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Sparse representation for machine learning has been exploited in past years. Several sparse representation based classification algorithms have been developed for some applications, for example, face recognition. In this paper, we propose an improved sparse representation based classification algorithm. Firstly, for a discriminative representation, a non-negative constraint of sparse coefficient is added to sparse representation problem. Secondly, Mahalanobis distance is employed instead of Euclidean distance to measure the similarity between original data and reconstructed data. The proposed classification algorithm for face recognition has been evaluated under varying illumination and pose using standard face databases. The experimental results demonstrate that the performance of our algorithm is better than that of the up-to-date face recognition algorithm based on sparse representation.