Positional Encoder Graph Neural Networks for Geographic Data

TL;DR

This paper introduces PE-GNN, a novel graph neural network framework that explicitly models complex non-Euclidean spatial structures using positional encoding and spatial autocorrelation, improving geographic data modeling.

Contribution

PE-GNN incorporates spatial context and autocorrelation explicitly into GNNs, advancing the modeling of non-Euclidean geographic data beyond traditional Euclidean-based methods.

Findings

Outperforms state-of-the-art GNNs on spatial interpolation and regression tasks.

Matches the performance of Gaussian processes in spatial interpolation.

Significantly improves spatial data modeling accuracy.

Abstract

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.