Groundwater quality assessment using data clustering based on hybrid Bayesian networks
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ORIGINAL PAPER
Groundwater quality assessment using data clustering based on hybrid Bayesian networks Pedro A. Aguilera • Antonio Ferna´ndez Rosa F. Ropero • Luı´s Molina
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Received: 9 May 2012 / Accepted: 4 December 2012 / Published online: 21 December 2012 Ó Springer-Verlag Berlin Heidelberg 2012
Abstract Bayesian networks (BNs) have become a standard in the field of Artificial Intelligence as a means of dealing with uncertainty and risk modelling. In recent years, there has been particular interest in the simultaneous use of continuous and discrete domains, obviating the need for discretization, using so-called hybrid BNs. In these hybrid environments, Mixtures of Truncated Exponentials (MTEs) provide a suitable solution for working without any restriction. The objective of this study is the assessment of groundwater quality through the design and application of a probabilistic clustering, based on hybrid Bayesian networks with MTEs. Firstly, the results obtained allows the differentiation of three groups of sampling points, indicating three different classes of groundwater quality. Secondly, the probability that a sampling point belongs to each cluster allows the uncertainty in the clusters to be assessed, as well as the risks associated in terms of water quality management. The methodology developed could be applied to other fields in environmental sciences.
P. A. Aguilera R. F. Ropero Informatics and Environment Laboratory, Department of Plant Biology and Ecology, University of Almerı´a, Almerı´a, Spain e-mail: [email protected] R. F. Ropero e-mail: [email protected] A. Ferna´ndez (&) Department of Statistics and Applied Mathematics, University of Almerı´a, Almerı´a, Spain e-mail: [email protected] L. Molina Department of Hydrogeology and Analytic Chemistry, University of Almerı´a, Almerı´a, Spain e-mail: [email protected]
Keywords Hybrid Bayesian networks Mixtures of truncated exponentials Probabilistic data clustering Groundwater quality
1 Introduction Groundwater quality is very important for sustaining both natural ecosystems and human activities (Lischeid 2009; Papaioannou et al. 2010; Garcı´a-Dı´az 2011). With the aim of assessing groundwater quality, multivariate procedures, such as cluster analysis, have been applied to physicochemical information obtained from monitoring programmes (Liu et al. 2011; Evin and Favre 2012; Ghorban 2012; Vousoughi et al. 2012; Wang and Jin 2012). Cluster analysis (Anderberg 1973; Jain et al. 1999) is a statistical technique that groups observations (sampling points) into clusters. Thus, sampling points with similar water quality can be grouped to optimize monitoring programmes (Atlas et al. 2011; Lu et al. 2011). However, when using these groups as part of a decision-making process, the uncertainty involved by including an observation into a group can not be quantified. In this context, managers have an increasing interest in the development of new operational tools to assess uncertainty and risk, which can facilitate the decision-making process (Refsgaard et
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