Graph convolution is a fundamental building block for many deep neural networks on graph-structured data. In this paper, we introduce a simple, yet very effective graph convolutional network with skip connections for semi-supervised anomaly detection. The proposed layerwise propagation rule of our model is theoretically motivated by the concept of implicit fairing in geometry processing, and comprises a graph convolution module for aggregating information from immediate node neighbors and a skip connection module for combining layer-wise neighborhood representations. This propagation rule is derived from the iterative solution of the implicit fairing equation via the Jacobi method. In addition to capturing information from distant graph nodes through skip connections between the network's layers, our approach exploits both the graph structure and node features for learning discriminative node representations. These skip connections are integrated by design in our proposed network architecture. The effectiveness of our model is demonstrated through extensive experiments on five benchmark datasets, achieving better or comparable anomaly detection results against strong baseline methods. We also demonstrate through an ablation study that skip connection helps improve the model performance.

翻译：图卷积是许多基于图结构数据的深度神经网络的基本构建模块。本文提出一种结构简单但效果显著的图卷积网络，该网络通过跳跃连接实现半监督异常检测。所提出模型的逐层传播规则在理论上受几何处理中隐式平滑概念的启发，包含用于聚合相邻节点信息的图卷积模块和用于组合层间邻域表示的跳跃连接模块。该传播规则通过雅可比方法迭代求解隐式平滑方程推导得出。除通过网络层间跳跃连接捕获远距离图节点信息外，本方法同时利用图结构与节点特征学习判别性节点表示。这些跳跃连接在本网络架构中经过设计实现集成。在五个基准数据集上的大量实验表明，本模型在异常检测任务中相较于强基线方法取得更优或相当的性能。消融研究进一步证明跳跃连接有助于提升模型性能。