L^2GC:Lorentzian Linear Graph Convolutional Networks for Node Classification

TL;DR

This paper introduces Lorentzian linear GCNs that embed node features into hyperbolic space to better capture hierarchical graph structures, achieving state-of-the-art accuracy and faster training times.

Contribution

It proposes a novel Lorentzian linear GCN framework that incorporates hyperbolic space for improved hierarchical data modeling in node classification tasks.

Findings

Achieves 74.7% accuracy on Citeseer

Achieves 81.3% accuracy on PubMed

Training is up to two orders of magnitude faster

Abstract

Linear Graph Convolutional Networks (GCNs) are used to classify the node in the graph data. However, we note that most existing linear GCN models perform neural network operations in Euclidean space, which do not explicitly capture the tree-like hierarchical structure exhibited in real-world datasets that modeled as graphs. In this paper, we attempt to introduce hyperbolic space into linear GCN and propose a novel framework for Lorentzian linear GCN. Specifically, we map the learned features of graph nodes into hyperbolic space, and then perform a Lorentzian linear feature transformation to capture the underlying tree-like structure of data. Experimental results on standard citation networks datasets with semi-supervised learning show that our approach yields new state-of-the-art results of accuracy 74.7$\%$ on Citeseer and 81.3$\%$ on PubMed datasets. Furthermore, we observe that our approach can be trained up to two orders of magnitude faster than other nonlinear GCN models on PubMed dataset. Our code is publicly available at https://github.com/llqy123/LLGC-master.