Abstract
This paper proposes a new method of fuzzy c-means using the entropy function as a regularizing term in the objective function of the fuzzy c-means. An entropy maximization method has already been proposed but introduction of the concept of regularization makes the method of the entropy function more useful, since the use of regularization implies that the entropy method can be discussed within the alternative optimization of the general fuzzy c-means algorithm. Consequently, variations of the standard fuzzy c-means such as the fuzzy c-varieties can be transformed into corresponding methods using the regularization by the entropy. Thus, a method of fuzzy c-varieties by the entropy can be developed. The standard method of fuzzy c-means generates a set of fuzzy prototype classification functions by which the membership of a new observation to each cluster is calculated. This means that the entropy method generates a set of new fuzzy classification functions. Theoretical properties of the classification functions by these two methods are investigated, and the way in which the classification functions and the Voronoi diagram in the computational geometry are related is disclosed. A numerical example is given to compare the clustering results and the classification functions.
