附加轮廓信息的图正则非负矩阵分解及在人脸识别中的应用

发布时间：2018-08-30 17:56

【摘要】：矩阵分解在信息重建、计算机视觉和模式识别等领域引起了广泛的兴趣和关注.非负矩阵分解由于其对局部构成整体思想的体现以及对数据低维特征的挖掘而备受关注.论文引言中介绍了已有的非负矩阵分解模型和图正则非负矩阵分解模型,并介绍了模型求解算法中较常用的乘子迭代算法和投影梯度算法.论文第二章提出了附加轮廓信息的图正则非负矩阵分解模型.并应用带积极集策略的共轭梯度(ASCG)算法求解该模型.论文第三章中我们在实际人脸数据库上进行了数值实验.我们将ASCG算法同MU算法和PG算法进行了比较.并使用ASCG算法求解GNMFO模型,在分解得到的低维矩阵因子上进行人脸分类.本论文最主要的创新点在于通过原始人脸图像矩阵的一阶差分信息表示人脸轮廓信息,并通过人脸轮廓信息构造了图正则项.这种构造的方式简单易行同时很好的提高了人脸识别的分类效果.另外,我们采取了带积极集策略的共轭梯度算法求解GNMFO模型,算法具有好的收敛性.我们将GNMFO模型及ASCG算法应用到实际高维人脸数据库中进行人脸分类,数值实验表明GNMFO模型可以稳健的提高人脸识别分类效果.同时数值实验体现了采用的ASCG算法求解问题的有效性。
[Abstract]:Matrix decomposition has attracted wide attention in the fields of information reconstruction, computer vision and pattern recognition. Non-negative matrix factorization has attracted much attention because of its representation of the whole idea of local composition and the mining of low-dimensional features of data. In the introduction of this paper, the existing nonnegative matrix decomposition model and graph regular nonnegative matrix factorization model are introduced. The multiplier iterative algorithm and projection gradient algorithm are also introduced. In chapter 2, a graph regular nonnegative matrix factorization model with contour information is proposed. The conjugate gradient (ASCG) algorithm with active set strategy is used to solve the model. In the third chapter, we carry out numerical experiments on the actual face database. We compare ASCG algorithm with MU algorithm and PG algorithm. The ASCG algorithm is used to solve the GNMFO model, and the face classification is carried out on the decomposed low dimensional matrix factor. The main innovation of this paper is that the first order difference information of the primitive human face image matrix is used to represent the face contour information and the graph regular term is constructed by the face contour information. This method is simple and easy to implement and improves the classification effect of face recognition. In addition, the conjugate gradient algorithm with positive set strategy is used to solve the GNMFO model, and the algorithm has good convergence. We apply GNMFO model and ASCG algorithm to face classification in the actual high-dimensional face database. Numerical experiments show that GNMFO model can improve the classification effect of face recognition stably. At the same time, the numerical experiments show the effectiveness of the ASCG algorithm.
【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP391.41

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