Signed directed networks are ubiquitous in real-world applications. However, there has been relatively little work proposing spectral graph neural network (GNN) methods for analyzing such networks. Here we introduce a signed directed Laplacian matrix, which we call the magnetic signed Laplacian, as a natural generalization of both the signed Laplacian on signed graphs and the magnetic Laplacian on directed graphs. We then use this matrix to construct a novel spectral GNN architecture and conduct extensive experiments on both node clustering and link prediction tasks. In these experiments, we consider tasks related to signed information, tasks related to directional information, and tasks related to both signed and directional information. We demonstrate that our proposed spectral GNN is effective for incorporating both signed and directional information, and attains leading performance on a wide range of data sets. Additionally, we provide a novel synthetic network model, which we refer to as the signed directed stochastic block model, and a number of novel real-world data sets based on lead-lag relationships in financial time series.
翻译:签署的定向网络在现实世界应用中是无处不在的,然而,在提议光谱图神经网络(GNN)方法分析这些网络方面开展的工作相对较少。在这里,我们引入了经过签名的Laplacian 矩阵,我们称之为磁签名的Laplacian,这是签名的图纸上的Laplacian和定向图纸上的磁拉placian的自然概括。我们然后使用这个矩阵来构建一个新的光谱GNN结构,并就节点组合和连接预测任务进行广泛的实验。在这些实验中,我们考虑了与已签名的信息有关的任务、与方向信息有关的任务以及与签名的和方向信息有关的任务。我们证明,我们拟议的光谱GNNN能够有效地将签名的信息和方向信息结合起来,并在广泛的数据集上取得领先性表现。此外,我们提供了一个新型的合成网络模型,我们称之为经签名的定向随机区块模型,以及一些基于金融时间序列中铅渣关系的新型现实世界数据集。