Rao–Burbea centroids applied to the statistical characterization of time series and images through ordinal patterns

Autores
Mateos, Diego Martín; Riveaud, Leonardo Esteban; Lamberti, Pedro Walter
Año de publicación
2023
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Divergences or similarity measures between probability distributions have become a very useful tool for studying different aspects of statistical objects, such as time series, networks, and images. Notably, not every divergence provides identical results when applied to the same problem. Therefore, it seems convenient to have the widest possible set of divergences to be applied to the problems under study. Besides this choice, an essential step in the analysis of every statistical object is the mapping of each one of their representing values into an alphabet of symbols conveniently chosen. In this work, we choose the family of divergences known as the Burbea–Rao centroids (BRCs). For the mapping of the original time series into a symbolic sequence, we work with the ordinal pattern scheme. We apply our proposals to analyze simulated and real time series and to real textured images. The main conclusion of our work is that the best BRC, at least in the studied cases, is the Jensen–Shannon divergence, besides the fact that it verifies some interesting formal properties.
Fil: Mateos, Diego Martín. Universidad Autónoma de Entre Ríos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Riveaud, Leonardo Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Comahue; Argentina
Fil: Lamberti, Pedro Walter. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
Materia
Rao Buerbea Centroids
Time series analysis
Geometric properties of divergences
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/239011
Acceder
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spelling Rao–Burbea centroids applied to the statistical characterization of time series and images through ordinal patternsMateos, Diego MartínRiveaud, Leonardo EstebanLamberti, Pedro WalterRao Buerbea CentroidsTime series analysisGeometric properties of divergenceshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1Divergences or similarity measures between probability distributions have become a very useful tool for studying different aspects of statistical objects, such as time series, networks, and images. Notably, not every divergence provides identical results when applied to the same problem. Therefore, it seems convenient to have the widest possible set of divergences to be applied to the problems under study. Besides this choice, an essential step in the analysis of every statistical object is the mapping of each one of their representing values into an alphabet of symbols conveniently chosen. In this work, we choose the family of divergences known as the Burbea–Rao centroids (BRCs). For the mapping of the original time series into a symbolic sequence, we work with the ordinal pattern scheme. We apply our proposals to analyze simulated and real time series and to real textured images. The main conclusion of our work is that the best BRC, at least in the studied cases, is the Jensen–Shannon divergence, besides the fact that it verifies some interesting formal properties.Fil: Mateos, Diego Martín. Universidad Autónoma de Entre Ríos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Riveaud, Leonardo Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Comahue; ArgentinaFil: Lamberti, Pedro Walter. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaAmerican Institute of Physics2023-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/239011Mateos, Diego Martín; Riveaud, Leonardo Esteban; Lamberti, Pedro Walter; Rao–Burbea centroids applied to the statistical characterization of time series and images through ordinal patterns; American Institute of Physics; Chaos; 33; 3; 3-2023; 1-111054-1500CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://pubs.aip.org/cha/article/33/3/033144/2881413/Rao-Burbea-centroids-applied-to-the-statisticalinfo:eu-repo/semantics/altIdentifier/doi/10.1063/5.0136240info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:06:51Zoai:ri.conicet.gov.ar:11336/239011instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 10:06:51.313CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Rao–Burbea centroids applied to the statistical characterization of time series and images through ordinal patterns
title Rao–Burbea centroids applied to the statistical characterization of time series and images through ordinal patterns
spellingShingle Rao–Burbea centroids applied to the statistical characterization of time series and images through ordinal patterns
Mateos, Diego Martín
Rao Buerbea Centroids
Time series analysis
Geometric properties of divergences
title_short Rao–Burbea centroids applied to the statistical characterization of time series and images through ordinal patterns
title_full Rao–Burbea centroids applied to the statistical characterization of time series and images through ordinal patterns
title_fullStr Rao–Burbea centroids applied to the statistical characterization of time series and images through ordinal patterns
title_full_unstemmed Rao–Burbea centroids applied to the statistical characterization of time series and images through ordinal patterns
title_sort Rao–Burbea centroids applied to the statistical characterization of time series and images through ordinal patterns
dc.creator.none.fl_str_mv Mateos, Diego Martín
Riveaud, Leonardo Esteban
Lamberti, Pedro Walter
author Mateos, Diego Martín
author_facet Mateos, Diego Martín
Riveaud, Leonardo Esteban
Lamberti, Pedro Walter
author_role author
author2 Riveaud, Leonardo Esteban
Lamberti, Pedro Walter
author2_role author
author
dc.subject.none.fl_str_mv Rao Buerbea Centroids
Time series analysis
Geometric properties of divergences
topic Rao Buerbea Centroids
Time series analysis
Geometric properties of divergences
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Divergences or similarity measures between probability distributions have become a very useful tool for studying different aspects of statistical objects, such as time series, networks, and images. Notably, not every divergence provides identical results when applied to the same problem. Therefore, it seems convenient to have the widest possible set of divergences to be applied to the problems under study. Besides this choice, an essential step in the analysis of every statistical object is the mapping of each one of their representing values into an alphabet of symbols conveniently chosen. In this work, we choose the family of divergences known as the Burbea–Rao centroids (BRCs). For the mapping of the original time series into a symbolic sequence, we work with the ordinal pattern scheme. We apply our proposals to analyze simulated and real time series and to real textured images. The main conclusion of our work is that the best BRC, at least in the studied cases, is the Jensen–Shannon divergence, besides the fact that it verifies some interesting formal properties.
Fil: Mateos, Diego Martín. Universidad Autónoma de Entre Ríos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Riveaud, Leonardo Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Comahue; Argentina
Fil: Lamberti, Pedro Walter. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
description Divergences or similarity measures between probability distributions have become a very useful tool for studying different aspects of statistical objects, such as time series, networks, and images. Notably, not every divergence provides identical results when applied to the same problem. Therefore, it seems convenient to have the widest possible set of divergences to be applied to the problems under study. Besides this choice, an essential step in the analysis of every statistical object is the mapping of each one of their representing values into an alphabet of symbols conveniently chosen. In this work, we choose the family of divergences known as the Burbea–Rao centroids (BRCs). For the mapping of the original time series into a symbolic sequence, we work with the ordinal pattern scheme. We apply our proposals to analyze simulated and real time series and to real textured images. The main conclusion of our work is that the best BRC, at least in the studied cases, is the Jensen–Shannon divergence, besides the fact that it verifies some interesting formal properties.
publishDate 2023
dc.date.none.fl_str_mv 2023-03
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/239011
Mateos, Diego Martín; Riveaud, Leonardo Esteban; Lamberti, Pedro Walter; Rao–Burbea centroids applied to the statistical characterization of time series and images through ordinal patterns; American Institute of Physics; Chaos; 33; 3; 3-2023; 1-11
1054-1500
CONICET Digital
CONICET
url http://hdl.handle.net/11336/239011
identifier_str_mv Mateos, Diego Martín; Riveaud, Leonardo Esteban; Lamberti, Pedro Walter; Rao–Burbea centroids applied to the statistical characterization of time series and images through ordinal patterns; American Institute of Physics; Chaos; 33; 3; 3-2023; 1-11
1054-1500
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://pubs.aip.org/cha/article/33/3/033144/2881413/Rao-Burbea-centroids-applied-to-the-statistical
info:eu-repo/semantics/altIdentifier/doi/10.1063/5.0136240
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Institute of Physics
publisher.none.fl_str_mv American Institute of Physics
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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