2024 • Conference Paper
Weather Data Imputation Using Graph-Based Low-Rank Matrix Completion with Variable Projection
Authors:
Loucheur, Benoît ,
Absil, Pierre-Antoine ,
Journée, Michel
Published in:
BNAIC/BeNeLearn 2024
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 matrix's inherent relationships between rows and columns. 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.