Joint Graph Rewiring and Feature Denoising via Spectral Resonance
This addresses the problem of noisy graph data for graph neural network users, offering a novel joint approach that is incremental over prior rewiring methods.
The paper tackles the problem of noisy graph structure and node features in graph learning by proposing JDR, an algorithm that jointly denoises features and rewires graphs through spectral alignment. The method consistently outperforms existing rewiring methods on various synthetic and real-world node classification tasks.
When learning from graph data, the graph and the node features both give noisy information about the node labels. In this paper we propose an algorithm to jointly denoise the features and rewire the graph (JDR), which improves the performance of downstream node classification graph neural nets (GNNs). JDR works by aligning the leading spectral spaces of graph and feature matrices. It approximately solves the associated non-convex optimization problem in a way that handles graphs with multiple classes and different levels of homophily or heterophily. We theoretically justify JDR in a stylized setting and show that it consistently outperforms existing rewiring methods on a wide range of synthetic and real-world node classification tasks.