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#' Localized Sliced Inverse Regression
#'
#' Localized SIR (SIR) is an extension of celebrated SIR method. As its name suggests,
#' the \emph{locality} concept is brought in that for each slice, only local data points
#' are considered in order to discover intrinsic structure of the data.
#'
#' @param X an \eqn{(n\times p)} matrix or data frame whose rows are observations
#' and columns represent independent variables.
#' @param response a length-\eqn{n} vector of response variable.
#' @param ndim an integer-valued target dimension.
#' @param h the number of slices to divide the range of response vector.
#' @param preprocess an additional option for preprocessing the data.
#' Default is "center". See also \code{\link{aux.preprocess}} for more details.
#' @param ycenter a logical; \code{TRUE} to center the response variable, \code{FALSE} otherwise.
#' @param numk size of determining neighborhood via \eqn{k}-nearest neighbor selection.
#' @param tau regularization parameter for adjusting rank-deficient scatter matrix.
#'
#' @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 swiss roll with auxiliary dimensions
#' ## it follows reference example from LSIR paper.
#' set.seed(100)
#' n = 123
#' theta = runif(n)
#' h = runif(n)
#' t = (1+2*theta)*(3*pi/2)
#' X = array(0,c(n,10))
#' X[,1] = t*cos(t)
#' X[,2] = 21*h
#' X[,3] = t*sin(t)
#' X[,4:10] = matrix(runif(7*n), nrow=n)
#'
#' ## corresponding response vector
#' y = sin(5*pi*theta)+(runif(n)*sqrt(0.1))
#'
#' ## try different number of neighborhoods
#' out1 = do.lsir(X, y, numk=5)
#' out2 = do.lsir(X, y, numk=10)
#' out3 = do.lsir(X, y, numk=25)
#'
#' ## visualize
#' opar <- par(no.readonly=TRUE)
#' par(mfrow=c(1,3))
#' plot(out1$Y, main="LSIR::nbd size=5")
#' plot(out2$Y, main="LSIR::nbd size=10")
#' plot(out3$Y, main="LSIR::nbd size=25")
#' par(opar)
#'
#' @references
#' \insertRef{wu_localized_2010}{Rdimtools}
#'
#' @seealso \code{\link{do.sir}}
#' @author Kisung You
#' @rdname linear_LSIR
#' @concept linear_methods
#' @export
do.lsir <- function(X, response, ndim=2, h=max(2, round(nrow(X)/5)),
preprocess=c("center","scale","cscale","decorrelate","whiten"),
ycenter=FALSE, numk = max(2, round(nrow(X)/10)), tau=1.0){
#------------------------------------------------------------------------
## PREPROCESSING
# 1. data matrix
aux.typecheck(X)
n = nrow(X)
p = ncol(X)
# 2. response
response = as.double(response)
if ((any(is.infinite(response)))||(!is.vector(response))||(any(is.na(response)))){
stop("* do.sir : 'response' should be a vector containing no NA values.")
}
# 3. ndim
ndim = as.integer(ndim)
if (!check_ndim(ndim,p)){stop("* do.lsir : 'ndim' is a positive integer in [1,#(covariates)).")}
# 4. h : number of slices
h = as.integer(h)
if (!is.factor(response)){
if (!check_NumMM(h,2,ceiling(n/2),compact=TRUE)){stop("* do.lsir : the number of slices should be in [2,n/2].")}
} # 5. preprocess
if (missing(preprocess)){
algpreprocess = "center"
} else {
algpreprocess = match.arg(preprocess)
}
# 6. numk
numk = as.integer(numk)
if (!check_NumMM(numk,1,(n-1),compact=TRUE)){stop("* do.lsir : 'numk' should be in [1,n-1].")}
# 7. tau
tau = as.double(tau)
if (!check_NumMM(tau,0,Inf,compact=TRUE)){stop("* do.lsir : 'tau' should be a nonnegative real number.")}
#------------------------------------------------------------------------
## COMPUTATION : PRELIMINARY
# 1. preprocessing of data
tmplist = (X,type=algpreprocess,algtype="linear")
trfinfo = tmplist$info
pX = tmplist$pX
if (!is.logical(ycenter)){
stop("* do.lsir : 'ycenter' should be a logical variable.")
}
if (ycenter==TRUE){
response = response-mean(response)
}
# 2. build label matrix
if (!is.factor(response)){
label = as.integer(sir_makelabel(response, h))
} else {
label = as.integer(response)
}
ulabel = unique(label)
nlabel = length(ulabel)
# 3. compute classwise and overall mean
class_mean = array(0,c(nlabel,p))
class_count = rep(0,nlabel)
for (i in 1:nlabel){
idxclass = which(label==ulabel[i])
class_mean[i,] = as.vector(colMeans(pX[idxclass,]) )
class_count[i] = length(idxclass)
}
all_mean = as.vector(colMeans(pX))
# 4. compute Empirical Covariance
mat_Sigma = aux_scatter(pX, all_mean)/n
# 5. compute Empirical Between-ness Covariance with localization
mean_local = array(0,c(n,p))
for (i in 1:n){
# 5-1. target label index
tgtlabel = setdiff(which(label==label[i]), i)
# 5-2. get the logical of smallest distances
tvec = as.vector(pX[i,])
tmat = pX[tgtlabel,]
partidx = lsir_smallest(tvec, tmat, numk)
partlabel = tgtlabel[partidx]
# 5-3. compute the mean
mean_local[i,] = as.vector(colMeans(pX[partlabel,]))
}
# 5-4. compute mean scatter
mat_Gamma = aux_scatter(mean_local, all_mean)/n + tau*diag(p)
#------------------------------------------------------------------------
## COMPUTATION : MAIN COMPUTATION
# 1. do matrix inversion.. I hate it.
costInv = aux.bicgstab(mat_Sigma, mat_Gamma, verbose=FALSE)$x
# 2. find top eigenvectors
projection = aux.adjprojection(RSpectra::eigs(costInv, ndim)$vectors)
#------------------------------------------------------------------------
## RETURN
result = list()
result$Y = pX%*%projection
result$trfinfo = trfinfo
result$projection = projection
return(result)
}
# ------------------------------------------------------------------------
#' @keywords internal
#' @noRd
lsir_smallest <- function(tvec, tmat, numk){
n = nrow(tmat)
distvec = rep(0,n)
for (i in 1:n){
vecdiff = tvec-as.vector(tmat[i,])
distvec[i] = sum(vecdiff*vecdiff)
}
orderdist = order(distvec)
orderpart = orderdist[1:max(min(n,numk),1)]
logicalvec = rep(FALSE,n)
logicalvec[orderpart] = TRUE
return(logicalvec)
}
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