Graph-Regularized Low-Rank Matrix Completion by Variable Projection
2026-07-10 • Machine Learning
Machine Learning
AI summaryⓘ
The authors improve a method for filling in missing numbers in a big table by adding clues about how the rows and columns are connected. They build on an existing technique that treats the problem like moving on a curved surface shaped by the table’s low-rank structure. Their new method, called Graph-Regularized RTRMC, uses these connections to guess missing values more accurately, especially when rows or columns are closely related. This helps make the completed table more reliable.
low-rank matrix completionRiemannian Trust-RegionGrassmann manifoldgraph regularizationunconstrained optimizationmatrix correlationsmatrix factorizationmanifold optimization
Authors
Benoît Loucheur, P. -A. Absil, Michel Journée
Abstract
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.