Effective Eigendecomposition based Graph Adaptation for Heterophilic Networks

TL;DR

This paper introduces EigenNetwork, an eigendecomposition-based method that adapts graph eigenvalues to significantly improve GNN performance on heterophilic graphs, outperforming existing methods.

Contribution

The paper proposes a novel eigendecomposition-based approach with learnable eigenvalue modulation and regularization, enhancing GNNs on heterophilic graphs.

Findings

Achieves up to 11% performance improvement over state-of-the-art methods.

Effectively modulates graph eigenvalues for better heterophilic graph adaptation.

Regularization via parameter sharing further boosts performance.

Abstract

Graph Neural Networks (GNNs) exhibit excellent performance when graphs have strong homophily property, i.e. connected nodes have the same labels. However, they perform poorly on heterophilic graphs. Several approaches address the issue of heterophily by proposing models that adapt the graph by optimizing task-specific loss function using labelled data. These adaptations are made either via attention or by attenuating or enhancing various low-frequency/high-frequency signals, as needed for the task at hand. More recent approaches adapt the eigenvalues of the graph. One important interpretation of this adaptation is that these models select/weigh the eigenvectors of the graph. Based on this interpretation, we present an eigendecomposition based approach and propose EigenNetwork models that improve the performance of GNNs on heterophilic graphs. Performance improvement is achieved by learning flexible graph adaptation functions that modulate the eigenvalues of the graph. Regularization of these functions via parameter sharing helps to improve the performance even more. Our approach achieves up to 11% improvement in performance over the state-of-the-art methods on heterophilic graphs.