A roadmap for the computation of persistent homology

2015/06/30 by Nina Otter, Mason A. Porter, Ulrike Tillmann +2 · 9 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Benchmarking #Computation #Computational science #Computer science #Data Visualization and Analytics #Data structure #Homotopy and Cohomology in Algebraic Topology #Implementation #Pipeline (software) #Programming language #Scripting language #Software #Theoretical computer science #Topological and Geometric Data Analysis #cs.CG #math.AT #physics.data-an #q-bio.QM

paper · pdf · doi:10.1140/epjds/s13688-017-0109-5

published as EPJ Data Science 2017 6:17, Springer Nature · Final version; minor changes throughout, added a section to the tutorial

openalex publication_date 2017/08/09 · arxiv created 2017/09/12 · arxiv updated 2017/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

(PH) is a method used in topological data analysis (TDA) to study qualitative features of data that persist across multiple scales. It is robust to perturbations of input data, independent of dimensions and coordinates, and provides a compact representation of the qualitative features of the input. The computation of PH is an open area with numerous important and fascinating challenges. The field of PH computation is evolving rapidly, and new algorithms and software implementations are being updated and released at a rapid pace. The purposes of our article are to (1) introduce theory and computational methods for PH to a broad range of computational scientists and (2) provide benchmarks of state-of-the-art implementations for the computation of PH. We give a friendly introduction to PH, navigate the pipeline for the computation of PH with an eye towards applications, and use a range of synthetic and real-world data sets to evaluate currently available open-source implementations for the computation of PH. Based on our benchmarking, we indicate which algorithms and implementations are best suited to different types of data sets. In an accompanying tutorial, we provide guidelines for the computation of PH. We make publicly available all scripts that we wrote for the tutorial, and we make available the processed version of the data sets used in the benchmarking. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1140/epjds/s13688-017-0109-5) contains supplementary material.

Citations

• Robust Topological Inference: Distance To a Measure and Kernel Distance
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• Persistent homology of time-dependent functional networks constructed from coupled time series
• Modeling the spread of the Zika virus using topological data analysis
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• Graduate Texts in Mathematics

Cited by

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• Financial Anomaly Detection for the Canadian Market
• Topological Clustering via Sliced Wasserstien Kernels
• Discrete homology computations by reduction to zero differentials
• Classification of Firn Data via Topological Features
• Strong discrete Morse theory
• Topological model selection: a case-study in tumour-induced angiogenesis
• Persistent Homology-Based Indicator of Orientational Ordering in Two-Dimensional Quasi-Particle Systems Applied to Skyrmion Lattices
• A persistent homology approach to heart rate variability analysis with an application to sleep-wake classification

Related

• Persistent Homology: A Pedagogical Introduction with Biological Applications
• A Brief History of Persistence
• A Framework for Fast and Stable Representations of Multiparameter Persistent Homology Decompositions
• Dory: Overcoming Barriers to Computing Persistent Homology
• Modeling of Persistent Homology