Topological Time Series Analysis

TL;DR

This paper explores how topological data analysis and dynamical systems theory can be combined to analyze time series data, providing insights across sciences and engineering.

Contribution

It introduces a novel approach integrating topological methods with dynamical systems for time series analysis, supported by theoretical and practical applications.

Findings

Effective in identifying features in complex time series

Applicable to biological and engineering data

Provides a new perspective on data dynamics

Abstract

Time series are ubiquitous in our data rich world. In what follows I will describe how ideas from dynamical systems and topological data analysis can be combined to gain insights from time-varying data. We will see several applications to the live sciences and engineering, as well as some of the theoretical underpinnings.