Geom-GCN: Geometric Graph Convolutional Networks

GraphDML-UIUC-JLU: Graph-structured Data Mining and Machine Learning at University of Illinois at Urbana-Champaign (UIUC) and Jilin University (JLU)

Abstract

Message-passing neural networks (MPNNs) have been successfully applied in a wide variety of applications in the real world. 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, 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

Required Packages

Python 3.7
PyTorch 1.7.1 Cuda 9.2
NetworkX 2.5
Deep Graph Library 0.3 Cuda 9.2
Numpy 1.19.2
Scipy 1.5.2
Scikit-Learn 0.23.2
Tensorflow 1.14.0
TensorboardX 2.1

Table 3

To replicate the Geom-GCN results from Table 3, run

bash NewTableThreeGeomGCN_runs.txt

To replicate the GCN results from Table 3, run

bash NewTableThreeGCN_runs.txt

To replicate the GAT results from Table 3, run

bash NewTableThreeGAT_runs.txt

Results will be stored in runs.

Combination of Embedding Methods

To replicate the results for utilizing all embedding methods simultaneously, run

bash ExperimentTwoAllGeomGCN_runs.txt