图正则化稀疏判别非负矩阵分解

非负矩阵分解是一种流行的数据表示方法，利用图正则化约束能有效地揭示数据之间的局部流形结构。为了更好地提取图像特征，给出了一种基于图正则化的稀疏判别非负矩阵分解算法（graph regularization sparse discriminant non-negative matrix factorization，GSDNMF-L_2，1）。利用同类样本之间的稀疏线性表示来构建对应的图及权矩阵；以L_2，1范数进行稀疏性约束；以最大间距准则为优化目标函数，利用数据集的标签信息来保持数据样本之间的流形结构和特征的判别性，并给出了算法的迭代更新规则。在若干图像数据集上的实验表明，GSDNMF-L_2，1在特征提取方面的分类精度优于各对比算法。

Graph-regularized,sparse discriminant,non-negative matrix factorization

Non-negative matrix factorization is a popular data representation method. Using graph regularization constraints can effectively reveal the local manifold structure between data. In order to better extract image features, a graph-regularized, sparse-discriminant, non-negative matrix factorization algorithm is proposed in this paper. The sparse linear representation between similar samples was used to construct the corresponding graph and weight matrix. The objective function using the maximum margin criterion with L_2,1 -norm constraint was optimized, using the tag information of the dataset to maintain the manifold structure of samples and discrimination of characteristics, and the iterative update rules of the algorithm are given. Experiments were carried out on the ORL, AR, and COIL20 datasets. Compared with other algorithms, GSDNMF-L_2,1 showed higher classification accuracy in feature extraction.