Fuzzy possibility c-mean clustering algorithms based on complete Mahalanobis distances

[[abstract]]Two well 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 fail to consider the relationships between cluster centers in the objective function, needing additional prior information.. In our previous studies, we developed two improved algorithms, FCM-M and FPCM-M, based on unsupervised Mahalanobis distance without any additional prior information. And FPCM-M is better than FCM-M, since the former has the more information about the typicalities than the later. In this paper, an improved new unsupervised algorithm, "fuzzy possibility c-mean based on complete Mahalanobis distance without any prior information (FPCM-CM)", is proposed. In our new algorithm, not only the local covariance matrix of each cluster but also the overall covariance matrix was considered. It can get more information and higher accuracy by considering the additional overall covariance matrix than FPCM-M. A real data set was applied to prove that the performance of the FPCM-CM algorithm is better than those of the traditional FCM and FPCM algorithm and our previous FCM-M