Kernel approach to possibilistic C -means clustering

Kernel approaches can improve the performance of conventional clustering or classification algorithms for complex distributed data. This is achieved by using a kernel function, which is defined as the inner product of two values obtained by a transformation function. In doing so, this allows algorithms to operate in a higher dimensional space (i.e., more degrees of freedom for data to be meaningfully partitioned) without having to compute the transformation. As a result, the fuzzy kernel C-means (FKCM) algorithm, which uses a distance measure between patterns and cluster prototypes based on a kernel function, can obtain more desirable clustering results than fuzzy C-means (FCM) for not only spherical data but also nonspherical data. However, it can still be sensitive to noise as in the FCM algorithm. In this paper, to improve the drawback of FKCM, we propose a kernel possibilistic C-means (KPCM) algorithm that applies the kernel approach to the possibilistic C-means (PCM) algorithm. The method includes a variance updating method for Gaussian kernels for each clustering iteration. Several experimental results show that the proposed algorithm can outperform other algorithms for general data with additive noise. © 2009 Wiley Periodicals, Inc.

[1]  Mark A. Girolami,et al.  Mercer kernel-based clustering in feature space , 2002, IEEE Trans. Neural Networks.

[2]  Jiang-She Zhang,et al.  Improved possibilistic C-means clustering algorithms , 2004, IEEE Trans. Fuzzy Syst..

[3]  Gunnar Rätsch,et al.  Input space versus feature space in kernel-based methods , 1999, IEEE Trans. Neural Networks.

[4]  James M. Keller,et al.  A possibilistic approach to clustering , 1993, IEEE Trans. Fuzzy Syst..

[5]  James M. Keller,et al.  The possibilistic C-means algorithm: insights and recommendations , 1996, IEEE Trans. Fuzzy Syst..

[6]  Xiao-Hong Wu,et al.  Possibilistic Fuzzy c-Means Clustering Model Using Kernel Methods , 2005, International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC'06).

[7]  Mauro Barni,et al.  Comments on "A possibilistic approach to clustering" , 1996, IEEE Trans. Fuzzy Syst..

[8]  Rajesh N. Davé,et al.  Robust clustering methods: a unified view , 1997, IEEE Trans. Fuzzy Syst..

[9]  Sadaaki Miyamoto,et al.  Possibilistic Approach to Kernel-Based Fuzzy c-Means Clustering with Entropy Regularization , 2005, MDAI.

[10]  Zhongdong Wu,et al.  Fuzzy C-means clustering algorithm based on kernel method , 2003, Proceedings Fifth International Conference on Computational Intelligence and Multimedia Applications. ICCIMA 2003.

[11]  Dao-Qiang Zhang,et al.  Clustering Incomplete Data Using Kernel-Based Fuzzy C-means Algorithm , 2003, Neural Processing Letters.

[12]  Gunnar Rätsch,et al.  An introduction to kernel-based learning algorithms , 2001, IEEE Trans. Neural Networks.