Fuzzy clustering using deterministic annealing method and its statistical mechanical characteristics

This paper deals with statistical mechanical characteristics of fuzzy clustering regularized with the fuzzy entropy, especially a "phase transition" phenomena. We derive the critical temperature at which the phase transition occurs in the fuzzy clustering. Then, by combining the cluster divisions by phase transitions with an adequate division termination condition, we propose a hierarchical fuzzy clustering method which can determine a number of clusters. Numerical experiment shows that the proposed method works properly.