Graph neural networks (GNNs) have attracted considerable attention from the research community. It is well established that GNNs are usually roughly divided into spatial and spectral methods. Despite that spectral GNNs play an important role in both graph signal processing and graph representation learning, existing studies are biased toward spatial approaches, and there is no comprehensive review on spectral GNNs so far. In this paper, we summarize the recent development of spectral GNNs, including model, theory, and application. Specifically, we first discuss the connection between spatial GNNs and spectral GNNs, which shows that spectral GNNs can capture global information and have better expressiveness and interpretability. Next, we categorize existing spectral GNNs according to the spectrum information they use, \ie, eigenvalues or eigenvectors. In addition, we review major theoretical results and applications of spectral GNNs, followed by a quantitative experiment to benchmark some popular spectral GNNs. Finally, we conclude the paper with some future directions.

本文总结了谱图神经网络的最新发展，包括模型、理论和应用等方面的内容，其中介绍了谱性GNN能够捕捉全局信息，并具有更好的可表达性和可解释性。通过对现有谱性GNN的分析，本文梳理了主要理论结果和应用，最后进行了定量实验来评估几种常见的谱性GNN模型，为未来的研究提出了一些方向。

谱图神经网络调研