Over the last two decades, topological data analysis (TDA) has emerged as a very powerful data analytic approach which 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. Our aim in this article is to introduce TDA concepts to a statistical audience and provide an approach to analyze multivariate time series data. The application focus will be on multivariate brain signals and brain connectivity networks. Finally, the 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 effects models to capture variations in the topological properties of data collected from multiple subjects
翻译:在过去20年中,地形数据分析(TDA)已成为一种非常有力的数据分析分析方法,可以处理各种复杂程度不同的数据模式。在TDA中,最常用的工具之一是持久性同族学(PH),它可以从不同尺度的数据中提取表象学特性。我们本条的目的是向统计受众介绍TDA概念,提供分析多变量时间序列数据的方法。应用重点将放在多变量脑信号和脑连通网络上。最后,文件最后概述了TDA在模拟脑网络方向性方面的一些公开问题和潜在应用,以及在混合效应模型中选择TDA以捕捉从多个主题收集的数据的表象特性的变化。