基于稀疏重构的判别分析

Sparsity reconstruction-based discriminant analysis

为了解决现有判别分析算法对残缺和遮挡等外部干扰比较敏感的问题,从局部稀疏表示的角度,提出一种基于稀疏重构的判别分析（SDA）降维算法.该算法首先利用稀疏表示完成各个类内局部稀疏重构,然后通过非所在类内的样本均值完成各样本的类间局部稀疏重构,最后在降维过程中保持类间和类内的稀疏重构信息之比.在AR和UMIST人脸库人脸数据集上的实验结果表明,与基于图优化的Fisher分析（GbFA）算法和基于重构判别分析（RDA）算法相比,该算法提高了基于近邻分类的最高识别准确率2％ ～ 10％.

In order to solve the problem of being sensitive to external interference such as defects and occlusions in the existing discriminant analysis, a Sparsity reconstruction-based Discriminant Analysis （SDA） for dimensionality reduction was proposed in the term of local sparse representation. The algorithm firstly made use of sparse representation to complete local sparsity reconstruction in each class, and then completed between-class sparsity reconstruction with the average of each different class. Finally the algorithm preserved the ratio between the between-class sparsity reconstruction information and the within-class sparsity reconstruction information in the process of dimensionality reduction. The algorithm promotes the computational efficiency of sparse representation and the robust performance of discriminant analysis. The experimental resuhs on AR and UMIST face datasets show, compared with Graph-based Fisher Analysis （GbFA） algorithm and Reconstructive- based Discriminant Analysis （RDA） algorithm, the proposed algorithm promotes 2 - 10 percent in the highest recognition accuracy based on nearest neighbor classification.