Optimal Fuzzy Clustering in Overlapping Clusters

Ouafa Ammor1, Abdelmonaime Lachkar2, Khadija Slaoui3, and Noureddine Rais1
1 Department of Mathematics, Faculty of Sciences and Technology of Fes, Morocco
2 ESTM, Moulay Ismail University, Morocco
3 Department of Physics, Faculty of Sciences Dhar Mehraz of Fes, Morocco

Abstract: The fuzzy c-means clustering algorithm has been widely used to obtain the fuzzy k-partitions. This algorithm requires that the user gives the number of clusters k. To find automatically the “right” number of clusters, k, for a given data set, many validity indexes algorithms have been proposed in the literature. Most of these indexes do not work well for clusters with different overlapping degree. They usually have a tendency to fails in selecting the correct optimal clusters number when dealing with some data sets containing overlapping clusters. To overcome this limitation, we propose in this paper, a new and efficient clusters validity measure for determination of the optimal number of clusters which can deal successfully with or without situation of overlapping. This measure is based on maximum entropy principle. Our approach does not require any parameter adjustment, it is then completely automatic. Many simulated and real examples are presented, showing the superiority of our measure to the existing ones.