Reciprocal kernel-based weighted collaborative–competitive representation for robust face recognition

Abstract

The Gaussian kernel function is widely used to encode the nonlinear correlations of the face images. However, some issues greatly limit its superiority, for example, it is sensitive to the parameter setting because of its definition based on the exponential operation, on the other hand, the Gaussian kernel needs costly computational time. Besides, the hidden information such as the distance information of the samples is conducive to improving the performance of face recognition. To overcome the above problems, we propose a reciprocal kernel-based weighted collaborative–competitive representation for face recognition. Different from other methods, a new reciprocal kernel is designed to realize the nonlinear representation of the samples. Moreover, a new weight based on the reciprocal kernel is imposed on coding coefficients to disclose the hidden information of the samples in the nonlinear space. With the help of the collaborative–competitive method, the proposed method can well achieve the trade-off between collaborative and competitive representation to promote the performance of face recognition. These factors explicitly encourage the proposed method to be a better representation-type classifier. Finally, extensive experiments are conducted on five benchmark datasets, and the experimental results show that the proposed approach outperforms many state-of-the-art approaches.

This is a preview of subscription content, access via your institution.

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

Notes

  1. 1.

    http://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html.

  2. 2.

    http://www2.ece.ohio-state.edu/∼aleix/ARdatabase.html.

  3. 3.

    http://www.anefian.com/research/face_reco.htm.

  4. 4.

    http://www.imm.dtu.dk/∼ aam/datasets/datasets.html.

  5. 5.

    http://vis-www.cs.umass.edu/lfw/.

References

  1. 1.

    Wright, J., Yang, A., Ganesh, A., Shankar, S., Ma, Y.: Robust face recognition via sparse representation. IEEE Trans. Pattern Anal. Mach. Intell. 31, 210–227 (2009)

    Article  Google Scholar 

  2. 2.

    Wright, J., Ma, Y., Mairal, J., Sapiro, G., Huang, T., Yan, S.: Sparse representation for computer vision and pattern recognition. Proc. IEEE 98(6), 1031–1044 (2010)

    Article  Google Scholar 

  3. 3.

    Wang, J., Lu, C., Wang, M., Li, P., Yan, H., Hu, X.: Robust face recognition via adaptive sparse representation. IEEE Trans. Cybern. 44(12), 2368–2378 (2014)

    Article  Google Scholar 

  4. 4.

    Zhang, L., Yang, M., Feng, X.: Sparse representation or collaborative representation: which helps face recognition? In: IEEE International Conference on Computer Vision, 6–13 Nov. 2011, Barcelona, Spain, pp. 471–478

  5. 5.

    Deng, W., Hu, J., Guo, J.: recognition via collaborative representation: its discriminant nature and superposed representation. IEEE Trans. Pattern Anal. Mach. Intell. 40, 2513–2521 (2018)

    Article  Google Scholar 

  6. 6.

    Cai, S., Zhang, L., Zuo, W., Feng, X.: A probabilistic collaborative representation based approach for pattern classification. In: IEEE International Conference on Computer Vision, pp. 2950–2959 (2016)

  7. 7.

    Gou, J., Xu, Y., Zhang, D., Mao, Q., Du, L., Zhan, Y.: Two-phase linear reconstruction measure-based classification for face recognition. Inf. Sci. 433, 17–36 (2018)

    MathSciNet  Article  Google Scholar 

  8. 8.

    Li, W., Du, Q., Zhang, F., Hu, W.: Hyperspectral image classification by fusing collaborative and sparse representations. IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 9(9), 4178–4187 (2016)

    Article  Google Scholar 

  9. 9.

    Lan, R., Zhou, Y.: An extended probabilistic collaborative representation based classifier for image classification. In: Proceedings of IEEE International Conference on Multimedia and Expo (ICME), pp. 1392–1397 (2017)

  10. 10.

    Lei, Y., Guo, Y., Hayat, M., Bennamoun, M., Zhou, X.: A two-phase weighted collaborative representation for 3D partial face recognition with single sample. Pattern Recognit. 52, 218–237 (2016)

    Article  Google Scholar 

  11. 11.

    Liu, Z., Pu, J., Xu, M., Qiu, Y.: Face recognition via weighted two phase test sample sparse representation. Neural Process. Lett. 41(1), 43–53 (2015)

    Article  Google Scholar 

  12. 12.

    Lu, C.-Y., Min, H., Gui, J.: Face recognition via weighted sparse representation. J. Vis. Commun. Image Represent. 24, 111–116 (2013)

    Article  Google Scholar 

  13. 13.

