  Recent years have witnessed an upsurge of interest in the problem of anomaly
detection on attributed networks due to its importance in both research and
practice. Although various approaches have been proposed to solve this problem,
two major limitations exist: (1) unsupervised approaches usually work much less
efficiently due to the lack of supervisory signal, and (2) existing anomaly
detection methods only use local contextual information to detect anomalous
nodes, e.g., one- or two-hop information, but ignore the global contextual
information. Since anomalous nodes differ from normal nodes in structures and
attributes, it is intuitive that the distance between anomalous nodes and their
neighbors should be larger than that between normal nodes and their neighbors
if we remove the edges connecting anomalous and normal nodes. Thus, hop counts
based on both global and local contextual information can be served as the
indicators of anomaly. Motivated by this intuition, we propose a hop-count
based model (HCM) to detect anomalies by modeling both local and global
contextual information. To make better use of hop counts for anomaly
identification, we propose to use hop counts prediction as a self-supervised
task. We design two anomaly scores based on the hop counts prediction via HCM
model to identify anomalies. Besides, we employ Bayesian learning to train HCM
model for capturing uncertainty in learned parameters and avoiding overfitting.
Extensive experiments on real-world attributed networks demonstrate that our
proposed model is effective in anomaly detection.
