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DUPLEX: Dual GAT for Complex Embedding of Directed Graphs
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Proposes DUPLEX, a self-supervised inductive digraph embedding method that encodes each node as a complex embedding via a dual GAT encoder (amplitude and phase) and reconstructs the Hermitian adjacency matrix with two parameter-free decoders.
Problem
Directed graph embedding methods handle low in/out-degree nodes poorly, lack inductive ability for new nodes, and are tied to specific tasks.
Approach
Represent each node by a single complex embedding whose conjugate parts serve as source and target roles, encoded by separate undirected (amplitude) and direction-aware (phase) spatial GAT aggregators, and trained to reconstruct the Hermitian adjacency matrix via parameter-free direction- and connection-aware decoders.
Key results
- On link prediction existence prediction, DUPLEX reaches 98.6% AUC on Citeseer vs 98.0% for DUPLEX* and 91.4% for SigMaNet (best in 7 of 8 AUC cases per authors).
- On inductive node classification on Citeseer, DUPLEX achieves 71.7 macro F1 vs 70.8 for the next best (GAT).
- On transductive node classification on Citeseer, DUPLEX achieves 53.0 macro F1, exceeding baselines by at least 4.0 points.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add fusion layer (DUPLEX vs DUPLEX*) (ablation) | DUPLEX · link prediction and node classification (Cora-ml, Citeseer, Cora, Epinions) | ACC/AUC/F1: e.g., Cora-ml transductive macro F1 76.0 to 77.9 | Helped |
| replace phase and amplitude aggregators with undirected aggregator only (DUPLEX-am) (ablation) | DUPLEX dual encoder · Citeseer link prediction | TP ACC (%): 94.8 to 73.4 TP ACC | Hurt |
| use directed aggregator for both amplitude and phase (DUPLEX-ph) (ablation) | DUPLEX dual encoder · Citeseer and Cora link prediction | ACC: Citeseer TP 94.8 to 82.9; Cora TP 92.2 to 88.3 | Hurt |
| use GAT backbone instead of GCN backbone (ablation) | DUPLEX · Citeseer transductive node classification | mac. F1: 51.2 (GCN) to 53.0 (GAT) | Helped |
| dual encoder with separate amplitude and phase encoders vs single encoder (dual vs undirected-only in amplitude) | DUPLEX · Cora-ml inductive node classification | mac. F1 | No clear effect |
| add DUPLEX dual-GAT complex embedding vs dual embedding baselines on low-degree nodes | link existence prediction on extremely low-degree test nodes · Citeseer and Cora | AUC: gains of 25.9% to 55.0% on Citeseer and 16.3% to 47.8% on Cora over dual embedding methods | Helped |
| use DUPLEX self-supervised embeddings vs supervised end-to-end DUPLEX-S for node classification | DUPLEX · Citeseer and Cora-ml transductive node classification | mac. F1: Citeseer 53.0 (DUPLEX) vs 40.0 (DUPLEX-S) | Helped |
| DUPLEX (self-supervised, dual GAT) vs NERD on Cora-ml transductive node classification | DUPLEX · Cora-ml transductive node classification | mac. F1: 77.9 vs 78.8 for NERD | Hurt |
Surprising findings
- NERD outperforms DUPLEX on Cora-ml transductive node classification (78.8 vs 77.9 macro F1).
- Supervised DUPLEX-S lags far behind the self-supervised DUPLEX on transductive node classification (40.0 vs 53.0 macro F1 on Citeseer).
Limitations
- Claim that dual embedding methods cluster low-degree nodes is not rigorously proven, per the authors' appendix.
- Inductive node classification compares against transductive MagNet and SigMaNet with extra label-free training information, so comparisons are not fully matched.
- Complex-valued matrix methods (MagNet, SigMaNet) are described as more computationally expensive; DUPLEX's efficiency gain is argued analytically rather than measured.
Experimental setup
Datasets: Cora-ml Citeseer Cora Epinions Twitter
Benchmarks: Cora-ml Citeseer Cora Epinions Twitter
Metrics: AUC ACC macro F1 micro F1
Baselines: NERD DGGAN DiGAE ODIN MagNet SigMaNet Dir-GNN GAT GraphSAGE
Builds on: GAT MagNet Hermitian adjacency matrix Dir-GNN
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