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 with standard anomaly detection methods it is usually assumed that instances are independent and identically distributed, in many real-world applications, instances are often explicitly connected with each other, resulting in so-called attributed graphs. The proposed method embeds nodes (instances) on the attributed graph in the latent space by taking into account their attributes as well as the graph structure based on 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 achieves better performance than various existing anomaly detection methods.

本文提出一种在具有少量实例标签信息的属性图上检测异常实例的简单而有效的方法，该方法使用图卷积网络将节点嵌入到潜空间中，以捕获节点间的关系，然后通过最小化超球体的体积来训练节点嵌入算法以检测异常实例。该方法在五个真实世界的属性图数据集上的实验结果表明，该方法比各种现有的异常检测方法具有更好的性能。

属性图上的半监督异常检测