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Signal, Image and Video Processing

, Volume 12, Issue 1, pp 107–115 | Cite as

Robust classwise and projective low-rank representation for image classification

  • Shengke Xue
  • Xinyu JinEmail author
Original Paper

Abstract

Several variations of the low-rank representation have been suggested intensively for diverse applications, recently. They perform properly on image alignment but undesirably on classification. That is, they are intractable when a new image arrives with an unknown label to be classified. Hence, inspired by a recent research of the fast projection, this paper proposes a supervised approach called the robust classwise and projective low-rank representation (CPLRR), which is the first attempt to align images classwise and learn a projective nonlinear function, simultaneously. It separates out the low-rank components explicitly with the parametric transformation corrections and projects the original images to the low-rank representations of corresponding categories, in an efficient manner. With the advantage of fast projection, CPLRR is appropriate for image classification. Extensive experiments conducted on MNIST, Extended Yale B, and CMU PIE datasets validate the effect of the robust low-rank alignment and the rapid projection, against different domain deformations, noises, and illumination conditions.

Keywords

Low-rank Supervised Robust Alignment Projection Classification 

References

  1. 1.
    Bao, B.K., Liu, G., Xu, C., Yan, S.: Inductive robust principal component analysis. IEEE Trans. Image Process. 21(8), 3794–3800 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Cai, J.F., Candès, E.J., Shen, Z.: A singular value thresholding algorithm for matrix completion. SIAM J. Optim. 20(4), 1956–1982 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Candès, E.J., Li, X., Ma, Y., Wright, J.: Robust principal component analysis? J. ACM 58(3), 11:1–11:37 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Chen, C., He, B., Ye, Y., Yuan, X.: The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent. Math. Program. 155(1), 57–79 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Du, H.S., Hu, Q.P., Qiao, D.F., Pitas, I.: Robust face recognition via low-rank sparse representation-based classification. Int. J. Autom. Comput. 12(6), 579–587 (2015)CrossRefGoogle Scholar
  6. 6.
    Gao, Z., Cheong, L.F., Wang, Y.X.: Block-sparse RPCA for salient motion detection. IEEE Trans. Pattern Anal. Mach. Intell. 36(10), 1975–1987 (2014)CrossRefGoogle Scholar
  7. 7.
    Jiang, X., Lai, J.: Sparse and dense hybrid representation via dictionary decomposition for face recognition. IEEE Trans. Pattern Anal. Mach. Intell. 37(5), 1067–1079 (2015)CrossRefGoogle Scholar
  8. 8.
    Lecun, Y., Bottou, L., Bengio, Y., Haffner, P.: Gradient-based learning applied to document recognition. Proc. IEEE 86(11), 2278–2324 (1998)CrossRefGoogle Scholar
  9. 9.
    Lee, K.C., Ho, J., Kriegman, D.J.: Acquiring linear subspaces for face recognition under variable lighting. IEEE Trans. Pattern Anal. Mach. Intell. 27(5), 684–698 (2005)CrossRefGoogle Scholar
  10. 10.
    Li, J., Kong, Y., Zhao, H., Yang, J., Fu, Y.: Learning fast low-rank projection for image classification. IEEE Trans. Image Process. 25(10), 4803–4814 (2016)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Li, L., Li, S., Fu, Y.: Learning low-rank and discriminative dictionary for image classification. Image Vis. Comput. 32(10), 814–823 (2014)CrossRefGoogle Scholar
  12. 12.
    Li, S., Fu, Y.: Learning robust and discriminative subspace with low-rank constraints. IEEE Trans. Neural Netw. Learn. Syst. 27(11), 2160–2173 (2016)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Lin, Z., Liu, R., Su, Z.: Linearized alternating direction method with adaptive penalty for low-rank representation. In: Advances in Neural Information Processing Systems, pp. 612–620 (2011)Google Scholar
  14. 14.
