Nathalie Villa

Support vector machine for functional data classification

In many applications, input data are sampled functions taking their values in infinite-dimensional spaces rather than standard vectors. This fact has complex consequences on data analysis algorithms that motivate their modifications. In fact most of the traditional data analysis tools for regression, classification and clustering have been adapted to functional inputs under the general name of functional data analysis (FDA). In this paper, we investigate the use of support vector machines (SVMs) for FDA and we focus on the problem of curve discrimination. SVMs are large margin classifier tools based on implicit nonlinear mappings of the considered data into high-dimensional spaces thanks to kernels. We show how to define simple kernels that take into account the functional nature of the data and lead to consistent classification. Experiments conducted on real world data emphasize the benefit of taking into account some functional aspects of the problems.

Recent Advances in the Use of SVM for Functional Data Classification

In the past years, several works were dealing with the use of Support Vector Machine (SVM) for classifying functional data. Here, we propose to give an overview of these works and to introduce a new result based on the use of smoothing conditions on the observed functions. The originality of this approach both lies in the fact that the consistency result allows to work with the derivatives of the function instead of the function itself but also that it is relative to the observed discretization and not to the entire knowledge of the functions.

Various Approaches for Predicting Land Cover in Mountain Areas

Using former maps, geographers intend to study the evolution of the land cover in order to have a prospective approach on the future landscape; predictions of the future land cover, by the use of older maps and environmental variables, are usually done through the GIS (Geographic Information System). We propose here to confront this classical geographical approach with statistical approaches: a linear parametric model (polychotomous regression modeling) and a nonparametric one (multilayer perceptron). These methodologies have been tested on two real areas on which the land cover is known at various dates; this allows us to emphasize the benefit of these two statistical approaches compared to GIS and to discuss the way GIS could be improved by the use of statistical models.

Tropical deforestation modelling: comparative analysis of different predictive approaches. The case study of Peten, Guatemala

The frequent use of predictive models for analyzing of complex, natural or artificial phenomena is changing the traditional approaches to environmental and hazard problems. The continuous improvement of computer performance allows for more detailed numerical methods, based on space-time discretisation, to be developed and run for a predictive modelling of complex real systems, reproducing the way their spatial patterns evolve and pointing out the degree of simulation accuracy. In this contribution we present an application of several methods (Geomatics, Neural Networks, Land Cover Modeler and Dinamica EGO) in the tropical training area of Peten, Guatemala. During the last few decades this region, included in the Biosphere Maya reserve, has seen a fast demographic raise and a subsequent uncontrolled pressure on its own geo-resources. The test area can be divided into several sub-regions characterized by different land use dynamics. Understanding and quantifying these differences permits a better approximation of a real system; moreover we have to consider all the physical, socio-economic parameters, which will be of use for representing the complex and sometimes random human impact. Because of the absence of detailed data from our test area, nearly all the information was derived from the image processing of 11 ETM+, TM and SPOT scenes; we studied the past environmental dynamics and we built the input layers for the predictive models. The data from 1998 and 2000 were used during the calibration to simulate the land cover changes in 2003, selected as reference date for the validation. The basic statistics permit to highlight the qualities or the weaknesses for each model on the different sub-regions.

Prospective modelling of environmental dynamics: A methodological comparison applied to mountain land cover changes

During the last 10 years, scientists have made significant advances in modelling environmental dynamics. A wide range of new methodological approaches in geomatics –such as neural networks, multi-agent systems or fuzzy logics– have been developed. Despite this progress, the modelling softwares available have to be considered as experimental tools rather than improved procedures that are able to work for environmental management or decision support. In particular, the authors think that a large number of publications suffer from discrepancies, when trying to validate their model’s results.