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Fast algorithms for recovering a corrupted low-rank matrix
Abstract
This paper studies algorithms for solving the problem of recovering a low-rank matrix with a fraction of its entries arbitrarily corrupted. This problem can be viewed as a robust version of classical PCA, and arises in a number of application domains, including image processing, web data ranking, and bioinformatic data analysis. It was recently shown that under surprisingly broad conditions, it can be exactly solved via a convex programming surrogate that combines nuclear norm minimization and ¿1-norm minimization. This paper develops and compares two complementary approaches for solving this convex program. The first is an accelerated proximal gradient algorithm directly applied to the primal; while the second is a gradient algorithm applied to the dual problem. Both are several orders of magnitude faster than the previous state-of-the-art algorithm for this problem, which was based on iterative thresholding. Simulations demonstrate the performance improvement that can be obtained via these two algorithms, and clarify their relative merits.
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Citations
Cites
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
Beck, A., & Teboulle, M. (2009) · SIAM Journal on Imaging Sciences · doi:10.1137/080716542 · Cited by 11,952
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RASL: Robust Alignment by Sparse and Low-Rank Decomposition for Linearly Correlated Images
Peng, Y., Ganesh, A., Wright, J., Xu, W., & Ma, Y. (2012) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2011.282 · Cited by 817
Self-citationRobust Photometric Stereo via Low-Rank Matrix Completion and Recovery
Wu, L., Ganesh, A., Shi, B., Matsushita, Y., Wang, Y., & Ma, Y. (2011) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-19318-7_55 · Cited by 298
Self-citationInformation retrieval, fusion, completion, and clustering for employee expertise estimation
Horesh, R., Varshney, K. R., & Yi, J. (2016) · 2016 IEEE International Conference on Big Data (Big Data) · doi:10.1109/bigdata.2016.7840746 · Cited by 14
Metadata
- Authors
- Ganesh, A., Lin, Z., Wright, J., Wu, L., Chen, M., & Ma, Y.
- Venue
- 2009 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)
- Publisher
- IEEE
- Published
- 2009-12
- Pages
- 213-216
- OpenAlex
- W1976632974
- Cited by
- 211
- References
- 1
- FWCI
- 22.61
- Type
- conference paper
- Language
- en
- Open access
- closed
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- Ganesh, A., Lin, Z., Wright, J., Wu, L., Chen, M., & Ma, Y. (2009). Fast algorithms for recovering a corrupted low-rank matrix. 2009 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP). https://doi.org/10.1109/camsap.2009.5413299
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