Exploring chaotic time series and phase spaces
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da USP |
Texto Completo: | https://www.teses.usp.br/teses/disponiveis/55/55134/tde-10062020-100009/ |
Resumo: | Technology advances have allowed and inspired the study of data produced along time from applications such as health treatment, biology, sentiment analysis, and entertainment. Those types of data, typically referred to as time series or data streams, have motivated several studies mainly in the area of Machine Learning and Statistics to infer models for performing prediction and classification. However, several studies either employ batchdriven strategies to address temporal data or do not consider chaotic observations, thus missing recurrent patterns and other temporal dependencies especially in real-world data. In that scenario, we consider Dynamical Systems and Chaos Theory tools to improve datastream modeling and forecasting by investigating time-series phase spaces, reconstructed according to Takens embedding theorem. This theorem relies on two essential embedding parameters, known as embedding dimension and time delay , which are complex to be estimated for real-world scenarios. Such difficulty derives from inconsistencies related to phase space partitioning, computation of probabilities, the curse of dimensionality, and noise. Moreover, an optimal phase space may be represented by attractors with different structures for different systems, which also aggregates to the problem. Our research confirmed those issues, especially for entropy. Although we verified that a well-reconstructed phase space can be described in terms of low entropy of phase states, the inverse is not necessarily true: a set of phase states that presents low levels of entropy does not necessarily describe an optimal phase space. As a consequence, we learned that defining a set of features to describe an optimal phase space is not a trivial task. As alternative, this Ph.D. proposed a new approach to estimate embedding parameters using an artificial neural network training on an overestimated phase space. Then, without the need of explicitly defining any phase-space features, we let the network filter nonrelevant dimensions and learn those features implicitly, whatever they are. After training iterations, we infer and from the skeletal architecture of the neural network. As we show, this method was consistent with benchmarks datasets, and robust in regarding different random initializations of neurons weights and chosen parameters. After obtaining embedding parameters and reconstructing the phase space, we show how we can model time-series recurrences more effectively in a wider scope, thereby enabling a deeper analysis of the underlying data. |
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Exploring chaotic time series and phase spacesExplorando séries temporais caóticas e espaços faseAprendizado de máquinaChaotic time seriesComputational visualizationDinamical systemsMachine learningModelagem e prediçãoModeling and forecastingSéries temporais caóticasSistemas dinâmicosVisualização computacionalTechnology advances have allowed and inspired the study of data produced along time from applications such as health treatment, biology, sentiment analysis, and entertainment. Those types of data, typically referred to as time series or data streams, have motivated several studies mainly in the area of Machine Learning and Statistics to infer models for performing prediction and classification. However, several studies either employ batchdriven strategies to address temporal data or do not consider chaotic observations, thus missing recurrent patterns and other temporal dependencies especially in real-world data. In that scenario, we consider Dynamical Systems and Chaos Theory tools to improve datastream modeling and forecasting by investigating time-series phase spaces, reconstructed according to Takens embedding theorem. This theorem relies on two essential embedding parameters, known as embedding dimension and time delay , which are complex to be estimated for real-world scenarios. Such difficulty derives from inconsistencies related to phase space partitioning, computation of probabilities, the curse of dimensionality, and noise. Moreover, an optimal phase space may be represented by attractors with different structures for different systems, which also aggregates to the problem. Our research confirmed those issues, especially for entropy. Although we verified that a well-reconstructed phase space can be described in terms of low entropy of phase states, the inverse is not necessarily true: a set of phase states that presents low levels of entropy does not necessarily describe an optimal phase space. As a consequence, we learned that defining a set of features to describe an optimal phase space is not a trivial task. As alternative, this