[1]王中元,刘惊雷.低秩分块矩阵的核近似[J].智能系统学报,2019,14(06):1209-1216.[doi:10.11992/tis.201904058]
 WANG Zhongyuan,LIU Jinglei.Kernel approximation of a low-rank block matrix[J].CAAI Transactions on Intelligent Systems,2019,14(06):1209-1216.[doi:10.11992/tis.201904058]
点击复制

低秩分块矩阵的核近似(/HTML)
分享到:

《智能系统学报》[ISSN:1673-4785/CN:23-1538/TP]

卷:
第14卷
期数:
2019年06期
页码:
1209-1216
栏目:
出版日期:
2019-11-05

文章信息/Info

Title:
Kernel approximation of a low-rank block matrix
作者:
王中元 刘惊雷
烟台大学 计算机与控制工程学院, 山东 烟台 264005
Author(s):
WANG Zhongyuan LIU Jinglei
School of Computer and Control Engineering, Yantai University, Yantai 264005, China
关键词:
低秩近似块对角矩阵稀疏矩阵核近似矩阵分解交替向量乘子法子空间聚类图像识别
Keywords:
low-rank approximationblock diagonal matrixsparse matrixkernel approximationmatrix factorizationalternating direction method of multipliers (ADMM)subspace clusteringimage identification
分类号:
TP181
DOI:
10.11992/tis.201904058
摘要:
为了探讨结构受限下的矩阵分解问题,通过最小化块外对角线来增强类与类之间数据表示的不相关性,从而实现分块约束,即数据来源于不同的聚类结构,是一种局部结构的约束;同时通过增强样本的自表达属性并缩小样本之间的差距来增强类内数据表示的相关性,从而实现低秩约束,即数据行出现冗余,是一种全局结构的约束。随后设计了一个低秩分块矩阵的核近似算法,通过交替方向乘子法迭代求解。最后将该方法分别在人脸识别和字符识别上进行测试。实验结果表明,所提出的低秩分块矩阵分解算法在收敛速度和近似精度上都具有一定的优势。
Abstract:
In order to explore the matrix decomposition problem under structural constraints, irrelevance of data representation between classes was enhanced in this paper by minimizing the diagonal outside the block, thus realizing the block constraint, i.e., the data is derived from different cluster structures. It is a local structure constraint. At the same time, by enhancing the self-expressing property of the sample and narrowing the gap between samples, the correlation of the data representation in the class was enhanced, thereby realizing the low-rank constraint, i.e., the redundancy of the data row was a constraint of the global structure, thereby realizing the low-rank constraint. A kernel approximation algorithm for low-rank block matrix was then designed and solved iteratively by alternating the direction method of multipliers (ADMM). Finally, the method was tested on face recognition and character recognition. Experimental results showed that the proposed low-rank block matrix decomposition algorithm has certain advantages in solving speed and approximate accuracy.

参考文献/References:

