Fuzzy Possibility Clustering Algorithm Based on Complete Mahalanobis Distances

The two known fuzzy partition clustering algorithms, FCM and FPCM are based on Euclidean distance function, which can only be used to detect spherical structural clusters. GK clustering algorithm and GG clustering algorithm, were developed to detect non-spherical structural clusters, but both of them need additional prior information. In our previous studies, we developed four improved algorithms, FCM-M, FPCM-M, FCM-CM and FPCM-CM based on unsupervised Mahalanobis distance without any additional prior information. In first two algorithms, only the local covariance matrix of each cluster was considered, In last two algorithms, not only the local covariance matrix of each cluster but also the overall covariance matrix was considered, and FPCM-CM is the better one. In this paper, a more information about “separable criterion” is considered, and the further improved new algorithm, “fuzzy possibility c-mean based on complete Mahalanobis distance and separable criterion, (FPCM-CMS)” is proposed. It can get more information and higher accuracy by considering the additional separable criterion than FPCM-CM. A real data set was applied to prove that the performance of the FPCM-CMS algorithm is better than those of above six algorithms.