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 practice. Geographic information datasets 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.

KEYWORDS:

• Spatio-temporal data modelling
• spatial data mining
• geographic information systems
• geographic information science

Acknowledgments

We want to thank the Natural Resources Institute Finland (LUKE), Geological Survey of Finland (GTK), Natural Land Survey of Finland (NLS) and Finnish Meteorological Institute (FMI) for providing the datasets. This work was supported by the funding from the Academy of Finland (Grant 295336). The preprocessing of the data was partially funded by the Finnish Funding Agency for Innovation (Tekes).

Disclosure statement

No potential conflict of interest was reported by the authors.

Supplemental Material

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Additional information

Funding

This work was supported by the funding from the Academy of Finland [Grant 295336]. The preprocessing of the data was partially funded by the Finnish Funding Agency for Innovation (Tekes).