| silhouette {cluster} | R Documentation |
Compute silhouette information according to a given clustering in k clusters.
silhouette(x, ...)
silhouette.default (x, dist, ...)
silhouette.partition(x, ...)
sortSilhouette(object, ...)
summary(object, FUN = mean, ...)
plot(x, nmax.lab = 40, max.strlen = 5,
main = NULL, sub = NULL, xlab = expression("Silhouette width "* s[i]),
col = "gray", border = 0, cex.names = par("cex.axis"),
do.n.k = TRUE, do.clus.stat = TRUE, ...)
x |
an object of appropriate class; for the default
method an integer vector with cluster codes in 1:k or a list
with such an x$clustering component. |
dist |
a dissimilarity object inheriting from class
dist or coercible to one. |
object |
an object of class silhouette. |
... |
further arguments passed to and from methods. |
FUN |
function used summarize silhouette widths. |
nmax.lab |
integer indicating the number of labels which is considered too large for single-name labeling the silhouette plot. |
max.strlen |
positive integer giving the length to which strings are truncated in silhouette plot labeling. |
main, sub, xlab |
arguments to title; have a
sensible non-NULL default here. |
col, border, cex.names |
arguments passed
barplot(); note that the default used to be col
= heat.colors(n), border = par("fg") instead.
|
do.n.k |
logical indicating if n and k ``title text'' should be written. |
do.clus.stat |
logical indicating if cluster size and averages should be written right to the silhouettes. |
For each observation i, the silhouette width s(i) is
defined as follows:
Put a(i) = average dissimilarity between i and all other points of the
cluster to which i belongs. For all other clusters C, put
d(i,C) = average dissimilarity of i to all observations of C. The
smallest of these d(i,C) is b(i) := min_C d(i,C),
and can be seen as the dissimilarity between i and its ``neighbor''
cluster, i.e., the nearest one to which it does not belong.
Finally,
s(i) := ( b(i) - a(i) ) / max( a(i), b(i) ).
Observations with a large s(i) (almost 1) are very well clustered, a small s(i) (around 0) means that the observation lies between two clusters, and observations with a negative s(i) are probably placed in the wrong cluster.
silhouette() returns an object, sil, of class
silhouette which is an [n x 3] matrix with attributes. For
each observation i, sil[i,] contains the cluster to which i
belongs as well as the neighbor cluster of i (the cluster, not
containing i, for which the average dissimilarity between its
observations and i is minimal), and the silhouette width s(i) of
the observation. The colnames correspondingly are
c("cluster", "neighbor", "sil_width").
summary(sil) returns an object of class
summary.silhouette, a list with components
si.summary |
numerical summary of the individual
silhouette widths s(i). |
clus.avg.widths |
numeric (rank 1) array of clusterwise
means of silhouette widths where mean = FUN is used. |
avg.width |
the total mean FUN(s) where s are the
individual silhouette widths. |
clus.sizes |
table of the k cluster sizes. |
call |
if available, the call creating sil. |
Ordered |
logical identical to attr(sil, "Ordered"), see
below. |
sortSilhouette(sil) orders the rows of sil as in the
silhouette plot, by cluster (increasingly) and decreasing silhouette
width s(i).
attr(sil, "Ordered") is a logical indicating if sil is
ordered as by sortSilhouette(). In that case,
rownames(sil) will contain case labels or numbers.
While silhouette() is intrinsic to the
partition clusterings, and hence has a (trivial) method
for these, it is straightforward to get silhouettes from hierarchical
clusterings from silhouette.default() with
cutree() and distance as input.
Rousseeuw, P.J. (1987) Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math., 20, 53–65.
chapter 2 of Kaufman, L. and Rousseeuw, P.J. (1990), see
the references in plot.agnes.
partition.object, plot.partition.
data(ruspini)
pr4 <- pam(ruspini, 4)
str(si <- silhouette(pr4))
(ssi <- summary(si))
plot(si) # silhouette plot
si2 <- silhouette(pr4$clustering, dist(ruspini, "canberra"))
summary(si2) # has small values: "canberra"'s fault
plot(si2, nmax= 80, cex.names=0.6)
par(mfrow = c(3,2), oma = c(0,0, 3, 0))
for(k in 2:6)
plot(silhouette(pam(ruspini, k=k)), main = paste("k = ",k), do.n.k=FALSE)
mtext("PAM(Ruspini) as in Kaufman & Rousseeuw, p.101",
outer = TRUE, font = par("font.main"), cex = par("cex.main"))
## Silhouette for a hierarchical clustering:
ar <- agnes(ruspini)
si3 <- silhouette(cutree(ar, k = 5), # k = 4 gave the same as pam() above
daisy(ruspini))
plot(si3, nmax = 80, cex.names = 0.5)