Geom-GCN: Geometric Graph Convolutional Networks

TL;DR

Geom-GCN introduces a geometric aggregation scheme for graph neural networks that preserves structural information and captures long-range dependencies, achieving state-of-the-art results on various graph datasets.

Contribution

The paper proposes a novel geometric aggregation scheme for GCNs that addresses structural information loss and long-range dependency issues, enhancing graph representation learning.

Findings

Achieved state-of-the-art performance on multiple graph datasets.

Demonstrated the effectiveness of geometric aggregation in preserving structural info.

Improved long-range dependency modeling in disassortative graphs.

Abstract

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.