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:	Andrei Velichko, Hanif Heidari
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	entropy time series neural network classification MNIST-10 database LogNNet Science Q Astrophysics QB460-466 Physics QC1-999
Acceso en línea:	https://doaj.org/article/6b26c1afc8c546a7992fae3357703527
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spelling	oai:doaj.org-article:6b26c1afc8c546a7992fae33577035272021-11-25T17:29:37ZA Method for Estimating the Entropy of Time Series Using Artificial Neural Networks10.3390/e231114321099-4300https://doaj.org/article/6b26c1afc8c546a7992fae33577035272021-10-01T00:00:00Zhttps://www.mdpi.com/1099-4300/23/11/1432https://doaj.org/toc/1099-4300Measuring 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.Andrei VelichkoHanif HeidariMDPI AGarticleentropytime seriesneural networkclassificationMNIST-10 databaseLogNNetScienceQAstrophysicsQB460-466PhysicsQC1-999ENEntropy, Vol 23, Iss 1432, p 1432 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	entropy time series neural network classification MNIST-10 database LogNNet Science Q Astrophysics QB460-466 Physics QC1-999
spellingShingle	entropy time series neural network classification MNIST-10 database LogNNet Science Q Astrophysics QB460-466 Physics QC1-999 Andrei Velichko Hanif Heidari A Method for Estimating the Entropy of Time Series Using Artificial Neural Networks
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.
format	article
author	Andrei Velichko Hanif Heidari
author_facet	Andrei Velichko Hanif Heidari
author_sort	Andrei Velichko
title	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_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_sort	method for estimating the entropy of time series using artificial neural networks
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/6b26c1afc8c546a7992fae3357703527
work_keys_str_mv	AT andreivelichko amethodforestimatingtheentropyoftimeseriesusingartificialneuralnetworks AT hanifheidari amethodforestimatingtheentropyoftimeseriesusingartificialneuralnetworks AT andreivelichko methodforestimatingtheentropyoftimeseriesusingartificialneuralnetworks AT hanifheidari methodforestimatingtheentropyoftimeseriesusingartificialneuralnetworks
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A Method for Estimating the Entropy of Time Series Using Artificial Neural Networks

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