Estimating the Prediction Performance of Spatial Models via Spatial k-Fold Cross Validation

Abstract

In machine learning one often assumes the data are independent when evaluating model performance. However, this rarely holds in practise. Geographic information data sets are an example where the data points have stronger dependencies among each other the closer they are geographically. This phenomenon known as spatial autocorrelation (SAC) causes the standard cross validation (CV) methods to produce optimistically biased prediction performance estimates for spatial models, which can result in increased costs and accidents in practical applications. To overcome this problem we propose a modified version of the CV method called spatial k-fold cross validation (SKCV), which provides a useful estimate for model prediction performance without optimistic bias due to SAC. We test SKCV with three real world cases involving open natural data showing that the estimates produced by the ordinary CV are up to 40% more optimistic than those of SKCV. Both regression and classification cases are considered in our experiments. In addition, we will show how the SKCV method can be applied as a criterion for selecting data sampling density for new research area.