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<p>This study evaluates geographically weighted (GW) machine-learning models and, for the first time, introduces and empirically assesses spatially multiscale geographically weighted (SM-GW) models, in which kernel bandwidths vary by location. We compare Linear Regression, Random Forest, Support Vector Machines, and Extreme Gradient Boosting in global form, with single-bandwidth GW variants and SM-GW extensions, using 135 synthetic datasets that systematically vary spatial autocorrelation, relationship complexity, and the magnitude and form of spatial non-stationarity. Results show that single-bandwidth GW models consistently outperform global baselines when spatial dependence and non-stationarity are pronounced, with the largest gains observed for Linear Regression under moderate nonlinearity and high autocorrelation. Random Forest, Support Vector Machines, and Extreme Gradient Boosting also benefit from spatial weighting, though their inherent flexibility limits improvement. Adding geographic coordinates to global models proves unreliable and often degrades accuracy. SM-GW models do not consistently exceed single bandwidth formulations due to instability from isotropic neighborhoods, local bandwidth variance, and interpolation effects. However, SM-GW bandwidth surfaces provide valuable diagnostic insight into spatial variation in interaction scales. Overall, single-bandwidth GW models offer the most robust balance between accuracy and stability, while SM-GW models extend the methodological toolkit by making spatial scale variation explicit.</p>

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Efficiency of spatially multiscale machine learning models in addressing spatial non-stationarity and enhancing predictive accuracy

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月1日

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  • Daniel Bicák,
  • Lukáš Brodský

摘要

This study evaluates geographically weighted (GW) machine-learning models and, for the first time, introduces and empirically assesses spatially multiscale geographically weighted (SM-GW) models, in which kernel bandwidths vary by location. We compare Linear Regression, Random Forest, Support Vector Machines, and Extreme Gradient Boosting in global form, with single-bandwidth GW variants and SM-GW extensions, using 135 synthetic datasets that systematically vary spatial autocorrelation, relationship complexity, and the magnitude and form of spatial non-stationarity. Results show that single-bandwidth GW models consistently outperform global baselines when spatial dependence and non-stationarity are pronounced, with the largest gains observed for Linear Regression under moderate nonlinearity and high autocorrelation. Random Forest, Support Vector Machines, and Extreme Gradient Boosting also benefit from spatial weighting, though their inherent flexibility limits improvement. Adding geographic coordinates to global models proves unreliable and often degrades accuracy. SM-GW models do not consistently exceed single bandwidth formulations due to instability from isotropic neighborhoods, local bandwidth variance, and interpolation effects. However, SM-GW bandwidth surfaces provide valuable diagnostic insight into spatial variation in interaction scales. Overall, single-bandwidth GW models offer the most robust balance between accuracy and stability, while SM-GW models extend the methodological toolkit by making spatial scale variation explicit.