Esta tese investiga uma abordagem não supervisionada para o problema da detecção de mudanças em imagens multiespectrais e multitemporais de sensoriamento remoto empregando Support Vector Machines (SVM) com o uso dos kernels polinomial e RBF e de uma nova métrica de pertinência de pixels. A proposta metodológica está baseada na diferença das imagens-fração produzidas para cada data. Em imagens de cenas naturais essa diferença nas frações de solo e vegetação tendem a apresentar uma distribuição simétrica próxima à origem. Essa caracteristica pode ser usada para modelar as distribuições normais multivariadas das classes mudança e não-mudança. O algoritmo Expectation-Maximization (EM) é implementado com a finalidade de estimar os parâmetros (vetor de médias, matriz de covariância e probabilidade a priori) associados a essas duas distribuições. A seguir, amostras aleatórias e normalmente distribuidas são extraídas dessas distribuições e rotuladas segundo sua pertinência em uma das classes. Essas amostras são então usadas no treinamento do classificador SVM. A partir desta classificação é estimada uma nova métrica de pertinência de pixels. A metodologia proposta realiza testes com o uso de conjuntos de dados multitemporais de imagens multiespectrais Landsat-TM que cobrem a mesma cena em duas datas diferentes. A métrica de pertinência proposta é validada através de amostras de teste controladas obtidas a partir da técnica Change Vetor Analysis, além disso, os resultados de pertinência obtidos para a imagem original com essa nova métrica são comparados aos resultados de pertinência obtidos para a mesma imagem pela métrica proposta em (Zanotta, 2010). Baseado nos resultados apresentados neste trabalho que mostram que a métrica para determinação de pertinência é válida e também apresenta resultados compatíveis com outra técnica de pertinência publicada na literatura e considerando que para obter esses resultados utilizou-se poucas amostras de treinamento, espera-se que essa métrica deva apresentar melhores resultados que os que seriam apresentados com classificadores paramétricos quando aplicado a imagens multitemporais e hiperespectrais. / This thesis investigates a unsupervised approach to the problem of change detection in multispectral and multitemporal remote sensing images using Support Vector Machines (SVM) with the use of polynomial and RBF kernels and a new metric of pertinence of pixels. The methodology is based on the difference-fraction images produced for each date. In images of natural scenes. This difference in the fractions of bare soil and vegetation tend to have a symmetrical distribution close to the origin. This feature can be used to model the multivariate normal distributions of the classes change and no-change. The Expectation- Maximization algorithm (EM) is implemented in order to estimate the parameters (mean vector, covariance matrix and a priori probability) associated with these two distributions. Then random and normally distributed samples are extracted from these distributions and labeled according to their pertinence to the classes. These samples are then used in the training of SVM classifier. From this classification is estimated a new metric of pertinence of pixel. The proposed methodology performs tests using multitemporal data sets of multispectral Landsat-TM images that cover the same scene at two different dates. The proposed metric of pertinence is validated via controlled test samples obtained from Change Vector Analysis technique. In addition, the results obtained at the original image with the new metric are compared to the results obtained at the same image applying the pertinence metric proposed in (Zanotta, 2010). Based on the results presented here showing that the metric of pertinence is valid, and also provides results consistent with other published in the relevant technical literature, and considering that to obtain these results was used a few training samples, it is expected that the metric proposed should present better results than those that would be presented with parametric classifiers when applied to multitemporal and hyperspectral images.

Doctor of Philosophy / Department of Statistics / Weixing Song / In this dissertation, we proposed a new robust estimation procedure for two multivariate mixture regression models and applied this novel method to functional mapping of dynamic traits. In the first part, a robust estimation procedure for the mixture of classical multivariate linear regression models is discussed by assuming that the error terms follow a multivariate Laplace distribution. An EM algorithm is developed based on the fact that the multivariate Laplace distribution is a scale mixture of the multivariate standard normal distribution. The performance of the proposed algorithm is thoroughly evaluated by some simulation and comparison studies. In the second part, the similar idea is extended to the mixture of linear mixed regression models by assuming that the random effect and the regression error jointly follow a multivariate Laplace distribution. Compared with the existing robust t procedure in the literature, simulation studies indicate that the finite sample performance of the proposed estimation procedure outperforms or is at least comparable to the robust t procedure. Comparing to t procedure, there is no need to determine the degrees of freedom, so the new robust estimation procedure is computationally more efficient than the robust t procedure. The ascent property for both EM algorithms are also proved. In the third part, the proposed robust method is applied to identify quantitative trait loci (QTL) underlying a functional mapping framework with dynamic traits of agricultural or biomedical interest. A robust multivariate Laplace mapping framework was proposed to replace the normality assumption. Simulation studies show the proposed method is comparable to the robust multivariate t-distribution developed in literature and outperforms the normal procedure. As an illustration, the proposed method is also applied to a real data set.

