  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.
