Robust Nonlinear Mapping of Soil Contamination Using Support Regression

Spatial data analysis mapping and visualization is of great importance in various fields: environment, pollution, natural hazards and risks, epidemiology, spatial econometrics, etc. A basic task of spatial mapping is to make predictions based on some empirical data (measurements). A number of state-of-the-art methods can be used for the task: deterministic interpolations, methods of geostatistics: the family of kriging estimators (Deutsch and Journel, 1997), machine learning algorithms such as artificial neural networks (ANN) of different architectures, hybrid ANN-geostatistics models (Kanevski and Maignan, 2004; Kanevski et al., 1996), etc. All the methods mentioned above can be used for solving the problem of spatial data mapping. Environmental empirical data are always contaminated/corrupted by noise, and often with noise of unknown nature. That's one of the reasons why deterministic models can be inconsistent, since they treat the measurements as values of some unknown function that should be interpolated. Kriging estimators treat the measurements as the realization of some spatial randomn process. To obtain the estimation with kriging one has to model the spatial structure of the data: spatial correlation function or (semi-)variogram. This task can be complicated if there is not sufficient number of measurements and variogram is sensitive to outliers and extremes. ANN is a powerful tool, but it also suffers from the number of reasons. of a special type ? multiplayer perceptrons ? are often used as a detrending tool in hybrid (ANN+geostatistics) models (Kanevski and Maignank, 2004). Therefore, development and adaptation of the method that would be nonlinear and robust to noise in measurements, would deal with the small empirical datasets and which has solid mathematical background is of great importance. The present paper deals with such model, based on Statistical Learning Theory (SLT) - Support Vector Regression. SLT is a general mathematical framework devoted to the problem of estimation of the dependencies from empirical data (Hastie et al, 2004; Vapnik, 1998). SLT models for classification - Support Vector Machines - have shown good results on different machine learning tasks. The results of SVM classification of spatial data are also promising (Kanevski et al, 2002). The properties of SVM for regression - Support Vector Regression (SVR) are less studied. First results of the application of SVR for spatial mapping of physical quantities were obtained by the authorsin for mapping of medium porosity (Kanevski et al, 1999), and for mapping of radioactively contaminated territories (Kanevski and Canu, 2000). The present paper is devoted to further understanding of the properties of SVR model for spatial data analysis and mapping. Detailed description of the SVR theory can be found in (Cristianini and Shawe-Taylor, 2000; Smola, 1996) and basic equations for the nonlinear modeling are given in section 2. Section 3 discusses the application of SVR for spatial data mapping on the real case study - soil pollution by Cs137 radionuclide. Section 4 discusses the properties of the modelapplied to noised data or data with outliers.

Advanced mapping of environmental data: Geostatistics, Machine Learning and Bayesian Maximum Entropy

This book combines geostatistics and global mapping systems to present an up-to-the-minute study of environmental data. Featuring numerous case studies, the reference covers model dependent (geostatistics) and data driven (machine learning algorithms) analysis techniques such as risk mapping, conditional stochastic simulations, descriptions of spatial uncertainty and variability, artificial neural networks (ANN) for spatial data, Bayesian maximum entropy (BME), and more.

GeoKernels: Modeling of Spatial Data on GeoManifolds

This paper presents a review of methodology for semi-supervised modeling with kernel methods, when the manifold assumption is guaranteed to be satisfied. It concerns environmental data modeling on natural manifolds, such as complex topographies of the mountainous regions, where environmental processes are highly influenced by the relief. These relations, possibly regionalized and nonlinear, can be modeled from data with machine learning using the digital elevation models in semi-supervised kernel methods. The range of the tools and methodological issues discussed in the study includes feature selection and semisupervised Support Vector algorithms. The real case study devoted to data-driven modeling of meteorological fields illustrates the discussed approach.

Multitask learning of environmental spatial data

The present research deals with an application of artificial neural networks for multitask learning from spatial environmental data. The real case study (sediments contamination of Geneva Lake) consists of 8 pollutants. There are different relationships between these variables, from linear correlations to strong nonlinear dependencies. The main idea is to construct a subsets of pollutants which can be efficiently modeled together within the multitask framework. The proposed two-step approach is based on: 1) the criterion of nonlinear predictability of each variable ?k? by analyzing all possible models composed from the rest of the variables by using a General Regression Neural Network (GRNN) as a model; 2) a multitask learning of the best model using multilayer perceptron and spatial predictions. The results of the study are analyzed using both machine learning and geostatistical tools.

Machine learning analysis and modeling of interest rate curves

The present research deals with the review of the analysis and modeling of Swiss franc interest rate curves (IRC) by using unsupervised (SOM, Gaussian Mixtures) and supervised machine (MLP) learning algorithms. IRC are considered as objects embedded into different feature spaces: maturities; maturity-date, parameters of Nelson-Siegel model (NSM). Analysis of NSM parameters and their temporal and clustering structures helps to understand the relevance of model and its potential use for the forecasting. Mapping of IRC in a maturity-date feature space is presented and analyzed for the visualization and forecasting purposes.

Data-driven topo-climatic mapping with machine learning methods

Automatic environmental monitoring networks enforced by wireless communication technologies provide large and ever increasing volumes of data nowadays. The use of this information in natural hazard research is an important issue. Particularly useful for risk assessment and decision making are the spatial maps of hazard-related parameters produced from point observations and available auxiliary information. The purpose of this article is to present and explore the appropriate tools to process large amounts of available data and produce predictions at fine spatial scales. These are the algorithms of machine learning, which are aimed at non-parametric robust modelling of non-linear dependencies from empirical data. The computational efficiency of the data-driven methods allows producing the prediction maps in real time which makes them superior to physical models for the operational use in risk assessment and mitigation. Particularly, this situation encounters in spatial prediction of climatic variables (topo-climatic mapping). In complex topographies of the mountainous regions, the meteorological processes are highly influenced by the relief. The article shows how these relations, possibly regionalized and non-linear, can be modelled from data using the information from digital elevation models. The particular illustration of the developed methodology concerns the mapping of temperatures (including the situations of Föhn and temperature inversion) given the measurements taken from the Swiss meteorological monitoring network. The range of the methods used in the study includes data-driven feature selection, support vector algorithms and artificial neural networks.