A new cluster-validity for fuzzy clustering

A new heuristic method based on the combination of two functions to evaluate the quality of fuzzy c-partitions produced by fuzzy clustering algorithms, and its effectiveness is compared to some existing cluster-validity criterion.

Abstract

Fuzzy cluster-validity criterion tends to evaluate the quality of fuzzy c-partitions produced by fuzzy clustering algorithms. Many functions have been proposed. Some methods use only the properties of fuzzy membership degrees to evaluate partitions. Others techniques combine the properties of membership degrees and the structure of data. In this paper a new heuristic method is based on the combination of two functions. The search of good clustering is measured by a fuzzy compactness–separation ratio. The first function calculates this ratio by considering geometrical properties and membership degrees of data. The second function evaluates it by using only the properties of membership degrees. Four numerical examples are used to illustrate its use as a validity functional. Its effectiveness is compared to some existing cluster-validity criterion.