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Updated: Oct 30, 2025
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Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
Published on: June 27, 2013
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A Two-Steps-Ahead Estimator for Bubble Entropy
George Manis1, Matteo Bodini2, Massimo W Rivolta2
1Department of Computer Science and Engineering, University of Ioannina, 45500 Ioannina, Greece.
Entropy (Basel, Switzerland)
|July 2, 2021
Summary
Bubble entropy (bEn) analysis was advanced with a new two-steps-ahead estimator, showing improved statistical significance and regular behavior in heart rate variability (HRV) data. This research refines understanding of bEn for physiological signal analysis.
Area of Science:
- Complexity and Information Theory
- Biomedical Signal Processing
Background:
- Bubble entropy (bEn) is an entropy metric with limited parameter dependence.
- bEn assesses changes in the ordering of samples, not direct conditional entropy.
- Autoregressive (AR) process analysis revealed differing bEn relations for odd/even sample lengths (m).
Purpose of the Study:
- Investigate a two-steps-ahead estimator for bubble entropy.
- Compare the new estimator with the original bEn on simulated and real-world data.
- Explore a novel normalization factor for bEn, ensuring a value of 1 for white Gaussian noise (WGN).
Main Methods:
- Theoretical analysis of expected values for AR processes.
- Comparison of original and two-steps-ahead bEn estimators on simulated time series.
- Application and evaluation of estimators on heart rate variability (HRV) data.
Main Results:
- Both bEn estimators demonstrated comparable discriminating power.
- The two-steps-ahead estimator exhibited slightly higher statistical significance and regularity for 10
- Minimal dependence on the parameter m was observed for the new estimator.
Conclusions:
- The study enhances the understanding of bubble entropy, particularly for HRV analysis.
- The two-steps-ahead estimator offers improved performance characteristics.
- Further insights into the definition and application of bEn estimators were gained.
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