Fisher discrimination-based $$l_{2,1} $$l2,1-norm sparse representation for face recognition

AbstractIn 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 $$l_{2,1}$$l2,1-norm Sparse Representation framework that constrains the noise penalty by the $$l_{2,1}$$l2,1-norm. The $$l_{2,1} $$l2,1-norm takes advantage of both the discriminative nature of the $$l_1 $$l1-norm and the systemic representation of the $$l_2 $$l2-norm. In addition, we use the nuclear norm to constrain the coefficient matrix. Motivated by the Fisher criterion, we propose the Fisher discriminant-based $$l_{2,1} $$l2,1-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.