Tsallis entropy is a q-parameter extension of Shannon entropy. By extremizing Tsallis entropy within the framework of fuzzy c-means clustering (FCM), 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. Combining FCM and deterministic annealing (DA) method, DA FCM using Tsallis entropy has been proposed.

One of the important problems in this method is determining an appropriate q value according to a data distribution.

A combinatorial method of q-incrementation and DA of Tsallis-entropy-based FCM is proposed and investigated herein. In the proposed method, in order to determine an appropriate q value automatically, q is increased while lowering the temperature.

Experiments are performed using the iris dataset, and the proposed method is confirmed to determine an appropriate q value in many cases, and the number of computation iterations can be reduced. However, it is also found that there exists a few combinations of q and temperature that dramatically increase the number of iterations.

fuzzy c-means, entropy maximization, Tsallis entropy, deterministic annealing.