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Basics of Multivariate Analysis in Neuroimaging Data
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Network structure of multivariate time series.

Lucas Lacasa1, Vincenzo Nicosia1, Vito Latora1

  • 1School of Mathematical Sciences, Queen Mary University of London, Mile End Road, E14NS London, UK.

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This study introduces a novel method for analyzing complex multivariate time series by converting them into multilayer networks. This approach effectively extracts dynamics and synchronizations in systems like financial markets.

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Area of Science:

  • Multivariate time series analysis
  • Complex systems science
  • Network science

Background:

  • Analysis of multivariate time series is crucial across physics, biology, and economics.
  • Existing methods struggle with massive, high-dimensional datasets.
  • Need for scalable and generalizable signal processing techniques is increasing.

Purpose of the Study:

  • To present a non-parametric method for analyzing multivariate time series.
  • To map high-dimensional time series data into a multilayer network structure.
  • To extract dynamical information from complex systems using network analysis.

Main Methods:

  • Mapping multivariate time series data into a multilayer network.
  • Utilizing structural descriptors of the multiplex network for analysis.
  • Application to coupled chaotic maps and financial time series.

Main Results:

  • The multiplex network approach successfully quantifies dynamics in chaotic systems.
  • Identified transitions between dynamical phases and onset of synchronization.
  • Demonstrated efficacy in discriminating financial crises from stable periods.

Conclusions:

  • The proposed method is simple, general, scalable, and suitable for large, heterogeneous, non-stationary time series.
  • Multiplex network analysis offers a powerful alternative to traditional methods, especially when symbolization fails.
  • This technique provides novel insights into the behavior of complex dynamical systems.