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#' @title DUPLEX algorithm for calibration sampling
#' @description
#' Select calibration samples from a large multivariate data using the DUPLEX
#' algorithm
#' @usage
#' duplex(X,
#' k,
#' metric = c("mahal", "euclid"),
#' pc,
#' group,
#' .center = TRUE,
#' .scale = FALSE)
#' @param X a numeric matrix.
#' @param k the number of calibration/validation samples.
#' @param metric the distance metric to be used: 'euclid' (Euclidean distance)
#' or 'mahal' (Mahalanobis distance, default).
#' @param pc optional. The number of Principal Components to be used to select
#' the samples. If not specified, distance are computed in the Euclidean space.
#' Alternatively, distances are computed in the principal component space and
#' `pc` is the number of principal components retained.
#' If `pc < 1`, the number of principal components kept corresponds to the
#' number
#' of components explaining at least (`pc * 100`) percent of the total variance.
#' @param group An optional `factor` (or vector that can be coerced to a factor
#' by \code{\link{as.factor}}) of length equal to nrow(X), giving the identifier
#' of related observations (e.g. samples of the same batch of measurements,
#' samples of the same origin, or of the same soil profile). When one
#' observation is
#' selected by the procedure all observations of the same group are removed
#' together and assigned to the calibration/validation sets. This allows to
#' select calibration and validation samples that are independent from each
#' other.
#' @param .center logical value indicating whether the input matrix must be
#' centered before projecting `X` onto the Principal Component space.
#' Analysis. Default set to \code{TRUE}.
#' @param .scale logical value indicating whether the input matrix must be
#' scaled before `X` onto the Principal Component space.
#' Analysis. Default set to \code{FALSE}.
#' @return a `list` with components:
#' \itemize{
#' \item{'`model`': numeric vector giving the row indices of the input data
#' selected for calibration}
#' \item{'`test`': numeric vector giving the row indices of the input data
#' selected for validation}
#' \item{'`pc`': if the `pc` argument is specified, a numeric matrix of the
#' scaled pc scores}
#' }
#' @references
#' Kennard, R.W., and Stone, L.A., 1969. Computer aided design of experiments.
#' Technometrics 11, 137-148.
#'
#' Snee, R.D., 1977. Validation of regression models: methods and examples.
#' Technometrics 19, 415-428.
#' @details
#' The DUPLEX algorithm is similar to the Kennard-Stone algorithm (see
#' \code{\link{kenStone}}) but allows to select both calibration and validation
#' points that are independent. Similarly to the Kennard-Stone algorithm,
#' it starts by selecting the pair of points that are the farthest apart. They
#' are assigned to the calibration sets and removed from the list of points.
#' Then, the next pair of points which are farthest apart are assigned to the
#' validation sets and removed from the list. In a third step, the procedure
#' assigns each remaining point alternatively to the calibration
#' and validation sets based on the distance to the points already selected.
#' Similarly to the Kennard-Stone algorithm, the default distance metric used
#' by the procedure is the Euclidean distance, but the Mahalanobis distance can
#' be used as well using the `pc` argument (see \code{\link{kenStone}}).
