Guarantees of Riemannian optimization for low rank matrix completion

DOI10.3934/ipi.2020011zbMath1439.65059arXiv1603.06610OpenAlexW3004863648MaRDI QIDQ2176515

Tony F. Chan, Shingyu Leung, Ke Wei, Jian-Feng Cai

Publication date: 5 May 2020

Published in: Inverse Problems and Imaging (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.06610

zbMATH Keywords

matrix completiongradient descent methodsRiemannian optimizationtangent spacelow-rank matrix manifold

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Matrix completion problems (15A83) Numerical methods for low-rank matrix approximation; matrix compression (65F55)

Related Items

Fully-connected tensor network decomposition for robust tensor completion problem, Fast gradient method for low-rank matrix estimation, Matrix completion with sparse measurement errors, Nonnegative Low Rank Matrix Completion by Riemannian Optimalization Methods, A Three-Operator Splitting Algorithm for Nonconvex Sparsity Regularization, Riemannian conjugate gradient descent method for fixed multi rank third-order tensor completion

Uses Software

• LMaFit
• RTRMC
• ADMiRA
• PhaseLift
• Wirtinger Flow

Cites Work

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• Convergence of fixed-point continuation algorithms for matrix rank minimization
• Low rank matrix completion by alternating steepest descent methods
• Convex multi-task feature learning
• A geometric analysis of phase retrieval
• Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm
• Matrix recipes for hard thresholding methods
• Fixed-rank matrix factorizations and Riemannian low-rank optimization
• The local convexity of solving systems of quadratic equations
• Exact matrix completion via convex optimization
• Guarantees of Riemannian Optimization for Low Rank Matrix Recovery
• Low-Rank Matrix Completion by Riemannian Optimization
• Normalized Iterative Hard Thresholding for Matrix Completion
• Incoherence-Optimal Matrix Completion
• Phase Retrieval via Wirtinger Flow: Theory and Algorithms
• Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systems
• Blind Deconvolution Using Convex Programming
• A Singular Value Thresholding Algorithm for Matrix Completion
• Solving systems of phaseless equations via Kaczmarz methods: a proof of concept study
• The complexity of matrix completion
• Interior-Point Method for Nuclear Norm Approximation with Application to System Identification
• Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
• Strong converse for identification via quantum channels
• CGIHT: conjugate gradient iterative hard thresholding for compressed sensing and matrix completion
• Semidefinite Programming
• Tight Oracle Inequalities for Low-Rank Matrix Recovery From a Minimal Number of Noisy Random Measurements
• Recovering Low-Rank Matrices From Few Coefficients in Any Basis
• ADMiRA: Atomic Decomposition for Minimum Rank Approximation
• Matrix Completion From a Few Entries
• The Power of Convex Relaxation: Near-Optimal Matrix Completion
• Blind Deconvolution Meets Blind Demixing: Algorithms and Performance Bounds
• A Simpler Approach to Matrix Completion
• Low-rank matrix completion using alternating minimization
• Phase Retrieval via Matrix Completion