A possibilistic fuzzy Gath-Geva clustering algorithm using the exponential distance

Abstract

As a famous clustering algorithm, Gath-Geva (GG) clustering has been widely applied in many fields. Unlike fuzzy c-means (FCM) clustering, GG clustering uses the exponential distance with the fuzzy covariance matrix instead of Euclidean distance to cluster hyperellipsoidal data accurately. Due to the existence of probabilistic constraint, GG clustering is sensitive to noise data. For possibilistic fuzzy c-means (PFCM), the type of clustering data limits its application. To solve the noise sensitivity problem of GG clustering and extend PFCM for clustering hyperellipsoidal data, a possibilistic fuzzy Gath-Geva (PFGG) clustering algorithm is proposed. The PFGG clustering is derived from GG clustering in combination with PFCM clustering. FCM, GG, PFCM and PFGG are run on the several datasets to compare their clustering results. The experimental results show that the performance of PFGG is significantly better than the other clustering algorithms.