NonLinear Principal Component Analysis (NLPCA) using three-hidden-layer feed-forward neural networks can produce solutions that over-fit the data and are non-unique. These problems have been dealt with by subjective methods during the network training. This study shows that these problems are intrinsic due to the three-hidden-layer architecture. A simplified two-hidden-layer feed-forward neural network that has no encoding layer and no bottleneck and output biases is proposed. This new, compact NLPCA model alleviates these problems without employing the subjective methods and is called quasi-objective. The compact NLPCA is applied to the zonal winds observed at seven pressure levels between 10 and 70 hPa in the equatorial stratosphere to represent the Quasi-Biennial Oscillation (QBO) and investigate its variability and structure. The two nonlinear principal components of the dataset offer a clear picture of the QBO. In particular, their structure shows that the QBO phase consists of a predominant 28.4-month cycle that is modulated by an 11-year cycle and a longer-period cycle. The significant difference in variability of the winds between cold and warm seasons and the tendency for a seasonal synchronization of the QBO phases are well captured. The one-dimensional NLPCA approximation of the dataset provides a better representation of the QBO than the classical principal component analysis and a better description of the asymmetry of the QBO between westerly and easterly shear zones and between their transitions. The compact NLPCA is then applied to the Arctic Oscillation (AO) index and aforementioned zonal winds to investigate the relationship of the AO with the QBO. The NLPCA of the AO index and zonal-winds dataset shows clearly that, of covariation of the two oscillations, the phase defined by the two nonlinear principal components progresses with a predominant 28.4-month periodicity, plus the 11-year and longer-period modulations. Large positive values of the AO index occur when westerlies prevail near the middle and upper levels of the equatorial stratosphere. Large negative values of the AO index arise when easterlies occupy over half the layer of the equatorial stratosphere.

NonLinear Principal Component Analysis (NLPCA) using three-hidden-layer feed-forward neural networks can produce solutions that over-fit the data and are non-unique. These problems have been dealt with by subjective methods during the network training. This study shows that these problems are intrinsic due to the three-hidden-layer architecture. A simplified two-hidden-layer feed-forward neural network that has no encoding layer and no bottleneck and output biases is proposed. This new, compact NLPCA model alleviates these problems without employing the subjective methods and is called quasi-objective. The compact NLPCA is applied to the zonal winds observed at seven pressure levels between 10 and 70 hPa in the equatorial stratosphere to represent the Quasi-Biennial Oscillation (QBO) and investigate its variability and structure. The two nonlinear principal components of the dataset offer a clear picture of the QBO. In particular, their structure shows that the QBO phase consists of a predominant 28.4-month cycle that is modulated by an 11-year cycle and a longer-period cycle. The significant difference in variability of the winds between cold and warm seasons and the tendency for a seasonal synchronization of the QBO phases are well captured. The one-dimensional NLPCA approximation of the dataset provides a better representation of the QBO than the classical principal component analysis and a better description of the asymmetry of the QBO between westerly and easterly shear zones and between their transitions. The compact NLPCA is then applied to the Arctic Oscillation (AO) index and aforementioned zonal winds to investigate the relationship of the AO with the QBO. The NLPCA of the AO index and zonal-winds dataset shows clearly that, of covariation of the two oscillations, the phase defined by the two nonlinear principal components progresses with a predominant 28.4-month periodicity, plus the 11-year and longer-period modulations. Large positive values of the AO index occur when westerlies prevail near the middle and upper levels of the equatorial stratosphere. Large negative values of the AO index arise when easterlies occupy over half the layer of the equatorial stratosphere.

