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

Abstract

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.

Fusion and classification algorithm of octacalcium phosphate production based on XRD and FTIR data

“…For example, each class could be rotated concerning the other to occupy different portions of the Cartesian plane; in this way, the classes could create a non-overlapping map with well-defined point clouds. One approach for reducing data structure dependence could be applying spatial filters 25 – 28 paired with a transformation highlighting the presence of clusters. These two methods applied in sequence to the data might facilitate the identification of a decision boundary for scoring OCP production phases.…”

“…The first and last eigenvectors of P according to the eigenvalues could be selected as spatial filters. Similar method based on eigenvectors was applied on other disciplines to evaluate spatial dependence 26 , 28 , 59 – 61 .…”

Quantifying urban three-dimensional building form effects on land surface temperature: a case study of Beijing, China

“…This methodology incorporates the impact of geographical location on the forecasting outcomes, so capturing the intricate and nonlinear associations with greater efficacy. Although this approach may not completely mimic the spatial weight matrix found in spatial models, it offers a way to describe spatial dependencies and perhaps improve the predictive accuracy of the model 38 …”

“…Although this approach may not completely mimic the spatial weight matrix found in spatial models, it offers a way to describe spatial dependencies and perhaps improve the predictive accuracy of the model. 38…”

A Decision Rule and Machine Learning-Based Hybrid Approach for Automated Land-Cover Type Local Climate Zones (LCZs) Mapping Using Multi-Source Remote Sensing Data

“…Moreover, several studies have used commercial satellite/Lidar derived plant height data to distinguish low/high plant types which are not cost-effective and efficient solution and may not be adopted at the region/global scale [17], [18]. Another important limitation isprevious studies overlooked spatial dependence property of geospatial data [19], [20]. In other words, previous studies overlooked Tobler's first law of geography: "everything is related to everything else, but near things are more related than distant things" [21].…”