Abstract
The more sophisticated fuzzy clustering algorithms, like the Gustafson–Kessel algorithm [11] and the fuzzy maximum likelihood estimation (FMLE) algorithm [10] offer the possibility of inducing clusters of ellipsoidal shape and different sizes. The same holds for the EM algorithm for a mixture of Gaussians. However, these additional degrees of freedom often reduce the robustness of the algorithm, thus sometimes rendering their application problematic. In this paper we suggest shape and size regularization methods that handle this problem effectively.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York (1981)
Bezdek, J.C., Keller, J., Krishnapuram, R., Pal, N.: Fuzzy Models and Algorithms for Pattern Recognition and Image Processing. Kluwer, Dordrecht (1999)
Bilmes, J.: A Gentle Tutorial on the EM Algorithm and Its Application to Parameter Estimation for Gaussian Mixture and Hidden Markov Models. University of Berkeley, Tech. Rep. ICSI-TR-97-021 (1997)
Blake, C.L., Merz, C.J.: UCI Repository of Machine Learning Databases, http://www.ics.uci.edu/~mlearn/MLRepository.html
Bock, H.H.: Automatische Klassifikation. Vandenhoeck & Ruprecht, Göttingen (1974)
Dempster, A.P., Laird, N., Rubin, D.: Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society (Series B) 39, 1–38 (1977)
Duda, R.O., Hart, P.E.: Pattern Classification and Scene Analysis. J. Wiley & Sons, New York (1973)
Engl, H., Hanke, M., Neubauer, A.: Regularization of Inverse Problems. Kluwer, Dordrecht (1996)
Everitt, B.S., Hand, D.J.: Finite Mixture Distributions. Chapman & Hall, London (1981)
Gath, I., Geva, A.B.: Unsupervised Optimal Fuzzy Clustering. IEEE Trans. Pattern Analysis & Machine Intelligence 11, 773–781 (1989)
Gustafson, E.E., Kessel, W.C.: Fuzzy Clustering with a Fuzzy Covariance Matrix. In: Proc. 18th IEEE Conference on Decision and Control (IEEE CDC, San Diego, CA), pp. 761–766. IEEE Press, Piscataway (1979)
Höppner, F., Klawonn, F., Kruse, R., Runkler, T.: Fuzzy Cluster Analysis. J.Wiley & Sons, Chichester (1999)
Keller, A., Klawonn, F.: Adaptation of Cluster Sizes in Objective Function Based Fuzzy Clustering. In: Leondes, C.T. (ed.) Database and Learning Systems IV, pp. 181–199. CRC Press, Boca Raton (2003)
Klawonn, F., Kruse, R.: Constructing a Fuzzy Controller from Data. Fuzzy Sets and Systems 85, 177–193 (1997)
Kohonen, T.: Learning Vector Quantization for Pattern Recognition. Technical Report TKK-F-A601. Helsinki University of Technology, Finland (1986)
Kohonen, T.: Self-Organizing Maps. Springer, Heidelberg (1995) (3rd ext. edn. 2001)
Krishnapuram, R., Keller, J.: A Possibilistic Approach to Clustering. IEEE Transactions on Fuzzy Systems 1, 98–110 (1993)
Tikhonov, A.N., Arsenin, V.Y.: Solutions of Ill-Posed Problems. J. Wiley & Sons, New York (1977)
Timm, H., Borgelt, C., Kruse, R.: A Modification to Improve Possibilistic Cluster Analysis. In: Proc. IEEE Int. Conf. on Fuzzy Systems (FUZZ-IEEE 2002, Honolulu, Hawaii), IEEE Press, Piscataway (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Borgelt, C., Kruse, R. (2004). Shape and Size Regularization in Expectation Maximization and Fuzzy Clustering. In: Boulicaut, JF., Esposito, F., Giannotti, F., Pedreschi, D. (eds) Knowledge Discovery in Databases: PKDD 2004. PKDD 2004. Lecture Notes in Computer Science(), vol 3202. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30116-5_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-30116-5_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23108-0
Online ISBN: 978-3-540-30116-5
eBook Packages: Springer Book Archive