Low-rank tensor completion by Riemannian optimization

DOI10.1007/s10543-013-0455-zzbMath1300.65040arXiv1508.02988OpenAlexW2081962379WikidataQ115384194 ScholiaQ115384194MaRDI QIDQ398628

Michael Steinlechner, Daniel Kressner, Bart Vandereycken

Publication date: 15 August 2014

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.02988

zbMATH Keywords

algorithmnumerical resultsreconstructionnonlinear conjugate gradient methodlow-rank approximationhigh-dimensionalityRiemannian optimizationTucker decompositiontensor completion problem

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Nonlinear programming (90C30) Vector and tensor algebra, theory of invariants (15A72) Matrix completion problems (15A83)

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Uses Software

• TensorToolbox

Cites Work

• Unnamed Item
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• Tensor Decompositions and Applications
• The geometry of algorithms using hierarchical tensors
• Learning with tensors: a framework based on convex optimization and spectral regularization
• Fixed-rank matrix factorizations and Riemannian low-rank optimization
• Low rank tensor recovery via iterative hard thresholding
• Smoothness and Periodicity of Some Matrix Decompositions
• Low-Rank Matrix Completion by Riemannian Optimization
• A literature survey of low-rank tensor approximation techniques
• Projection-like Retractions on Matrix Manifolds
• Dynamical Tensor Approximation
• Tensor completion and low-n-rank tensor recovery via convex optimization
• Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs
• A Multilinear Singular Value Decomposition
• The Power of Convex Relaxation: Near-Optimal Matrix Completion

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