Schatten-p Norm Based Linear Regression Discriminant Analysis for Face Recognition

  • Lijiang Chen
  • Wentao Dou
  • Xia MaoEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 875)


Locality-regularized linear regression classification (LLRC) shows good performance on face recognition. However, it sorely performs on the original space, which results in degraded classification efficiency. To solve this problem, we propose a dimensionality reduction algorithm named schatten-p norm based linear regression discriminant analysis (SPLRDA) for image feature extraction. First, it defines intra-class and inter-class scatters based on schatten-p norm, which improves the capability to deal with illumination changes. Then the objective function which incorporates discriminant analysis is derived from the minimization of intra-class compactness and the maximization of inter-class separability. Experiments carried on some typical databases validate the effectiveness and robustness of our method.


Dimensionality reduction Schatten-p norm Linear regression Feature extraction Face recognition Discriminant analysis 


  1. 1.
    Turk, M., Pentland, A.: Eigenfaces for recognition. J. Cogn. Neurosci. 3(1), 71–86 (1991)CrossRefGoogle Scholar
  2. 2.
    Belhumeur, P.N., Hespanha, J.P., Kriegman, D.J.: Eigenfaces vs. fisherfaces: recognition using class specific linear projection. IEEE Trans. Pattern Anal. Mach. Intell. 19(7), 711–720 (1997)CrossRefGoogle Scholar
  3. 3.
    Lee, D.D., Seung, H.S.: Learning the parts of objects by non-negative matrix factorization. Nature 401, 788 (1999). EPCrossRefGoogle Scholar
  4. 4.
    Raudys, S.J., Jain, A.K.: Small sample size effects in statistical pattern recognition: recommendations for practitioners. IEEE Trans. Pattern Anal. Mach. Intell. 13(3), 252–264 (1991)CrossRefGoogle Scholar
  5. 5.
    Tenenbaum, J.B., De Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290(5500), 2319–2323 (2000)CrossRefGoogle Scholar
  6. 6.
    Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 15(6), 1373–1396 (2003)CrossRefGoogle Scholar
  7. 7.
    Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500), 2323–2326 (2000)CrossRefGoogle Scholar
  8. 8.
    He, X., Yan, S., Hu, Y., Niyogi, P., Zhang, H.J.: Face recognition using Laplacianfaces. IEEE Trans. Pattern Anal. Mach. Intell. 27, 328–340 (2005)CrossRefGoogle Scholar
  9. 9.
    Cover, T., Hart, P.: Nearest neighbor pattern classification. IEEE Trans. Inf. Theory 13(1), 21–27 (1967)CrossRefGoogle Scholar
  10. 10.
    Naseem, I., Togneri, R., Bennamoun, M.: Linear regression for face recognition. IEEE Trans. Pattern Anal. Mach. Intell. 32(11), 2106–2112 (2010)CrossRefGoogle Scholar
  11. 11.
    Brown, D., Li, H., Gao, Y.: Locality-regularized linear regression for face recognition. In: Proceedings of the 21st International Conference on Pattern Recognition, ICPR 2012, pp. 1586–1589 (2012)Google Scholar
  12. 12.
    Chen, Y., Jin, Z.: Reconstructive discriminant analysis: a feature extraction method induced from linear regression classification. Neurocomputing 87, 41–50 (2012)CrossRefGoogle Scholar
  13. 13.
    Huang, P., Li, T., Shu, Z., Gao, G., Yang, G., Qian, C.: Locality-regularized linear regression discriminant analysis for feature extraction. Inf. Sci. 429, 164–176 (2018)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Du, H., Hu, Q., Jiang, M., Zhang, F.: Two-dimensional principal component analysis based on Schatten p-norm for image feature extraction. J. Vis. Commun. Image Represent. 32, 55–62 (2015)CrossRefGoogle Scholar
  15. 15.
    Du, H., Zhao, Z., Wang, S., Hu, Q.: Two-dimensional discriminant analysis based on Schatten p-norm for image feature extraction. J. Vis. Commun. Image Represent. 45, 87–94 (2017)CrossRefGoogle Scholar
  16. 16.
    Shi, X., Nie, F., Lai, Z., Guo, Z.: Robust principal component analysis via optimal mean by joint l2,1 and Schatten p-norms minimization. Neurocomputing 283, 205–213 (2018)CrossRefGoogle Scholar
  17. 17.
    Samaria, F.S., Harter, A.C.: Parameterisation of a stochastic model for human face identification. In: Proceedings of 1994 IEEE Workshop on Applications of Computer Vision, pp. 138–142 (1994)Google Scholar
  18. 18.
    Sim, T., Baker, S., Bsat, M.: The CMU pose, illumination, and expression (PIE) database. In: Proceedings of Fifth IEEE International Conference on Automatic Face Gesture Recognition, pp. 46–51 (2002)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.School of Electronic and Information EngineeringBeihang UniversityBeijingChina

Personalised recommendations