[1] 雷恒鑫, 刘惊雷. 基于行列联合选择矩阵分解的偏好特征提取[J]. 模式识别与人工智能, 2017, 30(3):279-288 LEI Hengxin, LIU Jinglei. Preference feature extraction based on column union row matrix decomposition[J]. Pattern recognition and artificial intelligence, 2017, 30(3):279-288
[2] 张恒敏, 杨健, 郑玮. 低秩矩阵近似与优化问题研究进展[J]. 模式识别与人工智能, 2018, 31(1):23-36 ZHANG Hengmin, YANG Jian, ZHENG Wei. Research progress of low-rank matrix approximation and optimization problem[J]. Pattern recognition and artificial intelligence, 2018, 31(1):23-36
[3] CHIANG K Y, DHILLON I S, HSIEH C J. Using side information to reliably learn low-rank matrices from missing and corrupted observations[J]. Journal of machine learning research, 2018, 19(76):1-35.
[4] LU Canyi, FENG Jiashi, LIN Zhouchen. Subspace clustering by block diagonal representation[J]. IEEE transactions on pattern analysis and machine intelligence, 2019, 41(2):487-501.
[5] ZHANG Zheng, XU Yong, SHAO Ling. Discriminative block-diagonal representation learning for image recognition[J]. IEEE transactions on neural networks and learning systems, 2018, 29(7):3111-3125.
[6] WEI C P, CHEN C F, WANG Y C F. Robust face recognition with structurally incoherent low-rank matrix decomposition[J]. IEEE transactions on image processing, 2014, 23(8):3294-3307.
[7] NI Yuzhao, SUN Ju, YUAN Xiaotong, et al. Robust low-rank subspace segmentation with semidefinite guarantees[C]//Proceedings of 2010 IEEE International Conference on Data Mining Workshops. Sydney, NSW, Australia, 2010:1179-1188.
[8] LEE K C, HO J, KRIEGMAN D J. Acquiring linear subspaces for face recognition under variable lighting[J]. IEEE transactions on pattern analysis and machine intelligence, 2005, 27(5):684-698.
[9] CANDèS E J, LI Xiaodong, MA Yi. Robust principal component analysis?[J]. Journal of the ACM, 2011, 58(3):11.
[10] LIU Guangcan, LIN Zhouchen, YAN Shuicheng. Robust recovery of subspace structures by low-rank representation[J]. IEEE transactions on pattern analysis and machine intelligence, 2013, 35(1):171-184.
[11] CHEN Yudong, JALALI A, SANGHAVI S, et al. Clustering partially observed graphs via convex optimization[J]. The journal of machine learning research, 2014, 15(1):2213-2238.
[12] LIN Zhouchen, CHEN Minming, MA Yi. The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices[J]. arXiv preprint arXiv:1009.5055, 2010.
[13] LU Canyi, FENG Jiashi, YAN Shuicheng. A unified alternating direction method of multipliers by majorization minimization[J]. IEEE transactions on pattern analysis and machine intelligence, 2018, 40(3):527-541.
[14] 刘松华, 张军英, 丁彩英. 核矩阵列相关低秩近似分解算法[J]. 模式识别与人工智能, 2011, 24(6):776-782 LIU Songhua, ZHAGN Junying, DING Caiying. Low-Rank approximation and decomposition for kernel matrix based on column correlation[J]. Pattern recognition and artificial intelligence, 2011, 24(6):776-782
[15] YIN Ming, GAO Junbin, LIN Zhouchen. Laplacian regularized low-rank representation and its applications[J]. IEEE transactions on pattern analysis and machine intelligence, 2016, 38(3):504-517.
[16] HE Xiaofei, CAI Deng, SHAO Yuanlong, et al. Laplacian regularized Gaussian mixture model for data clustering[J]. IEEE transactions on knowledge and data engineering, 2011, 23(9):1406-1418.
[17] NASEEM I, TOGNERI R, BENNAMOUN M. Linear regression for face recognition[J]. IEEE transactions on pattern analysis and machine intelligence, 2010, 32(11):2106-2112.
[18] 丁立中, 廖士中. KMA-α:一个支持向量机核矩阵的近似计算算法[J]. 计算机研究与发展, 2012, 49(4):746-753 DING Lizhong, LIAO Shizhong. KMA-α:a kernel matrix approximation algorithm for support vector machines[J]. Journal of computer research and development, 2012, 49(4):746-753
[19] TIAN Shangxuan, LU Shijian, SU Bolan. Scene text recognition using co-occurrence of histogram of oriented gradients[C]//Proceedings of the 12th International Conference on Document Analysis and Recognition. Washington, DC, USA, 2013:912-916.
[20] PHAN T Q, SHIVAKUMARA P, TIAN S X. Recognizing text with perspective distortion in natural scenes[C]//Proceedings of 2013 IEEE International Conference on Computer Vision. Sydney, NSW, Australia, 2013:569-576.
[21] TAN Zhirong, TIAN Shangxuan, TAN C L. Using pyramid of histogram of oriented gradients on natural scene text recognition[C]//Proceedings of 2014 IEEE International Conference on Image Processing. Paris, France, 2014:2629-2633.
[22] LEE C Y, BHARDWAJ A, DI Wei, et al. Region-based discriminative feature pooling for scene text recognition[C]//Proceedings of 2014 IEEE Conference on Computer Vision and Pattern Recognition. Columbus, OH, USA, 2014:4050-4057.

备注/Memo

备注/Memo:
收稿日期:2019-04-24。
基金项目:国家自然科学基金项目(61572419,61773331,61703360);山东省高等学校科技计划(J17KA091).
作者简介:王中元,男,1996年生,硕士研究生,主要研究方向为核方法与矩阵分解;刘惊雷,男,1970年生,教授,博士,主要研究方向为人工智能和理论计算机科学。主持国家自然科学基金面上项目、山东省自然科学基金面上项目各1项。发表学术论文40余篇。
通讯作者:刘惊雷.E-mail:jinglei_liu@sina.com
更新日期/Last Update: 2019-12-25