Relaxed local preserving regression for image feature extraction

The latest linear least regression (LSR) methods improved the performance of image feature extraction effectively by relaxing strict zero-one labels as slack forms. However, these methods have the following three disadvantages: 1) LSR-based methods are sensitive to the noises and may lose effectiveness in feature extraction task; 2) they only focus on the global structures of data, but ignore locality which is important to improve the performance; 3) they suffer from small-class problem, which means the number of projections learned by methods is limited by the number of classes. To address these problems, we propose a novel method called Relaxed Local Preserving Regression (RLPR) for image feature extraction. By incorporating the relaxed label matrix and similarity graph-based regularization term, RLPR can not only explore the latent structure information of data, but also solve the small-class problem. In order to enhance the robustness to noises, we further proposed an extended version of RLPR based on l_{2, 1}-norm, termed as ERLPR. The experimental results on image databases consistently show that the recognition rates of RLPR and ERLPR are superior to the compared methods and can achieve 98% in normal cases. Especially, even on the corrupted databases, the proposed methods can also achieve the classification accuracy of more than 58%.