# Topological Time Series Analysis

arXiv: https://arxiv.org/abs/1812.05143 · HTML: https://mlsanity.com/paper/1812.05143/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Nov 2018.

## Built on by (most cited first, 10 of 10)

- [Time Series Classification via Topological Data Analysis](https://mlsanity.com/paper/2102.01956/) (2021)
- [Topology-driven identification of repetitions in multi-variate time series](https://mlsanity.com/paper/2505.10004/) (2025)
- [Homological Time Series Analysis of Sensor Signals from Power Plants](https://mlsanity.com/paper/2106.02493/) (2021)
- [Topological Signal Processing using the Weighted Ordinal Partition Network](https://mlsanity.com/paper/2205.08349/) (2022)
- [Topological Data Analysis in smart manufacturing: State of the art and futuredirections](https://mlsanity.com/paper/2310.09319/) (2023)
- [Filtration learning in exact multi-parameter persistent homology and classification of time-series data](https://mlsanity.com/paper/2406.19587/) (2024)
- [Detection of Small Holes by the Scale-Invariant Robust Density-Aware Distance (RDAD) Filtration](https://mlsanity.com/paper/2204.07821/) (2022)
- [Topology-enhanced machine learning for speech signal processing](https://mlsanity.com/paper/2311.15210/) (2023)
- [A Vectorization Method Induced By Maximal Margin Classification For Persistent Diagrams](https://mlsanity.com/paper/2407.21298/) (2024)
- [Topological Detection of Hopf Bifurcations via Persistent Homology: A Functional Criterion from Time Series](https://mlsanity.com/paper/2603.27395/) (2026)

## Abstract (arXiv)

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.