An ensemble spatial prediction method considering geospatial heterogeneity

Ensemble learning synthesizes the advantages of different models and has been widely applied in the field of spatial prediction. However, the nonlinear constraints of spatial heterogeneity on the model ensemble process make it difficult to adaptively determine the ensemble weights, greatly limiting the predictive ability of the ensemble learning model. This paper therefore proposes a novel geographical spatial heterogeneous ensemble learning method (GSH-EL). Firstly, the geographically weighted regression model, geographically optimal similarity model, and random forest model are used as three base learners to express local spatial heterogeneity, global feature correlation, and nonlinear relationship of geographic elements, respectively. Then, a spatially weighted ensemble neural network module (SWENN) of GSH-EL is proposed to express spatial heterogeneity by exploring the complex nonlinear relationship between the spatial proximity and ensemble weights. Finally, the outputs of the three base learners are combined with the spatial heterogeneous ensemble weights from SWENN to obtain the spatial prediction results. The proposed method is validated on the PM2.5 air quality and landslide dataset in China, both of which obtain more accurate prediction results than the existing ensemble learning strategies. The results confirm the need to accurately express spatial heterogeneity in the model ensemble process.