Doctor of Philosophy / This thesis is based on research on financial time series analysis using pattern recognition methods. The first part of this research focuses on univariate time series analysis using different pattern recognition methods. First, probabilities of basic patterns are used to represent the features of a section of time series. This feature can remove noise from the time series by statistical probability. It is experimentally proven that this feature is successful for pattern repeated time series. Second, a multiscale Gaussian gravity as a pattern relationship measurement which can describe the direction of the pattern relationship is introduced to pattern clustering. By searching for the Gaussian-gravity-guided nearest neighbour of each pattern, this clustering method can easily determine the boundaries of the clusters. Third, a method that unsupervised pattern classification can be transformed into multiscale supervised pattern classification by multiscale supervisory time series or multiscale filtered time series is presented. The second part of this research focuses on multivariate time series analysis using pattern recognition. A systematic method is proposed to find the independent variables of a group of share prices by time series clustering, principal component analysis, independent component analysis, and object recognition. The number of dependent variables is reduced and the multivariate time series analysis is simplified by time series clustering and principal component analysis. Independent component analysis aims to find the ideal independent variables of the group of shares. Object recognition is expected to recognize those independent variables which are similar to the independent components. This method provides a new clue to understanding the stock market and to modelling a large time series database.

Doctor of Philosophy / This thesis is based on research on financial time series analysis using pattern recognition methods. The first part of this research focuses on univariate time series analysis using different pattern recognition methods. First, probabilities of basic patterns are used to represent the features of a section of time series. This feature can remove noise from the time series by statistical probability. It is experimentally proven that this feature is successful for pattern repeated time series. Second, a multiscale Gaussian gravity as a pattern relationship measurement which can describe the direction of the pattern relationship is introduced to pattern clustering. By searching for the Gaussian-gravity-guided nearest neighbour of each pattern, this clustering method can easily determine the boundaries of the clusters. Third, a method that unsupervised pattern classification can be transformed into multiscale supervised pattern classification by multiscale supervisory time series or multiscale filtered time series is presented. The second part of this research focuses on multivariate time series analysis using pattern recognition. A systematic method is proposed to find the independent variables of a group of share prices by time series clustering, principal component analysis, independent component analysis, and object recognition. The number of dependent variables is reduced and the multivariate time series analysis is simplified by time series clustering and principal component analysis. Independent component analysis aims to find the ideal independent variables of the group of shares. Object recognition is expected to recognize those independent variables which are similar to the independent components. This method provides a new clue to understanding the stock market and to modelling a large time series database.

In our study we identify dominant hydroclimatic variables and large-scale patterns that lead to high streamflow events in the Santa Cruz, Salt, and Verde River in Arizona for the period 1979-2009 using Principal Component Analysis (PCA). We used winter (Nov - March) data from the USGS daily streamflow database and 11 variables from the North American Reanalysis (NARR) database, in addition to weather maps from the Hydrometeorological Prediction Center (HPC). Using streamflow data, we identify precipitation events that led to the highest 98th percentile of daily streamflow events and find dominant hydroclimatic variables associated with these events. We find that upper level winds and moisture fluxes are dominant variables that characterize events. The dominant mode for all three basins is associated with frontal systems, while the second mode is associated with cut-off upper level low pressure systems. Our goal is to provide forecasting agencies with tools to improve flood forecasting practices.

In this paper a resilient sensor network is built in order to lessen the effects of a small portion of corrupted sensors when an aggregated result such as the average needs to be obtained. By examining the variance in sensor readings, a change in the pattern can be spotted and minimized in order to maintain a stable aggregated reading. Offset in sensors readings are also analyzed and compensated to help reduce a bias change in average. These two analytical techniques are later combined in Kalman filter to produce a smooth and resilient average given by the readings of individual sensors. In addition, principal components analysis is used to detect variations in the sensor network. Experiments are held using real sensors called MICAz, which are use to gather light measurements in a small area and display the light average generated in that area.

