Joint Graph Rewiring and Feature Denoising via Spectral Resonance

Graph neural networks (GNNs) take as input the graph structure and the feature vectors associated with the nodes. Both contain noisy information about the labels. Here we propose joint denoising and rewiring (JDR)--an algorithm to jointly denoise the graph structure and features, which can improve the performance of any downstream algorithm. We do this by defining and maximizing the alignment between the leading eigenspaces of graph and feature matrices. To approximately solve this computationally hard problem, we propose a heuristic that efficiently handles real-world graph datasets with many classes and different levels of homophily or heterophily. We experimentally verify the effectiveness of our approach on synthetic data and real-world graph datasets. The results show that JDR consistently outperforms existing rewiring methods on node classification tasks using GNNs as downstream models.