Graph-Regularized Low-Rank Matrix Completion by Variable Projection

2026-07-10

AI Summary

This work addresses the limited accuracy and robustness of low-rank matrix completion in scenarios where rows or columns exhibit high correlation. To overcome this challenge, the authors introduce graph regularization into the Riemannian Trust-Region Matrix Completion (RTRMC) framework for the first time. By formulating an unconstrained optimization model on the Grassmann manifold and leveraging variable projection techniques, the proposed method effectively incorporates structural priors derived from row and column relationships. This integration significantly enhances completion performance, particularly on highly correlated data, demonstrating both theoretical novelty and practical utility.

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.

Problem

• low-rank matrix completion
• graph regularization
• matrix correlations
• accuracy
• robustness

Innovation

• Graph regularization
• Low-rank matrix completion
• Riemannian optimization
• Grassmann manifold
• Variable projection