A wide variety of spatially explicit modeling algorithms has recently mushroomed in geoinformation research. These algorithms establish local models with data from spatially confined subsets, thereby offering a new impetus for addressing the issue of spatiotemporal non-stationarity. However, a significant challenge persists in literature that local models are primarily predicated on linear assumptions, limiting their capacity to capture the non-linear relationships prevalent in real-world geographical phenomena. This study remedies this gap through proposing a novel approach that integrates the bagging and stacking approaches of ensemble learning into the spatially explicit modeling framework. We specifically develop the SpatioTemporal Random Forest (STRF) and SpatioTemporal Stacking Tree (STST) algorithms11Python package link: https://github.com/46319943/GeoRegression., which capture and interpret the non-linearity in the spatial and temporal context more effectively. Additionally, we introduce the ‘local importance score’ and ‘spatiotemporally accumulated local effects’ as novel interpretable metrics for visualizing and unraveling the dynamics of non-stationarity in spatial analyses. Simulation and real data experiments validate that the STRF and STST outperform over traditional spatially explicit modeling algorithms to a large content. This study contributes to the methodological innovation of spatially explicit modeling by bringing the nonlinearity in spatiotemporal non-stationarity to the fore.

中文翻译：

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时空随机森林和时空堆叠树：一种新颖的空间显式集成学习方法，用于在时空非平稳性中对非线性进行建模


最近，地理信息研究中涌现了各种各样的空间显式建模算法。这些算法使用来自空间受限子集的数据建立局部模型，从而为解决时空非平稳性问题提供了新的动力。然而，文献中仍然存在一个重大挑战，即局部模型主要基于线性假设，这限制了它们捕捉现实世界地理现象中普遍存在的非线性关系的能力。本研究通过提出一种新的方法来弥补这一差距，该方法将集成学习的 bagging 和 stacking 方法集成到空间显式建模框架中。我们专门开发了时空随机森林 （STRF） 和时空堆叠树 （STST） 算法11Python 包 link： https://github.com/46319943/GeoRegression.，它们可以更有效地捕获和解释空间和时间上下文中的非线性。此外，我们引入了 “局部重要性得分 ”和 “时空累积的局部效应 ”作为新颖的可解释指标，用于可视化和解开空间分析中非平稳性的动态。仿真和真实数据实验验证了 STRF 和 STST 在大型内容方面的性能优于传统的空间显式建模算法。本研究通过将时空非平稳性的非线性置于前台，为空间显式建模的方法创新做出了贡献。