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 language | English |
---|---|
Title of host publication | 34th International Symposium on Computational Geometry, SoCG 2018 |
Publisher | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
Pages | 151-1513 |
Number of pages | 1363 |
Volume | 99 |
ISBN (Electronic) | 9783959770668 |
DOIs | |
Publication status | Published - 1 Jun 2018 |
Event | 34th International Symposium on Computational Geometry: SoCG 2018 - Budapest, Hungary Duration: 11 Jun 2018 → 14 Jun 2018 |
Conference
Conference | 34th International Symposium on Computational Geometry |
---|---|
Country/Territory | Hungary |
City | Budapest |
Period | 11/06/18 → 14/06/18 |
Keywords
- Commutative ladders
- Multi-persistence
- Persistent homology
- Quivers
- Representation theory
- Vietoris-Rips filtration
ASJC Scopus subject areas
- Software