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Topological Data Analysis for Multivariate Time Series Data.

Anass B El-Yaagoubi1, Moo K Chung2, Hernando Ombao1

  • 1Statistics Program, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia.

Entropy (Basel, Switzerland)
|November 24, 2023
PubMed
Summary
This summary is machine-generated.

Topological data analysis (TDA) offers powerful methods for analyzing complex data, including brain signals. This study introduces persistent homology (PH) for multivariate time series, enhancing statistical approaches to brain connectivity networks.

Keywords:
brain dependence networksmultivariate time series analysispersistence diagrampersistence landscapetopological data analysis

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Area of Science:

  • Statistics
  • Data Science
  • Computational Neuroscience

Background:

  • Topological Data Analysis (TDA) has become a significant data analytic approach over the past 20 years.
  • Persistent Homology (PH) is a key tool in TDA, extracting topological features across multiple data scales.
  • Existing methods may not fully capture the complexities of multivariate time series, particularly in neuroscience.

Purpose of the Study:

  • To introduce Topological Data Analysis (TDA) concepts to a statistical audience.
  • To present a novel approach for analyzing multivariate time series data using TDA.
  • To apply TDA to the analysis of brain signals and brain connectivity networks.

Main Methods:

  • Utilizing persistent homology (PH) to analyze topological structures within data.
  • Applying TDA techniques to multivariate time series data, focusing on brain signals.
  • Exploring the integration of TDA with statistical modeling, including mixed-effects models.

Main Results:

  • Demonstrated the efficacy of TDA and PH in extracting meaningful topological properties from complex data.
  • Provided a framework for applying TDA to multivariate brain signals and connectivity networks.
  • Identified potential applications in modeling directionality and subject variations in brain networks.

Conclusions:

  • TDA, particularly PH, offers a robust framework for analyzing complex multivariate time series.
  • The presented approach has significant implications for understanding brain connectivity and neural dynamics.
  • Future directions include advanced modeling of brain network directionality and inter-subject variability using TDA.