基于共轭梯度的2DNMF算法研究

发布时间：2018-05-20 11:23

本文选题：二维非负矩阵分解 + 共轭梯度　；参考：《大连海事大学》2016年硕士论文

【摘要】：人脸识别是通过分析人脸特征,比对特征信息来识别身份。基于子空间分析的人脸识别方法,是近年来研究者非常关注的提取人脸特征的方法之一。但在提取特征和识别判断的过程中,负值的出现是不易解释甚至没有物理意义的。因此,人们转而考虑基于子空间分析下的非负矩阵分解算法(NMF)。该算法通过引入非负约束,提取出人脸局部的特征,不仅体现了局部构成整体的思想,而且分解结果没有负值,可解释性强,有明确的物理意义。然而,传统的NMF算法是基于梯度下降法的思想来设计的,它利用乘性迭代规则交替更新。这种迭代方式收敛速度慢,用于特征提取的训练时间较长,难以适应大规模数据的处理。在综合研究各类非负矩阵分解算法的基础上,并考虑人脸图像在遮挡、噪声情况下的识别特性,本文提出两个基于2DNMF的改进算法：(1)针对传统2DNMF的分解所用的乘性迭代公式,用基于矩阵形式的共轭梯度法结合交替迭代得到新的迭代格式,从而得到新的列基和行基；再对这两个基,以一种加权和的方式进行类别索引,进行人脸识别。(2)通过在目标函数中引入基矩阵正交的约束条件,推导出新的迭代格式,以此替换传统的乘性迭代,得到新的列基和行基；再对这两者以加权和的方式进行类别索引,进行人脸识别。通过尽可能地考虑人脸图像行列之间的结构信息,采用分别提取的办法,使得人脸信息更加完善。实验表明,改进算法在有遮挡的人脸图像的身份识别中,得到了比较理想的识别效果。
[Abstract]:Face recognition is to identify the identity by analyzing the features of the face and comparing the feature information. The face recognition method based on subspace analysis is one of the methods for extracting the features of the face in recent years. However, in the process of extracting features and recognition, the appearance of negative values is not easy to explain or even have no physical meaning. People consider non negative matrix factorization algorithm based on subspace analysis (NMF). This algorithm by introducing non negative constraints, extract the local facial features, not only reflects the local integral thought, and no negative decomposition results, strong interpretability, clear physical meanings. However, the traditional NMF algorithm is based on gradient The idea of descending method is designed, which uses the multiplicative iterative rules alternately. This iterative method has a slow convergence speed, long training time for feature extraction and difficult to adapt to the processing of large-scale data. Based on the comprehensive study of various non negative matrix decomposition algorithms, the recognition characteristics of face images under occlusion and noise are considered. Two improved algorithms based on 2DNMF are proposed in this paper: (1) the multiplicative iterative formula used for the decomposition of traditional 2DNMF is presented, and a new iterative scheme is obtained by combining the conjugate gradient method based on matrix form and alternating iteration to obtain new column and row bases, and then the two bases are indexed in a weighted sum, and face the face. (2) a new iterative scheme is derived by introducing the orthogonal constraint conditions of the base matrix into the objective function to replace the traditional multiplicative iteration and get new column and row bases. Then, the two are indexed by weighted sum, and face recognition. By considering the structure letter between the ranks of the face images as much as possible. The experimental results show that the improved algorithm has an ideal recognition effect in the identity recognition of the covered face image.
【学位授予单位】：大连海事大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TP391.41;O224

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