Enhanced Group Sparse Regularized Nonconvex Regression for Face Recognition

Regression analysis based methods have shown strong robustness and achieved great success in face recognition. In these methods, convex l_1 l1 -norm and nuclear norm are usually utilized to approximate the l_0 l0 -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 l_1 l1 -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 \gamma γ -norm and matrix \gamma γ -norm induced from the nonconvex function. Furthermore, an l_{2,\gamma } l2,γ -norm based regularizer is designed to directly seek the interclass sparsity or group sparsity instead of traditional l_{2,1} l2,1 -norm. The locality of data, i.e., the distance between the query sample and multi-subspaces, is also taken into consideration. This