Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Multidimensional Persistence and Noise
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0001-6007-9273
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Show others and affiliations
2016 (English)In: Foundations of Computational Mathematics, ISSN 1615-3375, E-ISSN 1615-3383, 1-40 p.Article in journal (Refereed) 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.

Place, publisher, year, edition, pages
Springer-Verlag New York, 2016. 1-40 p.
Keyword [en]
Multidimensional persistence, Noise systems, Persistence modules, Stable invariants, Computational methods, Mathematical techniques, Functors, Persistent feature, Pseudo-metrices, Algebra
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:kth:diva-197199DOI: 10.1007/s10208-016-9323-yScopusID: 2-s2.0-84976493395OAI: oai:DiVA.org:kth-197199DiVA: diva2:1055452
Note

QC 20161212

Available from: 2016-12-12 Created: 2016-11-30 Last updated: 2016-12-12Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Scolamiero, MartinaChachólski, WojciechLundman, AndersRamanujam, RyanÖberg, Sebastian
By organisation
Mathematics (Div.)
In the same journal
Foundations of Computational Mathematics
Algebra and Logic

Search outside of DiVA

GoogleGoogle Scholar

Altmetric score

Total: 13 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf