The nature of heterophilous graphs is significantly different with that of
homophilous graphs, which suggests aggregations beyond 1-hop neighborhood and
causes difficulties in early graph neural network models. 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 deisgn
a graph framelet neural network model PEGFAN using 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 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.

本文提出了 Haar-type graph framelets 及其相关的神经网络模型 PEGFAN，适用于在异质图上进行多尺度特征提取与深度学习任务，并通过实验验证其在大多数异质图数据集上表现良好。