Fuzzy clustering by quadratic regularization

Abstract

A quadratic regularization method is proposed as a variation of the fuzzy c-means. The standard fuzzy c-means is regarded as a regularization of the crisp k-means, and hence other regularization methods can be studied as fuzzy versions of the crisp c-means. A new algorithm for calculating membership values is derived, whereas calculation of cluster centers is similar to the standard method. The nearest prototype classification functions which has been derived from the standard fuzzy c-means is transformed into the corresponding method within the present method of quadratic regularization. It should be noted that the present method yields piecewise linear classification functions.