Permutation Equivariant Graph Framelets for Heterophilous Graph Learning

TL;DR

This paper introduces permutation equivariant graph framelets and a neural network model PEGFAN for improved learning on heterophilous graphs, demonstrating superior performance on several benchmark datasets.

Contribution

The paper develops Haar-type graph framelets with permutation equivariance and sparsity, and designs the PEGFAN model for heterophilous graph learning, advancing multi-scale graph analysis.

Findings

Achieves state-of-the-art results on heterophilous graph datasets.

Demonstrates effectiveness of permutation equivariant framelets.

Shows competitive performance on various benchmark datasets.

Abstract

The nature of heterophilous graphs is significantly different from that of homophilous graphs, which causes difficulties in early graph neural network models and suggests aggregations beyond the 1-hop neighborhood. In this paper, we develop a new way to implement multi-scale extraction via constructing Haar-type graph framelets with desired properties of permutation equivariance, efficiency, and sparsity, for deep learning tasks on graphs. We further design a graph framelet neural network model PEGFAN (Permutation Equivariant Graph Framelet Augmented Network) based on our constructed graph framelets. The experiments are conducted on a synthetic dataset and 9 benchmark datasets to compare performance with other state-of-the-art models. The result shows that our model can achieve the best performance on certain datasets of heterophilous graphs (including the majority of heterophilous datasets with relatively larger sizes and denser connections) and competitive performance on the remaining.