Multilayer perceptron with local constraint as an emerging method in spatial data analysis

The use of Geographic Information Systems has revolutionalized the handling and the visualization of geo-referenced data and has underlined the critic role of spatial analysis. The usual tools for such a purpose are geostatistics which are widely used in Earth science. Geostatistics are based upon several hypothesis which are not always verified in practice. On the other hand, Artificial Neural Network (ANN) a priori can be used without special assumptions and are known to be flexible. This paper proposes to discuss the application of ANN in the case of the interpolation of a geo-referenced variable.

Advanced geostatistical and machine-learning models for spatial data analysis of radioactively contaminated regions

Radioactive soil-contamination mapping and risk assessment is a vital issue for decision makers. Traditional approaches for mapping the spatial concentration of radionuclides employ various regression-based models, which usually provide a single-value prediction realization accompanied (in some cases) by estimation error. Such approaches do not provide the capability for rigorous uncertainty quantification or probabilistic mapping. Machine learning is a recent and fast-developing approach based on learning patterns and information from data. Artificial neural networks for prediction mapping have been especially powerful in combination with spatial statistics. A data-driven approach provides the opportunity to integrate additional relevant information about spatial phenomena into a prediction model for more accurate spatial estimates and associated uncertainty. Machine-learning algorithms can also be used for a wider spectrum of problems than before: classification, probability density estimation, and so forth. Stochastic simulations are used to model spatial variability and uncertainty. Unlike regression models, they provide multiple realizations of a particular spatial pattern that allow uncertainty and risk quantification. This paper reviews the most recent methods of spatial data analysis, prediction, and risk mapping, based on machine learning and stochastic simulations in comparison with more traditional regression models. The radioactive fallout from the Chernobyl Nuclear Power Plant accident is used to illustrate the application of the models for prediction and classification problems. This fallout is a unique case study that provides the challenging task of analyzing huge amounts of data ('hard' direct measurements, as well as supplementary information and expert estimates) and solving particular decision-oriented problems.

Machine learning algorithms for spatial data. Case studies: Environmental pollution, natural hazards, renewable resources

This paper presents general problems and approaches for the spatial data analysis using machine learning algorithms. Machine learning is a very powerful approach to adaptive data analysis, modelling and visualisation. The key feature of the machine learning algorithms is that they learn from empirical data and can be used in cases when the modelled environmental phenomena are hidden, nonlinear, noisy and highly variable in space and in time. Most of the machines learning algorithms are universal and adaptive modelling tools developed to solve basic problems of learning from data: classification/pattern recognition, regression/mapping and probability density modelling. In the present report some of the widely used machine learning algorithms, namely artificial neural networks (ANN) of different architectures and Support Vector Machines (SVM), are adapted to the problems of the analysis and modelling of geo-spatial data. Machine learning algorithms have an important advantage over traditional models of spatial statistics when problems are considered in a high dimensional geo-feature spaces, when the dimension of space exceeds 5. Such features are usually generated, for example, from digital elevation models, remote sensing images, etc. An important extension of models concerns considering of real space constrains like geomorphology, networks, and other natural structures. Recent developments in semi-supervised learning can improve modelling of environmental phenomena taking into account on geo-manifolds. An important part of the study deals with the analysis of relevant variables and models' inputs. This problem is approached by using different feature selection/feature extraction nonlinear tools. To demonstrate the application of machine learning algorithms several interesting case studies are considered: digital soil mapping using SVM, automatic mapping of soil and water system pollution using ANN; natural hazards risk analysis (avalanches, landslides), assessments of renewable resources (wind fields) with SVM and ANN models, etc. The dimensionality of spaces considered varies from 2 to more than 30. Figures 1, 2, 3 demonstrate some results of the studies and their outputs. Finally, the results of environmental mapping are discussed and compared with traditional models of geostatistics.

Regression analysis of spatial data.

Many of the most interesting questions ecologists ask lead to analyses of spatial data. Yet, perhaps confused by the large number of statistical models and fitting methods available, many ecologists seem to believe this is best left to specialists. Here, we describe the issues that need consideration when analysing spatial data and illustrate these using simulation studies. Our comparative analysis involves using methods including generalized least squares, spatial filters, wavelet revised models, conditional autoregressive models and generalized additive mixed models to estimate regression coefficients from synthetic but realistic data sets, including some which violate standard regression assumptions. We assess the performance of each method using two measures and using statistical error rates for model selection. Methods that performed well included generalized least squares family of models and a Bayesian implementation of the conditional auto-regressive model. Ordinary least squares also performed adequately in the absence of model selection, but had poorly controlled Type I error rates and so did not show the improvements in performance under model selection when using the above methods. Removing large-scale spatial trends in the response led to poor performance. These are empirical results; hence extrapolation of these findings to other situations should be performed cautiously. Nevertheless, our simulation-based approach provides much stronger evidence for comparative analysis than assessments based on single or small numbers of data sets, and should be considered a necessary foundation for statements of this type in future.

