Topological Data Analysis for Multivariate Time Series Data

Anass B. El-Yaagoubi*, Moo K. Chung, Hernando Ombao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Over the last two decades, topological data analysis (TDA) has emerged as a very powerful data analytic approach that can deal with various data modalities of varying complexities. One of the most commonly used tools in TDA is persistent homology (PH), which can extract topological properties from data at various scales. The aim of this article is to introduce TDA concepts to a statistical audience and provide an approach to analyzing multivariate time series data. The application’s focus will be on multivariate brain signals and brain connectivity networks. Finally, this paper concludes with an overview of some open problems and potential application of TDA to modeling directionality in a brain network, as well as the casting of TDA in the context of mixed effect models to capture variations in the topological properties of data collected from multiple subjects.

Original languageEnglish (US)
Article number1509
JournalEntropy
Volume25
Issue number11
DOIs
StatePublished - Nov 2023

Keywords

  • brain dependence networks
  • multivariate time series analysis
  • persistence diagram
  • persistence landscape
  • topological data analysis

ASJC Scopus subject areas

  • Information Systems
  • Mathematical Physics
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Electrical and Electronic Engineering

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