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Integrating Co-Training with Edge Discrimination to Enhance Graph Neural Networks Under Heterophily
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Proposes EG-GCN, a co-training GNN that uses an edge discriminator to split each node's neighborhood into homophilic and heterophilic groups, aggregates each group with separate graph convolutions, and expands the edge training set with confident pseudo-labeled nodes.
Problem
Standard GNNs assume homophily and use uniform message passing, which performs poorly on heterophilic graphs where neighbors often have different classes; identifying and separately handling homophilic and heterophilic neighbors is hard with limited labels.
Approach
Jointly train an edge discriminator (MLP over features and random-walk structural encodings) that classifies edges as homophilic or heterophilic, and a group graph convolution with separate weight matrices for each neighbor group; high-confidence pseudo-labeled nodes expand the edge training set so both components reinforce each other.
Key results
- On heterophilic datasets (Texas, Wisconsin, Actor), EG-GCN averages 2.51% higher accuracy and 5.53% higher Macro-F1 than the second-best model; on Wisconsin it beats the best baseline by 4.31% accuracy.
- On three homophilic citation datasets, EG-GCN averages 0.80% higher accuracy and 1.02% higher Macro-F1 than the best baseline.
- On Penn94 EG-GCN reaches 84.86% accuracy, the best reported, and on Genius 90.80% accuracy, the highest reported.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use EG-GCN instead of the strongest baseline | Node classification · Cora | Accuracy: 87.81±0.73 -> 88.07±1.16 | Helped |
| Use EG-GCN instead of the strongest baseline | Node classification · Citeseer | Accuracy: 76.22±1.33 -> 78.09±1.20 | Helped |
| Use EG-GCN instead of the strongest baseline | Node classification · PubMed | Accuracy: 89.37±0.35 -> 89.64±0.38 | Helped |
| Use EG-GCN instead of the strongest baseline | Node classification · Texas | Accuracy: 86.76±4.90 -> 88.92±3.30 | Helped |
| Use EG-GCN instead of the strongest baseline | Node classification · Wisconsin | Macro-F1: 67.18±10.79 -> 78.49±10.07 | Helped |
| Use EG-GCN instead of the strongest baseline | Node classification · Actor | Accuracy: 37.02±0.87 -> 37.80±0.64 | Helped |
| Use EG-GCN instead of the strongest baseline | Node classification · Penn94 | Accuracy: 84.78±0.32 -> 84.86±0.33 | Helped |
| Use EG-GCN instead of the strongest baseline | Node classification · Genius | Macro-F1: 79.63±0.52 -> 79.49±0.88 | Hurt |
| Vary the confidence threshold τ from 0.7 to 1 (ablation) | EG-GCN · Citeseer | Accuracy | Mixed |
| Vary the confidence threshold τ from 0.7 to 1 (ablation) | EG-GCN · Wisconsin | Accuracy | Mixed |
| Increase the total number of iterations T from 2 to 6 (ablation) | EG-GCN · Citeseer | Accuracy | Helped |
| Increase the total number of iterations T from 2 to 6 (ablation) | EG-GCN · Wisconsin | Accuracy | Helped |
Surprising findings
- EG-GCN also improves on homophilic graphs, although it was designed for heterophily.
Limitations
- Hyperparameters tuned with Optuna over 200 trials, and baselines used default settings, so comparison fairness depends on tuning.
- Improvements on some heterophilic datasets (e.g., Actor, Genius Macro-F1) are small or within standard deviation.
Experimental setup
Datasets: Cora Citeseer PubMed Texas Wisconsin Actor Penn94 Genius
Benchmarks: Cora Citeseer PubMed Texas Wisconsin Actor Penn94 Genius
Metrics: Accuracy Macro-F1
Baselines: MLP GCN GAT H2GCN BM-GCN GREET LSGNN UniFilter PCNet
Builds on: GCN focal loss Geom-GCN H2GCN
Closest papers by meaning
- Finding Global Homophily in Graph Neural Networks When Meeting Heterophily (ICML 2022 · similarity 0.93)
- On the Impact of Feature Heterophily on Link Prediction with Graph Neural Networks (NeurIPS 2024 · similarity 0.90)
- Understanding Heterophily for Graph Neural Networks (ICML 2024 · similarity 0.90)
- Making Classic GNNs Strong Baselines Across Varying Homophily: A Smoothness–Generalization Perspective (NeurIPS 2025 · similarity 0.90)
- Graph Neural Networks Are More Than Filters: Revisiting and Benchmarking from A Spectral Perspective (ICLR 2025 · similarity 0.89)
- NLGT: Neighborhood-based and Label-enhanced Graph Transformer Framework for Node Classification (AAAI 2025 · similarity 0.89)
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