Levenberg-Marquardt Algorithm for Mackey-Glass Chaotic Time Series Prediction
For decades, Mackey-Glass chaotic time series prediction has attracted more and more attention. When the multilayer perceptron is used to predict the Mackey-Glass chaotic time series, what we should do is to minimize the loss function. As is well known, the convergence speed of the loss function is...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/193758 |
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| _version_ | 1832563579236122624 |
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| author | Junsheng Zhao Yongmin Li Xingjiang Yu Xingfang Zhang |
| author_facet | Junsheng Zhao Yongmin Li Xingjiang Yu Xingfang Zhang |
| author_sort | Junsheng Zhao |
| collection | DOAJ |
| description | For decades, Mackey-Glass chaotic time series prediction has attracted more and more attention. When the multilayer perceptron is used to predict the Mackey-Glass chaotic time series, what
we should do is to minimize the loss function. As is well known, the convergence speed of the loss function is rapid in the beginning of the learning process, while the convergence speed is very slow when the parameter is near to the minimum point. In order to overcome these problems, we introduce the Levenberg-Marquardt algorithm (LMA). Firstly, a rough introduction is given to the multilayer perceptron, including the structure and the model approximation method. Secondly, we introduce the LMA and discuss how to implement the LMA. Lastly, an illustrative example is carried out to show the prediction efficiency of the LMA. Simulations show that the LMA can give more accurate prediction than the gradient descent method. |
| format | Article |
| id | doaj-art-8efa0339c2ed489481fd3d94278c5012 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-8efa0339c2ed489481fd3d94278c50122025-02-03T01:13:08ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/193758193758Levenberg-Marquardt Algorithm for Mackey-Glass Chaotic Time Series PredictionJunsheng Zhao0Yongmin Li1Xingjiang Yu2Xingfang Zhang3School of Mathematics, Liaocheng University, Liaocheng 252059, ChinaSchool of Science, Huzhou University, Huzhou 313000, ChinaSchool of Mathematics, Liaocheng University, Liaocheng 252059, ChinaSchool of Mathematics, Liaocheng University, Liaocheng 252059, ChinaFor decades, Mackey-Glass chaotic time series prediction has attracted more and more attention. When the multilayer perceptron is used to predict the Mackey-Glass chaotic time series, what we should do is to minimize the loss function. As is well known, the convergence speed of the loss function is rapid in the beginning of the learning process, while the convergence speed is very slow when the parameter is near to the minimum point. In order to overcome these problems, we introduce the Levenberg-Marquardt algorithm (LMA). Firstly, a rough introduction is given to the multilayer perceptron, including the structure and the model approximation method. Secondly, we introduce the LMA and discuss how to implement the LMA. Lastly, an illustrative example is carried out to show the prediction efficiency of the LMA. Simulations show that the LMA can give more accurate prediction than the gradient descent method.http://dx.doi.org/10.1155/2014/193758 |
| spellingShingle | Junsheng Zhao Yongmin Li Xingjiang Yu Xingfang Zhang Levenberg-Marquardt Algorithm for Mackey-Glass Chaotic Time Series Prediction Discrete Dynamics in Nature and Society |
| title | Levenberg-Marquardt Algorithm for Mackey-Glass Chaotic Time Series Prediction |
| title_full | Levenberg-Marquardt Algorithm for Mackey-Glass Chaotic Time Series Prediction |
| title_fullStr | Levenberg-Marquardt Algorithm for Mackey-Glass Chaotic Time Series Prediction |
| title_full_unstemmed | Levenberg-Marquardt Algorithm for Mackey-Glass Chaotic Time Series Prediction |
| title_short | Levenberg-Marquardt Algorithm for Mackey-Glass Chaotic Time Series Prediction |
| title_sort | levenberg marquardt algorithm for mackey glass chaotic time series prediction |
| url | http://dx.doi.org/10.1155/2014/193758 |
| work_keys_str_mv | AT junshengzhao levenbergmarquardtalgorithmformackeyglasschaotictimeseriesprediction AT yongminli levenbergmarquardtalgorithmformackeyglasschaotictimeseriesprediction AT xingjiangyu levenbergmarquardtalgorithmformackeyglasschaotictimeseriesprediction AT xingfangzhang levenbergmarquardtalgorithmformackeyglasschaotictimeseriesprediction |