Skip to main content

Building a Sparse Kernel Classifier on Riemannian Manifold

  • Conference paper
  • 1272 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 4270))

Abstract

It is difficult to deal with large datasets by kernel based methods since the number of basis functions required for an optimal solution equals the number of samples. We present an approach to build a sparse kernel classifier by adding constraints to the number of support vectors and to the classifier function. The classifier is considered on Riemannian manifold. And the sparse greedy learning algorithm is used to solve the formulated problem. Experimental results over several classification benchmarks show that the proposed approach can reduce the training and runtime complexities of kernel classifier applied to large datasets without scarifying high classification accuracy.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Burges, C.J.C.: Simplified support vector decision rules. In: Proc. 13th International Conference on Machine Learning, pp. 71–77. Morgan Kaufmann, San Francisco (1996)

    Google Scholar 

  2. Nair, P.B., Choudhury, A., Keane, A.J.: Some greedy learning algorithms for sparse regression and classification with mercer kernels. Journal of Machine Learning Research 3, 781–801 (2002)

    Article  MathSciNet  Google Scholar 

  3. Tipping, M.E.: Sparse bayesian learning and the relevance vector machine. Journal of Machine Learning Research 1, 211–244 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  4. Lee, Y.J., Mangasarian, O.L.: RSVM: reduced support vector machines. In: CD Proceedings of the First SIAM International Conference on Data Mining, Chicago (2001)

    Google Scholar 

  5. Wu, M., Scholkopf, B., Bakir, G.: Building sparse large margin classifiers. In: Proceedings of the 22th International Conference on Machine Learning, Bonn, Germany (2005)

    Google Scholar 

  6. Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation 15(6), 1373–1396 (2003)

    Article  MATH  Google Scholar 

  7. Smola, A.J., Scholkopf, B.: Sparse greedy matrix approximation for machine learning. In: Proceedings of the 17th International Conference on Machine Learning, pp. 911–918. Morgan Kaufmann, San Francisco (2000)

    Google Scholar 

  8. Natarajan, B.K.: Sparse approximate solutions to linear systems. SIAM Journal of Computing 25(2), 227–234 (1995)

    Article  MathSciNet  Google Scholar 

  9. Mallat, S., Zhang, Z.: Matching pursuit in a time-frequency dictionary. IEEE Transactions on Signal Processing 41, 3397–3415 (1993)

    Article  MATH  Google Scholar 

  10. The repository at: http://ida.first.gmd.de/~raetsch/

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Qu, Y., Yuan, Z., Zheng, N. (2006). Building a Sparse Kernel Classifier on Riemannian Manifold. In: Zha, H., Pan, Z., Thwaites, H., Addison, A.C., Forte, M. (eds) Interactive Technologies and Sociotechnical Systems. VSMM 2006. Lecture Notes in Computer Science, vol 4270. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11890881_18

Download citation

  • DOI: https://doi.org/10.1007/11890881_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-46304-7

  • Online ISBN: 978-3-540-46305-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics