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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.