Finite mixtures of von Mises-Fisher distributions allow to apply model-based clustering methods to data which is of standardized length, i.e., all data points lie on the unit sphere. The R package movMF contains functionality to draw samples from finite mixtures of von Mises-Fisher distributions and to fit these models using the expectation-maximization algorithm for maximum likelihood estimation. Special features are the possibility to use sparse matrix representations for the input data, different variants of the expectationmaximization algorithm, different methods for determining the concentration parameters in the M-step and to impose constraints on the concentration parameters over the components. In this paper we describe the main fitting function of the package and illustrate its application. In addition we compare the clustering performance of finite mixtures of von Mises-Fisher distributions to spherical k-means. We also discuss the resolution of several numerical issues which occur for estimating the concentration parameters and for determining the normalizing constant of the von Mises-Fisher distribution. (authors' abstract)

Esta tese investiga uma abordagem supervisionada para o problema da detecção de mudanças em imagens multitemporais de sensoriamento remoto empregando Support Vector Machines (SVM) com o uso dos kernels polinomial e gaussiano (RBF). A proposta metodológica está baseada na diferença das imagens-fração produzidas para cada data. Em imagens de cenas naturais a diferença nas frações de solo e vegetação tendem a apresentar uma distribuição simétrica em torno da origem. Esse fato pode ser usado para modelar duas distribuições normais multivariadas: mudança e não-mudança. O algoritmo Expectation-Maximization (EM) é implementado para estimar os parâmetros (vetor de médias, matriz de covariância e probabilidade a priori) associados a essas duas distribuições. Amostras aleatórias são extraídas dessas distribuições e usadas para treinar o classificador SVM nesta abordagem supervisionada. A metodologia proposta realiza testes com o uso de conjuntos de dados multitemporais de imagens multiespectrais TM-Landsat, que cobrem a mesma cena em duas datas diferentes. Os resultados são comparados com outros procedimentos, incluindo trabalhos anteriores, um conjunto de dados sintéticos e o classificador SVM One-Class. / In this thesis, we investigate a supervised approach to change detection in remote sensing multi-temporal image data by applying Support Vector Machines (SVM) technique using polynomial kernel and Gaussian kernel (RBF). The methodology is based on the difference-fraction images produced for two dates. In natural scenes, the difference in the fractions such as vegetation and bare soil occurring in two different dates tend to present a distribution symmetric around the origin of the coordinate system. This fact can be used to model two normal multivariate distributions: class change and no-change. The Expectation-Maximization algorithm (EM) is implemented to estimate the parameters (mean vector, covariance matrix and a priori probability) associated with these two distributions. Random samples are drawn from these distributions and used to train the SVM classifier in this supervised approach.The proposed methodology performs tests using multi-temporal TMLandsat multispectral image data covering the same scene in two different dates. The results are compared to other procedures including previous work, a synthetic data set and SVM One-Class.

