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#' @include generics.R
#' @include archetypes-kit-blocks.R
#' @include archetypes-class.R
{}
#' Perform archetypal analysis on a data matrix.
#'
#' @param data A numeric \eqn{n \times m} data matrix.
#' @param k The number of archetypes.
#' @param weights Data weights matrix or vector (used as elements of
#' the diagonal weights matrix).
#' @param maxIterations The maximum number of iterations.
#' @param minImprovement The minimal value of improvement between two
#' iterations.
#' @param maxKappa The limit of kappa to report an ill-ness warning.
#' @param verbose Print some details during execution.
#' @param saveHistory Save each execution step in an environment for
#' further analyses.
#' @param family Blocks defining the underlying problem solving mechanisms;
#' see \code{\link{archetypesFamily}}.
#' @param ... Additional arguments for family blocks.
#'
#' @return An object of class \code{archetypes}, see
#' \code{\link{as.archetypes}}.
#'
#' @family archetypes
#'
#' @references Cutler and Breiman. Archetypal Analysis. Technometrics,
#' 36(4), 1994. 338-348.
#'
#' @examples
#' data(toy)
#' a <- archetypes(toy, 3)
#'
#' @export
archetypes <- function(data, k, weights = NULL, maxIterations = 100,
minImprovement = sqrt(.Machine$double.eps),
maxKappa = 1000, verbose = FALSE, saveHistory = TRUE,
family = archetypesFamily('original'), ...) {
### Helpers:
mycall <- match.call()
famargs <- list(...)
memento <- NULL
snapshot <- function(i) {
a <- list(archetypes = as.archetypes(t(family$rescalefn(x, family$undummyfn(x, zs))),
k, alphas = t(alphas), betas = t(betas), rss = rss, kappas = kappas,
zas = t(family$rescalefn(x, family$undummyfn(x, zas))),
residuals = resid, reweights = reweights, weights = weights,
family = list(class = family$class)))
memento$save(i, a)
}
printIter <- function(i) {
cat(i, ': rss = ', formatC(rss, 8, format = 'f'),
', improvement = ', formatC(imp, 8, format = 'f'),
'\n', sep = '')
}
### Data preparation:
x1 <- t(data)
x1 <- family$scalefn(x1, ...)
x1 <- family$dummyfn(x1, ...)
x0 <- family$globweightfn(x1, weights, ...)
x <- x0
n <- ncol(x)
m <- nrow(x)
### Initialization:
init <- family$initfn(x, k, ...)
betas <- init$betas
alphas <- init$alphas
zas <- NULL
zs <- x %*% betas
resid <- zs %*% alphas - x
rss <- family$normfn(resid, ...) / n
reweights <- rep(1, n)
kappas <- c(alphas=kappa(alphas), betas=kappa(betas),
zas=-Inf, zs=kappa(zs))
isIll <- c(kappas) > maxKappa
errormsg <- NULL
if ( saveHistory ) {
memento <- new.memento()
snapshot(0)
}
### Main loop:
i <- 1
imp <- +Inf
tryCatch(while ( (i <= maxIterations) & (imp >= minImprovement) ) {
## Reweight data:
reweights <- family$reweightsfn(resid, reweights, ...)
x <- family$weightfn(x0, reweights, ...)
## Alpha's:
alphas <- family$alphasfn(alphas, zs, x, ...)
zas <- family$zalphasfn(alphas, x, ...)
rss1 <- family$normfn(zas %*% alphas - x, ...) / n
kappas[c('alphas', 'zas')] <- c(kappa(alphas), kappa(zas))
## Beta's:
betas <- family$betasfn(betas, x, zas, ...)
zs <- x %*% betas
kappas[c('betas', 'zs')] <- c(kappa(betas), kappa(zs))
## Residuals, RSS and improvement:
alphas0 <- family$alphasfn(alphas, zs, x0, ...)
resid <- zs %*% alphas0 - x0
rss2 <- family$normfn(resid, ...) / n
imp <- rss - rss2
rss <- rss2
## Loop Zeugs:
kappas <- c(alphas = kappa(alphas), betas = kappa(betas),
zas = kappa(zas), zs = kappa(zs))
isIll <- isIll & (kappas > maxKappa)
if ( verbose )
printIter(i)
if ( saveHistory )
snapshot(i)
i <- i + 1
},
error = function(e) errormsg <<- e)
### Check illness:
if ( !is.null(errormsg) ) {
warning('k=', k, ': ', errormsg)
return(as.archetypes(NULL, k, NULL, NA, iters = i,
call = mycall, history = history,
kappas = kappas))
}
if ( any(isIll) )
warning('k=', k, ': ', paste(names(isIll)[isIll], collapse = ', '),
' > maxKappa', sep = '')
### Rescale and recalculate for original data:
alphas <- family$alphasfn(alphas, zs, x1)
betas <- family$betasfn(betas, x1, zs)
zs <- family$undummyfn(x1, zs)
zs <- family$rescalefn(x1, zs)
#resid <- zs %*% alphas - t(data)
return(as.archetypes(t(zs), k, t(alphas), rss, iters = (i-1),
call = mycall, history = memento, kappas = kappas,
betas = t(betas), family = family,
familyArgs = famargs, residuals = t(resid),
weights = weights, reweights = reweights,
scaling = attr(x1, ".Meta")))
}
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