cluster (version 1.9.8)

pam: Partitioning Around Medoids

Description

Partitioning (clustering) of the data into k clusters ``around medoids'', a more robust version of K-means.

Usage

pam(x, k, diss = inherits(x, "dist"), metric = "euclidean",
    medoids = NULL, stand = FALSE, cluster.only = FALSE,
    keep.diss = !diss && !cluster.only && n < 100,
    keep.data = !diss && !cluster.only)

Arguments

x

data matrix or data frame, or dissimilarity matrix or object, depending on the value of the diss argument.

In case of a matrix or data frame, each row corresponds to an observation, and each column corresponds to a variable. All

k

positive integer specifying the number of clusters, less than the number of observations.

diss

logical flag: if TRUE (default for 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 var

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

medoids

NULL (default) or length-k vector of integer indices (in 1:n) specifying initial medoids instead of using the build algorithm.

stand

logical; if true, the measurements in 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 me

cluster.only

logical; if true, only the clustering will be computed and returned, see details.

keep.diss, keep.data

logicals indicating if the dissimilarities and/or input data x should be kept in the result. Setting these to FALSE can give much smaller results and hence even save memory allocation time.

Value

• an object of class "pam" representing the clustering. See ?pam.object for details.

Details

pam 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)) 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).

See Also

agnes for background and references; pam.object, clara, daisy, partition.object, plot.partition, dist.

Examples

## 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)))
stopifnot(all.equal(pamx[-c(3,8)], p2m[-c(3,8)], tol=1e-14),
           all.equal(pamx[[3]][2],  p2m[[3]][2],  tol=1e-14))
pam(daisy(x, metric = "manhattan"), 2, diss = TRUE)

data(ruspini)
## Plot similar to Figure 4 in Stryuf et al (1996)
plot(pam(ruspini, 4), ask = TRUE)
plot(pam(ruspini, 4))