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.

基于回归的误差模型中最重要的问题之一是对由图像中的各种损坏和环境变化引起的复杂表示误差进行建模。例如，在鲁棒的人脸识别中，图像通常会受到不同类型和级别的损坏的影响，例如随机像素损坏、块遮挡或伪装。然而，现有的工作不足以解决这个问题，因为它们不能很好地对复杂的损坏错误进行建模。在本文中，我们通过统一的稀疏权重学习和低秩近似回归模型解决了这个问题，该模型能够同时处理图像中的随机噪声和连续遮挡。对于随机噪声，我们定义了一个广义相关熵 (GC) 函数来匹配误差分布。对于由遮挡或伪装引起的结构化错误，我们提出了一种基于 GC 函数的秩近似来衡量错误矩阵的秩。由于提出的目标函数是非凸的，因此开发了一种有效的迭代优化算法来实现最优权重学习和低秩逼近。在三个公共人脸数据库上的大量实验结果表明，所提出的模型可以很好地拟合误差分布和结构，从而与现有方法相比获得更好的识别精度。