基于判别超图和非负矩阵分解的人脸识别方法

doi:10.15960/j.cnki.issn.1007-6093.2015.03.013

运筹学学报 ›› 2015, Vol. 19 ›› Issue (3): 108-115.doi: 10.15960/j.cnki.issn.1007-6093.2015.03.013

基于判别超图和非负矩阵分解的人脸识别方法

张欣玥¹, 黄正海^1,*, 李志明¹

1. 天津大学理学院数学系, 天津 300072

收稿日期:2015-05-21 出版日期:2015-09-15 发布日期:2015-09-15
通讯作者: 黄正海 huangzhenghai@tju.edu.cn
基金资助:
国家自然科学基金(Nos. 10571112, 11431002)

A face recognition method based on discriminative hypergraph and nonnegative matrix factorization

ZHANG Xinyue¹, HUANG Zhenghai^1,*, LI Zhiming¹

1. Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, China

Received:2015-05-21 Online:2015-09-15 Published:2015-09-15

摘要/Abstract

摘要：

非负矩阵分解是一种流行的数据表示方法,已广泛应用于图像处理和模式识别等问题.但是非负矩阵分解忽略了数据的几何结构. 而现有的基于简单图的学习方法只考虑了图像的成对信息,并且对计算相似度时的参数选择非常敏感. 超图学习方法可以有效地解决这些问题. 超图利用超边将多个顶点相连接用以表示图像的高维结构信息. 然而, 现有的大部分超图学习方法都是无判别的学习方法.为了提高识别效果, 提出了基于具有判别信息的超图和非负矩阵分解方法的新模型, 利用交替方向法进行迭代求解新模型, 并结合最近邻方法进行人脸识别. 在几个常用标准人脸图像数据库上进行实验, 实验结果表明提出的方法是有效的.

关键词: 人脸特征提取, 人脸分类, 非负矩阵分解, 超图

Abstract:

Nonnegative matrix factorization (NMF) has become a popular data representation method and has been widely used in image processing and pattern recognition problems. However, NMF ignores the local geometric structure of data. Existing simple graph-based transductive learning only considering the image information in pairs, and they are sensitive to the radius parameter used in similarity calculation. Hypergraph learning has been investigated to solve the problems. Hypergraph models the high-order relationship of samples by using the hyperedges to link multiple samples. However, most of the existing hypergraph learning methods are unsupervised methods. Based on the discriminative hypergraph and nonnegative matrix factorization, we propose a new model and solve the new model by using the alternating direction method of multipliers. The new method, together with the nearest neighbor method, is applied to face recognition. Experimental results on several standard face datasets show the effectiveness of our method.

Key words: facial feature extraction, face classification, nonnegative matrix factorization, hypergraph

张欣玥, 黄正海, 李志明. 基于判别超图和非负矩阵分解的人脸识别方法[J]. 运筹学学报, 2015, 19(3): 108-115.

ZHANG Xinyue, HUANG Zhenghai, LI Zhiming. A face recognition method based on discriminative hypergraph and nonnegative matrix factorization[J]. Operations Research Transactions, 2015, 19(3): 108-115.

参考文献

Fukunaga K. Introduction to Statistical Pattern Recognition [M]. New York: Academic, 1991.

Belhumeur P, Hespanha J, Kriegman D. Eigenfaces vs. fisherfaces: Recognition using class specific linear projection [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence}, 1997, 19(7): 711-720.

Lee D D, Seung H S. Learning the parts of objects by non-negative matrix factorization [J]. Nature, 1999, 401(21): 788-791.

Li S Z, Hou X W, Zhang H J, et al. Learning spatially localized, parts-based representation [C] // Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Washington, USA: IEEE, 2001, 207-212.

Cai D, He X, Wu X, et al. Non-negative matrix factorization on manifold [C] // Proceeding of the 8th IEEE International Conference on Data Mining, Pisa, Italy: IEEE, 2008, 63-72.

Yu J, Tao D, Wang M. Adaptive hypergraph learning and its application in image classification [J]. IEEE Transactions on Image Processing, 2012, 21(7): 3262-3272.

Hong C, Yu J, Li J, et al. Multi-view hypergraph learning by patch alignment framework [J]. Neurocomputing, 2013, 118: 79-86.

Huang S, Yang D. Discrimination hyper-laplacian projections with its application to face recognition [C]// International Conference on Multimedia and Expo Workshops, Chengdu, China: IEEE, 2014, 1-6.

Guan N, Tao D. Manifold regularized discriminative nonnegative matrix factorization with fast gradient descent [J]. IEEE Transactions on Image Processing, 2011, 20(7): 2030-2048.

Zhou D, Huang J, Sch\"{A}olkopf B. Learning with hypergraphs: Clustering, classication, and embedding [C] // Advances in neural information processing systems, Vancouver／Whistler，\\Canada：IEEE，2006, 1601-1608.

Xu D, Yan S, Tao D, et al. Enhanced marginal fisher analysis for human gait recognition and content based image retrieval [J]. IEEE Transactions on Image Processing, 2007, 16(11): 2811-2821.

Ding C, Li T, Peng W, et al. Orthogonal nonnegative matrix tri-factorizations for clustering [C]// Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining}, New York, USA: ACM Press, 2006, 126-135.

Bian W, Tao D. Biased discriminant Euclidean embedding for content based image retrieval [J]. IEEE Transactions on Image Processing, 2010, 19(2): 545-554.

Hong M, Luo Z Q, Razaviyayn M. Convergence analysis of alternating direction method of multipliers for a family of nonconvex problems [J].//[Online]. Available: http://arxiv.org/pdf/1410.\\3390.pdf

[1]	李瞳, 王光辉, 周文玲. 图与超图中的彩色匹配综述[J]. 运筹学学报, 2019, 23(3): 77-90.
[2]	裴建峰, 林上为. 极大限制边连通超图的两个充分条件[J]. 运筹学学报, 2019, 23(2): 120-126.
[3]	李姗, 单而芳, 张琳. 5-正则图的全控制数的一个注记[J]. 运筹学学报, 2017, 21(1): 125-128.
[4]	林苡, 倪振羽, 单而芳. 5-一致超图的全横贯[J]. 运筹学学报, 2016, 20(2): 97-104.

基于判别超图和非负矩阵分解的人脸识别方法

A face recognition method based on discriminative hypergraph and nonnegative matrix factorization

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 4

编辑推荐

Metrics

本文评价