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    initial (distinct) cluster centres.  If a number, a random set of
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    initial (distinct) cluster centres.  If a number, a random set of
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    (distinct) rows in \code{x} is chosen as the initial centres.}
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    (distinct) rows in \code{x} is chosen as the initial centres.}
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  \item{iter.max}{the maximum number of iterations allowed.}
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  \item{iter.max}{the maximum number of iterations allowed.}
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  \item{nstart}{if \code{centers} is a number, how many random sets
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  \item{nstart}{if \code{centers} is a number, how many random sets
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    should be chosen?}
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    should be chosen?}
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  \item{algorithm}{character: may be abbreviated.}
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  \item{algorithm}{character: may be abbreviated.  Note that
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    \code{"Lloyd"} and \code{"Forgy"} and alternative names for one
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    algorithm.}
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  \item{object}{an \R object of class \code{"kmeans"}, typically the
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  \item{object}{an \R object of class \code{"kmeans"}, typically the
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    result \code{ob} of \code{ob <- kmeans(..)}.}
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    result \code{ob} of \code{ob <- kmeans(..)}.}
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  \item{method}{character: may be abbreviated. \code{"centers"} causes
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  \item{method}{character: may be abbreviated. \code{"centers"} causes
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    \code{fitted} to return cluster centers (one for each input point) and
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    \code{fitted} to return cluster centers (one for each input point) and
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    \code{"classes"} causes \code{fitted} to return a vector of class
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    \code{"classes"} causes \code{fitted} to return a vector of class
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    A vector of integers (from \code{1:k}) indicating the cluster to
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    A vector of integers (from \code{1:k}) indicating the cluster to
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    which each point is allocated.
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    which each point is allocated.
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  }
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  }
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  \item{centers}{A matrix of cluster centres.}
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  \item{centers}{A matrix of cluster centres.}
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  \item{totss}{The total sum of squares.}
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  \item{totss}{The total sum of squares.}
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  \item{withinss}{Vector of within-cluster sum of squares, one component per cluster.}
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  \item{withinss}{Vector of within-cluster sum of squares,
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    one component per cluster.}
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  \item{tot.withinss}{Total within-cluster sum of squares, i.e., \code{sum(withinss)}.}
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  \item{tot.withinss}{Total within-cluster sum of squares,
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    i.e., \code{sum(withinss)}.}
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  \item{betweenss}{The between-cluster sum of squares, i.e. \code{totss-tot.withinss}.}
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  \item{betweenss}{The between-cluster sum of squares,
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    i.e. \code{totss-tot.withinss}.}
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  \item{size}{The number of points in each cluster.}
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  \item{size}{The number of points in each cluster.}
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  \item{iter}{The number of (outer) iterations.}
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  \item{iter}{The number of (outer) iterations.}
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  \item{ifault}{possibly an algorithm problem indicator for experts.}
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  \item{ifault}{integer: indicator of a possible algorithm problem
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    -- for experts.}
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}
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}
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\references{
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\references{
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  Forgy, E. W. (1965) Cluster analysis of multivariate data:
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  Forgy, E. W. (1965) Cluster analysis of multivariate data:
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  efficiency vs interpretability of classifications.
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  efficiency vs interpretability of classifications.
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  \emph{Biometrics} \bold{21}, 768--769.
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  \emph{Biometrics} \bold{21}, 768--769.
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## random starts do help here with too many clusters
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## random starts do help here with too many clusters
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## (and are often recommended anyway!):
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## (and are often recommended anyway!):
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(cl <- kmeans(x, 5, nstart = 25))
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(cl <- kmeans(x, 5, nstart = 25))
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plot(x, col = cl$cluster)
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plot(x, col = cl$cluster)
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points(cl$centers, col = 1:5, pch = 8)
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points(cl$centers, col = 1:5, pch = 8)
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## Artificial example [was "infinite loop" on x86_64; PR#15364]
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rr <- c(rep(-0.4, 5), rep(-0.4- 1.11e-16, 14), -.5)
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r. <- signif(rr, 12)
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try ( k3 <- kmeans(rr, 3, trace=2) ) ## Warning: Quick-Transfer.. steps exceed
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try ( k. <- kmeans(r., 3) ) # after rounding, have only two distinct points
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      k. <- kmeans(r., 2)   # fine
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}
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}
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\keyword{multivariate}
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\keyword{multivariate}
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\keyword{cluster}
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\keyword{cluster}