Tangent Space-Free Lorentz Spatial Temporal Graph Convolution Networks

Spatial Temporal Graph Convolution Networks (ST-GCNs) have been proposed to embed spatio-temporal graphs. However, these networks used the Euclidean space as the embedding space which does not exploit the structure of the embedded graphs. Euclidean space has been shown not to be the ideal space for embedding graphs especially with tree-like structures. In this work, we make use of hyperbolic geometry and introduce a compact tangent space-free Lorentz ST-GCN and call it LSTGCN that perform the network operations directly on the manifold without resorting to the tangent space. The network uses spatial and temporal modules to propagate features between adjacent nodes in both, the spatial domain and the temporal domain, respectively. In addition, we introduce an attention module which can automatically determine the similarity of nodes without the need for the graph adjacency matrix. Experiments have been conducted on traffic flow forecasting tasks to show the effectiveness of the proposed compact Lorentz model.