Multi-q extension of Tsallis entropy based fuzzy c-means clustering

Abstract

Tsallis entropy is a q-parameter extension of Shannon entropy. By extremizing Tsallis entropy within the framework of fuzzy c-means (FCM) clustering, a membership function similar to the statistical mechanical distribution function is obtained. The extent of the membership function is determined by a system temperature and q. In this study, a multi-q extension method of Tsallis entropy based FCM is proposed and investigated. In this method qs are assigned to all clusters one by one. Each q value is determined to make the membership function to fit to a corresponding cluster distribution. This method is combined with the deterministic annealing (DA) method, and Tsallis entropy based multi-q DA clustering algorithm is developed. Experiments are performed on the numerical and Iris data, and it is confirmed that the proposed method improves the accuracy of clustering, and is superior to the standard Tsallis entropy based FCM.