Silhouette Plot Of Nonhierarchical Clusterings
DESCRIPTION:
Creates the silhouette plot of a partition object.
USAGE: 
plot.partition(x, ...)
REQUIRED ARGUMENTS:
x:
an object of class "partition", e.g. created by the functions pam, clara, and fanny.

Graphical parameters may also be supplied as arguments to this function (see par).

VALUE:
a NULL value is returned.
SIDE EFFECTS:
A silhouette plot is plotted on the current graphics device.
DETAILS:
A silhouette plot of the nonhierarchical clustering is created. The silhouette plot is fully described in Rousseeuw (1987) and in chapter 2 of Kaufman and Rousseeuw (1990). For each object i, a bar is drawn, representing the silhouette width s(i) of the object. Objects are grouped per cluster, starting with cluster 1 at the top. Objects with a large s(i) (almost 1) are very well clustered, a small s(i) (around 0) means that the object lies between two clusters, and objects with a negative s(i) are probably placed in the wrong cluster. A clustering can be performed for several values of k (the number of clusters). Finally, choose the value of k with the largest overall average silhouette width.

The silhouette width is computed as follows: Put a(i) = average dissimilarity between i and all other points of the cluster to which i belongs. For all clusters C, put d(i,C) = average dissimilarity of i to all objects of C. The smallest of these d(i,C) is denoted as b(i), and can be seen as the dissimilarity between i and its neighbor cluster. Finally, put s(i) = ( b(i) - a(i) ) / max( a(i), b(i) ). The overall average silhouette width is then simply the average of s(i) over all objects i.

NOTE:
Object labels are only printed when the number of objects is limited to less than 40, for readability.
REFERENCES:
Kaufman, L. and Rousseeuw, P.J. (1990). Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York.

Rousseeuw, P.J. (1987). Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math., 20, 53-65.

SEE ALSO:
partition.object , pam , pam.object , clara , clara.object , fanny, fanny.object , par .
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)))


plot(pam(x, 2))