On utilization of k-means for determination of q-parameter for tsallis-entropy-maximized-FCM

In this article, we consider a combinatorial algorithm of fuzzy c-means (FCM) clustering maximized with the Tsallis entropy and the deterministic annealing method. The Tsallis entropy is determined as a q-parameter extension of the Shannon entropy. Membership functions similar to statistical mechanical distribution functions have been derived by maximizing the Tsallis entropy within the framework of FCM. One of the major issues when using this method is, it is still unknown how to determine an appropriate q value and the initial or highest annealing temperature (T
_high
) for a given data set. Accordingly, in this article, we present a new method that determines these values simultaneously without introducing any additional parameters. In our method, the membership function is simplified by approximating by a high-temperature series expansion method and the k-means clustering algorithm is utilized as a preprocessing step to estimate a radius of each cluster. The experimental results indicate that the proposed method is effective, and both q and T
_high
can be determined automatically, algebraically and properly for a given data set.