Fuzzy c-Mean Algorithm Based on Complete Mahalanobis Distances and Separable Criterion

The well known fuzzy partition clustering algorithms are most 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 FCM-CM based on unsupervised Mahalanobis distance without any additional prior information. And FCM-CM is better than FCM-M, since the former has the more information about the overall covariance matrix than the later. In this paper, an improved new unsupervised algorithm, ldquofuzzy c-mean based on complete Mahalanobis distance and separable criterion without any prior information (FCM-CMS)rdquo, is proposed. In our new algorithm, not only the local and overall covariance matrices of all clusters but also an additional separable criterion were considered. It can get more information and higher accuracy by considering the additional separable criterion than FCM-CMx. A real data set was applied to prove that the performance of the FCM-CMS algorithm is better than those of the traditional FCM algorithm and our previous FCM-M.