Skip to main content
SpringerLink
Log in

Structured dictionary learning using mixed-norms and group-sparsity constraint

  • Original Article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

Recently, sparse representation and dictionary learning have shown significant performance in machine vision. In particular, several supervised dictionary learning methods have been proposed for classification aim and increasing its accuracy. Among them, structured dictionary learning is an interesting approach which captures the discriminative properties of each class and common features among all classes in class-specific sub-dictionaries and a distinct shared sub-dictionary, respectively. It extracts the structural information that exists in samples of each class to increase the classification accuracy. Therefore, in this paper, a group-based structured dictionary learning method is proposed that captures structural information in each class and learns class-specific and shared sub-dictionaries based on mixed \(l_{2,1}\) norm. Also, mixed \(l_{2,1}\) norm is used for acquiring the sparse coefficients of data samples based on the learned sub-dictionaries. Then, classification is done by finding the class with (1) minimum reconstruction error or (2) maximum number of nonzero groups based on \(l_{1,0}\) norm. The proposed method is evaluated by conducting experiments on Extended YaleB, AR and CMU-PIE face databases and the USPS handwritten digits database. The experimental results demonstrate the effectiveness of the proposed method in data representation and classification.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Elad, M., Aharon, M.: Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans. Image Process. 15(12), 3736 (2006)

    Article  MathSciNet  Google Scholar 

  2. Yang, M., Dai, D., Shen, L., Van Gool, L.: Latent dictionary learning for sparse representation based classification. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 4138–4145 (2014)

  3. Xu, Y., Li, Z., Yang, J., Zhang, D.: A survey of dictionary learning algorithms for face recognition. In: IEEE Access, vol. 5, pp. 8502–8514 (2017)

  4. Mallat, S.: A Wavelet Tour of Signal Processing. Academic Press, Cambridge (1999)

    MATH  Google Scholar 

  5. Le Pennec, E., Mallat, S.: Sparse geometric image representations with bandelets. IEEE Trans. Image Process. 14(4), 423 (2005)

    Article  MathSciNet  Google Scholar 

  6. Aharon, M., Elad, M., Bruckstein, A.: K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans Signal Process 54, 4311–4322 (2006). https://doi.org/10.1109/TSP.2006.881199

    Article  MATH  Google Scholar 

  7. Bryt, O., Elad, M.: Compression of facial images using the K-SVD algorithm. J. Vis. Commun. Image Represent. 19(4), 270 (2008)

    Article  Google Scholar 

  8. Sprechmann, P., Sapiro, G.: Dictionary learning and sparse coding for unsupervised clustering. In: 2010 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), pp. 2042–2045. IEEE (2010)

  9. Mairal, J., Ponce, J., Sapiro, G., Zisserman, A., Bach, F.R.: Supervised dictionary learning. In: Advances in Neural Information Processing Systems, pp. 1033–1040 (2009)

  10. Zhang, Q., Li, B.: Discriminative K-SVD for dictionary learning in face recognition. In: 2010 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 2691–2698. IEEE (2010)

  11. Jiang, Z., Lin, Z., Davis, L.S.: Label consistent K-SVD: learning a discriminative dictionary for recognition. IEEE Trans. Pattern Anal. Mach. Intell. 35(11), 2651 (2013)

    Article  Google Scholar 

  12. 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 (2009)

    Article  Google Scholar 

  13. Yang, M., Zhang, L., Yang, J., Zhang, D.: Metaface learning for sparse representation based face recognition. In: 2010 17th IEEE International Conference on Image Processing (ICIP), pp. 1601–1604. IEEE (2010)

  14. Ramirez, I., Sprechmann, P., Sapiro, G.: Classification and clustering via dictionary learning with structured incoherence and shared features. In: 2010 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 3501–3508. IEEE (2010)

  15. Yang, M., Zhang, L., Feng, X., Zhang, D.: Sparse representation based fisher discrimination dictionary learning for image classification. Int. J. Comput. Vis. 109(3), 209 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  16. Lu, J., Wang, G., Zhou, J.: Simultaneous feature and dictionary learning for image set based face recognition. IEEE Trans. Image Process. 26(8), 4042 (2017). https://doi.org/10.1109/TIP.2017.2713940

    Article  MathSciNet  MATH  Google Scholar 

  17. Foroughi, H., Ray, N., Zhang, H.: Object classification with joint projection and low-rank dictionary learning. IEEE Trans. Image Process. 27(2), 806 (2018). https://doi.org/10.1109/TIP.2017.2766446

    Article  MathSciNet  MATH  Google Scholar 

  18. Wang, X., Lid, Y., You, S., Li, H., Wang, S.: Unidirectional representation based efficient dictionary learning. IEEE Trans. Circuits Syst. Video Technol. (2018). https://doi.org/10.1109/TCSVT.2018.2886600

    Article  Google Scholar 

  19. Wen, Z., Hou, B., Jiao, L.: Discriminative dictionary learning with two-level low rank and group sparse decomposition for image classification. IEEE Trans Cybernetics 47, 3758–3771 (2017). https://doi.org/10.1109/TCYB.2016.2581

    Article  Google Scholar 

  20. Wang, D., Kong, S.: A classification-oriented dictionary learning model: explicitly learning the particularity and commonality across categories. Pattern Recognit. 47(2), 885 (2014)

    Article  MATH  Google Scholar 

  21. Wang, C.P., Wei, W., Zhang, J.S., Song, H.B.: Robust face recognition via discriminative and common hybrid dictionary learning. Appl. Intell. 48(1), 156 (2018)

    Article  Google Scholar 

  22. Xu, Y., Quan, Y., Zheng, B.: Discriminative structured dictionary learning with hierarchical group sparsity. Comput. Vis. Image Underst. 136, 59 (2015)

