Heavy metal soil pollution has become a worldwide problems. Accurate predictions of pollution at un-observed locations using a limited number of observations remains a challenge, because of the many natural and human influencing factors and their heterogeneous relationships with contaminations. The availability of related big data gives opportunities to address this challenge. This study proposes a two point machine learning method to fully leverage the spatial relationships and high dimensional ancillary variables to improve the prediction accuracy. It models the difference between paired points, predicts concentration differences between observation points and prediction points, and uses the predicted differences to choose neighbors to predict concentration at prediction points. The method puts forward an innovative way to integrate the first and third law of geography into one in a unified machine learning method. Its performance is illustrated with two studies. It demonstrates that it can greatly improve the prediction accuracy when autocorrelation exists. The method may in the future be applied to spatial prediction of other variables of the earth system, whereas machine learning might be replaced with other supervised learning models. We conclude that our method achieves a higher accuracy as compared to existing methods, with prospects of a wide applicability.

两点机器学习法；,空间插值,空间异质性关系