NonLinear Principal Component Analysis (NLPCA) using three-hidden-layer feed-forward neural networks can produce solutions that over-fit the data and are non-unique. These problems have been dealt with by subjective methods during the network training. This study shows that these problems are intrinsic due to the three-hidden-layer architecture. A simplified two-hidden-layer feed-forward neural network that has no encoding layer and no bottleneck and output biases is proposed. This new, compact NLPCA model alleviates these problems without employing the subjective methods and is called quasi-objective. The compact NLPCA is applied to the zonal winds observed at seven pressure levels between 10 and 70 hPa in the equatorial stratosphere to represent the Quasi-Biennial Oscillation (QBO) and investigate its variability and structure. The two nonlinear principal components of the dataset offer a clear picture of the QBO. In particular, their structure shows that the QBO phase consists of a predominant 28.4-month cycle that is modulated by an 11-year cycle and a longer-period cycle. The significant difference in variability of the winds between cold and warm seasons and the tendency for a seasonal synchronization of the QBO phases are well captured. The one-dimensional NLPCA approximation of the dataset provides a better representation of the QBO than the classical principal component analysis and a better description of the asymmetry of the QBO between westerly and easterly shear zones and between their transitions. The compact NLPCA is then applied to the Arctic Oscillation (AO) index and aforementioned zonal winds to investigate the relationship of the AO with the QBO. The NLPCA of the AO index and zonal-winds dataset shows clearly that, of covariation of the two oscillations, the phase defined by the two nonlinear principal components progresses with a predominant 28.4-month periodicity, plus the 11-year and longer-period modulations. Large positive values of the AO index occur when westerlies prevail near the middle and upper levels of the equatorial stratosphere. Large negative values of the AO index arise when easterlies occupy over half the layer of the equatorial stratosphere. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

abstract: Feature learning and the discovery of nonlinear variation patterns in high-dimensional data is an important task in many problem domains, such as imaging, streaming data from sensors, and manufacturing. This dissertation presents several methods for learning and visualizing nonlinear variation in high-dimensional data. First, an automated method for discovering nonlinear variation patterns using deep learning autoencoders is proposed. The approach provides a functional mapping from a low-dimensional representation to the original spatially-dense data that is both interpretable and efficient with respect to preserving information. Experimental results indicate that deep learning autoencoders outperform manifold learning and principal component analysis in reproducing the original data from the learned variation sources. A key issue in using autoencoders for nonlinear variation pattern discovery is to encourage the learning of solutions where each feature represents a unique variation source, which we define as distinct features. This problem of learning distinct features is also referred to as disentangling factors of variation in the representation learning literature. The remainder of this dissertation highlights and provides solutions for this important problem. An alternating autoencoder training method is presented and a new measure motivated by orthogonal loadings in linear models is proposed to quantify feature distinctness in the nonlinear models. Simulated point cloud data and handwritten digit images illustrate that standard training methods for autoencoders consistently mix the true variation sources in the learned low-dimensional representation, whereas the alternating method produces solutions with more distinct patterns. Finally, a new regularization method for learning distinct nonlinear features using autoencoders is proposed. Motivated in-part by the properties of linear solutions, a series of learning constraints are implemented via regularization penalties during stochastic gradient descent training. These include the orthogonality of tangent vectors to the manifold, the correlation between learned features, and the distributions of the learned features. This regularized learning approach yields low-dimensional representations which can be better interpreted and used to identify the true sources of variation impacting a high-dimensional feature space. Experimental results demonstrate the effectiveness of this method for nonlinear variation pattern discovery on both simulated and real data sets. / Dissertation/Thesis / Doctoral Dissertation Industrial Engineering 2016

