Geom-GCN: Geometric Graph Convolutional Networks
This addresses limitations in graph neural networks for applications like social networks or bioinformatics, but it is incremental as it builds on existing geometric ideas.
The paper tackled the problem of message-passing neural networks losing structural information in neighborhoods and lacking long-range dependencies in disassortative graphs, resulting in Geom-GCN achieving state-of-the-art performance on a wide range of open graph datasets.
Message-passing neural networks (MPNNs) have been successfully applied to representation learning on graphs in a variety of real-world applications. However, two fundamental weaknesses of MPNNs' aggregators limit their ability to represent graph-structured data: losing the structural information of nodes in neighborhoods and lacking the ability to capture long-range dependencies in disassortative graphs. Few studies have noticed the weaknesses from different perspectives. From the observations on classical neural network and network geometry, we propose a novel geometric aggregation scheme for graph neural networks to overcome the two weaknesses. The behind basic idea is the aggregation on a graph can benefit from a continuous space underlying the graph. The proposed aggregation scheme is permutation-invariant and consists of three modules, node embedding, structural neighborhood, and bi-level aggregation. We also present an implementation of the scheme in graph convolutional networks, termed Geom-GCN (Geometric Graph Convolutional Networks), to perform transductive learning on graphs. Experimental results show the proposed Geom-GCN achieved state-of-the-art performance on a wide range of open datasets of graphs. Code is available at https://github.com/graphdml-uiuc-jlu/geom-gcn.