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Sparse representation (SR) has been being applied as a state-of-the-art machine learning approach. Sparse representation classification (SRC1) approaches based on l1 norm regularization and non-negative-least-squares (NNLS) classification approach based on non-negativity have been proposed to be powerful and robust. However, these approaches are extremely slow when the size of training samples is very large, because both of them use the whole training set as dictionary. In this paper, we briefly survey the existing SR techniques for classification, and then propose a fast approach which uses non-negative matrix factorization as supervised dictionary learning method and NNLS as non-negative sparse coding method. Experiment shows that our approach can obtain comparable accuracy with the benchmark approaches and can dramatically speed up the computation particularly in the case of large sample size and many classes.