Support Vector Machines With Uncertainty Option and Incremental Sampling for Kriging

Abstract

ABSTRACTThis paper presents a novel approach to pollution assessment by investigating support vector machines (SVM) with an uncertainty option to overcome the limitations of traditional kriging. While kriging is a major tool for geostatistical modelling, allowing to estimate the distribution of contaminants in a region from a small set of samples, it does not allow to extract also the uncertainty map. An uncertainty map is of great interest, as it allows to identify regions of high uncertainty where one should sample in order to reduce high level of uncertainties. In this paper, we propose two variants of the SVM with an uncertainty option, each using a different hinge loss to improve the accuracy and efficiency. These losses allow to estimate different levels of contaminations, as well as uncertainty, such as the three levels: positive, uncertain and negative, namely for pollution estimation: high‐pollution, uncertain and low‐pollution. In addition to the exploration of SVM variants, we propose an innovative active sample selection strategy based on the uncertainty criterion. This strategy is designed to systematically reduce uncertainties in pollution assessment, thus providing adaptability to dynamic environmental changes. An incremental SVM with an uncertainty option is introduced to further optimise the sample selection process. Furthermore, the decision‐making process is refined through the introduction of a novel three‐hinge loss. The corresponding optimization problem and its resolution allow for a more nuanced contamination assessment with multiple levels of estimation, providing a valuable tool for characterising contamination levels with increased granularity. Extensive experiments on synthetic and real data validate the proposed methodology. Synthetic data simulations assess the quality of the approach, while real data from a two‐dimensional porosity measurement demonstrate practical applicability. This research contributes to the advancement of pollution assessment methodologies, providing an adaptable solution for environmental monitoring.