Skip to main content

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 103))

  • 3572 Accesses

Abstract

In this chapter, we study support vector machines (SVM). We will see that optimization methodology plays an important role in building and training of SVM.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Vapnik, V.: The Nature of Statistical Learning Theory. Springer, New York (1995)

    Book  MATH  Google Scholar 

  2. Vapnik, V.: Statistical Learning Theory. Wiley, New York (1998)

    MATH  Google Scholar 

  3. Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines and Other Kernel-Based Learning Methods. Cambridge University Press, Cambridge (2000)

    Book  Google Scholar 

  4. Schölkopf, B., Smola, A.J.: Learning with Kernels: Support Vector Machines, Regularization, Optimization and Beyond. MIT, Cambridge (2002)

    Google Scholar 

  5. Steinwart, I., Christmann, A.: Support Vector Machines. Springer, New York (2008)

    MATH  Google Scholar 

  6. Abe, S.: Support Vector Machines for Pattern Classification, 2nd edn. Springer, London (2010)

    Book  MATH  Google Scholar 

  7. Sra, S., Nowozin, S., Wright, S.J.: Introduction: optimization and machine learning. In: Sra, S., Nowozin, S., Wright, S.J. (eds.) Optimization for Machine Learning, pp. 1–17. MIT, Cambridge (2012)

    Google Scholar 

  8. Cortes, C., Vapnik, V.: Support-vector networks. Mach. Learn. 20(3), 273–297 (1995)

    MATH  Google Scholar 

  9. Mercer, J.: Functions of positive and negative type and their connection with the theory of integral equations. Philos. Trans. R. Soc. A 209(441–458), 415–446 (1909)

    Article  MATH  Google Scholar 

  10. Berlinet, A., Thomas, C.: Reproducing Kernel Hilbert Spaces in Probability and Statistics. Kluwer Academic, Boston (2004)

    Book  MATH  Google Scholar 

  11. Müller, K.-R., Mika, S., Rätsch, G., Tsuda, K., Schölkopf, B.: An introduction to kernel-based learning algorithms. IEEE Trans. Neural Netw. 12(2), 181–201 (2001)

    Article  Google Scholar 

  12. Gärtner, T.: Kernels for Structured Data. World Scientific, Singapore/Hackensack (2009)

    Google Scholar 

  13. Mohri, M., Rostamizadeh, A., Talwalkar, A.: Foundations of Machine Learning. MIT, Cambridge (2012)

    MATH  Google Scholar 

  14. Bach, F.R., Lanckriet, G.R.G., Jordan, M.I.: Multiple kernel learning, conic duality, and the SMO algorithm. In: Proceedings of ACM International Conference on Machine Learning, Banff (2004)

    Book  Google Scholar 

  15. Sonnenburg, S., Rätsch, G., Schäfer, C., Schölkopf, B.: Large scale multiple kernel learning. J. Mach. Learn. Res. 7, 1531–1565 (2006)

    MATH  MathSciNet  Google Scholar 

  16. Gönen, M., Alpaydin, E.: Multiple kernel learning algorithms. J. Mach. Learn. Res. 12, 2211–2268 (2011)

    MATH  MathSciNet  Google Scholar 

  17. Crammer, K., Singer, Y.: On the algorithmic implementation of multiclass kernel-based vector machines. J. Mach. Learn. Res. 2, 265–292 (2001)

    Google Scholar 

  18. Keerthi, S.S., Sundararajan, S., Chang, K.-W., Hsieh, C.-J., Lin, C.-J.: A sequential dual method for large scale multi-class linear SVMs. In: Proceedings of ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Las Vegas, pp. 408–416 (2008)

    Google Scholar 

  19. Hsu, C.-W., Lin, C.-J.: A comparison of methods for multiclass support vector machines. IEEE Trans. Neural Netw. 13(2), 415–425 (2002)

