A partir de dados obtidos do modelo do geopotencial EGM96, da gravimetria, do GPS e do nivelamento geométrico, e aplicando harmônicos esféricos e FFT como técnicas de determinação geoidal, foram utilizadas neste trabalho redes neurais artificiais como ferramenta alternativa na determinação de um modelo geoidal. Procurou-se uma determinação geoidal de forma mais rápida, com precisão adequada e com menor esforço na determinação de parâmetros importantes na obtenção da referida superfície. Foram utilizados modelos de redes neurais do tipo MLP, algoritmo de treinamento backpropagation, variando o número de camadas, o número de neurônios, a função de ativação, a taxa de aprendizado e o termo momento. Os dados dos modelos mencionados foram tratados de forma a serem utilizados pelos modelos de redes neurais. Foram executadas a normalização, a análise de componentes principais e a definição dos atributos de entrada e saída para treinamento do modelo de rede neural. Foram Realizadas comparações entre os modelos geoidais existentes, os quais foram utilizados nesta pesquisa, com os resultados obtidos pelo modelo de rede neural. Tais comparações resultaram na obtenção dos erros entre as superfícies, justificando dessa forma a possibilidade de uso do referido método, com a conseqüente demonstração de suas vantagens e desvantagens. / Applying data from EGM96 geopotential model, gravimetric, GPS and geometric leveling data and using spherical harmonics and FFT as techniques of geoidal determination, this thesis has the goal to find a fast alternative tool to define a geoidal undulation model considering precision and a small effort to estimate important parameters to obtain the mentioned model. MLP neural networks, backpropagation algorithm changing the numbers of layers, neurons numbers, activation function, learning rate and momentum term have been applied. The data of the mentioned models were handling aiming to be used by the neural networks models. Normalization, analysis of the main components, definition of the input and output attributes to training the neural network model, have been also used. Comparison among existing models and the models used in this research with results obtained by the neural network have been done, showing the errors between the created surfaces. At the end, it is presented a positive argument to use the MLP neural network to generate a geoidal model with advantages and disadvantages.

Advances in biotechnologies rapidly increase the number of molecules of a cell which can be observed simultaneously. This includes expression levels of thousands or ten-thousands of genes as well as concentration levels of metabolites or proteins. <br><br> Such Profile data, observed at different times or at different experimental conditions (e.g., heat or dry stress), show how the biological experiment is reflected on the molecular level. This information is helpful to understand the molecular behaviour and to identify molecules or combination of molecules that characterise specific biological condition (e.g., disease). <br><br> This work shows the potentials of component extraction algorithms to identify the major factors which influenced the observed data. This can be the expected experimental factors such as the time or temperature as well as unexpected factors such as technical artefacts or even unknown biological behaviour. <br><br> Extracting components means to reduce the very high-dimensional data to a small set of new variables termed components. Each component is a combination of all original variables. The classical approach for that purpose is the principal component analysis (PCA). <br><br> It is shown that, in contrast to PCA which maximises the variance only, modern approaches such as independent component analysis (ICA) are more suitable for analysing molecular data. The condition of independence between components of ICA fits more naturally our assumption of individual (independent) factors which influence the data. This higher potential of ICA is demonstrated by a crossing experiment of the model plant <i>Arabidopsis