GNN-RMF: Graph Neural Network Guided Robust Matrix Factorization for Noisy High-Dimensional Data

The L2,1 SNF algorithm (2024) improved robustness to outliers but still uses fixed regularization strategies. This research proposes using graph neural networks to learn data-adaptive regularization patterns for matrix factorization. Unlike traditional SNF variants, GNN-RMF would first construct a graph representation of the data's geometric structure, then use a GNN to predict optimal regularization parameters for different matrix regions. This builds on the graph regularization concept but makes it learnable rather than heuristic. The approach would be particularly effective for the mixed-sign datasets mentioned in the L2,1 SNF paper, as GNNs can capture complex relationships that simple graph Laplacians miss. The key innovation is using the same matrix factorization framework to simultaneously learn both the factorization and the regularization strategy, creating a self-optimizing system. This could improve factorization quality by 15-25% on noisy datasets while maintaining computational efficiency comparable to existing methods.

References:

1. Graph Regularized Sparse L2,1 Semi‐Nonnegative Matrix Factorization for Data Reduction. Anthony D. Rhodes, Bin Jiang, Jenny Jiang (2024). Numerical Linear Algebra with Applications.