Measuring the Distance Between Merge Trees

Autor:	Gunther H. Weber, Dmitriy Morozov, Damir Yeliussizov, Bernd Hamann, Kenes Beketayev
Rok vydání:	2014
Předmět:	Discrete mathematics Tree distance Naive algorithm Persistent homology business.industry Computer science Norm (mathematics) Scalar (mathematics) Edit distance Artificial intelligence business Reeb graph Bottleneck
Zdroj:	Mathematics and Visualization ISBN: 9783319040981 Topological Methods in Data Analysis and Visualization
DOI:	10.1007/978-3-319-04099-8_10
Popis:	Merge trees represent the topology of scalar functions. To assess the topological similarity of functions, one can compare their merge trees. To do so, one needs a notion of a distance between merge trees, which we define. We provide examples of using our merge tree distance and compare this new measure to other ways used to characterize topological similarity (bottleneck distance for persistence diagrams) and numerical difference (L ∞ -norm of the difference between functions).
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::4b2a9ee8bed2e8f8dffe4fb0c847f95d https://doi.org/10.1007/978-3-319-04099-8_10 Zobrazit plný text záznamu