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About this paper
Nina Otter, Mason A. Porter, Ulrike Tillmann, Peter Grindrod, Heather A. Harrington
This paper offers a comprehensive guide to computing Persistent Homology, combining an accessible introduction to the theory with an empirical benchmarking of leading open-source software libraries. It identifies ripser as the top-performing tool for Vietoris-Rips complexes and provides practical recommendations for software selection across various data types and computational scenarios.
Key insights
- Dual algorithms for Persistent Homology computation consistently outperform standard algorithms in terms of both computation time and memory usage.
- The choice of simplicial complex (e.g., Vietoris-Rips, Alpha, Cubical) significantly impacts the computational efficiency and suitability of software for different data types.
- There is a trade-off between computational performance and ease of use, with some user-friendly tools being less efficient for large datasets but suitable for beginners.
Summary by alphaXiv.
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