Abstract—In this paper, we present a sparse correntropy framework for computing robust sparse representations of face images for recognition. Compared with the state-of-the-art l1norm-based sparse representation classifier (SRC), which assumes that noise also has a sparse representation, our sparse algorithm is developed based on the maximum correntropy criterion, which is much more insensitive to outliers. In order to develop a more tractable and practical approach, we in particular impose nonnegativity constraint on the variables in the maximum correntropy criterion and develop a half-quadratic optimization technique to approximately maximize the objective function in an alternating way so that the complex optimization problem is reduced to learning a sparse representation through a weighted linear least squares problem with nonnegativity constraint at each iteration. Our extensive experiments demonstrate that the proposed method is more robust and efficient in dealing with the occlusion and corruption problems in face recognition as compared to the related state-of-the-art methods. In particular, it shows that the proposed method can improve both recognition accuracy and receiver operator characteristic (ROC) curves, while the computational cost is much lower than the SRC algorithms. Index Terms—Information theoretical learning, correntropy, linear least squares, half-quadratic optimization, sparse representation, M-estimator, face recognition, occlusion and corruption. Ç 1

This paper proposes a novel robust sparse representation method, called the two-stage sparse representation (TSR), for robust recognition on a large-scale database. Based on the divide and conquer strategy, TSR divides the procedure of robust recognition into outlier detection stage and recogni-tion stage. In the first stage, a weighted linear regression is used to learn a metric in which noise and outliers in im-age pixels are detected. In the second stage, based on the learnt metric, the large-scale dataset is firstly filtered into a small set according to the nearest neighbor criterion. Then a sparse representation is computed by the non-negative least squares technique. The sparse solution is unique and can be optimized efficiently. The extensive numerical experiments on several public databases demonstrate that the proposed TSR approach generally obtains better classification accuracy than the state-of-the-art Sparse Representation Classification (SRC). At the same time, by using the TSR, a significant re-duction of computational cost is reached by over fifty times in comparison with the SRC, which enables the TSR to be deployed more suitably for large-scale dataset. 1

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