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EnglishFinite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of the spaces that are invariant under strictly increasing rescaling of the distance functions. In this paper, we analyse some of the possible complete and incomplete invariants for weak isometry and we introduce a dissimilarity measure that asses how far two spaces are from being weakly isometric. Furthermore, we compare these ideas with the theory of persistent homology, to study how the two are related.
On the notion of weak isometry for finite metric spaces / De Gregorio, Alessandro; Fugacci, Ulderico; Memoli, Facundo; Vaccarino, Francesco. - ELETTRONICO. - (2020).
| Titolo: | On the notion of weak isometry for finite metric spaces | |
| Autori: | ||
| Data di pubblicazione: | 2020 | |
| Abstract: | Finite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of the spaces that are invariant under strictly increasing rescaling of the distance functions. In this paper, we analyse some of the possible complete and incomplete invariants for weak isometry and we introduce a dissimilarity measure that asses how far two spaces are from being weakly isometric. Furthermore, we compare these ideas with the theory of persistent homology, to study how the two are related. | |
| Appare nelle tipologie: | 5.12 Altro |
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http://hdl.handle.net/11583/2821495
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