A Max-Margin Perspective on Sparse Representation-Based Classification

Sparse Representation-based Classification (SRC) is a powerful tool in distinguishing signal categories which lie on different subspaces. Despite its wide application to visual recognition tasks, current understanding of SRC is solely based on a reconstructive perspective, which neither offers any guarantee on its classification performance nor provides any insight on how to design a discriminative dictionary for SRC. In this paper, we present a novel perspective towards SRC and interpret it as a margin classifier. The decision boundary and margin of SRC are analyzed in local regions where the support of sparse code is stable. Based on the derived margin, we propose a hinge loss function as the gauge for the classification performance of SRC. A stochastic gradient descent algorithm is implemented to maximize the margin of SRC and obtain more discriminative dictionaries. Experiments validate the effectiveness of the proposed approach in predicting classification performance and improving dictionary quality over reconstructive ones. Classification results competitive with other state-of-the-art sparse coding methods are reported on several data sets.