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Multidimensional Persistence and Noise
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).ORCID-id: 0000-0001-6007-9273
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
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2017 (engelsk)Inngår i: Foundations of Computational Mathematics, ISSN 1615-3375, E-ISSN 1615-3383, Vol. 17, nr 6, s. 1367-1406Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

In this paper, we study multidimensional persistence modules (Carlsson and Zomorodian in Discrete Comput Geom 42(1):71–93, 2009; Lesnick in Found Comput Math 15(3):613–650, 2015) via what we call tame functors and noise systems. A noise system leads to a pseudometric topology on the category of tame functors. We show how this pseudometric can be used to identify persistent features of compact multidimensional persistence modules. To count such features, we introduce the feature counting invariant and prove that assigning this invariant to compact tame functors is a 1-Lipschitz operation. For one-dimensional persistence, we explain how, by choosing an appropriate noise system, the feature counting invariant identifies the same persistent features as the classical barcode construction.

sted, utgiver, år, opplag, sider
Springer-Verlag New York, 2017. Vol. 17, nr 6, s. 1367-1406
Emneord [en]
Multidimensional persistence, Noise systems, Persistence modules, Stable invariants, Computational methods, Mathematical techniques, Functors, Persistent feature, Pseudo-metrices, Algebra
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Identifikatorer
URN: urn:nbn:se:kth:diva-197199DOI: 10.1007/s10208-016-9323-yISI: 000415739500001Scopus ID: 2-s2.0-84976493395OAI: oai:DiVA.org:kth-197199DiVA, id: diva2:1055452
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QC 20161212

Tilgjengelig fra: 2016-12-12 Laget: 2016-11-30 Sist oppdatert: 2017-12-08bibliografisk kontrollert

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