Recent advancements in Graph Neural Networks have led to state-of-the-art performance on representation learning of graphs for node classification. However, the majority of existing works process directed graphs by symmetrization, which may cause loss of directional information. In this paper, we propose the magnetic Laplacian that preserves edge directionality by encoding it into complex phase as a deformation of the combinatorial Laplacian. In addition, we design an Auto-Regressive Moving-Average (ARMA) filter that is capable of learning global features from graphs. To reduce time complexity, Taylor expansion is applied to approximate the filter. We derive complex-valued operations in graph neural network and devise a simplified Magnetic Graph Convolution network, namely sMGC. Our experiment results demonstrate that sMGC is a fast, powerful, and widely applicable GNN.
翻译：图表神经网络最近的进展导致对用于节点分类的图表的演示学习取得最先进的性能,然而,大多数现有的工程过程通过对称化引导图形,这可能导致方向信息丢失。在本文中,我们提议将磁拉拉拉西恩作为组合式拉拉普拉西恩的变形,将其编码为复杂阶段,从而保持边缘方向性。此外,我们设计了一个自动反向移动动动动过滤器,能够从图表中学习全球特征。为了降低时间复杂性,泰勒的扩展应用到接近过滤器。我们在图形神经网络中生成了复杂价值的操作,并设计了一个简化的磁动动网络,即SMGC。我们的实验结果表明,SMCC是一个快速、强大和广泛应用的GNN。
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