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On Quantization Errors in Approximate and Sample Entropy.

Dragana Bajić¹, Nina Japundžić-Žigon²

¹Faculty of Technical Sciences, Department of Communications and Signal Processing, University of Novi Sad, Trg Dositeja Obradovica 6, 21000 Novi Sad, Serbia.

Entropy (Basel, Switzerland)

|January 21, 2022

Summary

Approximate entropy and sample entropy inconsistencies stem from coarse quantization of matching probabilities. Increasing time series length resolves these errors, while asymmetric distributions and interpolation introduce persistent inaccuracies in entropy estimation.

Keywords:

approximate entropy interpolation matching probabilities quantization error sample entropy

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Area of Science:

Time Series Analysis
Information Theory
Signal Processing

Background:

Approximate entropy (ApEn) and sample entropy (SampEn) are widely used for time series regularity and unpredictability quantification.
Inconsistencies in these entropy measures have been observed, impacting their reliability in various applications.
Understanding the sources of these inconsistencies is crucial for accurate time series analysis.

Purpose of the Study:

To investigate the underlying causes of inconsistencies in approximate entropy and sample entropy.
To identify the factors contributing to errors in entropy estimation.
To provide insights into improving the accuracy and reliability of these entropy measures.

Main Methods:

Analysis of coarse quantization effects on matching probabilities.
Examination of error distribution symmetry and its impact on ApEn and SampEn.
Investigation of time series length, distribution, and interpolation effects on entropy errors.

Main Results:

Coarse quantization of matching probabilities is identified as the primary source of entropy estimation errors.
Symmetric error distributions in SampEn lead to error cancellation, while asymmetric distributions in ApEn cause error accumulation.
Increasing time series length mitigates errors; asymmetric distributions and artificial interpolation induce persistent errors.

Conclusions:

The accuracy of ApEn and SampEn is significantly affected by quantization errors, time series characteristics, and data manipulation techniques.
Time series length is a critical factor in minimizing entropy estimation errors.
Careful consideration of data properties and analysis methods is necessary for reliable entropy-based time series analysis.