Estimation of Spatial Distribution Using the Gaussian Mixture Model with Multivariate Geoscience Data

Abstract

Spatial estimation of geoscience data (geo-data) is challenging due to spatial heterogeneity, data scarcity, and high dimensionality. A novel spatial estimation method is needed to consider the characteristics of geo-data. In this study, we proposed the application of Gaussian Mixture Model (GMM) among machine learning algorithms with multivariate data for robust spatial predictions. The performance of the proposed approach was tested through soil chemical concentration data from a former smelting area. The concentrations of As and Pb determined by ex-situ ICP-AES were the primary variables to be interpolated, while the other metal concentrations by ICP-AES and all data determined by in-situ portable X-ray fluorescence (PXRF) were used as auxiliary variables in GMM and ordinary cokriging (OCK). Among the multidimensional auxiliary variables, important variables were selected using a variable selection method based on the random forest. The results of GMM with important multivariate auxiliary data decreased the root mean-squared error (RMSE) down to 0.11 for As and 0.33 for Pb and increased the correlations (r) up to 0.31 for As and 0.46 for Pb compared to those from ordinary kriging and OCK using univariate or bivariate data. The use of GMM improved the performance of spatial interpretation of anthropogenic metals in soil. The multivariate spatial approach can be applied to understand complex and heterogeneous geological and geochemical features.

Spatial Prediction of Soil Contaminants Using a Hybrid Random Forest–Ordinary Kriging Model

“…2024, 14, 1666 2 of 19 of data for a predictive map is unclear, making it important to maximize utility while minimizing opportunity costs. Although producing highly reliable predictive maps based on small amounts of sampled distribution data is crucial, the techniques used to create these maps have inherent limitations, thereby necessitating a thorough evaluation and analysis of the influencing factors to minimize errors and generate highly reliable maps [1].…”

Optimization of Soil Contamination Distribution Prediction Error using Geostatistical Technique and Interpretation of Contributory Factor Based on Machine Learning Algorithm

“…• Soil contamination map with the lowest prediction errors was generated using ordinary kriging technique depending on the numerous combination of different options and set values. (Jung and Lee, 2001, Lee et al, 2003, Jung et al, 2004 (Kim et al, 2022). and Choi, 2008, Kim et al, 2012a, Kim et al, 2012b.…”