The natural pseudo-distance dG associated with a group G of self-homeomorphisms of a topological space X is a pseudo-metric developed to compare real-valued functions defined on X, when the equivalence between functions is expressed by the group G. In this paper, we illustrate dG, its role in topological data analysis, its main properties and its link with persistent homology.
An Introduction to the Notion of Natural Pseudo-distance in Topological Data Analysis
Frosini P.
2021-01-01
Abstract
The natural pseudo-distance dG associated with a group G of self-homeomorphisms of a topological space X is a pseudo-metric developed to compare real-valued functions defined on X, when the equivalence between functions is expressed by the group G. In this paper, we illustrate dG, its role in topological data analysis, its main properties and its link with persistent homology.File in questo prodotto:
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