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Classification of Stochastic Processes with Topological Data Analysis

arXiv 2206.03973 ↗First posted 8 Jun 2022stat.ML cs.LGcited by 3

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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.

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

14 of 71 references.

References · 14

  1. 2016XGBoost: A Scalable Tree Boosting Systemcited by 5,166
  2. 2015Persistence Images: A Stable Vector Representation of Persistent Homologycited by 236
  3. 2017An introduction to Topological Data Analysis: fundamental and practical aspects for data scientistscited by 172
  4. 2015A roadmap for the computation of persistent homologycited by 127
  5. 2019Ripser: efficient computation of Vietoris-Rips persistence barcodescited by 117
  6. 2020giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Explorationcited by 55
  7. 2016Geometry Helps to Compare Persistence Diagramscited by 39
  8. 2019Persistence Curves: A canonical framework for summarizing persistence diagramscited by 33
  9. 2017Feature-based time-series analysiscited by 28
  10. 2020GPU-Accelerated Computation of Vietoris-Rips Persistence Barcodescited by 27
  11. 2018The persistence landscape and some of its propertiescited by 19
  12. 2021giotto-ph: A Python Library for High-Performance Computation of Persistent Homology of Vietoris-Rips Filtrationscited by 11
2 more
  1. 2016Persistent Homology of Attractors For Action Recognitioncited by 10
  2. 2017Persistence Terrace for Topological Inference of Point Cloud Datacited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 2.

3 papers.

  1. 2026Topological descriptors of foot clearance gait dynamics improve differential diagnosis of Parkinsonismcited by 1
  2. 2025Robust Short-Term OEE Forecasting in Industry 4.0 via Topological Data Analysiscited by 0
  3. 2026Persistent Homology of Time Series through Complex Networkscited by 0