Measuring instantaneous and spectral information entropies by shannon entropy of choi-williams distribution in the context of electroencephalography

The theory of Shannon entropy was applied to the Choi-Williams time-frequency distribution (CWD) of time series in order to extract entropy information in both time and frequency domains. In this way, four novel indexes were defined: (1) partial instantaneous entropy, calculated as the entropy of th...

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Autores: Melia, Umberto Sergio Pio|||0000-0003-3033-0505, Clarià Sancho, Francesc, Vallverdú Ferrer, Montserrat|||0000-0002-2031-3261, Caminal Magrans, Pere|||0000-0002-2301-8153
Formato: artículo
Fecha de publicación:2014
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/23365
Acesso em linha:https://hdl.handle.net/2117/23365
https://dx.doi.org/10.3390/e16052530
Access Level:acceso abierto
Palavra-chave:Shannon entropy
Complexity
Electroencephalography
Entropy
Time-frequency representation
Entropia (Teoria de la informació)
Àrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica::Bioinformàtica
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spelling Measuring instantaneous and spectral information entropies by shannon entropy of choi-williams distribution in the context of electroencephalographyMelia, Umberto Sergio Pio|||0000-0003-3033-0505Clarià Sancho, FrancescVallverdú Ferrer, Montserrat|||0000-0002-2031-3261Caminal Magrans, Pere|||0000-0002-2301-8153Shannon entropyComplexityElectroencephalographyEntropyTime-frequency representationEntropia (Teoria de la informació)Àrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica::BioinformàticaThe theory of Shannon entropy was applied to the Choi-Williams time-frequency distribution (CWD) of time series in order to extract entropy information in both time and frequency domains. In this way, four novel indexes were defined: (1) partial instantaneous entropy, calculated as the entropy of the CWD with respect to time by using the probability mass function at each time instant taken independently; (2) partial spectral information entropy, calculated as the entropy of the CWD with respect to frequency by using the probability mass function of each frequency value taken independently; (3) complete instantaneous entropy, calculated as the entropy of the CWD with respect to time by using the probability mass function of the entire CWD; (4) complete spectral information entropy, calculated as the entropy of the CWD with respect to frequency by using the probability mass function of the entire CWD. These indexes were tested on synthetic time series with different behavior (periodic, chaotic and random) and on a dataset of electroencephalographic (EEG) signals recorded in different states (eyes-open, eyes-closed, ictal and non-ictal activity). The results have shown that the values of these indexes tend to decrease, with different proportion, when the behavior of the synthetic signals evolved from chaos or randomness to periodicity. Statistical differences (p-value < 0.0005) were found between values of these measures comparing eyes-open and eyes-closed states and between ictal and non-ictal states in the traditional EEG frequency bands. Finally, this paper has demonstrated that the proposed measures can be useful tools to quantify the different periodic, chaotic and random components in EEG signals. © 2014 by the authors; licensee MDPI, Basel, Switzerland.Peer Reviewed20142014-05-0120142014-07-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/23365https://dx.doi.org/10.3390/e16052530reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/233652026-05-27T15:37:01Z
dc.title.none.fl_str_mv Measuring instantaneous and spectral information entropies by shannon entropy of choi-williams distribution in the context of electroencephalography
title Measuring instantaneous and spectral information entropies by shannon entropy of choi-williams distribution in the context of electroencephalography
spellingShingle Measuring instantaneous and spectral information entropies by shannon entropy of choi-williams distribution in the context of electroencephalography
Melia, Umberto Sergio Pio|||0000-0003-3033-0505
Shannon entropy
Complexity
Electroencephalography
Entropy
Time-frequency representation
Entropia (Teoria de la informació)
Àrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica::Bioinformàtica
title_short Measuring instantaneous and spectral information entropies by shannon entropy of choi-williams distribution in the context of electroencephalography
title_full Measuring instantaneous and spectral information entropies by shannon entropy of choi-williams distribution in the context of electroencephalography
title_fullStr Measuring instantaneous and spectral information entropies by shannon entropy of choi-williams distribution in the context of electroencephalography
title_full_unstemmed Measuring instantaneous and spectral information entropies by shannon entropy of choi-williams distribution in the context of electroencephalography
title_sort Measuring instantaneous and spectral information entropies by shannon entropy of choi-williams distribution in the context of electroencephalography
dc.creator.none.fl_str_mv Melia, Umberto Sergio Pio|||0000-0003-3033-0505
Clarià Sancho, Francesc
Vallverdú Ferrer, Montserrat|||0000-0002-2031-3261
Caminal Magrans, Pere|||0000-0002-2301-8153
author Melia, Umberto Sergio Pio|||0000-0003-3033-0505
author_facet Melia, Umberto Sergio Pio|||0000-0003-3033-0505
Clarià Sancho, Francesc
Vallverdú Ferrer, Montserrat|||0000-0002-2031-3261
Caminal Magrans, Pere|||0000-0002-2301-8153
author_role author
author2 Clarià Sancho, Francesc
Vallverdú Ferrer, Montserrat|||0000-0002-2031-3261
Caminal Magrans, Pere|||0000-0002-2301-8153
author2_role author
author
author
dc.subject.none.fl_str_mv Shannon entropy
Complexity
Electroencephalography
Entropy
Time-frequency representation
Entropia (Teoria de la informació)
Àrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica::Bioinformàtica
topic Shannon entropy
Complexity
Electroencephalography
Entropy
Time-frequency representation
Entropia (Teoria de la informació)
Àrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica::Bioinformàtica
description The theory of Shannon entropy was applied to the Choi-Williams time-frequency distribution (CWD) of time series in order to extract entropy information in both time and frequency domains. In this way, four novel indexes were defined: (1) partial instantaneous entropy, calculated as the entropy of the CWD with respect to time by using the probability mass function at each time instant taken independently; (2) partial spectral information entropy, calculated as the entropy of the CWD with respect to frequency by using the probability mass function of each frequency value taken independently; (3) complete instantaneous entropy, calculated as the entropy of the CWD with respect to time by using the probability mass function of the entire CWD; (4) complete spectral information entropy, calculated as the entropy of the CWD with respect to frequency by using the probability mass function of the entire CWD. These indexes were tested on synthetic time series with different behavior (periodic, chaotic and random) and on a dataset of electroencephalographic (EEG) signals recorded in different states (eyes-open, eyes-closed, ictal and non-ictal activity). The results have shown that the values of these indexes tend to decrease, with different proportion, when the behavior of the synthetic signals evolved from chaos or randomness to periodicity. Statistical differences (p-value < 0.0005) were found between values of these measures comparing eyes-open and eyes-closed states and between ictal and non-ictal states in the traditional EEG frequency bands. Finally, this paper has demonstrated that the proposed measures can be useful tools to quantify the different periodic, chaotic and random components in EEG signals. © 2014 by the authors; licensee MDPI, Basel, Switzerland.
publishDate 2014
dc.date.none.fl_str_mv 2014
2014-05-01
2014
2014-07-01
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://hdl.handle.net/2117/23365
https://dx.doi.org/10.3390/e16052530
url https://hdl.handle.net/2117/23365
https://dx.doi.org/10.3390/e16052530
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
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
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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