Collaborative coding and dictionary learning for nearest subspace classification

Sparse representation (SR) has been widely studied and successfully applied to many areas of computer science in recent years. However, whether sparsity is essential to improve the classification performance is still an open question. Some studies reveal that it is the collaborative representation (CR) rather than SR that truly improves the classification performance. In this paper, the advantage of CR is further investigated and exploited, and a CR-based coding method is proposed. This method improves the classification performance by applying CR to the traditional nearest subspace (NS) method. Compared to the other NS method which codes the test sample on each class separately, the proposed method employs all samples to code the test sample collaboratively and preserves the subspace structure at the same time. The test sample is then classified to the class with the smallest representation error. Besides, a corresponding dictionary learning algorithm is also proposed so that the coding can be conducted on a dictionary learned from the training dataset. Since analytical solutions for coding and dictionary learning have been derived, our algorithm can be implemented efficiently. Experiments are conducted on seven face databases and the USPS handwritten digit database, and the results show that the proposed algorithm outperforms many state-of-the-art coding methods and dictionary learning methods, which demonstrates the power brought by CR.