mlsanityData to 7 Oct 2026

Low-rank tensor completion: a Riemannian manifold preconditioning approach

arXiv 1605.08257 ↗First posted 26 May 2016cs.LG cs.NA math.NAcited by 19

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Abstract (arXiv)

We propose a novel Riemannian manifold preconditioning approach for the tensor completion problem with rank constraint. A novel Riemannian metric or inner product is proposed that exploits the least-squares structure of the cost function and takes into account the structured symmetry that exists in Tucker decomposition. The specific metric allows to use the versatile framework of Riemannian optimization on quotient manifolds to develop preconditioned nonlinear conjugate gradient and stochastic gradient descent algorithms for batch and online setups, respectively. Concrete matrix representations of various optimization-related ingredients are listed. Numerical comparisons suggest that our proposed algorithms robustly outperform state-of-the-art algorithms across different synthetic and real-world datasets.

Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 May 2016.

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Citing papers per year: 2021: 7; 2022: 4; 2023: 4; 2024: 1; 2025: 3.

19 papers.

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  1. 2021Scaling and Scalability: Provable Nonconvex Low-Rank Tensor Estimation from Incomplete Measurementscited by 28
  2. 2022Tensor-on-Tensor Regression: Riemannian Optimization, Over-parameterization, Statistical-computational Gap, and Their Interplaycited by 15
  3. 2021Low-rank Tensor Estimation via Riemannian Gauss-Newton: Statistical Optimality and Second-Order Convergencecited by 13
  4. 2022Subquadratic Kronecker Regression with Applications to Tensor Decompositioncited by 6
  5. 2023Provably Accelerating Ill-Conditioned Low-rank Estimation via Scaled Gradient Descent, Even with Overparameterizationcited by 6
  6. 2021Fast Low-Rank Tensor Decomposition by Ridge Leverage Score Samplingcited by 5
  7. 2021New Riemannian preconditioned algorithms for tensor completion via polyadic decompositioncited by 4
  8. 2021Patch Tracking-based Streaming Tensor Ring Completion for Visual Data Recoverycited by 2
  9. 2025Faster Convergence of Riemannian Stochastic Gradient Descent with Increasing Batch Sizecited by 2
  10. 2022Low-rank Tensor Learning with Nonconvex Overlapped Nuclear Norm Regularizationcited by 1
  11. 2022Partial Least Square Regression via Three-factor SVD-type Manifold Optimization for EEG Decodingcited by 1
  12. 2023Nonnegative Low-Rank Tensor Completion via Dual Formulation with Applications to Image and Video Completioncited by 1
7 more
  1. 2024Streamlining in the Riemannian Realm: Efficient Riemannian Optimization with Loopless Variance Reductioncited by 1
  2. 2021Riemannian Manifold Optimization for Discriminant Subspace Learningcited by 0
  3. 2021Tensor Full Feature Measure and Its Nonconvex Relaxation Applications to Tensor Recoverycited by 0
  4. 2023Structured Low-Rank Tensor Learningcited by 0
  5. 2023Tensor Completion Leveraging Graph Information: A Dynamic Regularization Approach with Statistical Guaranteescited by 0
  6. 2025Higher Order Reduced Rank Regressioncited by 0
  7. 2025An Interdisciplinary and Cross-Task Review on Missing Data Imputationcited by 0