Affine-Constrained Group Sparse Coding and Its Application to Image-Based Classifications

This paper proposes a novel approach for sparse coding that further improves upon the sparse representation-based classification (SRC) framework. The proposed framework, Affine-Constrained Group Sparse Coding (ACGSC), extends the current SRC framework to classification problems with multiple input samples. Geometrically, the affineconstrained group sparse coding essentially searches for the vector in the convex hull spanned by the input vectors that can best be sparse coded using the given dictionary. The resulting objective function is still convex and can be efficiently optimized using iterative block-coordinate descent scheme that is guaranteed to converge. Furthermore, we provide a form of sparse recovery result that guarantees, at least theoretically, that the classification performance of the constrained group sparse coding should be at least as good as the group sparse coding. We have evaluated the proposed approach using three different recognition experiments that involve illumination variation of faces and textures, and face recognition under occlusions. Preliminary experiments have demonstrated the effectiveness of the proposed approach, and in particular, the results from the recognition/occlusion experiment are surprisingly accurate and robust.