Surveys

1. Fundamentals

1.1 Robust PCA

N. Vaswani, P. Narayanamurthy, "Static and Dynamic Robust PCA via Low-Rank + Sparse Matrix Decomposition: A Review", Proceedings of IEEE, July 2018.

N. Vaswani, T. Bouwmans, S. Javed, P. Narayanamurthy, “Robust Principal Component Analysis, Subspace Learning, and Tracking”, IEEE Signal Processing Magazine, July 2018. [pdf]

1.2 Robust Matrix Completion

Y. Chi, "Low-Rank Matrix Completion", IEEE Signal Processing Magazine, Volume 35, No. 5, pages 178-181, September 2018.

L. Nguyen, J. Kim, B. Shim, "Low-Rank Matrix Completion: A Contemporary Survey", IEEE Access, Volume 7, pages 94215-94237, 2019.

H. Zhang, J. Yang, J. Qian, C. Gong, X. Ning, Z. Zha, B. Wen, "Faster nonconvex low-rank matrix learning for image low-level and high-level vision: A unified framework", Information Fusion, March 2024.

1.3 Robust Subspace Recovery

G. Lerman, T. Maunu, “An Overview of Robust Subspace Recovery”, Preprint, March 2018.

1.4 Low-Rank Matrix

N. Kumar, J. Shneider, "Literature survey on low rank approximation of matrices", Preprint, 2016.

Y. Chen, Y. Chi, "Harnessing Structures in Big Data via Guaranteed Low-Rank Matrix Estimation", IEEE Signal Processing Magazine, July 2018.

Y. Chi, Y. Lu, Y. Chen ‘Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview”, Preprint, September 2018.

M. Balcan, Y. Li, D. Woodruff, H. Zhang, “Testing Matrix Rank, Optimally”, Preprint, October 2018.

V. Charisopoulos, Y. Chen, D. Davis, M. Daz L. Ding, D. Drusvyatskiy, “Low-rank matrix recovery with composite optimization: good conditioning and rapid convergence”, Preprint, April 2019.

Z. Hu, F. Nie, R. Wang , X. Li, “ Low Rank Regularization: A review”, Neural Networks, 2020.

2. Solvers

J. Kim, Y. He, H. Park, "Algorithms for nonnegative matrix and tensor factorizations: A unified view based on block coordinate descent framework", Journal of Global Optimization, Volume 58, No. 2, pages 285-319, 2014.

X. Feng, X. He, "Robust low-rank data matrix approximations", Science China Mathematics, December 2016.

C. Lu, J. Feng, Z. Lin, S. Ya, "A Unified Alternating Direction Method of Multipliers by Majorization Minimization", IEEE Transactions on Pattern Analysis and Machine Intelligence, 2017.

S. Ma, N. Aybat, "Efficient Optimization Algorithms for Robust Principal Component Analysis and Its Variants", Proceedings of IEEE, July 2018.

3. Regularization Strategies

Y. Tian, Y. Zhang, "A comprehensive survey on regularization strategies in machine learning",  Information Fusion, 2021.

4. Applications

4.1 Application to background/Foreground Separation

T. Bouwmans, E. Zahzah, “Robust PCA via Principal Component Pursuit: A Review for a Comparative Evaluation in Video Surveillance”, Special Issue on Background Models Challenge, Computer Vision and Image Understanding, CVIU 2014, Volume 122, pages 22–34, May 2014. [pdf]

T. Bouwmans, A. Sobral, S. Javed, S. Jung, E. Zahzah, "Decomposition into Low-rank plus Additive Matrices for Background/Foreground Separation: A Review for a Comparative Evaluation with a Large-Scale Dataset", Computer Science Review, Volume 23, pages 1-71, February 2017. [pdf]

C. Xie, Y. Yan, H. Wang, L. Lin, R. Wang, “A Survey of Background Modeling Based on Robust Subspace Learning via Sparse and Low-rank Matrix Decomposition”, ICIMCS 2016, 2016.

4.2 Application to Image Analysis

X. Zhou, C. Yang, H. Zhao, W. Yu,  "Low-rank modeling and its applications in image  analysis", Preprint, 2014.

Z. Hu, F. Nie, L.Tian, X. Li, “A Comprehensive Survey for Low Rank Regularization”, Preprint, 2018.

4.3 Application to Data Analysis

Z. Lin, “A Review on Low-Rank Models in Data Analysis”, Preprint, 2016 .

4.4. Application to Industrial Process

J. Zhu, Z. Ge, Z. Song, F. Gao, "Review and big data perspectives on robust data mining approaches for industrial process modeling with outliers and missing data", Annual Reviews in Control, 2018.