k clusters “around
medoids”, a more robust version of K-means.
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, pamonce = FALSE, trace.lev = 0)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 (NAs)
are allowed---as long as every pair of observations has at
least one case not missing.
In case of a dissimilarity matrix, x is typically the output
of daisy or 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 not
allowed.
dist or
dissimilarity objects), then x will be considered as a
dissimilarity matrix. If FALSE, then x will be considered as
a matrix of observations by variables.
x is already a dissimilarity matrix, then
this argument will be ignored.
k vector of integer
indices (in 1:n) specifying initial medoids instead of using
the ‘build’ algorithm.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 x is already a dissimilarity matrix, then this
argument will be ignored.TRUE, correspond to the
original algorithm. On the other hand, the swap phase is
much more computer intensive than the build one for large
$n$, so can be skipped by do.swap = FALSE.x should be kept in the result. Setting
these to FALSE can give much smaller results and hence even save
memory allocation time.0:2 specifying algorithmic
short cuts as proposed by Reynolds et al. (2006), see below.0 does not print anything; higher values print
increasingly more."pam" representing the clustering. See
?pam.object for details.
pam algorithm is fully described in chapter 2 of
Kaufman and Rousseeuw(1990). Compared to the k-means approach in kmeans, the
function 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
plot.partition) (d) it allows to select the number of clusters
using mean(silhouette(pr)[, "sil_width"]) on the result
pr <- pam(..), or directly its component
pr$silinfo$avg.width, see also pam.object. When cluster.only is true, the result is simply a (possibly
named) integer vector specifying the clustering, i.e.,
pam(x,k, cluster.only=TRUE) is the same as
pam(x,k)$clustering but computed more efficiently.
The pam-algorithm is based on the search for 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 k medoids, k clusters are
constructed by assigning each observation to the nearest medoid. The
goal is to find k representative objects which minimize the sum
of the dissimilarities of the observations to their closest
representative object.
By default, when medoids are not specified, the algorithm first
looks for a good initial set of medoids (this is called the
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 swap phase).
When the medoids are specified, their order does not
matter; in general, the algorithms have been designed to not depend on
the order of the observations.
The pamonce option, new in cluster 1.14.2 (Jan. 2012), has been
proposed by Matthias Studer, University of Geneva, based on the
findings by Reynolds et al. (2006).
The default FALSE (or integer 0) corresponds to the
original “swap” algorithm, whereas pamonce = 1 (or
TRUE), corresponds to the first proposal ....
and pamonce = 2 additionally implements the second proposal as
well.
Reynolds, A., Richards, G., de la Iglesia, B. and Rayward-Smith, V. (1992) Clustering rules: A comparison of partitioning and hierarchical clustering algorithms; Journal of Mathematical Modelling and Algorithms 5, 475--504 (http://dx.doi.org/10.1007/s10852-005-9022-1).
agnes for background and references;
pam.object, clara, daisy,
partition.object, plot.partition,
dist.
## 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 # Medoids: '7' and '25' ...
summary(pamx)
plot(pamx)
## use obs. 1 & 16 as starting medoids -- same result (typically)
(p2m <- pam(x, 2, medoids = c(1,16)))
## no _build_ *and* no _swap_ phase: just cluster all obs. around (1, 16):
p2.s <- pam(x, 2, medoids = c(1,16), do.swap = FALSE)
p2.s
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)
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