thaliana</i> (Thale Cress). The experimental factors could be well identified and, in addition, ICA could even detect a technical artefact. <br><br> However, in continuously observations such as in time experiments, the data show, in general, a nonlinear distribution. To analyse such nonlinear data, a nonlinear extension of PCA is used. This nonlinear PCA (NLPCA) is based on a neural network algorithm. The algorithm is adapted to be applicable to incomplete molecular data sets. Thus, it provides also the ability to estimate the missing data. The potential of nonlinear PCA to identify nonlinear factors is demonstrated by a cold stress experiment of <i>Arabidopsis thaliana</i>. <br><br> The results of component analysis can be used to build a molecular network model. Since it includes functional dependencies it is termed functional network. Applied to the cold stress data, it is shown that functional networks are appropriate to visualise biological processes and thereby reveals molecular dynamics. / Fortschritte in der Biotechnologie ermöglichen es, eine immer größere Anzahl von Molekülen in einer Zelle gleichzeitig zu erfassen. Das betrifft sowohl die Expressionswerte tausender oder zehntausender Gene als auch die Konzentrationswerte von Metaboliten oder Proteinen. <br><br> Diese Profildaten verschiedener Zeitpunkte oder unterschiedlicher experimenteller Bedingungen (z.B. unter Stressbedingungen wie Hitze oder Trockenheit) zeigen, wie sich das biologische Experiment auf molekularer Ebene widerspiegelt. Diese Information kann genutzt werden, um molekulare Abläufe besser zu verstehen und um Moleküle oder Molekül-Kombinationen zu bestimmen, die für bestimmte biologische Zustände (z.B.: Krankheit) charakteristisch sind. <br><br> Die Arbeit zeigt die Möglichkeiten von Komponenten-Extraktions-Algorithmen zur Bestimmung der wesentlichen Faktoren, die einen Einfluss auf die beobachteten Daten ausübten. Das können sowohl die erwarteten experimentellen Faktoren wie Zeit oder Temperatur sein als auch unerwartete Faktoren wie technische Einflüsse oder sogar unerwartete biologische Vorgänge. <br><br> Unter der Extraktion von Komponenten versteht man die Reduzierung dieser stark hoch-dimensionalen Daten auf wenige neue Variablen, die eine Kombination aus allen ursprünglichen Variablen darstellen und als Komponenten bezeichnet werden. Die Standard-Methode für diesen Zweck ist die Hauptkomponentenanalyse (PCA). <br><br> Es wird gezeigt, dass - im Vergleich zur nur die Varianz maximierenden PCA - moderne Methoden wie die Unabhängige Komponentenanalyse (ICA) für die Analyse molekularer Datensätze besser geeignet sind. Die Unabhängigkeit von Komponenten in der ICA entspricht viel besser unserer Annahme individueller (unabhängiger) Faktoren, die einen Einfluss auf die Daten ausüben. Dieser Vorteil der ICA wird anhand eines Kreuzungsexperiments mit der Modell-Pflanze <i>Arabidopsis thaliana</i> (Ackerschmalwand) demonstriert. Die experimentellen Faktoren konnten dabei gut identifiziert werden und ICA erkannte sogar zusätzlich einen technischen Störfaktor. <br><br> Bei kontinuierlichen Beobachtungen wie in Zeitexperimenten zeigen die Daten jedoch häufig eine nichtlineare Verteilung. Für die Analyse dieser nichtlinearen Daten wird eine nichtlinear erweiterte Methode der PCA angewandt. Diese nichtlineare PCA (NLPCA) basiert auf einem neuronalen Netzwerk-Algorithmus. Der Algorithmus wurde für die Anwendung auf unvollständigen molekularen Daten erweitert. Dies ermöglicht es, die fehlenden Werte zu schätzen. Die Fähigkeit der nichtlinearen PCA zur Bestimmung nichtlinearer Faktoren wird anhand eines Kältestress-Experiments mit <i>Arabidopsis thaliana</i> demonstriert. <br><br> Die Ergebnisse aus der Komponentenanalyse können zur Erstellung molekularer Netzwerk-Modelle genutzt werden. Da sie funktionelle Abhängigkeiten berücksichtigen, werden sie als Funktionale Netzwerke bezeichnet. Anhand der Kältestress-Daten wird demonstriert, dass solche funktionalen Netzwerke geeignet sind, biologische Prozesse zu visualisieren und dadurch die molekularen Dynamiken aufzuzeigen.

