Permutation Equivariant Graph Framelets for Heterophilous Graph Learning.

Area of Science:

• Graph Neural Networks
• Deep Learning on Graphs
• Computational Graph Theory

Background:

• Heterophilous graphs present unique challenges for traditional graph neural network (GNN) models.
• Existing GNN architectures often struggle with aggregations beyond immediate neighbors in complex graph structures.
• The distinct nature of heterophilous graphs necessitates novel approaches for effective data representation and analysis.

Purpose of the Study:

• To develop a novel multiscale extraction technique for graph data.
• To construct Haar-type graph framelets with properties of permutation equivariance, efficiency, and sparsity.
• To design and evaluate a graph framelet neural network model for deep learning on graphs.

Main Methods:

• Construction of Haar-type graph framelets enabling multiscale feature extraction.
• Development of the permutation equivariant graph framelet augmented network (PEGFAN) model.
• Empirical evaluation on synthetic and nine benchmark heterophilous graph datasets.

Main Results:

• The PEGFAN model achieves state-of-the-art performance on specific heterophilous graph datasets.
• The model shows particular strength on larger and denser heterophilous graph structures.
• Competitive performance is observed across a range of heterophilous graph benchmarks.

Conclusions:

• The proposed graph framelet approach effectively addresses limitations of existing GNNs on heterophilous graphs.
• PEGFAN offers a powerful new tool for deep learning tasks involving complex graph data.
• This work advances the capabilities of GNNs in analyzing non-homophilous graph structures.