#'
#' @author Antoine Stevens & \href{https://orcid.org/0000-0002-5369-5120}{Leonardo Ramirez-Lopez}
#' @examples
#' data(NIRsoil)
#' sel <- duplex(NIRsoil$spc, k = 30, metric = "mahal", pc = .99)
#' plot(sel$pc[, 1:2], xlab = "PC1", ylab = "PC2")
#' points(sel$pc[sel$model, 1:2], pch = 19, col = 2) # points selected for calibration
#' points(sel$pc[sel$test, 1:2], pch = 18, col = 3) # points selected for validation
#' # Test on artificial data
#' X <- expand.grid(1:20, 1:20) + rnorm(1e5, 0, .1)
#' plot(X[, 1], X[, 2], xlab = "VAR1", ylab = "VAR2")
#' sel <- duplex(X, k = 25, metric = "mahal")
#' points(X[sel$model, ], pch = 19, col = 2) # points selected for calibration
#' points(X[sel$test, ], pch = 15, col = 3) # points selected for validation
#' @seealso
#' \code{\link{kenStone}}, \code{\link{honigs}}, \code{\link{shenkWest}},
#' \code{\link{naes}}
#' @export
duplex <- function(X,
k,
metric = c("mahal", "euclid"),
pc,
group,
.center = TRUE,
.scale = FALSE) {
if (missing(k)) {
stop("'k' must be specified")
}
if (ncol(X) < 2) {
stop("'X' must have at least 2 columns")
}
if (k < 2) {
stop("Invalid argument: 'k' must be higher than 2")
}
metric <- match.arg(metric)
if (is.data.frame(X)) {
x <- X <- as.matrix(X)
}
if (!missing(pc)) {
pca <- prcomp(X, center = .center, scale = .scale)
if (pc < 1) {
pvar <- pca$sdev^2 / sum(pca$sdev^2)
pcsum <- cumsum(pvar) < pc
if (any(pcsum)) {
pc <- max(which(pcsum)) + 1
} else {
pc <- 1
}
}
scores <- X <- pca$x[, 1:pc, drop = F]
}
if (metric == "mahal") {
# Project in the Mahalanobis distance space
X <- e2m(X, sm.method = "svd")
if (!missing(pc)) {
scores <- X
}
}
m <- nrow(X)
n <- 1:nrow(X)
half <- floor(m / 2)
if (k > half) {
k <- half
}
if (!missing(group)) {
if (length(group) != nrow(X)) {
stop("length(group) must be equal to nrow(X)")
}
if (!is.factor(group)) {
group <- as.factor(group)
warning("group has been coerced to a factor")
}
}
# Fist two most distant points to model set
D <- fastDist(X, X, "euclid")
id <- c(arrayInd(which.max(D), rep(m, 2)))
if (!missing(group)) {
id <- which(group %in% group[id])
group <- group[-id]
}
model <- n[id]
n <- n[-id]
# Another two most distant points to test set
id <- c(arrayInd(which.max(D[, -id]), rep(m - 2, 2)))
if (!missing(group)) {
id <- which(group %in% group[id])
group <- group[-id]
}
test <- n[id]
n <- n[-id]
ini <- i <- length(model)
while (i < k) {
# cal
if (i == ini) {
d <- D[model, -c(model, test), drop = FALSE]
mins_cal <- do.call(pmin.int, lapply(seq_len(nrow(d)), function(i) d[i, ]))
} else {
d <- rbind(D[nid_cal, -c(model, test), drop = FALSE], mins_cal)
mins_cal <- do.call(pmin.int, lapply(seq_len(nrow(d)), function(i) d[i, ]))
}
id <- which.max(mins_cal)
if (!missing(group)) {
id <- which(group %in% group[id])
group <- group[-id]
}
nid_cal <- n[id]
model <- c(model, nid_cal)
n <- n[-id]
mins_cal <- mins_cal[-id]
if (i != ini) {
mins_val <- mins_val[-id]
}
# test
if (i == ini) {
d <- D[test, -c(model, test), drop = FALSE]
mins_val <- do.call(pmin.int, lapply(seq_len(nrow(d)), function(i) d[i, ]))
} else {
d <- rbind(D[nid_val, -c(model, test), drop = FALSE], mins_val)
mins_val <- do.call(pmin.int, lapply(seq_len(nrow(d)), function(i) d[i, ]))
}
id <- which.max(mins_val)
if (!missing(group)) {
id <- which(group %in% group[id])
group <- group[-id]
}
nid_val <- n[id]
test <- c(test, nid_val)
n <- n[-id]
mins_val <- mins_val[-id]
mins_cal <- mins_cal[-id]
i <- length(model)
}
if (missing(pc)) {
return(list(model = model, test = test))
} else {
return(list(model = model, test = test, pc = scores))
}
}
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