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Optimization of the reconstruction of phase spaces for time series

Grant number: 15/22406-4
Support Opportunities:Scholarships in Brazil - Doctorate
Effective date (Start): March 01, 2016
Effective date (End): February 29, 2020
Field of knowledge:Physical Sciences and Mathematics - Computer Science - Computer Systems
Principal Investigator:Rodrigo Fernandes de Mello
Grantee:Lucas de Carvalho Pagliosa
Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Associated research grant:13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID
Associated scholarship(s):18/10652-9 - Exploring time series with visualization analysis, BE.EP.DR


The increase in the amount of data coming from different sources has lead to more complex data analysis and processing, making it difficult to to find patterns, trends and cycles. Among the types of analyzed data, there is special attention to those collected over time, commonly arranged in the form of time series. These data can describe different phenomena, whether natural or produced by human intervention, such as temperatures in a region of the planet, population growth or Web data. In this context, tools propose the decomposition of such series into stochastic and deterministic components in order to create better representative models for both parties and allow higher quality analysis. For predominantly deterministic data, the branch of Dynamic Systems proposes the reconstruction of the time series phase space, in order to apply a regression and obtain the rule or function of the generating data. However, current methods for obtaining the phase space are not reliable and robust to noisy and/or chaotic data, requiring human supervision. This gap motivated the development of this doctoral research plan, which aims to design a method to estimate, with higher quality and robustness, the parameters required for the reconstruction of a suitable phase space to the collected data. It is expected that this method can be applied on both batch data as over those obtained continuously over time.

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
PAGLIOSA, LUCAS DE CARVALHO; DE MELLO, RODRIGO FERNANDES. Applying a kernel function on time-dependent data to provide supervised-learning guarantees. EXPERT SYSTEMS WITH APPLICATIONS, v. 71, p. 216-229, . (15/22406-4, 14/13323-5)
PAGLIOSA, LUCAS DE CARVALHO; DE MELLO, RODRIGO FERNANDES. Semi-supervised time series classification on positive and unlabeled problems using cross-recurrence quantification analysis. PATTERN RECOGNITION, v. 80, p. 53-63, . (15/22406-4, 14/13323-5)
Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
PAGLIOSA, Lucas de Carvalho. Exploring chaotic time series and phase spaces. 2020. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.

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