Possibilistic Approach to Kernel-Based Fuzzy c-Means Clustering with Entropy Regularization
The fuzzy c-means (FCM) is sensitive to noise or outliers because this method has the probabilistic constraint that the memberships of a data point across classes sum to one. To solve the problem, a possibilistic c-means clustering (PCM) has been proposed by Krishnapuram and Keller. An advantage of PCM is highly robust in a noisy environment. On the other hand, some clustering algorithms using the kernel trick, e.g., kernel-based FCM and kernel-based LVQ clustering, have been studied to obtain nonlinear classification boundaries. In this paper, an entropy-based possibilistic c-means clustering using the kernel trick has been proposed as more robust method. Numerical examples are shown and effect of the kernel method is discussed.
KeywordsProbabilistic Constraint Kernel Principal Component Analysis Kernel Trick Fisher Discriminant Analysis Possibilistic Approach
Unable to display preview. Download preview PDF.
- 6.Ichihashi, H., Honda, K., Tani, N.: Gaussian mixture PDF approximation and fuzzy c-means clustering with entropy regularization. In: Proc. of the 4th Asian Fuzzy System Symposium, Tsukuba, Japan, May 31-June 3, pp. 212–221 (2000)Google Scholar
- 7.Inokuchi, R., Miyamoto, S.: LVQ clustering and SOM using a kernel function. In: Proc. of the IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2004), Budapest, Hungary, July 25-29, pp. 182–185 (2004)Google Scholar
- 9.Liu, Z.Q., Miyamoto, S. (eds.): Soft Computing and Human-Centered Machines. Springer, Tokyo (2000)Google Scholar
- 10.Mika, S., Rätsch, G., Weston, J., Schölkopf, B., Müller, K.-R.: Fisher discriminant analysis with kernels. In: Hu, Y.-H., et al. (eds.) Neural Network for Signal Processing IX, pp. 41–48. IEEE, Los Alamitos (1999)Google Scholar
- 11.Miyamoto, S., Mukaidono, M.: Fuzzy c - means as a regularization and maximum entropy approach. In: Proc. of the 7th International Fuzzy Systems Association World Congress (IFSA 1997), Prague, Czech, June 25-30, vol. II, pp. 86–92 (1997)Google Scholar
- 12.Miyamoto, S., Suizu, D.: Fuzzy c-means clustering using kernel functions in support vector machines. J. of Advanced Computational Intelligence and Intelligent Informatics 7(1), 25–30 (2003)Google Scholar