Thesis (Ph.D.)--Rochester Institute of Technology, 2008. / Typescript. Includes bibliographical references (p. 175-179) and index.

Includes bibliographical references (p. 162-177).

Thesis (Ph. D.)--University of Florida, 2001. / Title from first page of PDF file. Document formatted into pages; contains xi, 124 p.; also contains graphics. Vita. Includes bibliographical references (p. 120-123).

Η ανάλυση σε κύριες συνιστώσες είναι μια τεχνική μείωσης του δείγματος. Χρησιμοποιείται όταν έχουμε ψηλά συσχετισμένες μεταβλητές. Μειώνει τον αριθμό των αρχικών μεταβλητών σε ένα μικρότερο αριθμό κύριων συνιστωσών που μετρούν τη μεγαλύτερη δυνατή διασπορά του δείγματος. Είναι μια διαδικασία που εφαρμόζεται για μεγάλα δείγματα. Η παραγοντική ανάλυση είναι μια τεχνική μείωσης των μεταβλητών του δείγματος η οποία αναγνωρίζει τον αριθμό των λανθάνουσων δομών και δημιουργεί μια δομή, ένα νέο σύνολο μεταβλητών, τους κοινούς παράγοντες που ερμηνεύουν το δείγμα. Προϋποθέτει μια δομή από μη παρατηρήσιμες μεταβλητές που δεν μπορούν να μετρηθούν άμεσα. Εκτιμά τους παράγοντες εκείνους που έχουν επίδραση και αντανακλούν τις αρχικές μεταβλητές. Επιτρέπει στον ερευνητή να περιγράψει αλλά ακόμη και να αναγνωρίσει τους παράγοντες εκείνους που παριστάνουν το δείγμα. Συμπεριλαμβάνει τους ειδικούς παράγοντες (ειδικά σφάλματα) που οφείλονται για την αναξιοπιστία των μετρήσεων. / Principal component analysis is a technique for reducing the sample, used when we have high correlated variables. It reduces the number of input variables into a smaller number of key components that measure the maximum sample variance. It is a process applied to large samples. Factor analysis is a technique to reduce the variables in the sample that identifies the number of latent structures and creates a structure, a new set of variables, called common factors explaining the sample. Implies a structure of non-observable variables that can not be measured directly. It considers the factors that affect and reflect the original variables. It allows the researcher to describe and even to identify the factors that represent the sample. Includes special factors (specific errors) due to unreliability of measurement.

Thesis (MSc (Mathematical Statistics))--University of Stellenbosch, 2008. / In this study several procedures for finding robust principal components (RPCs) for low and high dimensional data sets are investigated in parallel with robust principal component analysis (RPCA) biplots. These RPCA biplots will be used for the simultaneous visualisation of the observations and variables in the subspace spanned by the RPCs. Chapter 1 contains: a brief overview of the difficulties that are encountered when graphically investigating patterns and relationships in multidimensional data and why PCA can be used to circumvent these difficulties; the objectives of this study; a summary of the work done in order to meet these objectives; certain results in matrix algebra that are needed throughout this study. In Chapter 2 the derivation of the classic sample principal components (SPCs) is first discussed in detail since they are the „building blocks‟ of classic principal component analysis (CPCA) biplots. Secondly, the traditional CPCA biplot of Gabriel (1971) is reviewed. Thirdly, modifications to this biplot using the new philosophy of Gower & Hand (1996) are given attention. Reasons why this modified biplot has several advantages over the traditional biplot – some of which are aesthetical in nature – are given. Lastly, changes that can be made to the Gower & Hand (1996) PCA biplot to optimally visualise the correlations between the variables is discussed. Because the SPCs determine the position of the observations as well as the orientation of the arrows (traditional biplot) or axes (Gower and Hand biplot) in the PCA biplot subspace, it is useful to give estimates of the standard errors of the SPCs together with the biplot display as an indication of the stability of the biplot. A computer-intensive statistical technique called the Bootstrap is firstly discussed that is used to calculate the standard errors of the SPCs without making underlying distributional assumptions. Secondly, the influence of outliers on Bootstrap results is investigated. Lastly, a robust form of the Bootstrap is briefly discussed for calculating standard error estimates that remain stable with or without the presence of outliers in the sample. All the preceding topics are the subject matter of Chapter 3. In Chapter 4, reasons why a PC analysis should be made robust in the presence of outliers are firstly discussed. Secondly, different types of outliers are discussed. Thirdly, a method for identifying influential observations and a method for identifying outlying observations are investigated. Lastly, different methods for constructing robust estimates of location and dispersion for the observations receive attention. These robust estimates are used in numerical procedures that calculate RPCs. In Chapter 5, an overview of some of the procedures that are used to calculate RPCs for lower and higher dimensional data sets is firstly discussed. Secondly, two numerical procedures that can be used to calculate RPCs for lower dimensional data sets are discussed and compared in detail. Details and examples of robust versions of the Gower & Hand (1996) PCA biplot that can be constructed using these RPCs are also provided. In Chapter 6, five numerical procedures for calculating RPCs for higher dimensional data sets are discussed in detail. Once RPCs have been obtained by using these methods, they are used to construct robust versions of the PCA biplot of Gower & Hand (1996). Details and examples of these robust PCA biplots are also provided. An extensive software library has been developed so that the biplot methodology discussed in this study can be used in practice. The functions in this library are given in an appendix at the end of this study. This software library is used on data sets from various fields so that the merit of the theory developed in this study can be visually appraised.

