| pam {cluster} | R Documentation |
Return a partitioning (clustering) of the data into k clusters.
pam(x, k, diss = FALSE, metric = "euclidean", stand = FALSE)
x |
data matrix or dataframe, or dissimilarity matrix, depending on the
value of the diss argument.
In case of a matrix or dataframe, each row corresponds to an observation, and each column corresponds to a variable. All variables must be numeric. Missing values ( NAs) are allowed.
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, 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.
|
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. |
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)
which also allows to select the number of clusters.
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.
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).
an object of class "pam" representing the clustering. See
pam.object for details.
Cluster analysis divides a dataset into groups (clusters) of observations that
are similar to each other. Partitioning methods like pam, clara, and
fanny require that the number of clusters be given by the user.
Hierarchical methods like agnes, diana, and mona construct a
hierarchy of clusterings, with the number of clusters ranging from one to
the number of observations.
For datasets larger than (say) 200 observations, pam will take a lot of
computation time. Then the function clara is preferable.
Kaufman, L. and Rousseeuw, P.J. (1990) Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York.
Anja Struyf, Mia Hubert & Peter J. Rousseeuw (1996) Clustering in an Object-Oriented Environment. Journal of Statistical Software, 1. http://www.stat.ucla.edu/journals/jss/
Struyf, A., Hubert, M. and Rousseeuw, P.J. (1997) Integrating Robust Clustering Techniques in S-PLUS, Computational Statistics and Data Analysis, 26, 1737.
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
summary(pamx)
plot(pamx)
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)