Persistent homology for time series: a selective review

TMLR Paper6815 Authors

Abstract: Over the last ten years, persistent homology has been increasingly used to analyze the structure and shape of various types of data, including time series. This article is a review of persistent homology applied to (univariate or multivariate) time series data. We review 84 articles that apply methods involving persistent homology to time series data, published between 2014 and 2025 in several domains of application, such as biomedicine, industry, and economics. We introduce the main concepts of persistent homology, give an overview of the application fields and tasks, and propose a general framework to describe the main characteristics of all the methods.

Submission Type: Long submission (more than 12 pages of main content)

Assigned Action Editor: ~Serguei_Barannikov1

Submission Number: 6815