Two Newton methods on the manifold of fixed-rank matrices endowed with Riemannian quotient geometries

DOI10.1007/s00180-013-0441-6zbMath1306.65015arXiv1209.0068OpenAlexW2078248112WikidataQ115389083 ScholiaQ115389083MaRDI QIDQ2259739

Luca Amodei, Gilles Meyer, Pierre-Antoine Absil

Publication date: 5 March 2015

Published in: Computational Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.0068

zbMATH Keywords

geodesicsRiemannian submersionLevi-Civita connectionRiemannian connectionRiemannian exponential mapfixed-rank manifold

Mathematics Subject Classification ID

Computational methods for problems pertaining to statistics (62-08) Numerical mathematical programming methods (65K05)

Related Items (12)

A quadratically convergent algorithm for structured low-rank approximation ⋮ Optimization on flag manifolds ⋮ Kantorovich's theorem on Newton's method under majorant condition in Riemannian manifolds ⋮ On the superlinear convergence of Newton's method on Riemannian manifolds ⋮ Damped Newton's method on Riemannian manifolds ⋮ Dynamically Orthogonal Runge–Kutta Schemes with Perturbative Retractions for the Dynamical Low-Rank Approximation ⋮ Transformed Schatten-1 penalty based full-rank latent label learning for incomplete multi-label classification ⋮ Low-rank retractions: a survey and new results ⋮ Sparse matrices in data analysis ⋮ Fixed-rank matrix factorizations and Riemannian low-rank optimization ⋮ Riemannian Preconditioning ⋮ Low-rank matrix completion via preconditioned optimization on the Grassmann manifold

Uses Software

• Manopt
• RTRMC

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Manifolds, tensor analysis, and applications.
• Critical points of matrix least squares distance functions
• Optimization and dynamical systems
• Fixed-rank matrix factorizations and Riemannian low-rank optimization
• Grassmann algorithms for low rank approximation of matrices with missing values
• Trust-region methods on Riemannian manifolds
• The fundamental equations of a submersion
• Low-Rank Matrix Completion by Riemannian Optimization
• Newton's method on Riemannian manifolds and a geometric model for the human spine
• The Geometry of Algorithms with Orthogonality Constraints
• Optimization Techniques on Riemannian Manifolds
• Subspace Evolution and Transfer (SET) for Low-Rank Matrix Completion
• A Geometric Approach to Low-Rank Matrix Completion
• Low-Rank Optimization with Trace Norm Penalty

This page was built for publication: Two Newton methods on the manifold of fixed-rank matrices endowed with Riemannian quotient geometries