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Correntropy with Nonnegative Constraint

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

Abstract

Nonnegativity constraint is more consistent with the biological modeling of visual data and often leads to better performance for data representation and graph learning [66]. In this chapter, we present an overview of some recent advances in correntropy with nonnegative constraint. We begin with an introduction of an 1 regularized nonnegative sparse coding algorithm to learn a nonnegative sparse representation (NSR). Then we show how to use correntropy to learn a robust NSR. Finally, based on the divide and conquer strategy, a two-stage framework is discussed for large-scale sparse representation problems.

Keywords

Recognition Rate Sparse Representation Sparse Code Full Column Rank High Recognition Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 10.
    Bjorck, A.: A direct method for sparse least-squares problems with lower and upper bounds, numer. Math 54, 19–32 (1988)MathSciNetGoogle Scholar
  2. 11.
    Black, M., Jepson, A.: Eigentracking: Robust matching and tracking of articulated objects using a view-based representation. International Journal of Computer Vision 26(1), 63–84 (1998)CrossRefGoogle Scholar
  3. 14.
    Bruckstein, A.M., Elad, M., Zibulevskyy, M.: On the uniqueness of nonnegative sparse solutions to underdetermined systems of equations. IEEE Transactions on Information Theory 54(11), 4813–4820 (2008)CrossRefGoogle Scholar
  4. 16.
    Candés, E.J., Romberg, J.: l1-magic: recovery of sparse signals via convex programming. http://www.acm.caltech.edu/l1magic/ (2005)
  5. 41.
    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)MathSciNetGoogle Scholar
  6. 49.
    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)CrossRefGoogle Scholar
  7. 53.
    Gao, W., Cao, B., Shan, S., Chen, X., Zhou, D., Zhang, X., Zhao, D.: The cas-peal large-scale Chinese face database and baseline evaluations. IEEE Transactions on System Man, and Cybernetics (Part A) 38(1), 149–161 (2008)Google Scholar
  8. 59.
    He, R., Hu, B.G., Yuan, X.: Robust discriminant analysis based on nonparametric maximum entropy. In: Asian Conference on Machine Learning (2009)Google Scholar
  9. 61.
    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. 65.
    He, R., Zheng, W.S., Hu, B.G.: Maximum correntropy criterion for robust face recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence 33(8), 1561–1576 (2011)CrossRefGoogle Scholar
  11. 66.
    He, R., Zheng, W.S., Hu, B.G., Kong, X.W.: Nonnegative sparse coding for discriminative semi-supervised learning. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 2849–2856 (2011)Google Scholar
  12. 68.
    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
  13. 84.
    Ji, Y., Lin, T., Zha, H.: Mahalanobis distance based non-negative sparse representation for face recognition. In: Proceedings of International Conference on Machine Learning and Applications, pp. 41–46 (2009)Google Scholar
  14. 89.
    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
  15. 90.
    Lei, Z., Chu, R., He, R., Liao, S., Li, S.Z.: Face recognition by discriminant analysis with Gabor tensor representation. In: Advances in Biometrics (2010)Google Scholar
  16. 98.
    Liu, R., Li, S.Z., Yuan, X., He, R.: Online determination of track loss using template inverse matching. In: International Workshop on Visual Surveillance-VS (2008)Google Scholar
  17. 99.
    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)CrossRefMathSciNetGoogle Scholar
  18. 103.
    Martinez, A.M., Benavente, R.: The AR face database. Tech. rep., Computer Vision Center (1998)Google Scholar
  19. 109.
    Naseem, I., Togneri, R., Bennamoun, M.: Linear regression for face recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence 32(11), 2106–2112 (2010)CrossRefGoogle Scholar
  20. 112.
    Nikolova, M., NG, M.K.: Analysis of half-quadratic minimization methods for signal and image recovery. SIAM Journal on Scientific Computing 27(3), 937–966 (2005)Google Scholar
  21. 123.
    Portugal, L.F., Judice, J.J., Vicente, L.N.: A comparison of block pivoting and interior-point algorithms for linear least squares problems with nonnegative variables. Mathematics of Computation 63(208), 625–643 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
  22. 149.
    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
  23. 155.
    Wright, J., Yang, A.Y., Ganesh, A., Sastry, S.S., Ma, Y.: Robust face recognition via sparse representation. IEEE Transactions on Pattern Analysis and Machine Intelligence 31(2), 210–227 (2009)CrossRefGoogle Scholar
  24. 157.
    Xing, E.P., Ng, A.Y., Jordan, M.I., Russell, S.: Distance metric learning with application to clustering with side-information. In: Proceedings of Advances in Neural Information Processing Systems, vol. 15, pp. 505–512 (2002)Google Scholar
  25. 162.
    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
  26. 163.
    Yang, S., Zha, H., Zhou, S., Hu, B.G.: Variational graph embedding for globally and locally consistent feature extraction. In: Europe Conference on Machine Learning (ECML), pp. 538–553 (2009)Google Scholar
  27. 165.
    Yuan, X.T., Hu, B.G.: Robust feature extraction via information theoretic learning. In: Proceedings of International Conference on Machine Learning, pp. 1193–1200 (2009)Google Scholar
  28. 167.
    Zhang, L., Yang, M., Feng, X.: Sparse representation or collaborative representation: Which helps face recognition? In: Proceedings of IEEE International Conference on Computer Vision (2011)Google Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.National Laboratory of Pattern RecognitionInstitute of Automation Chinese Academy of SciencesBeijingChina
  2. 2.School of Information and ControlNanjing University of Information Science and TechnologyNanjingChina

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