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.
Originalsprache | englisch |
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Titel | 34th International Symposium on Computational Geometry, SoCG 2018 |
Herausgeber (Verlag) | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
Seiten | 151-1513 |
Seitenumfang | 1363 |
Band | 99 |
ISBN (elektronisch) | 9783959770668 |
DOIs | |
Publikationsstatus | Veröffentlicht - 1 Juni 2018 |
Veranstaltung | 34th International Symposium on Computational Geometry: SoCG 2018 - Budapest, Ungarn Dauer: 11 Juni 2018 → 14 Juni 2018 |
Konferenz
Konferenz | 34th International Symposium on Computational Geometry |
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Land/Gebiet | Ungarn |
Ort | Budapest |
Zeitraum | 11/06/18 → 14/06/18 |
ASJC Scopus subject areas
- Software