Range Entropy: A Bridge between Signal Complexity and Self-Similarity
Approximate entropy (<i>ApEn</i>) and sample entropy (<i>SampEn</i>) are widely used for temporal complexity analysis of real-world phenomena. However, their relationship with the Hurst exponent as a measure of self-similarity is not widely studied. Additionally, <i>ApE...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-12-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/20/12/962 |
| _version_ | 1798003925981331456 |
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| author | Amir Omidvarnia Mostefa Mesbah Mangor Pedersen Graeme Jackson |
| author_facet | Amir Omidvarnia Mostefa Mesbah Mangor Pedersen Graeme Jackson |
| author_sort | Amir Omidvarnia |
| collection | DOAJ |
| description | Approximate entropy (<i>ApEn</i>) and sample entropy (<i>SampEn</i>) are widely used for temporal complexity analysis of real-world phenomena. However, their relationship with the Hurst exponent as a measure of self-similarity is not widely studied. Additionally, <i>ApEn</i> and <i>SampEn</i> are susceptible to signal amplitude changes. A common practice for addressing this issue is to correct their input signal amplitude by its standard deviation. In this study, we first show, using simulations, that <i>ApEn</i> and <i>SampEn</i> are related to the Hurst exponent in their tolerance <i>r</i> and embedding dimension <i>m</i> parameters. We then propose a modification to <i>ApEn</i> and <i>SampEn</i> called <i>range entropy</i> or <i>RangeEn</i>. We show that <i>RangeEn</i> is more robust to nonstationary signal changes, and it has a more linear relationship with the Hurst exponent, compared to <i>ApEn</i> and <i>SampEn</i>. <i>RangeEn</i> is bounded in the tolerance <i>r</i>-plane between 0 (maximum entropy) and 1 (minimum entropy) and it has no need for signal amplitude correction. Finally, we demonstrate the clinical usefulness of signal entropy measures for characterisation of epileptic EEG data as a real-world example. |
| first_indexed | 2024-04-11T12:15:23Z |
| format | Article |
| id | doaj.art-ced7007efbeb481eb852a2e3bfba20f7 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T12:15:23Z |
| publishDate | 2018-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-ced7007efbeb481eb852a2e3bfba20f72022-12-22T04:24:20ZengMDPI AGEntropy1099-43002018-12-01201296210.3390/e20120962e20120962Range Entropy: A Bridge between Signal Complexity and Self-SimilarityAmir Omidvarnia0Mostefa Mesbah1Mangor Pedersen2Graeme Jackson3The Florey Institute of Neuroscience and Mental Health, Austin Campus, Heidelberg, VIC 3084, AustraliaDepartment of Electrical and Computer Engineering, Sultan Qaboos University, Muscat 123, OmanThe Florey Institute of Neuroscience and Mental Health, Austin Campus, Heidelberg, VIC 3084, AustraliaThe Florey Institute of Neuroscience and Mental Health, Austin Campus, Heidelberg, VIC 3084, AustraliaApproximate entropy (<i>ApEn</i>) and sample entropy (<i>SampEn</i>) are widely used for temporal complexity analysis of real-world phenomena. However, their relationship with the Hurst exponent as a measure of self-similarity is not widely studied. Additionally, <i>ApEn</i> and <i>SampEn</i> are susceptible to signal amplitude changes. A common practice for addressing this issue is to correct their input signal amplitude by its standard deviation. In this study, we first show, using simulations, that <i>ApEn</i> and <i>SampEn</i> are related to the Hurst exponent in their tolerance <i>r</i> and embedding dimension <i>m</i> parameters. We then propose a modification to <i>ApEn</i> and <i>SampEn</i> called <i>range entropy</i> or <i>RangeEn</i>. We show that <i>RangeEn</i> is more robust to nonstationary signal changes, and it has a more linear relationship with the Hurst exponent, compared to <i>ApEn</i> and <i>SampEn</i>. <i>RangeEn</i> is bounded in the tolerance <i>r</i>-plane between 0 (maximum entropy) and 1 (minimum entropy) and it has no need for signal amplitude correction. Finally, we demonstrate the clinical usefulness of signal entropy measures for characterisation of epileptic EEG data as a real-world example.https://www.mdpi.com/1099-4300/20/12/962approximate entropysample entropyrange entropycomplexity, self-similarityHurst exponent |
| spellingShingle | Amir Omidvarnia Mostefa Mesbah Mangor Pedersen Graeme Jackson Range Entropy: A Bridge between Signal Complexity and Self-Similarity Entropy approximate entropy sample entropy range entropy complexity, self-similarity Hurst exponent |
| title | Range Entropy: A Bridge between Signal Complexity and Self-Similarity |
| title_full | Range Entropy: A Bridge between Signal Complexity and Self-Similarity |
| title_fullStr | Range Entropy: A Bridge between Signal Complexity and Self-Similarity |
| title_full_unstemmed | Range Entropy: A Bridge between Signal Complexity and Self-Similarity |
| title_short | Range Entropy: A Bridge between Signal Complexity and Self-Similarity |
| title_sort | range entropy a bridge between signal complexity and self similarity |
| topic | approximate entropy sample entropy range entropy complexity, self-similarity Hurst exponent |
| url | https://www.mdpi.com/1099-4300/20/12/962 |
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