\HeaderA{pam}{Partitioning Around Medoids}{pam}
\keyword{cluster}{pam}
\begin{Description}\relax
Partitioning (clustering) of the data into \code{k} clusters ``around
medoids'', a more robust version of K-means.
\end{Description}
\begin{Usage}
\begin{verbatim}
pam(x, k, diss = inherits(x, "dist"), metric = "euclidean",
    medoids = NULL, stand = FALSE, cluster.only = FALSE,
    do.swap = TRUE,
    keep.diss = !diss && !cluster.only && n < 100,
    keep.data = !diss && !cluster.only, trace.lev = 0)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{x}] data matrix or data frame, or dissimilarity matrix or object,
depending on the value of the \code{diss} argument.

In case of a matrix or data frame, each row corresponds to an
observation, and each column corresponds to a variable.  All
variables must be numeric.  Missing values (\code{\LinkA{NA}{NA}}s)
\emph{are} allowed---as long as every pair of observations has at
least one case not missing.

In case of a dissimilarity matrix, \code{x} is typically the output
of \code{\LinkA{daisy}{daisy}} or \code{\LinkA{dist}{dist}}.  Also a vector of
length n*(n-1)/2 is allowed (where n is the number of observations),
and will be interpreted in the same way as the output of the
above-mentioned functions. Missing values (NAs) are \emph{not}
allowed.

\item[\code{k}] positive integer specifying the number of clusters, less than
the number of observations.
\item[\code{diss}] logical flag: if TRUE (default for \code{dist} or
\code{dissimilarity} objects), then \code{x} will be considered as a
dissimilarity matrix.  If FALSE, then \code{x} will be considered as
a matrix of observations by variables.

\item[\code{metric}] character string specifying the metric to be used for calculating
dissimilarities between observations.\\
The currently available options are "euclidean" and
"manhattan".  Euclidean distances are root sum-of-squares of
differences, and manhattan distances are the sum of absolute
differences.  If \code{x} is already a dissimilarity matrix, then
this argument will be ignored.

\item[\code{medoids}] NULL (default) or length-\code{k} vector of integer
indices (in \code{1:n}) specifying initial medoids instead of using
the \sQuote{\emph{build}} algorithm.
\item[\code{stand}] logical; if true, the measurements in \code{x} are
standardized before calculating the dissimilarities.  Measurements
are standardized for each variable (column), by subtracting the
variable's mean value and dividing by the variable's mean absolute
deviation.  If \code{x} is already a dissimilarity matrix, then this
argument will be ignored.
\item[\code{cluster.only}] logical; if true, only the clustering will be
computed and returned, see details.
\item[\code{do.swap}] logical indicating if the \bold{swap} phase should
happen. The default, \code{TRUE}, correspond to the
original algorithm.  On the other hand, the \bold{swap} phase is
much more computer intensive than the \bold{build} one for large
\eqn{n}{}, so can be skipped by \code{do.swap = FALSE}.
\item[\code{keep.diss, keep.data}] logicals indicating if the dissimilarities
and/or input data \code{x} should be kept in the result.  Setting
these to \code{FALSE} can give much smaller results and hence even save
memory allocation \emph{time}.
\item[\code{trace.lev}] integer specifying a trace level for printing
diagnostics during the build and swap phase of the algorithm.
Default \code{0} does not print anything; higher values print
increasingly more.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
\code{pam} is fully described in chapter 2 of Kaufman and Rousseeuw
(1990).  Compared to the k-means approach in \code{kmeans}, the
function \code{pam} has the following features: (a) it also accepts a
dissimilarity matrix; (b) it is more robust because it minimizes a sum
of dissimilarities instead of a sum of squared euclidean distances;
(c) it provides a novel graphical display, the silhouette plot (see
\code{plot.partition}) (d) it allows to select the number of clusters
using \code{mean(\LinkA{silhouette}{silhouette}(pr))} on the result
\code{pr <- pam(..)}, or directly its component
\code{pr\$silinfo\$avg.width}, see also \code{\LinkA{pam.object}{pam.object}}.

When \code{cluster.only} is true, the result is simply a (possibly
named) integer vector specifying the clustering, i.e.,\\
\code{pam(x,k, cluster.only=TRUE)} is the same as \\
\code{pam(x,k)\$clustering} but computed more efficiently.

The \code{pam}-algorithm is based on the search for \code{k}
representative objects or medoids among the observations of the
dataset.  These observations should represent the structure of the
data.  After finding a set of \code{k} medoids, \code{k} clusters are
constructed by assigning each observation to the nearest medoid.  The
goal is to find \code{k} representative objects which minimize the sum
of the dissimilarities of the observations to their closest
representative object.
\\
By default, when \code{medoids} are not specified, the algorithm first
looks for a good initial set of medoids (this is called the
\bold{build} phase).  Then it finds a local minimum for the
objective function, that is, a solution such that there is no single
switch of an observation with a medoid that will decrease the
objective (this is called the \bold{swap} phase).

When the \code{medoids} are specified, their order does \emph{not}
matter; in general, the algorithms have been designed to not depend on
the order of the observations.
\end{Details}
\begin{Value}
an object of class \code{"pam"} representing the clustering.  See
\code{?\LinkA{pam.object}{pam.object}} for details.
\end{Value}
\begin{Note}\relax
For large datasets, \code{pam} may need too much memory or too much
computation time since both are \eqn{O(n^2)}{}.  Then,
\code{\LinkA{clara}{clara}()} is preferable, see its documentation.
\end{Note}
\begin{SeeAlso}\relax
\code{\LinkA{agnes}{agnes}} for background and references;
\code{\LinkA{pam.object}{pam.object}}, \code{\LinkA{clara}{clara}}, \code{\LinkA{daisy}{daisy}},
\code{\LinkA{partition.object}{partition.object}}, \code{\LinkA{plot.partition}{plot.partition}},
\code{\LinkA{dist}{dist}}.
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
## generate 25 objects, divided into 2 clusters.
x <- rbind(cbind(rnorm(10,0,0.5), rnorm(10,0,0.5)),
           cbind(rnorm(15,5,0.5), rnorm(15,5,0.5)))
pamx <- pam(x, 2)
pamx
summary(pamx)
plot(pamx)
## use obs. 1 & 16 as starting medoids -- same result (typically)
(p2m <- pam(x, 2, medoids = c(1,16)))

p3m <- pam(x, 3, trace = 2)
## rather stupid initial medoids:
(p3m. <- pam(x, 3, medoids = 3:1, trace = 1))


pam(daisy(x, metric = "manhattan"), 2, diss = TRUE)

data(ruspini)
## Plot similar to Figure 4 in Stryuf et al (1996)
## Not run: plot(pam(ruspini, 4), ask = TRUE)

\end{ExampleCode}
\end{Examples}

