New cluster validity index with fuzzy functions

Abstract

A new cluster validity index is introduced to validate the results obtained by the recent Improved Fuzzy Clustering (IFC), which combines two different methods, i.e., fuzzy c-means clustering and fuzzy c-regression, in a novel way. Proposed validity measure determines the optimum number of clusters of the IFC based on a ratio of the compactness to separability of the clusters. The compactness is represented with: (i) the sum of the average distances of each object to their cluster centers, and (ii) the error measure of their fuzzy functions, which utilizes membership values as additional input variables. The separability is based on the ratio between: (i) the maximum distance between the cluster representatives, and (ii) the angles between their representative fuzzy functions. The experiments exhibit that the new cluster validity index is a useful function when selecting the parameters of the IFC. © 2007 Springer-Verlag Berlin Heidelberg.