# Topology-driven identification of repetitions in multi-variate time series

arXiv: https://arxiv.org/abs/2505.10004 · HTML: https://mlsanity.com/paper/2505.10004/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 15 references that are in the map.
- First posted on arXiv 15 May 2025.

## Builds on (most cited first, 4 of 4)

- [(Quasi)Periodicity Quantification in Video Data, Using Topology](https://mlsanity.com/paper/1704.08382/) (2017)
- [Topological Time Series Analysis](https://mlsanity.com/paper/1812.05143/) (2018)
- [Open Challenges in Time Series Anomaly Detection: An Industry Perspective](https://mlsanity.com/paper/2502.05392/) (2025)
- [Topological phase estimation method for reparameterized periodic functions](https://mlsanity.com/paper/2205.14390/) (2022)

## Built on by (most cited first, 2 of 2)

- [Anomaly Detection for Sparse and Irregular Multivariate Time Series with Latent SDEs](https://mlsanity.com/paper/2606.18898/) (2026)
- [Generative Modeling of Approximately Periodic Time Series by a Posterior-Weighted Gaussian Process](https://mlsanity.com/paper/2605.13150/) (2026)

## Abstract (arXiv)

Many multi-variate time series obtained in the natural sciences and engineering possess a repetitive behavior, as for instance state-space trajectories of industrial machines in discrete automation. Recovering the times of recurrence from such a multi-variate time series is of a fundamental importance for many monitoring and control tasks. For a periodic time series this is equivalent to determining its period length. In this work we present a persistent homology framework to estimate recurrence times in multi-variate time series with different generalizations of cyclic behavior (periodic, repetitive, and recurring). To this end, we provide three specialized methods within our framework that are provably stable and validate them using real-world data, including a new benchmark dataset from an injection molding machine.