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The Systematic Bias of Entropy Calculation in the Multi-Scale Entropy Algorithm.
1School of Mathematics, Physics and Information Science, Shaoxing University, Shaoxing 312000, China.
Entropy (Basel, Switzerland)
|June 2, 2021
Summary
Multi-scale sample entropy (MSE) analysis, a complexity measure, suffers from systematic bias due to a fixed threshold. This study mathematically presents the bias and offers correction methods for accurate multi-scale entropy calculations.
Area of Science:
- Complexity Science
- Information Theory
- Time Series Analysis
Background:
- Entropy quantifies system irregularity and complexity.
- Multi-scale entropy (MSE) analysis, using Sample Entropy (SampEn), assesses complexity across different time scales.
- Current MSE methods use a fixed matching threshold, potentially introducing bias.
Purpose of the Study:
- To mathematically define the systematic bias in MSE calculations.
- To propose methods for correcting this bias in SampEn.
- To improve the accuracy of multi-scale entropy analysis.
Main Methods:
- Analysis of SampEn formula and its dependence on data standard deviation.
- Mathematical derivation of bias introduced by a fixed matching threshold.
- Development of corrected thresholding strategies for MSE.
Main Results:
- Identified a systematic bias in MSE stemming from scale-dependent standard deviation changes.
- Demonstrated how a fixed threshold distorts SampEn values at different scales.
- Provided a mathematical framework for understanding and correcting MSE bias.
Conclusions:
- The fixed threshold in standard MSE algorithms introduces significant bias.
- Correcting the threshold based on scale-specific standard deviations is crucial for accurate complexity assessment.
- This work offers a vital correction for the widespread MSE user community.
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