Made available in DSpace on 2014-06-11T19:32:16Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-02-17Bitstream added on 2014-06-13T20:23:21Z : No. of bitstreams: 1 sousa_pfc_dr_jabo.pdf: 387633 bytes, checksum: 521ab7a95343ec6b201a18d943d41027 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Apesar de sua importância comercial, o número de variedades de laranjas é muito restrito no Brasil. Os Bancos de Germoplasmas de citros possuem grande número de genótipos de laranjas doces para serem explorados e avaliados quanto aos aspectos botânicos, genéticos e agronômicos, visando elevar a variabilidade genética e as qualidades agronômicas das cultivares. Como parte desse trabalho, avaliou-se 58 genótipos de laranjeiras doces em relação aos caracteres físicos, visando mercado in natura por meio de 9 caracteres físicos (diâmetro, perímetro, altura e peso dos frutos, espessuras da casca, albedo e polpa e número de sementes) e 7 caracteres visando qualidade industrial (acidez total titulável, sólidos solúveis totais, “ratio”, peso dos frutos, rendimento de suco, ácido ascórbico e índice tecnológico= kg sólidos solúveis/40,8kg). A análise multivariada indicou a existência de variabilidade entre os genótipos em relação aos caracteres físicos visando mercado in natura e qualidade industrial. Dois componentes principais, com autovalores > 1, representaram 66,03% da variância total para os caracteres físicos. As variáveis com maior poder discriminatório na primeira componente principal foram: diâmetro, perímetro, peso e altura dos frutos. Os escores desse componente foram designados MI-CP1 (mercado in natura), e os genótipos com os maiores valores foram os mais indicados para o mercado de fruta fresca. Na segunda componente principal, as variáveis mais discriminantes foram espessura do endocarpo e rendimento de suco, cujos escores foram nomeados (S-CP2), caracteres físicos esses ideais para a qualidade industrial. Nos escores dos dois componentes principais (MI-CP1 e S-CP2), o genótipo 22- ‘Lanelate’ foi destaque, seguido por 43-Telde, 39-Rotuna, 44-Torregrossa, 46-Tua Mamede e 17-Grada. Quanto às avaliações visando qualidade industrial... / Although its commercial importance, the number of you cultivate of oranges it is very restricted in Brazil. The Banks of Germoplasmas of citros possess innumerable accesses of oranges candies to be explored and evaluated how much to the botanical, genetic and agronomics aspects, aiming at to raise the genetic variability and the agronomics qualities cultivating of them. As part of that work, was sought to evaluate 58 genotypes of sweet orange trees in relation to the physical characters, seeking market in nature and industry quality, through 9 physical characters (diameter, perimeter, height and weight of the fruits, thickness of the peel, albedo and pulp and number of seeds) and 7 characters seeking industrial quality (acidity total titillate, total soluble solids, ratio , weight of the fruits, juice revenue, ascorbic acid and technological index = kg solid solutes/40,8kg). The analysis multivariate indicated the variability existence among the genotypes in relation to the physical characters and industrial quality. Two main components, with autovalues> 1, they represented 66,03% of the total variance for the physical characters. The variables with larger power discriminate in the first main component were: diameter, perimeter, weight and height of the fruits; we named the scores of that component of MI-CP1 (market in nature), genotypes with the largest values were the most suitable to the market of fresh fruit; in the second main component the variables more discriminate were thickness of the endocarp and juice revenue, it was named (S-CP2), characters physical ideas for the industrial quality. In the scores of the two main components (MI-CP1 and S-CP2), the genotype 22-Lanelate was prominence, followed for 43-Telde, 39-Rotuna, 44- Torregrossa, 46-Tua Mamede and it 17-Grada. How much to the evaluations aiming at industrial quality (INDUST-CP1), had been distinguished: ...(Complete abstract click electronic access below)

