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Enhancing the Influence of Labels on Unlabeled Nodes in Graph Convolutional Networks
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Proposes ELU-GCN, a two-step framework that learns a label-utilizing (ELU) graph via a closed-form, label-propagation-consistent objective and then applies a contrastive loss between the ELU graph and original graph to improve GCN node classification.
Problem
GCN message passing propagates label information to unlabeled neighbors, but this propagated label information does not always help predictions; existing structure learning methods do not ensure labels effectively benefit unlabeled nodes.
Approach
Defines "effective label utilization" as agreement between GCN predictions and label-propagation (LPA) outputs, learns a parameter-free ELU graph S in closed form (with Woodbury identity for efficiency), and uses a contrastive loss to align consistent information and separate mutually exclusive information between the ELU graph and the original graph.
Key results
- ELU-GCN reaches 84.29% on Cora, 74.23% on Citeseer and 80.51% on Pubmed, the best among compared methods in the main table.
- On heterophilic Chameleon and Squirrel, ELU-GCN achieves 70.90% and 56.91%, versus 60.82% and 43.43% for GCN.
- Ablation: adding the ELU graph improves GCN on average by about 2.9%, and the contrastive loss adds about 1.3% on average.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add the ELU graph (ablation) | GCN · Cora | accuracy: 81.61 $\pm$0.42 -> 83.49 $\pm$0.55 | Helped |
| add the ELU graph (ablation) | GCN · Citeseer | accuracy: 70.35 $\pm$0.45 -> 72.02 $\pm$0.36 | Helped |
| add the ELU graph (ablation) | GCN · Pubmed | accuracy: 79.01 $\pm$0.62 -> 80.25 $\pm$0.79 | Helped |
| add the ELU graph (ablation) | GCN · Computers | accuracy: 81.62 $\pm$2.43 -> 82.56 $\pm$1.23 | Helped |
| add the ELU graph (ablation) | GCN · Photo | accuracy: 90.44 $\pm$1.23 -> 90.52 $\pm$1.33 | No clear effect |
| add the ELU graph (ablation) | GCN · Chameleon | accuracy: 60.82 $\pm$2.24 -> 65.12 $\pm$1.43 | Helped |
| add the ELU graph (ablation) | GCN · Squirrel | accuracy: 43.43 $\pm$2.18 -> 54.12 $\pm$1.32 | Helped |
| add contrastive loss (ablation) | GCN + ELU graph · Cora | accuracy: 83.49 $\pm$0.55 -> 84.29 $\pm$0.39 | Helped |
| add contrastive loss (ablation) | GCN + ELU graph · Citeseer | accuracy: 72.02 $\pm$0.36 -> 74.23 $\pm$0.62 | Helped |
| add contrastive loss (ablation) | GCN + ELU graph · Pubmed | accuracy: 80.25 $\pm$0.79 -> 80.51 $\pm$0.21 | Helped |
| add contrastive loss (ablation) | GCN + ELU graph · Computers | accuracy: 82.56 $\pm$1.23 -> 83.73 $\pm$2.31 | Helped |
| add contrastive loss (ablation) | GCN + ELU graph · Photo | accuracy: 90.52 $\pm$1.33 -> 90.81 $\pm$1.33 | No clear effect |
Limitations
- Final ELU graph is dense O(n^2) and requires sparsification by threshold for efficiency.
- Theoretical guarantees rely on approximations (LPA as proxy for true labels and pre-trained MLP predictions as proxy for ground truth).
Experimental setup
Datasets: Cora Citeseer Pubmed Computers Photo Chameleon Squirrel Caltech UF Hamilton Tulane
Benchmarks: Cora Citeseer Pubmed Computers Photo Chameleon Squirrel
Metrics: classification accuracy
Baselines: GCN GAT APPNP GPRGNN PCNet GCN-LPA NeuralSparse-GCN PTDNet-GCN CoGSL NodeFormer GSR BAGCN
Builds on: GCN GCN-LPA Pro-GNN PTDNet SimP-GCN
Closest papers by meaning
- On Which Nodes Does GCN Fail? Enhancing GCN From the Node Perspective (ICML 2024 · similarity 0.89)
- L2-GCN: Layer-Wise and Learned Efficient Training of Graph Convolutional Networks (CVPR 2020 · similarity 0.89)
- L2DGCN: Learnable Enhancement and Label Selection Dynamic Graph Convolutional Networks for Mitigating Degree Bias (NeurIPS 2025 · similarity 0.89)
- Deeper Insights Into Graph Convolutional Networks for Semi-Supervised Learning (AAAI 2018 · similarity 0.89)
- Semi-Supervised Learning With Graph Learning-Convolutional Networks (CVPR 2019 · similarity 0.88)
- GLDL: Graph Label Distribution Learning (AAAI 2024 · similarity 0.87)
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