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LSEnet: Lorentz Structural Entropy Neural Network for Deep Graph Clustering
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Proposes differentiable structural information (DSI) and a hyperbolic Lorentz neural network (LSEnet) that learns a partitioning tree for deep graph clustering without a predefined number of clusters.
Problem
Deep graph clustering methods require a predefined cluster number K, which is often unknown and expensive to estimate; classic structural entropy is discrete, non-differentiable, and ignores node features.
Approach
Reformulates structural entropy with level-wise soft assignment matrices so it is differentiable, uses it as a K-free clustering objective, and learns the partitioning tree with a Lorentz (hyperbolic) GNN using Lorentz attention, aggregation, and a Lorentz assigner.
Key results
- On Cora, Citeseer, AMAP and Computer, LSEnet reports NMI of 63.97, 52.26, 71.72 and 55.03 with K set to ground truth, the best on three of four datasets (DinkNet is best on AMAP NMI at 74.36).
- Against classic structural entropy (CSE) at 2 dimensions, LSEnet improves NMI by 1.75 on Cora and 2.23 on Citeseer.
- On AMAP, LSEnet is reported to gain over 20% NMI over RGC, the K-free baseline.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use LSEnet instead of the strongest listed baseline | Graph clustering · Cora | NMI (%): 63.16 -> 63.97 | Helped |
| Use LSEnet instead of the strongest listed baseline | Graph clustering · Cora | ARI (%): 63.14 -> 63.35 | Helped |
| Use LSEnet instead of the strongest listed baseline | Graph clustering · Citeseer | NMI (%): 50.92 -> 52.26 | Helped |
| Use LSEnet instead of the strongest listed baseline | Graph clustering · Citeseer | ARI (%): 47.64 -> 48.01 | Helped |
| Use LSEnet instead of the strongest listed baseline | Graph clustering · AMAP | NMI (%): 74.36 -> 71.72 | Hurt |
| Use LSEnet instead of the strongest listed baseline | Graph clustering · AMAP | ARI (%): 68.40 -> 65.08 | Hurt |
| Use LSEnet instead of the strongest listed baseline | Graph clustering · Computer | NMI (%): 54.80 -> 55.03 | Helped |
| Use LSEnet instead of the strongest listed baseline | Graph clustering · Computer | ARI (%): 40.07 -> 42.15 | Helped |
| Use LSEnet instead of CSE for the two-level partitioning tree | Graph clustering · Cora | NMI (%): +1.75 | Helped |
| Use LSEnet instead of CSE for the two-level partitioning tree | Graph clustering · Citeseer | NMI (%): +2.23 | Helped |
| Increase partitioning-tree height H (ablation) | LSEnet · Cora, Citeseer, AMAP, and Computer | clustering performance | Helped |
| Use LSEnet instead of the strongest listed link-prediction baseline | Link prediction embeddings · Citeseer | AUC: 94.39 -> 94.32 | Hurt |
Surprising findings
- LSEnet does not win on AMAP NMI, where DinkNet (74.36) and DCRN (73.70) are higher.
- Most baselines are given the ground-truth K, while LSEnet and RGC are K-free, so the comparison is not like-for-like.
Limitations
- Evaluation uses K set to ground-truth classes for baselines, and the paper's K-free setting is only compared against RGC.
- Node-count per internal level must be set large enough as a hyperparameter; tree height H is also a hyperparameter.
- Theoretical bound on the tree approximation relies on constraints on the assignment (tau and epsilon conditions) that are not verified empirically.
Experimental setup
Datasets: Cora Citeseer AMAP Computer Football Karate
Benchmarks: Cora Citeseer AMAP Computer Football Karate
Metrics: NMI ARI AUC
Baselines: K-Means VGAE ARGA MVGRL Sublime ProGCL GRACE DEC MCGC DCRN FT-VGAE gCooL
Builds on: structural information (Li and Pan 2016) Lorentz linear layer (LGCN) Riemannian Adam conductance
Closest papers by meaning
- Hyperbolic Continuous Structural Entropy for Hierarchical Clustering (AAAI 2026 · similarity 0.90)
- Dink-Net: Neural Clustering on Large Graphs (ICML 2023 · similarity 0.88)
- Structural Entropy Based Graph Structure Learning for Node Classification (AAAI 2024 · similarity 0.87)
- Deep Multi-modal Graph Clustering via Graph Transformer Network (AAAI 2025 · similarity 0.86)
- The Map Equation Goes Neural: Mapping Network Flows with Graph Neural Networks (NeurIPS 2024 · similarity 0.86)
- Neural Gaussian Similarity Modeling for Differential Graph Structure Learning (AAAI 2024 · similarity 0.85)
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