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27 août 2018
- handle: 10670/1.wxqcqe
- hal: hal-02060057
- doi: 10.1007/978-3-319-99740-7_18
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info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-319-99740-7_18
http://creativecommons.org/licenses/by/ , info:eu-repo/semantics/OpenAccess
Mots-clés
Natural pseudo-distance Filtering function Group action Group equivariant non-expansive operator Persistent homology group Topological data analysisSujets proches
Natural science Sciences Science of scienceCiter ce document
Francesco Camporesi et al., « On a New Method to Build Group Equivariant Operators by Means of Permutants », HAL-SHS : sciences de l'information, de la communication et des bibliothèques, ID : 10.1007/978-3-319-99740-7_18
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Résumé
The use of group equivariant operators is becoming more and more important in machine learning and topological data analysis. In this paper we introduce a new method to build G-equivariant non-expansive operators from a set $$\varPhi $$ of bounded and continuous functions $$\varphi :X\rightarrow \mathbb {R}$$ to $$\varPhi $$ itself, where X is a topological space and G is a subgroup of the group of all self-homeomorphisms of X.