Several robust extensions of collaborative representation for image classification.

Collaborative representation (CR) is one of the well-known representation methods and has been widely used in computer vision and pattern recognition. The collaborative representation-based classification (CRC) and its extension called the probabilistic collaborative representation-based classification (PCRC) have obtained promising performance in image classification. However, the representation fidelity is usually measured by the ℓ2-norm , which is not robust to outliers. Moreover, CRC and PCRC only consider the global distribution of data and ignore the locality of data. To overcome those problems, in this paper, we propose the residual-based extensions and the weighted version of CRC and PCRC. Specifically, for the residual-based extensions of CRC and PCRC, we measure the representation fidelity by jointing ℓ1-norm and the ℓ2-norm of coding residuals. For the weighted extensions of CRC and PCRC with different coding residuals, we constrained the representation coefficients with locality of data. To verify the effectiveness of the proposed methods, we conduct extensive experiments on six popular face databases and three image databases. Experimental results have demonstrated that the ℓ1-norm of coding residual, jointing both the ℓ1-norm and the ℓ2-norm of coding residuals and the locality constraint of representation coefficients can enhance pattern discrimination effectively.