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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Main Authors | , |
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Format | Journal Article |
Language | English |
Published |
27.03.2022
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Subjects | |
Online Access | Get full text |
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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. |
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DOI: | 10.48550/arxiv.2203.14289 |