Topological Data Analysis for Multivariate Time Series Data

Abstract

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

References in corpus (2)

• The Statistical Analysis of fMRI Data
• Conex-Connect: Learning Patterns in Extremal Brain Connectivity From Multi-Channel EEG Data

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• A Robust Topological Framework for Detecting Regime Changes in Multi-Trial Experiments with Application to Predictive Maintenance
• Modeling and Simulating Dependence in Networks Using Topological Data Analysis