Combining Euclidean and Hyperbolic Representations for Node-level Anomaly Detection

2025-10-13

AI Summary

Node-level anomaly detection (NAD) faces significant modeling challenges due to the high heterogeneity of graph structures and node feature distributions. To address this, we propose Janus, the first framework that jointly leverages Euclidean and hyperbolic graph neural networks within a multi-graph autoencoder architecture to learn complementary geometric representations. It further incorporates contrastive learning to align multi-view embeddings and quantifies anomalies via inter-view inconsistency—effectively capturing subtle and complex anomalies that resist reconciliation across geometries. Additionally, Janus enhances representation robustness by integrating structural features derived from random walks and node degrees. Evaluated on four real-world datasets, Janus consistently outperforms state-of-the-art shallow and deep baselines, achieving average AUC improvements of 6.2%–14.8%. These results empirically validate the efficacy and generalizability of multi-geometric joint modeling for NAD.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Detecting node anomalies in graphs with diverse structural patterns
• Combining Euclidean and hyperbolic spaces for complementary representations
• Identifying nodes with irreconcilable views across geometric spaces as anomalies

Innovation

• Combining Euclidean and Hyperbolic Graph Neural Networks
• Using multi Graph-Autoencoder with contrastive learning
• Aligning node embeddings across different geometric spaces