Fuzzy Entropy Based Fuzzy c-Means Clustering with Deterministic and Simulated Annealing Methods

This article explains how to apply the deterministic annealing (DA) and simulated annealing (SA) methods to fuzzy entropy based fuzzy c-means clustering. By regularizing the fuzzy c-means method with fuzzy entropy, a membership function similar to the Fermi-Dirac distribution function, well known in statistical mechanics, is obtained, and, while optimizing its parameters by SA, the minimum of the Helmholtz free energy for fuzzy c-means clustering is searched by DA. Numerical experiments are performed and the obtained results indicate that this combinatorial algorithm of SA and DA can represent various cluster shapes and divide data more properly and stably than the standard single DA algorithm. key words: fuzzy c-means clustering, fuzzy entropy, Fermi-Dirac distribution, deterministic annealing, simulated annealing