A study on statistical mechanical characteristics of fuzzy clustering

This paper is dealing with the fuzzy clustering method which combines the deterministic annealing approach and the fuzzy entropy. Regularizing fuzzy c-Means with the fuzzy entropy, we obtain the Fermi-Dirac type distribution function as the membership function. Then we examine the meanings of Fermi-Dirac function and the fuzzy entropy from the statistical mechanical point of view, and show that the mechanism of this fuzzy clustering is no other than the Fermi-Dirac statistics. Also we propose the algorithm which performs deterministic annealing of the membership function. Numerical experiment demonstrates that the proposed method can cluster a given set of data points properly.