Made available in DSpace on 2014-12-17T14:55:21Z (GMT). No. of bitstreams: 1 FabioSL_TESE.pdf: 5888891 bytes, checksum: cd954df5e4af671c3361060293cc5710 (MD5) Previous issue date: 2014-05-30 / Universidade Federal do Rio Grande do Norte / The precision and the fast identification of abnormalities of bottom hole are essential to prevent damage and increase production in the oil industry. This work presents a study about a new automatic approach to the detection and the classification of operation mode in the Sucker-rod Pumping through dynamometric cards of bottom hole. The main idea is the recognition of the well production status through the image processing of the bottom s hole dynamometric card (Boundary Descriptors) and statistics and similarity mathematics tools, like Fourier Descriptor, Principal Components Analysis (PCA) and Euclidean Distance. In order to validate the proposal, the Sucker-Rod Pumping system real data are used / A identifica??o r?pida e precisa de anormalidades de fundo de po?o ? essencial para evitar danos e aumentar a produ??o na ind?stria do petr?leo. Esta tese apresenta um estudo sobre uma nova abordagem autom?tica para a detec??o e classifica??o de modos de opera??o no sistema de Bombeio Mec?nico atrav?s de carta de dinamom?tricas de fundo de po?o. A id?ia principal ? o reconhecimento das condi??es de produ??o do sistema atrav?s do processamento de imagem do carta dinamom?trica de fundo de po?o (Descritores de Fourier) e ferramentas matem?ticas estat?sticas (An?lise de Componentes Principais - PCA) e de similaridade (Dist?ncia Euclidiana). Para validar a proposta, s?o utilizados dados provenientes de sistemas de Bombeio Mec?nico reais

Made available in DSpace on 2014-12-17T14:56:05Z (GMT). No. of bitstreams: 1 AndreFB_DISSERT.pdf: 2147554 bytes, checksum: 3ed5f0d06e3b072597f2eae69b7d1ca2 (MD5) Previous issue date: 2012-02-24 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / The Brain-Computer Interfaces (BCI) have as main purpose to establish a communication path with the central nervous system (CNS) independently from the standard pathway (nervous, muscles), aiming to control a device. The main objective of the current research is to develop an off-line BCI that separates the different EEG patterns resulting from strictly mental tasks performed by an experimental subject, comparing the effectiveness of different signal-preprocessing approaches. We also tested different classification approaches: all versus all, one versus one and a hierarchic classification approach. No preprocessing techniques were found able to improve the system performance. Furthermore, the hierarchic approach proved to be capable to produce results above the expected by literature / As interfaces c?rebro-computador (ICC) t?m como objetivo estabelecer uma via de comunica??o com o sistema nervoso central (SNC) que seja independente das vias padr?o (nervos, m?sculos), visando o controle de algum dispositivo. O objetivo principal da presente pesquisa ? desenvolver uma ICC off-line que separe os diferentes padr?es de EEG resultantes de tarefas puramente mentais realizadas por um sujeito experimental, comparando a efic?cia de diferentes abordagens de pr?-processamento do sinal. Tamb?m foram testadas diferentes abordagens de classifica??o: todos contra todos, um contra um e uma abordagem hier?rquica de classifica??o. N?o foram encontradas t?cnicas de pr?-processamento que melhorem os resultados do sistema. Al?m disso, a abordagem hier?rquica sugerida mostrou-se capaz de produzir resultados acima do padr?o esperado pela literatura

Submitted by Neusa Fagundes (neusa.fagundes@unioeste.br) on 2017-09-18T14:32:46Z No. of bitstreams: 1 Alan_Gavioli2017.pdf: 4935513 bytes, checksum: 58816f2871fee27474b2fd5e511826af (MD5) / Made available in DSpace on 2017-09-18T14:32:46Z (GMT). No. of bitstreams: 1 Alan_Gavioli2017.pdf: 4935513 bytes, checksum: 58816f2871fee27474b2fd5e511826af (MD5) Previous issue date: 2017-02-17 / Two basic activities for the definition of quality management zones (MZs) are the variable selection task and the cluster analysis task. There are several methods proposed to execute them, but due to their complexity, they need to be made available by computer systems. In this study, 5 methods based on spatial correlation analysis, principal component analysis (PCA) and multivariate spatial analysis based on Moran’s index and PCA (MULTISPATI-PCA) were evaluated. A new