R3MC: A Riemannian three-factor algorithm for low-rank matrix completion
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Abstract (arXiv)
We exploit the versatile framework of Riemannian optimization on quotient manifolds to develop R3MC, a nonlinear conjugate-gradient method for low-rank matrix completion. The underlying search space of fixed-rank matrices is endowed with a novel Riemannian metric that is tailored to the least-squares cost. Numerical comparisons suggest that R3MC robustly outperforms state-of-the-art algorithms across different problem instances, especially those that combine scarcely sampled and ill-conditioned data.
Key facts. Cited by 11 papers in the map (data through 14 Oct 2026). First posted on arXiv 11 Jun 2013.
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Citing papers per year: 2021: 4; 2022: 1; 2023: 1; 2024: 2; 2025: 1; 2026: 2.
11 papers.
- 2025StelLA: Subspace Learning in Low-rank Adaptation using Stiefel Manifoldcited by 14
- 2021A Scalable Second Order Method for Ill-Conditioned Matrix Completion from Few Samplescited by 13
- 2021GNMR: A provable one-line algorithm for low rank matrix recoverycited by 10
- 2022Accelerated Riemannian Optimization: Handling Constraints with a Prox to Bound Geometric Penaltiescited by 4
- 2024Riemannian Federated Learning via Averaging Gradient Streamscited by 4
- 2023Get the Best of Both Worlds: Improving Accuracy and Transferability by Grassmann Class Representationcited by 3
- 2021Faster Randomized Methods for Orthogonality Constrained Problemscited by 2
- 2024Streamlining in the Riemannian Realm: Efficient Riemannian Optimization with Loopless Variance Reductioncited by 2
- 2021Accurate and fast matrix factorization for low-rank learningcited by 1
- 2026Riemannian Optimization for Hadamard Products of Low-Rank Matricescited by 0
- 2026Retraction-Based Gradient Projection Algorithms on Manifoldscited by 0
- 2026Retraction-Based Gradient Projection Algorithms on Manifolds25 Sep 2026
- 2026Riemannian Optimization for Hadamard Products of Low-Rank Matrices31 May 2026
- 2025StelLA: Subspace Learning in Low-rank Adaptation using Stiefel Manifold2 Oct 2025
- 2024Riemannian Federated Learning via Averaging Gradient Streams11 Sep 2024
- 2024Streamlining in the Riemannian Realm: Efficient Riemannian Optimization with Loopless Variance Reduction11 Mar 2024
- 2023Get the Best of Both Worlds: Improving Accuracy and Transferability by Grassmann Class Representation3 Aug 2023
- 2022Accelerated Riemannian Optimization: Handling Constraints with a Prox to Bound Geometric Penalties26 Nov 2022
- 2021GNMR: A provable one-line algorithm for low rank matrix recovery24 Jun 2021
- 2021Faster Randomized Methods for Orthogonality Constrained Problems22 Jun 2021
- 2021A Scalable Second Order Method for Ill-Conditioned Matrix Completion from Few Samples3 Jun 2021
- 2021Accurate and fast matrix factorization for low-rank learning21 Apr 2021