Regularization and Constraints in Fuzzy c-Means and Possibilistic Clustering

Abstract

This paper proposes a new computational method in possibilistic clustering and compares solutions of them with those by the fuzzy c-means using probabilistic partitions. Two objective functions for both the probabilistic partitions in fuzzy c-means and possibilistic partitions in possibilistic clustering are considered for this purpose, namely, a regularized objective function obtained from the standard fuzzy c-means and that of the entropy regularization are employed. Relations between solutions for probabilistic and possibilistic partitions are investigated. Ordinary algorithm in possibilistic clustering is shown to be improved by using many initial cluster centers instead of the c centers, whereby the number of clusters is estimated after the iteration of the new algorithm. Classification functions using this method is moreover proposed. Numerical results using the iris data show effectiveness of the present method of computation.