Higher-order Sparse Convolutions in Graph Neural Networks
This addresses the challenge of infeasible higher-order methods for large-scale graphs in GNNs, though it appears incremental as it builds on existing convolution techniques.
The paper tackled the problem of capturing higher-order relationships in Graph Neural Networks (GNNs) for large-scale graphs by introducing a new higher-order sparse convolution based on the Sobolev norm, resulting in competitive performance in semi-supervised learning applications compared to state-of-the-art methods.
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.