On Utilization of K-Means for Determination of <i>q</i>-Parameter for Tsallis-Entropy-Maximized-FCM

Abstract

In this paper, we consider a fuzzy c-means (FCM) clustering algorithm combined with the deterministic annealing method and the Tsallis entropy maximization. The Tsallis entropy is a q -parameter extension of the Shannon entropy. By maximizing the Tsallis entropy within the framework of FCM, membership functions similar to statistical mechanical distribution functions can be derived. One of the major considerations when using this method is how to determine appropriate q values and the highest annealing temperature, T h igh , for a given data set. Accordingly, in this paper, a method for determining these values simultaneously without introducing any additional parameters is presented. In our approach, the membership function is approximated by a series of expansion methods and the K-means clustering algorithm is utilized as a preprocessing step to estimate a radius of each data distribution. The results of experiments indicate that the proposed method is effective and both q and T high can be determined automatically and algebraically from a given data set.