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PieClam: A Universal Graph Autoencoder Based on Overlapping Inclusive and Exclusive Communities
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Proposes PieClam, a probabilistic graph autoencoder/generative model that embeds nodes into inclusive and exclusive overlapping communities via a Lorentz-inner-product decoder with a learned normalizing-flow prior, proves universality under a new log cut distance, and reports competitive unsupervised node anomaly detection AUC.
Problem
Graph autoencoders and community affiliation models (e.g., BigClam) cannot represent graphs with bipartite-like structure due to triangle-inequality-type limits, and they are not generative; a fixed-dimension universal graph decoder is needed.
Approach
Extends BigClam with exclusive communities via a Lorentz inner product decoder (IeClam), adds a normalizing-flow prior over the affiliation space to make it a generative model (PieClam), and introduces the log cut distance to prove universal approximation of any graph with a fixed code dimension.
Key results
- (S)-IeClam achieves AUC 0.639 on Reddit and 0.592 on Photo, the best on those datasets, per the reported table.
- (P)-PieClam achieves AUC 0.610 on Elliptic, first place on that dataset, with (PS)-PieClam at 0.551 second.
- The paper claims PieClam/IeClam methods are first or second on all three datasets, but this rests on AUC numbers taken from a prior paper's table.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use star probability scoring with IeClam instead of TAM | IeClam node anomaly detection · Reddit | AUC: 0.606 -> 0.639 | Helped |
| Use star probability scoring with IeClam instead of AnomalyDAE | IeClam node anomaly detection · Elliptic | AUC: 0.496 -> 0.440 | Hurt |
| Use star probability scoring with IeClam instead of TAM | IeClam node anomaly detection · Photo | AUC: 0.568 -> 0.592 | Helped |
| Use prior probability scoring with PieClam instead of AnomalyDAE | PieClam node anomaly detection · Elliptic | AUC: 0.496 -> 0.610 | Helped |
| Use star probability scoring with PieClam instead of AnomalyDAE | PieClam node anomaly detection · Elliptic | AUC: 0.496 -> 0.435 | Hurt |
| Use prior star probability scoring with PieClam instead of AnomalyDAE | PieClam node anomaly detection · Elliptic | AUC: 0.496 -> 0.551 | Helped |
| Use star probability scoring with BigClam instead of TAM | BigClam node anomaly detection · Reddit | AUC: 0.606 -> 0.637 | Helped |
| Use star probability scoring with BigClam instead of AnomalyDAE | BigClam node anomaly detection · Elliptic | AUC: 0.496 -> 0.434 | Hurt |
| Use star probability scoring with BigClam instead of TAM | BigClam node anomaly detection · Photo | AUC: 0.568 -> 0.581 | Helped |
Surprising findings
- BigClam cannot approximate bipartite graphs at all with a fixed number of communities, whereas IeClam can approximate bipartite structure with C=1.
Limitations
- For attributed graphs, node features only enter through the prior, not the edge probabilities.
- The log cut distance is mainly appropriate for dense graphs; sparse extension is future work.
Experimental setup
Datasets: Reddit Elliptic Photo
Benchmarks: Reddit Elliptic Photo
Metrics: AUC
Baselines: DOMINANT AnomalyDAE OCGNN AEGIS GAAN TAM BigClam
Builds on: BigClam stochastic block model realNVP DOMINANT
Closest papers by meaning
- GraphCroc: Cross-Correlation Autoencoder for Graph Structural Reconstruction (NeurIPS 2024 · similarity 0.85)
- ADA-GAD: Anomaly-Denoised Autoencoders for Graph Anomaly Detection (AAAI 2024 · similarity 0.85)
- Community-Centric Graph Unlearning (AAAI 2025 · similarity 0.85)
- Equivalence is All: A Unified View for Self-supervised Graph Learning (ICML 2025 · similarity 0.85)
- Rethinking Reconstruction-based Graph-Level Anomaly Detection: Limitations and a Simple Remedy (NeurIPS 2024 · similarity 0.85)
- Learning on Large Graphs using Intersecting Communities (NeurIPS 2024 · similarity 0.85)
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