pam {cluster} R Documentation

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 = c("euclidean", "manhattan"),
medoids = if(is.numeric(nstart)) "random",
nstart = if(variant == "faster") 1 else NA,
stand = FALSE, cluster.only = FALSE,
do.swap = TRUE,
keep.diss = !diss && !cluster.only && n < 100,
keep.data = !diss && !cluster.only,
variant = c("original", "o_1", "o_2", "f_3", "f_4", "f_5", "faster"),
pamonce = FALSE, trace.lev = 0)


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 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. 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 variables. 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 x is already a dissimilarity matrix, then this argument will be ignored. medoids NULL (default) or length-k vector of integer indices (in 1:n) specifying initial medoids instead of using the ‘build’ algorithm. nstart used only when medoids = "random": specifies the number of random “starts”; this argument corresponds to the one of kmeans() (from R's package stats). 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 mean absolute deviation. If x is already a dissimilarity matrix, then this argument will be ignored. cluster.only logical; if true, only the clustering will be computed and returned, see details. do.swap logical indicating if the swap phase should happen. The default, 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. 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. pamonce logical or integer in 0:6 specifying algorithmic short cuts as proposed by Reynolds et al. (2006), and Schubert and Rousseeuw (2019, 2021) see below. variant a character string denoting the variant of PAM algorithm to use; a more self-documenting version of pamonce which should be used preferably; note that "faster" not only uses pamonce = 6 but also nstart = 1 and hence medoids = "random" by default. trace.lev integer specifying a trace level for printing diagnostics during the build and swap phase of the algorithm. Default 0 does not print anything; higher values print increasingly more.

Details

The basic 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

Author(s)

Kaufman and Rousseeuw's orginal Fortran code was translated to C and augmented in several ways, e.g. to allow cluster.only=TRUE or do.swap=FALSE, by Martin Maechler.
Matthias Studer, Univ.Geneva provided the pamonce (1 and 2) implementation.
Erich Schubert, TU Dortmund contributed the pamonce (3 to 6) implementation.

References

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. doi:10.1007/s10852-005-9022-1.

Erich Schubert and Peter J. Rousseeuw (2019) Faster k-Medoids Clustering: Improving the PAM, CLARA, and CLARANS Algorithms; SISAP 2020, 171–187. doi:10.1007/978-3-030-32047-8_16.

Erich Schubert and Peter J. Rousseeuw (2021) Fast and Eager k-Medoids Clustering: O(k) Runtime Improvement of the PAM, CLARA, and CLARANS Algorithms; Preprint, to appear in Information Systems (https://arxiv.org/abs/2008.05171).

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 # 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)



[Package cluster version 2.1.4 Index]