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#' Multi-Cluster Feature Selection
#'
#' Multi-Cluster Feature Selection (MCFS) is an unsupervised feature selection method. Based on
#' a multi-cluster assumption, it aims at finding meaningful features using sparse reconstruction of
#' spectral basis using LASSO.
#'
#' @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 K assumed number of clusters in the original dataset.
#' @param lambda \eqn{\ell_1} regularization parameter in \eqn{(0,\infty)}.
#' @param t bandwidth parameter for heat kernel in \eqn{(0,\infty)}.
#'
#' @return a named list containing
#' \describe{
#' \item{Y}{an \eqn{(n\times ndim)} matrix whose rows are embedded observations.}
#' \item{featidx}{a length-\eqn{ndim} vector of indices with highest scores.}
#' \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 data of 3 types with clear difference
#' dt1 = aux.gensamples(n=20)-100
#' dt2 = aux.gensamples(n=20)
#' dt3 = aux.gensamples(n=20)+100
#'
#' ## merge the data and create a label correspondingly
#' X = rbind(dt1,dt2,dt3)
#' label = rep(1:3, each=20)
#'
#' ## try different regularization parameters
#' out1 = do.mcfs(X, lambda=0.01)
#' out2 = do.mcfs(X, lambda=0.1)
#' out3 = do.mcfs(X, lambda=1)
#'
#' ## visualize
#' opar <- par(no.readonly=TRUE)
#' par(mfrow=c(1,3))
#' plot(out1$Y, pch=19, col=label, main="lambda=0.01")
#' plot(out2$Y, pch=19, col=label, main="lambda=0.1")
#' plot(out3$Y, pch=19, col=label, main="lambda=1")
#' par(opar)
#'
#' @references
#' \insertRef{cai_unsupervised_2010}{Rdimtools}
#'
#' @rdname feature_MCFS
#' @author Kisung You
#' @concept feature_methods
#' @export
do.mcfs <- function(X, ndim=2, type=c("proportion",0.1),
preprocess=c("null","center","scale","cscale","whiten","decorrelate"),
K=max(round(nrow(X)/5),2), lambda=1.0, t=10.0){
#------------------------------------------------------------------------
## PREPROCESSING
# 1. data matrix
aux.typecheck(X)
n = nrow(X)
p = ncol(X)
# 2. ndim
ndim = as.integer(ndim)
if (!check_ndim(ndim,p)){
stop("* do.mcfs : 'ndim' is a positive integer in [1,#(covariates)].")
}
# 3. type
nbdtype = type
nbdsymmetric = "union"
# 4. preprocess
if (missing(preprocess)){
algpreprocess = "null"
} else {
algpreprocess = match.arg(preprocess)
}
# 5. K : cluster numbers
K = as.integer(K)
if (!check_NumMM(K,2,round(nrow(X)/5))){stop("* do.mcfs : 'K' is an assumed cluster size in [2,#(samples)/2].")}
# 6. lambda
lambdaval = as.double(lambda)
if (!check_NumMM(lambdaval,0,Inf,compact=FALSE)){stop("* do.mcfs : 'lambda' is a LASSO parameter in (0,Inf).")}
# 7. t : bandwidth parameter
t = as.double(t)
if (!check_NumMM(t,1e-10,Inf,compact=TRUE)){stop("* do.mcfs : 't' is a bandwidth parameter in (0,Inf).")}
#------------------------------------------------------------------------
## COMPUTATION : PRELIMINARY
# 1. preprocessing of data : note that output pX still has (n-by-p) format
tmplist = (X,type=algpreprocess,algtype="linear")
trfinfo = tmplist$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 MULTI-CLUSTER FEATURE SELECTION
# 1. construct nbd graph with weights; W
Dsqmat = exp(-(as.matrix(dist(pX))^2)/t)
W = Dsqmat*nbdmask
# 2. solve generalized eigenvalue problem
D = diag(rowSums(W))
L = D-W
Y = aux.geigen(L,D,K,maximal=FALSE)
# 3. solve K number of LASSO problems
A = array(0,c(p,K))
for (i in 1:K){
# 3-1. take one column vector
y = as.vector(Y[,i])
# 3-2. solve with LASSO; I will do it with mine
# solved = ADMM ::admm.lasso(pX, y, lambda=lambdaval)$x
# 3-3. record the solved
# A[,i] = as.vector(solved)
A[,i] = as.vector(admm_lasso(pX, y, lambdaval))
}
# 4. find the solution
fscore = rep(0,p)
for (i in 1:p){
# 4-1. select one vector
veca = base::abs(as.vector(A[i,]))
# 4-2. take the largest
fscore[i] = max(veca)
}
# 5. select the largest ones
idxvec = base::order(fscore, decreasing=TRUE)[1:ndim]
# 6. find the projection matrix
projection = aux.featureindicator(p,ndim,idxvec)
#------------------------------------------------------------------------
## RETURN
result = list()
result$Y = pX%*%projection
result$featidx = idxvec
result$trfinfo = trfinfo
result$projection = projection
return(result)
}
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