A fuzzy c-means-type algorithm for clustering of data with mixed numeric and categorical attributes employing a probabilistic dissimilarity functional

Abstract

Gath-Geva (GG) algorithm is one of the most popular methodologies for fuzzy c-means (FCM)-type clustering of data comprising numeric attributes; it is based on the assumption of data deriving from clusters of Gaussian form, a much more flexible construction compared to the spherical clusters assumption of the original FCM. In this paper, we introduce an extension of the GG algorithm to allow for the effective handling of data with mixed numeric and categorical attributes. Traditionally, fuzzy clustering of such data is conducted by means of the fuzzy k-prototypes algorithm, which merely consists in the execution of the original FCM algorithm using a different dissimilarity functional, suitable for attributes with mixed numeric and categorical attributes. On the contrary, in this work we provide a novel FCM-type algorithm employing a fully probabilistic dissimilarity functional for handling data with mixed-type attributes. Our approach utilizes a fuzzy objective function regularized by Kullback-Leibler (KL) divergence information, and is formulated on the basis of a set of probabilistic assumptions regarding the form of the derived clusters. We evaluate the efficacy of the proposed approach using benchmark data, and we compare it with competing fuzzy and non-fuzzy clustering algorithms