Triple Sparse Denoising Discriminantive Least Squares Regression for image classification

Discriminantive Least Squares Regression (DLSR) is an algorithm that employs $\varepsilon$-draggings techniques to enhance intra-class similarity. However, it overlooks that an increase in intra-class closeness may simultaneously lead to a decrease in the distance between similar but different classes. To address this issue, we propose a new approach called Triple Sparse Denoising Discriminantive Least Squares Regression (TSDDLSR), which combines three sparsity constraints: sparsity constraints between classes to amplify the growth of the distance between similar classes; sparsity constraints on relaxation matrices to capture more local structure; sparsity constraints on noise matrices to minimize the effect of outliers. In addition, we position the matrix decomposition step in the label space strategically with the objective of enhancing denoising capabilities, safeguarding it from potential degradation, and preserving its underlying manifold structure. Our experiments evaluate the classification performance of the method under face recognition tasks (AR, CMU PIE, Extended Yale B, Georgia Tech, FERET datasets), biometric recognition tasks (PolyU Palmprint dataset), and object recognition tasks (COIL-20, ImageNet datasets). Meanwhile, the results show that TSDDLSR significantly improves classification performance compared to existing methods.