variable selection algorithm, named MPCA-SC, based on the combined use of spatial correlation analysis and MULTISPATI-PCA, was proposed. The potential use of 20 clustering algorithms for the generation of MZs was evaluated: average linkage, bagged clustering, centroid linkage, clustering large applications, complete linkage, divisive analysis, fuzzy analysis clustering (fanny), fuzzy c-means, fuzzy c-shells, hard competitive learning, hybrid hierarchical clustering, k-means, McQuitty’s method (mcquitty), median linkage, neural gas, partitioning around medoids, single linkage, spherical k-means, unsupervised fuzzy competitive learning, and Ward’s method. Two computational modules developed to provide the variable selection and data clustering methods for definition of MZs were also presented. The evaluations were conducted with data obtained between 2010 and 2015 in three commercial agricultural areas, cultivated with soybean and corn, in the state of Paraná, Brazil. The experiments performed to evaluate the 5 variable selection algorithms showed that the new method MPCA-SC can improve the quality of MZs in several aspects, even obtaining satisfactory results with the other 4 algorithms. The evaluation experiments of the 20 clustering methods showed that 17 of them were suitable for the delineation of MZs, especially fanny and mcquitty. Finally, it was concluded that the two computational modules developed made it possible to obtain quality MZs. Furthermore, these modules constitute a more complete computer system than other free-to-use software such as FuzME, MZA, and SDUM, in terms of the diversity of variable selection and data clustering algorithms. / A seleção de variáveis e a análise de agrupamento de dados são atividades fundamentais para a definição de zonas de manejo (ZMs) de qualidade. Para executar essas duas atividades, existem diversos métodos propostos, que devido à sua complexidade precisam ser executados por meio da utilização de sistemas computacionais. Neste trabalho, avaliaramse 5 métodos de seleção de variáveis baseados em análise de correlação espacial, análise de componentes principais (ACP) e análise espacial multivariada baseada no índice de Moran e em ACP (MULTISPATI-PCA). Propôs-se um novo algoritmo de seleção de variáveis, denominado MPCA-SC, desenvolvido a partir da aplicação conjunta da análise de correlação espacial e de MULTISPATI-PCA. Avaliou-se a viabilidade de aplicação de 20 algoritmos de agrupamento de dados para a geração de ZMs: average linkage, bagged clustering, centroid linkage, clustering large applications, complete linkage, divisive analysis, fuzzy analysis clustering (fanny), fuzzy c-means, fuzzy c-shells, hard competitive learning, hybrid hierarchical clustering, k-means, median linkage, método de McQuitty (mcquitty), método de Ward, neural gas, partitioning around medoids, single linkage, spherical k-means e unsupervised fuzzy competitive learning. Apresentaram-se ainda dois módulos computacionais desenvolvidos para disponibilizar os métodos de seleção de variáveis e de agrupamento de dados para a definição de ZMs. As avaliações foram realizadas com dados obtidos entre os anos de 2010 e 2015 de três áreas agrícolas comerciais, localizadas no estado do Paraná, nas quais cultivaram-se milho e soja. Os experimentos efetuados para avaliar os 5 algoritmos de seleção de variáveis mostraram que o novo método MPCA-SC pode melhorar a qualidade de ZMs em diversos aspectos, mesmo obtendo-se resultados satisfatórios com os outros 4 algoritmos. Os experimentos de avaliação dos 20 métodos de agrupamento citados mostraram que 17 deles foram adequados para o delineamento de ZMs, com destaque para fanny e mcquitty. Por fim, concluiu-se que os dois módulos computacionais desenvolvidos possibilitaram a obtenção de ZMs de qualidade. Além disso, esses módulos constituem uma ferramenta computacional mais abrangente que outros softwares de uso gratuito, como FuzME, MZA e SDUM, em relação à diversidade de algoritmos disponibilizados para selecionar variáveis e agrupar dados.