Semi-supervised Anomaly Detection on Attributed Graphs

We propose a simple yet effective method for detecting anomalous instances on an attribute graph with label information of a small number of instances. Although standard anomaly detection methods usually assume that instances are independent and identically distributed, in many real-world applications, instances are often explicitly connected, resulting in so-called attributed graphs. The proposed method embeds nodes (instances) on the attributed graph in a latent space by taking into account their attributes as well as the graph structure on the basis of graph convolutional networks (GCNs). To learn node embeddings specialized for anomaly detection, in which there is a class imbalance due to the rarity of anomalies, the parameters of a GCN are trained to minimize the volume of a hypersphere that encloses the node embeddings of normal instances while embedding anomalous ones outside the hypersphere. This enables us to detect anomalies by simply calculating the distances between the node embeddings and hypersphere center. The proposed method can effectively propagate label information on a small amount of nodes to unlabeled ones by taking into account the node's attributes, graph structure, and class imbalance. In experiments with five real-world attributed graph datasets, we demonstrate that the proposed method outperforms various existing anomaly detection methods.