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.

Kernel-based Mapping of Meteorological Fields in Complex Orography

Due to the advances in sensor networks and remote sensing technologies, the acquisition and storage rates of meteorological and climatological data increases every day and ask for novel and efficient processing algorithms. A fundamental problem of data analysis and modeling is the spatial prediction of meteorological variables in complex orography, which serves among others to extended climatological analyses, for the assimilation of data into numerical weather prediction models, for preparing inputs to hydrological models and for real time monitoring and short-term forecasting of weather.In this thesis, a new framework for spatial estimation is proposed by taking advantage of a class of algorithms emerging from the statistical learning theory. Nonparametric kernel-based methods for nonlinear data classification, regression and target detection, known as support vector machines (SVM), are adapted for mapping of meteorological variables in complex orography.With the advent of high resolution digital elevation models, the field of spatial prediction met new horizons. In fact, by exploiting image processing tools along with physical heuristics, an incredible number of terrain features which account for the topographic conditions at multiple spatial scales can be extracted. Such features are highly relevant for the mapping of meteorological variables because they control a considerable part of the spatial variability of meteorological fields in the complex Alpine orography. For instance, patterns of orographic rainfall, wind speed and cold air pools are known to be correlated with particular terrain forms, e.g. convex/concave surfaces and upwind sides of mountain slopes.Kernel-based methods are employed to learn the nonlinear statistical dependence which links the multidimensional space of geographical and topographic explanatory variables to the variable of interest, that is the wind speed as measured at the weather stations or the occurrence of orographic rainfall patterns as extracted from sequences of radar images. Compared to low dimensional models integrating only the geographical coordinates, the proposed framework opens a way to regionalize meteorological variables which are multidimensional in nature and rarely show spatial auto-correlation in the original space making the use of classical geostatistics tangled.The challenges which are explored during the thesis are manifolds. First, the complexity of models is optimized to impose appropriate smoothness properties and reduce the impact of noisy measurements. Secondly, a multiple kernel extension of SVM is considered to select the multiscale features which explain most of the spatial variability of wind speed. Then, SVM target detection methods are implemented to describe the orographic conditions which cause persistent and stationary rainfall patterns. Finally, the optimal splitting of the data is studied to estimate realistic performances and confidence intervals characterizing the uncertainty of predictions.The resulting maps of average wind speeds find applications within renewable resources assessment and opens a route to decrease the temporal scale of analysis to meet hydrological requirements. Furthermore, the maps depicting the susceptibility to orographic rainfall enhancement can be used to improve current radar-based quantitative precipitation estimation and forecasting systems and to generate stochastic ensembles of precipitation fields conditioned upon the orography.

Spatial statistical analysis and selection of genotypes in plant breeding

The objective of this study was to evaluate the efficiency of spatial statistical analysis in the selection of genotypes in a plant breeding program and, particularly, to demonstrate the benefits of the approach when experimental observations are not spatially independent. The basic material of this study was a yield trial of soybean lines, with five check varieties (of fixed effect) and 110 test lines (of random effects), in an augmented block design. The spatial analysis used a random field linear model (RFML), with a covariance function estimated from the residuals of the analysis considering independent errors. Results showed a residual autocorrelation of significant magnitude and extension (range), which allowed a better discrimination among genotypes (increase of the power of statistical tests, reduction in the standard errors of estimates and predictors, and a greater amplitude of predictor values) when the spatial analysis was applied. Furthermore, the spatial analysis led to a different ranking of the genetic materials, in comparison with the non-spatial analysis, and a selection less influenced by local variation effects was obtained.

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.

Interest rates mapping

The present study deals with the analysis and mapping of Swiss franc interest rates. Interest rates depend on time and maturity, defining term structure of the interest rate curves (IRC). In the present study IRC are considered in a two-dimensional feature space - time and maturity. Exploratory data analysis includes a variety of tools widely used in econophysics and geostatistics. Geostatistical models and machine learning algorithms (multilayer perceptron and Support Vector Machines) were applied to produce interest rate maps. IR maps can be used for the visualisation and pattern perception purposes, to develop and to explore economical hypotheses, to produce dynamic asset-liability simulations and for financial risk assessments. The feasibility of an application of interest rates mapping approach for the IRC forecasting is considered as well. (C) 2008 Elsevier B.V. All rights reserved.

