MODELING OF THE SPATIAL DISTRIBUTION OF CHROME AND MANGANESE IN SOIL: SELECTION OF A TRAINING SUBSET

Abstract

The selection of a method for dividing the raw data into training and test subsets in models based on artificial neural networks (ANN) is an insufficiently studied problem of continuous space-time field interpolation. In particular, selecting the best training subset for modeling the spatial distribution of elements in the topsoil is not a trivial task, since the sampling points are not equivalent. They contain a different amount of “information” in point of each specific model, therefore, when modeling, it is advisable to use most of the points containing information which is “useful” for this model. Incorrect data division may lead to inaccurate and highly variable model characteristics, high variance and bias in the generated results. The raw data included contents of chromium (Cr) and manganese (Mn) in the topsoil in residential areas of Noyabrsk (a city in Russian subarctic zone). A three-stage algorithm for extracting raw data with a division into training and test subsets has been developed for modeling the spatial distribution of heavy metals. According to the algorithm, the initial data set was randomly divided into training and test subsets. For each training subset, an ANN based on multilayer perceptron (MLP) was built and trained. MLP was used to model the spatial distribution of heavy metals in the upper soil layer, which took into account spatial heterogeneity and learning rules. The MLP structure was chosen by minimizing the root mean square error (RMSE). The networks with the lowest RMSE were selected, and the number of hits into the training subset of each point in space was calculated. By the number of hits in the training subset, all points were divided into three classes: “useful”, “ordinary” and “useless”. Taking this information into account, at the stage of the raw data division it possible to increase the accuracy of the predictive model.