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.
@article{arxiv.2302.10505,
title = {Higher-order Sparse Convolutions in Graph Neural Networks},
author = {Jhony H. Giraldo and Sajid Javed and Arif Mahmood and Fragkiskos D. Malliaros and Thierry Bouwmans},
journal= {arXiv preprint arXiv:2302.10505},
year = {2023}
}
Comments
Accepted in IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP) 2023