An elastic competitive and discriminative collaborative representation method for image classification

Abstract

Collaborative representation-based (CR) methods have become prevalent for pattern classification tasks, achieving formidable performance. Theoretically, we expect the learned class-specific representation of the correct class to be discriminative against others, with the representation of the correct class contributing dominantly in CR. However, most existing CR methods focus on improving discrimination while having a limited impact on enhancing the representation contribution of the correct category. In this work, we propose a novel CR approach for image classification called the elastic competitive and discriminative collaborative representation-based classifier (ECDCRC) to simultaneously strengthen representation contribution and discrimination of the correct class. The ECDCRC objective function penalizes two key terms by fully incorporating label information. The competitive term integrates the nearest subspace representation with corresponding elastic factors into the model, allowing each class to have varying competition intensities based on similarity with the query sample. This enhances the representation contribution of the correct class in CR. To further improve discrimination, the discriminative term introduces an elastic factor as a weight in the model to represent the gap between the query sample and the representation of each class. Moreover, instead of focusing on representation coefficients, the designed ECDCRC weights associated with representation components directly relate to the representation of each class, enabling more direct and precise discrimination improvement. Concurrently, sparsity is also enhanced through the two terms, further boosting model performance. Additionally, we propose a robust ECDCRC (R-ECDCRC) to handle image classification with noise. Extensive experiments on seven public databases demonstrate the proposed method's superior performance over related state-of-the-art CR methods.

Keywords: Collaborative representation; Competitive representation; Sparse representation.