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Convergence of a Generalized Gradient Selection Approach for the Decomposition Method

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Algorithmic Learning Theory (ALT 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3244))

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Abstract

The decomposition method is currently one of the major methods for solving the convex quadratic optimization problems being associated with support vector machines. For a special case of such problems the convergence of the decomposition method to an optimal solution has been proven based on a working set selection via the gradient of the objective function. In this paper we will show that a generalized version of the gradient selection approach and its associated decomposition algorithm can be used to solve a much broader class of convex quadratic optimization problems.

This work was supported in part by the IST Programm of the European Community, under the PASCAL Network of Excellence, IST-2002-506778. This publication only reflects the authors views.

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References

  1. Boser, B.E., Guyon, I.M., Vapnik, V.N.: A Training Algorithm for Optimal Margin Classifiers. In: Proceedings of the 5th Annual Workshop on Computational Learning Theory, pp. 144–153. ACM Press, New York (1992)

    Chapter  Google Scholar 

  2. Christianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  3. Schölkopf, B., Smola, A.J.: Learning with Kernels, 2nd edn. MIT Press, Cambridge (2002)

    Google Scholar 

  4. Osuna, E., Freund, R., Girosi, F.: An Improved Training Algorithm for Support Vector Machines. In: Principe, J., Gile, L., Morgan, N., Wilson, E. (eds.) Neural Networks for Signal Processing VII – Proceedings of the 1997 IEEE Workshop, New York, pp. 276–285. IEEE, Los Alamitos (1997)

    Chapter  Google Scholar 

  5. Joachims, T.: 11. In: [18], pp. 169–184

    Google Scholar 

  6. Platt, J.C.: 12. In: [18], pp. 185–208

    Google Scholar 

  7. Keerthi, S.S., Shevade, S.K., Bhattacharyya, C., Murthy, K.R.K.: Improvements to Platt’s SMO algorithm for SVM classifier design. Neural Computation 13, 637–649 (2001)

    Article  MATH  Google Scholar 

  8. Lin, C.J.: On the Convergence of the Decomposition Method for Support Vector Machines. IEEE Transactions on Neural Networks 12, 1288–1298 (2001)

    Article  Google Scholar 

  9. Keerthi, S.S., Gilbert, E.G.: Convergence of a generalized SMO algorithm for SVM classifier design. Machine Learning 46, 351–360 (2002)

    Article  MATH  Google Scholar 

  10. Schölkopf, B., Smola, A.J., Williamson, R., Bartlett, P.: New Support Vector Algorithms. Neural Computation 12, 1207–1245 (2000)

    Article  Google Scholar 

  11. Chen, P.H., Lin, C.J., Schölkopf, B.: A Tutorial on ν–Support Vector Machines, http://www.csie.ntu.edu.tw/~cjlin/papers/nusvmtutorial.pdf

  12. Chang, C.C., Lin, C.C.: Training ν- Support Vector Classifiers: Theory and Algorithms. Neural Computation 10, 2119–2147 (2001)

    Article  Google Scholar 

  13. Simon, H.U., List, N.: A General Convergence Theorem for the Decomposition Method. In: Shawe-Taylor, J., Singer, Y. (eds.) COLT 2004. LNCS (LNAI), vol. 3120, pp. 363–377. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  14. Lin, C.J.: Asymptotic Convergence of an SMO Algorithm without any Assumptions. IEEE Transactions on Neural Networks 13, 248–250 (2002)

    Article  Google Scholar 

  15. Golub, G.H., Loan, C.F.: Matrix Computations, 3rd edn. The John Hopkins University Press (1996)

    Google Scholar 

  16. Lin, C.C.: Linear Convergence of a Decomposition Method for Support Vector Machines, http://www.csie.ntu.edu.tw/~cjlin/papers/linearconv.pdf

  17. Hush, D., Scovel, C.: Polynomial-time Decomposition Algorithms for Support Vector Machines. Machine Learning 51, 51–71 (2003)

    Article  MATH  Google Scholar 

  18. Schölkopf, B., Burges, C.J.C., Smola, A.J. (eds.): Advances in Kernel Methods – Support Vector Learning. MIT Press, Cambridge (1999)

    Google Scholar 

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List, N. (2004). Convergence of a Generalized Gradient Selection Approach for the Decomposition Method. In: Ben-David, S., Case, J., Maruoka, A. (eds) Algorithmic Learning Theory. ALT 2004. Lecture Notes in Computer Science(), vol 3244. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30215-5_26

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  • DOI: https://doi.org/10.1007/978-3-540-30215-5_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23356-5

  • Online ISBN: 978-3-540-30215-5

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