Low-rank matrix completion via preconditioned optimization on the Grassmann manifold

DOI10.1016/j.laa.2015.02.027zbMath1312.90092OpenAlexW2126407450MaRDI QIDQ2347362

Nicolas Boumal, Pierre-Antoine Absil

Publication date: 27 May 2015

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2015.02.027

zbMATH Keywords

Grassmann manifoldlow-rank matrix completionsecond-order methodsoptimization on manifoldsfixed-rank geometrypreconditioned Riemannian conjugate gradientspreconditioned Riemannian trust-regionsRCGMCRTRMC

Mathematics Subject Classification ID

Applications of mathematical programming (90C90) Methods of local Riemannian geometry (53B21) Matrix completion problems (15A83)

Related Items

Non intrusive method for parametric model order reduction using a bi-calibrated interpolation on the Grassmann manifold, Continuation Methods for Riemannian Optimization, GNMR: A Provable One-Line Algorithm for Low Rank Matrix Recovery, Sparsifying the resolvent forcing mode via gradient-based optimisation, A Grassmann manifold handbook: basic geometry and computational aspects, Riemannian Natural Gradient Methods, Generalized left-localized Cayley parametrization for optimization with orthogonality constraints, Geometric Subspace Updates with Applications to Online Adaptive Nonlinear Model Reduction, A Riemannian BFGS Method Without Differentiated Retraction for Nonconvex Optimization Problems, Cayley-transform-based gradient and conjugate gradient algorithms on Grassmann manifolds, Fixed-rank matrix factorizations and Riemannian low-rank optimization, Dimension Reduction via Gaussian Ridge Functions, Majorized proximal alternating imputation for regularized rank constrained matrix completion, RTRMC, Robust Low-Rank Matrix Completion by Riemannian Optimization, A Riemannian rank-adaptive method for low-rank matrix completion, A Riemannian gossip approach to subspace learning on Grassmann manifold, Rank $2r$ Iterative Least Squares: Efficient Recovery of Ill-Conditioned Low Rank Matrices from Few Entries, Nonlinear matrix recovery using optimization on the Grassmann manifold

Uses Software

• Manopt
• Jellyfish
• ADMiRA

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm
• Two Newton methods on the manifold of fixed-rank matrices endowed with Riemannian quotient geometries
• Matrix estimation by universal singular value thresholding
• Trust-region methods on Riemannian manifolds
• Parallel stochastic gradient algorithms for large-scale matrix completion
• Zur Riemannschen Geometrie in Grassmannschen Mannigfaltigkeiten
• Exact matrix completion via convex optimization
• Low-Rank Matrix Completion by Riemannian Optimization
• Manopt, a Matlab toolbox for optimization on manifolds
• Recovering Low-Rank and Sparse Components of Matrices from Incomplete and Noisy Observations
• A Singular Value Thresholding Algorithm for Matrix Completion
• Rank-Sparsity Incoherence for Matrix Decomposition
• Low-Rank Matrix Approximation with Weights or Missing Data Is NP-Hard
• Global Convergence Properties of Conjugate Gradient Methods for Optimization
• Numerical Optimization
• Trust Region Methods
• Subspace Evolution and Transfer (SET) for Low-Rank Matrix Completion
• A new, globally convergent Riemannian conjugate gradient method
• A Geometric Approach to Low-Rank Matrix Completion
• ADMiRA: Atomic Decomposition for Minimum Rank Approximation
• Low-Rank Optimization with Trace Norm Penalty