A Validity Criterion for Fuzzy Clustering

This paper describes a new validity index for fuzzy clustering: Pattern Distances Ratio (PDR) and some modifications improving its performance as cluster number selection criterion for Fuzzy C-means. It also presents experimental results concerning them. As other validity indices, solution presented in this paper may be used when a need for assessing of clustering or fuzzy clustering result adequacy arises. Most common example of such situation is when clustering algorithm that requires certain parameter, for example number of clusters, is selected but we lack a priori knowledge of this parameter and we would use educated guesses in concert with trial and error procedures. Validity index may allow to automate such process whenever it is necessary or convenient. In particular, it might ease incorporation of fuzzy clustering into more complex, intelligent systems.