Robust Low-Rank Matrix Completion by Riemannian Optimization

DOI10.1137/15M1025153zbMath1352.65149OpenAlexW2266965707WikidataQ115246968 ScholiaQ115246968MaRDI QIDQ2830625

Pierre-Antoine Absil, Leopold Cambier

Publication date: 28 October 2016

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1025153

zbMATH Keywords

outliersalgorithmconvergencenumerical experimentsmoothing techniquesnonsmoothlow-rank matrix completionRiemannian optimization\(\ell_1\) normfixed-rank manifold

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Linear programming (90C05) Matrix completion problems (15A83)

Related Items

A penalty method for rank minimization problems in symmetric matrices, A Riemannian optimization approach to the radial distribution network load flow problem, An efficient damped Newton-type algorithm with globalization strategy on Riemannian manifolds, Selecting Regularization Parameters for Nuclear Norm--Type Minimization Problems, Damped Newton's method on Riemannian manifolds, Completely positive factorization by a Riemannian smoothing method, Riemannian smoothing gradient type algorithms for nonsmooth optimization problem on compact Riemannian submanifold embedded in Euclidean space, A trust region method for solving multicriteria optimization problems on Riemannian manifolds, An image inpainting algorithm using exemplar matching and low-rank sparse prior, A brief introduction to manifold optimization, An efficient method for non-negative low-rank completion, Robust low-rank matrix estimation, Accurate and fast matrix factorization for low-rank learning., Simple algorithms for optimization on Riemannian manifolds with constraints, Guarantees of Riemannian Optimization for Low Rank Matrix Recovery, A gradient system for low rank matrix completion, Unnamed Item, A Gradient Sampling Method on Algebraic Varieties and Application to Nonsmooth Low-Rank Optimization

Uses Software

• Manopt
• RTRMC
• RASL

Cites Work

• Unnamed Item
• Exact low-rank matrix completion from sparsely corrupted entries via adaptive outlier pursuit
• Low-rank retractions: a survey and new results
• Robust matrix completion
• Theory of semidefinite programming for sensor network localization
• Compressed sensing and matrix completion with constant proportion of corruptions
• Low-rank matrix completion via preconditioned optimization on the Grassmann manifold
• Exact matrix completion via convex optimization
• Low-Rank Matrix Completion by Riemannian Optimization
• Manopt, a Matlab toolbox for optimization on manifolds
• Robust principal component analysis?
• A Riemannian geometry with complete geodesics for the set of positive semidefinite matrices of fixed rank