A Locally Stable Edit Distance for Functions Defined on Merge Trees

In this work we define a metric structure for functions defined on merge trees. The metric introduced possesses some stability properties and can be computed with a dynamical integer linear programming approach. We showcase the effectiveness of the whole framework with simulated data sets. Using fun...

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Bibliographic Details
Published inarXiv.org
Main Author Pegoraro, Matteo
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 26.04.2023
Subjects
Data analysis
Integer programming
Linear programming
Scalars
Summaries
Topology
Trees (mathematics)
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Summary:In this work we define a metric structure for functions defined on merge trees. The metric introduced possesses some stability properties and can be computed with a dynamical integer linear programming approach. We showcase the effectiveness of the whole framework with simulated data sets. Using functions defined on merge trees proves to be very effective in situation where other topological data analysis tools, like persistence diagrams, can not be meaningfully employed.
ISSN:2331-8422