fanny.object: Fuzzy Analysis (FANNY) Object
Description
The objects of class "fanny" represent a fuzzy clustering of a
dataset.Value
- A legitimate
fanny object is a list with the following components: - objectivethe objective function and the number of iterations the
fanny
algorithm needed to reach this minimal value. - membershipmatrix containing the memberships for each pair consisting of an
observation and a cluster.
- coeffDunn'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 observations. 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.
- clusteringthe clustering vector of the nearest crisp clustering. A vector with length
equal to the number of observations, giving for each observation the number
of the cluster to which it has the largest membership.
- silinfolist with all information necessary to construct a silhouette plot of the
nearest crisp clustering. This list is only available when 1 < k < n.
The first component is a matrix, with for each observation 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 observations
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. - dissan object of class
"dissimilarity", representing the total dissimilarity
matrix of the dataset. - dataa matrix containing the original or standardized measurements, depending
on the
stand option of the function fanny. If a dissimilarity matrix was
given as input structure, then this component is not available.
GENERATION
These objects are returned from fanny.METHODS
The "fanny" class has methods for the following generic functions:
print, summary.INHERITANCE
The class "fanny" inherits from "partition".
Therefore, the generic functions plot and clusplot can
be used on a fanny object.