Abstract
The Support Vector Machine error bound is a function of the margin and radius. Standard SVM algorithms maximize the margin within a given feature space, therefore the radius is fixed and thus ignored in the optimization.
We propose an extension of the standard SVM optimization in which we also account for the radius in order to produce an even tighter error bound than what we get by controlling only for the margin.
We use a second set of parameters, μ, that control the radius introducing like that an explicit feature weighting mechanism in the SVM algorithm. We impose an l 1 constraint on μ which results in a sparse vector, thus performing feature selection. Our original formulation is not convex, we give a convex approximation and show how to solve it. We experiment with real world datasets and report very good predictive performance compared to standard SVM.
Chapter PDF
Similar content being viewed by others
References
Weston, J., Mukherjee, S., Chapelle, O., Pontil, M., Poggio, J., Vapnik, V.: Feature selection for svms. Advances in Neural Information Processing Systems 13, 668–674 (2000)
Rakotomamonjy, A.: Variable selection using svm-based criteria. Journal of Machine Learning Research 3, 1357–1370 (2003)
Guyon, I., Weston, J., Barnhill, S., Vapnik, V.: Gene selection for cancer classification using suppor vector machine. Machine Learning 46, 389–422 (2002)
Chapelle, O., Vapnik, V., Bousquet, O., Mukherjee, S.: Choosing multiple parameters for support vector machines. Machine Learning 46(1-3), 131–159 (2002)
Duan, K., Keerthi, S.S., Poo, A.N.: Evaluation of simple performance measures for tuning svm hyperparameters. Neurocomputing 51, 41–59 (2002)
Tibshirani, R.: Regression shrinkage and selection via the lasso. Roal statistics 58, 276–288 (1996)
Efron, B., Hastie, T., Tibshirani, R.: Least angle regression. Annals of statistics (2003)
Zou, H.: The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006)
Hastie, T., Tibshirani, R., Friedman, J.: The elements of statistical learning theory. Springer, Heidelberg (2001)
Cristianini, N., Shawe-Taylor, J.: An introduction to Support Vector Machines. Cambridge University Press, Cambridge (2000)
Vapnik, V.: Statistical learning theory. Wiley Interscience, Hoboken (1998)
Bach, F., Rakotomamonjy, A., Canu, S., Grandvalet, Y.: SimpleMKL. Journal of Machine Learning Research (2008)
Bonnans, J., Shapiro, A.: Optimization problems with perturbation: A guided tour. SIAM Review 40(2), 202–227 (1998)
Kalousis, A., Prados, J., Hilario, M.: Stability of feature selection algorithms: a study on high dimensional spaces. Knowledge and Information Systems 12(1), 95–116 (2007)
Shawe-Taylor, J., Cristianini, N.: Kernel methods for pattern analysis. Cambridge University Press, Cambridge (2004)
Leo Liberti, N.M.: Global OPtimization - From Theory to Implementation. Springer, Heidelberg (2006)
Collobert, R., Weston, J., Bottou, L.: Trading convexity for scalability. In: Proceedings of the 23th Conference on Machine Learning (2006)
Stephen Boyd, L.V. (ed.): Convex optimization. Cambridge University Press, Cambridge (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Do, H., Kalousis, A., Hilario, M. (2009). Feature Weighting Using Margin and Radius Based Error Bound Optimization in SVMs. In: Buntine, W., Grobelnik, M., Mladenić, D., Shawe-Taylor, J. (eds) Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2009. Lecture Notes in Computer Science(), vol 5781. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04180-8_38
Download citation
DOI: https://doi.org/10.1007/978-3-642-04180-8_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04179-2
Online ISBN: 978-3-642-04180-8
eBook Packages: Computer ScienceComputer Science (R0)