MagNet: A Neural Network for Directed Graphs
MagNet: A Neural Network for Directed Graphs
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发表时间：
2021-02
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通讯作者：
Xitong Zhang;Yixuan He;Nathan Brugnone;Michael Perlmutter;M. Hirn
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作者：
Xitong Zhang;Yixuan He;Nathan Brugnone;Michael Perlmutter;M. Hirn
基于图的数据的流行促进了图神经网络（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，网站和流量网络，但绝大多数研究都集中在无向图上。在本文中，我们提出了MagNet，这是一种基于复杂的Hermitian矩阵（称为磁拉普拉斯算子）的有向图GNN。该矩阵在其条目的幅度中对无向几何结构进行编码，并在其相位中对方向信息进行编码。一个“电荷”参数调谐光谱信息之间的变化有向循环。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，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的基本原理是，它可以适应其他GNN架构。
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 MagNet, 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.