Assessing the Quality of Fuzzy Partitions Using Relative Intersection

Abstract

In this paper, conventional validity indexes are reviewed and the shortcomings of the fuzzy cluster validation index based on inter-cluster proximity are examined. Based on these considerations, a new cluster validity index is proposed for fuzzy partitions obtained from the fuzzy c-means algorithm. The proposed validity index is defined as the average value of the relative intersections of all possible pairs of fuzzy clusters in the system. It computes the overlap between two fuzzy clusters by considering the intersection of each data point in the overlap. The optimal number of clusters is obtained by minimizing the validity index with respect to c. Experiments in which the proposed validity index and several conventional validity indexes were applied to well known data sets highlight the superior qualities of the proposed index.