Linear Fuzzy Clustering by Regularization of Dimensional Coefficients

Abstract

This paper considers the problem of detecting local linear substructures of a system in a high-dimensional data space by applying a fuzzy clustering technique. A problem in the adaptive method is pointed out. Namely, the value of the objective function does not have the monotonically decreasing property in the adaptive method. A new clustering method using an objective function with regularization of dimensional coefficients is proposed, whereby the monotonically decreasing property is guaranteed. In this paper, additive regularization using entropy, as well as the standard regularization by Bezdek, is studied in order to regularize membership values and dimensional coefficients. Illustrative examples are shown.