Enhanced Group Sparse Regularized Nonconvex Regression for Face Recognition

Chao Zhang, Huaxiong Li, Chunlin Chen, Yuhua Qian, Xianzhong Zhou

Abstract: Regression analysis based methods have shown strong robustness and achieved great success in face recognition. In these methods, convex <inline-formula><tex-math notation="LaTeX">$l_1$</tex-math></inline-formula> -norm and nuclear norm are usually utilized to approximate the <inline-formula><tex-math notation="LaTeX">$l_0$</tex-math></inline-formula> -norm and rank function. However, such convex relaxations may introduce a bias and lead to a suboptimal solution. In this paper, we propose a novel Enhanced Group Sparse regularized Nonconvex Regression (EGSNR) method for robust face recognition. An upper bounded nonconvex function is introduced to replace <inline-formula><tex-math notation="LaTeX">$l_1$</tex-math></inline-formula> -norm for sparsity, which alleviates the bias problem and adverse effects caused by outliers. To capture the characteristics of complex errors, we propose a mixed model by combining <inline-formula><tex-math notation="LaTeX">$\gamma$</tex-math></inline-formula> -norm and matrix <inline-formula><tex-math notation="LaTeX">$\gamma$</tex-math></inline-formula> -norm induced from the nonconvex function. Furthermore, an <inline-formula><tex-math notation="LaTeX">$l_{2,\gamma }$</tex-math></inline-formula> -norm based regularizer is designed to directly seek the interclass sparsity or group sparsity instead of traditional <inline-formula><tex-math notation="LaTeX">$l_{2,1}$</tex-math></inline-formula> -norm. The locality of data, i.e., the distance between the query sample and multi-subspaces, is also taken into consideration. This enhanced group sparse regularizer enables EGSNR to learn more discriminative representation coefficients. Comprehensive experiments on several popular face datasets demonstrate that the proposed EGSNR outperforms the state-of-the-art regression based methods for robust face recognition.