El-Yaagoubi Anass B, Chung Moo K, Ombao Hernando
Statistics Program, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia.
Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI 53706, USA.
Entropy (Basel). 2023 Nov 1;25(11):1509. 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.
在过去二十年中，拓扑数据分析（TDA）已成为一种非常强大的数据分析方法，能够处理各种复杂程度不同的数据模态。TDA中最常用的工具之一是持久同调（PH），它可以从不同尺度的数据中提取拓扑性质。本文旨在向统计学领域的读者介绍TDA概念，并提供一种分析多元时间序列数据的方法。应用重点将放在多元脑信号和脑连接网络上。最后，本文概述了一些开放性问题以及TDA在脑网络方向性建模中的潜在应用，以及在混合效应模型背景下应用TDA来捕捉从多个受试者收集的数据拓扑性质的变化。
