Abstract
In this paper, the application of Wolfe’s method in Support Vector Machines learning stage is presented. This stage is usually performed by solving a quadratic programming problem and a common approach for solving it, is breaking down that problem in smaller subproblems easier to solve and manage. In this manner, instead of dividing the problem, the application of Wolfe’s method is proposed. The method transforms a quadratic programming problem into an Equivalent Linear Model and uses a variation of simplex method employed in linear programming. The proposed approach is compared against QuadProg Matlab function used to solve quadratic programming problems. Experimental results show that the proposed approach has better quality of classification compared with that function.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Suykens, J., Van Gestel, T., De Brabanter, J., De Moor, B., Vandewalle, J.: Least Square Support Vector Machines. World Scientific Publishing Co., Singapore (2002)
García-Gamboa, A., Hernández-Gress, N., González-Mendoza, M., Ibarra-Orozco, R., Mora-Vargas, J.: Heuristics to reduce the training time of SVM algorithm. In: First International Conference in Neural Network and Associative Memories (2006)
Burges, C.: A Tutorial on Support Vector Machines for Pattern Recognition. In: Data Mining and Knowledge Discovery. Kluwer Academic Publishers, Netherlands (1998)
Sideris, A., Estévez, S.: A Proximity Algorithm for Support Vector Machine Classification. In: Proceedings of the 44th IEEE Conference on Decision and Control (2005)
Vapnik, V.: Computational Learning Theory. John Wiley & Sons, Chichester (1998)
Joachims, T.: Training Linear SVMs in Linear Time. In: Proceedings of the ACM Conference on Knowledge Discovery and Data Mining, KDD (2006)
Keerthi, S.S., Shevade, S.K.: SMO Algorithm for Least Squares SVM Formulations. Neural Computation 15(2) (2003)
Welling, M.: Support Vector Machines, Class notes. University of Toronto, Department of Computer Science
Fletcher, R.: Practical Methods of Optimization. John Wiley & Sons, Chichester (2000)
Platt, J.: Fast Training of Support Vector Machines using Sequential Minimal Optimization. Microsoft Research (1998)
Scheinberg, K.: An Efficient Implementation of an Active Set Method for SVMs. IBM T. J. Watson Research Center, Mathematical Science Department (2006)
Prawda, J.: Methods and Models in Operations Research (Spanish Edition), vol. 1. Limusa (2005)
Mangasarian, O.: Generalized Support Vector Machines. Advances in Large Margin Classifiers. MIT Press, Cambridge (2000)
Chvátal, V.: Linear Programming. W. H. Freeman and Company, New York (1983)
McMillan Jr, C.: Mathematical Programming. John Wiley and Sons, Inc., Chichester (1970)
Bertsekas, D.: Network Optimization: Continuous and Discrete Models. Athena Sc. (1998)
Winston, W.: Operations Research Applications and Algorithms. Thomson (2005)
Wolfe, P.: The Simplex Method for Quadratic Programming. Econometrica 27 (1959)
UC Irvine Machine Learning Repository, http://archive.ics.uci.edu/ml/
Amari, S., Wu, S.: Improving Support Vector Machine Classifiers by Modifying Kernel Functions. Neural Networks 12, 783–789 (2000)
Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines and other kernel-based learning methods. Cambridge University Press, Cambridge (2000)
Cristianini, N.: Support Vector and Kernel Machines, Tutorial. In: International Conference in Machine Learning (2001)
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
Frausto-Solís, J., González-Mendoza, M., López-Díaz, R. (2009). Using Wolfe’s Method in Support Vector Machines Learning Stage. In: Aguirre, A.H., Borja, R.M., Garciá, C.A.R. (eds) MICAI 2009: Advances in Artificial Intelligence. MICAI 2009. Lecture Notes in Computer Science(), vol 5845. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05258-3_43
Download citation
DOI: https://doi.org/10.1007/978-3-642-05258-3_43
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05257-6
Online ISBN: 978-3-642-05258-3
eBook Packages: Computer ScienceComputer Science (R0)