The Extended Collaborative Representation-Based Classification

Collaborative representation (CR), one of the well-known representation methods, has been widely used in pattern recognition. The collaborative representation-based classification (CRC) is to represent a test sample by the collaborative subspace of all the training samples from all classes. As an effective extension of CRC, the probabilistic collaborative representation based classification (PCRC) calculates the probability of a test sample belonging to the collaborative subspace of all classes for classification. In the related CRC works, the representation fidelity is often measured by the l(2)-norm of coding residual, but the l(1)-norm fidelity is used very little. In fact, the representation fidelity with different coding residuals has a great effect on the CR-based classification performance. In this paper, to further improve the CR-based classification accuracy, we propose the extended CRC and PCRC by jointing the l(1)-norm and l(2)-norm of coding residuals on the representation fidelity. Besides, the extension of CRC is introduced by constraining the coding residual with l(1)-norm. The experiments on four popular face databases show that the proposed extensions of CRC and PCRC perform very well.