Ph.D. proposed a new approach to estimate embedding parameters using an artificial neural network training on an overestimated phase space. Then, without the need of explicitly defining any phase-space features, we let the network filter nonrelevant dimensions and learn those features implicitly, whatever they are. After training iterations, we infer and from the skeletal architecture of the neural network. As we show, this method was consistent with benchmarks datasets, and robust in regarding different random initializations of neurons weights and chosen parameters. After obtaining embedding parameters and reconstructing the phase space, we show how we can model time-series recurrences more effectively in a wider scope, thereby enabling a deeper analysis of the underlying data.Avanços tecnológicos permitiram e inspiraram o estudo de dados produzidos ao longo do tempo a partir de aplicações de tratamento de saúde, biologia, análise de sentimentos e entretenimento. Esses tipos de dados, geralmente chamados de séries temporais ou fluxos de dados, motivaram vários estudos principalmente na área de Aprendizado de Máquina e Estatística a inferir modelos de previsão e classificação. No entanto, vários estudos empregam estratégias orientadas por lotes para tratar dados temporais ou não consideram observações caóticas, perdendo assim padrões recorrentes e outras dependências temporais especialmente em dados do mundo real. Nesse cenário, consideramos as ferramentas de Sistemas Dinâmicos e Teoria do Caos para melhorar a modelagem e previsão do fluxo de dados investigando os espaços fase das séries temporais, reconstruídos de acordo com o teorema de mergulho de Takens. Esse teorema baseia-se em dois parâmetros essenciais de mergulho, conhecidos como dimensão de mergulho e tempo de atraso , que são complexos de serem estimados para cenários do mundo real. Essa dificuldade deriva de inconsistências relacionadas ao particionamento do espaço fase, ao cálculo de probabilidades, à maldição da dimensionalidade e a ruídos. Além disso, um espaço fase ideal pode ser representado por atratores com estruturas diferentes para sistemas diferentes, o que também se agrega ao problema. Nossa pesquisa confirmou esses problemas especialmente para entropia e, embora tenhamos verificado que um espaço fase bem reconstruído pode ser descrito em termos de baixa entropia de seus estados, o inverso não é necessariamente verdadeiro: um conjunto de estados do espaço fase que apresenta baixos níveis de entropia não descreve necessariamente um espaço fase ideal. Como conseqüência, aprendemos que definir um conjunto de recursos para descrever um espaço fase ideal não é uma tarefa trivial. Como alternativa, este doutorado propôs uma nova abordagem para estimar parâmetros de mergulho a partir do treinamento de uma rede neural artificial em um espaço fase superestimado. Então, sem a necessidade de definir explicitamente quaisquer características de espaço fase, deixamos a rede filtrar dimensões não relevantes e aprender essas caractereísticas implicitamente, sejam elas quais forem. Após o treinamento das iterações, inferimos e a partir da arquitetura esquelética da rede neural. Como mostramos, esse método mostrou-se consistente com conjuntos de dados conhecidos, e robusto em relação a diferentes inicializações aleatórias de pesos de neurônios e parâmetros da rede. Após obter os parâmetros de mergulho e reconstruir o espaço fase, podemos modelar as recorrências de séries temporais com mais eficiência em um escopo mais amplo, prosseguindo para uma análise mais profunda dos dados.Biblioteca Digitais de Teses e Dissertações da USPMello, Rodrigo Fernandes dePagliosa, Lucas de Carvalho2020-04-17info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisapplication/pdfhttps://www.teses.usp.br/teses/disponiveis/55/55134/tde-10062020-100009/reponame:Biblioteca Digital de Teses e Dissertações da USPinstname:Universidade de São Paulo (USP)instacron:USPLiberar o conteúdo para acesso público.info:eu-repo/semantics/openAccesseng2020-06-10T16:10:02Zoai:teses.usp.br:tde-10062020-100009Biblioteca Digital de Teses e Dissertaçõeshttp://www.teses.usp.br/PUBhttp://www.teses.usp.br/cgi-bin/mtd2br.plvirginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.bropendoar:27212020-06-10T16:10:02Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP)false |
dc.title.none.fl_str_mv |
Exploring chaotic time series and phase spaces Explorando séries temporais caóticas e espaços fase |
title |
Exploring chaotic time series and phase spaces |
spellingShingle |
Exploring chaotic time series and phase spaces Pagliosa, Lucas de Carvalho Aprendizado de máquina Chaotic time series Computational visualization Dinamical systems Machine learning Modelagem e predição Modeling and forecasting Séries temporais caóticas Sistemas dinâmicos Visualização computacional |
title_short |
