Generalized entropy based possibilistic fuzzy C-Means for clustering noisy data and its convergence proof

Abstract

A Generalized Entropy based Possibilistic Fuzzy C-Means algorithm (GEPFCM) is proposed in this paper for clustering noisy data. The main objective of GEPFCM is to determine accurate cluster centers of noisy data by generalizing Entropy C-Means (ECM) combined with Possibilistic Fuzzy C-Means (PFCM). GEPFCM utilizes functions of distance instead of the distance itself in the fuzzy, possibilistic, and entropy terms of the clustering objective function to decrease noise contributions on the cluster centers. This study shows that GEPFCM is more accurate than PFCM algorithm. A measure based on the distance between the actual and computed cluster centers demonstrates that error of GEPFCM is about 80% less than that of PFCM.