Positional Encoder Graph Neural Networks for Geographic Data
This addresses the challenge of handling non-Euclidean spatial structures in geographic data for applications like spatial interpolation and regression, representing an incremental improvement over existing GNN methods.
The paper tackles the problem of modeling complex non-Euclidean spatial data like road networks with graph neural networks, proposing PE-GNN to incorporate spatial context and correlation, which improves performance over state-of-the-art GNNs and matches Gaussian processes in spatial interpolation tasks.
Graph neural networks (GNNs) provide a powerful and scalable solution for modeling continuous spatial data. However, they often rely on Euclidean distances to construct the input graphs. This assumption can be improbable in many real-world settings, where the spatial structure is more complex and explicitly non-Euclidean (e.g., road networks). Here, we propose PE-GNN, a new framework that incorporates spatial context and correlation explicitly into the models. Building on recent advances in geospatial auxiliary task learning and semantic spatial embeddings, our proposed method (1) learns a context-aware vector encoding of the geographic coordinates and (2) predicts spatial autocorrelation in the data in parallel with the main task. On spatial interpolation and regression tasks, we show the effectiveness of our approach, improving performance over different state-of-the-art GNN approaches. We observe that our approach not only vastly improves over the GNN baselines, but can match Gaussian processes, the most commonly utilized method for spatial interpolation problems.