Esta tese investiga uma abordagem não supervisionada para o problema da detecção de mudanças em imagens multiespectrais e multitemporais de sensoriamento remoto empregando Support Vector Machines (SVM) com o uso dos kernels polinomial e RBF e de uma nova métrica de pertinência de pixels. A proposta metodológica está baseada na diferença das imagens-fração produzidas para cada data. Em imagens de cenas naturais essa diferença nas frações de solo e vegetação tendem a apresentar uma distribuição simétrica próxima à origem. Essa caracteristica pode ser usada para modelar as distribuições normais multivariadas das classes mudança e não-mudança. O algoritmo Expectation-Maximization (EM) é implementado com a finalidade de estimar os parâmetros (vetor de médias, matriz de covariância e probabilidade a priori) associados a essas duas distribuições. A seguir, amostras aleatórias e normalmente distribuidas são extraídas dessas distribuições e rotuladas segundo sua pertinência em uma das classes. Essas amostras são então usadas no treinamento do classificador SVM. A partir desta classificação é estimada uma nova métrica de pertinência de pixels. A metodologia proposta realiza testes com o uso de conjuntos de dados multitemporais de imagens multiespectrais Landsat-TM que cobrem a mesma cena em duas datas diferentes. A métrica de pertinência proposta é validada através de amostras de teste controladas obtidas a partir da técnica Change Vetor Analysis, além disso, os resultados de pertinência obtidos para a imagem original com essa nova métrica são comparados aos resultados de pertinência obtidos para a mesma imagem pela métrica proposta em (Zanotta, 2010). Baseado nos resultados apresentados neste trabalho que mostram que a métrica para determinação de pertinência é válida e também apresenta resultados compatíveis com outra técnica de pertinência publicada na literatura e considerando que para obter esses resultados utilizou-se poucas amostras de treinamento, espera-se que essa métrica deva apresentar melhores resultados que os que seriam apresentados com classificadores paramétricos quando aplicado a imagens multitemporais e hiperespectrais. / This thesis investigates a unsupervised approach to the problem of change detection in multispectral and multitemporal remote sensing images using Support Vector Machines (SVM) with the use of polynomial and RBF kernels and a new metric of pertinence of pixels. The methodology is based on the difference-fraction images produced for each date. In images of natural scenes. This difference in the fractions of bare soil and vegetation tend to have a symmetrical distribution close to the origin. This feature can be used to model the multivariate normal distributions of the classes change and no-change. The Expectation- Maximization algorithm (EM) is implemented in order to estimate the parameters (mean vector, covariance matrix and a priori probability) associated with these two distributions. Then random and normally distributed samples are extracted from these distributions and labeled according to their pertinence to the classes. These samples are then used in the training of SVM classifier. From this classification is estimated a new metric of pertinence of pixel. The proposed methodology performs tests using multitemporal data sets of multispectral Landsat-TM images that cover the same scene at two different dates. The proposed metric of pertinence is validated via controlled test samples obtained from Change Vector Analysis technique. In addition, the results obtained at the original image with the new metric are compared to the results obtained at the same image applying the pertinence metric proposed in (Zanotta, 2010). Based on the results presented here showing that the metric of pertinence is valid, and also provides results consistent with other published in the relevant technical literature, and considering that to obtain these results was used a few training samples, it is expected that the metric proposed should present better results than those that would be presented with parametric classifiers when applied to multitemporal and hyperspectral images.

Esta tese investiga uma abordagem supervisionada para o problema da detecção de mudanças em imagens multitemporais de sensoriamento remoto empregando Support Vector Machines (SVM) com o uso dos kernels polinomial e gaussiano (RBF). A proposta metodológica está baseada na diferença das imagens-fração produzidas para cada data. Em imagens de cenas naturais a diferença nas frações de solo e vegetação tendem a apresentar uma distribuição simétrica em torno da origem. Esse fato pode ser usado para modelar duas distribuições normais multivariadas: mudança e não-mudança. O algoritmo Expectation-Maximization (EM) é implementado para estimar os parâmetros (vetor de médias, matriz de covariância e probabilidade a priori) associados a essas duas distribuições. Amostras aleatórias são extraídas dessas distribuições e usadas para treinar o classificador SVM nesta abordagem supervisionada. A metodologia proposta realiza testes com o uso de conjuntos de dados multitemporais de imagens multiespectrais TM-Landsat, que cobrem a mesma cena em duas datas diferentes. Os resultados são comparados com outros procedimentos, incluindo trabalhos anteriores, um conjunto de dados sintéticos e o classificador SVM One-Class. / In this thesis, we investigate a supervised approach to change detection in remote sensing multi-temporal image data by applying Support Vector Machines (SVM) technique using polynomial kernel and Gaussian kernel (RBF). The methodology is based on the difference-fraction images produced for two dates. In natural scenes, the difference in the fractions such as vegetation and bare soil occurring in two different dates tend to present a distribution symmetric around the origin of the coordinate system. This fact can be used to model two normal multivariate distributions: class change and no-change. The Expectation-Maximization algorithm (EM) is implemented to estimate the parameters (mean vector, covariance matrix and a priori probability) associated with these two distributions. Random samples are drawn from these distributions and used to train the SVM classifier in this supervised approach.The proposed methodology performs tests using multi-temporal TMLandsat multispectral image data covering the same scene in two different dates. The results are compared to other procedures including previous work, a synthetic data set and SVM One-Class.

