基于图学习正则判别非负矩阵分解的人脸识别

doi:10.11772/j.issn.1001-9081.2021060979

《计算机应用》唯一官方网站 ›› 2021, Vol. 41 ›› Issue (12): 3455-3461.DOI: 10.11772/j.issn.1001-9081.2021060979

• 第十八届中国机器学习会议(CCML 2021) • 上一篇

基于图学习正则判别非负矩阵分解的人脸识别

杜汉¹^,², 龙显忠¹^,²(), 李云¹^,²

^1.南京邮电大学计算机学院、软件学院、网络空间安全学院，南京 210023
^2.江苏省大数据安全与智能处理重点实验室（南京邮电大学），南京 210023

收稿日期:2021-05-12 修回日期:2021-07-23 接受日期:2021-08-05 发布日期:2021-12-28 出版日期:2021-12-10
通讯作者: 龙显忠
作者简介:杜汉（1998—），男，河南南阳人，硕士研究生，主要研究方向：机器学习算法在图像分类中的应用
李云（1974—），男，安徽安庆人，教授，博士生导师，博士，CCF会员，主要研究方向：人工智能、机器学习。
基金资助:
国家自然科学基金青年项目(61906098)

Graph learning regularized discriminative non-negative matrix factorization based face recognition

Han DU¹^,², Xianzhong LONG¹^,²(), Yun LI¹^,²

^1.School of Computer Science，Nanjing University of Posts and Telecommunications，Nanjing Jiangsu 210023，China
^2.Jiangsu Key Laboratory of Big Data Security and Intelligent Processing （Nanjing University of Posts and Telecommunications），Nanjing Jiangsu 210023，China

Received:2021-05-12 Revised:2021-07-23 Accepted:2021-08-05 Online:2021-12-28 Published:2021-12-10
Contact: Xianzhong LONG
About author:DU Han， born in 1998， M. S. candidate. His research interests include application of machine learning algorithms in image classification.
LI Yun， born in 1974， Ph. D.， professor. His research interests include artificial intelligence， machine learning.
Supported by:
the Young Scientists Fund of National Natural Science Foundation of China(61906098)

摘要/Abstract

摘要：

基于图正则非负矩阵分解（NMF）算法充分利用了高维数据通常位于一个低维流形空间的假设从而构造拉普拉斯矩阵，但该算法的缺点是构造出的拉普拉斯矩阵是提前计算得到的，并没有在乘性更新过程中对它进行迭代。为了解决这个问题，结合子空间学习中的自表示方法生成表示系数，并进一步计算相似性矩阵从而得到拉普拉斯矩阵，而且在更新过程中对拉普拉斯矩阵进行迭代。另外，利用训练集的标签信息构造类别指示矩阵，并引入两个不同的正则项分别对该类别指示矩阵进行重构。该算法被称为图学习正则判别非负矩阵分解（GLDNMF），并给出了相应的乘性更新规则和目标函数的收敛性证明。在两个标准数据集上的人脸识别实验结果显示，和现有典型算法相比，所提算法的人脸识别的准确率提升了1% ~ 5%，验证了其有效性。

关键词: 非负矩阵分解, 自表示, 图学习, 判别信息, 人脸识别

Abstract:

The Non-negative Matrix Factorization （NMF） algorithm based on graph regularization makes full use of the assumption that high-dimensional data are usually located in a low-dimensional manifold space to construct the Laplacian matrix. The disadvantage of this algorithm is that the constructed Laplacian matrix is calculated in advance and will not be iterated during the multiplicative update process. In order to solve this problem， the self-representation method in subspace learning was combined to generate the representation coefficient， and the similarity matrix was further calculated to obtain the Laplacian matrix， and the Laplacian matrix was iterated during the update process. In addition， the label information of the training set was used to construct the class indicator matrix， and two different regularization items were introduced to reconstruct the category indicator matrix respectively. This algorithm was called Graph Learning Regularized Discriminative Non-negative Matrix Factorization （GLDNMF）， and the corresponding multiplicative update rules and the convergence proof of the objective function were given. Face recognition experimental results on two standard datasets show that the accuracy of the proposed algorithm for face recognition is increased by 1% - 5% compared to the existing classic algorithms， verifying the effectiveness of the proposed method.

