Realizations of indecomposable persistence modules of arbitrarily large dimension

Mickaël Buchet, Emerson G. Escolar

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in einem KonferenzbandBegutachtung

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.

Originalspracheenglisch
Titel34th International Symposium on Computational Geometry, SoCG 2018
Herausgeber (Verlag)Schloss Dagstuhl - Leibniz-Zentrum für Informatik
Seiten151-1513
Seitenumfang1363
Band99
ISBN (elektronisch)9783959770668
DOIs
PublikationsstatusVeröffentlicht - 1 Juni 2018
Veranstaltung34th International Symposium on Computational Geometry: SoCG 2018 - Budapest, Ungarn
Dauer: 11 Juni 201814 Juni 2018

Konferenz

Konferenz34th International Symposium on Computational Geometry
Land/GebietUngarn
OrtBudapest
Zeitraum11/06/1814/06/18

ASJC Scopus subject areas

  • Software

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