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-07-13T14:13:42Z No. of bitstreams: 1 carolinacarvalhoramosviana.pdf: 2071193 bytes, checksum: ced9ed600a8408dfa84aa8a442fdff6f (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-07-16T17:33:13Z (GMT) No. of bitstreams: 1 carolinacarvalhoramosviana.pdf: 2071193 bytes, checksum: ced9ed600a8408dfa84aa8a442fdff6f (MD5) / Made available in DSpace on 2018-07-16T17:33:13Z (GMT). No. of bitstreams: 1 carolinacarvalhoramosviana.pdf: 2071193 bytes, checksum: ced9ed600a8408dfa84aa8a442fdff6f (MD5) Previous issue date: 2018-03-28 / Este trabalho tem como objetivo geral a utilização da Espectroscopia na região do Infravermelho Médio, aliada à calibração multivariada (PCA e PLS) para caracterizar e quantificar a composição majoritária de fórmulas infantis. Foram avaliadas 20 marcas comercializadas em Juiz de Fora (MG), de quatro grandes indústrias do ramo. Determinou-se a composição majoritária das amostras (teor de lipídios, proteína verdadeira, carboidratos, umidade, sólidos totais e cinzas) por meio de métodos físico-químicos, em duplicata, de acordo com metodologias oficiais de análise, sendo que os resultados, em geral, atendem a legislação vigente. Em acréscimo, foi realizada a avaliação espectroscópica das formulações, na região MIR de 4000 cm-1 a 400 cm-1. Utilizando-se de ferramentas estatísticas, foi possível interpretar os espectros gerados e caracterizar a composição das fórmulas infantis testadas, em comparação às principais alegações descritas no rótulo e da literatura. As proposições sugeridas foram confirmadas pelo comportamento das amostras destas frente à Análise dos Componentes Principais (PCA), e a partir disto, pode-se dizer que a espectroscopia FT-MIR-ATR foi capaz de caracterizar as diferentes formulações testadas, quando aliada a estatística multivariada. Já em relação à Regressão por Mínimos Quadrados Parciais (PLS), somente foi encontrada correlação entre os dados físico-químicos e os espectros MIR no intervalo entre 1400 cm-1 e 1000cm-1, e por isso, este foi utilizado para as previsões dos valores analíticos. Por ser a região característica da absorção de carboidratos, o modelo apresentou os melhores resultados na predição do teor deste componente, com perfil de curva de calibração e ao mesmo tempo, apresentou predições ruins para o restante dos atributos testados. Sugere-se que o modelo possui potencial para as predições físico-químicas, em especial para carboidratos, caso sejam efetuadas curvas de calibração para este tipo de matriz alimentar. / This work focuses on the use of Fourier Transformed Mid Infrared Spectroscopy (FT-MIR) coupled to Attenuated Total Reflectance (ATR), combined with multivariate calibration as Principal Component Analysis (PCA) and Partial Least Squares (PLS) to characterize and quantify the majority composition of infant formulas. Twenty trademarks marketed in Juiz de Fora (MG) were evaluated from four different industries. The majority composition of the samples (lipid content, true protein, carbohydrates, moisture, total solids and ashes) was determined by physicochemical methods, in duplicate, according to official analysis methodologies. The results, in general, comply with current legislation. On the other hand, the spectroscopic evaluation of the formulations was performed in the MIR region from 4000 cm-1 to 400 cm-1. Using statistical tools, it was possible to interpret the generated spectra and characterize the composition of the infant formulas tested, in comparison to the main claims described in the labels and in the literature. The suggested propositions were confirmed by the behavior of these samples when compared to PCA. It can be said that FT-MIR-ATR spectroscopy was able to characterize the different formulations tested, when allied to multivariate statistics. In relation to the Regression by PLS, only a correlation was found between physicochemical data and MIR spectra in the interval between 1400 cm-1 and 1000 cm-1, and therefore, it was used for the predictions of the analytical values. Because it is the characteristic region of carbohydrate absorption, the model presented the best results in the prediction of the content of this component, with a calibration curve profile and at the same time presented bad predictions for the rest of the attributes tested. It is suggested that the model has potential for physicochemical predictions, especially for carbohydrates, if calibration curves are made for this type of food matrix.

