Source-linked AI summary
Refined Composite Multiscale Dispersion Entropy and its Application to Biomedical Signals
Hamed Azami, Mostafa Rostaghi, Daniel Abasolo, Javier Escudero
TL;DR
MSE is useful for biomedical complexity analysis but can be undefined or unstable for short signals and computationally slow. The paper introduces MDE and RCMDE, evaluates them against MSE-based methods, and finds similar complexity profiles with faster computation and improved short/noisy-signal behavior.
Problem
MSE and RCMSE can be undefined or unstable for short signals and require O(N^2) computation, limiting some applications.
Method
The paper introduces multiscale dispersion entropy (MDE) and refined composite MDE (RCMDE) as complexity estimators, evaluated on synthetic and biomedical signals.
Results
MDE and RCMDE show similar complexity behavior to MSE and RCMSE while being significantly faster; RCMDE is more stable than MDE for noisy signals.
Takeaways & Limitations
MDE and RCMDE are expected to be useful for physiological-signal analysis because they distinguish different types of dynamics.
Abstract
from arXiv · showhide
Multiscale entropy (MSE) is a widely-used tool to analyze biomedical signals. It was proposed to overcome the deficiencies of conventional entropy methods when quantifying the complexity of time series. However, MSE is undefined for very short signals and slow for real-time applications because of the use of sample entropy (SampEn). To overcome these shortcomings, we introduce multiscale dispersion entropy (DisEn - MDE) as a very fast and powerful method to quantify the complexity of signals. MDE is based on our recently developed DisEn, which has a computation cost of O(N), compared with O(N2) for SampEn. We also propose the refined composite MDE (RCMDE) to improve the stability of MDE. We evaluate MDE, RCMDE, and refined composite MSE (RCMSE) on synthetic signals and find that these methods have similar behaviors but the MDE and RCMDE are significantly faster than MSE and RCMSE, respectively. The results also illustrate that RCMDE is more stable than MDE for short and noisy signals, which are common in biomedical applications. To evaluate the proposed methods on real signals, we employ three biomedical datasets, including focal and non-focal electroencephalograms (EEGs), blood pressure recordings in Fantasia database, and resting-state EEGs activity in Alzheimer's disease (AD). The results again demonstrate a similar behavior of RCMSE, MDE and RCMDE, although the RCMDE and MDE are significantly faster and lead to larger differences between physiological conditions known to alter the complexity of the physiological recordings. To sum up, MDE and RCMDE are expected to be useful for the analysis of physiological signals thanks to their ability to distinguish different types of dynamics.
I. INTRODUCTION
The paper motivates multiscale complexity analysis for biomedical signals by identifying limitations in existing entropy methods, then introduces MDE and RCMDE as faster alternatives evaluated on synthetic and physiological data.
- Entropy quantifies time-series irregularity and uncertainty, with higher values indicating greater uncertainty.
- Single-scale entropy can misrepresent physiological complexity because random signals may have maximum entropy despite less meaningful structural richness than correlated signals.
- MSE quantifies signal complexity across multiple temporal scales and has been applied to pathological states including depression, Parkinson’s disease, and Alzheimer’s disease.
- MSE and RCMSE can be undefined or unstable for short signals and require O(N^2) computation, limiting some applications.
- The study introduces MDE and RCMDE and evaluates them on synthetic signals, focal and non-focal EEGs, Fantasia blood-pressure recordings, and Alzheimer’s-disease EEGs.
- Compared with existing estimators, MDE and RCMDE are reported to avoid undefined short-signal values, improve stability, run faster, and produce larger differences between physiological conditions.
II. METHODS
MDE applies dispersion entropy across coarse-grained signal scales, while RCMDE aggregates shifted coarse-grained sequences to improve stability. The method maps amplitudes through an NCDF, forms dispersion patterns, and computes their Shannon entropy.
- Multiscale Dispersion Entropy (MDE): MDE keeps the NCDF mean and standard deviation fixed from the original signal across all scale factors, rather than recomputing them after coarse-graining.
- Multiscale Dispersion Entropy (MDE): MDE first divides a signal into non-overlapping segments of length τ and averages each segment to create coarse-grained signals.
- Dispersion entropy: Dispersion entropy maps signal samples into c classes using the NCDF, whose mean and standard deviation are computed from the signal.
- Dispersion patterns: The mapped sequence is embedded using dimension m and delay d, producing dispersion patterns with c^m possible combinations.
- Dispersion patterns: Each dispersion pattern’s relative frequency is calculated from its occurrences among the embedded signals.
- Dispersion entropy: DisEn is computed as Shannon entropy over dispersion-pattern probabilities, reaching ln(c^m) when all patterns are equally likely.
B. Refined Composite Dispersion Entropy (RCMDE)
For each scale factor, RCMDE averages dispersion-pattern distributions from τ shifted coarse-grained series and computes their Shannon entropy.
- RCMDE creates τ time series from different starting points in the coarse-graining process for each scale factor.
- RCMDE computes Shannon entropy from the averaged dispersion-pattern distributions of those shifted sequences.
C. Parameters of MDE and RCMDE
MDE and RCMDE use embedding dimension, class number, time delay, and maximum scale factor, with recommended settings and a short-signal reliability condition.
