Time series analysis using persistent homology of distance matrix

TL;DR

This paper introduces a novel approach using persistent homology on distance matrices to analyze nonlinear time series data, revealing topological features and noise effects in various systems.

Contribution

The study presents a new method applying persistent homology to the distance matrix for topological analysis of time series, enhancing nonlinear dynamics understanding.

Findings

Effectively identifies nonlocal attractor characteristics

Classifies data based on noise levels

Applies successfully to diverse systems

Abstract

The analysis of nonlinear dynamics is an important issue in numerous fields of science. In this study, we propose a new method to analyze the time series data using persistent homology (PH). The key idea is the application of PH to the distance matrix. Using this method, we can obtain the topological features embedded in the trajectories. We apply this method to the logistic map, R\"ossler system, and electrocardiogram data. The results reveal that our method can effectively identify nonlocal characteristics of the attractor and can classify data based on the amount of noise.