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Structural Entropy Based Graph Structure Learning for Node Classification
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Proposes a structural-entropy-based graph structure learning framework that builds encoding trees for basic views, enhances views with kNN similarity graphs, and fuses them by community influence and prediction confidence for node classification.
Problem
Graph structure learning for node classification typically fuses simple structural features and ignores hierarchical community semantics, making it fragile on noisy real-world graphs.
Approach
Uses K-dimensional structural entropy minimization to build encoding trees that capture hierarchical communities, enhances each basic view with a kNN similarity graph selected by 1D structural entropy, and fuses views using community influence plus prediction confidence, trained with a min-max mutual-information objective and hierarchical contrastive loss.
Key results
- Achieves F1-micro of 61.3 on Texas, 58.6 on Wisconsin and 74.1 on Citeseer, outperforming the second-best PROSE across the eight datasets.
- On Texas and MS Academic under random edge deletion and addition attacks, the method stays above GAT, gCooL and PROSE baselines.
- Fusion ablation shows the community-influence plus confidence fusion beats average, attention and confidence-only fusion (e.g., 74.1 vs 73.4 average on Citeseer).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use structural-entropy encoding trees and community-influence fusion | SE-GSL · Texas | F1-micro (%): 58.4±2.1 -> 61.3±3.0 | Helped |
| use structural-entropy encoding trees and community-influence fusion | SE-GSL · Wisconsin | F1-micro (%): 58.2±1.9 -> 58.6±1.2 | Helped |
| use structural-entropy encoding trees and community-influence fusion | SE-GSL · Cancer | F1-micro (%): 95.4±0.4 -> 95.8±0.5 | Helped |
| use structural-entropy encoding trees and community-influence fusion | SE-GSL · Digits | F1-micro (%): 92.8±0.5 -> 93.7±0.3 | Helped |
| use structural-entropy encoding trees and community-influence fusion | SE-GSL · Polblogs | F1-micro (%): 95.5±0.4 -> 95.9±0.1 | Helped |
| use structural-entropy encoding trees and community-influence fusion | SE-GSL · Citeseer | F1-micro (%): 73.3±0.1 -> 74.1±0.6 | Helped |
| use structural-entropy encoding trees and community-influence fusion | SE-GSL · Wiki-CS | F1-micro (%): 75.0±0.7 -> 75.6±0.3 | Helped |
| use structural-entropy encoding trees and community-influence fusion | SE-GSL · MS Academic | F1-micro (%): 91.8±0.2 -> 92.7±0.1 | Helped |
| replace community-influence plus confidence fusion with average fusion (ablation) | SE-GSL · Cancer, Polblogs, Citeseer, Wiki-CS | F1-micro (%): 95.8 -> 95.0; 95.9 -> 95.6; 74.1 -> 73.4; 75.6 -> 74.9 | Hurt |
| replace community-influence plus confidence fusion with attention fusion (ablation) | SE-GSL · Cancer, Polblogs, Citeseer, Wiki-CS | F1-micro (%): 95.8 -> 95.2; 95.9 -> 95.3; 74.1 -> 71.8; 75.6 -> 70.7 | Hurt |
| replace community-influence plus confidence fusion with confidence-only fusion (ablation) | SE-GSL · Cancer, Polblogs, Citeseer, Wiki-CS | F1-micro (%): 95.8 -> 95.3; 95.9 -> 94.7; 74.1 -> 73.3; 75.6 -> 75.2 | Hurt |
| use encoding-tree community extraction instead of kNN or Louvain (ablation) | SE-GSL · Cancer, Digits, Citeseer, Wiki-CS | F1-micro (%) | Helped |
Surprising findings
- SE-GSL performs much worse on Wiki-CS (53.2) and Digits (82.7), which the authors attribute to needing large labeled training data.
Limitations
- Constructing high-level encoding trees is time-consuming, so K is fixed at 3 by default.
- Building an optimal encoding tree is intractable, so a greedy approximation is used.
Experimental setup
Datasets: Polblogs Texas Wisconsin Citeseer Wiki-CS MS Academic Breast Cancer Digits
Benchmarks: Polblogs Texas Wisconsin Citeseer Wiki-CS MS Academic Cancer Digits
Metrics: F1-micro
Baselines: GCN GAT GATv2 GraphSAGE DGI gCooL MGEDE IDGL Pro-GNN GEN CoGSL SE-GSL
Builds on: CoGSL GIB structural entropy InfoNCE GCN
Closest papers by meaning
- USER: Unsupervised Structural Entropy-Based Robust Graph Neural Network (AAAI 2023 · similarity 0.89)
- OpenGSL: A Comprehensive Benchmark for Graph Structure Learning (NeurIPS 2023 · similarity 0.89)
- Learning Graph Representation via Graph Entropy Maximization (ICML 2024 · similarity 0.89)
- Structural Information Enhanced Graph Representation for Link Prediction (AAAI 2024 · similarity 0.89)
- On the Interplay between Graph Structure and Learning Algorithms in Graph Neural Networks (ICML 2025 · similarity 0.87)
- LSEnet: Lorentz Structural Entropy Neural Network for Deep Graph Clustering (ICML 2024 · similarity 0.87)
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