Weighted discriminative collaborative competitive representation for robust image classification.

Collaborative representation-based classification (CRC) is a famous representation-based classification method in pattern recognition. Recently, many variants of CRC have been designed for many classification tasks with the good classification performance. However, most of them ignore the inter-class pattern discrimination among the class-specific representations, which is very critical for strengthening the pattern discrimination of collaborative representation (CR). In this article, we propose a novel CR approach for image classification, called weighted discriminative collaborative competitive representation (WDCCR). The proposed WDCCR designs the discriminative and competitive collaborative representation among all the classes by fully considering the class information. On the one hand, we incorporate two discriminative constraints into the unified WDCCR model. Both constraints are the competitive class-specific representation residuals and the pairs of class-specific representations for each query sample. On the other hand, the constraint of the weighted categorical representation coefficients is introduced into the proposed model for further enhancing the power of discriminative and competitive representation. In the weighted constraint, we assume that the different classes of each query sample should have less contribution to the representation with the small representation coefficients, and then two types of weight factors are designed to constrain the representation coefficients. Furthermore, the robust WDCCR (R-WDCCR) is proposed with l1-norm representation fidelity for recognizing noisy images. Extensive experiments on six image data sets demonstrate the effective and robust superiorities of the proposed WDCCR and R-WDCCR over the related state-of-the-art representation-based classification methods.