Abstract
In this paper, an unsupervised Mercer kernel based fuzzy c-means (MKFCM) clustering algorithm is proposed, in which the implicit assumptions about the shapes of clusters in the FCM algorithm is removed so that the new algorithm possesses strong adaptability to cluster structures within data samples. A new method for calculating the prototypes of clusters in input space is also proposed, which is essential for data clustering applications. Experimental results have demonstrated the promising performance of the MKFCM algorithm in different scenarios.
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References
Vapnik, V.N.: The Nature of Statistical Learning Theory. Springer, New York (1995)
Schölkopf, B., Smola, A.J., Müller, K.-R.: Nonlinear Component Analysis as a Kernel Eigenvalue Problem. Neural Computation 10, 1299–1319 (1998)
Ben-Hur, A., Horn, D., Siegelmann, H.T., Vapnik, V.: Support Vector Clustering. Journal of Machine Learning Research 2, 125–137 (2001)
Girolami, M.: Mercer Kernel-based Clustering in Feature Space. IEEE Trans. on NN 13, 780–784 (2002)
Lin, C.-F., Wang, S.-D.: Fuzzy Support Vector Machines. IEEE Trans. on NN 13, 464–471 (2002)
Chiang, J.-H., Hao, P.-Y.: A New Kernel-based Fuzzy Clustering Approach: Support Vector Clustering with Cell Growing. IEEE Trans. on FS 11, 518–527 (2003)
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York (1981)
Gustafson, D.E., Kessel, W.: Fuzzy Clustering with a Fuzzy Covariance Matrix. In: Fu, K.S. (ed.) Proc. IEEE-CDC, vol. 2, pp. 761–766. IEEE Press, Piscataway (1979)
Bezdek, J.C., Anderson, I.: An Application of the C-varieties Clustering Algorithm to Polygonal Curve Fitting. IEEE Trans. on SMC 15, 637–641 (1985)
Jerome, C., Noel, B., Michel, H.: A New Fuzzy Clustering Technique based on PDF Estimation. In: Proceedings of Information Processing and Managing of Uncertainty (IPMU), pp. 225–232 (2002)
Schölkopf, B., Mika, S., Burges, C.J.C., Knirsch, P., Müller, K.-R., Ratsch, G., Smola, A.J.: Input Space versus Feature Space in Kernel based Methods. IEEE Trans. on NN 10, 1000–1017 (1999)
Breiman, L.: Bias, Variance and Arcing Classifiers. Tech. Report 460, Statistics department, University of California, USA (1996)
Breiman, L., Friedman, J., Stone, C.J., Olshen, R.A.: Classification and Regression Trees. Chapman & Hall / CRC (1984)
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Zhou, S., Gan, J.Q. (2004). Mercer Kernel, Fuzzy C-Means Algorithm, and Prototypes of Clusters. In: Yang, Z.R., Yin, H., Everson, R.M. (eds) Intelligent Data Engineering and Automated Learning – IDEAL 2004. IDEAL 2004. Lecture Notes in Computer Science, vol 3177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28651-6_90
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DOI: https://doi.org/10.1007/978-3-540-28651-6_90
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22881-3
Online ISBN: 978-3-540-28651-6
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