Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Combining Euclidean and Hyperbolic Representations for Node-level Anomaly Detection

Simone Mungari, Ettore Ritacco, Pietro Sabatino

TL;DR

This work tackles node-level anomaly detection on graphs by integrating Euclidean and Hyperbolic representations through a dual-branch graph autoencoder augmented with contrastive learning. Each node is described by two views, X^s in Euclidean space and X^g mapped to Hyperbolic space, with encoders/decoders for both geometries and a product-metric contrastive loss to align cross-space representations. The approach, Janus, demonstrates state-of-the-art performance on four real-world datasets, achieving substantial improvements in ROC-AUC and Average Precision over strong baselines, and includes extensive ablations to justify the multi-geometry design. The authors provide reproducible code and experiments, underscoring the practical potential of hybrid geometric representations for robust NAD in complex graphs.

Abstract

Node-level anomaly detection (NAD) is challenging due to diverse structural patterns and feature distributions. As such, NAD is a critical task with several applications which range from fraud detection, cybersecurity, to recommendation systems. We introduce Janus, a framework that jointly leverages Euclidean and Hyperbolic Graph Neural Networks to capture complementary aspects of node representations. Each node is described by two views, composed by the original features and structural features derived from random walks and degrees, then embedded into Euclidean and Hyperbolic spaces. A multi Graph-Autoencoder framework, equipped with a contrastive learning objective as regularization term, aligns the embeddings across the Euclidean and Hyperbolic spaces, highlighting nodes whose views are difficult to reconcile and are thus likely anomalous. Experiments on four real-world datasets show that Janus consistently outperforms shallow and deep baselines, empirically demonstrating that combining multiple geometric representations provides a robust and effective approach for identifying subtle and complex anomalies in graphs.

Combining Euclidean and Hyperbolic Representations for Node-level Anomaly Detection

TL;DR

This work tackles node-level anomaly detection on graphs by integrating Euclidean and Hyperbolic representations through a dual-branch graph autoencoder augmented with contrastive learning. Each node is described by two views, X^s in Euclidean space and X^g mapped to Hyperbolic space, with encoders/decoders for both geometries and a product-metric contrastive loss to align cross-space representations. The approach, Janus, demonstrates state-of-the-art performance on four real-world datasets, achieving substantial improvements in ROC-AUC and Average Precision over strong baselines, and includes extensive ablations to justify the multi-geometry design. The authors provide reproducible code and experiments, underscoring the practical potential of hybrid geometric representations for robust NAD in complex graphs.

Abstract

Node-level anomaly detection (NAD) is challenging due to diverse structural patterns and feature distributions. As such, NAD is a critical task with several applications which range from fraud detection, cybersecurity, to recommendation systems. We introduce Janus, a framework that jointly leverages Euclidean and Hyperbolic Graph Neural Networks to capture complementary aspects of node representations. Each node is described by two views, composed by the original features and structural features derived from random walks and degrees, then embedded into Euclidean and Hyperbolic spaces. A multi Graph-Autoencoder framework, equipped with a contrastive learning objective as regularization term, aligns the embeddings across the Euclidean and Hyperbolic spaces, highlighting nodes whose views are difficult to reconcile and are thus likely anomalous. Experiments on four real-world datasets show that Janus consistently outperforms shallow and deep baselines, empirically demonstrating that combining multiple geometric representations provides a robust and effective approach for identifying subtle and complex anomalies in graphs.

Paper Structure

This paper contains 19 sections, 22 equations, 2 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Node‑Level Anomaly Detection with GNNs.
  4. Hyperbolic Graph Neural Networks.
  5. Combination of different spaces.
  6. Geometric preliminaries
  7. Product metric spaces.
  8. Hyperbolic Setting.
  9. Approach
  10. Experiments
  11. Experimental Setup
  12. Datasets.
  13. Competitors.
  14. Evaluation Protocol.
  15. Results
  16. ...and 4 more sections

Figures (2)

  • Figure 1: Cumulative Gain charts across datasets. The y-axis shows the percentage of detected anomalies, while the x-axis shows the increasing fraction of samples of the dataset adopted.
  • Figure 2: Comparison of models across datasets. Top row: AP vs Time. Bottom row: ROC-AUC vs Time. The legend is shared across all subplots.