L^2GC:Lorentzian Linear Graph Convolutional Networks for Node Classification
This addresses the challenge of modeling hierarchical structures in real-world graph datasets for researchers and practitioners in graph machine learning, representing an incremental improvement by integrating hyperbolic geometry into existing linear GCN frameworks.
The paper tackles the problem of node classification in graph data by introducing hyperbolic space into linear Graph Convolutional Networks to capture tree-like hierarchical structures, achieving state-of-the-art accuracy of 74.7% on Citeseer and 81.3% on PubMed datasets and training up to two orders of magnitude faster than nonlinear models on PubMed.
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.