Hongbin Pei, Bingzhe Wei, Kevin Chen-Chuan Chang, Yu Lei, Bo Yang
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.
| Task | Dataset | Metric | Value | Model |
|---|---|---|---|---|
| Node Classification | Wisconsin | Accuracy | 64.12 | Geom-GCN-P |
| Node Classification | Wisconsin | Accuracy | 58.24 | Geom-GCN-I |
| Node Classification | Wisconsin | Accuracy | 56.67 | Geom-GCN-S |
| Node Classification | Texas (60%/20%/20% random splits) | 1:1 Accuracy | 67.57 | Geom-GCN* |
| Node Classification | Squirrel | Accuracy | 38.14 | Geom-GCN-P |
| Node Classification | Squirrel | Accuracy | 36.24 | Geom-GCN-S |
| Node Classification | Squirrel | Accuracy | 33.32 | Geom-GCN-I |
| Node Classification | Squirrel (60%/20%/20% random splits) | 1:1 Accuracy | 38.14 | Geom-GCN* |
| Node Classification | Texas | Accuracy | 67.57 | Geom-GCN-P |
| Node Classification | Texas | Accuracy | 59.73 | Geom-GCN-S |
| Node Classification | Texas | Accuracy | 57.58 | Geom-GCN-I |
| Node Classification | Cornell | Accuracy | 60.81 | Geom-GCN-P |
| Node Classification | Cornell | Accuracy | 56.76 | Geom-GCN-I |
| Node Classification | Cornell | Accuracy | 55.68 | Geom-GCN-S |
| Node Classification | Chameleon (60%/20%/20% random splits) | 1:1 Accuracy | 60.9 | Geom-GCN* |
| Node Classification | Chameleon | Accuracy | 60.9 | Geom-GCN-P |
| Node Classification | Chameleon | Accuracy | 60.31 | Geom-GCN-I |
| Node Classification | Chameleon | Accuracy | 59.96 | Geom-GCN-S |
| Node Classification | Cornell (60%/20%/20% random splits) | 1:1 Accuracy | 60.81 | Geom-GCN* |
| Node Classification | PubMed (60%/20%/20% random splits) | 1:1 Accuracy | 90.05 | Geom-GCN* |
| Node Classification | Film (60%/20%/20% random splits) | 1:1 Accuracy | 31.63 | Geom-GCN* |
| Node Classification | Wisconsin (60%/20%/20% random splits) | 1:1 Accuracy | 64.12 | Geom-GCN* |
| Node Classification | CiteSeer (60%/20%/20% random splits) | 1:1 Accuracy | 77.99 | Geom-GCN* |
| Node Classification | Actor | Accuracy | 31.63 | Geom-GCN-P |
| Node Classification | Actor | Accuracy | 30.3 | Geom-GCN-S |
| Node Classification | Actor | Accuracy | 29.09 | Geom-GCN-I |
| Node Classification | Cora (60%/20%/20% random splits) | 1:1 Accuracy | 85.27 | Geom-GCN* |
| Node Classification | Cornell (60%/20%/20% random splits) | 1:1 Accuracy | 60.81 | Geom-GCN* |
| Node Classification | Chameleon(60%/20%/20% random splits) | 1:1 Accuracy | 60.9 | Geom-GCN* |
| Node Classification | Texas(60%/20%/20% random splits) | 1:1 Accuracy | 67.57 | Geom-GCN* |
| Node Classification | Wisconsin(60%/20%/20% random splits) | 1:1 Accuracy | 64.12 | Geom-GCN* |