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Applications of machine learning methods in spatial analysis of Zinc Data

Germanou Maria-Konstantina

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Summary

This thesis explores the integration of geostatistical methods with advanced machine learning techniques for improving spatial data modeling with emphasis on the predic- tion of zinc concentration. It also aims to establish the effectiveness of these methods in refining uncertainty quantification and providing insights into complex spatial depen- dencies. The core methodologies that are employed include Ordinary Kriging (OK), Gaussian Process Regression (GPR), and Self-Organizing Maps (SOMs), selected for their complementary strengths in spatial modeling. OK is a powerful geostatistical baseline that uses variogram modeling to capture spatial correlations, thus provid- ing consistent and interpretable predictions. However, because of the assumptions of linearity it offers limited adaptability for non-linear or heterogeneous spatial struc- tures. GPR introduces a very flexible, non-parametric approach for modeling complex spatial relationships. GPR with an Automatic Relevance Determination Exponential Kernel captures anisotropic spatial dependencies by modeling correlations between lo- cations as a function of their separation distance. The optimized parameters of the kernel through Maximum Likelihood Estimation, ensure accurate predictions of zinc concentrations at unsampled locations and estimates of prediction uncertainty. More- over, SOMs adds value by providing localized neuron-based data clustering leading to neighborhood-specific kriging predictions and enhancing localized anomaly detection capability (although its overall accuracy is similar to that of OK). These results high- light that OK, GPR, and SOM provide an efficient and flexible framework for analyzing spatial data. The combination of these approaches, harmoniously balances predictive accuracy, uncertainty quantification, and detection of local patterns, thus offering a comprehensive toolkit to address challenging tasks of spatial modeling. In conclusion, this thesis demonstrates how geostatistical techniques in combination with machine learning techniques can push the frontiers of spatial analysis. In addition, refining methodological approaches and optimization of parameters will make such techniques amenable to better decision-making for environmental monitoring and resource man- agement. Future work could also focus on further enhancements of these methods or explore novel hybrid models for answering challenges in spatial data analysis.

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