Zhang Xitong, He Yixuan, Brugnone Nathan, Perlmutter Michael, Hirn Matthew
Michigan State University, Department of Computational Mathematics, Science & Engineering, East Lansing, Michigan, United States.
University of Oxford, Department of Statistics, Oxford, England, United Kingdom.
Adv Neural Inf Process Syst. 2021 Dec;34:27003-27015.
The prevalence of graph-based data has spurred the rapid development of graph neural networks (GNNs) and related machine learning algorithms. Yet, despite the many datasets naturally modeled as directed graphs, including citation, website, and traffic networks, the vast majority of this research focuses on undirected graphs. In this paper, we propose , a GNN for directed graphs based on a complex Hermitian matrix known as the magnetic Laplacian. This matrix encodes undirected geometric structure in the magnitude of its entries and directional information in their phase. A "charge" parameter attunes spectral information to variation among directed cycles. We apply our network to a variety of directed graph node classification and link prediction tasks showing that MagNet performs well on all tasks and that its performance exceeds all other methods on a majority of such tasks. The underlying principles of MagNet are such that it can be adapted to other GNN architectures.
基于图的数据的流行推动了图神经网络（GNN）和相关机器学习算法的快速发展。然而，尽管有许多数据集自然地建模为有向图，包括引用网络、网站和交通网络，但绝大多数此类研究都集中在无向图上。在本文中，我们提出了一种基于称为磁拉普拉斯算子的复埃尔米特矩阵的有向图GNN。该矩阵在其元素的大小中编码无向几何结构，并在其相位中编码方向信息。一个“电荷”参数使频谱信息适应有向循环之间的变化。我们将我们的网络应用于各种有向图节点分类和链接预测任务，结果表明MagNet在所有任务上都表现良好，并且在大多数此类任务上其性能超过了所有其他方法。MagNet的基本原理使其能够适应其他GNN架构。
