HC-GLAD: Dual Hyperbolic Contrastive Learning for Unsupervised Graph-Level Anomaly Detection

TL;DR

This paper proposes a novel Dual Hyperbolic Contrastive Learning for Unsupervised Graph-Level Anomaly Detection (HC-GLAD), the first work to simultaneously apply hypergraph with node group information and hyperbolic geometry in this field.

Abstract

Unsupervised graph-level anomaly detection (UGAD) has garnered increasing attention in recent years due to its significance. Most existing methods that rely on traditional GNNs mainly consider pairwise relationships between first-order neighbors, which is insufficient to capture the complex high-order dependencies often associated with anomalies. This limitation underscores the necessity of exploring high-order node interactions in UGAD. In addition, most previous works ignore the underlying properties (e.g., hierarchy and power-law structure) which are common in real-world graph datasets and therefore are indispensable factors in the UGAD task. In this paper, we propose a novel Dual Hyperbolic Contrastive Learning for Unsupervised Graph-Level Anomaly Detection (HC-GLAD in short). To exploit high-order node group information, we construct hypergraphs based on pre-designed gold motifs and subsequently perform hypergraph convolution. Furthermore, to preserve the hierarchy of real-world graphs, we introduce hyperbolic geometry into this field and conduct both graph and hypergraph embedding learning in hyperbolic space with the hyperboloid model. To the best of our knowledge, this is the first work to simultaneously apply hypergraph with node group information and hyperbolic geometry in this field. Extensive experiments on 13 real-world datasets of different fields demonstrate the superiority of HC-GLAD on the UGAD task. The code is available at https://github.com/Yali-F/HC-GLAD.

Figures (9)

• Figure 1: (a) Normal molecular graphs usually have 1-2 node groups in blue areas, while abnormal ones have 3-4. Normal financial transaction networks show simple patterns, while abnormal ones show chaotic circular or cross-transactions in gray areas; (b) With an exponential increase of nodes in tree-like data, Euclidean space is difficult to embed nodes separately. In contrast, hyperbolic space, which can be regarded as a continuous version of the tree, can still maintain certain distances between the embedded nodes.
• Figure 2: Degree distributions of dataset REDDIT-B (on the left) and IMDB-B (on the right).
• Figure 3: The overall framework of HC-GLAD. Firstly, the input graphs undergo data augmentation in Euclidean space, obtaining two augmented views and forming the graph channel below. Secondly, based on pre-designed gold motifs, we construct hypergraphs from the augmented graphs, forming the hypergraph channel above. Thirdly, we perform the aggregation operation for graph and hypergraph channel in hyperbolic space, obtaining final hyperbolic embeddings used for calculating multi-level contrastive loss. Lastly, graph and hypergraph contrastive losses are employed to calculate graphs' anomaly scores.
• Figure 4: Hyper-parameter analysis (trade-off parameter $\lambda_1$) on representative datasets.
• Figure 5: Ablation study on representative datasets.

Theorems & Definitions (4)

• definition 1: Minkowski Inner Product
• definition 2: Hyperboloid Manifold
• definition 3: Tangent Space
• definition 4: Exponential and Logarithmic Maps