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Alternatives to Parameter Selection for Kernel Methods

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4131))

Abstract

In this paper we propose alternative methods to parameter selection techniques in order to build a kernel matrix for classification purposes using Support Vector Machines (SVMs). We describe several methods to build a unique kernel matrix from a collection of kernels built using a wide range of values for the unkown parameters. The proposed techniques have been successfully evaluated on a variety of artificial and real data sets. The new methods outperform the best individual kernel under consideration and they can be used as an alternative to the parameter selection problem in kernel methods.

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References

  1. Bousquet, O., Herrmann, D.J.L.: On the complexity of learning the kernel matrix. In: Becker, S., Thurn, S., Obermayer, K. (eds.) Advances in Neural Information Processing Systems, 15, pp. 415–422. The MIT Press, Cambridge (2003)

    Google Scholar 

  2. Chapelle, O., Vapnik, V., Bousquet, O., Mukherjee, S.: Choosing multiple parameters for support vector machines. Machine Learning 46(1/3), 131–159 (2002)

    Article  MATH  Google Scholar 

  3. Cristianini, N., Shawe-Taylor, J., Elisseeff, A., Kandola, J.: On Kernel-Target Alignment, pp. 367–373. MIT Press, Cambridge (2002)

    Google Scholar 

  4. Gower, J.C., Legendre, P.: Metric and euclidean properties of dissimilarity coefficients. Journal of Classification 3, 5–48 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  5. Keerthi, S.S., Lin, C.: Asymptotic behaviors of support vector machines with gaussian kernel. Neural Computation 15, 1667–1689 (2003)

    Article  MATH  Google Scholar 

  6. Lanckriet, G.R.G., Cristianini, N., Barlett, P., El Ghaoui, L., Jordan, M.I.: Learning the kernel matrix with semi-definite programming. Journal of Machine Learning Research 5, 27–72 (2004)

    Google Scholar 

  7. Lee, J.-H., Lin, C.-J.: Automatic model selection for support vector machines. Technical report, National Taiwan University (2000)

    Google Scholar 

  8. Lehmann, E.L.: NonParametrics: Statistical Methods Based on Ranks. McGraw- Hill, New York (1975)

    MATH  Google Scholar 

  9. Mangasarian, O.L., Wolberg, W.H.: Cancer diagnosis via linear programming. SIAM News 23(5), 1–18 (1990)

    Google Scholar 

  10. Moguerza, J.M., de Diego, I.M., Muñoz, A.: Improving support vector classificacion via the combination of multiple sources of information. In: Fred, A., Caelli, T.M., Duin, R.P.W., Campilho, A.C., de Ridder, D. (eds.) SSPR&SPR 2004. LNCS, vol. 3138, pp. 592–600. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  11. Pękalska, E., Duin, R.P.W., Günter, S., Bunke, H.: On not making dissimilarities euclidean. In: Fred, A., Caelli, T.M., Duin, R.P.W., Campilho, A.C., de Ridder, D. (eds.) SSPR&SPR 2004. LNCS, vol. 3138, pp. 1145–1154. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  12. Pȩkalska, E., Paclík, P., Duin, R.P.W.: A generalized kernel approach to dissimilarity-based classification. Journal of Machine Learning Research, Special Issue on Kernel Methods 2(12), 175–211 (2001)

    Google Scholar 

  13. Schittkowski, K.: Optimal parameter selection in support vector machines. Journal of Industrial and Management Optimization 1(4), 465–476 (2005)

    MATH  MathSciNet  Google Scholar 

  14. Schölkopf, B., Mika, S., Burges, C.J.C., Müller, K.-R., Knirsch, P., Rätsch, G., Smola, A.J.: Input space vs. feature space in kernel-based methods. IEEE Transactions on Neural Networks (1999)

    Google Scholar 

  15. Shawe-Taylor, J., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press, Cambridge (2004)

    Google Scholar 

  16. Silverman, B.: Density Estimation for Statistics and Data Analysis. Chapman and Hall, London (1986)

    MATH  Google Scholar 

  17. Vandenberghe, L., Boyd, S.: Semidefinite programming. SIAM Review 38(1), 49–95 (1996)

    Article  MATH  MathSciNet  Google Scholar 

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© 2006 Springer-Verlag Berlin Heidelberg

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Muñoz, A., de Diego, I.M.n., Moguerza, J.M. (2006). Alternatives to Parameter Selection for Kernel Methods. In: Kollias, S.D., Stafylopatis, A., Duch, W., Oja, E. (eds) Artificial Neural Networks – ICANN 2006. ICANN 2006. Lecture Notes in Computer Science, vol 4131. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11840817_23

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  • DOI: https://doi.org/10.1007/11840817_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-38625-4

  • Online ISBN: 978-3-540-38627-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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