通过变量投影进行图正则化低秩矩阵填充
Graph-Regularized Low-Rank Matrix Completion by Variable Projection
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中文总结 AI 辅助
研究低秩矩阵填充问题，核心方法是将图正则化纳入RTRMC框架得到GR-RTRMC，利用矩阵行列内在关系，主要贡献是提高矩阵填充在行列强相关场景下的准确性与鲁棒性。
中文摘要 AI 辅助
我们通过将图正则化纳入现有的黎曼信任区域矩阵填充（RTRMC）框架来解决低秩矩阵填充问题。RTRMC利用低秩约束的几何结构将问题重塑为单个格拉斯曼流形上的无约束优化问题。我们的方法，即图正则化RTRMC（GR-RTRMC），利用矩阵行与列之间的内在关系，旨在提高矩阵填充的准确性和鲁棒性，特别是在基础数据在行或列之间表现出强相关性的场景中。
英文摘要
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.
发表机构
- Royal Meteorological Institute of Belgium（比利时皇家气象研究所）
机构由 AI 辅助整理，请以论文原文为准。
