Combining spatial autocorrelation with machine learning increases prediction accuracy of soil heavy metals

A hybrid approach was proposed to simulate the spatial distribution of a number of heavy metals in the surface layer of the soil. The idea of the method is to simulate a nonlinear large-scale trend using an artificial neural network (ANN) and the subsequent modelling of the residuals by geostatistical methods. A comparison was made with the basic modelling methods based on ANN: generalised regression neural network (GRNN) and multilayer perceptron (MLP). The raw data for the surface layer modelling of Cuprum (Cu), Manganese (Mn) and Niccolum (Ni) were obtained as a result of the soil screening in the subarctic city Novy Urengoy, Russia. The ANN structures were selected by the computer simulation based on the root mean square error (RMSE) minimization. The predictive accuracy of each selected approach was verified by the correlation coefficient, the coefficient of determination, RMSE, Willmott's index of agreement (d), a ratio of performance to interquartile distance (RPIQ) between the prediction and raw data from the test data set. It was confirmed that the use of the hybrid approach provides an increase in prediction accuracy in comparison with the basic ANN models. The proposed hybrid approach for each element showed the best predictive accuracy in comparison with other models based on ANN.