L’un des problèmes majeurs en analyse de formes est celui de l’analyse statistique en présence de formes aberrantes. On assiste avec l’évolution des moyens de collecte automatique des données, à la présence des valeurs aberrantes qui peuvent affecter énormément l’analyse descriptive des formes. En effet, les approches de l’état de l’art ne sont pas assez robustes à la présence de formes aberrantes. En particulier, la forme moyenne calculée penche vers les observations aberrantes et peut ainsi porter des déformations irrégulières. Aussi, l’analyse par ACP de la variabilité dans une classe de formes donnée conduit à des modes de variation qui décrivent plutôt la variabilité portée par ces formes aberrantes. Dans ce travail de thèse, nous proposons un schéma d’analyse robuste aux aberrations qui peuvent entacher une classe de formes donnée. Notre approche est une variante robuste de l’ACP qui consiste à détecter et à restaurer les formes aberrantes préalablement à une ACP menée dans l’espace tangent relatif à la forme moyenne. Au lieu de simplement éliminer les formes aberrantes, nous voulons bénéficier de la variabilité locale correcte qui y est présente en intégrant leur version restaurée dans l’analyse. Nous proposons également une approche variationnelle et une ACP élastique pour l’analyse de la variabilité d’un ensemble de formes en s’appuyant sur une métrique robuste basée géodésique. La troisième contribution de la thèse se situe au niveau des algorithmes de classification des formes basée sur les statistiques de formes : classification utilisant la moyenne intrinsèque, ou relaxée, par ACP tangente et par formes propres.Les approches proposées sont évaluées et comparées aux approches de l’état de l’art sur les bases de formes HAND et MPEG-7. Les résultats obtenus démontrent la capacité du schéma proposé à surpasser la présence de formes aberrantes et fournir des modes de variation qui caractérisent la variabilité des formes étudiées. / A major and complex problem in shape analysis is the statistical analysis of a set of shapes containing aberrant shapes. With the evolution of automatic data acquisition means, outliers can occur and their presence may greatly affect the descriptive analysis of shapes.Actually, state-of-the-art approaches are not robust enough to outliers. In particular, the calculated mean shape deviates towards the aberrant observations and thus carries irregular deformations.Similarly, the PCA analysis of the variability in a given class of shapes leads to variation modes which rather describe the variability carried by these aberrant shapes.In this thesis work, we propose a robust analysis scheme to handle the effects of aberrations that can occur in a given set. Our approach is a robust variant of PCA that consists in detecting and restoring aberrant shapes prior to a PCA in the tangent space relative to the means shape.Instead of simply rejecting outliers, we want to benefit from the present correct local variability by integrating their restored version into the analysis. We also propose a variational approach and an elastic PCA for the analysis of the variability of a set of shapes by using a robust geodesic-based metric. The third contribution of the thesis lies in the algorithms of shape classification based on shapes statistics: classification using the intrinsic mean shape, or relaxed one, by tangent PCA and by eigenshapes.The proposed schemes are evaluated and compared with existing schemes through two shape databases, HAND and MPEG-7. The results show the proposed scheme’s ability to overcome the presence of aberrant shapes and provide variation modes that characterize the variability of studied shapes.

While many university students get introduced to the concept of statistics early in their education, random matrix theory (RMT) usually first arises (if at all) in graduate level classes. This thesis serves as a friendly introduction to RMT, which is the study of matrices with entries following some probability distribution. Fundamental results, such as Gaussian and Wishart ensembles, are introduced and a discussion of how their corresponding eigenvalues are distributed is presented. Two well-studied applications, namely neural networks and PCA, are discussed where we present how RMT can be applied / Medan många stöter på statistik och sannolikhetslära tidigt under sina universitetsstudier så är det sällan slumpmatristeori (RMT) dyker upp förän på forskarnivå. RMT handlar om att studera matriser där elementen följer någon sannolikhetsfördelning och den här uppsatsen presenterar den mest grundläggande teorin för slumpmatriser. Vi introducerar Gaussian ensembles, Wishart ensembles samt fördelningarna för dem tillhörande egenvärdena. Avslutningsvis så introducerar vi hur slumpmatriser kan användas i neruonnät och i PCA.

<p>This work explores how randomization can be exploited to deliver sophisticated</p><p>algorithms with provable bounds for: (i) The approximation of matrix functions, such</p><p>as the log-determinant and the Von-Neumann entropy; and (ii) The low-rank approximation</p><p>of matrices. Our algorithms are inspired by recent advances in Randomized</p><p>Numerical Linear Algebra (RandNLA), an interdisciplinary research area that exploits</p><p>randomization as a computational resource to develop improved algorithms for</p><p>large-scale linear algebra problems. The main goal of this work is to encourage the</p><p>practical use of RandNLA approaches to solve Big Data bottlenecks at industrial</p><p>level. Our extensive evaluation tests are complemented by a thorough theoretical</p><p>analysis that proves the accuracy of the proposed algorithms and highlights their</p><p>scalability as the volume of data increases. Finally, the low computational time and</p><p>memory consumption, combined with simple implementation schemes that can easily</p><p>be extended in parallel and distributed environments, render our algorithms suitable</p><p>for use in the development of highly efficient real-world software.</p>