Abstract: Sparse coding represents a signal by a linear combination of only a few atoms of a learned over-complete dictionary. While sparse coding exhibits compelling performance for various machine learning tasks, the process of obtaining sparse code with fixed dictionary is independent for each data point without considering the geometric information and manifold structure of the entire data. We propose Support Regularized Sparse Coding (SRSC) which produces sparse codes that account for the manifold structure of the data by encouraging nearby data in the manifold to choose similar dictionary atoms. In this way, the obtained support regularized sparse codes capture the locally linear structure of the data manifold and enjoy robustness to data noise. We present the optimization algorithm of SRSC with theoretical guarantee for the optimization over the sparse codes. We also propose a feed-forward neural network termed Deep Support Regularized Sparse Coding (Deep-SRSC) as a fast encoder to approximate the sparse codes generated by SRSC. Extensive experimental results demonstrate the effectiveness of SRSC and Deep-SRSC.