A Validity Criterion for Fuzzy Clustering

This paper describes a validity index for fuzzy clustering: Pattern Distances Ratio (PDR) and a cluster number selection procedure using that index. 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. The validity index presented in this paper might be seen as measuring the goodness of clustering of individual examples. When it is averaged over the clustered set, it bears some resemblance to the validity indices based on notions of compactness and separation. During experiments it was used as a cluster number selection criterion for fuzzy c-means. Those experiments showed that PDR can perform well in this role but a special selection procedure should be followed, instead of usual minimum search. The procedure is also described.