Geographical random forests: a spatial extension of the random forest algorithm to address spatial heterogeneity in remote sensing and population modelling

Machine learning algorithms such as Random Forest (RF) are being increasingly applied on traditionally geographical topics such as population estimation. Even though RF is a well performing and generalizable algorithm, the vast majority of its implementations is still 'aspatial' and may not address spatial heterogenous processes. At the same time, remote sensing (RS) data which are commonly used to model population can be highly spatially heterogeneous. From this scope, we present a novel geographical implementation of RF, named Geographical Random Forest (GRF) as both a predictive and exploratory tool to model population as a function of RS covariates. GRF is a disaggregation of RF into geographical space in the form of local sub-models. From the first empirical results, we conclude that GRF can be more predictive when an appropriate spatial scale is selected to model the data, with reduced residual autocorrelation and lower Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) values. Finally, and of equal importance, GRF can be used as an effective exploratory tool to visualize the relationship between dependent and independent variables, highlighting interesting local variations and allowing for a better understanding of the processes that may be causing the observed spatial heterogeneity.