Q-increment deterministic annealing fuzzy c-means clsutering using Tsallis entropy

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 a q-value. By combining with the deterministic annealing (DA) method, DA FCM using Tsallis entropy has been proposed. One of the important problems of this method is how to determine an appropriate q value according to a data distribution. In this article, a combinatorial method of q-increment and deterministic annealing of Tsallis entropy based FCM is proposed and investigated. In this method, in order to determine an appropriate q value automatically, q is increased while lowering the temperature. Experiments are performed on the Iris dataset, and it is confirmed that the proposed method determines an appropriate q value in many cases and a number of iterations of computation can be reduced.