Four c-regression methods and classification functions

Abstract

Four methods of c-regression are compared. Two of them are methods of fuzzy clustering: (a) the fuzzy c-regression methods, and (b) an entropy method proposed by the authors. Two others are probabilistic methods of (c) the deterministic annealing, and (d) the mixture distribution method using the EM algorithm. It is shown that the entropy method yields the same formula as that of the deterministic annealing. Clustering results as well as classification functions are compared. The classification functions for fuzzy clustering are fuzzy rules interpolating cluster memberships, while those for the latter two are probabilistic rules. Theoretical properties of the classification functions are studied. A numerical example is shown.