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Hyperbolic Graph Wavelet Neural Network
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DOI：10.26599/TST.2024.9010032.png)
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Abstract
En 中文
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 Poincar & eacute; manifold and efficient message passing via diffeomorphic transformations between the hyperboloid and Poincar & eacute; models. Experiments on four benchmark datasets demonstrate the effectiveness of our proposed HGWNN over baseline systems.
Keywords:
Manifolds
Wavelet transforms
Geometry
Convolution
Message passing
Nonlinear distortion
Benchmark testing
Graph neural networks
Complexity theory
Spectral analysis
graph neural network (GNN)
hyperbolic embedding
hyperbolic space
Journal
T
IF:
3.5
Papers:
987
Citations:
2.5K