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
this https URL

本文提出了一种基于 Lorentzian 线性 GCN 的新框架，将学习到的图节点特征映射到双曲空间，并进行 Lorentzian 线性特征转换以捕捉数据的树状层次结构，并通过在标准引文网络数据集上的半监督学习实验证明，我们的方法在 Citeseer 达到了 74.7% 的准确率，在 PubMed 达到了 81.3% 的准确率，并且观察到在 PubMed 数据集上，我们的方法训练速度比其他非线性 GCN 模型快了两个数量级。