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

Approximate entropy () and sample entropy () 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, and 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 and are related to the Hurst exponent in their tolerance and embedding dimension parameters. We then propose a modification to and called or . We show that is more robust to nonstationary signal changes, and it has a more linear relationship with the Hurst exponent, compared to and . is bounded in the tolerance -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.