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Structured Sparsity via Half-Quadratic Minimization

  • Jinghuan Wei
  • Zhihang Li
  • Dong Cao
  • Man ZhangEmail author
  • Cheng Zeng
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 634)

Abstract

This paper proposes a general framework for the problem of structured sparsity via half-quadratic (HQ) minimization. Based on the theory of convex conjugacy, we firstly define an \(l_{2,1}^\varepsilon \)-norm and induce a family of penalty functions for structured sparsity. Then we build and discuss some important properties of these functions. By introducing the multiplicative auxiliary variable in HQ, we further reformulate the structured sparsity problem as an augmented half-quadratic optimization problem, and propose a general iteratively reweighted framework to alternately minimize the cost function. The proposed framework can be used in sparse representation, group sparse representation and multi-task joint sparse representation. Finally, in terms of the task of multi-biometric information fusion, we apply our proposed methods to obtain a novel fusion strategy, named structured fusion. Experimental results on the multi-biometric problems corroborate our claims and validate the proposed methods.

Keywords

Structured sparsity Half-quadratic Biometric 

References

  1. 1.
    Bach, F.R.: Consistency of the group lasso and multiple kernel learning. J. Mach. Learn. Res. 9, 1179–1225 (2008)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)CrossRefzbMATHGoogle Scholar
  3. 3.
    Chartrand, R., Yin, W.: Iteratively reweighted algorithms for compressive sensing. In: Proceedings of the IEEE Conference on Acoustics, Speech and Signal Processing, pp. 3869–3872 (2008)Google Scholar
  4. 4.
    Daubechies, I., Devore, R., Fornasier, M., Gunturk, C.S.: Iteratively reweighted least squares minimization for sparse recovery. Commun. Pure Appl. Math. 63(1), 1–38 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Fornasier, M.: Theoretical Foundations and Numerical Methods for Sparse Recovery. Walter de Gruyter, Berlin (2010)CrossRefzbMATHGoogle Scholar
  6. 6.
    Fornasier, M., Rauhut, H., Ward, R.: Low-rank matrix recovery via iteratively reweighted least squares minimization. SIAM J. Optim. 21(4), 1614–1640 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    He, R., Sun, Z., Tan, T., Zheng, W.-S.: Recovery of corrupted low-rank matrices via half-quadratic based nonconvex minimization. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2889–2896 (2011)Google Scholar
  8. 8.
    He, R., Zheng, W.S., Hu, B.G.: Maximum correntropy criterion for robust face recognition. IEEE Trans. Pattern Anal. Mach. Intell. 33(8), 1561–1576 (2011)CrossRefGoogle Scholar
  9. 9.
    Jenatton, R., Audibert, J.-Y., Bach, F.: Structured variable selection with sparsity-inducing norms. J. Mach. Learn. Res. 12, 2777–2824 (2011)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Jenatton, R., Obozinski, G., Bach, F.: Structured sparse principal component analysis. In: Proceedings of the International Conference on Artificial Intelligence and Statistics (2009)Google Scholar
  11. 11.
    Li, A., Shan, S., Chen, X., Gao, W.: Face recognition based on non-corresponding region matching. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 1060–1067 (2011)Google Scholar
  12. 12.
    Moayedi, F., Azimifar, Z., Boostani, R.: Structured sparse representation for human action recognition. Neurocomputing 161, 38–46 (2015)CrossRefGoogle Scholar
  13. 13.
    Morales, J., Micchelli, C.A., Pontil, M.: A family of penalty functions for structured sparsity. In: Advances in Neural Information Processing Systems, pp. 1612–1623 (2010)Google Scholar
  14. 14.
    Nie, F., Huang, H., Cai, X., Ding, C.: Efficient and robust feature selection via joint \(l_{2,1}\)-norms minimization. In: Advances in Neural Information Processing Systems, pp. 1813–1821 (2010)Google Scholar
  15. 15.
    Nikolova, M., Ng, M.K.: Analysis of half-quadratic minimization methods for signal and image recovery. SIAM J. Sci. Comput. 27(3), 937–966 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Pillai, J.K., Patel, V.M., Chellappa, R., Ratha, N.K.: Secure and robust iris recognition using random projections and sparse representations. IEEE Trans. Pattern Anal. Mach. Intell. 33(9), 1877–1893 (2011)CrossRefGoogle Scholar
  17. 17.
    Suk, H.-I., Wee, C.-Y., Lee, S.-W., Shen, D.: Supervised discriminative group sparse representation for mild cognitive impairment diagnosis. Neuroinformatics 13(3), 277–295 (2015)CrossRefGoogle Scholar
  18. 18.
    Sun, Y., Wang, X., Tang, X.: Deeply learned face representations are sparse, selective, and robust. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2892–2900 (2015)Google Scholar
  19. 19.
    Wang, L., Pan, C.: Visual tracking via manifold regularized local structured sparse representation model. In: IEEE International Conference on Image Processing, pp. 1150–1154 (2015)Google Scholar
  20. 20.
    Wipf, D., Nagarajan, S.: Iterative reweighted \(l_1\) and \(l_2\) methods for finding sparse solutions. IEEE J. Sel. Top. Signal Process. 4(2), 317–329 (2010)CrossRefGoogle Scholar
  21. 21.
    Wright, J., Ma, Y., Mairal, J., Sapiro, G., Huang, T.S., Yan, S.: Sparse representation for computer vision and pattern recognition. Proc. IEEE 98(6), 1031–1044 (2010)CrossRefGoogle Scholar
  22. 22.
    Yang, M., Zhang, L., Yang, J., Zhang, D.: Robust sparse coding for face recognition. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 625–632 (2011)Google Scholar
  23. 23.
    Yuan, X., Liu, X., Yan, S.: Visual classification with multitask joint sparse representation. IEEE Trans. Image Process. 21, 4349–4360 (2012)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Zhang, H., Nasrabadi, N.M., Zhang, Y., Huang, T.S.: Joint dynamic sparse representation for multi-view face recognition. Pattern Recogn. 45(4), 1290–1298 (2012)CrossRefGoogle Scholar
  25. 25.
    Zhang, Z.: Parameter estimation techniques: a tutorial with application to conic fitting. Image Vis. Comput. 15(1), 59–76 (1997)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Singapore 2016

Authors and Affiliations

  • Jinghuan Wei
    • 1
  • Zhihang Li
    • 2
  • Dong Cao
    • 2
  • Man Zhang
    • 2
    Email author
  • Cheng Zeng
    • 1
  1. 1.Hebei University of TechnologyTianjinChina
  2. 2.CaZ, CasBeijingChina

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