Made available in DSpace on 2015-03-26T13:32:06Z (GMT). No. of bitstreams: 1 texto completo.pdf: 358534 bytes, checksum: 24e75168f2f6257c7ffe917ef5ade7c8 (MD5) Previous issue date: 2009-02-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nowadays research often collect information on many variables from a great number of experimental units, hence produce and store large amount of data, which in turn requires methods that can handle such situations. Statistical methods such as the principal component analysis (PCA), that can reduce the dimensionality of the analysis without significant information loss, are of great interest. PCA can use either the covariance (S) or the correlation (R) matrix among variables, but the analysis may result in different Principal Components (PC) resulting from R or S. In order to indicate the best strategies for different scenarios, we conducted a simulation study to investigate the effects of variable scaling over the viability and quality of the results from PCA analysis used to cluster experimental units. In addition to this first simulation study, we also conducted a second one using animal science and economical variables from 255 dairy producers from three locations of Minas Gerais State. The goal was to verify the most appropriate data structure for cluster analysis, such that it best classifies the most economically viable producers. In both studies we used a transformation of variables based on its coefficient of variation, which resulted in a new covariance matrix named S*. Results showed that the use of matrix S favored economical variables with larger variances, while use of R matrix resulted as the most important variables the ones with larger correlations among them. Calculations of PC using matrix S* minimized these scaling problems when S and R matrices are used. Analysis using S is entirely affected by the variable scale while using R is not affected by the scale at all. We concluded that the S* matrix was the most appropriate for the present case study because it considered the most important economical variables to be the ones most related to the animal science variables. / Com o aumento substancial na quantidade de dados armazenados, surge a necessidade da utilização de métodos que permitam analisar simultaneamente várias variáveis medidas em cada elemento amostral, e ainda com a possibilidade de reduzir a dimensionalidade desse conjunto sem perda significativa de informação. Entre eles, pode-se citar o método dos componentes principais, cuja obtenção pode envolver a matriz de covariâncias (S) ou a de correlações (R) das variáveis de interesse. Como a utilização dessas matrizes pode fornecer diferentes componentes, objetivou-se investigar, por meio da simulação de dados, os efeitos das escalas das características sobre a qualidade e a viabilidade da classificação dos elementos amostrais, buscando assim, indicar estratégias de análise mais adequadas em diferentes casos. Além do estudo de simulação, foi realizado outro com variáveis zootécnicas e econômicas referentes a 255 produtores de leite de três regiões do estado de Minas Gerais, com o objetivo de verificar qual a melhor estrutura de dados em classificar de forma mais apropriada os produtores mais viáveis economicamente. Em ambos os estudos, foi efetuada uma transformação nos valores das variáveis baseada nos respectivos coeficientes de variação, cuja matriz de covariâncias foi denominada de S*. Observou-se que a utilização da matriz S privilegiou as variáveis econômicas de maiores variâncias, enquanto a matriz R considerou as variáveis mais correlacionadas entre si como as mais importantes. A obtenção dos CPs com base na matriz S* minimizou os problemas das escalas inerentes aos usos das matrizes S e R. A primeira, por considerá-la totalmente e, a segunda, por desconsiderá-la. Desta forma, considerou-se a matriz S* como a mais indicada no presente estudo de caso, uma vez que priorizou como mais importantes, as variáveis econômicas mais relacionadas às variáveis zootécnicas.

