Realizations of indecomposable persistence modules of arbitrarily large dimension

Mickaël Buchet, Emerson G. Escolar

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

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 fü Informatik GmbH
Seiten151-1513
Seitenumfang1363
Band99
ISBN (elektronisch)9783959770668
DOIs
PublikationsstatusVeröffentlicht - 1 Jun 2018
Veranstaltung34th International Symposium on Computational Geometry, SoCG 2018 - Budapest, Ungarn
Dauer: 11 Jun 201814 Jun 2018

Konferenz

Konferenz34th International Symposium on Computational Geometry, SoCG 2018
LandUngarn
OrtBudapest
Zeitraum11/06/1814/06/18

Schlagwörter

    ASJC Scopus subject areas

    • Software

    Dies zitieren

    Buchet, M., & Escolar, E. G. (2018). Realizations of indecomposable persistence modules of arbitrarily large dimension. in 34th International Symposium on Computational Geometry, SoCG 2018 (Band 99, S. 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. Band 99 Schloss Dagstuhl, Leibniz-Zentrum fü Informatik GmbH, 2018. S. 151-1513.

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

    Buchet, M & Escolar, EG 2018, Realizations of indecomposable persistence modules of arbitrarily large dimension. in 34th International Symposium on Computational Geometry, SoCG 2018. Bd. 99, Schloss Dagstuhl, Leibniz-Zentrum fü Informatik GmbH, S. 151-1513, Budapest, Ungarn, 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. Band 99. Schloss Dagstuhl, Leibniz-Zentrum fü Informatik GmbH. 2018. S. 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. Band 99 Schloss Dagstuhl, Leibniz-Zentrum fü Informatik GmbH, 2018. S. 151-1513
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