Modeling spatial heterogeneity in the data generation process is essential for understanding and predicting geographical phenomena. Despite their prevalence in geospatial tasks, neural network models usually assume spatial stationarity, which could limit their performance in the presence of spatial process heterogeneity. By allowing model parameters to vary over space, several approaches have been proposed to incorporate spatial heterogeneity into neural networks. However, current geographically weighting approaches are ineffective on graph neural networks, yielding no significant improvement in prediction accuracy. We assume the crux lies in the over-fitting risk brought by a large number of local parameters. Accordingly, we propose to model spatial process heterogeneity at the regional level rather than at the individual level, which largely reduces the number of spatially varying parameters. We further develop a heuristic optimization procedure to learn the region partition adaptively in the process of model training. Our proposed spatial-heterogeneity-aware graph convolutional network, named RegionGCN, is applied to the spatial prediction of county-level vote share in the 2016 US presidential election based on socioeconomic attributes. Results show that RegionGCN achieves significant improvement over the basic and geographically weighted GCNs. We also offer an exploratory analysis tool for the spatial variation of non-linear relationships through ensemble learning of regional partitions from RegionGCN. Our work contributes to the practice of Geospatial Artificial Intelligence (GeoAI) in tackling spatial heterogeneity.

翻译：在数据生成过程中建模空间异质性对于理解和预测地理现象至关重要。尽管神经网络模型在地理空间任务中应用广泛，但其通常假设空间平稳性，这在空间过程存在异质性的情况下可能限制模型性能。通过允许模型参数随空间变化，已有若干方法尝试将空间异质性融入神经网络。然而，现有地理加权方法在图神经网络上效果有限，未能显著提升预测精度。我们认为问题的核心在于大量局部参数带来的过拟合风险。为此，我们提出在区域层面而非个体层面建模空间过程异质性，从而大幅减少空间变化参数的数量。我们进一步设计了一种启发式优化程序，在模型训练过程中自适应学习区域划分。我们提出的空间异质性感知图卷积网络（RegionGCN）基于社会经济属性，应用于2016年美国总统选举县级投票份额的空间预测。结果表明，RegionGCN相较于基础图卷积网络及地理加权图卷积网络均取得显著改进。我们还通过集成学习RegionGCN的区域划分结果，提供了一种探索非线性关系空间变化的分析工具。本研究为地理空间人工智能（GeoAI）应对空间异质性挑战提供了实践参考。