# Graph-Regularized Low-Rank Matrix Completion by Variable Projection

arXiv: https://arxiv.org/abs/2607.09546 · HTML: https://mlsanity.com/paper/2607.09546/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 32 references that are in the map.
- First posted on arXiv 10 Jul 2026.

## Builds on (most cited first, 5 of 5)

- [Manopt, a Matlab toolbox for optimization on manifolds](https://mlsanity.com/paper/1308.5200/) (2013)
- [Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiation](https://mlsanity.com/paper/1603.03236/) (2016)
- [Matrix Completion on Graphs](https://mlsanity.com/paper/1408.1717/) (2014)
- [Matrix Completion with Hierarchical Graph Side Information](https://mlsanity.com/paper/2201.01728/) (2022)
- [Graph-Based Matrix Completion Applied to Weather Data](https://mlsanity.com/paper/2306.08627/) (2023)

## Abstract (arXiv)

We address the low-rank matrix completion problem by incorporating graph regularization into the existing Riemannian Trust-Region Matrix Completion (RTRMC) framework. The latter uses the geometry of the low-rank constraint to remodel the problem as an unconstrained optimization problem on a single Grassmann manifold. Our approach, named Graph-Regularized RTRMC (GR-RTRMC), exploits the inherent relationships between rows and columns of the matrix. By using these relationships, we aim to improve the accuracy and robustness of matrix completion, particularly in scenarios where the underlying data exhibits strong correlations between rows or columns.