    Chi, H., Xia, H., Zhang, L., Zhang, C.: Competitive and collaborative representation for classification. Pattern Recognit. Lett. (2018). https://doi.org/10.1016/j.patrec.2018.06.019

    Article  Google Scholar 

  14. 14.

    Vo, D.M., Lee, S.-W.: Robust face recognition via hierarchical collaborative representation. Inf. Sci. 432, 332–346 (2018)

    MathSciNet  Article  Google Scholar 

  15. 15.

    Liu, S., Wang, Y., Peng, Y., Hou, S., Zhang, K., Wu, X.: Singular value decomposition based virtual representation for face recognition. Mach. Vis. Appl. 31(3), 1–9 (2020)

    Article  Google Scholar 

  16. 16.

    Xu, Y., Zhong, Z., Yang, J., You, J., Zhang, D.: A new discriminative sparse representation method for robust face recognition via l2 regularization. IEEE Trans. Neural Netw. Learn. Syst. 28(10), 2233–2242 (2017)

    MathSciNet  Article  Google Scholar 

  17. 17.

    Chi, Y., Porikli, F.: Classification and boosting with multiple collaborative representations. IEEE Trans. Pattern Anal. Mach. Intell. 36(8), 1519–1531 (2014)

    Article  Google Scholar 

  18. 18.

    Lee, K., Ho, J., Kriegman, D.: Acquiring linear subspaces for face recognition under variable lighting. IEEE Trans. Pattern Anal. Mach. Intell. 27, 684–698 (2005)

    Article  Google Scholar 

  19. 19.

    Yuan, H., Li, X., Xu, F., Wang, Y., Lai, L., Tang, Y.Y.: A collaborative–competitive representation based classifier model. Neurocomputing 275(31), 627–635 (2018)

    Article  Google Scholar 

  20. 20.

    Gou, J., Wang, L., Yi, Z., Yuan, Y., Ou, W., Mao, Q.: Discriminative group collaborative competitive representation for visual Classification. In: Proceedings of IEEE International Conference on Multimedia and Expo, pp. 1474–1479 (2019)

  21. 21.

    Gou, J., Wu, H., Song, H., Du, L., Ke, J.: Double competitive constraints-based collaborative representation for pattern classification. Comput. Electr. Eng. 84, 106632 (2020)

    Article  Google Scholar 

  22. 22.

    Kang, C., Liao, S., Xiang, S., Pan, C.: Kernel sparse representation with local patterns for face recognition. In: International Conference on Image Processing, pp. 3009–3012 (2011)

  23. 23.

    Yang, W., Wang, Z., Yin, J., Sun, C., Ricanek, K.: Image classification using kernel collaborative representation with regularized least square. Appl. Math. Comput. 222, 13–28 (2013)

    MathSciNet  MATH  Google Scholar 

  24. 24.

    Wang, Z., Yang, W., Yin, J., Sun, C.: Kernel collaborative representation with regularized least square for face recognition. In: International Conference on Service-Oriented Computing, pp. 130–137 (2013)

  25. 25.

    Wang, K., Hu, H., Liu, T.: Discriminative kernel sparse representation via l2 regularization for face recognition. Electron. Lett. 54(23), 1324–1326 (2018)

    Article  Google Scholar 

  26. 26.

    Liu, W., Yu, Z., Lu, L., Wen, Y., Li, H., Zou, Y.: KCRC-LCD: discriminative kernel collaborative representation with locality constrained dictionary for visual categorization. Pattern Recognit. 48(10), 3076–3092 (2014)

    Article  Google Scholar 

  27. 27.

    Wang, D., Lu, H., Yang, M.H.: Kernel collaborative face recognition. Pattern Recognit. 48(10), 3025–3037 (2015)

    Article  Google Scholar 

  28. 28.

    Panda, B., Kumar, S., Misra, R.K.: Solving singularly perturbed problems using multi-quadric/inverse multi-quadric radial basis function method. Indian J. Ind. Appl. Math. 7, 43–57 (2016)

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grants 61806006, China Postdoctoral Science Foundation under Grant No. 2019M660149, the Graduate Innovation Foundation of Jiangsu Province under Grant No. KYLX16_0781, the Natural Science Foundation of Jiangsu Province under Grants No. BK20181340, the 111 Project under Grants No. B12018 and PAPD of Jiangsu Higher Education Institutions.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Hongwei Ge.

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

Verify currency and authenticity via CrossMark

Cite this article

Wang, S., Ge, H., Yang, J. et al. Reciprocal kernel-based weighted collaborative–competitive representation for robust face recognition. Machine Vision and Applications 32, 40 (2021). https://doi.org/10.1007/s00138-020-01165-3

Download citation

Keywords

  • Reciprocal kernel
  • Collaborative–competitive representation
  • Nonlinear representation
  • Face recognition