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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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/11/1432 |
| _version_ | 1827676675348889600 |
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| author | Andrei Velichko Hanif Heidari |
| author_facet | Andrei Velichko Hanif Heidari |
| author_sort | Andrei Velichko |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-10T05:31:31Z |
| format | Article |
| id | doaj.art-6b26c1afc8c546a7992fae3357703527 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T05:31:31Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-6b26c1afc8c546a7992fae33577035272023-11-22T23:14:53ZengMDPI AGEntropy1099-43002021-10-012311143210.3390/e23111432A Method for Estimating the Entropy of Time Series Using Artificial Neural NetworksAndrei Velichko0Hanif Heidari1Institute of Physics and Technology, Petrozavodsk State University, 185910 Petrozavodsk, RussiaDepartment of Applied Mathematics, School of Mathematics and Computer Sciences, Damghan University, Damghan 36715-364, IranMeasuring 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.https://www.mdpi.com/1099-4300/23/11/1432entropytime seriesneural networkclassificationMNIST-10 databaseLogNNet |
| spellingShingle | Andrei Velichko Hanif Heidari A Method for Estimating the Entropy of Time Series Using Artificial Neural Networks Entropy entropy time series neural network classification MNIST-10 database LogNNet |
| 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 | entropy time series neural network classification MNIST-10 database LogNNet |
| url | https://www.mdpi.com/1099-4300/23/11/1432 |
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