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Evaluation of Bubble Entropy Using Heart Rate Variability
Dimitrios Platakis1, Roberto Sassi2, George Manis1
1Department of Computer Science and Engineering, University of Ioannina, 45500 Ioannina, Greece.
Entropy (Basel, Switzerland)
|June 26, 2026
Summary
Bubble entropy, a new entropy definition, effectively classifies cardiac RR time series. It outperforms Sample entropy, Approximate entropy, and Permutation entropy in accuracy and feature ranking for biomedical engineering applications.
Area of Science:
- Biomedical Engineering
- Complex Systems Analysis
- Information Theory
Background:
- Entropy measures are crucial for analyzing physiological time series, particularly RR intervals in electrocardiography.
- Existing entropy measures like Sample Entropy, Approximate Entropy, and Permutation Entropy have limitations in capturing complex signal dynamics.
- Bubble entropy offers a novel approach with a physical interpretation based on ordering vectors in an embedding space.
Purpose of the Study:
- To evaluate the efficacy of Bubble entropy in classifying cardiac RR time series.
- To compare Bubble entropy's performance against established entropy measures (Sample Entropy, Approximate Entropy, Permutation Entropy).
- To assess the utility of Bubble entropy as a feature for machine learning-based cardiac patient classification.
Main Methods:
- RR time series data from healthy individuals and cardiac patients were analyzed.
- Bubble entropy was calculated and compared with Sample entropy, Approximate entropy, and Permutation entropy.
- Machine learning classifiers (k-NN, SVM, Logistic Regression, Gaussian Naive Bayes) were employed for classification tasks.
- Feature evaluation methods were used to assess the discriminative power of each entropy measure.
Main Results:
- Bubble entropy demonstrated superior classification accuracy compared to Sample entropy, Approximate entropy, and Permutation entropy.
- Feature ranking analysis indicated that Bubble entropy provides more effective features for distinguishing between healthy and patient groups.
- The proposed Bubble entropy metric showed robust performance across different machine learning models.
Conclusions:
- Bubble entropy is a promising new metric for the analysis of biomedical time series, particularly RR intervals.
- Its ability to accurately classify cardiac conditions suggests potential clinical applications in cardiology.
- Bubble entropy offers advantages over traditional entropy measures in terms of both discriminatory power and feature interpretability.
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