The goal of this research is to exploit and adapt methodologies borrowed from artificial intelligence —in particular artificial neural networks (ANN)— for the analysis of environmental spatial data. ANNs are universal function approximators and we will demonstrate that understanding their statistical properties and adequately using their abilities can be extremely efficient to tackle difficult problems of geostatistics in the domain of environmental spatial data analysis.

This work addresses a series of basic research items of spatial data analysis that was not addressed by the geostatistics specialists, even according to their latest announcements at Geostat’96 and IAMG’97:

• highly non stationary spatial processes,
• cartography of distribution functions, as opposed to cartography of the mean value,
• user and data-driven parameterization for the discrimination between a stochastic trend and auto-correlated residuals,
• cartography of stochastic deviations related to advection-diffusion models.

Some benefits of ANNs in geostatistics have already been experienced through a first-phase research carried out by the principal applicant and by Professor M. Kanevski (see [1,2,3,4]):

• An ANN performs a non-linear mapping and is thus able to capture some non-linear trends in the data. It has been shown to be very efficient to capture large-scale non-linear trends [3], as well as medium-scale variations [4,5,6].
• A neuromimetic approach is adaptive and data driven, while the classical approaches in geostatistics are ad hoc for each different type of problem, requiring a lot of expertise and hand tuning [3].
• ANNs are robust against noisy data and work on global and local scales [6,7].

• A typical problem in geostatistics is the estimation of a function f(x,y) given some observations of f in different locations (x,y). In practice however, the computation of an estimation f’ of f is not of a great use if it is not accompanied with the estimation of the variance s ’(x,y) of the error between f and f’. The latter information is crucial for a decision-maker. Lately, some authors proposed new neural networks designed to predict simultaneously the output and an associated confidence. In this project, we plan to evaluate this type of approach for spatial data analysis. (Personal communication with Dr hab S. Canu for spatial estimation of distributions).
• Ideally, instead of predicting for each location (x,y) a single value f’(x,y) or this value plus a variance s ’(x,y), it would be interesting to estimate the probability density of the value f(x,y). In a simpler way, the decision-maker will be highly interested in knowing the probability density function Pr[f(x,y) ³ t] for a fixed critical threshold t and for any location (x,y). We will demonstrate that again, an adequate usage of statistical learning tools can efficiently address this problem. This is related to the classical problem of cartography for time-repeated measurements at the same location.
• An important characteristic of environmental data analysis is their statistical multivariate composition. Some of them are cheap and available for a large number of locations (e.g. meteorological measurements); while others are expensive and are known only on a spare set of places (e.g. laboratory chemical analysis). The statistical correlation and spatial cross-correlation between these variables can be taken into account in the estimation process [4].

The verification and validation of the new developments in this research project will be carried out using unique environmental data sets chosen dealing with: post-Chernobyl pollution, chemical analysis of water and sediments of the lake of Geneva, and heavy metal soil contamination. The methods developed within this project will be extensively compared with classical geostatistical methods (such as kriging).

[1] M. Kanevski. Neural networks and geostatistical spatial interpolations, IBRAE internal report, 1994.

[2] M. Kanevski and M. Maignan. Neural network kriging estimations, Japanese Journal of Geoinformatics, 1995.

[3] M. Kanevski, V. Demyanov, and M. Maignan. Mapping of soil contamination by using ANNs and multivariate geostatistics, Proceedings of the International Conference on Neural Networks, ICANN'97, pp 1125-1131, 1997.

[4] M. de Bollivier, G. Dubois, M. Maignan, and M. Kanevski. Multilayer perceptron with local constraints as an emerging method in spatial data analysis, New computing techniques in physics research V, pp. 226-229, 1997.

[5] M. Chentouf, C. Jutten, M. Maignan, and M. Kanevski. Incremental neural networks for function approximation, New computing techniques in physics research V, pp 268-270, 1997.

[6] S. Shibli, P. Wong, and M. Maignan. Radial basis function for spatial estimation, New computing techniques for physics research V, 1997.

[7] M. Kanevski, M. Maignan, V. Demyanov, and M.-F. Maignan. Environmental decision-oriented mapping with algorithms imitating nature, IAMG 97 Int. Assoc. Mathematical Geology, pp 520-526, 1997.

[8] M. Kanevski, M. Maignan, V. Demyanov, and M.-F. Maignan. How neural network 2-D interpolations can improve spatial data analysis: neural network residual kriging, IAMG 97 Int. Assoc. Mathematical Geology, pp 549-554, 1997.