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

• Main Authors: Amir Omidvarnia, Mostefa Mesbah, Mangor Pedersen, Graeme Jackson
• Format: Article
• Language: English
• Published: MDPI AG 2018-12-01
• Series: Entropy
• Subjects: approximate entropy; sample entropy; range entropy; complexity, self-similarity; Hurst exponent
• Online Access: https://www.mdpi.com/1099-4300/20/12/962

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.