Incorporating spatial information in machine learning: The Moran eigenvector spatial filter approach

Spatial statistical models are highly effective for modeling geospatial data as they consider spatial information of geographic spaces and other non-spatial covariates, enabling them to minimize spatial autocorrelation by addressing spatial dependence. In contrast, machine learning (ML) models are highly effective for predicting non-spatial data, but they are not as effective for modeling and predicting geospatial data because of spatial autocorrelation issues. One of the frequently reported limitations of ML models for geospatial data modeling is that there is no standard method of incorporating spatial information of geographic space into the model, and consequently they cannot minimize spatial autocorrelation. In this study, we have presented a local spatial information-embedded ML method capable of minimizing spatial autocorrelation by addressing spatial dependence while predicting a geospatial phenomenon. Our study applied the eigenvector spatial filter method to extract approximated eigenvectors from spatial coordinates and embed them within ML models as a set of vectors along with the selected non-spatial covariates. We have also presented a comparison of relative prediction performance between traditional spatial statistical and ML-based models. The experiment demonstrates that incorporating spatially filtered eigenvectors to represent spatial information in ML model specification significantly improves the prediction performance.