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Entropy 2018, 20(12), 962;

Range Entropy: A Bridge between Signal Complexity and Self-Similarity

The Florey Institute of Neuroscience and Mental Health, Austin Campus, Heidelberg, VIC 3084, Australia
Faculty of Medicine, Dentistry and Health Sciences, The University of Melbourne, VIC 3010, Australia
Department of Electrical and Computer Engineering, Sultan Qaboos University, Muscat 123, Oman
Department of Neurology, Austin Health, Melbourne, VIC 3084, Australia
Author to whom correspondence should be addressed.
Received: 1 November 2018 / Revised: 3 December 2018 / Accepted: 6 December 2018 / Published: 13 December 2018
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Approximate entropy (ApEn) and sample entropy (SampEn) 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, ApEn and SampEn 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 ApEn and SampEn are related to the Hurst exponent in their tolerance r and embedding dimension m parameters. We then propose a modification to ApEn and SampEn called range entropy or RangeEn. We show that RangeEn is more robust to nonstationary signal changes, and it has a more linear relationship with the Hurst exponent, compared to ApEn and SampEn. RangeEn is bounded in the tolerance r-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. View Full-Text
Keywords: approximate entropy; sample entropy; range entropy; complexity, self-similarity; Hurst exponent approximate entropy; sample entropy; range entropy; complexity, self-similarity; Hurst exponent

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Omidvarnia, A.; Mesbah, M.; Pedersen, M.; Jackson, G. Range Entropy: A Bridge between Signal Complexity and Self-Similarity. Entropy 2018, 20, 962.

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