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The Visual Computer

, Volume 32, Issue 9, pp 1165–1178 | Cite as

Fisher discrimination-based \(l_{2,1} \)-norm sparse representation for face recognition

  • Lu ZhaoEmail author
  • Yong Zhang
  • Baocai Yin
  • Yanfeng Sun
  • Yongli Hu
  • Xinglin Piao
  • Qianjun Wu
Original Article

Abstract

In recent years, sparse representation-based classification (SRC) has made great progress in face recognition (FR). However, SRC emphasizes noise sparsity too much and it is not suitable for the real world. In this paper, we propose a robust \(l_{2,1}\)-norm Sparse Representation framework that constrains the noise penalty by the \(l_{2,1}\)-norm. The \(l_{2,1} \)-norm takes advantage of both the discriminative nature of the \(l_1 \)-norm and the systemic representation of the \(l_2 \)-norm. In addition, we use the nuclear norm to constrain the coefficient matrix. Motivated by the Fisher criterion, we propose the Fisher discriminant-based \(l_{2,1} \)-norm sparse representation method for FR which utilizes a supervised approach. Thus, we consider the within-class scatter and between-class scatter when all of the label information is available. The paper shows that the model can provide stronger discriminant power than the classical sparse representation models and can be solved by the alternating direction method of multiplier. Additionally, it is robust to the contiguous occlusion noise. Extensive experiments demonstrate that our method achieves significantly better results than SRC and some other sparse representation methods for FR when addressing large regions with contiguous occlusion.

Keywords

Sparse representation \(l_{2 , 1}\)-Norm Face recognition Fisher discriminant 

Notes

Acknowledgments

The research project was supported by the National Natural Foundation of China under Grant No. 61390510, 61300065, 61370119, 61171169 and Beijing Natural Science Foundation No. 4132013, 4142010 and supported by the Beijing science and technology project No. Z151100002115040, and also supported by PHR(IHLB).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Lu Zhao
    • 1
    Email author
  • Yong Zhang
    • 1
  • Baocai Yin
    • 1
    • 2
    • 3
  • Yanfeng Sun
    • 1
  • Yongli Hu
    • 1
  • Xinglin Piao
    • 1
  • Qianjun Wu
    • 1
  1. 1.Beijing Key Laboratory of Multimedia and Intelligent Software Technology, College of Metropolitan TransportationBeijing University of TechnologyBeijingChina
  2. 2.School of Software TechnologyDalian University of TechnologyDalianChina
  3. 3.Collaborative Innovation Center of Electric Vehicles in BeijingBeijingChina

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