Geochemistry plays a vital role in our understanding mechanisms behind major geological systems such as the Earth's crust and its oceans (Albarède, F. 2003). More recently, geo-chemistry has played a vital role in the field of forensic investigation and in period dating. Forensic soil samples have been traditionally analysed via examinations of colour, texture and mineral content by physical or chemical methods. However, these methods leave any organic or water-soluble fractions unexamined. Tephrochronology (the dating of sedimentary sequences using volcanic ash layers) is an important tool for the dating and correlation of sedimentary sequences containing archives and proxies of past environmental change. Its importance in this area has increased since the increased free carbon in out atmosphere has made radio-carbon dating unreliable. Tephrochronology requires successful geo-chemical identification of the tephras, a method reliant on electron probe micro-analysis (EPMA) to analyse major element composition. However, it is often impossible to differentiate key tephra layers using EPMA alone. Raman spectroscopy is commonly used in chemistry, since vibrational information is specific to the chemical bonds and symmetry of molecules, and can provide a fingerprint by which these can be identified. Here, we demonstrate how Raman spectroscopy can be used for the successful discrimination of mineral species in tephra through the analysis of individual glass shards. We further demonstrate how, with the use of oxidative preparation methods, Raman spectroscopy can be used to successfully discriminate between soil types using mineralogy as well as the organic and water-soluble fractions of soils.

Esta pesquisa analisa a variação espaço-temporal de NDVI (Índice de Vegetação da Diferença Normalizada) em área de aproveitamento hidroelétrico, na UHE Santo Antônio, Porto Velho, Rondônia. Para tanto elabora mapeamento do uso e cobertura do solo a partir de imagem Landsat TM nas seguintes classes: Floresta Ombrófila Aberta, Floresta Ombrófila Densa, Desmatamento, Queimadas e Solo exposto; obtém uma série temporal de imagens de NDVI/MODIS para o período 2000-2011; gera espectros temporais; relaciona os padrões a partir da série temporal de imagens MODIS com as classes de uso e cobertura do solo; analisa a variação espaço-temporal de NDVI com base em Análise de Séries Temporais, a partir de CP’s (Componentes Principais). As técnicas para identificação de padrões a partir de Análise de Séries Temporais e de análise dos espectros temporais de índices de vegetação se constituem em uma importante ferramenta na avaliação e monitoramento da variação da vegetação ao longo do tempo. A área da UHE Santo Antonio é caracterizada pela sazonalidade de períodos secos e chuvosos bem definidos, o que permitiu identificar padrões sazonais. Quanto a análise por Componentes Principais esta técnica mostrou-se um bom método para identificar a variação da cobertura vegetal e avaliar as mudanças na cobertura da terra. A análise dos resultados do mapeamento do uso do solo evidenciou o seguinte: uma grande dificuldade em separar no processo de classificação digital as duas classes de floresta; extensas áreas de solo exposto, desmatamento e queimadas no entorno do rio Madeira e nas áreas próximas a UHE Santo Antonio. Com relação aos espectros temporais, as variações nos valores de NDVI apresentam duas variações bem definidas: uma relacionada a sazonalidade dos períodos úmido e seco, e outra relacionada a mudança de uso e ocupação do solo, como a retirada da vegetação existente e as queimadas. Os resultados das Componentes Principais são relativos as variações expressas nas três primeiras CP’s da série da seguinte forma: (a) com todas as imagens; (b) somente período seco e somente período chuvoso; (c) por cada ano da série. A CP1 do conjunto (a) apresentou um percentual de representatividade de 85,83%, com valores de NDVI altos e homogêneos para a cobertura florestal, indicando significativa presença de biomassa, já que os valores altos relacionam-se aos padrões encontrados em classes de vegetação. Na CP2 e CP3 de (a) (b) e (c) a variação expressa permitiu identificar as áreas de queimadas e principalmente as etapas de transformação das áreas de florestas até os desmatamentos mais recentes. / This research examines the spatio-temporal variability of NDVI (Normalized Difference vegetation index) in hydroelectric area, in Santo Antônio hpp, Porto Velho, Rondônia. From Landsat TM image, elaborates mapping of use and soil coverage in the following classes: Open Evergreen forest, dense Ombrophilous Forest Fires, deforestation, and soil exposed; Gets a time series of images of NDVIMODIS for the period 2000-2011; generates time spectrum; lists the patterns from the time series of MODIS images with the classes of land cover and use; examines the spatio-temporal variability of NDVI based on time series Analysis, from CP's (main components). The techniques for identifying patterns from time series analysis and temporal Spectra analysis of vegetation indexes are an important tool in the evaluation and monitoring of vegetation change over time. The area of Santo Antonio hydroelectric power plant is characterized by seasonality of rainy and dry periods well defined, which allowed to identify seasonal patterns. The technique of analysis by principal components proved to be a good method to identify the variation of vegetation cover and assess the changes in coverage of the Earth. The analysis of the results of the mapping of land use showed the following: a great difficulty in separating the digital classification process the two classes of forest; extensive areas of exposed soil, deforestation and burning around the Madeira River and in areas near the Santo Antonio hydroelectric power plant. With respect to temporal changes in spectra, NDVI values have two well-defined variations: one related to seasonality of wet and dry periods, and another related to change of use and occupation of the soil, such as the withdrawal of existing vegetation and fire. The results of the main components are related to changes expressed in the first three CP's series as follows: (a) with all images; (b) when only dry and rainy period only; (c) for each year of the series. The CP1 (a) presented a percentage of representativeness of 85.83 NDVI values high and homogeneous for forest cover, indicating significant presence of biomass, since the high values relate to patterns found in vegetation classes. In CP2 and CP3 (a) (b) and (c) the change expressed identified the areas burned and mainly the processing steps of forest areas up to the latest deforestation.

