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Outlier-Robust Matrix Completion via lp-Minimization

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Citation Author(s):
Wen-Jun Zeng, Hing Cheung So
Submitted by:
Hing Cheung So
Last updated:
2 March 2018 - 1:57am
Document Type:
Presentation Slides



Matrix completion refers to the recovery of a low‐rank matrix from only a subset of its possibly noisy entries, and has a variety of important applications such as collaborative filtering, image inpainting and restoration, system identification, node localization and genotype imputation. It is because many real-world signals can be approximated by a matrix whose rank is much smaller than the row and column numbers. Most techniques for matrix completion in the literature assume Gaussian noise and thus they are not robust to outliers. In this presentation, we introduce two algorithms for robust matrix completion based on low‐rank matrix factorization and lp‐norm minimization of the residual with 0<p<2. The first method tackles the low‐rank matrix factorization with missing data by iteratively solving multiple linear lp‐regression problems, while the second applies the alternating direction method of multipliers in the lp‐space. This presentation is a companion work of: W.-J. Zeng and H.C. So, “Outlier-robust matrix completion via lp-minimization,” IEEE Transactions on Signal Processing, vol.66, no.5, pp.1125-1140, March 2018 (DOI: 10.1109/TSP.2017.2784361)

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