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The quality of environmental data analysis and propagation of errors are heavily affected by the representativity of the initial sampling design [CRE 93, DEU 97, KAN 04a, LEN 06, MUL07]. Geostatistical methods such as kriging are related to field samples, whose spatial distribution is crucial for the correct detection of the phenomena. Literature about the design of environmental monitoring networks (MN) is widespread and several interesting books have recently been published [GRU 06, LEN 06, MUL 07] in order to clarify the basic principles of spatial sampling design (monitoring networks optimization) based on Support Vector Machines was proposed. Nonetheless, modelers often receive real data coming from environmental monitoring networks that suffer from problems of non-homogenity (clustering). Clustering can be related to the preferential sampling or to the impossibility of reaching certain regions.

Semivariogram models for estimating fig fly population density throughout the year

The objective of this work was to select semivariogram models to estimate the population density of fig fly (Zaprionus indianus; Diptera: Drosophilidae) throughout the year, using ordinary kriging. Nineteen monitoring sites were demarcated in an area of 8,200 m2, cropped with six fruit tree species: persimmon, citrus, fig, guava, apple, and peach. During a 24 month period, 106 weekly evaluations were done in these sites. The average number of adult fig flies captured weekly per trap, during each month, was subjected to the circular, spherical, pentaspherical, exponential, Gaussian, rational quadratic, hole effect, K-Bessel, J-Bessel, and stable semivariogram models, using ordinary kriging interpolation. The models with the best fit were selected by cross-validation. Each data set (months) has a particular spatial dependence structure, which makes it necessary to define specific models of semivariograms in order to enhance the adjustment to the experimental semivariogram. Therefore, it was not possible to determine a standard semivariogram model; instead, six theoretical models were selected: circular, Gaussian, hole effect, K-Bessel, J-Bessel, and stable.

Flight movement and spatial distribution of immunomarked thrips in onion, potato, and tomato

The objective of this work was to evaluate the spatial distribution of thrips in different crops, and the correlation between meterological parameters and the flight movements of this pest, using immunomarking. The experiment was conducted in cultivated areas, with tomato (Solanum lycopersicum), potato (Solanum tuberosum), and onion (Allium cepa); and non-cultivated areas, with weedy plants. The areas with tomato (100 days), potato (20 days), and weeds were sprayed with casein, albumin, and soy milk, respectively, to mark adult thrips; however, the areas with onion (50 days) and tomato (10 days) were not sprayed. Thrips were captured with georeferenced blue sticky traps, transferred into tubes, and identified by treatment area with the Elisa test. The dependence between the samples and the capture distance was determined using geostatistics. Meteorlogical parameters were correlated with thrips density in each area. The three protein types used for immunomarking were detected in different proportions in the thrips. There was a correlation between casein-marked thrips and wind speed. The thrips flew a maximum distance of 3.5 km and dispersed from the older (tomato) to the younger crops (potato). The immunomarking method is efficient to mark large quantities of thrips.

Estudio de la distribución espacial de Cydia pomonella (L.) y Pandemis heparana (Denis & Schiffermüller) en Torregrossa (Lleida) mediante métodos geoestadísticos

El estudio de la distribución espacial de una especie por me'todos geoestadísticos se realiza mediante el conocimiento de la función semivariograma. Después de calcular el semivariograma se procede a la estimación de la variable regionalizada en cualquier punto de la zona de estudio. Esta estimación se realiza mediante técnicas de interpolación lineal llamadas «krigeado», en honor a Krige y Matheron, fundadores de la geoestadística. El «krigeado» se basa en la minimización de la varianza del error en cada punto de estudio, previamente localizado en el espacio por sus coordenadas de situación. Cydia pomonella (L.) y Pandemis heparana (Denis & Schiffermüller) son dos tortrícidos plaga del manzano y del peral. La estimación de sus poblaciones se realiza mediante trampas de feromona y es posible disponer de una amplia base de datos. El objetivo de este trabajo fue analizar la idoneidad de los métodos geoestadísticos para el estudio de poblaciones de insectos y aplicarlas al caso concreto de C. pomonella y P. heparana. Se utilizaron las capturas en 55 estaciones con trampas de feromonas (difusor de origen Wageningen) colocadas en parcelas comerciales de manzano y peral en 1996 y 1997 en el término municipal de Torregrossa (Lleida). La idoneidad de los métodos geoestadísticos quedó demostrada por el hecho de que la variable número acumulado de machos por trampa fue regionalizable. Una vez calculadas las funciones semivariograma para cada especie y año, se han dibujado los mapas de distribución mediante el uso de isolíneas. En el futuro, se plantea la posibilidad de ampliar la zona de estudio a toda la zona frutera de Lleida y analizar la influencia de variables independientes (climáticas ...) sobre la distribución espacial mediante métodos de «co-krigeado».