Key words: Non-negative Matrix Factorization (NMF), self-representation, graph learning, discriminative information, face recognition

中图分类号:

TP391.4

杜汉, 龙显忠, 李云. 基于图学习正则判别非负矩阵分解的人脸识别[J]. 计算机应用, 2021, 41(12): 3455-3461.

Han DU, Xianzhong LONG, Yun LI. Graph learning regularized discriminative non-negative matrix factorization based face recognition[J]. Journal of Computer Applications, 2021, 41(12): 3455-3461.

图/表 7

参考文献 36

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数据集	样本数	每类的样本数	维度	类的个数
UMIST	575	19~48	1 600	20
Yale	165	11	1 600	15

数据集	样本数	每类的样本数	维度	类的个数
UMIST	575	19~48	1 600	20
Yale	165	11	1 600	15

算法	3train	5train	7train	9train	11train	13 train	15train
PCA^［28］	0.618 0	0.714 1	0.777 7	0.826 8	0.867 0	0.873 9	0.905 8
LPP^［29］	0.593 0	0.666 3	0.732 4	0.795 4	0.836 3	0.872 0	0.913 4
NMF^［1］	0.649 1	0.772 8	0.854 7	0.908 1	0.934 3	0.948 5	0.966 1
LNMF^［11］	0.662 9	0.789 4	0.850 1	0.905 3	0.936 9	0.941 9	0.962 9
GNMF^［13］	0.663 6	0.789 4	0.864 8	0.909 6	0.947 3	0.951 7	0.968 0
GDNMF^［27］	0.657 6	0.785 2	0.863 2	0.918 2	0.945 9	0.953 9	0.975 2
RCGLDNMF	0.693 7	0.854 3	0.899 7	0.921 0	0.949 2	0.976 1	0.974 1
GLDNMF	0.744 0	0.869 8	0.930 5	0.950 1	0.973 5	0.980 0	0.990 9

算法	3train	5train	7train	9train	11train	13 train	15train
PCA^［28］	0.618 0	0.714 1	0.777 7	0.826 8	0.867 0	0.873 9	0.905 8
LPP^［29］	0.593 0	0.666 3	0.732 4	0.795 4	0.836 3	0.872 0	0.913 4
NMF^［1］	0.649 1	0.772 8	0.854 7	0.908 1	0.934 3	0.948 5	0.966 1
LNMF^［11］	0.662 9	0.789 4	0.850 1	0.905 3	0.936 9	0.941 9	0.962 9
GNMF^［13］	0.663 6	0.789 4	0.864 8	0.909 6	0.947 3	0.951 7	0.968 0
GDNMF^［27］	0.657 6	0.785 2	0.863 2	0.918 2	0.945 9	0.953 9	0.975 2
RCGLDNMF	0.693 7	0.854 3	0.899 7	0.921 0	0.949 2	0.976 1	0.974 1
GLDNMF	0.744 0	0.869 8	0.930 5	0.950 1	0.973 5	0.980 0	0.990 9

算法	3train	5train	7train	9train
PCA^［28］	0.641 6	0.672 2	0.675 0	0.700 0
LPP^［29］	0.654 1	0.680 0	0.685 0	0.720 0
NMF^［1］	0.722 5	0.720 0	0.723 3	0.743 3
LNMF^［11］	0.655 0	0.658 8	0.653 3	0.676 6
GNMF^［13］	0.695 8	0.702 2	0.713 3	0.743 3
GDNMF^［27］	0.707 5	0.711 1	0.731 6	0.756 6
RCGLDNMF	0.765 8	0.777 7	0.778 3	0.803 3
GLDNMF	0.776 6	0.783 3	0.791 6	0.816 6

基于图学习正则判别非负矩阵分解的人脸识别

Graph learning regularized discriminative non-negative matrix factorization based face recognition

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