README.md

GCNH: A Simple Method For Representation Learning On Heterophilous Graphs

This repository contains the implementation of Graph Convolutional Network for Heterophily, the model described in our work GCNH: A Simple Method For Representation Learning On Heterophilous Graphs, accepted at IJCNN 2023 (preprint).

Description

GCNH extends Graph Neural Networks' representation capabilities on heterophilous graphs by learning two different functions to encode center node and neighborhood messages. These two encodings are merged into the final node embedding using a convex combination with a learned coefficient β. The layer propagation rule in GCNH works as follows:

$$h^l_u = (1-\beta)\bigoplus_{v \in \mathcal{N_u}}\left[ \sigma(h^{\ell-1}_v W_2) \right] + \beta\sigma(h^{\ell-1}_u W_1).$$

For a center node, GCNH flexibly assigns more or less importance to the neighborhood, depending on how informative neighbors are - this design greatly improves learning on heterophilous graphs. Experiments show that GCNH achieves state-of-the-art performance on 4 out of the 8 graph datasets used.

Usage

Requirements

• Python=3.9
• requirements.txt (pip install -r requirements.txt)
• torch-scatter (e.g., pip install torch_scatter -f https://data.pyg.org/whl/torch-2.0.0+{device}.html)

The folder GCNH/experiments contains the commands to reproduce the results of the main table of the paper and to test GCNH on the synthetic dataset used in the paper.

Contributors

• Andrea Cavallo
• Claas Grohnfeldt
• Michele Russo
• Giulio Lovisotto

Citation

If you find this code useful, please cite

@inproceedings{cavallo2023gcnh,
  title={{GCNH:} A Simple Method for Representation Learning on Heterophilous Graphs},
  author={Cavallo, Andrea and Grohnfeldt, Claas and Russo, Michele and Lovisotto, Giulio and Vassio, Luca},
  booktitle={2023 International Joint Conference on Neural Networks (IJCNN)},
  year={2022},
  organization={IEEE}
}