    Article  Google Scholar 

  20. Rifkin, R., Klautau, A.: In defense of one-vs-all classification. J. Mach. Learn. Res. 5, 101–141 (2004)

    MATH  MathSciNet  Google Scholar 

  21. Liu, Y.: Fisher consistency of multicategory support vector machines. In: Proceedings of International Conference on Artificial Intelligence and Statistics, San Juan, pp. 289–296 (2007)

    Google Scholar 

  22. Kaufman, L.: Solving the quadratic programming problem arising in support vector classification. In: Schölkopf, B., Burges, C.J.C., Smola, A.J. (eds.) Advances in Kernel Methods: Support Vector Learning, pp. 147–168. MIT, Cambridge (1998)

    Google Scholar 

  23. Joachims, T.: Making large-scale SVM learning practical. In: Schölkopf, B., Burges, C.J.C., Smola, A.J. (eds.) Advances in Kernel Methods: Support Vector Learning, pp. 169–184. MIT, Cambridge (1998)

    Google Scholar 

  24. Chang, C.-C., Hsu, C.-W., Lin, C.-J.: The analysis of decomposition methods for support vector machines. IEEE Trans. Neural Netw. 11(4), 1003–1008 (2000)

    Article  Google Scholar 

  25. Chang, E.Y., Bai, H., Zhu, K., Wang, H., Li, J., Qiu, Z.: PSVM: parallel support vector machines with incomplete Cholesky factorization. In: Bekkerman, R., Bilenko, M., Langford, J. (eds.) Scaling Up Machine Learning: Parallel and Distributed Approaches, pp. 109–126. Cambridge University Press, Cambridge/New York (2011)

    Chapter  Google Scholar 

  26. Platt, J.C.: Fast training of support vector machines using sequential minimal optimization. In: Schölkopf, B., Burges, C.J.C., Smola, A.J. (eds) Advances in Kernel Methods: Support Vector Learning, pp. 185–208. MIT, Cambridge (1998)

    Google Scholar 

  27. Keerthi, S.S., Shevade, S.K., Bhattacharyya, C., Murthy, K.R.K.: Improvements to Platt’s SMO algorithm for SVM classifier design. Neural Comput. 13(3), 637–649 (2001)

    Article  MATH  Google Scholar 

  28. Fan, R.-E., Chen, P.-H., Lin, C.-J.: Working set selection using second order information for training support vector machines. J. Mach. Learn. Res. 6, 1889–1918 (2005)

    MATH  MathSciNet  Google Scholar 

  29. Chen, P.-H., Fan, R.-E., Lin, C.-J.: A study on SMO-type decomposition methods for support vector machines. IEEE Trans. Neural Netw. 17(4), 893–908 (2006)

    Article  Google Scholar 

  30. López, J., Dorronsoro, J.R.: Simple proof of convergence of the SMO algorithm for different SVM variants. IEEE Trans. Neural Netw. Learn. Syst. 23(7), 1142–1147 (2012)

    Article  Google Scholar 

  31. LIBSVM: A library for support vector machines. http://www.csie.ntu.edu.tw/~cjlin/libsvm/

  32. Akata, Z., Perronnin, F., Harchaoui, Z., Schmid, C.: Good practice in large-scale learning for image classification. IEEE Trans. Pattern Anal. Mach. Intell. 36(3), 507–520 (2014)

    Article  Google Scholar 

  33. Novikov, A.B.J.: On convergence proofs on perceptrons. In: Proceedings of the Symposium on the Mathematical Theory of Automata, New York, vol. XII, pp. 615–622 (1962)

    Google Scholar 

  34. Tax, D.M.J., Duin, R.P.W.: Support vector data description. Mach. Learn. 54(1), 45–66 (2004)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Tsinghua University Press, Beijing and Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Li, L. (2015). Support Vector Machines. In: Selected Applications of Convex Optimization. Springer Optimization and Its Applications, vol 103. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46356-7_2

Download citation

Publish with us

Policies and ethics