The smoothing issue leads to indistinguishable node representations, which poses a significant challenge in the field of graph learning. However, this issue also presents an opportunity to reveal underlying properties behind different types of nodes, which have been overlooked in previous studies. Through empirical and theoretical analysis of real-world node anomaly detection (NAD) datasets, we observe that anomalous and normal nodes show different patterns in the smoothing process, which can be leveraged to enhance NAD tasks. Motivated by these findings, in this paper, we propose a novel unsupervised NAD framework. Specifically, according to our theoretical analysis, we design a Smoothing Learning Component. Subsequently, we introduce a Smoothing-aware Spectral Graph Neural Network, which establishes the connection between the spectral space of graphs and the smoothing process. Additionally, we demonstrate that the Dirichlet Energy, which reflects the smoothness of a graph, can serve as coefficients for node representations across different dimensions of the spectral space. Building upon these observations and analyses, we devise a novel anomaly measure for the NAD task. Extensive experiments on 9 real-world datasets show that SmoothGNN outperforms the best rival by an average of 14.66% in AUC and 7.28% in Precision, with 75x running time speed-up, which validates the effectiveness and efficiency of our framework.

通过对真实世界的节点异常检测数据集的实证和理论分析，我们观察到异常节点和正常节点在平滑过程中表现出不同的模式，这可以用来增强节点异常检测任务。基于这些发现，我们提出了一种新颖的无监督节点异常检测框架，其中包括涉及平滑过程的学习组件和基于平滑过程和图谱空间的图神经网络，以及用于NAD任务的新颖异常度量方法。通过对9个真实世界数据集的广泛实验，SmoothGNN在AUC上平均比最好的竞争方法提高了14.66％，在Precision上提高了7.28％，同时运行时间加快了75倍，验证了我们框架的有效性和效率。

SmoothGNN：基于平滑的图神经网络用于无监督节点异常检测