title: Analysis of the weighting exponent in the FCM.
abstract: The fuzzy c-means (FCM) algorithm is one of the most frequently used clustering algorithms. The weighting exponent m is a parameter that greatly influences the performance of the FCM. But there has been no theoretical basis for selecting the proper weighting exponent in the literature. In this paper, we develop a new theoretical approach to selecting the weighting exponent in the FCM. Based on this approach, we reveal the relation between the stability of the fixed points of the FCM and the data set itself. This relation provides the theoretical basis for selecting the weighting exponent in the FCM. The numerical experiments verify the effectiveness of our theoretical conclusion.
authors.affiliation: Department of Computer Science and Technology, Northern Jiaotong University, Beijing 100044, China. jianyu@center.njtu.edu.cn
authors.forename: Jian
authors.initials: J
authors.lastname: Yu
authors.forename: Qiansheng
authors.initials: Q
authors.lastname: Cheng
authors.forename: Houkuan
authors.initials: H
authors.lastname: Huang