Reconhecimento de padrões em imagens é uma área de grande interesse no mundo científico. Os chamados métodos de extração de características, possuem as habilidades de extrair características das imagens e também de reduzir a dimensionalidade dos dados gerando assim o chamado vetor de características. Considerando uma imagem de consulta, o foco de um sistema de reconhecimento de imagens de faces humanas é pesquisar em um banco de imagens, a imagem mais similar à imagem de consulta, de acordo com um critério dado. Este trabalho de pesquisa foi direcionado para a geração de vetores de características para um sistema de reconhecimento de imagens, considerando bancos de imagens de faces humanas, para propiciar tal tipo de consulta. Um vetor de características é uma representação numérica de uma imagem ou parte dela, descrevendo seus detalhes mais representativos. O vetor de características é um vetor n-dimensional contendo esses valores. Essa nova representação da imagem propicia vantagens ao processo de reconhecimento de imagens, pela redução da dimensionalidade dos dados. Uma abordagem alternativa para caracterizar imagens para um sistema de reconhecimento de imagens de faces humanas é a transformação do domínio. A principal vantagem de uma transformação é a sua efetiva caracterização das propriedades locais da imagem. As wavelets diferenciam-se das tradicionais técnicas de Fourier pela forma de localizar a informação no plano tempo-freqüência; basicamente, têm a capacidade de mudar de uma resolução para outra, o que as fazem especialmente adequadas para análise, representando o sinal em diferentes bandas de freqüências, cada uma com resoluções distintas correspondentes a cada escala. As wavelets foram aplicadas com sucesso na compressão, melhoria, análise, classificação, caracterização e recuperação de imagens. Uma das áreas beneficiadas onde essas propriedades tem encontrado grande relevância é a área de visão computacional, através da representação e descrição de imagens. Este trabalho descreve uma abordagem para o reconhecimento de imagens de faces humanas com a extração de características baseado na decomposição multiresolução de wavelets utilizando os filtros de Haar, Daubechies, Biorthogonal, Reverse Biorthogonal, Symlet, e Coiflet. Foram testadas em conjunto as técnicas PCA (Principal Component Analysis) e IMPCA (Image Principal Component Analysis), sendo que os melhores resultados foram obtidos utilizando a wavelet Biorthogonal com a técnica IMPCA / Image pattern recognition is an interesting area in the scientific world. The features extraction method refers to the ability to extract features from images, reduce the dimensionality and generates the features vector. Given a query image, the goal of a features extraction system is to search the database and return the most similar to the query image according to a given criteria. Our research addresses the generation of features vectors of a recognition image system for human faces databases. A feature vector is a numeric representation of an image or part of it over its representative aspects. The feature vector is a n-dimensional vector organizing such values. This new image representation can be stored into a database and allow a fast image retrieval. An alternative for image characterization for a human face recognition system is the domain transform. The principal advantage of a transform is its effective characterization for their local image properties. In the past few years researches in applied mathematics and signal processing have developed practical wavelet methods for the multi scale representation and analysis of signals. These new tools differ from the traditional Fourier techniques by the way in which they localize the information in the time-frequency plane; in particular, they are capable of trading on type of resolution for the other, which makes them especially suitable for the analysis of non-stationary signals. The wavelet transform is a set basis function that represents signals in different frequency bands, each one with a resolution matching its scale. They have been successfully applied to image compression, enhancement, analysis, classification, characterization and retrieval. One privileged area of application where these properties have been found to be relevant is computer vision, especially human faces imaging. In this work we describe an approach to image recognition for human face databases focused on feature extraction based on multiresolution wavelets decomposition, taking advantage of Biorthogonal, Reverse Biorthogonal, Symlet, Coiflet, Daubechies and Haar. They were tried in joint the techniques together the PCA (Principal Component Analysis) and IMPCA (Image Principal Component Analysis)

Patient medical records are a valuable resource that can be used for many purposes including managing and planning for future health needs as well as clinical research. Health databases such as the clinical practice research datalink (CPRD) and many other similar initiatives can provide researchers with a useful data source on which they can test their medical hypotheses. However, this can only be the case when researchers have a good set of hypotheses to test on the data. Conversely, the data may have other equally important areas that remain unexplored. There is a chance that some important signals in the data could be missed. Therefore, further analysis is required to make such hidden areas become more obvious and attainable for future exploration and investigation. Data mining techniques can be effective tools in discovering patterns and signals in large-scale patient data sets. These techniques have been widely applied to different areas in medical domain. Therefore, analysing patient data using such techniques has the potential to explore the data and to provide a better understanding of the information in patient records. However, the heterogeneity and complexity of medical data can be an obstacle in applying data mining techniques. Much of the potential value of this data therefore goes untapped. This thesis describes a novel methodology that reduces the dimensionality of primary care data, to make it more amenable to visualisation, mining and clustering. The methodology involves employing a combination of ontology-based semantic similarity and principal component analysis (PCA) to map the data into an appropriate and informative low dimensional space. The aim of this thesis is to develop a novel methodology that provides a visualisation of patient records. This visualisation provides a systematic method that allows the formulation of new and testable hypotheses which can be fed to researchers to carry out the subsequent phases of research. In a small-scale study based on Salford Integrated Record (SIR) data, I have demonstrated that this mapping provides informative views of patient phenotypes across a population and allows the construction of clusters of patients sharing common diagnosis and treatments. The next phase of the research was to develop this methodology and explore its application using larger patient cohorts. This data contains more precise relationships between features than small-scale data. It also leads to the understanding of distinct population patterns and extracting common features. For such reasons, I applied the mapping methodology to patient records from the CPRD database. The study data set consisted of anonymised patient records for a population of 2.7 million patients. The work done in this analysis shows that methodology scales as O(n) in ways that did not require large computing resources. The low dimensional visualisation of high dimensional patient data allowed the identification of different subpopulations of patients across the study data set, where each subpopulation consisted of patients sharing similar characteristics such as age, gender and certain types of diseases. A key finding of this research is the wealth of data that can be produced. In the first use case of looking at the stratification of patients with falls, the methodology gave important hypotheses; however, this work has barely scratched the surface of how this mapping could be used. It opens up the possibility of applying a wide range of data mining strategies that have not yet been explored. What the thesis has shown is one strategy that works, but there could be many more. Furthermore, there is no aspect of the implementation of this methodology that restricts it to medical data. The same methodology could equally be applied to the analysis and visualisation of many other sources of data that are described using terms from taxonomies or ontologies.

