Research on graph anomaly detection method based on hyperbolic space

Authors

Ya Shen

Affiliations

  1. Department of Computer Science North China Electric Power University (Baoding);
  2. Hebei Key Laboratory of Knowledge Computing for Energy & Power;
  3. Engineering Research Center for Intelligent Computing of Complex Energy Systems, Ministry of Education corresponding author(s): Yumei Ma (yumeim@ncepu.edu.cn)

Abstract: Graph node anomaly detection aims to identify anomalous nodes that deviate from regular patterns in complex networks, and the technique has important application value in the fields of cyber security, biomedicine, and social network analysis. Compared with traditional tabular data, the irregular topology of graph data tends to be hierarchical and follow the power law distribution law, which puts forward higher requirements on the spatial modelling ability of anomaly detection algorithms. Compared with the traditional Euclidean space, hyperbolic space shows significant advantages in modelling graph data with obvious hierarchical structure and complex topology due to its exponentially growing geometric properties. To this end, this paper builds a graph node anomaly detection model based on hyperbolic graph convolutional neural network, which achieves unsupervised node anomaly detection by constructing a self-encoder and exploiting the reconstruction error. In this paper, three types of models are designed to construct the autoencoder based on the Euclidean space, the Poincaré ball and the Lorentz model, respectively, and comparative experiments are carried out on eight benchmark graph datasets from different domains to evaluate their performance. The experimental results show that the model based on hyperbolic space outperforms the model based on Euclidean space on most datasets, especially in graphs possessing tree structure and power-law distribution properties. Meanwhile, the model’s ability to sense anomalous nodes is further verified through hyperparametric analysis and visualization experiments, confirming that the hyperbolic space-based autoencoder model can provide an effective solution for graph anomaly detection tasks.

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