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GPEN: Global Position Encoding Network for Enhanced Subgraph Representation Learning
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Proposes GPEN, which encodes each node's global position via a maximum-spanning-tree depth one-hot encoding and adds a boundary-aware convolution using difference vectors, for subgraph representation learning.
Problem
Subgraph representation learning relies on local neighborhoods and misses global structural information from multi-hop distant nodes, while naive aggregation of global information can dilute subgraph-specific structure.
Approach
Builds a tree from the graph using PageRank-derived edge weights and root selection, one-hot encodes each node's tree depth as a global position feature, and applies a boundary-aware convolution that mixes vanilla message passing with neighbor difference vectors via a balance factor b; optional tree perturbation generates extra subgraph samples from largest tree components.
Key results
- On em-user, GPEN reaches 0.912 micro-F1 vs 0.890 for S2N and 0.888 for GLASS (average of 10 runs).
- On ppi-bp, GPEN achieves 0.644 micro-F1, slightly above S2N (0.643) and SSNP (0.636).
- On synthetic cut-ratio, GPEN reaches 0.936 vs 0.892 for S2N; GPEN is best on three of four synthetic datasets.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use GPEN instead of the strongest reported baseline | Subgraph representation learning · ppi-bp | micro-F1: 0.643 ± 0.041 -> 0.644 ± 0.009 | Helped |
| Use GPEN instead of the strongest reported baseline | Subgraph representation learning · hpo-metab | micro-F1: 0.639 ± 0.072 -> 0.639 ± 0.009 | No clear effect |
| Use GPEN instead of the strongest reported baseline | Subgraph representation learning · hpo-neuro | micro-F1: 0.686 ± 0.019 -> 0.691 ± 0.006 | Helped |
| Use GPEN instead of the strongest reported baseline | Subgraph representation learning · em-user | micro-F1: 0.888 ± 0.019 -> 0.912 ± 0.013 | Helped |
| Use GPEN instead of the strongest reported baseline | Subgraph representation learning · density | micro-F1: 0.963 ± 0.057 -> 0.956 ± 0.016 | Hurt |
| Use GPEN instead of the strongest reported baseline | Subgraph representation learning · cut-ratio | micro-F1: 0.935 ± 0.019 -> 0.936 ± 0.016 | Helped |
| Use GPEN instead of the strongest reported baseline | Subgraph representation learning · coreness | micro-F1: 0.840 ± 0.028 -> 0.876 ± 0.019 | Helped |
| Use GPEN instead of the strongest reported baseline | Subgraph representation learning · component | micro-F1: 1.000 ± 0.000 -> 1.000 ± 0.000 | No clear effect |
| Add Optional Tree Perturbation (OTP) (ablation) | GPEN · ppi-bp | micro-F1: 0.633 ± 0.019 -> 0.644 ± 0.009 | Helped |
| Add Optional Tree Perturbation (OTP) (ablation) | GPEN · em-user | micro-F1: 0.898 ± 0.032 -> 0.912 ± 0.013 | Helped |
| Add Boundary-aware Convolution (BWC) (ablation) | GPEN · ppi-bp | micro-F1: 0.590 ± 0.016 -> 0.644 ± 0.009 | Helped |
| Add Boundary-aware Convolution (BWC) (ablation) | GPEN · em-user | micro-F1: 0.796 ± 0.050 -> 0.912 ± 0.013 | Helped |
Surprising findings
- Individual modules alone may not improve performance and can even worsen results on em-user; gains appear only when modules are combined.
- Batch size: smaller batches generally performed better, with degradation at larger batch sizes.
Limitations
- Gains on several real-world datasets (e.g., ppi-bp, hpo-metab) over S2N/GLASS are small relative to standard deviations.
- Optional tree perturbation benefits depend on a size threshold c and the tree construction choice; sensitivity varies across datasets.
Experimental setup
Datasets: ppi-bp hpo-metab hpo-neuro em-user density cut-ratio coreness component
Benchmarks: ppi-bp hpo-metab hpo-neuro em-user density cut-ratio coreness component
Metrics: micro-F1
Baselines: MLP GBDT Sub2Vec GNN-seg SubGNN GLASS SSNP S2N
Builds on: SubGNN GLASS PageRank
Closest papers by meaning
- Translating Subgraphs to Nodes Makes Simple GNNs Strong and Efficient for Subgraph Representation Learning (ICML 2024 · similarity 0.91)
- Subgraphormer: Unifying Subgraph GNNs and Graph Transformers via Graph Products (ICML 2024 · similarity 0.89)
- Graph Positional and Structural Encoder (ICML 2024 · similarity 0.89)
- A Flexible, Equivariant Framework for Subgraph GNNs via Graph Products and Graph Coarsening (NeurIPS 2024 · similarity 0.87)
- Positional Encoding meets Persistent Homology on Graphs (ICML 2025 · similarity 0.87)
- Union Subgraph Neural Networks (AAAI 2024 · similarity 0.87)
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