Representation-based classification methods (RBCM) have garnered significant attention in the field of image classification over the past decade. However, the effectiveness of \(\ell _1\) or \(\ell _2\) -regularization in improving classification performance remains ambiguous. To address this issue, the nonnegative representation-based classification (NRC) method proposes a constructive approach that emphasizes strong positive correlations between samples from the same classes while treating samples from different classes as irrelevant. Despite its merits, NRC overlooks some critical aspects. Firstly, it fails to incorporate an affine constraint, which is necessary for ensuring that all samples reside in a specific affine space. Additionally, the absence of local information among samples results in reduced discriminability, as NRC relies solely on global representation. Lastly, the instability of the solution to representation coefficients can be attributed to the lack of regularization terms in NRC’s objective function, leading to increased misclassification probabilities. To address these limitations, we introduce the affine locality-sensitive nonnegative representation (ALNR) model as a novel approach for image classification. More specifically, ALNR enforces an affine constraint on representation coefficients and introduces a regularization term involving a locality-sensitive matrix in the objective function. Extensive experiments conducted on diverse datasets demonstrate the strong competitiveness of our proposed method. Habitually, the ALNR’s source code can be made publicly accessible on my profile page at https://github.com/li-zi-qi/ALNR.
