Fuzzy Analysis Object
- DESCRIPTION:
-
These are objects of class
"fanny"
They represent a fuzzy clustering of a dataset.
- GENERATION:
-
This class of objects is returned from fanny.
- METHODS:
-
The "fanny" class has methods for the following generic functions:
print, summary.
- INHERITANCE:
-
The class "fanny" inherits from "partition".
By that, the generic function plot can be used with a fanny object.
- STRUCTURE:
-
A legitimate fanny object is a list with the following components:
- objective:
-
the objective function and the number of iterations the fanny algorithm
needed to reach this minimal value.
- membership:
-
matrix containing the memberships for each pair consisting of an
object and a cluster.
- coeff:
-
Dunn's partition coefficient F(k) of the clustering, where k is the number
of clusters.
F(k) is the sum of all squared membership coefficients,
divided by the number of objects. Its value is always between 1/k and 1.
The normalized form of the coefficient is also given. It is defined as
(F(k) - 1/k) / (1 - 1/k), and ranges between 0 and 1.
A low value of Dunn's coefficient indicates a very fuzzy clustering,
whereas a value close to 1 indicates a near-crisp clustering.
- clustering:
-
the clustering vector of the nearest crisp clustering. A vector with length
equal to the number of objects, giving for each object the number of the
cluster to which it has the largest membership.
- silinfo:
-
list with all information necessary to construct a silhouette plot of the
nearest crisp clustering.
The first component is a matrix, with for each object i 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 objects and i is
minimal), and the silhouette width of i.
The other two components give the average silhouette width per cluster and
the average silhouette width for the dataset.
See plot.partition for more information.
- diss:
-
an object of class "dissimilarity", representing the total dissimilarity
matrix of the dataset.
- SEE ALSO:
-
dissimilarity.object
,
fanny
,
partition.object
,
plot.partition
.