  One of the most important problems in regression-based error model is
modeling the complex representation error caused by various corruptions and
environment changes in images. For example, in robust face recognition, images
are often affected by varying types and levels of corruptions, such as random
pixel corruptions, block occlusions, or disguises. However, existing works are
not robust enough to solve this problem due to they cannot model the complex
corrupted errors very well. In this paper, we address this problem by a unified
sparse weight learning and low-rank approximation regression model, which
enables the random noises and contiguous occlusions in images to be treated
simultaneously. For the random noise, we define a generalized correntropy (GC)
function to match the error distribution. For the structured error caused by
occlusions or disguises, we propose a GC function based rank approximation to
measure the rank of error matrices. Since the proposed objective function is
non-convex, an effective iterative optimization algorithm is developed to
achieve the optimal weight learning and low-rank approximation. Extensive
experimental results on three public face databases show that the proposed
model can fit the error distribution and structure very well, thus obtain
better recognition accuracies in comparison with the existing methods.
