An Introduction to Multiparameter Persistence

In topological data analysis (TDA), one often studies the shape of data by constructing a filtered topological space, whose structure is then examined using persistent homology. However, a single filtered space often does not adequately capture the structure of interest in the data, and one is led t...

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Bibliographic Details
Published inarXiv.org
Main Authors Magnus Bakke Botnan, Lesnick, Michael
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 13.03.2023
Subjects
Data analysis
Homology
Topology
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Summary:In topological data analysis (TDA), one often studies the shape of data by constructing a filtered topological space, whose structure is then examined using persistent homology. However, a single filtered space often does not adequately capture the structure of interest in the data, and one is led to consider multiparameter persistence, which associates to the data a space equipped with a multiparameter filtration. Multiparameter persistence has become one of the most active areas of research within TDA, with exciting progress on several fronts. In this article, we introduce multiparameter persistence and survey some of this recent progress, with a focus on ideas likely to lead to practical applications in the near future.
ISSN:2331-8422