A Política Nacional do Meio Ambiente visa compatibilizar o desenvolvimento socioeconômico com a qualidade ambiental. A Avaliação de Impacto Ambiental, um de seus instrumentos, utiliza-se do Estudo de Impacto Ambiental (EIA) na sua aplicação em projetos ou empreendimentos. A elaboração do EIA envolve a etapa de diagnóstico para análise da qualidade ambiental da área. A qualidade do EIA e do diagnóstico tem sido objeto de críticas e descrédito junto à sociedade, principalmente à comunidade científica e às associações ambientalistas. Sabe-se que a qualidade do diagnóstico influencia diretamente a efetividade processual do EIA e seu papel como influenciador da tomada de decisão; assim, uma avaliação da qualidade dessa etapa do EIA contribui com a aplicação mais efetiva desse instrumento. A pesquisa visou avaliar a qualidade do diagnóstico biótico dos EIAs do Estado de São Paulo elaborados entre 2005 e 2014. Para isso, proposições ao diagnóstico biótico foram reunidas em uma lista de verificação, utilizada para a avaliação de 55 diagnósticos bióticos e 35 termos de referência de EIAs. Os resultados foram analisados qualitativamente e em comparação com as recomendações dos termos de referência (TRs) analisados. Posteriormente, a qualidade dos diagnósticos foi analisada sob três perspectivas: aprovação dos estudos, tipo de empreendimento e ano de elaboração do EIA. Por fim, foi realizada análise de componentes principais não-linear (NLPCA) para os dados de diagnóstico, no intuito de testar a sugestão de aplicação dessa ferramenta para a identificação dos critérios determinantes para a qualidade dos diagnósticos e possíveis relações entre esses critérios e entre os estudos. A qualidade dos diagnósticos bióticos analisados foi mais satisfatória para aspectos descritivos do que analíticos. Foram determinantes para a qualidade dos estudos critérios relativos à coleta de dados quantitativos e levantamentos para espécies raras, segundo a NLPCA. Tempo de levantamento e sazonalidade foram considerados insatisfatórios, e apresentaram relação estatística com a identificação do grau de vulnerabilidade da área. Os resultados realçaram a importância da sistematização de dados de biodiversidade em fontes confiáveis e atualizadas para elaboração e análise de diagnósticos, e para TRs mais específicos, uma vez que, apesar de estarem sendo cumpridos pelos estudos, os TRs são genéricos e apresentam mais recomendações descritivas do que analíticas. Não houve diferença representativa entre a qualidade dos diagnósticos referentes a estudos aprovados e não aprovados, o setor de Obras Hidráulicas apresentou avaliações mais satisfatórias, o que foi salientado pela NLPCA e pode estar relacionado ao porte do projeto, e a análise temporal evidenciou uma tendência de melhora dos estudos e TRs. Tanto a lista de verificação quanto a NLPCA se mostraram ferramentas adequadas para a investigação da qualidade de diagnósticos biológicos de EIA / The Brazilian National Environmental Policy established Environmental Impact Assessment (EIA) as one of the 13 tools to reconcile socio-economic development with environmental quality. EIA involves the Environmental Impact Statements (EIS) in its application to development projects. EIS drafting involves a baseline step for analysis of environmental quality of the area. The quality of the EIS and the baseline process has been criticized by society, especially by scientific community and environmental groups, and this quality directly influences the effectiveness of the EIA procedure and its role as a decision making tool. Thus, an evaluation of the quality of this EIS step contributes to a more effective application of this instrument. The research aimed to evaluate the quality of biotic baseline studies of EIS drawn up between 2005 and 2014 in the state of São Paulo. We assessed 55 biotic baseline studies and 35 terms of reference (TRs) of EISs by a checklist which consists of a set of recommendations from literature and regulations to biotic baseline studies. The results of baseline and TRs were analyzed qualitatively and compared to one another. Then, we looked at the baseline quality under three approaches: license emission, sector and project type of activity, and year of EIS preparation. Finally, multivariate analysis was performed by Nonlinear Principal Component Analysis (NLPCA) for the baseline quality data in order to test the application of this analysis for the identification of critical and determinant criteria for the quality of baseline and the investigation of how these criteria and the EISs are related to one another. Results point to more satisfactory descriptive than analytical issues. Criteria of quantitative data collecting and surveys of rare species were determinants for baseline quality. Time of survey and seasonality was an unsatisfactory criterion, and statistically related to the vulnerability degree of the area. Results highlighted the importance of systematization of biodiversity data in reliable and updated sources useful for EISs preparation and analysis and for the draft of TRs in a more specific way. TRs were satisfactorily complied by the baseline content, but they are generic and present more descriptive than analytical recommendations. There was no representative difference between the quality of baseline of approved and not approved EISs. Hydraulic project showed more satisfactory evaluations, emphasized by NLPCA, and it may be related to the size of the project. Temporal analysis highlighted an improvement trend of studies and TRs. Thus, both the checklist as NLPCA proved to be suitable tools to the assessment of biological baseline studies of EIS

