Skip to main content
Log in

Analytic center cutting plane method for multiple kernel learning

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript


Multiple Kernel Learning (MKL) is a popular generalization of kernel methods which allows the practitioner to optimize over convex combinations of kernels. We observe that many recent MKL solutions can be cast in the framework of oracle based optimization, and show that they vary in terms of query point generation. The popularity of such methods is because the oracle can fortuitously be implemented as a support vector machine. Motivated by the success of centering approaches in interior point methods, we propose a new approach to optimize the MKL objective based on the analytic center cutting plane method (accpm). Our experimental results show that accpm outperforms state of the art in terms of rate of convergence and robustness. Further analysis sheds some light as to why MKL may not always improve classification accuracy over naive solutions.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others


  1. Schölkopf, B., Smola, A.J.: Learning with Kernels. MIT Press, Cambridge, MA (2002)

    Google Scholar 

  2. Lanckriet, G., De Bie, T., Cristianini, N., Jordan, M.I., Stafford Noble, W.: A statistical framework for genomic data fusion. Bioinfomatics 20(16), 2626–2635 (2004).

    Article  Google Scholar 

  3. Borgwardt, K.M., Ong, C.S., Schönauer, S., Vishwanathan, S.V.N., Smola, A.J., Kriegel, H.-P.: Protein function prediction via graph kernels. In: Proceedings of the International Conference on Intelligent Systems for Molecular Biology (2005)

  4. Sonnenburg, S., Rätsch, G., Schäfer, C.: A general and efficient multiple kernel learning algorithm. In: Neural Information Processings Systems (2005)

  5. Ong, C.S., Zien, A.: An automated combination of kernels for predicting protein subcellular localization. In: Crandall, K.A., Lagergren, J. (eds.) WABI, pp. 86–197. Springer (2008)

  6. Lanckriet, G., Cristianini, N., Bartlett, P., El Ghaoui, L., Jordan, M.I.: Learning the kernel matrix with semi-definite programming. J. Mach. Learn. Res. 5, 27–72 (2004).

    MATH  Google Scholar 

  7. 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 

  8. Bach, F.R., Lanckriet, G.R.G., Jordan, M.I.: Multiple kernel learning, conic duality, and the SMO algorithm. In: ICML (2004)

  9. Bach, F.R.: Consistency of the group lasso and multiple kernel learning. J. Mach. Learn. Res. 9, 1179–1225 (2008)

    MATH  MathSciNet  Google Scholar 

  10. Rakotomamonjy, A., Bach, F.R., Canu, S., Grandvalet, Y.: Simplemkl. J. Mach. Learn. Res. 9, 2491–2521 (2008)

    MATH  MathSciNet  Google Scholar 

  11. Xu, Z., Jin, R., King, I., Lyu, M.R.: An extended level method for efficient multiple kernel learning. In: NIPS (2008)

  12. Vial, J., Goffin, J.: Convex nondifferentiable optimization: a survey focused on the analytic center cutting plane method. Optim. Methods Softw. 17(5), 805–867 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  13. Zien, A., Ong, C.S.: Multiclass multiple kernel learning. In: ICML (2007)

  14. Babonneau, F., Beltran, C., Haurie, A., Tadonki, C., Vial, J.-P.: Proximal-ACCPM: a versatile oracle based optimization method. In: Kontoghiorghes, E.J., Gatu, C. (eds.) Optimisation, Econometric and Financial Analysis (2007)

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Cheng Soon Ong.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wulff, S., Ong, C.S. Analytic center cutting plane method for multiple kernel learning. Ann Math Artif Intell 69, 225–241 (2013).

Download citation

  • Published:

  • Issue Date:

  • DOI:


Mathematics Subject Classification (2010)