Sparse representation methods based on \(l _2\) norm regularization have attracted much attention due to its low computational cost and competitive performance. How to enhance the discriminability of \(l _2\) norm regularization-based representation method is a meaningful work. In this paper, we put forward a novel \(l _2\) norm regularization-based representation method, called Weighted Discriminative Sparse Representation for Classification (WDSRC), in which we consider the global discriminability and the local discriminability using two discriminative regularization terms of representation. The global discriminability is obtained by decorrelating the representation results stemming from all distinct classes. The local discriminability is achieved by the weighted representation in which the representation coefficient of the training images dissimilar to the test image will be reduced and the representation coefficient of the training images similar to the test image will be increased, which restrains the training images dissimilar to the test image and promotes the training images similar to the test image as much as possible in representing the test sample. By considering the global and local discriminability of representations simultaneously, the proposed WDSRC method can gain more discriminative representation for classification. Extensive experiments on benchmark datasets of object, face, action and flower demonstrate the effectiveness of the proposed WDSRC method.

基于\（l _2 \）范数正则化的稀疏表示方法由于其较低的计算成本和竞争性能而备受关注。如何增强基于规范化的\（l _2 \）表示方法的可分辨性是一项有意义的工作。在本文中，我们提出了一种新颖的\（l _2 \）基于规范正则化的表示方法，称为加权区分性稀疏分类表示（WDSRC），其中我们使用两个区分性正则化表示项来考虑全局可区分性和局部可区分性。全局可分辨性是通过对所有不同类的表示结果进行解相关获得的。局部判别是通过加权表示来实现的，在该加权表示中，与测试图像不同的训练图像的表示系数将减小，与测试图像相似的训练图像的表示系数将增大，从而抑制了训练图像与测试图像的差异。测试图像，并在表示测试样本时尽可能促进与测试图像相似的训练图像。通过同时考虑表示的全局和局部可分辨性，提出的WDSRC方法可以获得更多的可区分表示用于分类。在对象，面部，动作和花朵的基准数据集上进行的大量实验证明了所提出的WDSRC方法的有效性。