Hyperbolic Graph Wavelet Neural Network

IF 6.6 1区 计算机科学 Q1 Multidisciplinary
Wenjie Zheng;Guofeng Zhang;Xiaoran Zhao;Zhikang Feng;Lekang Song;Huaizhen Kou
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引用次数: 0

Abstract

Graph neural networks (GNNs), grounded in spatial or spectral domains, have achieved remarkable success in learning graph representations in Euclidean space. Recent advances in spatial GNNs reveal that embedding graph nodes with hierarchical structures into hyperbolic space is more effective, reducing distortion compared to Euclidean embeddings. However, extending spectral GNNs to hyperbolic space remains several challenges, particularly in defining spectral graph convolution and enabling message passing within the hyperbolic geometry. To address these challenges, we propose the hyperbolic graph wavelet neural network (HGWNN), a novel approach for modeling spectral GNNs in hyperbolic space. Specifically, we first define feature transformation and spectral graph wavelet convolution on the hyperboloid manifold using exponential and logarithmic mappings, without increasing model parameter complexity. Moreover, we enable non-linear activation on the Poincaré manifold and efficient message passing via diffeomorphic transformations between the hyperboloid and Poincaré models. Experiments on four benchmark datasets demonstrate the effectiveness of our proposed HGWNN over baseline systems.
双曲图小波神经网络
基于空间域或谱域的图神经网络(gnn)在学习欧几里得空间中的图表示方面取得了显著的成功。空间gnn的最新进展表明,与欧几里得嵌入相比,将具有层次结构的图节点嵌入双曲空间更有效,减少了失真。然而,将谱gnn扩展到双曲空间仍然存在一些挑战,特别是在定义谱图卷积和在双曲几何中实现信息传递方面。为了解决这些挑战,我们提出了双曲图小波神经网络(HGWNN),这是一种在双曲空间中建模谱gnn的新方法。具体来说,我们首先在不增加模型参数复杂度的情况下,使用指数和对数映射在双曲面流形上定义特征变换和谱图小波卷积。此外,我们实现了在庞卡罗莱流形上的非线性激活,并通过双曲面模型和庞卡罗莱模型之间的微分同构变换实现了有效的消息传递。在四个基准数据集上的实验证明了我们所提出的HGWNN优于基线系统的有效性。
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来源期刊
Tsinghua Science and Technology
Tsinghua Science and Technology COMPUTER SCIENCE, INFORMATION SYSTEMSCOMPU-COMPUTER SCIENCE, SOFTWARE ENGINEERING
CiteScore
10.20
自引率
10.60%
发文量
2340
期刊介绍: Tsinghua Science and Technology (Tsinghua Sci Technol) started publication in 1996. It is an international academic journal sponsored by Tsinghua University and is published bimonthly. This journal aims at presenting the up-to-date scientific achievements in computer science, electronic engineering, and other IT fields. Contributions all over the world are welcome.
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