    Article  Google Scholar 

  23. Pati, Y.C., Rezaiifar, R., Krishnaprasad, P.S.: Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition. In: 1993 Conference Record of The 27th Asilomar Conference on Signals, Systems and Computers, 1993, pp. 40–44. IEEE (1993)

  24. Efron, B., Hastie, T., Johnstone, I., Tibshirani, R., et al.: Least angle regression. Ann. Stat. 32(2), 407 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  25. Chen, S.S., Donoho, D.L., Saunders, M.A.: Atomic decomposition by basis pursuit. SIAM Rev. 43(1), 129 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  26. Elhamifar, E., Vidal, R.: Robust classification using structured sparse representation. In: 2011 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1873–1879. IEEE (2011)

  27. Sun, Y., Quan, Y., Fu, J.: Sparse coding and dictionary learning with class-specific group sparsity. Neural Comput. Appl. 30(4), 1265–1275 (2018). https://doi.org/10.1007/s00521-016-2764-z

    Article  Google Scholar 

  28. Sun, Y., Liu, Q., Tang, J., Tao, D.: Learning discriminative dictionary for group sparse representation. IEEE Trans. Image Process. 23(9), 3816 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  29. Zhao, L., Zhang, Y., Yin, B., Sun, Y., Hu, Y., Piao, X., Wu, Q.: Fisher discrimination-based L2,1-norm sparse representation for face recognition. Vis. Comput. 32(9), 1165 (2016). https://doi.org/10.1007/s00371-015-1169-9

    Article  Google Scholar 

  30. Fan, C., Hu, C., Liu, B.: Linearized kernel dictionary learning with group sparse priors for action recognition. Vis. Comput. (2018). https://doi.org/10.1007/s00371-018-1603-x

    Article  Google Scholar 

  31. Jacob, L., Obozinski, G., Vert, J.P.: Group lasso with overlap and graph lasso. In: Proceedings of the 26th Annual International Conference on Machine Learning, pp. 433–440. ACM (2009)

  32. Kim, S., Xing, E.P.: Tree-guided group lasso for multi-response regression with structured sparsity, with an application to eQTL mapping. Ann. Appl. Stat. 6(3), 1095–1117 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  33. Bengio, S., Pereira, F., Singer, Y., Strelow, D.: Group sparse coding. In: Proceedings of the 22nd International Conference on Neural Information Processing Systems, NIPS’09. Curran Associates Inc

  34. Huang, J., Zhang, T., Metaxas, D.: Learning with structured sparsity. J. Mach. Learn. Res. 12(Nov), 3371 (2011)

    MathSciNet  MATH  Google Scholar 

  35. Gu, G., Hou, Z., Chen, C., Zhao, Y.: A dimensionality reduction method based on structured sparse representation for face recognition. Artif. Intell. Rev. 46(4), 431 (2016)

    Article  Google Scholar 

  36. Fan, B., Cong, Y., Tang, Y.: Online structured sparse learning with labeled information for robust object tracking. J. Electron. Imaging 26(1), 013007 (2017)

    Article  Google Scholar 

  37. Zhang, Z., Xu, Y., Yang, J., Li, X., Zhang, D.: A survey of sparse representation: algorithms and applications. IEEE Access 3, 490 (2015)

    Article  Google Scholar 

  38. Suo, Y., Dao, M., Tran, T., Mousavi, H., Srinivas, U., Monga, V.: Group structured dirty dictionary learning for classification. In: 2014 IEEE International Conference on Image Processing, ICIP 2014, pp. 150–154 (2014)

  39. Wright, S.J., Nowak, R.D., Figueiredo, M.A.: Sparse reconstruction by separable approximation. IEEE Trans. Signal Process. 57(7), 2479 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  40. Chi, Y.T., Ali, M., Rajwade, A., Ho, J.: Block and Group Regularized Sparse Modeling for Dictionary Learning. In: The IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2013)

  41. Lee, Kuang-Chih, Ho, J., Kriegman, D.J.: Acquiring linear subspaces for face recognition under variable lighting. IEEE Trans. Pattern Anal. Mach. Intell. 27(5), 684 (2005)

    Article  Google Scholar 

  42. Martinez, A.M.: The ar face database. Tech. rep. CVC technical report (1998)

  43. Sim, T., Baker, S., Bsat, M.: The CMU pose, illumination, and expression (PIE) database. 5, vol. 4, pp. 53–58. IEEE (2002)

  44. Hull, J.J.: A database for handwritten text recognition research. IEEE Trans. Pattern Anal. Mach. Intell. 16(5), 550 (1994)

    Article  Google Scholar 

  45. Liu, H.D., Yang, M., Gao, Y., Yin, Y., Chen, L.: Bilinear discriminative dictionary learning for face recognition. Pattern Recognit. 47(5), 1835 (2014)

    Article  Google Scholar 

  46. Akhtar, N., Mian, A., Porikli, F.: Joint discriminative bayesian dictionary and classifier learning, In: 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 3919–3928. (2017) https://doi.org/10.1109/CVPR.2017.417

Download references

Funding

We received no funding for this research.

Author information

Authors and Affiliations

  1. Computer Engineering Department, Shahid Bahonar University of Kerman, Kerman, Iran

    Zivar Ataee & Hadis Mohseni

Authors
  1. Zivar Ataee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hadis Mohseni
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hadis Mohseni.

Ethics declarations

Conflict of interest

Author Zivar Ataee declares that she has no conflict of interest. Author Hadis Mohseni declares that she has no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ataee, Z., Mohseni, H. Structured dictionary learning using mixed-norms and group-sparsity constraint. Vis Comput 36, 1679–1692 (2020). https://doi.org/10.1007/s00371-019-01766-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-019-01766-8

Keywords

Search

Navigation