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Filtration Simplification for Persistent Homology via Edge Contraction
Journal of Mathematical Imaging and Vision ( IF 1.353 ) Pub Date : 2020-05-19 , DOI: 10.1007/s10851-020-00956-7
Tamal K. Dey, Ryan Slechta

Persistent homology is a popular data analysis technique that is used to capture the changing homology of an indexed sequence of simplicial complexes. These changes are summarized in persistence diagrams. A natural problem is to contract edges in complexes in the initial sequence to obtain a sequence of simplified complexes while controlling the perturbation between the original and simplified persistence diagrams. This paper is an extended version of Dey and Slechta (in: Discrete geometry for computer imagery, Springer, New York, 2019), where we developed two contraction operators for the case where the initial sequence is a filtration. In addition to the content in the original version, this paper presents proofs relevant to the filtration case and develops contraction operators for towers and multiparameter filtrations.
更新日期:2020-05-19

 

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