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A Two-Steps-Ahead Estimator for Bubble Entropy
Aims: Bubble entropy ([Formula: see text]) is an entropy metric with a limited dependence on parameters. [Formula: see text] does not directly quantify the conditional entropy of the series, but it assesses the change in entropy of the ordering of portions of its samples of length m, when adding an...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2021
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8235094/ https://www.ncbi.nlm.nih.gov/pubmed/34208771 http://dx.doi.org/10.3390/e23060761 |
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author | Manis, George Bodini, Matteo Rivolta, Massimo W. Sassi, Roberto |
author_facet | Manis, George Bodini, Matteo Rivolta, Massimo W. Sassi, Roberto |
author_sort | Manis, George |
collection | PubMed |
description | Aims: Bubble entropy ([Formula: see text]) is an entropy metric with a limited dependence on parameters. [Formula: see text] does not directly quantify the conditional entropy of the series, but it assesses the change in entropy of the ordering of portions of its samples of length m, when adding an extra element. The analytical formulation of [Formula: see text] for autoregressive (AR) processes shows that, for this class of processes, the relation between the first autocorrelation coefficient and [Formula: see text] changes for odd and even values of m. While this is not an issue, per se, it triggered ideas for further investigation. Methods: Using theoretical considerations on the expected values for AR processes, we examined a two-steps-ahead estimator of [Formula: see text] , which considered the cost of ordering two additional samples. We first compared it with the original [Formula: see text] estimator on a simulated series. Then, we tested it on real heart rate variability (HRV) data. Results: The experiments showed that both examined alternatives showed comparable discriminating power. However, for values of [Formula: see text] , where the statistical significance of the method was increased and improved as m increased, the two-steps-ahead estimator presented slightly higher statistical significance and more regular behavior, even if the dependence on parameter m was still minimal. We also investigated a new normalization factor for [Formula: see text] , which ensures that [Formula: see text] [Formula: see text] when white Gaussian noise (WGN) is given as the input. Conclusions: The research improved our understanding of bubble entropy, in particular in the context of HRV analysis, and we investigated interesting details regarding the definition of the estimator. |
format | Online Article Text |
id | pubmed-8235094 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-82350942021-06-27 A Two-Steps-Ahead Estimator for Bubble Entropy Manis, George Bodini, Matteo Rivolta, Massimo W. Sassi, Roberto Entropy (Basel) Article Aims: Bubble entropy ([Formula: see text]) is an entropy metric with a limited dependence on parameters. [Formula: see text] does not directly quantify the conditional entropy of the series, but it assesses the change in entropy of the ordering of portions of its samples of length m, when adding an extra element. The analytical formulation of [Formula: see text] for autoregressive (AR) processes shows that, for this class of processes, the relation between the first autocorrelation coefficient and [Formula: see text] changes for odd and even values of m. While this is not an issue, per se, it triggered ideas for further investigation. Methods: Using theoretical considerations on the expected values for AR processes, we examined a two-steps-ahead estimator of [Formula: see text] , which considered the cost of ordering two additional samples. We first compared it with the original [Formula: see text] estimator on a simulated series. Then, we tested it on real heart rate variability (HRV) data. Results: The experiments showed that both examined alternatives showed comparable discriminating power. However, for values of [Formula: see text] , where the statistical significance of the method was increased and improved as m increased, the two-steps-ahead estimator presented slightly higher statistical significance and more regular behavior, even if the dependence on parameter m was still minimal. We also investigated a new normalization factor for [Formula: see text] , which ensures that [Formula: see text] [Formula: see text] when white Gaussian noise (WGN) is given as the input. Conclusions: The research improved our understanding of bubble entropy, in particular in the context of HRV analysis, and we investigated interesting details regarding the definition of the estimator. MDPI 2021-06-16 /pmc/articles/PMC8235094/ /pubmed/34208771 http://dx.doi.org/10.3390/e23060761 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Manis, George Bodini, Matteo Rivolta, Massimo W. Sassi, Roberto A Two-Steps-Ahead Estimator for Bubble Entropy |
title | A Two-Steps-Ahead Estimator for Bubble Entropy |
title_full | A Two-Steps-Ahead Estimator for Bubble Entropy |
title_fullStr | A Two-Steps-Ahead Estimator for Bubble Entropy |
title_full_unstemmed | A Two-Steps-Ahead Estimator for Bubble Entropy |
title_short | A Two-Steps-Ahead Estimator for Bubble Entropy |
title_sort | two-steps-ahead estimator for bubble entropy |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8235094/ https://www.ncbi.nlm.nih.gov/pubmed/34208771 http://dx.doi.org/10.3390/e23060761 |
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