基于潜在特征空间的低秩表示算法
Low-Rank Representation Algorithm Based on Latent Feature Space
DOI: 10.12677/CSA.2021.114117, PDF,   
作者: 周翊航：广东工业大学计算机学院，广东 广州
关键词: 潜在特征；正交字典；低秩表示；Latent Features； Orthogonal Dictionary； Low-Rank Representation
摘要: 现有的大多低秩表示算法都是直接使用原始数据矩阵作为特征字典，然而原始数据中的冗余特征和噪声信息很可能会导致算法效果不佳。针对这种情况，本文提出一种基于潜在特征空间的低秩表示算法，通过正交字典来学习原始数据的潜在表示，然后利用潜在表示作为字典进行低秩表示学习，从而避免原始数据中的不利影响。
Abstract: Most of the existing low-rank representation algorithms directly use the original data matrix as the feature dictionary, but the redundant features and noise information in the original data may cause the algorithm to perform poorly. In response to this situation, a low-rank representation algorithm based on the latent feature space is proposed. The latent representation of the original data is learned through an orthogonal dictionary, and then the latent representation is used as a dictionary for low-rank representation learning, so as to avoid the adverse effects of the original data.
文章引用：周翊航. 基于潜在特征空间的低秩表示算法[J]. 计算机科学与应用, 2021, 11(4): 1140-1148. https://doi.org/10.12677/CSA.2021.114117

参考文献

[1] Liu, G., Lin, Z., Yan, S., Sun, J., Yu, Y. and Ma, Y. (2013) Robust Recovery of Subspace Structures by Low-Rank Representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35, 171-184. [Google Scholar] [CrossRef] 
[2] Lin, Z., Chen, M. and Ma, Y. (2010) The Augmented Lagrange Mul-tiplier Method for Exact Recovery of Corrupted Low-Rank Matrices. Mathematical Programming, 9, arXiv:1009.5055.
[3] Wahba, G. (1965) A Least Squares Estimate of Satellite Attitude. Siam Review, 7, 409-409. [Google Scholar] [CrossRef] 
[4] Cai, J.F., Candès, E.J. and Shen, Z.W. (2010) A Singular Value Threshold-ing Algorithm for Matrix Completion. SIAM Journal on Optimization, 20, 1956-1982. [Google Scholar] [CrossRef] 
[5] Georghiades, A.S., Belhumeur, P.N. and Kriegman, D.J. (2001) From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23, 643-660. [Google Scholar] [CrossRef] 
[6] Sim, T., Baker, S. and Bsat, M. (2003) The CMU Pose, Illumination, and Expression Database. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25, 1615-1618. [Google Scholar] [CrossRef] 
[7] Martínez, A. and Benavente, R. (1998) The AR Face Database. Technical Report. Computer Vision Center, Number 24, Bellatera. http://www.cat.uab.cat/Public/Publications/1998/MaB1998
[8] Nene, S.A., Nayar, S.K. and Murase, H. (1996) Co-lumbia Object Image Library (Coil-20). Technical Report CUCS-005-96, February 1996.
[9] He, X., Cai, D. and Han, J. (2005) Document Clustering Using Locality Preserving Indexing. IEEE Transactions on Knowledge and Data Engi-neering, 17, 1624-1637. [Google Scholar] [CrossRef] 
[10] Wessel, W. (1988) Lovász, L.; Plummer, M. D., Matching Theory. Budapest, Akadémiai Kiadó 1986. XXXIII, 544 S., Ft 680,—. ISBN 9630541688. Journal of Ap-plied Mathematics and Mechanics, 68, 146-146. https://onlinelibrary.wiley.com/ [Google Scholar] [CrossRef]