Terrain forms and spatial variability of soil properties in an area cultivatedwith citrus

The technique of precision agriculture and soil-landscape allows delimiting areas for localized management, allowing a localized application of agricultural inputs and thereby may contribute to preservation of natural resources. Therefore, the objective of this work was to characterize the spatial variability of chemical properties and clay content in the context of soil-landscape relationship in a Latosol (Oxisol) under cultivation of citrus. Soil samples were collected at a depth of 0.0-0.2 m in an area of 83.5 ha planted with citrus, as a 50-m intervals grid, with 129 points in concave terrain and 206 points in flat terrain, totaling 335 points. Values for the variables that express the chemical characteristics and clay content of soil properties were analyzed with descriptive statistics and geostatistical modeling of semivariograms for making maps of kriging. The values of range and kriging maps indicated higher variability in the shape of concave topography (top segment) compared with the shape of flat topography (slope and hillside segments below). The identification of different forms of terrain proved to be efficient in understanding the spatial variability of chemical properties and clay content of soil under cultivation of citrus.

Determination of management zones from normalized and standardized equivalent produtivity maps in the soybean culture

Through the site-specific management, the precision agriculture brings new techniques for the agricultural sector, as well as a larger detailing of the used methods and increase of the global efficiency of the system. The objective of this work was to analyze two techniques for definition of management zones using soybean yield maps, in a productive area handled with localized fertilization and other with conventional fertilization. The sampling area has 1.74 ha, with 128 plots with site-specific fertilization and 128 plots with conventional fertilization. The productivity data were normalized by two techniques (normalized and standardized equivalent productivity), being later classified in management zones. It can be concluded that the two methods of management zones definition had revealed to be efficient, presenting similarities in the data disposal. Due to the fact that the equivalent standardized productivity uses standard score, it contemplates a better statistics justification.

GPS receivers for georeferencing of spatial variability of soil attributes

The characterization of the spatial variability of soil attributes is essential to support agricultural practices in a sustainable manner. The use of geostatistics to characterize spatial variability of these attributes, such as soil resistance to penetration (RP) and gravimetric soil moisture (GM) is now usual practice in precision agriculture. The result of geostatistical analysis is dependent on the sample density and other factors according to the georeferencing methodology used. Thus, this study aimed to compare two methods of georeferencing to characterize the spatial variability of RP and GM as well as the spatial correlation of these variables. Sampling grid of 60 points spaced 20 m was used. For RP measurements, an electronic penetrometer was used and to determine the GM, a Dutch auger (0.0-0.1 m depth) was used. The samples were georeferenced using a GPS navigation receiver, Simple Point Positioning (SPP) with navigation GPS receiver, and Semi-Kinematic Relative Positioning (SKRP) with an L1 geodetic GPS receiver. The results indicated that the georeferencing conducted by PPS did not affect the characterization of spatial variability of RP or GM, neither the spatial structure relationship of these attributes.

Spatial variability of the rainfall erosive potential in the State of Mato Grosso do Sul, Brazil

Information about rainfall erosivity is important during soil and water conservation planning. Thus, the spatial variability of rainfall erosivity of the state Mato Grosso do Sul was analyzed using ordinary kriging interpolation. For this, three pluviograph stations were used to obtain the regression equations between the erosivity index and the rainfall coefficient EI30. The equations obtained were applied to 109 pluviometric stations, resulting in EI30 values. These values were analyzed from geostatistical technique, which can be divided into: descriptive statistics, adjust to semivariogram, cross-validation process and implementation of ordinary kriging to generate the erosivity map.Highest erosivity values were found in central and northeast regions of the State, while the lowest values were observed in the southern region. In addition, high annual precipitation values not necessarily produce higher erosivity values.