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Hyperedge Anomaly Detection with Hypergraph Neural Network

Md. Tanvir Alam, Chowdhury Farhan Ahmed, Carson K. Leung

TL;DR

Hyperedge anomaly detection in hypergraphs is addressed with HAD, an end-to-end hypergraph neural network that learns node embeddings and derives hyperedge embeddings via max-min pooling. A dynamic centroid-based one-class objective scores hyperedge anomalies as the Euclidean distance to the hypergraph centroid, enabling unsupervised training without labels. HAD demonstrates superior AUROC on six real-world hypergraphs compared to hashing-based and variational baselines, highlighting the value of incorporating node features and higher-order structure. The approach offers a scalable, generalizable framework for detecting unusual multi-entity interactions in diverse domains.

Abstract

Hypergraph is a data structure that enables us to model higher-order associations among data entities. Conventional graph-structured data can represent pairwise relationships only, whereas hypergraph enables us to associate any number of entities, which is essential in many real-life applications. Hypergraph learning algorithms have been well-studied for numerous problem settings, such as node classification, link prediction, etc. However, much less research has been conducted on anomaly detection from hypergraphs. Anomaly detection identifies events that deviate from the usual pattern and can be applied to hypergraphs to detect unusual higher-order associations. In this work, we propose an end-to-end hypergraph neural network-based model for identifying anomalous associations in a hypergraph. Our proposed algorithm operates in an unsupervised manner without requiring any labeled data. Extensive experimentation on several real-life datasets demonstrates the effectiveness of our model in detecting anomalous hyperedges.

Hyperedge Anomaly Detection with Hypergraph Neural Network

TL;DR

Hyperedge anomaly detection in hypergraphs is addressed with HAD, an end-to-end hypergraph neural network that learns node embeddings and derives hyperedge embeddings via max-min pooling. A dynamic centroid-based one-class objective scores hyperedge anomalies as the Euclidean distance to the hypergraph centroid, enabling unsupervised training without labels. HAD demonstrates superior AUROC on six real-world hypergraphs compared to hashing-based and variational baselines, highlighting the value of incorporating node features and higher-order structure. The approach offers a scalable, generalizable framework for detecting unusual multi-entity interactions in diverse domains.

Abstract

Hypergraph is a data structure that enables us to model higher-order associations among data entities. Conventional graph-structured data can represent pairwise relationships only, whereas hypergraph enables us to associate any number of entities, which is essential in many real-life applications. Hypergraph learning algorithms have been well-studied for numerous problem settings, such as node classification, link prediction, etc. However, much less research has been conducted on anomaly detection from hypergraphs. Anomaly detection identifies events that deviate from the usual pattern and can be applied to hypergraphs to detect unusual higher-order associations. In this work, we propose an end-to-end hypergraph neural network-based model for identifying anomalous associations in a hypergraph. Our proposed algorithm operates in an unsupervised manner without requiring any labeled data. Extensive experimentation on several real-life datasets demonstrates the effectiveness of our model in detecting anomalous hyperedges.

Paper Structure

This paper contains 18 sections, 6 equations, 9 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related works
  3. Hypergraph Learning Methods
  4. Hypergraph Anomaly Detection
  5. Preliminaries
  6. Notations
  7. Problem Definition
  8. Proposed Methods
  9. Learning Node Embeddings
  10. Learning Hyperedge Embeddings
  11. One Class Classifier
  12. Experimental Results
  13. Experimental Setup
  14. Datasets
  15. Baselines
  16. ...and 3 more sections

Figures (9)

  • Figure 1: A hypergraph H containing four vertices $v_1$, $v_2$, $v_3$, and $v_4$. There are two hyperedges $e_1$ and $e_2$ where $e_1$ associates the vertices $v_1$, $v_2$, $v_3$ and $e_2$ associates the vertices $v_3$, $v_4$. The hyperedge embeddings $Z_E^l$ are learned by aggregating the features from the matrix $X$, and then the node embeddings $Z_V^l$ are derived. At the final level, the hyperedge embeddings are learned by applying $maxmin$ pooling to the node embeddings. Finally, a one-class classifier is applied to find the anomaly scores.
  • Figure 2: Loss value analysis over epochs
  • Figure : (a) Mushroom
  • Figure : (a) Mushroom
  • Figure : (b) Citeseer
  • ...and 4 more figures