Deterministic and Simulated Annealing Approach to Fuzzy C-means Clustering

This paper explains the approximation of a membership function obtained by entropy regularization of the fuzzy c-means (FCM) method. By regularizing FCM with fuzzy entropy, a membership function similar to the Fermi-Dirac distribution function is obtained. We propose a new clustering method, in which the minimum of the Helmholtz free energy for FCM is searched by deterministic annealing (DA), while optimizing the parameters of the membership function by simulated annealing (SA). However, it takes a long time to execute SA repeatedly because the membership function contains an exponential function. Thus, the membership function is approximated by linear functions. Numerical experiments are performed and the obtained results indicate that this method can cluster data properly and shorten the computational time.