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Robust Matrix Completion

Abstract : This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank matrix, which we wish to recover, with a second matrix having a complementary sparse structure such as element-wise or column-wise sparsity. We analyze a class of estimators obtained by solving a constrained convex optimization problem that combines the nuclear norm and a convex relaxation for a sparse constraint. Our results are obtained for the simultaneous presence of random and deterministic patterns in the sampling scheme. We provide guarantees for recovery of low-rank and sparse components from partial and corrupted observations in the presence of noise and show that the obtained rates of convergence are minimax optimal.
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https://hal.archives-ouvertes.fr/hal-01098492
Contributor : Olga Klopp <>
Submitted on : Friday, July 1, 2016 - 10:35:23 PM
Last modification on : Thursday, March 5, 2020 - 5:52:26 PM

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  • HAL Id : hal-01098492, version 2
  • ARXIV : 1412.8132

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Olga Klopp, Karim Lounici, Alexandre B. Tsybakov. Robust Matrix Completion. Probability Theory and Related Fields, Springer Verlag, 2017, 169 (1 - 2), pp.523 - 564. ⟨hal-01098492v2⟩

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