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Regularization Paths for ν-SVM and ν-SVR

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Book cover Advances in Neural Networks – ISNN 2007 (ISNN 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4493))

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Abstract

This paper presents the ν-SVM and the ν-SVR full regularization paths along with a leave-one-out inspired stopping criterion and an efficient implementation. In the ν-SVR method, two parameters are provided by the user: the regularization parameter C and ν which settles the width of the ε-tube. In the classical ν-SVM method, parameter ν is an lower bound on the number of support vectors in the solution. Based on the previous works of [1,2], extensions of regularization paths for SVM and SVR are proposed and permit to automatically compute the solution path by varying ν or the regularization parameter.

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References

  1. Hastie, T., Rosset, S., Tibshirani, R., Zhu, J.: The entire regularization path for the support vector machine. Journal of Machine Learning Research 5, 1391–1415 (2004)

    MathSciNet  Google Scholar 

  2. Gunter, L., Zhu, J.: Computing the solution path for the regularized support vector regression. In: NIPS (2005)

    Google Scholar 

  3. Chen, P.H., Lin, C.J., Schölkopf, B.: A tutorial on v-support vector machines. Applied Stochastic Models in Business and Industry 21, 111–136 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  4. Schölkopf, B., Smola, A.: Leaning with Kernels. MIT Press, Cambridge (2001)

    Google Scholar 

  5. Argyriou, A., Hauser, R., Micchelli, C.A., Ponti, M.: A dc-programming algorithm for kernel selection. In: ICML (2006)

    Google Scholar 

  6. Micchelli, C.A., Pontil, M.: Learning the kernel function via regularization. Journal of Machine Learning Research 6, 1099–1125 (2005)

    MathSciNet  Google Scholar 

  7. Bach, F., Heckerman, D., Horvitz, E.: On the path to an ideal ROC curve: Considering cost asymmetry in learning classifiers. In: Cowell, R.G., Ghahramani, Z. (eds.) AISTATS, Society for Artificial Intelligence and Statistics, pp. 9–16 (2005)

    Google Scholar 

  8. Wahba, G.: Support Vector Machines, Reproducing Kernel Hilbert spaces and the randomized GACV. In: Schöolkopf, B., Burges, C., Smola, A. (eds.) Advances in Kernel Methods: Support Vector Learning, pp. 69–88. MIT Press, Cambridge (1999)

    Google Scholar 

  9. Vishwanathan, S.V.N., Smola, A.J., Murty, M.N.: Simple SVM. In: Proceedings of the Twentieth International Conference on Machine Learning (2003)

    Google Scholar 

  10. Wang, G., Yeung, D.Y., Lochovsky, F.: Two-dimensional solution path for support vector regression. In: Proc. of the 23rd International Conference on Machine Learning, ICML (2006)

    Google Scholar 

  11. Lee, J.H., Lin, C.J.: Automatic model selection for support vector machines. Technical report, Dept. of Computer Science and Information Engineering, National Taiwan University (2000)

    Google Scholar 

  12. Lee, M., Keerthi, S., Ong, C.J., DeCoste, D.: An efficient method for computing leave-one-out error in support vector machines with gaussian kernels. IEEE Transactions on Neural Networks 15, 750–757 (2004)

    Article  Google Scholar 

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Derong Liu Shumin Fei Zengguang Hou Huaguang Zhang Changyin Sun

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© 2007 Springer Berlin Heidelberg

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Loosli, G., Gasso, G., Canu, S. (2007). Regularization Paths for ν-SVM and ν-SVR. In: Liu, D., Fei, S., Hou, Z., Zhang, H., Sun, C. (eds) Advances in Neural Networks – ISNN 2007. ISNN 2007. Lecture Notes in Computer Science, vol 4493. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72395-0_62

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  • DOI: https://doi.org/10.1007/978-3-540-72395-0_62

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72394-3

  • Online ISBN: 978-3-540-72395-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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