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Toward Data-centric Directed Graph Learning: An Entropy-driven Approach
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Proposes EDEN, an entropy-driven data-centric knowledge distillation framework that builds a hierarchical knowledge tree from directed structural entropy and refines it with neural mutual-information estimation, usable as a standalone digraph learner or a plug-in module for (Di)GNNs.
Problem
Existing directed GNNs (DiGNNs) fail to fully exploit the structural and profile knowledge hidden in directed graphs, which limits predictive performance at the data level.
Approach
Build a coarse hierarchical knowledge tree (HKT) by minimizing directed structural entropy (with reverse random-walk probabilities), refine partitions with GAN-style neural MI estimation over node profiles, and use parent (teacher) and child (student) nodes for online data-level knowledge distillation with a random-walk leaf predictor.
Key results
- EDEN reaches 81.4% on WikiCS and 69.7% on Arxiv node classification, beating the best directed baseline HoloNet (79.2%, 67.5%).
- On Slashdot link existence, EDEN achieves AUC 91.8 vs 90.6 for the best baseline NSTE.
- As a plug-in module, EDEN improves Dir-GNN by up to 4.68% and DIMPA by up to 4.32% on average node classification gains across datasets.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| apply EDEN as the node-classification method | directed node classification · CoraML, CiteSeer, WikiCS, Tolokers, Empire, Rating, Arxiv | accuracy: 2.78% | Helped |
| apply EDEN to link-level prediction | directed link prediction · Slashdot and WikiTalk | AUC / accuracy: 2.24% | Helped |
| add diverse knowledge from other partitions (ablation) | EDEN · Tolokers Node-C, Slashdot existence, Rating Node-C, Epinions direction | accuracy / AUC: 80.90±0.4 -> 81.33±0.2; 91.40±0.2 -> 91.82±0.1; 45.76±0.6 -> 46.33±0.4; 89.02±0.1 -> 89.40±0.1 | Helped |
| add personalized knowledge transfer (ablation) | EDEN · Tolokers Node-C, Slashdot existence, Rating Node-C, Epinions direction | accuracy / AUC: 80.84±0.2 -> 81.33±0.2; 91.49±0.1 -> 91.82±0.1; 45.92±0.3 -> 46.33±0.4; 89.04±0.1 -> 89.40±0.1 | Helped |
| add tree-based random walk for leaf prediction (ablation) | EDEN · Tolokers Node-C, Slashdot existence, Rating Node-C, Epinions direction | accuracy / AUC: 80.67±0.3 -> 81.33±0.2; 91.16±0.1 -> 91.82±0.1; 45.84±0.4 -> 46.33±0.4; 88.99±0.1 -> 89.40±0.1 | Helped |
| add knowledge distillation loss (ablation) | EDEN · Tolokers Node-C, Slashdot existence, Rating Node-C, Epinions direction | accuracy / AUC: 80.01±0.3 -> 81.33±0.2; 90.84±0.1 -> 91.82±0.1; 45.45±0.5 -> 46.33±0.4; 88.61±0.1 -> 89.40±0.1 | Helped |
| add EDEN to existing directed and undirected GNNs | OptBG, NAG, DIMPA, Dir-GNN, HoloNet · CoraML, CiteSeer, WikiCS, Arxiv, Photo, Computer, PPI, Flickr | accuracy: ↑2.75%; ↑2.54%; ⇑4.32%; ⇑4.68%; ⇑4.46% | Helped |
Surprising findings
- Reported that the proportion of complete forward-only random walks drops sharply after about five steps on most digraphs, motivating reverse-probability walks.
- The lightweight plug-in version sometimes outperforms EDEN run as a standalone method, which the authors attribute to the lightweight implementation.
Limitations
- Significant algorithmic complexity with multi-step computations.
- Scalability challenges on billion-level graphs remain.
- The lightweight variant sacrifices some accuracy relative to the full method.
Experimental setup
Datasets: Slashdot WikiTalk CoraML CiteSeer WikiCS Arxiv Tolokers Empire Rating Photo Computer PPI
Benchmarks: Slashdot WikiTalk CoraML CiteSeer WikiCS Arxiv Tolokers Empire Rating Photo Computer PPI
Metrics: accuracy AUC AP
Baselines: GCN GAT NSTE Dir-GNN MagNet MGC GCNII GATv2 AGT DGCN DIMPA D-HYPR
Builds on: structural entropy MINE Deep Graph Infomax Dir-GNN HoloNet
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