Weighted sparse coding regularized nonconvex matrix regression for robust face recognition

Most existing regression based classification methods for robust face recognition usually characterize the representation error using L1-norm or Frobenius-norm for the pixel-level noise or nuclear norm for the image-level noise, and code the coefficients vector by l1-norm or l2-norm. To our best knowledge, nuclear norm can be used to describe the low-rank structural information but may lead to the suboptimal solution, while l1-norm or l2-norm can promote the sparsity or cooperativity but may neglect the prior information (e.g., the locality and similarity relationship) among data. To solve these drawbacks, we propose two weighted sparse coding regularized nonconvex matrix regression models including weighted sparse coding regularized matrix γ-norm based matrix regression (WSγMR) for the structural noise and weighted sparse coding regularized matrix γ-norm plus minimax concave plus (MCP) function based matrix regression (WSγM2R) for the mixed noise (e.g, structural noise plus sparse noise). The MCP induced nonconvex function can overcome the imbalanced penalization of different singular values and entries of the error image matrix, and the weighted sparse coding can consider the prior information by borrowing a novel distance metric. The variants of inexact augmented Lagrange multiplier (iALM) algorithm including nonconvex iALM (NCiALM) and majorization-minimization iALM (MMiALM) are developed to solve the proposed models, respectively. The matrix γ-norm based classifier is devised for classification. Finally, experiments on four popular face image databases can validate the superiority of our methods compared with the-state-of-the-art regression methods.