Alternative fuzzy clustering algorithms with l1-norm and covariance matrix

Authors:
Miin-Shen Yang;Wen-Liang Hung;Tsiung-Iou Chung
Affiliations:
Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, Taiwan;Department of Applied Mathematics, National Hsinchu University of Education, Hsin-Chu, Taiwan;Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, Taiwan
Venue:
ACIVS'06 Proceedings of the 8th international conference on Advanced Concepts For Intelligent Vision Systems
Year:
2006

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Abstract

In fuzzy clustering, the fuzzy c-means (FCM) algorithm is the best known and most used method. Although FCM is a very useful method, it is sensitive to noise and outliers so that Wu and Yang (2002) proposed an alternative FCM (AFCM) algorithm. In this paper, we consider the AFCM algorithms with L1-norm and fuzzy covariance. These generalized AFCM algorithms can detect elliptical shapes of clusters and also robust to noise and outliers. Some numerical experiments are performed to assess the performance of the proposed algorithms. Numerical results clearly indicate the proposed algorithms to be superior to the existing methods.