2005 Volume 17 Issue 4 Pages 468-476
In this paper, we summarize the statistical mechanical representation of fuzzy clustering. Then, we give a framework of a possibilistic clustering based on a Bose-Einstein type membership function, and examine its clustering mechanisms. The fuzzy c-means clustering (FCM) method regularized with Shannon entropy gives the Maxwell-Boltzmann (or Gibbs) distribution function as a membership function. Similarly, by introducing fuzzy entropy to the FCM, we obtain the Fermi-Dirac type membership function. In these cases, the constraint that the sum of all particles is fixed is correspondent with the normalization constraint in fuzzy clustering. Furthermore, it is known that the state in which the total number of particles is not conserved exists and written by the Bose-Einstein distribution function. Thus, by the analogy of statistical mechanics, we obtain the Bose-Einstein type membership function without the constraint of normalization and propose a new fuzzy clustering algorithms.
