Abstract
Support Vector Machines (SVMs) for classification tasks produce sparse models by maximizing the margin. Two limitations of this technique are considered in this work: firstly, the number of support vectors can be large and, secondly, the model requires the use of (Mercer) kernel functions. Recently, some works have proposed to maximize the margin while controlling the sparsity. These works also require the use of kernels. We propose a search process to select a subset of basis functions that maximize the margin without the requirement of being kernel functions. The sparsity of the model can be explicitly controlled. Experimental results show that accuracy close to SVMs can be achieved with much higher sparsity. Further, given the same level of sparsity, more powerful search strategies tend to obtain better generalization rates than simpler ones.
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References
Vapnik, V.: The Nature of Statistical Learning Theory. Springer, Heidelberg (1995)
Schölkopf, B., Tsuda, J.P.V.K.: Kernel methods in computational biology. MIT Press, Cambridge (2004)
Balcan, M.F., Blum, A.: On a theory of learning with similarity functions. In: Proceedings of the 23rd International Conference on Machine Learning, pp. 73–80. ACM Press, New York (2006)
Steinwart, I.: Sparseness of support vector machines. Journal of Machine Learning Research 4, 1071–1105 (2003)
Tipping, M.: Sparse Bayesian learning and the relevance vector machine. Journal of Machine Learning Research 1, 211–244 (2001)
Vincent, P., Bengio, Y.: Kernel matching pursuit. Machine Learning 48(1-3), 165–187 (2002)
Bradley, P.S., Mangasarian, O.L.: Feature selection via concave minimization and support vector machines. In: 15th International Conf. on Machine Learning, pp. 82–90. Morgan Kaufmann, San Francisco (1998)
Wu, M., Schölkopf, B., Bakir, G.: Building sparse large margin classifiers. In: 22nd International Conf. on Machine learning, pp. 996–1003. ACM Press, New York (2005)
Keerthi, S., Chapelle, O., DeCoste, D.: Building Support Vector Machines with Reduced Classifier Complexity. Journal of Machine Learning Research 8, 1–22 (2006)
Keerthi, S., DeCoste, D.: A modified finite Newton method for fast solution of large scale linear SVMs. Journal of Machine Learning Research 6, 341–361 (2005)
Kittler, J.: Feature selection and extraction. In: Young, F. (ed.) Handbook of Pattern Recognition and Image Processing, Academic Press, London (1986)
Pudil, P., Novovičová, J., Kittler, J.: Floating Search Methods in Feature Selection. Pattern Recognition Letters 15(11), 1119–1125 (1994)
Lee, Y.J., Mangasarian, O.L.: Rsvm: Reduced support vector machines. In: SIAM International Conference on Data Mining (2001)
Lin, K.M., Lin, C.J.: A study on reduced support vector machines. IEEE Transactions on Neural Networks 14(6), 1449–1559 (2003)
Schölkopf, B., Sung, K., Burges, C., Girosi, F., Niyogi, P., Poggio, T., Vapnik, V.: Comparing support vector machines with Gaussian kernels to radial basis function classifiers. IEEE Transactions on Signal Processing 45(11), 2758–2765 (1997)
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Barrio, I., Romero, E., Belanche, L. (2007). Selection of Basis Functions Guided by the L2 Soft Margin. In: de Sá, J.M., Alexandre, L.A., Duch, W., Mandic, D. (eds) Artificial Neural Networks – ICANN 2007. ICANN 2007. Lecture Notes in Computer Science, vol 4668. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74690-4_43
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DOI: https://doi.org/10.1007/978-3-540-74690-4_43
Publisher Name: Springer, Berlin, Heidelberg
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