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Hypergraph Joint Representation Learning for Hypervertices and Hyperedges via Cross Expansion
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Proposes cross expansion, which turns hypervertices and hyperedges into vertices of a standard graph with direct connections, and learns a joint embedding space with GCN trained on classification plus hypergraph reconstruction losses.
Problem
Hypergraph representation learning for hypervertices and hyperedges: existing expansions (clique, star) lose higher-order information or add intermediate-hop information decay, and prior methods learn separate embedding spaces for the two entity types.
Approach
A cross expansion converts both hypervertices and hyperedges into vertices of a standard graph, connecting v-v, e-e and v-e pairs directly, so a GCN can learn one shared joint embedding space for both, regularized by a hypergraph reconstruction loss.
Key results
- HJRL reaches 67.1% accuracy on Citeseer hypervertex classification versus 66.5% for HCoN, and 89.1% on DBLP versus 88.9% for TriCL.
- On Citeseer hyperedge classification HJRL reaches 75.6% accuracy and 81.2 F1 versus HCoN's 70.7% accuracy and 75.5 F1.
- HJRL trains faster than HCoN and TriCL, e.g. 2.13 s vs 3.42 s (HCoN) and 16.85 s (TriCL) on Citeseer.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use joint representation learning with cross expansion instead of the strongest reported baseline | HJRL · Hypervertex classification: Citeseer, Pubmed, Cora, DBLP | accuracy: 72.0 ± 0.9 -> 73.1 ± 0.7; 80.4 ± 1.1 -> 81.0 ± 1.5; 66.5 ± 0.5 -> 67.1 ± 0.6; 88.9 ± 0.3 -> 89.1 ± 0.1 | Helped |
| Use joint representation learning with cross expansion instead of HCoN | HJRL · Hyperedge classification: Citeseer, Pubmed, Cora | F1-score: 75.5 ± 1.1 -> 81.2 ± 0.9; 85.9 ± 0.5 -> 86.1 ± 0.6; 46.6 ± 0.7 -> 58.7 ± 1.3 | Helped |
| Use joint representation learning with cross expansion instead of HCoN | HJRL · Hyperedge classification: Citeseer, Pubmed, Cora | accuracy: 70.7 ± 1.1 -> 75.6 ± 1.0; 79.9 ± 0.7 -> 80.2 ± 0.7; 43.5 ± 0.6 -> 54.0 ± 1.1 | Helped |
| Add hypergraph reconstruction loss (ablation) | HJRL · Hypervertex classification: Citeseer, Pubmed, Cora, DBLP | accuracy: 70.3 ± 0.9 -> 73.1 ± 0.7; 80.0 ± 2.2 -> 81.0 ± 1.5; 65.7 ± 0.6 -> 67.1 ± 0.6; 88.4 ± 0.2 -> 89.1 ± 0.1 | Helped |
| Add hypergraph reconstruction loss (ablation) | HJRL · Hyperedge classification: Citeseer, Pubmed, Cora | F1-score: 78.1 ± 1.3 -> 81.2 ± 0.9; 84.3 ± 0.8 -> 86.1 ± 0.6; 58.2 ± 1.5 -> 58.7 ± 1.3 | Helped |
| Replace clique expansion with cross expansion (ablation) | HJRL · Hypervertex classification: Citeseer, Pubmed, Cora, DBLP | accuracy: 71.4 ± 1.1 -> 73.1 ± 0.7; 79.5 ± 2.1 -> 81.0 ± 1.5; 62.9 ± 0.9 -> 67.1 ± 0.6; 88.7 ± 0.1 -> 89.1 ± 0.1 | Helped |
| Replace star expansion with cross expansion (ablation) | HJRL · Hypervertex classification: Citeseer, Pubmed, Cora, DBLP | accuracy: 72.1 ± 1.0 -> 73.1 ± 0.7; 78.5 ± 1.6 -> 81.0 ± 1.5; 64.3 ± 0.9 -> 67.1 ± 0.6; 86.8 ± 0.3 -> 89.1 ± 0.1 | Helped |
| Replace combined clique and star expansion with cross expansion (ablation) | HJRL · Hypervertex classification: Citeseer, Pubmed, Cora, DBLP | accuracy: 72.7 ± 0.8 -> 73.1 ± 0.7; 80.5 ± 1.6 -> 81.0 ± 1.5; 66.1 ± 0.8 -> 67.1 ± 0.6; 88.6 ± 0.1 -> 89.1 ± 0.1 | Helped |
| Replace star expansion with cross expansion (ablation) | HJRL · Citeseer hyperedge classification | F1-score: 78.2 ± 1.0 -> 81.2 ± 0.9 | Helped |
| Replace combined clique and star expansion with cross expansion (ablation) | HJRL · Citeseer hyperedge classification | F1-score: 80.0 ± 1.0 -> 81.2 ± 0.9 | Helped |
Surprising findings
- Clique expansion within the joint model (HJRL(Clique)) is competitive on some hypervertex tasks but the star-only variant is weaker on Pubmed hyperedge classification precision/accuracy trade-offs.
Limitations
- Hyperedge classification is not run on DBLP due to computational cost.
- Cross expansion graph construction is quadratic in the number of vertices and hyperedges, and the reconstruction term is O(|V||E|d).
Experimental setup
Datasets: Citeseer Pubmed Cora DBLP
Benchmarks: Citeseer Pubmed Cora DBLP
Metrics: accuracy precision recall F1-score exact match ratio 0/1 loss wall-clock time
Baselines: SVM NN GCN HyperGCN HGNN HNHN LEGCN TriCL HCNH HCoN
Builds on: GCN HNHN HCoN HGNN clique expansion star expansion
Closest papers by meaning
- Edge Representation Learning with Hypergraphs (NeurIPS 2021 · similarity 0.90)
- Hypergraph Learning for Unsupervised Graph Alignment via Optimal Transport (AAAI 2025 · similarity 0.89)
- Defining and Discovering Hyper-meta-paths for Heterogeneous Hypergraphs (NeurIPS 2025 · similarity 0.89)
- Hypergraph-enhanced Dual Semi-supervised Graph Classification (ICML 2024 · similarity 0.87)
- SPHINX: Structural Prediction using Hypergraph Inference Network (ICML 2025 · similarity 0.86)
- HypeBoy: Generative Self-Supervised Representation Learning on Hypergraphs (ICLR 2024 · similarity 0.86)
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