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A Method for Estimating the Entropy of Time Series Using Artificial Neural Networks

Measuring the predictability and complexity of time series using entropy is essential tool designing and controlling a nonlinear system. However, the existing methods have some drawbacks related to the strong dependence of entropy on the parameters of the methods. To overcome these difficulties, thi...

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Autores principales: Velichko, Andrei, Heidari, Hanif
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8621949/
https://www.ncbi.nlm.nih.gov/pubmed/34828130
http://dx.doi.org/10.3390/e23111432
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author Velichko, Andrei
Heidari, Hanif
author_facet Velichko, Andrei
Heidari, Hanif
author_sort Velichko, Andrei
collection PubMed
description Measuring the predictability and complexity of time series using entropy is essential tool designing and controlling a nonlinear system. However, the existing methods have some drawbacks related to the strong dependence of entropy on the parameters of the methods. To overcome these difficulties, this study proposes a new method for estimating the entropy of a time series using the LogNNet neural network model. The LogNNet reservoir matrix is filled with time series elements according to our algorithm. The accuracy of the classification of images from the MNIST-10 database is considered as the entropy measure and denoted by NNetEn. The novelty of entropy calculation is that the time series is involved in mixing the input information in the reservoir. Greater complexity in the time series leads to a higher classification accuracy and higher NNetEn values. We introduce a new time series characteristic called time series learning inertia that determines the learning rate of the neural network. The robustness and efficiency of the method is verified on chaotic, periodic, random, binary, and constant time series. The comparison of NNetEn with other methods of entropy estimation demonstrates that our method is more robust and accurate and can be widely used in practice.
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spelling pubmed-86219492021-11-27 A Method for Estimating the Entropy of Time Series Using Artificial Neural Networks Velichko, Andrei Heidari, Hanif Entropy (Basel) Article Measuring the predictability and complexity of time series using entropy is essential tool designing and controlling a nonlinear system. However, the existing methods have some drawbacks related to the strong dependence of entropy on the parameters of the methods. To overcome these difficulties, this study proposes a new method for estimating the entropy of a time series using the LogNNet neural network model. The LogNNet reservoir matrix is filled with time series elements according to our algorithm. The accuracy of the classification of images from the MNIST-10 database is considered as the entropy measure and denoted by NNetEn. The novelty of entropy calculation is that the time series is involved in mixing the input information in the reservoir. Greater complexity in the time series leads to a higher classification accuracy and higher NNetEn values. We introduce a new time series characteristic called time series learning inertia that determines the learning rate of the neural network. The robustness and efficiency of the method is verified on chaotic, periodic, random, binary, and constant time series. The comparison of NNetEn with other methods of entropy estimation demonstrates that our method is more robust and accurate and can be widely used in practice. MDPI 2021-10-29 /pmc/articles/PMC8621949/ /pubmed/34828130 http://dx.doi.org/10.3390/e23111432 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
Velichko, Andrei
Heidari, Hanif
A Method for Estimating the Entropy of Time Series Using Artificial Neural Networks
title A Method for Estimating the Entropy of Time Series Using Artificial Neural Networks
title_full A Method for Estimating the Entropy of Time Series Using Artificial Neural Networks
title_fullStr A Method for Estimating the Entropy of Time Series Using Artificial Neural Networks
title_full_unstemmed A Method for Estimating the Entropy of Time Series Using Artificial Neural Networks
title_short A Method for Estimating the Entropy of Time Series Using Artificial Neural Networks
title_sort method for estimating the entropy of time series using artificial neural networks
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8621949/
https://www.ncbi.nlm.nih.gov/pubmed/34828130
http://dx.doi.org/10.3390/e23111432
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