Abstract
By extremizing the Tsallis entropy within the framework of 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. The Tsallis-entropy-based DA-FCM algorithm was developed bycombining FCM with the deterministic annealing (DA) method.One of the challenges of this method is to determine anappropriate initial temperature and a q value, according to the data distribution. This is complex, because the center of a cluster isgiven as a weighted function of the membership function to the power of q (u^q_{ik}), and it changes its shape by decreasing the temperature or by increasing q.Quantitative relationships between the temperature and q are examined, and the results show that, in order to change u^q_{ik} equally, inverse changes must be made to the temperature and q.Accordingly, in this paper, we propose and investigate two kinds of combinatorial methods for q-incrementation and the reduction of temperature for use in the Tsallis-entropy-based FCM. In the proposedmethods, q is defined as a function of the temperature.Experiments are performed, and the proposed methods are confirmed to determine an appropriate q valuein many cases
