Abstract
This paper evaluates the robustness of two types of unsupervised learning methods, which work in feature spaces induced by a kernel function, kernel k-means and kernel symmetric non-negative matrix factorization. The main hypothesis is that the use of non-linear kernels makes these clustering algorithms more robust to noise and outliers. The hypothesis is corroborated by applying kernel and non-kernel versions of the algorithms to data with different degrees of contamination with noisy data. The results show that the kernel versions of the clustering algorithms are indeed more robust, i.e. producing estimates with lower bias in the presence of noise.
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
Cuesta-Albertos, J.A., Gordaliza, A., Matran, C.: Trimmed k-Means: An Attempt to Robustify Quantizers. The Annals of Statistics 25(2), 553–576 (1997)
Davé, R.N., Krishnapuram, R.: Robust clustering methods: a unified view. IEEE Transactions on Fuzzy Systems 5(2), 270–293 (1997)
Ding, C., Li, T., Jordan, M.I.: Convex and Semi-Nonnegative Matrix Factorizations. IEEE Transactions on Pattern Analysis and Machine Intelligence 32(1), 45–55 (2010)
Dolia, A., Harris, C., Shawetaylor, J., Titterington, D.: Kernel ellipsoidal trimming. Computational Statistics & Data Analysis 52(1), 309–324 (2007)
García-Escudero, L.A., Gordaliza, A., Matrán, C., Mayo-Iscar, A.: A review of robust clustering methods. Advances in Data Analysis and Classification 4(2-3), 89–109 (2010)
Hardin, J., Rocke, D.M.: Outlier detection in the multiple cluster setting using the minimum covariance determinant estimator. Computational Statistics & Data Analysis 44(4), 625–638 (2004)
Huber, P.J.: Robust Statistics. Wiley Series in Probability and Statistics. John Wiley & Sons, Inc., Hoboken (1981)
Hubert, M., Rousseeuw, P.J., Van Aelst, S.: High-Breakdown Robust Multivariate Methods. Statistical Science 23(1), 92–119 (2008)
Kwok, J.T.Y., Tsang, I.W.H.: The pre-image problem in kernel methods, vol. 15, pp. 1517–1525. IEEE (2004)
Maronna, R.A., Martin, R.D., Yohai, V.J.: Robust statistics. Wiley (2006)
Nasraoui, O., Krishnapuram, R.: A robust estimator based on density and scale optimization and its application to clustering. In: Proceedings of the Fifth IEEE International Conference on Fuzzy Systems, vol. 2, pp. 1031–1035. IEEE (1996)
Shawe-Taylor, J., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press, Cambridge (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
González, F.A., Bermeo, D., Ramos, L., Nasraoui, O. (2012). On the Robustness of Kernel-Based Clustering. In: Alvarez, L., Mejail, M., Gomez, L., Jacobo, J. (eds) Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications. CIARP 2012. Lecture Notes in Computer Science, vol 7441. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33275-3_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-33275-3_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33274-6
Online ISBN: 978-3-642-33275-3
eBook Packages: Computer ScienceComputer Science (R0)