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Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
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Range Entropy: A Bridge between Signal Complexity and Self-Similarity.
Amir Omidvarnia1,2, Mostefa Mesbah3, Mangor Pedersen1
1The Florey Institute of Neuroscience and Mental Health, Austin Campus, Heidelberg, VIC 3084, Australia.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
Approximate entropy (ApEn) and sample entropy (SampEn) are linked to the Hurst exponent. A new method, RangeEn, offers improved robustness and a linear relationship with the Hurst exponent for temporal complexity analysis.
Area of Science:
- Complexity Science
- Time Series Analysis
- Biomedical Signal Processing
Background:
- Approximate entropy (ApEn) and sample entropy (SampEn) are standard metrics for assessing temporal complexity.
- Existing entropy measures exhibit limitations, including susceptibility to signal amplitude variations and an unclear relationship with self-similarity (Hurst exponent).
- Standard practice involves amplitude correction, which may not fully resolve these issues.
Purpose of the Study:
- To investigate the relationship between ApEn, SampEn, and the Hurst exponent.
- To develop a novel entropy measure, RangeEn, that addresses the limitations of existing methods.
- To evaluate the performance of RangeEn in terms of robustness and linearity with the Hurst exponent.
Main Methods:
- Simulations were used to explore the relationship between ApEn, SampEn, and the Hurst exponent, focusing on parameters like tolerance (r) and embedding dimension (m).
- A new entropy measure, Range entropy (RangeEn), was developed.
- RangeEn was compared against ApEn and SampEn for robustness to nonstationary signals and linearity with the Hurst exponent. Its bounded nature (0-1) and independence from amplitude correction were also assessed.
Main Results:
- ApEn and SampEn demonstrate a relationship with the Hurst exponent influenced by tolerance (r) and embedding dimension (m).
- RangeEn exhibits greater robustness to nonstationary signal changes compared to ApEn and SampEn.
- RangeEn shows a more linear relationship with the Hurst exponent and does not require signal amplitude correction.
Conclusions:
- RangeEn offers an improved approach to temporal complexity analysis, overcoming limitations of ApEn and SampEn.
- The robustness and linear relationship with the Hurst exponent make RangeEn suitable for analyzing complex, real-world data.
- The study highlights the clinical utility of RangeEn for characterizing physiological signals, exemplified by its application to epileptic EEG data.
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