))-W
# 2. A with neighborhood
A = W*nbdmask; diag(A)=0;
L = diag(rowSums(A))-A
# 3. cost function
costW = t(pX)%*%(alpha*Ltilde - L)%*%pX
# 4. compute projection vectors
projection = aux.adjprojection(RSpectra::eigs(costW, ndim)$vectors)
#------------------------------------------------------------------------
## RETURN
result = list()
result$Y = pX%*%projection
result$trfinfo = trfinfo
result$projection = projection
return(result)
}
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.