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#' Cluster size statistics
#' @name cluster-statistics
#'
#' @param x Matrix in which each row lists the coordinates of a point
#' in a Euclidian space; or, where supported, `dist` object specifying
#' distances between each pair of points.
#' @param cluster Optional integer vector specifying the cluster or group to
#' which each row in `x` belongs.
#'
#' @examples
#' points <- rbind(matrix(1:16, 4), rep(1, 4), matrix(1:32, 8, 4) / 10)
#' cluster <- rep(1:3, c(4, 1, 8))
#'
#' plot(
#' points[, 1:2], # Plot first two dimensions of four-dimensional space
#' col = cluster, pch = cluster, # Style by cluster membership
#' asp = 1, # Fix aspect ratio to avoid distortion
#' ann = FALSE, frame = FALSE # Simple axes
#' )
#'
#' @family tree space functions
#' @family cluster functions
#' @template MRS
NULL
#' @return `SumOfRanges()` returns a numeric specifying the sum of ranges
#' within each cluster across all dimensions.
#' @rdname cluster-statistics
#' @examples SumOfRanges(points, cluster)
#' @export
SumOfRanges <- function(x, cluster = 1) {
if (is.null(dim(x))) {
warning(paste0("`x` lacks dimensions. ",
"Did you subset without specifying `drop = FALSE`?"))
x <- matrix(x, 1)
}
# Return:
vapply(seq_along(unique(cluster)),
function(i) .SumOfRanges(x[cluster == i, , drop = FALSE]),
numeric(1))
}
.SumOfRanges <- function(x) {
ranges <- apply(x, 2, range)
# Return:
sum(ranges[2, ] - ranges[1, ])
}
#' @rdname cluster-statistics
#' @return `SumOfVariances()` returns a numeric specifying the sum of variances
#' within each cluster across all dimensions.
#' @examples SumOfVariances(points, cluster)
#' @importFrom stats var
#' @export
SumOfVariances <- function(x, cluster = 1) {
if (is.null(dim(x))) {
warning(paste0("`x` lacks dimensions. ",
"Did you subset without specifying `drop = FALSE`?"))
x <- matrix(x, 1)
}
# Return:
vapply(seq_along(unique(cluster)),
function(i) .SumOfVariances(x[cluster == i, , drop = FALSE]),
numeric(1))
}
#' @rdname cluster-statistics
#' @export
SumOfVars <- SumOfVariances
.SumOfVariances <- function(x) {
sum(apply(x, 2, var))
}
#' @rdname cluster-statistics
#' @return `MeanCentroidDistance()` returns a numeric specifying the mean
#' distance from the centroid to points in each cluster.
#' @examples MeanCentroidDistance(points, cluster)
#' @export
MeanCentroidDistance <- function(x, cluster = 1, Average = mean) {
if (is.null(dim(x))) {
warning(paste0("`x` lacks dimensions. ",
"Did you subset without specifying `drop = FALSE`?"))
x <- matrix(x, 1)
}
# Return:
vapply(seq_along(unique(cluster)),
function(i) .MeanCentroidDist(x[cluster == i, , drop = FALSE],
Average = Average),
numeric(1))
}
#' @rdname cluster-statistics
#' @export
MeanCentDist <- MeanCentroidDistance
#' @rdname cluster-statistics
#' @export
MeanCentroidDist <- MeanCentroidDistance
.MeanCentroidDist <- function(x, Average = mean) {
recentred <- t(t(x) - apply(x, 2, mean))
# Return:
Average(sqrt(rowSums(recentred ^ 2)))
}
#' @rdname cluster-statistics
#' @param Average Function to use to summarize distances. Defaults to `mean`;
#' specifying `median` returns a value akin to the median absolute divergence
#' (see [`mad`]).
#' @return `DistanceFromMedian()` returns a numeric specifying the mean distance
#' of each point (except the median) from the median point of its cluster.
