.Bercow <- function (x) order(order(x, method = "radix"), method = "radix")
.Triangle <- function (n) n * (n + 1) / 2
.TrustSum <- function(r, rHat, N, k) {
sum(vapply(seq_len(N), function(i) {
Uk <- rHat[, i] <= k & r[, i] > k
sum(r[Uk, i] - k, na.rm = TRUE)
}, double(1)))
}
.MMax <- function (N, k) {
UkMax <- min(k, N - k)
if (UkMax < 1) {
warning("All points are nearest neighbours. Decrease `neighbours`.")
}
# Return:
N * ((UkMax * (N - k - 1)) - .Triangle(UkMax - 1))
}
#' Faithfulness of mapped distances
#'
#' `MappingQuality()` calculates the trustworthiness and continuity
#' of mapped distances \insertCite{Venna2001,Kaski2003}{TreeDist}.
#' Trustworthiness measures, on a scale from 0--1,
#' the degree to which points that are nearby in a mapping are truly close
#' neighbours; continuity, the extent to which points that are truly nearby
#' retain their close spatial proximity in a mapping.
#'
#'
#' @param original,mapped Square matrix or `dist` object containing
#' original / mapped pairwise distances.
#' @param neighbours Integer specifying number of nearest neighbours to use in
#' calculation. This should typically be small relative to the number of
#' points.
#'
#' @return `MappingQuality()` returns a named vector of length four,
#' containing the entries: `Trustworthiness`, `Continuity`, `TxC`
#' (the product of these values), and `sqrtTxC` (its square root).
#'
#' @examples
#' library("TreeTools", quietly = TRUE)
#' trees <- as.phylo(0:10, nTip = 8)
#' distances <- ClusteringInfoDistance(trees)
#' mapping <- cmdscale(distances)
#' MappingQuality(distances, dist(mapping), 4)
#' @template MRS
#'
#' @references
#' \insertAllCited{}
#' @family tree space functions
#' @export
MappingQuality <- function(original, mapped, neighbours = 10L) {
originalRank <- apply(as.matrix(original), 2, .Bercow) - 1
mappedRank <- apply(as.matrix(mapped), 2, .Bercow) - 1
diag(originalRank) <- diag(mappedRank) <- NA
if (!identical(dim(originalRank), dim(mappedRank))) {
stop("Original and mapped distances must have the same dimensions")
}
N <- dim(originalRank)[2]
k <- neighbours
MMax <- .MMax(N, k)
trust <- 1 - (.TrustSum(originalRank, mappedRank, N, neighbours) / MMax)
cont <- 1 - (.TrustSum(mappedRank, originalRank, N, neighbours) / MMax)
txc <- trust * cont
c("Trustworthiness" = trust,
"Continuity" = cont,
"TxC" = txc,
"sqrtTxC" = sqrt(txc))
}
#' @rdname MappingQuality
#' @export
ProjectionQuality <- MappingQuality
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