Probabilistic-fuzzy clustering algorithm

Clustering algorithms divide up a data set into classes/clusters, where similar data objects are assigned to the same cluster. When the boundary between clusters is ill defined, which yields situations where the same data object belongs to more than one class. The notion of fuzzy clustering becomes relevant. In this course, each datum belongs to a given class with some membership grade, between 0 and 1. The most prominent fuzzy clustering algorithm is the fuzzy c-means introduced by Bezdek, a fuzzification of k-means or ISODATA algorithm. On the other hand, several research issues have been risen regarding both the objective function to be minimized and the optimization constraints, which help to identify proper cluster shape. This paper addresses the issue where the data objects consist of Gaussian distributions. The approach advocated in this case is to use a probabilistic distance structure based on BHATTACHARYYA distance in standard fuzzy c-means algorithm. This leads to a modified FCM, with a probabilistic distance structure. The performances of the proposed algorithm are evaluated through some academic examples and the superiority of the modified FCM was clearly laid bare