Non-negative representation-based classification (NRC) has attracted significant attention since its inception. Unlike traditional representation-based classification methods (RBCM) that rely on \(\ell _{1}\) / \(\ell _{2}\) -norm constraints, NRC innovatively employs a non-negative constraint on representation coefficients, confining the representation capacity of heterogeneous samples and enhancing classification accuracy. However, the non-negative constraint alone is insufficient to restrict representation contribution of heterogeneous samples. Moreover, the absence of regularization terms in NRC increases the probability of misclassification. To address these limitations, we introduce a competitive constraint regularization term into NRC, proposing competitive and non-negative representation based classification (Co-NRC) method. The introduced competitive constraint allows training samples from all categories to competitively represent the query sample, further penalizing heterogeneous samples and ensuring that homogeneous samples contribute more to the representation. We conducted extensive experiments on various challenging datasets. The experiments on small-scale datasets demonstrated that Co-NRC outperforms various RBCM, while experiments on large-scale datasets showed that this method even surpasses multiple deep learning methods. These findings fully demonstrate the competitiveness of the proposed method. Habitually, the source code for Co-NRC can be publicly available on my profile page at https://github.com/li-zi-qi/Co-NRC.