    Liu, G., Lin, Z., Yan, S., Sun, J., Yu, Y., Ma, Y.: Robust recovery of subspace structures by low-rank representation. IEEE Trans. Pattern Anal. Mach. Intell. 35(1), 171–184 (2013)CrossRefGoogle Scholar
  15. 15.
    Liu, G., Yan, S.: Latent low-rank representation for subspace segmentation and feature extraction. In: IEEE International Conference on Computer Vision, pp. 1615–1622 (2011)Google Scholar
  16. 16.
    Liu, T., Gong, M., Tao, D.: Large-cone nonnegative matrix factorization. IEEE Trans. Neural Netw. Learn. Syst. 99, 1–14 (2016)Google Scholar
  17. 17.
    Ma, L., Wang, C., Xiao, B., Zhou, W.: Sparse representation for face recognition based on discriminative low-rank dictionary learning. In: IEEE International Conference on Computer Vision and Pattern Recognition, pp. 2586–2593 (2012)Google Scholar
  18. 18.
    Naseem, I., Togneri, R., Bennamoun, M.: Linear regression for face recognition. IEEE Trans. Pattern Anal. Mach. Intell. 32(11), 2106–2112 (2010)CrossRefGoogle Scholar
  19. 19.
    Peng, Y., Ganesh, A., Wright, J., Xu, W., Ma, Y.: RASL: Robust alignment by sparse and low-rank decomposition for linearly correlated images. IEEE Trans. Pattern Anal. Mach. Intell. 34(11), 2233–2246 (2012)CrossRefGoogle Scholar
  20. 20.
    Sim, T., Baker, S., Bsat, M.: The CMU pose, illumination, and expression (PIE) database. In: 5th IEEE International Conference on Automatic Face Gesture Recognition, pp. 46–51 (2002)Google Scholar
  21. 21.
    Song, W., Zhu, J., Li, Y., Chen, C.: Image alignment by online robust PCA via stochastic gradient descent. IEEE Trans. Circuits Syst. Video Technol. 26(7), 1241–1250 (2016)CrossRefGoogle Scholar
  22. 22.
    Tan, V.Y.F., Fevotte, C.: Automatic relevance determination in nonnegative matrix factorization with the \((\beta )\)-divergence. IEEE Trans. Pattern Anal. Mach. Intell. 35(7), 1592–1605 (2013)CrossRefGoogle Scholar
  23. 23.
    Wagner, A., Wright, J., Ganesh, A., Zhou, Z., Mobahi, H., Ma, Y.: Toward a practical face recognition system: Robust alignment and illumination by sparse representation. IEEE Trans. Pattern Anal. Mach. Intell. 34(2), 372–386 (2012)CrossRefGoogle Scholar
  24. 24.
    Wilf, P., Zhang, S., Chikkerur, S., Little, S.A., Wing, S.L., Serre, T.: Computer vision cracks the leaf code. Proc. Natl. Acad. Sci. USA 113(12), 3305–3310 (2016)CrossRefGoogle Scholar
  25. 25.
    Wright, J., Yang, A.Y., Ganesh, A., Sastry, S.S., Ma, Y.: Robust face recognition via sparse representation. IEEE Trans. Pattern Anal. Mach. Intell. 31(2), 210–227 (2009)CrossRefGoogle Scholar
  26. 26.
    Wu, Y., Shen, B., Ling, H.: Online robust image alignment via iterative convex optimization. In: IEEE International Conference on Computer Vision and Pattern Recognition, pp. 1808–1814 (2012)Google Scholar
  27. 27.
    Yang, C., Ye, M., Tang, S., Xiang, T., Liu, Z.: Semi-supervised low-rank representation for image classification. Signal Image Video Process. 11(1), 73–80 (2017)CrossRefGoogle Scholar
  28. 28.
    Yang, J., Luo, L., Qian, J., Tai, Y., Zhang, F., Xu, Y.: Nuclear norm based matrix regression with applications to face recognition with occlusion and illumination changes. IEEE Trans. Pattern Anal. Mach. Intell. 39(1), 156–171 (2017)CrossRefGoogle Scholar
  29. 29.
    Yang, M., Zhang, L., Feng, X., Zhang, D.: Fisher discrimination dictionary learning for sparse representation. In: IEEE International Conference on Computer Vision, pp. 543–550 (2011)Google Scholar
  30. 30.
    Zhang, T., Ghanem, B., Liu, S., Xu, C., Ahuja, N.: Low-rank sparse coding for image classification. In: IEEE International Conference on Computer Vision, pp. 281–288 (2013)Google Scholar
  31. 31.
    Zhang, Y., Jiang, Z., Davis, L.S.: Learning structured low-rank representations for image classification. In: IEEE International Conference on Computer Vision and Pattern Recognition, pp. 676–683 (2013)Google Scholar

Copyright information

© Springer-Verlag London Ltd. 2017

Authors and Affiliations

  1. 1.College of Information Science and Electronic EngineeringZhejiang UniversityHangzhouPeople’s Republic of China

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