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 = "euclidean", stand = FALSE, maxit = 500, tol = 1e15)
x 
data matrix or data frame, or dissimilarity matrix, 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. In case of a dissimilarity matrix, x is typically the output
of daisy or dist . Also a vector of
length n*(n1)/2 is allowed (where n is the number of observations),
and will be interpreted in the same way as the output of the
abovementioned functions. Missing values (NAs) are not allowed.

k 
integer giving the desired number of clusters. It is required that 0 < k < n/2 where n is the number of observations. 
diss 
logical flag: if TRUE (default for dist or
dissimilarity objects), then x is assumed to be a
dissimilarity matrix. If FALSE, then x is treated as
a matrix of observations by variables.

memb.exp 
number r strictly larger than 1 specifying the
membership exponent used in the fit criterion; see the
‘Details’ below. Default: 2 which used to be hardwired
inside FANNY. 
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 sumofsquares 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. 
maxit, tol 
maximal number of iterations and default tolerance
for convergence (relative convergence of the fit criterion) for the
FANNY algorithm. The defaults maxit = 500 and tol =
1e15 used to be hardwired inside the algorithm. 
In a fuzzy clustering, each observation is ``spread out'' over the various
clusters. Denote by u(i,v) 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 to allow user specified
memb.exp
.
Fanny aims to minimize the objective function
SUM_[v=1..k] (SUM_(i,j) u(i,v)^r u(j,v)^r d(i,j)) / (2 SUM_j u(j,v)^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 > 1 gives increasingly crisper
clusterings whereas r > Inf leads to complete
fuzzyness. K&R(1990), p.191 note that values too close to 1 can lead
to slow convergence.
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) ## Plot similar to Figure 6 in Stryuf et al (1996) plot(fanny(ruspini, 5))