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Image representation based on sparse coding generalizes the bag of words model. Although it reduces the reconstruction error for local features to achieve the state-of-the-art image classification performance, the large computational cost hinders the application of sparse coding-based image features. In this paper, we propose approximating a sparse code using the output of a simple neural network. The resulting parameter learning model for the neural network automatically incorporates non-negative and shift-invariant constraints, leading to an efficient normalized non-negative sparse coding (N3SC) sparse encoder. Without the use of the traditional iterative process to solve the sparse coding objective, the sparse encoder directly “converts” each local feature into a sparse code. We also introduce a method for training the encoder based on the auto-encoder method. In addition, we formally propose the corresponding sparse coding scheme called N3SC, which enforces both the non-negative constraint and the shift-invariant constraint in addition to the traditional sparse coding criteria. As demonstrated by several experiments, the obtained N3SC encoder requires only 3%–10% of the processing time for image feature extraction compared with the standard sparse coding scheme. At the same time, the features extracted using the exact solutions of the N3SC coding scheme and the N3SC encoder offer superior image classification accuracy compared to the accuracy of many existing sparse coding-based representations. [ABSTRACT FROM AUTHOR]