#' Intrinsic Dimension Estimation by a Minimal Neighborhood Information
#'
#' Unlike many intrinsic dimension (ID) estimation methods, \code{est.twonn} only requires
#' two nearest datapoints from a target point and their distances. This extremely minimal approach
#' is claimed to redue the effects of curvature and density variation across different locations
#' in an underlying manifold.
#'
#' @param X an \eqn{(n\times p)} matrix or data frame whose rows are observations.
#'
#' @return a named list containing containing \describe{
#' \item{estdim}{estimated intrinsic dimension.}
#' }
#'
#' @examples
#' \donttest{
#' ## create 3 datasets of intrinsic dimension 2.
#' X1 = aux.gensamples(dname="swiss")
#' X2 = aux.gensamples(dname="ribbon")
#' X3 = aux.gensamples(dname="saddle")
#'
#' ## acquire an estimate for intrinsic dimension
#' out1 = est.twonn(X1)
#' out2 = est.twonn(X2)
#' out3 = est.twonn(X3)
#'
#' ## print the results
#' line1 = paste0("* est.twonn : 'swiss' gives ",round(out1$estdim,2))
#' line2 = paste0("* est.twonn : 'ribbon' gives ",round(out2$estdim,2))
#' line3 = paste0("* est.twonn : 'saddle' gives ",round(out3$estdim,2))
#' cat(paste0(line1,"\n",line2,"\n",line3))
#' }
#'
#' @references
#' \insertRef{facco_estimating_2017}{Rdimtools}
#'
#' @rdname estimate_twonn
#' @author Kisung You
#' @export
est.twonn <- function(X){
##########################################################################
## Preprocessing and Default Parameter
aux.typecheck(X)
n = nrow(X)
D = as.matrix(stats::dist(X))
diag(D) = Inf
##########################################################################
## Computation
# 1. compute the ratio
mu = rep(0,n)
for (i in 1:n){
tgt = sort(as.vector(D[i,]), decreasing = FALSE)[1:2]
mu[i] = tgt[2]/tgt[1]
}
# 2. transform
mu.sorted = sort(mu)
empiF = (1:(n-1))/n
# 3. let's do the linear regression
x = log(mu.sorted)[1:(n-1)]
y = -log(1.0-empiF)
idsave = (!is.infinite(x))
x = x[idsave]
y = y[idsave]
##########################################################################
## Return the results
result = list()
result$estdim = sum(coefficients(stats::lm(y~x-1))[1])
return(result)
}
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