#' @examples DistanceFromMedian(points, cluster)
#' @export
DistanceFromMedian <- function(x, cluster = 1, Average = mean)
UseMethod("DistanceFromMedian")
#' @rdname cluster-statistics
#' @export
DistFromMed <- DistanceFromMedian
#' @export
DistanceFromMedian.dist <- function(x, cluster = 1, Average = mean) {
d <- as.matrix(x)
vapply(seq_along(unique(cluster)),
function(i) {
.DistanceFromMedian.dist(
d[cluster == i, cluster == i, drop = FALSE], Average = Average)
},
numeric(1))
}
#' @export
DistanceFromMedian.numeric <- function(x, cluster = 1, Average = mean) {
if (is.null(dim(x))) {
warning(paste0("`x` lacks dimensions. ",
"Did you subset without specifying `drop = FALSE`?"))
x <- matrix(x, 1)
}
# Return:
vapply(seq_along(unique(cluster)),
function(i) .DistanceFromMedian(x[cluster == i, , drop = FALSE],
Average = Average),
numeric(1))
}
.DistanceFromMedian <- function(x, Average = mean) {
if (dim(x)[[1]] > 1) {
.DistanceFromMedian.dist(as.matrix(dist(x)), Average = Average)
} else {
NA_real_
}
}
.DistanceFromMedian.dist <- function(d, Average = mean) {
if (dim(d)[[1]] > 1) {
medPoint <- which.min(unname(colSums(d)))
Average(d[medPoint, -medPoint])
} else {
NA_real_
}
}
#' @rdname cluster-statistics
#' @return `MeanNN()` returns a numeric specifying the mean distance from each
#' point within a cluster to its nearest neighbour.
#' @examples MeanNN(points, cluster)
#' @export
MeanNN <- function(x, cluster = 1, Average = mean) UseMethod("MeanNN")
#' @export
MeanNN.dist <- function(x, cluster = 1, Average = mean) {
d <- as.matrix(x)
diag(d) <- NA_real_
vapply(seq_along(unique(cluster)),
function(i) .MeanNN.dist(d[cluster == i, cluster == i, drop = FALSE],
Average = Average),
numeric(1))
}
.MeanNN.dist <- function(x, Average = mean) {
if (dim(x)[[1]] > 1) {
Average(apply(x, 1, min, na.rm = TRUE))
} else {
NA_real_
}
}
#' @export
MeanNN.numeric <- function(x, cluster = 1, Average = mean) {
if (is.null(dim(x))) {
warning(paste0("`x` lacks dimensions. ",
"Did you subset without specifying `drop = FALSE`?"))
x <- matrix(x, 1)
}
# Return:
vapply(seq_along(unique(cluster)),
function(i) .MeanNN(x[cluster == i, , drop = FALSE], Average = Average),
numeric(1))
}
.MeanNN <- function(x, Average = mean) {
if (dim(x)[[1]] > 1) {
distances <- as.matrix(dist(x))
diag(distances) <- NA_real_
# Return:
Average(apply(distances, 1, min, na.rm = TRUE))
} else {
# Return:
NA_real_
}
}
#' @rdname cluster-statistics
#' @return `MeanMSTEdge()` returns a numeric specifying the mean length of an
#' edge in the minimum spanning tree of points within each cluster.
#' @examples MeanMSTEdge(points, cluster)
#' @export
MeanMSTEdge <- function(x, cluster = 1) UseMethod("MeanMSTEdge")
#' @export
MeanMSTEdge.dist <- function(x, cluster = 1) {
d <- as.matrix(x)
diag(d) <- NA_real_
vapply(seq_along(unique(cluster)),
function(i) .MeanMSTEdge.dist(d[cluster == i, cluster == i, drop = FALSE]),
numeric(1))
}
#' @importFrom stats as.dist
.MeanMSTEdge.dist <- function(x) {
n <- dim(x)[[1]]
# Return:
if (n > 1) {
MSTLength(as.dist(x)) / (n - 1)
} else {
NA_real_
}
}
#' @export
MeanMSTEdge.numeric <- function(x, cluster = 1) {
if (is.null(dim(x))) {
warning(paste0("`x` lacks dimensions. ",
"Did you subset without specifying `drop = FALSE`?"))
x <- matrix(x, 1)
}
# Return:
vapply(seq_along(unique(cluster)),
function(i) .MeanMSTEdge(x[cluster == i, , drop = FALSE]),
numeric(1))
}
#' @importFrom TreeTools MSTLength
.MeanMSTEdge <- function(x) {
n <- dim(x)[[1]]
# Return:
if (n > 1) {
MSTLength(dist(x)) / (n - 1)
} else {
NA_real_
}
}
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