Fuzzy Possibility C-Mean with New Separable Criterion

Fuzzy clustering has been used widely in education, statistics, engineering, communication... etc. The well known fuzzy possibility c-mean algorithm can improve the problems of outlier and noise in fuzzy c-mean, but it was based on Euclidean distance function, which can only be used to detect spherical structural clusters. Extending Euclidean distance to Mahalanobis distance, Gustafson-Kessel (GK) clustering algorithm and Gath-Geva (GG) clustering algorithm were developed to detect non-spherical structural clusters, but these two algorithms fail to consider the relationships between cluster centers in the objective function. Yin-Tang-Sun-Sun (YTSS) clustering algorithm solved the relationships between cluster centers question, unfortunately, they did not consider the distance between the center of all data points and the center of each cluster. This problem was solved and presented in this paper. In this paper, a new fuzzy clustering algorithm (FPCM-S) was developed based on the conventional fuzzy c-means (FCM) to obtain more accurate clustering results with new separable criterion. It is different from YTSS cluster algorithm. The improved equations for the membership and the cluster center were derived from the alternating optimization algorithm. The noise and outlier were considered to obtain more accurate clustering results. Numerical data showed that the FPCM-S clustering algorithm gave more accurate clustering results than those of both FCM and YTSS clustering algorithms.