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

Entropy

Mostefa Mesbah¹  Graeme Jackson²  Amir Omidvarnia²  Mangor Pedersen² 

[1] Department of Electrical and Computer Engineering, Sultan Qaboos University, Muscat 123, Oman;The Florey Institute of Neuroscience and Mental Health, Austin Campus, Heidelberg, VIC 3084, Australia;

关键词: approximate entropy;    sample entropy;    range entropy;    complexity, self-similarity;    Hurst exponent;   

DOI  :  10.3390/e20120962

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown