fanny {cluster}  R Documentation 
Computes a fuzzy clustering of the data into k
clusters.
fanny(x, k, diss = inherits(x, "dist"), memb.exp = 2,
metric = c("euclidean", "manhattan", "SqEuclidean"),
stand = FALSE, iniMem.p = NULL, cluster.only = FALSE,
keep.diss = !diss && !cluster.only && n < 100,
keep.data = !diss && !cluster.only,
maxit = 500, tol = 1e15, trace.lev = 0)
x 
data matrix or data frame, or dissimilarity matrix, depending on the
value of the 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. In case of a dissimilarity matrix, 
k 
integer giving the desired number of clusters. It is
required that 
diss 
logical flag: if TRUE (default for 
memb.exp 
number 
metric 
character string specifying the metric to be used for
calculating dissimilarities between observations. Options are

stand 
logical; if true, the measurements in 
iniMem.p 
numeric 
cluster.only 
logical; if true, no silhouette information will be computed and returned, see details. 
keep.diss, keep.data 
logicals indicating if the dissimilarities
and/or input data 
maxit, tol 
maximal number of iterations and default tolerance
for convergence (relative convergence of the fit criterion) for the
FANNY algorithm. The defaults 
trace.lev 
integer specifying a trace level for printing
diagnostics during the Cinternal algorithm.
Default 
In a fuzzy clustering, each observation is “spread out” over
the various clusters. Denote by u_{iv}
the membership
of observation i
to cluster v
.
The memberships are nonnegative, and for a fixed observation i they sum to 1.
The particular method fanny
stems from chapter 4 of
Kaufman and Rousseeuw (1990) (see the references in
daisy
) and has been extended by Martin Maechler to allow
user specified memb.exp
, iniMem.p
, maxit
,
tol
, etc.
Fanny aims to minimize the objective function
\sum_{v=1}^k
\frac{\sum_{i=1}^n\sum_{j=1}^n u_{iv}^r u_{jv}^r d(i,j)}{
2 \sum_{j=1}^n u_{jv}^r}
where n
is the number of observations, k
is the number of
clusters, r
is the membership exponent memb.exp
and
d(i,j)
is the dissimilarity between observations i
and j
.
Note that r \to 1
gives increasingly crisper
clusterings whereas r \to \infty
leads to complete
fuzzyness. K&R(1990), p.191 note that values too close to 1 can lead
to slow convergence. Further note that even the default, r = 2
can lead to complete fuzzyness, i.e., memberships u_{iv} \equiv
1/k
. In that case a warning is signalled and the
user is advised to chose a smaller memb.exp
(=r
).
Compared to other fuzzy clustering methods, fanny
has the following
features: (a) it also accepts a dissimilarity matrix; (b) it is
more robust to the spherical cluster
assumption; (c) it provides
a novel graphical display, the silhouette plot (see
plot.partition
).
an object of class "fanny"
representing the clustering.
See fanny.object
for details.
agnes
for background and references;
fanny.object
, partition.object
,
plot.partition
, daisy
, dist
.
## generate 10+15 objects in two clusters, plus 3 objects lying
## between those 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)),
cbind(rnorm( 3,3.2,0.5), rnorm( 3,3.2,0.5)))
fannyx < fanny(x, 2)
## Note that observations 26:28 are "fuzzy" (closer to # 2):
fannyx
summary(fannyx)
plot(fannyx)
(fan.x.15 < fanny(x, 2, memb.exp = 1.5)) # 'crispier' for obs. 26:28
(fanny(x, 2, memb.exp = 3)) # more fuzzy in general
data(ruspini)
f4 < fanny(ruspini, 4)
stopifnot(rle(f4$clustering)$lengths == c(20,23,17,15))
plot(f4, which = 1)
## Plot similar to Figure 6 in Stryuf et al (1996)
plot(fanny(ruspini, 5))