# Classification of Stochastic Processes with Topological Data Analysis

arXiv: https://arxiv.org/abs/2206.03973 · HTML: https://mlsanity.com/paper/2206.03973/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 71 references that are in the map.
- First posted on arXiv 8 Jun 2022.

## Builds on (most cited first, 14 of 14)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [Ripser: efficient computation of Vietoris-Rips persistence barcodes](https://mlsanity.com/paper/1908.02518/) (2019)
- [giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration](https://mlsanity.com/paper/2004.02551/) (2020)
- [Geometry Helps to Compare Persistence Diagrams](https://mlsanity.com/paper/1606.03357/) (2016)
- [Persistence Curves: A canonical framework for summarizing persistence diagrams](https://mlsanity.com/paper/1904.07768/) (2019)
- [Feature-based time-series analysis](https://mlsanity.com/paper/1709.08055/) (2017)
- [GPU-Accelerated Computation of Vietoris-Rips Persistence Barcodes](https://mlsanity.com/paper/2003.07989/) (2020)
- [The persistence landscape and some of its properties](https://mlsanity.com/paper/1810.04963/) (2018)
- [giotto-ph: A Python Library for High-Performance Computation of Persistent Homology of Vietoris-Rips Filtrations](https://mlsanity.com/paper/2107.05412/) (2021)
- [Persistent Homology of Attractors For Action Recognition](https://mlsanity.com/paper/1603.05310/) (2016)
- [Persistence Terrace for Topological Inference of Point Cloud Data](https://mlsanity.com/paper/1705.02037/) (2017)

## Built on by (most cited first, 3 of 3)

- [Topological descriptors of foot clearance gait dynamics improve differential diagnosis of Parkinsonism](https://mlsanity.com/paper/2603.06212/) (2026)
- [Robust Short-Term OEE Forecasting in Industry 4.0 via Topological Data Analysis](https://mlsanity.com/paper/2507.02890/) (2025)
- [Persistent Homology of Time Series through Complex Networks](https://mlsanity.com/paper/2605.01624/) (2026)

## Abstract (arXiv)

In this study, we examine if engineered topological features can distinguish time series sampled from different stochastic processes with different noise characteristics, in both balanced and unbalanced sampling schemes. We compare our classification results against the results of the same classification tasks built on statistical and raw features. We conclude that in classification tasks of time series, different machine learning models built on engineered topological features perform consistently better than those built on standard statistical and raw features.