A cluster validity index for fuzzy clustering

Cluster validity indexes have been used to evaluate the fitness of partitions produced by clustering algorithms. This paper presents a new validity index for fuzzy clustering called a partition coefficient and exponential separation (PCAES) index. It uses the factors from a normalized partition coefficient and an exponential separation measure for each cluster and then pools these two factors to create the PCAES validity index. Considerations involving the compactness and separation measures for each cluster provide different cluster validity merits. In this paper, we also discuss the problem that the validity indexes face in a noisy environment. The efficiency of the proposed PCAES index is compared with several popular validity indexes. More information about these indexes is acquired in series of numerical comparisons and also three real data sets of Iris, Glass and Vowel. The results of comparative study show that the proposed PCAES index has high ability in producing a good cluster number estimate and in addition, it provides a new point of view for cluster validity in a noisy environment.