A Generalized Approach to Possibilistic Clustering Algorithms

Fuzzy clustering is an approach using the fuzzy set theory as a tool for data grouping, which has advantages over traditional clustering in many applications. Many fuzzy clustering algorithms have been developed in the literature including fuzzy c-means and possibilistic clustering algorithms, which are all objective-function based methods. Different from the existing fuzzy clustering approaches, in this paper, a general approach of fuzzy clustering is initiated from a new point of view, in which the memberships are estimated directly according to the data information using the fuzzy set theory, and the cluster centers are updated via a performance index. This new method is then used to develop a generalized approach of possibilistic clustering to obtain an infinite family of generalized possibilistic clustering algorithms. We also point out that the existing possibilistic clustering algorithms are members of this family. Following that, some specific possibilistic clustering algorithms in the new family are demonstrated by real data experiments, and the results show that these new proposed algorithms are efficient for clustering and easy for computer implementation.