Embedded Dimension and Time Series Length. Practical Influence on Permutation Entropy and Its Applications

[EN] Permutation Entropy (PE) is a time series complexity measure commonly used in a variety of contexts, with medicine being the prime example. In its general form, it requires three input parameters for its calculation: time series length N, embedded dimension m, and embedded delay ¿. Inappropriat...

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Authors: Cuesta Frau, David|||0000-0002-0076-0515, Murillo-Escobar, Juan Pablo, Orrego, Diana Alexandra, Delgado-Trejos, Edilson
Format: article
Publication Date:2019
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:riunet.upv.es:10251/156109
Online Access:https://riunet.upv.es/handle/10251/156109
Access Level:Open access
Keyword:Permutation entropy
Embedded dimension
Short time records
Signal classification
Relevance analysis
ARQUITECTURA Y TECNOLOGIA DE COMPUTADORES
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network_acronym_str ES
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spelling Embedded Dimension and Time Series Length. Practical Influence on Permutation Entropy and Its ApplicationsCuesta Frau, David|||0000-0002-0076-0515Murillo-Escobar, Juan PabloOrrego, Diana AlexandraDelgado-Trejos, EdilsonPermutation entropyEmbedded dimensionShort time recordsSignal classificationRelevance analysisARQUITECTURA Y TECNOLOGIA DE COMPUTADORES[EN] Permutation Entropy (PE) is a time series complexity measure commonly used in a variety of contexts, with medicine being the prime example. In its general form, it requires three input parameters for its calculation: time series length N, embedded dimension m, and embedded delay ¿. Inappropriate choices of these parameters may potentially lead to incorrect interpretations. However, there are no specific guidelines for an optimal selection of N, m, or ¿, only general recommendations such as N >> m!, ¿ = 1, or m = 3, . . . , 7. This paper deals specifically with the study of the practical implications of N >> m!, since long time series are often not available, or non-stationary, and other preliminary results suggest that low N values do not necessarily invalidate PE usefulness. Our study analyses the PE variation as a function of the series length N and embedded dimension m in the context of a diverse experimental set, both synthetic (random, spikes, or logistic model time series) and real¿world (climatology, seismic, financial, or biomedical time series), and the classification performance achieved with varying N and m. The results seem to indicate that shorter lengths than those suggested by N >> m! are sufficient for a stable PE calculation, and even very short time series can be robustly classified based on PE measurements before the stability point is reached. This may be due to the fact that there are forbidden patterns in chaotic time series, not all the patterns are equally informative, and differences among classes are already apparent at very short lengths.MDPI AGDepartamento de Informática de Sistemas y ComputadoresEscuela Politécnica Superior de AlcoyRepositorio Institucional de la Universitat Politècnica de València Riunet20192019-04-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/156109reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1561092026-06-13T07:49:27Z
dc.title.none.fl_str_mv Embedded Dimension and Time Series Length. Practical Influence on Permutation Entropy and Its Applications
title Embedded Dimension and Time Series Length. Practical Influence on Permutation Entropy and Its Applications
spellingShingle Embedded Dimension and Time Series Length. Practical Influence on Permutation Entropy and Its Applications
Cuesta Frau, David|||0000-0002-0076-0515
Permutation entropy
Embedded dimension
Short time records
Signal classification
Relevance analysis
ARQUITECTURA Y TECNOLOGIA DE COMPUTADORES
title_short Embedded Dimension and Time Series Length. Practical Influence on Permutation Entropy and Its Applications
title_full Embedded Dimension and Time Series Length. Practical Influence on Permutation Entropy and Its Applications
title_fullStr Embedded Dimension and Time Series Length. Practical Influence on Permutation Entropy and Its Applications
title_full_unstemmed Embedded Dimension and Time Series Length. Practical Influence on Permutation Entropy and Its Applications
title_sort Embedded Dimension and Time Series Length. Practical Influence on Permutation Entropy and Its Applications
dc.creator.none.fl_str_mv Cuesta Frau, David|||0000-0002-0076-0515
Murillo-Escobar, Juan Pablo
Orrego, Diana Alexandra
Delgado-Trejos, Edilson
author Cuesta Frau, David|||0000-0002-0076-0515
author_facet Cuesta Frau, David|||0000-0002-0076-0515
Murillo-Escobar, Juan Pablo
Orrego, Diana Alexandra
Delgado-Trejos, Edilson
author_role author
author2 Murillo-Escobar, Juan Pablo
Orrego, Diana Alexandra
Delgado-Trejos, Edilson
author2_role author
author
author
dc.contributor.none.fl_str_mv Departamento de Informática de Sistemas y Computadores
Escuela Politécnica Superior de Alcoy
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Permutation entropy
Embedded dimension
Short time records
Signal classification
Relevance analysis
ARQUITECTURA Y TECNOLOGIA DE COMPUTADORES
topic Permutation entropy
Embedded dimension
Short time records
Signal classification
Relevance analysis
ARQUITECTURA Y TECNOLOGIA DE COMPUTADORES
description [EN] Permutation Entropy (PE) is a time series complexity measure commonly used in a variety of contexts, with medicine being the prime example. In its general form, it requires three input parameters for its calculation: time series length N, embedded dimension m, and embedded delay ¿. Inappropriate choices of these parameters may potentially lead to incorrect interpretations. However, there are no specific guidelines for an optimal selection of N, m, or ¿, only general recommendations such as N >> m!, ¿ = 1, or m = 3, . . . , 7. This paper deals specifically with the study of the practical implications of N >> m!, since long time series are often not available, or non-stationary, and other preliminary results suggest that low N values do not necessarily invalidate PE usefulness. Our study analyses the PE variation as a function of the series length N and embedded dimension m in the context of a diverse experimental set, both synthetic (random, spikes, or logistic model time series) and real¿world (climatology, seismic, financial, or biomedical time series), and the classification performance achieved with varying N and m. The results seem to indicate that shorter lengths than those suggested by N >> m! are sufficient for a stable PE calculation, and even very short time series can be robustly classified based on PE measurements before the stability point is reached. This may be due to the fact that there are forbidden patterns in chaotic time series, not all the patterns are equally informative, and differences among classes are already apparent at very short lengths.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-04-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/156109
url https://riunet.upv.es/handle/10251/156109
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv MDPI AG
publisher.none.fl_str_mv MDPI AG
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869419937065336832
score 15,301603

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