Topological Data Analysis for Directed Dependence Networks of Multivariate Time Series Data

Anass El Yaagoubi, Hernando Ombao*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

1 Scopus citations

Abstract

Topological data analysis (TDA) approaches are becoming increasingly popular for studying the dependence patterns in multivariate time series data. In particular, various dependence patterns in brain networksmay be linked to specific tasks and cognitive processes, which can be altered by various neurological impairments such as epileptic seizures. Existing TDA approaches rely on the notion of distance between data points that is symmetric by definition for building graph filtrations. For brain dependence networks, this is a major limitation that constrains practitioners from using only symmetric dependence measures, such as correlations or coherence. However, it is known that the brain dependence network may be very complex and can contain a directed flow of information from one brain region to another. Such dependence networks are usually captured by more advanced measures of dependence such as partial directed coherence, which is a Granger causality-based dependence measure. These dependence measures will result in a non-symmetric distance function, especially during epileptic seizures. In this paper, we propose to solve this limitation by decomposing the weighted connectivity network into its symmetric and anti-symmetric components using matrix decomposition and comparing the anti-symmetric component prior to and post seizure. Our analysis of epileptic seizure EEG data shows promising results.

Original languageEnglish (US)
Title of host publicationResearch Papers in Statistical Inference for Time Series and Related Models
Subtitle of host publicationEssays in Honor of Masanobu Taniguchi
PublisherSpringer Nature
Pages403-417
Number of pages15
ISBN (Electronic)9789819908035
ISBN (Print)9789819908028
DOIs
StatePublished - Jan 1 2023

Bibliographical note

Publisher Copyright:
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023.

ASJC Scopus subject areas

  • General Mathematics

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