Robust Low Rank Minimization

Low-rank minimization (approximation or representation) is a minimization problem, in which the cost function measures the fit between a given data matrix A and an approximating matrix L, subject to a constraint that the approximating matrix L has reduced rank.

1 - Detecting Contiguous Outlier via Low-Rank Representation

• Contiguous Outliers Detection (DECOLOR) (2 papers)

• Contiguous Outliers Representation via Online Low-Rank Approximation (COROLA) (1 paper)

• Contiguous Outlier Detection via Contextual Regularization (CODCR) (2 papers)

• Contiguous Outliers in the Low-Rank Representation (DECELOR) (1 paper)

2 - Robust Matrix Factorization

• Direct Robust Matrix Factorization (DRMF)  (1 paper)

3 - Probabilistic Robust Matrix Factorization

• Probabilistic Robust Matrix Factorization (PRMF) (1 paper)

4 - Bayesian Robust Matrix Factorization

• Bayesian Robust Matrix Factorization (BRMF) (1 paper)

• Variational Bayesian Method (VM) (1 paper)

• Kernelized Bayesian Method (RKBMF) (1 paper)

5 - Robust Matrix Factorization with noises

• Practical Low-Rank Matrix Factorization (PLRMF) (1 paper)

• Low Rank Matrix Factorization with MoG noise (LRMF-MoG) (4 papers)

• Low-rank Matrix Factorization under General Mixture Noise Distributions (LRM) (2 papers)

• Low Rank Matrix Factorization with Mixture of Asymmetric Laplace Distributions (AQ-LRMF) (2 papers)

• Low-Rank Matrix Factorization with Generalized Diversity Difference (1 paper)

6 - Holistic Robust Matrix Factorization

• Unifying Nuclear Norm and Bilinear Factorization (UNN-BF) (1 paper)

• Elastic-Net Regularization (1 paper)

7 - Robust Rank Matrix Factorization

• Robust Rank Factorization (RRF) (1 paper)

8 - Robust Orthogonal Matrix Factorization

• Robust Orthogonal Matrix Factorization (1 paper)

9. Low-Rank Matrix Recovery

• Low-Rank Matrix Revovery (4 papers)

10 - Weighted Low-Rank Matrix Approximation

• Weighted Low-Rank Matrix Approximation (6 papers)

11 - Majorization Minimization

• Majorization-Minimization (2 papers)

12 - Online Matrix Factorization

• Online Matrix Factorization (3 papers)

13 - Non-convex Low Rank Representation (2 papers)

Y. Chen, Y. Wang, M. Li, G. He, "Augmented Lagrangian Alternating Direction Method for Low-Rank Minimization via Non-Convex Approximation",  Signal, Image and Video Processing, SIViP 2017, 2017.

J. Zhao, "A Novel Low-Rank Matrix Approximation Algorithm for Face Denoising and Background/Foreground Separation", Computational and Applied Mathematics, 2022.

14 - Multi-scale Low Rank Approximation (1 paper)

M. Abdolali, M. Rahmati,"Multi Scale Decomposition in Low Rank Approximation", IEEE Signal Processing Letters, 2017.

15 - UTV Decompositions (1 paper)

M. Kaloorazi, R. de Lamare, "Compressed Randomized UTV Decompositions for Low-Rank Matrix Approximations", IEEE Journal of Selected Topics in Signal Processing, December 2018.

16 - Rank-1 Approximation (1 paper)

F. Bossmann, J. Ma, “Enhanced image approximation using shifted rank-1 reconstruction”, preprint, October 2018.

17 - Inliers Selection (1 paper)

Z. Hu, F. Nie, X. Li, "Robust Low Rank Approximation via Inliers Selection”, IEEE International Conference on Image Processing, ICIP 2018, pages 3688-3692, Athens, Greece, 2018.

18 - Iterative Reconstrained Representation (1 paper)

J. Zheng, C. Lu, H. Yu, W. Wang, “Iterative Reconstrained Low-Rank Representation via Weighted Nonconvex Regularizer”, IEEE Access, Volume 6, pages 51693- 51707, October 2018.

19 -  Robust Structured Low-Rank Approximation (2 papers)

C. Hage, M. Kleinsteuber, "Robust Structured Low-Rank Approximation on the Grassmannian", International Conference on Latent Variable Analysis and Signal Separation, LVA  2015, pages 295-303, 2015.

C. Hage, "Robust Structured and Unstructured Low-Rank Approximation on the Grassmannian", PhD Thesis, TUM, Germany, 2016.

20 - Provable Algorithms (1 paper)

Y. Li, "Provable Algorithms for Scalable and Robust Low-Rank Matrix Recovery", PHD Thesis, Ohio State University, USA, 2018.

21  - Polynomial-time Approximation Scheme (1 paper)

F. Ban., V. Bhattiprolu, K. Bringmann, P. Kolev, E. Lee, D. Woodru.k, "A PTAS for lp-Low Rank Approximation", SIAM, pages 747-766, 2019.

22 - Compressive Sensing (3 papers)

X. Shu, N. Ahuja, “Imaging via Three-dimensional Compressive Sampling (3DCS)”, International Conference on Computer Vision, ICCV 2011, 2011.

B. Kang, W. Zhu, J. Yan, “Object detection oriented video reconstruction using compressed sensing”, EURASIP Journal on Advances in Signal Processing Sample, February 2015.

B. Kang, W. Zhu, “Robust moving object detection using compressed sensing”, IET Image Processing, 2015.

23 - Dictionary Low-Rank Representation

J. Zhou, X. Shen, S. Liu, L. Wang, Q. Zhu, P. Qia, "Multi-dictionary induced low-rank representation with multi-manifold regularization", Applied Intelligence, Volume 53, Pages 3576-3593, 2023.

24 - Accelerated Solvers (1 paper)

H. Zhang, B. Wen, Z. Zha, B. Zhang, Y. Tang, G. Yu, W. Du, "Accelerated PALM for Nonconvex Low-rank Matrix Recovery with Theoretical Analysis”, IEEE Transactions on Circuits and Systems for Video Technology, 2023.

25 - Learning based Recovery (1 paper)

Z. Xu, Y. Zhang, C. Ma, Y. Yan, Z. Peng, S. Xie, “LERE: Learning-Based Low-Rank Matrix Recovery with Rank Estimation”, AAAI Conference on Artificial Intelligence, pages 16228-16236, 2024.

26 - Triple Component Matrix Factorization (1 paper)

N. Shi, S. Fattahi, R. Kontar, “Triple Component Matrix Factorization: Untangling Global, Local, and Noisy Components”, Preprint, March 2024.

Author: Thierry BOUWMANS, Associate Professor, Lab. MIA, Univ.  Rochelle, France.

Fair Use Policy

As this website gives many information that come from my research, please cite my following survey papers:

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.

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]

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