Esta tese investiga uma abordagem não supervisionada para o problema da detecção de mudanças em imagens multiespectrais e multitemporais de sensoriamento remoto empregando Support Vector Machines (SVM) com o uso dos kernels polinomial e RBF e de uma nova métrica de pertinência de pixels. A proposta metodológica está baseada na diferença das imagens-fração produzidas para cada data. Em imagens de cenas naturais essa diferença nas frações de solo e vegetação tendem a apresentar uma distribuição simétrica próxima à origem. Essa caracteristica pode ser usada para modelar as distribuições normais multivariadas das classes mudança e não-mudança. O algoritmo Expectation-Maximization (EM) é implementado com a finalidade de estimar os parâmetros (vetor de médias, matriz de covariância e probabilidade a priori) associados a essas duas distribuições. A seguir, amostras aleatórias e normalmente distribuidas são extraídas dessas distribuições e rotuladas segundo sua pertinência em uma das classes. Essas amostras são então usadas no treinamento do classificador SVM. A partir desta classificação é estimada uma nova métrica de pertinência de pixels. A metodologia proposta realiza testes com o uso de conjuntos de dados multitemporais de imagens multiespectrais Landsat-TM que cobrem a mesma cena em duas datas diferentes. A métrica de pertinência proposta é validada através de amostras de teste controladas obtidas a partir da técnica Change Vetor Analysis, além disso, os resultados de pertinência obtidos para a imagem original com essa nova métrica são comparados aos resultados de pertinência obtidos para a mesma imagem pela métrica proposta em (Zanotta, 2010). Baseado nos resultados apresentados neste trabalho que mostram que a métrica para determinação de pertinência é válida e também apresenta resultados compatíveis com outra técnica de pertinência publicada na literatura e considerando que para obter esses resultados utilizou-se poucas amostras de treinamento, espera-se que essa métrica deva apresentar melhores resultados que os que seriam apresentados com classificadores paramétricos quando aplicado a imagens multitemporais e hiperespectrais. / This thesis investigates a unsupervised approach to the problem of change detection in multispectral and multitemporal remote sensing images using Support Vector Machines (SVM) with the use of polynomial and RBF kernels and a new metric of pertinence of pixels. The methodology is based on the difference-fraction images produced for each date. In images of natural scenes. This difference in the fractions of bare soil and vegetation tend to have a symmetrical distribution close to the origin. This feature can be used to model the multivariate normal distributions of the classes change and no-change. The Expectation- Maximization algorithm (EM) is implemented in order to estimate the parameters (mean vector, covariance matrix and a priori probability) associated with these two distributions. Then random and normally distributed samples are extracted from these distributions and labeled according to their pertinence to the classes. These samples are then used in the training of SVM classifier. From this classification is estimated a new metric of pertinence of pixel. The proposed methodology performs tests using multitemporal data sets of multispectral Landsat-TM images that cover the same scene at two different dates. The proposed metric of pertinence is validated via controlled test samples obtained from Change Vector Analysis technique. In addition, the results obtained at the original image with the new metric are compared to the results obtained at the same image applying the pertinence metric proposed in (Zanotta, 2010). Based on the results presented here showing that the metric of pertinence is valid, and also provides results consistent with other published in the relevant technical literature, and considering that to obtain these results was used a few training samples, it is expected that the metric proposed should present better results than those that would be presented with parametric classifiers when applied to multitemporal and hyperspectral images.

This thesis is intent on using mixtures of probability distributions in generalized linear model. The theoretical part is divided into two parts. In the first chapter a generalized linear model (GLM) is defined as an alternative to the classical linear regression model. The second chapter describes the mixture of probability distributions and estimate of their parameters. At the end of the second chapter, the previous theories are connected into the finite mixture generalized linear model. The last third part is practical and shows concrete examples of these models.

In binary-transaction data-mining, traditional frequent itemset mining often produces results which are not straightforward to interpret. To overcome this problem, probability models are often used to produce more compact and conclusive results, albeit with some loss of accuracy. Bayesian statistics have been widely used in the development of probability models in machine learning in recent years and these methods have many advantages, including their abilities to avoid overfitting. In this thesis, we develop two Bayesian mixture models with the Dirichlet distribution prior and the Dirichlet process (DP) prior to improve the previous non-Bayesian mixture model developed for transaction dataset mining. First, we develop a finite Bayesian mixture model by introducing conjugate priors to the model. Then, we extend this model to an infinite Bayesian mixture using a Dirichlet process prior. The Dirichlet process mixture model is a nonparametric Bayesian model which allows for the automatic determination of an appropriate number of mixture components. We implement the inference of both mixture models using two methods: a collapsed Gibbs sampling scheme and a variational approximation algorithm. Experiments in several benchmark problems have shown that both mixture models achieve better performance than a non-Bayesian mixture model. The variational algorithm is the faster of the two approaches while the Gibbs sampling method achieves a more accurate result. The Dirichlet process mixture model can automatically grow to a proper complexity for a better approximation. However, these approaches also show that mixture models underestimate the probabilities of frequent itemsets. Consequently, these models have a higher sensitivity but a lower specificity.

Object of this thesis is to construct a mixture model of earnings of the Czech households. In first part are described characteristics of mixtures of statistical distributions with the focus on the mixtures of normal distibutions. In practical part of this thesis are constructed models with parameters extimations based on the data from EU-SILC. Models made by graphical method, EM algorithm and method of maximum likelihood. The quality of models is measured by Akaike information criterion.