这篇论文在RTRMC基础上加入图正则化，处理行列关联强的数据时补全更准，做推荐系统或图像修复的值得一看。
论文提出GR-RTRMC方法，将图正则化融入已有RTRMC（黎曼信赖域矩阵补全）框架。RTRMC利用低秩约束的几何结构，将问题重构为单个Grassmann流形上的无约束优化。GR-RTRMC通过捕获矩阵行和列之间的内在关系（图结构），在数据具有强行列相关性时提升补全精度和鲁棒性。实验验证了该方法在合成与真实数据集上的性能改进。
Graph-Regularized Low-Rank Matrix Completion by Variable Projection
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.