Topological Data Analysis for Multivariate Time Series Data

• Published in: Entropy (Basel, Switzerland) Vol. 25; no. 11; p. 1509
• Main Authors: El-Yaagoubi, Anass B., Chung, Moo K., Ombao, Hernando
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI AG 01.11.2023
• Subjects: Brain; brain dependence networks; Data analysis; Deep learning; Electroencephalography; Euclidean space; Fourier transforms; Homology; Information management; Medical imaging; Multivariate analysis; multivariate time series analysis; Neural networks; Neuroimaging; Neurosciences; persistence diagram; persistence landscape; Time series; topological data analysis; Topology; persistence landscape; brain dependence networks; multivariate time series analysis; persistence diagram; topological data analysis
• ISSN: 1099-4300; 1099-4300
• DOI: 10.3390/e25111509

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.