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arXiv · 2302.10505

Higher-order Sparse Convolutions in Graph Neural Networks

Jhony H. Giraldo·Sajid Javed·Arif Mahmood·Fragkiskos D. Malliaros·Thierry Bouwmans
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Abstract

Graph Neural Networks (GNNs) have been applied to many problems in computer sciences. Capturing higher-order relationships between nodes is crucial to increase the expressive power of GNNs. However, existing methods to capture these relationships could be infeasible for large-scale graphs. In this work, we introduce a new higher-order sparse convolution based on the Sobolev norm of graph signals. Our Sparse Sobolev GNN (S-SobGNN) computes a cascade of filters on each layer with increasing Hadamard powers to get a more diverse set of functions, and then a linear combination layer weights the embeddings of each filter. We evaluate S-SobGNN in several applications of semi-supervised learning. S-SobGNN shows competitive performance in all applications as compared to several state-of-the-art methods.

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Jhony H. Giraldo, Sajid Javed, Arif Mahmood, Fragkiskos D. Malliaros, Thierry Bouwmans. 2023-02-21. Higher-order Sparse Convolutions in Graph Neural Networks. https://arxiv.org/abs/2302.10505

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