Abstract
It has been shown that many kernel methods can be equivalently formulated as minimal enclosing ball (MEB) problems in a certain feature space. Exploiting this reduction, efficient algorithms to scale up Support Vector Machines (SVMs) and other kernel methods have been introduced under the name of Core Vector Machines (CVMs). In this paper, we study a new algorithm to train SVMs based on an instance of the Frank-Wolfe optimization method recently proposed to approximate the solution of the MEB problem. We show that, specialized to SVM training, this algorithm can scale better than CVMs at the price of a slightly lower accuracy.
Chapter PDF
References
Bădoiu, M., Clarkson, K.: Smaller core-sets for balls. In: Proceedings of the SODA 2003, pp. 801–802. SIAM, Philadelphia (2003)
Chang, C.-C., Lin, C.-J.: LIBSVM: a library for support vector machines (2010)
Clarkson, K.: Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm. In: Proceedings of SODA 2008, pp. 922–931. SIAM, Philadelphia (2008)
Fan, R.-E., Chen, P.-H., Lin, C.-J.: Working set selection using second order information for training support vector machines. Journal of Machine Learning Research 6, 1889–1918 (2005)
Fine, S., Scheinberg, K.: Efficient SVM training using low-rank kernel representations. Journal of Machine Learning Research 2, 243–264 (2002)
Fung, G., Mangasarian, O.: Finite newton method for lagrangian support vector machine classification. Neurocomputing 55(1-2), 39–55 (2003)
Hettich, S., Bay, S.: The UCI KDD Archive (2010), http://kdd.ics.uci.edu
Joachims, T.: Making large-scale support vector machine learning practical, pp. 169–184. MIT Press, Cambridge (1999)
Kressel, U.: Pairwise classification and support vector machines. In: Advances in Kernel Methods: Support Vector Learning, pp. 255–268. MIT Press, Cambridge (1999)
Kumar, K., Bhattacharya, C., Hariharan, R.: A randomized algorithm for large scale support vector learning. In: Advances in Neural Information Processing Systems, vol. 20, pp. 793–800. MIT Press, Cambridge (2008)
Lee, Y.-J., Huang, S.: Reduced support vector machines: A statistical theory. IEEE Transactions on Neural Networks 18(1), 1–13 (2007)
Pavlov, D., Mao, J., Dom, B.: An improved training algorithm for support vector machines. In: Proceedings of the 15th International Conference on Pattern Recognition, vol. 2, pp. 2219–2222. IEEE, Los Alamitos (2000)
Platt, J.: Fast training of support vector machines using sequential minimal optimization, pp. 185–208 (1999)
Scheinberg, K.: An efficient implementation of an active set method for SVMs. Journal of Machine Learning Research 7, 2237–2257 (2006)
Schölkopf, B., Smola, A.J.: Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. MIT Press, Cambridge (2001)
Tsang, I., Kocsor, A., Kwok, J.: Simpler core vector machines with enclosing balls. In: ICML 2007, pp. 911–918. ACM, New York (2007)
Tsang, I., Kocsor, A., Kwok, J.: LibCVM Toolkit (2009)
Tsang, I., Kwok, J., Cheung, P.-M.: Core vector machines: Fast SVM training on very large data sets. J. of Machine Learning Research 6, 363–392 (2005)
Tsang, I., Kwok, J., Zurada, J.: Generalized core vector machines. IEEE Transactions on Neural Networks 17(5), 1126–1140 (2006)
Yildirim, E.A.: Two algorithms for the minimum enclosing ball problem. SIAM Journal on Optimization 19(3), 1368–1391 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Frandi, E., Gasparo, M.G., Lodi, S., Ñanculef, R., Sartori, C. (2010). A New Algorithm for Training SVMs Using Approximate Minimal Enclosing Balls. In: Bloch, I., Cesar, R.M. (eds) Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications. CIARP 2010. Lecture Notes in Computer Science, vol 6419. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16687-7_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-16687-7_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16686-0
Online ISBN: 978-3-642-16687-7
eBook Packages: Computer ScienceComputer Science (R0)