Monitoring network optimisation for spatial data classification using support vector machines

The paper presents a novel method for monitoring network optimisation, based on a recent machine learning technique known as support vector machine. It is problem-oriented in the sense that it directly answers the question of whether the advised spatial location is important for the classification model. The method can be used to increase the accuracy of classification models by taking a small number of additional measurements. Traditionally, network optimisation is performed by means of the analysis of the kriging variances. The comparison of the method with the traditional approach is presented on a real case study with climate data.

Subclinical hypothyroidism and the risk of coronary heart disease and mortality: an individual participant data analysis from nine prospective cohort studies

Texte intégral: http://www.springerlink.com/content/3q68180337551r47/fulltext.pdf

What spatial data do we need to develop global mammal conservation strategies?

Spatial data on species distributions are available in two main forms, point locations and distribution maps (polygon ranges and grids). The first are often temporally and spatially biased, and too discontinuous, to be useful (untransformed) in spatial analyses. A variety of modelling approaches are used to transform point locations into maps. We discuss the attributes that point location data and distribution maps must satisfy in order to be useful in conservation planning. We recommend that before point location data are used to produce and/or evaluate distribution models, the dataset should be assessed under a set of criteria, including sample size, age of data, environmental/geographical coverage, independence, accuracy, time relevance and (often forgotten) representation of areas of permanent and natural presence of the species. Distribution maps must satisfy additional attributes if used for conservation analyses and strategies, including minimizing commission and omission errors, credibility of the source/assessors and availability for public screening. We review currently available databases for mammals globally and show that they are highly variable in complying with these attributes. The heterogeneity and weakness of spatial data seriously constrain their utility to global and also sub-global scale conservation analyses.

Subclinical thyroid dysfunction and the risk of heart failure events: an individual participant data analysis from 6 prospective cohorts.

BACKGROUND: American College of Cardiology/American Heart Association guidelines for the diagnosis and management of heart failure recommend investigating exacerbating conditions such as thyroid dysfunction, but without specifying the impact of different thyroid-stimulation hormone (TSH) levels. Limited prospective data exist on the association between subclinical thyroid dysfunction and heart failure events. METHODS AND RESULTS: We performed a pooled analysis of individual participant data using all available prospective cohorts with thyroid function tests and subsequent follow-up of heart failure events. Individual data on 25 390 participants with 216 248 person-years of follow-up were supplied from 6 prospective cohorts in the United States and Europe. Euthyroidism was defined as TSH of 0.45 to 4.49 mIU/L, subclinical hypothyroidism as TSH of 4.5 to 19.9 mIU/L, and subclinical hyperthyroidism as TSH <0.45 mIU/L, the last two with normal free thyroxine levels. Among 25 390 participants, 2068 (8.1%) had subclinical hypothyroidism and 648 (2.6%) had subclinical hyperthyroidism. In age- and sex-adjusted analyses, risks of heart failure events were increased with both higher and lower TSH levels (P for quadratic pattern <0.01); the hazard ratio was 1.01 (95% confidence interval, 0.81-1.26) for TSH of 4.5 to 6.9 mIU/L, 1.65 (95% confidence interval, 0.84-3.23) for TSH of 7.0 to 9.9 mIU/L, 1.86 (95% confidence interval, 1.27-2.72) for TSH of 10.0 to 19.9 mIU/L (P for trend <0.01) and 1.31 (95% confidence interval, 0.88-1.95) for TSH of 0.10 to 0.44 mIU/L and 1.94 (95% confidence interval, 1.01-3.72) for TSH <0.10 mIU/L (P for trend=0.047). Risks remained similar after adjustment for cardiovascular risk factors. CONCLUSION: Risks of heart failure events were increased with both higher and lower TSH levels, particularly for TSH ≥10 and <0.10 mIU/L.

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.

On the Schoenberg transformations in data analysis: theory and illustrations

The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and visualized on artificial data sets by classical multidimensional scaling. A distance-based discriminant algorithm and a robust multidimensional centroid estimate illustrate the theory, closely connected to the Gaussian kernels of Machine Learning.

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.