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A roadmap for the computation of persistent homology
Nina Otter1,2, Mason A Porter1,3,4, Ulrike Tillmann1,2
11Mathematical Institute, University of Oxford, Oxford, OX2 6GG UK.
EPJ Data Science
|February 7, 2020
Summary
Persistent homology (PH) is a robust method for analyzing data features across scales. This study benchmarks PH computation algorithms, guiding users to optimal implementations for diverse datasets.
Area of Science:
- Topological Data Analysis (TDA)
- Computational Topology
- Data Science
Background:
- Persistent homology (PH) is a key TDA method for studying data features across scales.
- PH is robust to data perturbations, dimension, and coordinate systems.
- PH offers a compact representation of qualitative data features.
Purpose of the Study:
- Introduce PH theory and computational methods to computational scientists.
- Benchmark state-of-the-art PH computation implementations.
- Provide guidance on selecting optimal PH algorithms for different datasets.
Main Methods:
- Review of persistent homology theory and computational pipelines.
- Benchmarking of various open-source PH implementations.
- Evaluation using synthetic and real-world datasets.
Main Results:
- Comprehensive comparison of current PH computation algorithms.
- Identification of best-suited algorithms and implementations for specific data types.
- Publicly available scripts and processed datasets for reproducibility.
Conclusions:
- Persistent homology computation is a rapidly evolving field.
- Benchmarking provides essential guidance for practical PH applications.
- The study facilitates broader adoption and effective use of PH in data analysis.
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