Fuzzy C-Mean Algorithm Based on Mahalanobis Distance and New 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. Gustafson-Kessel (GK) clustering algorithm and Gath-Geva (GG) clustering algorithm, were developed to detect non-spherical structural clusters, but both of them based on semi-supervised Mahalanobis distance needed additional prior information. An improved fuzzy C-mean algorithm based on unsupervised Mahalanobis distance, FCM-M, was proposed by our previous work, but it didn´t consider the relationships between cluster centers in the objective function. In this paper, we proposed an improved fuzzy C-mean algorithm, FCM-MS, which is not only based on unsupervised Mahalanobis distance, but also considering the relationships between cluster centers, and the relationships between the center of all points and the cluster centers in the objective function, the singular and the initial values problems were also solved. A real data set was applied to prove that the performance of the FCM-MS algorithm gave more accurate clustering results than the FCM and FCM-M methods, and the ratio method which is proposed by us is the better of the two methods for selecting the initial values.