As técnicas de sensoriamento remoto têm se mostrado fundamentais como ferramenta auxiliar no mapeamento geológico básico. O avanço tecnológico gerado pelos novos sensores permite o desenvolvimento de técnicas mais apuradas na integração de dados litológicos e estruturais de várias fontes. Este trabalho buscou avaliar a potencialidade das imagens do sensor ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer) para identificação dos diferentes litotipos da área do Cerro Chato, em especial as unidades vulcânicas e hipabissais relacionadas. O Cerro Chato é caracterizado como uma feição geomorfológica situada à cerca de 15 km ao norte do município de Herval, na microrregião denominada Serra do Sudeste na porção sudeste do estado do Rio Grande do Sul. É constituído principalmente por uma seqüência de rochas efusivas e piroclásticas de composição riolítica relacionada a sistemas do tipo alta-sílica, vinculadas ao magmatismo granítico tardio do Batólito Pelotas. O objetivo deste trabalho foi testar e avaliar diversas técnicas de geoprocessamento buscando a diferenciação litológica, a identificação de alvos e a definição de morfoestruturas da área do Cerro Chato. O processamento utilizando a técnica de Transformação por Componentes Principais forneceu os melhores resultados realçando diferenças entre as rochas vulcânicas e hipabissais e as rochas encaixantes. Foram selecionadas as CP2 das imagens CP's 2, 3 e 5 na geração de uma composição colorida que permitiu delimitar três principais domínios de ocorrências das rochas de origem vulcânica no Cerro Chato. / The remote sensing techniques have been a very important and auxiliary tool to basic geological mapping. The new orbital sensors carried out a technologic increment that possibility the development of refined methods applied in the integration with diverse geologic data as petrology and structural. In this work were utilized images obtained from the ASTER sensor (Advanced Spaceborne Thermal Emission and Reflection Radiometer) to identify the lithologies in the Cerro Chato area, giving emphasis to the volcanic and hypabissal units. The Cerro Chato can be characterized as geomorphologic feature situated about 15 km to north of Herval town, in the Southeast Sierra micro region of the Rio Grande do Sul state, southernmost Brazil. It is constituted mainly by an effusive and pyroclastic rocks sequence of rhyolitic composition related to high silica systems, which magma has been associated to the younger granitic magmastim of the Pelotas Batholith. The main objective of this work was to test and evaluate diverse techniques of geoprocessment to try identifying different lithologic units and morphologic structures in the Cerro Chato area. The selective principal component analysis technique was used in the digital image processing, because it provided the best results enhancing the existent spectral differences between volcanic and country rocks. In this processing were selected the PC's2 images of the PC's 2, 3, and 5 to generated a color composite image that permitted the individualization of three main dominions of volcanic rocks in the Cerro Chato.

This thesis presents principal components as a useful tool for data dimensio- nality reduction. In the first part, the basic terminology and theoretical properties of principal components are described and a biplot construction is derived there as well. Besides, heuristic methods for a choice of the optimum number of prin- cipal components are summarised there. Subsequently, asymptotical properties of sample eigenvalues of covariance and white Wishart matrices are described and cases of equality of some eigenvalues are distinguished at the same time. In the second part of the thesis, asymptotic distribution of the largest eigenva- lue of white Wishart matrices is described, completed with graphic illustrations. A test of the number of significant eigenvalues is suggested on the basis of this limiting distribution, and the connection of this test to the number of suitable principal components is presented. The final part of the thesis provides an over- view of advanced computational methods for the choice of an adequate number of principal components. The thesis is completed with graphical illustrations and a simulation study using Wolfram Mathematica and R.