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

Anass El Yaagoubi () and Hernando Ombao ()
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Anass El Yaagoubi: King Abdullah University of Science and Technology
Hernando Ombao: King Abdullah University of Science and Technology

Chapter Chapter 17 in Research Papers in Statistical Inference for Time Series and Related Models, 2023, pp 403-417 from Springer

Abstract: 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 networks may 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.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-99-0803-5_17

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DOI: 10.1007/978-981-99-0803-5_17

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