General persistence theory: on the course to multiparameter persistent homology
We explore Persistence Theory in its full generality. As a particular instance, we first discuss one parameter persistence theory, which arises from uniparametric filtrations of spaces. Although enjoying many excellent properties, it often does not capture the structure of interest in the dataset. T...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/375068 |
| Acceso en línea: | https://hdl.handle.net/2117/375068 |
| Access Level: | acceso abierto |
| Palabra clave: | Algebra, Homological Categories (Mathematics) Topological Data Analysis General Persistence Theory Persistent Homology Multiparameter Persistent Homology Àlgebra homològica Categories (Matemàtica) Classificació AMS::55 Algebraic topology::55U Applied homological algebra and category theory Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria |
| Sumario: | We explore Persistence Theory in its full generality. As a particular instance, we first discuss one parameter persistence theory, which arises from uniparametric filtrations of spaces. Although enjoying many excellent properties, it often does not capture the structure of interest in the dataset. Therefore, this led us to consider Multiparamer Persistence Theory. Multiparameter persistence modules are more flexible and richer than the ones arising from one parameter persistence. However, as a result, they become more complex and opaque, which motivates us to seek alternative invariants. |
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