Exploring chaotic time series and phase spaces |
title_full |
Exploring chaotic time series and phase spaces |
title_fullStr |
Exploring chaotic time series and phase spaces |
title_full_unstemmed |
Exploring chaotic time series and phase spaces |
title_sort |
Exploring chaotic time series and phase spaces |
author |
Pagliosa, Lucas de Carvalho |
author_facet |
Pagliosa, Lucas de Carvalho |
author_role |
author |
dc.contributor.none.fl_str_mv |
Mello, Rodrigo Fernandes de |
dc.contributor.author.fl_str_mv |
Pagliosa, Lucas de Carvalho |
dc.subject.por.fl_str_mv |
Aprendizado de máquina Chaotic time series Computational visualization Dinamical systems Machine learning Modelagem e predição Modeling and forecasting Séries temporais caóticas Sistemas dinâmicos Visualização computacional |
topic |
Aprendizado de máquina Chaotic time series Computational visualization Dinamical systems Machine learning Modelagem e predição Modeling and forecasting Séries temporais caóticas Sistemas dinâmicos Visualização computacional |
description |
Technology advances have allowed and inspired the study of data produced along time from applications such as health treatment, biology, sentiment analysis, and entertainment. Those types of data, typically referred to as time series or data streams, have motivated several studies mainly in the area of Machine Learning and Statistics to infer models for performing prediction and classification. However, several studies either employ batchdriven strategies to address temporal data or do not consider chaotic observations, thus missing recurrent patterns and other temporal dependencies especially in real-world data. In that scenario, we consider Dynamical Systems and Chaos Theory tools to improve datastream modeling and forecasting by investigating time-series phase spaces, reconstructed according to Takens embedding theorem. This theorem relies on two essential embedding parameters, known as embedding dimension and time delay , which are complex to be estimated for real-world scenarios. Such difficulty derives from inconsistencies related to phase space partitioning, computation of probabilities, the curse of dimensionality, and noise. Moreover, an optimal phase space may be represented by attractors with different structures for different systems, which also aggregates to the problem. Our research confirmed those issues, especially for entropy. Although we verified that a well-reconstructed phase space can be described in terms of low entropy of phase states, the inverse is not necessarily true: a set of phase states that presents low levels of entropy does not necessarily describe an optimal phase space. As a consequence, we learned that defining a set of features to describe an optimal phase space is not a trivial task. As alternative, this Ph.D. proposed a new approach to estimate embedding parameters using an artificial neural network training on an overestimated phase space. Then, without the need of explicitly defining any phase-space features, we let the network filter nonrelevant dimensions and learn those features implicitly, whatever they are. After training iterations, we infer and from the skeletal architecture of the neural network. As we show, this method was consistent with benchmarks datasets, and robust in regarding different random initializations of neurons weights and chosen parameters. After obtaining embedding parameters and reconstructing the phase space, we show how we can model time-series recurrences more effectively in a wider scope, thereby enabling a deeper analysis of the underlying data. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-04-17 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://www.teses.usp.br/teses/disponiveis/55/55134/tde-10062020-100009/ |
url |
https://www.teses.usp.br/teses/disponiveis/55/55134/tde-10062020-100009/ |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
|
dc.rights.driver.fl_str_mv |
Liberar o conteúdo para acesso público. info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Liberar o conteúdo para acesso público. |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.coverage.none.fl_str_mv |
|
dc.publisher.none.fl_str_mv |
Biblioteca Digitais de Teses e Dissertações da USP |
publisher.none.fl_str_mv |
Biblioteca Digitais de Teses e Dissertações da USP |
dc.source.none.fl_str_mv |
reponame:Biblioteca Digital de Teses e Dissertações da USP instname:Universidade de São Paulo (USP) instacron:USP |
instname_str |
Universidade de São Paulo (USP) |
instacron_str |
USP |
institution |
USP |
reponame_str |
Biblioteca Digital de Teses e Dissertações da USP |
collection |
Biblioteca Digital de Teses e Dissertações da USP |
repository.name.fl_str_mv |
Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP) |
repository.mail.fl_str_mv |
virginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.br |
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