Geographically weighted regression with the integration of machine learning for spatial prediction

Conventional methods of machine learning have been widely used to generate spatial prediction models because such methods can adaptively learn the mapping relationships among spatial data with limited prior knowledge. However, the direct application of these methods to build a global model without considering spatial heterogeneity cannot accurately describe the local relationships among spatial variables, which might lead to inaccurate predictions. To avoid these shortcomings, we have presented a unified framework for handling spatial heterogeneity by incorporating the geographically weighted scheme into machine learning methods. The proposed framework has the potential to extend the existing models of machine learning for analysing heterogeneous spatial data. Furthermore, geographically weighted support vector regression (GWSVR) has been introduced as an implementation of the proposed framework. Experimental studies on environmental datasets were used to test the ability of model predictions. The results show that the mean absolute percentage error, normalized mean square error, and relative error percentage of the GWSVR model are 0.436, 0.903, and 0.558, respectively, when analysing soil metal chromium (Cr) concentrations and 0.221, 0.287, and 0.206, respectively, when predicting PM_2.5 concentrations; these values are lower than those obtained using support vector regression, geographically weighted regression (GWR), and GWR-kriging models. These case studies have proved the validity and feasibility of the proposed framework.