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\name{trimkmeans}
\alias{trimkmeans}
\alias{print.tkm}
\alias{plot.tkm}
\title{Trimmed k-means clustering}
\description{
The trimmed k-means clustering method by Cuesta-Albertos, Gordaliza
and Matran (1997). This optimizes the k-means criterion under trimming a
portion of the points.
}
\usage{
trimkmeans(data,k,trim=0.1, scaling=FALSE, runs=100, points=NULL,
countmode=runs+1, printcrit=FALSE,
maxit=2*nrow(as.matrix(data)))
\method{print}{tkm}(x, ...)
\method{plot}{tkm}(x, data, ...)
}
\arguments{
\item{data}{matrix or data.frame with raw data}
\item{k}{integer. Number of clusters.}
\item{trim}{numeric between 0 and 1. Proportion of points to be trimmed.}
\item{scaling}{logical. If \code{TRUE}, the variables are centered at their
means and scaled to unit variance before execution.}
\item{runs}{integer. Number of algorithm runs from initial
means (randomly chosen from the data points).}
\item{points}{\code{NULL} or a matrix with k vectors used
as means to initialize the algorithm. If
initial mean vectors are specified, \code{runs} should be 1
(otherwise the same initial means are used for all runs).}
\item{countmode}{optional positive integer. Every \code{countmode}
algorithm runs \code{trimkmeans} shows a message.}
\item{printcrit}{logical. If \code{TRUE}, all criterion values (mean
squares) of the algorithm runs are printed.}
\item{maxit}{integer. Maximum number of iterations within an algorithm
run. Each iteration determines all points which
are closer to a different cluster center than the one to which they are
currently assigned. The algorithm terminates if no more points have
to be reassigned, or if \code{maxit} is reached.}
\item{x}{object of class \code{tkm}.}
\item{...}{further arguments to be transferred to \code{plot} or
\code{\link[fpc]{plotcluster}}.}
}
\details{
\code{plot.tkm} calls \code{\link[fpc]{plotcluster}} if the
dimensionality of the data \code{p} is 1, shows a scatterplot
with non-trimmed regions if \code{p=2} and discriminant coordinates
computed from the clusters (ignoring the trimmed points) if \code{p>2}.
}
\value{
An object of class 'tkm' which is a LIST with components
\item{classification}{integer vector coding cluster membership with trimmed
observations coded as \code{k+1}.}
\item{means}{numerical matrix giving the mean vectors of the k
classes.}
\item{disttom}{vector of squared Euclidean distances of all points to
the closest mean.}
\item{ropt}{maximum value of \code{disttom} so that the corresponding
point is not trimmed.}
\item{k}{see above.}
\item{trim}{see above.}
\item{runs}{see above.}
\item{scaling}{see above.}
}
\references{
Cuesta-Albertos, J. A., Gordaliza, A., and Matran, C. (1997)
Trimmed k-Means: An Attempt to Robustify Quantizers,
Annals of Statistics, 25, 553-576.
}
\author{Christian Hennig
\email{chrish@stats.ucl.ac.uk}
\url{http://www.homepages.ucl.ac.uk/~ucakche/}
}
\seealso{ \code{\link[fpc]{plotcluster}}
}
\examples{
set.seed(10001)
n1 <-60
n2 <-60
n3 <-70
n0 <-10
nn <- n1+n2+n3+n0
pp <- 2
X <- matrix(rep(0,nn*pp),nrow=nn)
ii <-0
for (i in 1:n1){
ii <-ii+1
X[ii,] <- c(5,-5)+rnorm(2)
}
for (i in 1:n2){
ii <- ii+1
X[ii,] <- c(5,5)+rnorm(2)*0.75
}
for (i in 1:n3){
ii <- ii+1
X[ii,] <- c(-5,-5)+rnorm(2)*0.75
}
for (i in 1:n0){
ii <- ii+1
X[ii,] <- rnorm(2)*8
}
tkm1 <- trimkmeans(X,k=3,trim=0.1,runs=3)
# runs=3 is used to save computing time.
print(tkm1)
plot(tkm1,X)
}
\keyword{multivariate}
\keyword{cluster}
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