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#' Find a suitable k
#'
#' The \code{k} parameter for the k nearest neighbors used in \link{DiffusionMap} should be as big as possible while
#' still being computationally feasible. This function approximates it depending on the size of the dataset \code{n}.
#'
#' @param n Number of possible neighbors (nrow(dataset) - 1)
#' @param min_k Minimum number of neighbors. Will be chosen for \eqn{n \ge big}
#' @param small Number of neighbors considered small. If/where \eqn{n \le small}, n itself will be returned.
#' @param big Number of neighbors considered big. If/where \eqn{n \ge big}, \code{min_k} will be returned.
#'
#' @return A vector of the same length as \code{n} that contains suitable \code{k} values for the respective \code{n}
#'
#' @examples
#' curve(find_dm_k(n), 0, 13000, xname = 'n')
#' curve(find_dm_k(n) / n, 0, 13000, xname = 'n')
#' @export
find_dm_k <- function(n, min_k = 100L, small = 1000L, big = 10000L) {
stopifnot(small < big)
if (is.null(n)) return(NULL)
k <- rep(NA_integer_, length(n))
k[small >= n] <- n[small >= n]
k[n >= big] <- min_k
rest <- !is.na(n) & small < n & n < big
n_shifted <- (n[rest] - small) / (big - small) # linear transf [small, big] -> [0, 1]
k_shifted <- (cos(n_shifted * pi) + 1) / 2 # ease function [0, 1] -> [1, 0]
k_rest <- min_k + k_shifted * (n[rest] - min_k) # linear transf [0, 1] -> [min_k, n]
k[rest] <- as.integer(round(k_rest))
k
}
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