Distinguish between Stochastic and Chaotic Signals by a Local Structure-Based Entropy
As a measure of complexity, information entropy is frequently used to categorize time series, such as machinery failure diagnostics, biological signal identification, etc., and is thought of as a characteristic of dynamic systems. Many entropies, however, are ineffective for multivariate scenarios d...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/24/12/1752 |
| _version_ | 1797459335098400768 |
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| author | Zelin Zhang Jun Wu Yufeng Chen Ji Wang Jinyu Xu |
| author_facet | Zelin Zhang Jun Wu Yufeng Chen Ji Wang Jinyu Xu |
| author_sort | Zelin Zhang |
| collection | DOAJ |
| description | As a measure of complexity, information entropy is frequently used to categorize time series, such as machinery failure diagnostics, biological signal identification, etc., and is thought of as a characteristic of dynamic systems. Many entropies, however, are ineffective for multivariate scenarios due to correlations. In this paper, we propose a local structure entropy (LSE) based on the idea of a recurrence network. Given certain tolerance and scales, LSE values can distinguish multivariate chaotic sequences between stochastic signals. Three financial market indices are used to evaluate the proposed LSE. The results show that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mi>S</mi><msup><mi>E</mi><mrow><mi>F</mi><mi>S</mi><mi>T</mi><mi>E</mi><mn>100</mn></mrow></msup></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mi>S</mi><msup><mi>E</mi><mrow><mi>S</mi><mo>&</mo><mi>P</mi><mn>500</mn></mrow></msup></mrow></semantics></math></inline-formula> are higher than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mi>S</mi><msup><mi>E</mi><mrow><mi>S</mi><mi>Z</mi><mi>I</mi></mrow></msup></mrow></semantics></math></inline-formula>, which indicates that the European and American stock markets are more sophisticated than the Chinese stock market. Additionally, using decision trees as the classifiers, LSE is employed to detect bearing faults. LSE performs higher on recognition accuracy when compared to permutation entropy. |
| first_indexed | 2024-03-09T16:49:58Z |
| format | Article |
| id | doaj.art-814fbea75298431396fa36b0663a581b |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T16:49:58Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-814fbea75298431396fa36b0663a581b2023-11-24T14:42:20ZengMDPI AGEntropy1099-43002022-11-012412175210.3390/e24121752Distinguish between Stochastic and Chaotic Signals by a Local Structure-Based EntropyZelin Zhang0Jun Wu1Yufeng Chen2Ji Wang3Jinyu Xu4School of Mathematics, Physics and Optoelectronic Engineering, Hubei University of Automotive Technology, Shiyan 442002, ChinaSchool of Mathematics, Physics and Optoelectronic Engineering, Hubei University of Automotive Technology, Shiyan 442002, ChinaSchool of Electrical and Information Engineering, Hubei University of Automotive Technology, Shiyan 442002, ChinaSchool of Liberal Arts and Humanities, Sichuan Vocational College of Finance and Economics, Chengdu 610101, ChinaSchool of Electrical and Information Engineering, Hubei University of Automotive Technology, Shiyan 442002, ChinaAs a measure of complexity, information entropy is frequently used to categorize time series, such as machinery failure diagnostics, biological signal identification, etc., and is thought of as a characteristic of dynamic systems. Many entropies, however, are ineffective for multivariate scenarios due to correlations. In this paper, we propose a local structure entropy (LSE) based on the idea of a recurrence network. Given certain tolerance and scales, LSE values can distinguish multivariate chaotic sequences between stochastic signals. Three financial market indices are used to evaluate the proposed LSE. The results show that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mi>S</mi><msup><mi>E</mi><mrow><mi>F</mi><mi>S</mi><mi>T</mi><mi>E</mi><mn>100</mn></mrow></msup></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mi>S</mi><msup><mi>E</mi><mrow><mi>S</mi><mo>&</mo><mi>P</mi><mn>500</mn></mrow></msup></mrow></semantics></math></inline-formula> are higher than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mi>S</mi><msup><mi>E</mi><mrow><mi>S</mi><mi>Z</mi><mi>I</mi></mrow></msup></mrow></semantics></math></inline-formula>, which indicates that the European and American stock markets are more sophisticated than the Chinese stock market. Additionally, using decision trees as the classifiers, LSE is employed to detect bearing faults. LSE performs higher on recognition accuracy when compared to permutation entropy.https://www.mdpi.com/1099-4300/24/12/1752multivariate time seriesinformation entropychaotic sequencerandom signalmachinery fault diagnose |
| spellingShingle | Zelin Zhang Jun Wu Yufeng Chen Ji Wang Jinyu Xu Distinguish between Stochastic and Chaotic Signals by a Local Structure-Based Entropy Entropy multivariate time series information entropy chaotic sequence random signal machinery fault diagnose |
| title | Distinguish between Stochastic and Chaotic Signals by a Local Structure-Based Entropy |
| title_full | Distinguish between Stochastic and Chaotic Signals by a Local Structure-Based Entropy |
| title_fullStr | Distinguish between Stochastic and Chaotic Signals by a Local Structure-Based Entropy |
| title_full_unstemmed | Distinguish between Stochastic and Chaotic Signals by a Local Structure-Based Entropy |
| title_short | Distinguish between Stochastic and Chaotic Signals by a Local Structure-Based Entropy |
| title_sort | distinguish between stochastic and chaotic signals by a local structure based entropy |
| topic | multivariate time series information entropy chaotic sequence random signal machinery fault diagnose |
| url | https://www.mdpi.com/1099-4300/24/12/1752 |
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