Fuzzy clustering is a widely applied method for obtaining fuzzy models from data. It has been
applied successfully in various fields including finance and marketing. Despite the successful
applications, there are a number of issues that must be dealt with in practical applications of
fuzzy clustering algorithms. This technical report proposes two extensions to the objective
function based fuzzy clustering for dealing with these issues. First, the (point) prototypes are
extended to hypervolumes whose size is determined automatically from the data being
clustered. These prototypes are shown to be less sensitive to a bias in the distribution of the
data. Second, cluster merging by assessing the similarity among the clusters during
optimization is introduced. Starting with an over-estimated number of clusters in the data,
similar clusters are merged during clustering in order to obtain a suitable partitioning of the data.
An adaptive threshold for merging is introduced. The proposed extensions are applied to
Gustafson–Kessel and fuzzy c-means algorithms, and the resulting extended algorithms are
given. The properties of the new algorithms are illustrated in various examples.
|Name||ERIM Report Series Research in Management|