A Política Nacional do Meio Ambiente visa compatibilizar o desenvolvimento socioeconômico com a qualidade ambiental. A Avaliação de Impacto Ambiental, um de seus instrumentos, utiliza-se do Estudo de Impacto Ambiental (EIA) na sua aplicação em projetos ou empreendimentos. A elaboração do EIA envolve a etapa de diagnóstico para análise da qualidade ambiental da área. A qualidade do EIA e do diagnóstico tem sido objeto de críticas e descrédito junto à sociedade, principalmente à comunidade científica e às associações ambientalistas. Sabe-se que a qualidade do diagnóstico influencia diretamente a efetividade processual do EIA e seu papel como influenciador da tomada de decisão; assim, uma avaliação da qualidade dessa etapa do EIA contribui com a aplicação mais efetiva desse instrumento. A pesquisa visou avaliar a qualidade do diagnóstico biótico dos EIAs do Estado de São Paulo elaborados entre 2005 e 2014. Para isso, proposições ao diagnóstico biótico foram reunidas em uma lista de verificação, utilizada para a avaliação de 55 diagnósticos bióticos e 35 termos de referência de EIAs. Os resultados foram analisados qualitativamente e em comparação com as recomendações dos termos de referência (TRs) analisados. Posteriormente, a qualidade dos diagnósticos foi analisada sob três perspectivas: aprovação dos estudos, tipo de empreendimento e ano de elaboração do EIA. Por fim, foi realizada análise de componentes principais não-linear (NLPCA) para os dados de diagnóstico, no intuito de testar a sugestão de aplicação dessa ferramenta para a identificação dos critérios determinantes para a qualidade dos diagnósticos e possíveis relações entre esses critérios e entre os estudos. A qualidade dos diagnósticos bióticos analisados foi mais satisfatória para aspectos descritivos do que analíticos. Foram determinantes para a qualidade dos estudos critérios relativos à coleta de dados quantitativos e levantamentos para espécies raras, segundo a NLPCA. Tempo de levantamento e sazonalidade foram considerados insatisfatórios, e apresentaram relação estatística com a identificação do grau de vulnerabilidade da área. Os resultados realçaram a importância da sistematização de dados de biodiversidade em fontes confiáveis e atualizadas para elaboração e análise de diagnósticos, e para TRs mais específicos, uma vez que, apesar de estarem sendo cumpridos pelos estudos, os TRs são genéricos e apresentam mais recomendações descritivas do que analíticas. Não houve diferença representativa entre a qualidade dos diagnósticos referentes a estudos aprovados e não aprovados, o setor de Obras Hidráulicas apresentou avaliações mais satisfatórias, o que foi salientado pela NLPCA e pode estar relacionado ao porte do projeto, e a análise temporal evidenciou uma tendência de melhora dos estudos e TRs. Tanto a lista de verificação quanto a NLPCA se mostraram ferramentas adequadas para a investigação da qualidade de diagnósticos biológicos de EIA / The Brazilian National Environmental Policy established Environmental Impact Assessment (EIA) as one of the 13 tools to reconcile socio-economic development with environmental quality. EIA involves the Environmental Impact Statements (EIS) in its application to development projects. EIS drafting involves a baseline step for analysis of environmental quality of the area. The quality of the EIS and the baseline process has been criticized by society, especially by scientific community and environmental groups, and this quality directly influences the effectiveness of the EIA procedure and its role as a decision making tool. Thus, an evaluation of the quality of this EIS step contributes to a more effective application of this instrument. The research aimed to evaluate the quality of biotic baseline studies of EIS drawn up between 2005 and 2014 in the state of São Paulo. We assessed 55 biotic baseline studies and 35 terms of reference (TRs) of EISs by a checklist which consists of a set of recommendations from literature and regulations to biotic baseline studies. The results of baseline and TRs were analyzed qualitatively and compared to one another. Then, we looked at the baseline quality under three approaches: license emission, sector and project type of activity, and year of EIS preparation. Finally, multivariate analysis was performed by Nonlinear Principal Component Analysis (NLPCA) for the baseline quality data in order to test the application of this analysis for the identification of critical and determinant criteria for the quality of baseline and the investigation of how these criteria and the EISs are related to one another. Results point to more satisfactory descriptive than analytical issues. Criteria of quantitative data collecting and surveys of rare species were determinants for baseline quality. Time of survey and seasonality was an unsatisfactory criterion, and statistically related to the vulnerability degree of the area. Results highlighted the importance of systematization of biodiversity data in reliable and updated sources useful for EISs preparation and analysis and for the draft of TRs in a more specific way. TRs were satisfactorily complied by the baseline content, but they are generic and present more descriptive than analytical recommendations. There was no representative difference between the quality of baseline of approved and not approved EISs. Hydraulic project showed more satisfactory evaluations, emphasized by NLPCA, and it may be related to the size of the project. Temporal analysis highlighted an improvement trend of studies and TRs. Thus, both the checklist as NLPCA proved to be suitable tools to the assessment of biological baseline studies of EIS