Discriminating chaotic and stochastic time series using permutation entropy and artificial neural networks

Abstract Extracting relevant properties of empirical signals generated by nonlinear, stochastic, and high-dimensional systems is a challenge of complex systems research. Open questions are how to differentiate chaotic signals from stochastic ones, and how to quantify nonlinear and/or high-order temp...

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Autores principales:	B. R. R. Boaretto, R. C. Budzinski, K. L. Rossi, T. L. Prado, S. R. Lopes, C. Masoller
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/0920618b54bc4a88b32fead71a4318e4
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spelling	oai:doaj.org-article:0920618b54bc4a88b32fead71a4318e42021-12-02T17:06:31ZDiscriminating chaotic and stochastic time series using permutation entropy and artificial neural networks10.1038/s41598-021-95231-z2045-2322https://doaj.org/article/0920618b54bc4a88b32fead71a4318e42021-08-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-95231-zhttps://doaj.org/toc/2045-2322Abstract Extracting relevant properties of empirical signals generated by nonlinear, stochastic, and high-dimensional systems is a challenge of complex systems research. Open questions are how to differentiate chaotic signals from stochastic ones, and how to quantify nonlinear and/or high-order temporal correlations. Here we propose a new technique to reliably address both problems. Our approach follows two steps: first, we train an artificial neural network (ANN) with flicker (colored) noise to predict the value of the parameter, $$\alpha$$ α , that determines the strength of the correlation of the noise. To predict $$\alpha$$ α the ANN input features are a set of probabilities that are extracted from the time series by using symbolic ordinal analysis. Then, we input to the trained ANN the probabilities extracted from the time series of interest, and analyze the ANN output. We find that the $$\alpha$$ α value returned by the ANN is informative of the temporal correlations present in the time series. To distinguish between stochastic and chaotic signals, we exploit the fact that the difference between the permutation entropy (PE) of a given time series and the PE of flicker noise with the same $$\alpha$$ α parameter is small when the time series is stochastic, but it is large when the time series is chaotic. We validate our technique by analysing synthetic and empirical time series whose nature is well established. We also demonstrate the robustness of our approach with respect to the length of the time series and to the level of noise. We expect that our algorithm, which is freely available, will be very useful to the community.B. R. R. BoarettoR. C. BudzinskiK. L. RossiT. L. PradoS. R. LopesC. MasollerNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-10 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q B. R. R. Boaretto R. C. Budzinski K. L. Rossi T. L. Prado S. R. Lopes C. Masoller Discriminating chaotic and stochastic time series using permutation entropy and artificial neural networks
description	Abstract Extracting relevant properties of empirical signals generated by nonlinear, stochastic, and high-dimensional systems is a challenge of complex systems research. Open questions are how to differentiate chaotic signals from stochastic ones, and how to quantify nonlinear and/or high-order temporal correlations. Here we propose a new technique to reliably address both problems. Our approach follows two steps: first, we train an artificial neural network (ANN) with flicker (colored) noise to predict the value of the parameter, $$\alpha$$ α , that determines the strength of the correlation of the noise. To predict $$\alpha$$ α the ANN input features are a set of probabilities that are extracted from the time series by using symbolic ordinal analysis. Then, we input to the trained ANN the probabilities extracted from the time series of interest, and analyze the ANN output. We find that the $$\alpha$$ α value returned by the ANN is informative of the temporal correlations present in the time series. To distinguish between stochastic and chaotic signals, we exploit the fact that the difference between the permutation entropy (PE) of a given time series and the PE of flicker noise with the same $$\alpha$$ α parameter is small when the time series is stochastic, but it is large when the time series is chaotic. We validate our technique by analysing synthetic and empirical time series whose nature is well established. We also demonstrate the robustness of our approach with respect to the length of the time series and to the level of noise. We expect that our algorithm, which is freely available, will be very useful to the community.
format	article
author	B. R. R. Boaretto R. C. Budzinski K. L. Rossi T. L. Prado S. R. Lopes C. Masoller
author_facet	B. R. R. Boaretto R. C. Budzinski K. L. Rossi T. L. Prado S. R. Lopes C. Masoller
author_sort	B. R. R. Boaretto
title	Discriminating chaotic and stochastic time series using permutation entropy and artificial neural networks
title_short	Discriminating chaotic and stochastic time series using permutation entropy and artificial neural networks
title_full	Discriminating chaotic and stochastic time series using permutation entropy and artificial neural networks
title_fullStr	Discriminating chaotic and stochastic time series using permutation entropy and artificial neural networks
title_full_unstemmed	Discriminating chaotic and stochastic time series using permutation entropy and artificial neural networks
title_sort	discriminating chaotic and stochastic time series using permutation entropy and artificial neural networks
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/0920618b54bc4a88b32fead71a4318e4
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Discriminating chaotic and stochastic time series using permutation entropy and artificial neural networks

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