Sparse Representations for Image Classification: Learning Discriminative and Reconstructive Non-parametric Dictionaries

A framework for learning optimal dictionaries for simultaneous sparse signal representation and robust class classification is introduced in this paper. This problem for dictionary learning is solved by a class-dependent supervised simultaneous orthogonal matching pursuit, which learns the intra-class structure while increasing the inter-class discrimination, interleaved with an efficient dictionary update obtained via singular value decomposition. This framework addresses for the first time the explicit incorporation of both reconstruction and discrimination terms in the non-parametric dictionary learning and sparse coding energy. The work contributes to the understanding of the importance of learned sparse representations for signal classification, showing the relevance of learning discriminative and at the same time reconstructive dictionaries in order to achieve accurate and robust classification. The presentation of the underlying theory is complemented with examples with the standard MNIST and Caltech datasets, and results on the use of the sparse representation obtained from the learned dictionaries as local patch descriptors, replacing commonly used experimental ones.