论文标题
多元时间序列数据的拓扑数据分析
Topological Data Analysis for Multivariate Time Series Data
论文作者
论文摘要
在过去的二十年中，拓扑数据分析（TDA）已成为一种非常强大的数据分析方法，可以处理各种复杂性的各种数据模式。 TDA中最常用的工具之一是持续的同源性（PH），可以从各种尺度的数据中提取拓扑特性。我们在本文中的目的是向统计受众介绍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大脑信号和大脑连接网络上。最后，本文以一些开放性问题和TDA在大脑网络中建模方向性以及在混合效应模型的背景下对TDA进行建模的概述结束，以捕获从多个受试者收集的数据的拓扑特性的变化
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
