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Robust Low-Rank Matrix Completion by Riemannian Optimization

  • Title: Robust Low-Rank Matrix Completion by Riemannian Optimization
  • Authors: Léopold Cambier, P.-A. Absil
  • Abstract: Low-rank matrix completion is the problem where one tries to recover a low-rank matrix from noisy observations of a subset of its entries. In this paper, we propose RMC, a new method to deal with the problem of robust low-rank matrix completion, i.e., matrix completion where a fraction of the observed entries are corrupted by non-Gaussian noise, typically outliers. The method relies on the idea of smoothing the l1 norm and using Riemannian optimization to deal with the low-rank constraint. We first state the algorithms as the successive minimization of smooth approximations of the l1 norm and we analyze its convergence by showing the strict decrease of the objective function. We then perform numerical experiments on synthetic data and demonstrate the effectiveness on the proposed method on the Netflix dataset.
  • Key words: Low-Rank Matrix Completion; Riemannian optimization; outliers; smoothing techniques; l1 norm; non-smooth; fixed-rank manifold
  • Status: Published in Siam Journal of Scientific Computing, Volume 38, Issue 5, pp. A2611-S799, Special Section on Two Themes: CSE Software and Big Data in CSE. Link
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