{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T21:52:42Z","timestamp":1781905962703,"version":"3.54.5"},"reference-count":69,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,11,1]],"date-time":"2023-11-01T00:00:00Z","timestamp":1698796800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NIH","award":["EB028753"],"award-info":[{"award-number":["EB028753"]}]},{"name":"NIH","award":["MH133614"],"award-info":[{"award-number":["MH133614"]}]},{"name":"NIH","award":["2010778"],"award-info":[{"award-number":["2010778"]}]},{"name":"KAUST Competitive Research Grant","award":["EB028753"],"award-info":[{"award-number":["EB028753"]}]},{"name":"KAUST Competitive Research Grant","award":["MH133614"],"award-info":[{"award-number":["MH133614"]}]},{"name":"KAUST Competitive Research Grant","award":["2010778"],"award-info":[{"award-number":["2010778"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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\u2019s 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.<\/jats:p>","DOI":"10.3390\/e25111509","type":"journal-article","created":{"date-parts":[[2023,11,1]],"date-time":"2023-11-01T07:24:04Z","timestamp":1698823444000},"page":"1509","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Topological Data Analysis for Multivariate Time Series Data"],"prefix":"10.3390","volume":"25","author":[{"given":"Anass B.","family":"El-Yaagoubi","sequence":"first","affiliation":[{"name":"Statistics Program, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Moo K.","family":"Chung","sequence":"additional","affiliation":[{"name":"Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI 53706, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hernando","family":"Ombao","sequence":"additional","affiliation":[{"name":"Statistics Program, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Richeson, D.S. 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