Correntropy and Linear Representation

  • Chapter
  • First Online:
Robust Recognition via Information Theoretic Learning

Part of the book series: SpringerBriefs in Computer Science ((BRIEFSCOMPUTER))

  • 1030 Accesses

Abstract

The nearest neighbor (NN) classifier is the most popular method for image-based object recognition. In NN classifier, the representational capacity of an image database and the recognition rate depend on how registered samples are selected to represent object’s possible variations and also how many samples are available. However, in practice, only a small number of samples are available for an object class. Hence linear representation methods are developed to generalize the representational capacity of available samples.

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

Access this chapter

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

Chapter
EUR 29.95
Price includes VAT (Spain)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
EUR 42.79
Price includes VAT (Spain)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
EUR 51.99
Price includes VAT (Spain)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Boyd, S., Vandenberghe, L.: Convex optimization. Cambridge University Press (2004)

    Google Scholar 

  2. Chien, J.T., Wu, C.C.: Discriminant waveletfaces and nearest feature classifiers for face recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(12), 1644–1649 (2002)

    Article  Google Scholar 

  3. Donoho, D.L., Stodden, V.: Breakdown point of model selection when the number of variables exceeds the number of observations. In: Proceedings of the International Joint Conference on Neural Networks, pp. 16–21 (2006)

    Google Scholar 

  4. Donoho, D.L., Tanner, J.: Sparse nonnegative solutions of underdetermined linear equations by linear programming. In: Proceedings of the National Academy of Sciences, vol. 102, pp. 9446–9451 (2005)

    MathSciNet  Google Scholar 

  5. Donoho, D.L., Tsaig, Y.: Fast solution of l 1-norm minimization problems when the solution may be sparse. IEEE Transactions on Information Theory 54(11), 4789–4812 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  6. Fidler, S., Skocaj, D., Leonardis, A.: Combining reconstructive and discriminative subspace methods for robust classification and regression by subsampling. IEEE Transactions on Pattern Analysis and Machine Intelligence 28(3), 337–350 (2006)

    Article  Google Scholar 

  7. He, R., Hu, B.G., Yuan, X.: Robust discriminant analysis based on nonparametric maximum entropy. In: Asian Conference on Machine Learning (2009)

    Google Scholar 

  8. He, R., Hu, B.G., Yuan, X., Zheng, W.S.: Principal component analysis based on nonparametric maximum entropy. Neurocomputing 73, 1840–1952 (2010)

    Article  Google Scholar 

  9. He, R., Hu, B.G., Zheng, W.S., Guo, Y.Q.: Two-stage sparse representation for robust recognition on large-scale database. In: AAAI Conference on Artificial Intelligence, pp. 475–480 (2010)

    Google Scholar 

  10. He, R., Zheng, W.S., Hu, B.G., Kong, X.W.: Two-stage nonnegative sparse representation for large-scale face recognition. IEEE Transactions on Neural Network and Learning System 34(1), 35–46 (2013)

    Google Scholar 

  11. Hotelling, H.: Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology 24, 417–441 (1933)

    Article  Google Scholar 

  12. Hyvarinen, A.: Fast and robust fixed-point algorithms for independent component analysis. IEEE Transactions on Neural Networks 10, 626–634 (1999)

    Article  Google Scholar 

  13. Jia, H., Martinez, A.M.: Support vector machines in face recognition with occlusions. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, pp. 136–141 (2009)

    Google Scholar 

  14. Kapur, J.: Measures of information and their applications. John Wiley, New York (1994)

    MATH  Google Scholar 

  15. Lee, H., Battle, A., Raina, R., Ng, A.Y.: Efficient sparse coding algorithms. In: Proceedings of Neural Information Processing Systems, vol. 19, pp. 801–808 (2006)

    Google Scholar 

  16. Li, S.Z., Lu, J.: Face recognition using the nearest feature line method. IEEE Transactions Neural Network 10(2), 439–443 (1999)

    Article  Google Scholar 

  17. Li, W., Swetits, J.J.: The linear ℓ 1 estimator and the Huber m-estimator. SIAM Journal on Optimization 8(2), 457–475 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  18. Li, X.X., Dai, D.Q., Zhang, X.F., Ren, C.X.: Structured sparse error coding for face recognition with occlusion. IEEE Transactions on Image Processing 22(5), 1889–1900 (2013)

    Article  MathSciNet  Google Scholar 

  19. Liu, W.F., Pokharel, P.P., Principe, J.C.: Correntropy: Properties and applications in non-gaussian signal processing. IEEE Transactions on Signal Processing 55(11), 5286–5298 (2007)

    Article  MathSciNet  Google Scholar 

  20. Luenberger, D.: Optimization by vector space methods. Wiley (1969)

    Google Scholar 

  21. Newman, D., Hettich, S., Blake, C., Merz, C.: Uci repository of machine learning databases. http://www.ics.uci.edu/mlearn/MLRepository.html (1998)

  22. Niu, G., Dai, B., Yamada, M., Sugiyama, M.: Information-theoretic semi-supervised metric learning via entropy regularization. In: International Conference on Machine Learning (2012)

    Google Scholar 

  23. Roweis, S.: EM algorithms for PCA and SPCA. In: Neural Information Processing Systems (NIPS), pp. 626–632 (1997)

    Google Scholar 

  24. Sharma, A., Paliwal, K.: Fast principal component analysis using fixed-point algorithm. Pattern Recognition Letters 28, 1151–1155 (2007)

    Article  Google Scholar 

  25. Shi, Q., Eriksson, A., van den Hengel, A., Shen, C.: Face recognition really a compressive sensing problem. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, pp. 553–560 (2011)

    Google Scholar 

  26. Sun, X.: Matrix Perturbation Analysis. Chinese Science Press (2001)

    Google Scholar 

  27. Torkkola, K.: Feature extraction by nonparametric mutual information maximization. Journal of Machine Learning Research 3, 1415–1438 (2003)

    MATH  MathSciNet  Google Scholar 

  28. Vo, N., Moran, B., Challa, S.: Nonnegative-least-square classifier for face recognition. In: Proceedings of International Symposium on Neural Networks:Advances in Neural Networks, pp. 449–456 (2009)

    Google Scholar 

  29. Wakin, M., Laska, J., Duarte, M., Baron, D., Sarvotham, S., Takhar, D., Kelly, K., Baraniuk, R.: An architecture for compressive image. In: Proceedings of International Conference on Image Processing, pp. 1273–1276 (2006)

    Google Scholar 

  30. Yang, M., Zhang, L., Yang, J., Zhang, D.: Robust sparse coding for face recognition. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, pp. 625–632 (2011)

    Google Scholar 

  31. Zhang, Y., Sun, Z., He, R., Tan, T.: Robust low-rank representation via correntropy. In: Asian Conference on Pattern Recognition (2013)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2014 The Author(s)

About this chapter

Cite this chapter

He, R., Hu, B., Yuan, X., Wang, L. (2014). Correntropy and Linear Representation. In: Robust Recognition via Information Theoretic Learning. SpringerBriefs in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-319-07416-0_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-07416-0_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07415-3

  • Online ISBN: 978-3-319-07416-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Navigation