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Learning Persistent Community Structures in Dynamic Networks via Topological Data Analysis
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Proposes MFC, a matrix-factorization-based deep graph clustering module, and TopoReg, a persistent-homology (weight rank clique filtration) regularizer that enforces temporal consistency of inter-community networks for dynamic community detection.
Problem
Dynamic community detection on snapshot graphs lacks temporal consistency, so transient perturbations cause spurious community merges/splits; deep clustering also suffers representation collapse when self-supervised DEC-style clustering is used without node features.
Approach
Combine a relaxed matrix-factorization clustering head (MFC) on GAE embeddings with a differentiable topological loss: build probabilistic community networks per snapshot, compute their persistence diagrams via weight rank clique filtration, and penalize Wasserstein distances between neighboring snapshots' diagrams.
Key results
- On Highschool, MFC+Topo reaches 70.67 ACC and 50.87 ARI, versus 65.77 ACC for the best temporal baseline DECS.
- TopoReg gives average improvements of 11.54%, 5.90%, and 1.38% in ACC on GEC, DAEGC, and MFC backbones respectively.
- On the synthetic graph, clustering accuracy improves from 81% to 98% after applying the topological loss.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add TopoReg to the MFC backbone (ablation) | MFC · Enron, Highschool, DBLP, and Cora | ACC, NMI, ARI, and Modularity | Mixed |
| add TopoReg to the GEC backbone (ablation) | GEC · Enron, Highschool, DBLP, and Cora | ACC, NMI, ARI, and Modularity | Mixed |
| add TopoReg to the DAEGC backbone (ablation) | DAEGC · Enron, Highschool, DBLP, and Cora | ACC, NMI, ARI, and Modularity | Mixed |
| optimize the second synthetic snapshot with the topological loss | MFC+Topo · Synthetic data | clustering accuracy: 81% to 98% | Helped |
| use MFC_Q rather than GEC_Q with TopoReg (ablation) | TopoReg on DBLP_dyn · DBLP_dyn | ACC: 39.49 -> 42.82 | Helped |
| use MFC_Q rather than DAEGC_Q with TopoReg (ablation) | TopoReg on DBLP_dyn · DBLP_dyn | NMI: 2.13 -> 9.32 | Helped |
Surprising findings
- On Enron, plain MFC without topological regularization already outperforms MFC+Topo in ACC on some settings and GEC+Topo beats MFC+Topo on ACC (60.32 vs 59.31).
Limitations
- MFC fails when node embedding dimension is smaller than the number of clusters, since the pseudo-inverse does not exist.
- Baselines ESPRA and DECS run out of memory on DBLP and Cora, so comparisons are incomplete there.
- Gains from TopoReg are modest on some backbones (e.g., 1.38% average on MFC) and results are on small datasets without node features.
Experimental setup
Datasets: Enron Highschool DBLP Cora DBLP_dyn synthetic Gaussian random partition graphs
Benchmarks: Enron Highschool DBLP Cora DBLP_dyn
Metrics: ACC NMI ARI Modularity Wasserstein distance between persistence diagrams
Baselines: GEC DAEGC SDCN DECS ESPRA DynAE
Builds on: DAEGC DEC ESPRA weight rank clique filtration SDCN
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