Realizations of indecomposable persistence modules of arbitrarily large dimension

Mickaël Buchet, Emerson G. Escolar

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Abstract

While persistent homology has taken strides towards becoming a widespread tool for data analysis, multidimensional persistence has proven more difficult to apply. One reason is the serious drawback of no longer having a concise and complete descriptor analogous to the persistence diagrams of the former. We propose a simple algebraic construction to illustrate the existence of infinite families of indecomposable persistence modules over regular grids of sufficient size. On top of providing a constructive proof of representation infinite type, we also provide realizations by topological spaces and Vietoris-Rips filtrations, showing that they can actually appear in real data and are not the product of degeneracies.

Original languageEnglish
Title of host publication34th International Symposium on Computational Geometry, SoCG 2018
PublisherSchloss Dagstuhl, Leibniz-Zentrum fü Informatik GmbH
Pages151-1513
Number of pages1363
Volume99
ISBN (Electronic)9783959770668
DOIs
Publication statusPublished - 1 Jun 2018
Event34th International Symposium on Computational Geometry, SoCG 2018 - Budapest, Hungary
Duration: 11 Jun 201814 Jun 2018

Conference

Conference34th International Symposium on Computational Geometry, SoCG 2018
CountryHungary
CityBudapest
Period11/06/1814/06/18

Keywords

  • Commutative ladders
  • Multi-persistence
  • Persistent homology
  • Quivers
  • Representation theory
  • Vietoris-Rips filtration

ASJC Scopus subject areas

  • Software

Cite this

Buchet, M., & Escolar, E. G. (2018). Realizations of indecomposable persistence modules of arbitrarily large dimension. In 34th International Symposium on Computational Geometry, SoCG 2018 (Vol. 99, pp. 151-1513). Schloss Dagstuhl, Leibniz-Zentrum fü Informatik GmbH. https://doi.org/10.4230/LIPIcs.SoCG.2018.15

Realizations of indecomposable persistence modules of arbitrarily large dimension. / Buchet, Mickaël; Escolar, Emerson G.

34th International Symposium on Computational Geometry, SoCG 2018. Vol. 99 Schloss Dagstuhl, Leibniz-Zentrum fü Informatik GmbH, 2018. p. 151-1513.

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Buchet, M & Escolar, EG 2018, Realizations of indecomposable persistence modules of arbitrarily large dimension. in 34th International Symposium on Computational Geometry, SoCG 2018. vol. 99, Schloss Dagstuhl, Leibniz-Zentrum fü Informatik GmbH, pp. 151-1513, 34th International Symposium on Computational Geometry, SoCG 2018, Budapest, Hungary, 11/06/18. https://doi.org/10.4230/LIPIcs.SoCG.2018.15
Buchet M, Escolar EG. Realizations of indecomposable persistence modules of arbitrarily large dimension. In 34th International Symposium on Computational Geometry, SoCG 2018. Vol. 99. Schloss Dagstuhl, Leibniz-Zentrum fü Informatik GmbH. 2018. p. 151-1513 https://doi.org/10.4230/LIPIcs.SoCG.2018.15
Buchet, Mickaël ; Escolar, Emerson G. / Realizations of indecomposable persistence modules of arbitrarily large dimension. 34th International Symposium on Computational Geometry, SoCG 2018. Vol. 99 Schloss Dagstuhl, Leibniz-Zentrum fü Informatik GmbH, 2018. pp. 151-1513
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