Topological features of multivariate distributions: Dependency on the covariance matrix
Topological data analysis provides a new perspective on many problems in the domain of complex systems. Here, we establish the dependency of mean values of functional $p$ norms of 'persistence landscapes' on a uniform scaling of the underlying multivariate distribution. Furthermore, we dem...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/193830 |
| Acceso en línea: | https://hdl.handle.net/2445/193830 |
| Access Level: | acceso abierto |
| Palabra clave: | Processos estocàstics Estadística Grups topològics Homologia Stochastic processes Statistics Topological groups Homology |
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Topological features of multivariate distributions: Dependency on the covariance matrixAromi, Lloyd L.Katz, Yuri A.Vives i Santa Eulàlia, Josep, 1963-Processos estocàsticsEstadísticaGrups topològicsHomologiaStochastic processesStatisticsTopological groupsHomologyTopological data analysis provides a new perspective on many problems in the domain of complex systems. Here, we establish the dependency of mean values of functional $p$ norms of 'persistence landscapes' on a uniform scaling of the underlying multivariate distribution. Furthermore, we demonstrate that average values of $p$-norms are decreasing, when the covariance in a system is increasing. To illustrate the complex dependency of these topological features on changes in the variance-covariance matrix, we conduct numerical experiments utilizing bi-variate distributions with known statistical properties. Our results help to explain the puzzling behavior of $p$-norms derived from daily log-returns of major equity indices on European and US markets at the inception phase of the global financial meltdown caused by the COVID-19 pandemic.Elsevier B.V.2023202320212023info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2445/193830Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésVersió postprint del document publicat a: https://doi.org/10.1016/j.cnsns.2021.105996Communications In Nonlinear Science And Numerical Simulation, 2021, vol. 103, num. 105996https://doi.org/10.1016/j.cnsns.2021.105996cc-by-nc-nd (c) Elsevier B.V., 2021https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:2445/1938302026-05-29T05:05:01Z |
| dc.title.none.fl_str_mv |
Topological features of multivariate distributions: Dependency on the covariance matrix |
| title |
Topological features of multivariate distributions: Dependency on the covariance matrix |
| spellingShingle |
Topological features of multivariate distributions: Dependency on the covariance matrix Aromi, Lloyd L. Processos estocàstics Estadística Grups topològics Homologia Stochastic processes Statistics Topological groups Homology |
| title_short |
Topological features of multivariate distributions: Dependency on the covariance matrix |
| title_full |
Topological features of multivariate distributions: Dependency on the covariance matrix |
| title_fullStr |
Topological features of multivariate distributions: Dependency on the covariance matrix |
| title_full_unstemmed |
Topological features of multivariate distributions: Dependency on the covariance matrix |
| title_sort |
Topological features of multivariate distributions: Dependency on the covariance matrix |
| dc.creator.none.fl_str_mv |
Aromi, Lloyd L. Katz, Yuri A. Vives i Santa Eulàlia, Josep, 1963- |
| author |
Aromi, Lloyd L. |
| author_facet |
Aromi, Lloyd L. Katz, Yuri A. Vives i Santa Eulàlia, Josep, 1963- |
| author_role |
author |
| author2 |
Katz, Yuri A. Vives i Santa Eulàlia, Josep, 1963- |
| author2_role |
author author |
| dc.subject.none.fl_str_mv |
Processos estocàstics Estadística Grups topològics Homologia Stochastic processes Statistics Topological groups Homology |
| topic |
Processos estocàstics Estadística Grups topològics Homologia Stochastic processes Statistics Topological groups Homology |
| description |
Topological data analysis provides a new perspective on many problems in the domain of complex systems. Here, we establish the dependency of mean values of functional $p$ norms of 'persistence landscapes' on a uniform scaling of the underlying multivariate distribution. Furthermore, we demonstrate that average values of $p$-norms are decreasing, when the covariance in a system is increasing. To illustrate the complex dependency of these topological features on changes in the variance-covariance matrix, we conduct numerical experiments utilizing bi-variate distributions with known statistical properties. Our results help to explain the puzzling behavior of $p$-norms derived from daily log-returns of major equity indices on European and US markets at the inception phase of the global financial meltdown caused by the COVID-19 pandemic. |
| publishDate |
2021 |
| dc.date.none.fl_str_mv |
2021 2023 2023 2023 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion |
| format |
article |
| status_str |
acceptedVersion |
| dc.identifier.none.fl_str_mv |
https://hdl.handle.net/2445/193830 |
| url |
https://hdl.handle.net/2445/193830 |
| dc.language.none.fl_str_mv |
Inglés |
| language_invalid_str_mv |
Inglés |
| dc.relation.none.fl_str_mv |
Versió postprint del document publicat a: https://doi.org/10.1016/j.cnsns.2021.105996 Communications In Nonlinear Science And Numerical Simulation, 2021, vol. 103, num. 105996 https://doi.org/10.1016/j.cnsns.2021.105996 |
| dc.rights.none.fl_str_mv |
cc-by-nc-nd (c) Elsevier B.V., 2021 https://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
cc-by-nc-nd (c) Elsevier B.V., 2021 https://creativecommons.org/licenses/by-nc-nd/4.0/ |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
application/pdf |
| dc.publisher.none.fl_str_mv |
Elsevier B.V. |
| publisher.none.fl_str_mv |
Elsevier B.V. |
| dc.source.none.fl_str_mv |
Articles publicats en revistes (Matemàtiques i Informàtica) reponame:Recercat. Dipósit de la Recerca de Catalunya instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
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Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
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Recercat. Dipósit de la Recerca de Catalunya |
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Recercat. Dipósit de la Recerca de Catalunya |
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