#' Intrinsic Dimension Estimation via Clustering
#'
#' Instead of directly using neighborhood information, \code{est.clustering} adopts hierarchical
#' neighborhood information using \code{\link[stats]{hclust}} by recursively merging leafs
#' over the range of radii.
#'
#' @param X an \eqn{(n\times p)} matrix or data frame whose rows are observations.
#' @param kmin minimal number of neighborhood size to search over.
#'
#' @return a named list containing containing \describe{
#' \item{estdim}{estimated intrinsic dimension.}
#' }
#'
#' @examples
#' \donttest{
#' ## create 'swiss' roll dataset
#' X = aux.gensamples(dname="swiss")
#'
#' ## try different k values
#' out1 = est.clustering(X, kmin=5)
#' out2 = est.clustering(X, kmin=25)
#' out3 = est.clustering(X, kmin=50)
#'
#' ## print the results
#' line1 = paste0("* est.clustering : kmin=5 gives ",round(out1$estdim,2))
#' line2 = paste0("* est.clustering : kmin=25 gives ",round(out2$estdim,2))
#' line3 = paste0("* est.clustering : kmin=50 gives ",round(out3$estdim,2))
#' cat(paste0(line1,"\n",line2,"\n",line3))
#' }
#'
#' @references
#' \insertRef{eriksson_estimating_2012}{Rdimtools}
#'
#' @rdname estimate_clustering
#' @author Kisung You
#' @export
est.clustering <- function(X, kmin=round(sqrt(nrow(X)))){
##########################################################################
## Preprocessing and Default Parameter
aux.typecheck(X)
n = nrow(X)
D = as.matrix(dist(X))
rmax = max(D)
rmin = min(apply(D,1,sort)[kmin+1,])
##########################################################################
## Main Body
# 1. construct That using complete agglomerative clustering
That = stats::hclust(as.dist(D), method="complete")
clusters = stats::cutree(That, h=That$height)
histcl = array(0,dim(clusters))
# 2. iteration
for (i in 1:ncol(clusters)){
cclust = clusters[,i]
for (j in 1:length(unique(cclust))){
idxj = (cclust==j)
histcl[idxj,i] = max(D[idxj,idxj])
}
}
# 3. ID estimation via lm fitting
nslice = round(n/4)
vecr = seq(from=rmin,to=rmax,length.out=nslice)
logr = log(vecr)
logM = rep(0,nslice)
for (i in 1:nslice){
logM[i] = log(length(unique(histcl[, which(colMeans(histcl > vecr[i]) == 1)[1]])))
}
Dpack = abs(as.numeric(coefficients(lm(logM~logr))[2]))
##########################################################################
## Result plot
result = list()
result$estdim = max(Dpack,1)
return(result)
}
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