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Geometric Imbalance in Semi-Supervised Node Classification
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Introduces "geometric imbalance" on the hypersphere for semi-supervised imbalanced node classification and proposes UNREAL, a self-training framework with dual-path pseudo-labeling, RBO-based node reordering, and discarding ambiguous nodes.
Problem
Semi-supervised imbalanced node classification suffers from unreliable pseudo-labels for minority-class nodes because message passing creates geometric ambiguity in the normalized embedding space.
Approach
Defines geometric imbalance as the ambiguity of unlabeled node embeddings relative to class centers on the unit hypersphere (vMF view), and mitigates it via a dual-path pseudo-labeler (k-means cluster and classifier agreement), rank fusion of geometric and confidence rankings with RBO, and filtering nodes with a low GI index.
Key results
- On Cora with GCN at rho=10, the method reaches 78.33 bAcc and 76.44 F1, versus 72.19 bAcc and 72.67 F1 for the best baseline BIM.
- On Computers-Random with GAT, the method reaches 82.52 bAcc versus 77.01 for BIM (+5.51).
- On Ogbn-arxiv with GCN, the method reaches 51.21 bAcc versus 50.34 for the best baseline, a small gain.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use UNREAL instead of the strongest listed baseline | GCN · Cora (ρ=10) | balanced accuracy: +6.14 | Helped |
| Use UNREAL instead of the strongest listed baseline | GCN · CiteSeer (ρ=10) | F1: +8.13 | Helped |
| Use UNREAL instead of the strongest listed baseline | GCN · PubMed (ρ=10) | F1: +0.72 | Helped |
| Use UNREAL instead of the strongest listed baseline | GraphSAGE · Cora (ρ=100) | F1: +3.62 | Helped |
| Use UNREAL instead of the strongest listed baseline | GraphSAGE · CiteSeer (ρ=100) | F1: +5.63 | Helped |
| Use UNREAL instead of the strongest listed baseline | GraphSAGE · PubMed (ρ=100) | F1: +0.79 | Helped |
| Use UNREAL instead of the strongest listed baseline | GCN · Computers-Random | F1: +2.47 | Helped |
| Use UNREAL instead of the strongest listed baseline | GCN · CS-Random | F1: + 0.65 | Helped |
| Use UNREAL instead of the strongest listed baseline | GCN · Flickr | F1: +4.79 | Helped |
| Use UNREAL instead of the strongest listed baseline | GCN · Ogbn-arxiv | F1: +0.92 | Helped |
| Add confidence rankings (CR) (ablation) | UNREAL · Cora (ρ=10, GCN) | F1: 73.93±0.95 -> 75.85±0.82 | Helped |
| Add DGIS filtering (ablation) | UNREAL · Cora (ρ=10, GCN) | F1: 72.74±0.63 -> 76.44±1.06 | Helped |
Surprising findings
- On the large-scale Flickr and Ogbn-arxiv settings, several baselines (GraphSMOTE, ReNode, GraphENS) run out of memory, and the absolute bAcc values are low (around 25-51%).
Limitations
- The theoretical results (proportionality claims) rest on approximations and assumptions, such as fixed class centers and a loose entropy bound in the proof.
- The GI index used in practice is a simplified surrogate of the formal geometric imbalance score.
- Gains on some settings are small or negative (e.g., GAT on Flickr at rho about 10.8 and SAGE on Computers-Random), and results are reported over only 5 repetitions.
Experimental setup
Datasets: Cora CiteSeer PubMed Amazon-Computers Computers-Random CS-Random Flickr Ogbn-arxiv
Benchmarks: Cora CiteSeer PubMed Amazon-Computers Computers-Random CS-Random Flickr Ogbn-arxiv
Metrics: balanced accuracy Macro-F1
Baselines: GraphSMOTE GraphENS ReNode TAM GraphSR BIM Re-Weighting PC Softmax Balanced Softmax
Builds on: self-training GraphENS BIM TAM
Closest papers by meaning
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- IGL-Bench: Establishing the Comprehensive Benchmark for Imbalanced Graph Learning (ICLR 2025 · similarity 0.85)
- Equivariance Everywhere All At Once: A Recipe for Graph Foundation Models (NeurIPS 2025 · similarity 0.85)
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- DisRFM: Polar Riemannian Flow Matching for Structure-Preserving Graph Domain Adaptation (NeurIPS 2026 · similarity 0.85)
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