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A Primer on Persistent Homology of Finite Metric Spaces

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Abstract

Topological data analysis (TDA) is a relatively new area of research related to importing classical ideas from topology into the realm of data analysis. Under the umbrella term TDA, there falls, in particular, the notion of persistent homology PH, which can be described in a nutshell, as the study of scale-dependent homological invariants of datasets. In these notes, we provide a terse self-contained description of the main ideas behind the construction of persistent homology as an invariant feature of datasets, and its stability to perturbations.

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Acknowledgements

These notes are meant to supplement the lectures given by the first author during the TGDA@OSU TRIPODS Summer School held at MBI during May 2018. Videos of the lectures are available at TRIPODS (2018). We acknowledge NSF support through project CCF #1740761.

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  1. Department of Mathematics, The Ohio State University, Columbus, USA

    Facundo Mémoli & Kritika Singhal

  2. Department of Computer Science and Engineering, The Ohio State University, Columbus, USA

    Facundo Mémoli

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  1. Facundo Mémoli
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  2. Kritika Singhal
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Mémoli, F., Singhal, K. A Primer on Persistent Homology of Finite Metric Spaces. Bull Math Biol 81, 2074–2116 (2019). https://doi.org/10.1007/s11538-019-00614-z

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