摘要： 在非负矩阵分解算法中，为提升基矩阵的稀疏表达能力，在不事先设定稀疏度的情形下，提出一种基于投影梯度及下逼近方法的非负矩阵分解算法——PGNMU。通过引入上界的约束条件，利用基于投影梯度的交替迭代方法提取基矩阵的重要特征并加以应用。在人脸数据库CBCL和ORL上的实验结果表明，该方法能改进基矩阵的稀疏描述能力，且其识别率也优于已有方法。

关键词: 非负矩阵分解, 投影梯度, 下逼近, 松弛法, 稀疏度, 基矩阵

Abstract: In order to improve the ability of the parts-based representations of the Nonnegative Matrix Factorization(NMF) algorithm, this paper proposes a NMF based on projected gradient and underapproximation method——Projected Gradient Nonnegative Matrix Underapproximation (PGNMU). By adding the upper bound constraint, it applies the important features of the basis matrixs that are extracted by using the alternating iterative method based on the projected gradient methods to the experiments. Compared with previously published methods on the CBCL and ORL database, results show that the method has the better sparseness and better recognition rate than the others.

Key words: Nonnegative Matrix Factorization(NMF), projected gradient, underapproximation, relaxation method, sparsity, basis matrix

中图分类号: 

• TP391.4