Class mean-weighted discriminative collaborative representation for classification

Representation-based classification (RBC) has been attracting a great deal of attention in pattern recognition. As a typical extension to RBC, collaborative representation-based classification (CRC) has demonstrated its superior performance in various image classification tasks. Ideally, we expect that the learned class-specific representations for a testing sample are discriminative, and the representation computed for the true class dominates the final representation of the testing sample. Most existing CRC-based methods can learn pattern discrimination, but cannot differentiate the contribution of class-specific representations to the classification of each testing sample. It is challenging for a representation-based classifier to retain both properties. To address this challenge and further improve CRC's classification performance, we propose a novel CRC-based method, class mean-weighted discriminative collaborative representation-based classifier (CMW-DCRC). Its objective function penalises the standard (Formula presented.) -norm residuals with two discriminative regularisation terms. A decorrelating term makes the class-specific representations more discriminative, and a newly designed class mean-weighted term that promotes the training samples from individual classes to competitively reconstruct the testing sample while boosting the contribution of the true class. To further enhance the robustness of CRC, we extend CMW-DCRC by replacing the l₂-norm coding residual with a l₁-norm coding residual, and solve the optimisation problem with an iteratively reweighted least square algorithm. Extensive experimental results on nine image data sets have shown that our methods outperform the state-of-the-art RBC-based methods.