An Improvement to the Possibilistic Fuzzy c-Means Clustering Algorithm

Abstract

In this work we propose to use the Gustafson-Kessel (GK) algorithm within the PFCM (Possibilistic Fuzzy c-Means), such that the cluster distributions have a better adaptation with the natural distribution of the data. The PFCM, proposed by Pal et al. on 2005, is founded on the fuzzy membership degrees of the FCM and the typicality values of the PCM. Nevertheless, this algorithm uses the Euclidian distance which gives circular clusters. So, incorporating the GK algorithm and the Mahalanobis measure for the calculus of the distance, we have the possibility to get ellipsoidal forms as well, allowing a better representation of the clusters.