Range entropy: A bridge between signal complexity and self-similarity

TL;DR

This paper introduces RangeEn, a new entropy measure that better links signal complexity with self-similarity, is more robust to nonstationary signals, and does not require amplitude correction, demonstrated on EEG data.

Contribution

The paper proposes RangeEn, an improved entropy measure that enhances robustness and linearity in relation to the Hurst exponent, addressing limitations of ApEn and SampEn.

Findings

RangeEn is more robust to nonstationary signals.

RangeEn has a more linear relationship with the Hurst exponent.

RangeEn does not require amplitude correction.

Abstract

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.