O gênero Mikania (Asteraceae, tribo Eupatorieae) apresenta aproximadamente 450 espécies, muitas delas especialmente importantes por seu uso em medicina tradicional. Para a análise quimiotaxonômica, um banco de dados acerca da composição micromolecular de Mikania foi criado. Foram elaboradas análises de agrupamento e de componentes principais, bem como o cálculo de parâmetros evolutivos usados em quimiotaxonomia. O perfil químico e a análise estatística multivariada demonstraram que diterpenóides, lactonas sesquiterpenoídicas e cumarinas são os marcadores químicos mais importantes para este gênero. A presença de dicotomia entre a produção de lactonas sesquiterpenoídicas e diterpenóides não foi estritamente confirmada para o gênero, embora esteja claro que a produção de um interfere negativamente na do outro. As relações SH/(AC+IPP) e FV/FL foram compatíveis com o posicionamento de Mikania na família Asteraceae. As análises de componentes principais (PCA) e de agrupamento forneceram informações que correlacionam caracteres morfológicos e geográficos com dados químicos. As espécies distribuídas predominantemente no Brasil são consideradas muito mais ricas em diterpenos do tipo kaurano, assim como tendem a apresentar inflorescências tirsóides. Por outro lado, espécies não-brasileiras tendem a acumular lactonas sesquiterpenoídicas e apresentar preferencialmente inflorescências do tipo corimbosa. / The genus Mikania (Asteraceae, tribe Eupatorieae) encompasses around 450 species, many of which especially important due to their use in folk medicine. A database of the micromolecular composition of Mikania was generated for a chemotaxonomic analysis. Clustering and Principal Components Analysis (PCA) were performed, as well the calculation of evolutive parameters used in chemotaxonomy. The chemical profile and the statistical multivariate analysis demonstrated that diterpenes, sesquiterpene lactones and coumarins are the most important chemical markers in this genus. The presence of dicotomy between the production of sesquiterpene lactones and diterpenes was not strictly confirmed for the genus, although it is clear that the production of one interferes negatively with the other. The SH/(AC+IPP) and FV/FL ratios are compatible with the positioning of Mikania in the Asteraceae family. The PCA and clustering analysis provided information correlating morphological characters and geographical patterns with chemical data. The species distributed predominantly in Brazil are considered very rich in kaurane diterpenes quite prone to present thyrsoid inflorescences. In contrast, non-Brazilian species trend to accumulate mostly sesquiterpene lactones, preferentially presenting the corymbose inflorescence type.

Information Technology systems generate system log messages to allow for the monitoring of the system. In increasingly large and complex systems the volume of log data can overwhelm the analysts tasked with monitoring these systems. A system was developed that utilizes Principal Component Analysis to assist the analyst in the characterization of system health and events. Once trained, the system was able to accurately identify a state of heavy load on a device with a low false positive rate. The system was also able to accurately identify an error condition when trained on a single event. The method employed is able to assist in the real time monitoring of large complex systems, increasing the efficiency of trained analysts.

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Computational research making use of molecular dynamics (MD) simulations has begun to expand the paradigm of structural biology to include dynamics as the mediator between structure and function. This work aims to expand the utility of MD simulations by developing Principal Component Analysis (PCA) techniques to extract the biologically relevant information in these increasingly complex data sets. Gramicidin is a simple protein with a very clear functional role and a long history of experimental, theoretical and computational study, making it an ideal candidate for detailed quantitative study and the development of new analysis techniques. First we quantify the convergence of our PCA results to underwrite the scope and validity of three 64 ns simulations of gA and two covalently linked analogs (SS and RR) solvated in a glycerol mono-oleate (GMO) membrane. Next we introduce a number of statistical measures for identifying regions of anharmonicity on the free energy landscape and highlight the utility of PCA in identifying functional modes of motion at both long and short wavelengths. We then introduce a simple ansatz for extracting physically meaningful modes of collective dynamics from the results of PCA, through a weighted superposition of eigenvectors. Applied to the gA, SS and RR backbone, this analysis results in a small number of collective modes which relate structural differences among the three analogs to dynamic properties with functional interpretations. Finally, we apply elements of our analysis to the GMO membrane, yielding two simple modes of motion from a large number of noisy and complex eigenvectors. Our results demonstrate that PCA can be used to isolate covariant motions on a number of different length and time scales, and highlight the need for an adequate structural and dynamical account of many more PCs than have been conventionally examined in the analysis of protein motion.