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

Abstract

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.

Importance of spatial predictor variable selection in machine learning applications – Moving from data reproduction to spatial prediction

“…However, predictor variables that describe the spatial location rather than the environmental properties are commonly included. Spatial coordinates are used especially often (Li et al, 2011;Langella et al, 2010;Shi et al, 2015;Janatian et al, 2017;Walsh et al, 2017;Jing et al, 2016;Wang et al, 2017;Georganos et al, 2019). Distances to certain points (e.g.…”

Modelling the Wealth Index of Demographic and Health Surveys within Cities Using Very High-Resolution Remotely Sensed Information

“…As an evaluation metric to select the best model we selected the root mean squared error (RMSE) coming from the out-of-bag (OOB) predictions of the random forest (RF) regressor. RF is a decision-tree ensemble machine learning algorithm that has been shown resilient to overfitting and robust to model the complex non-linear relationships among satellite derived features and socio-economic and demographic indicators [16,30,33]. For optimizing the parameters of the three final RF models (P0, P1, P2) we used the cross-validation functions of the "caret" package in R statistical software [34,35].…”

“…The LULC products are publicly available with a LC map at 0.5 resolution and a LU map at the street block level ( Figure 4) [18,28]. These products have been successfully used for urban local climate zone validation [29] and population models at similar geographical scales [16,30]. The overall accuracy of the LC and LU maps was 89.5% and 79%, respectively [16].…”

Machine learning for digital soil mapping: applications, challenges and suggested solutions

“…have tested random forest for different scenarios of spatial autocorrelation in the observations and confirmed that the presence of spatial autocorrelation leads to high variance of the residuals. ML algorithms accounting for autocorrelated observations have recently been formulated, such as geographical random forest(Georganos et al, 2019), or spatial ensemble techniques(Jiang et al, 2017). The two methods boil down to geographically weighted regression by fitting spatially local sub-models using only neighbouring observations Jiang et al (2017).…”

“…The two methods boil down to geographically weighted regression by fitting spatially local sub-models using only neighbouring observations Jiang et al (2017). decomposed the area into geographic disjoint sub-areas, and fitted a local model in each sub-area Georganos et al (2019).…”