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. 2021 Dec:34:27003-27015.

MagNet: A Neural Network for Directed Graphs

Xitong Zhang  1 , Yixuan He  2 , Nathan Brugnone  1   3 , Michael Perlmutter  4 , Matthew Hirn  1   5   6
Affiliations

MagNet: A Neural Network for Directed Graphs

Xitong Zhang et al. Adv Neural Inf Process Syst. 2021 Dec.

Abstract

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.

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Figures

Figure 1:
Figure 1:
MagNet (L = 2) applied to node classification.
Figure 2:
Figure 2:
Meta-graphs for the synthetic data sets.
Figure 3:
Figure 3:
Node classification accuracy. Error bars are one standard error. MagNet is bold red.
See this image and copyright information in PMC

References

    1. Atwood James and Towsley Don. Diffusion-convolutional neural networks. In Lee D, Sugiyama M, Luxburg U, Guyon I, and Garnett R, editors, Advances in Neural Information Processing Systems, volume 29, pages 1993–2001. Curran Associates, Inc., 2016.
    1. Belkin Mikhail and Niyogi Partha. Laplacian eigenmaps for dimensionality reduction and data representation. Neural computation, 15(6):1373–1396, 2003.
    1. Benson Austin R, Gleich David F, and Leskovec Jure. Higher-order organization of complex networks. Science, 353(6295):163–166, 2016. - PMC - PubMed
    1. Bojchevski Aleksandar and Günnemann Stephan. Deep Gaussian embedding of graphs: Unsupervised inductive learning via ranking. In ICLR Workshop on Representation Learning on Graphs and Manifolds, 2017.
    1. Bovet Alexandre and Grindrod Peter. The activity of the far right on telegram. https://www.researchgate.net/publication/346968575_The_Activity_of_the_F..., 2020.

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