- MDE has four parameters: embedding dimension m, number of classes c, time delay d, and maximum scale factor τmax.
- The authors recommend d = 1 because aliasing may occur for d > 1, and use c = 6 for all signals.
- Reliable DisEn statistics require the number of potential dispersion patterns to be smaller than the signal length, expressed as c^m < L.
- For RCMDE, the total number of calculated sample points is approximately L, so the condition c^m < L supports more reliable results, especially for short signals.
III. EVALUATION SIGNALS
The study evaluates MDE and RCMDE using synthetic and real signals.
- The evaluation uses synthetic and real signals to assess the behavior of MDE and RCMDE.
A. Synthetic Signals
The synthetic evaluation uses WGN, 1/f noise, a noisy amplitude-modulated quasi-periodic signal, and a logistic map to examine entropy behavior across signal dynamics.
- 1/f noise has higher complexity but lower irregularity than WGN, making both useful for evaluating multiscale entropy methods.
- An amplitude-modulated quasi-periodic signal with additive WGN of diverse power tests relationships among MDE, RCMDE, RCMSE, and noise level.
- A logistic map with α varying from 3.5 to 3.99 tests entropy dependence on transitions from periodicity to non-periodic non-linearity.
B. Real Biomedical Datasets
The study evaluates MDE and RCMDE on biomedical recordings spanning focal brain activity, age-related blood pressure differences, and Alzheimer’s disease.
- Focal and Non-focal Brain Activity: MDE and RCMDE are used to discriminate focal from non-focal EEG signals in a publicly available dataset.The dataset contains 5 patients, with 750 focal and 750 non-focal 20-second signals per patient.
- Focal and Non-focal Brain Activity: The focal and non-focal EEG recordings were sampled at 512 Hz and filtered with Butterworth and Hamming-window FIR band-pass filters.The final FIR filtering used cut-off frequencies of 0.5 Hz and 40 Hz.
- Fantasia Blood Pressure Dataset: MDE and RCMDE are evaluated on continuous non-invasive blood pressure recordings from 10 young and 10 older healthy individuals in the Fantasia database.Each age group included 5 women and 5 men, and participants remained inactive in sinus rhythm while watching a movie.
- Surface EEG Dataset of Brain Activity in AD: A surface EEG dataset compares 11 Alzheimer’s disease patients with 11 age-matched control subjects during eyes-closed resting-state recordings.The recordings used the international 10-20 system and a sampling frequency of 256 Hz.
A. Synthetic Signals
Synthetic tests compare MDE, RCMDE, and RCMSE on noise, logistic-map, and quasi-periodic signals. The methods show similar entropy behavior, while RCMDE improves stability and MDE-based methods offer computational advantages.
- Noise Signals: For 40 WGN and 1/f noise signals, all methods reflect that 1/f noise is more complex whereas WGN is more irregular.The tests used signals of length 20,000 samples.
- Noise Signals: At short scales, WGN has higher entropy than 1/f noise, while at larger scales 1/f entropy remains nearly constant and WGN entropy decreases.The coarse-graining behavior indicates that WGN contains information mainly at small time scales.
- Noise Signals: RCMDE achieves the smallest coefficient-of-variation values for both 1/f noise and WGN.At scale factor 10, RCMDE is more stable than MDE, and MDE and RCMDE have smaller CVs than MSE and RCMSE, respectively.
- Computational Comparison: MDE and RCMDE avoid undefined values for short signals, whereas MSE and RCMSE produce undefined values at several scale factors for signals of 100 and 300 samples.MDE and RCMDE are also noticeably faster than MSE and RCMSE, with the advantage increasing as signal length grows.
- Quasi-periodic Signals: With increasing noise in quasi-periodic signals, all three methods produce increasing entropy profiles, while RCMDE varies more smoothly than MDE.At high noise levels, RCMDE is more stable than MDE.
- Logistic-map Signals: For a logistic map with changing parameter α, MDE, RCMDE, and RCMSE generally increase along the signal and show downward spikes during periodic behavior.When noise is not noticeable, MDE and RCMDE perform similarly, although MDE is significantly faster.
B. Real Biomedical Datasets
MDE, RCMDE, and RCMSE produced comparable complexity patterns across focal EEGs, blood pressure recordings, and Alzheimer’s disease EEGs. MDE and RCMDE generally offered stronger discrimination between physiological conditions, with RCMDE providing improved stability in relevant settings.
- Focal and Non-focal Brain Activity: Non-focal EEG signals were more complex than focal signals, with MDE and RCMDE matching RCMSE while running significantly faster than MSE-based methods.The comparison used focal and non-focal EEG recordings.
- Fantasia Blood Pressure Recordings: Elderly subjects had lower average entropy than young subjects across all scale factors for MDE, RCMDE, and RCMSE.This pattern agreed with results from another entropy-based method.
- Dataset Overview: The figures summarize mean and SD results for entropy methods across focal EEGs, Fantasia blood pressure recordings, and resting-state AD EEGs.The datasets are arranged across panels for MDE, RCMDE, and RCMSE.
- Fantasia Blood Pressure Recordings: MDE and RCMDE produced very significant elderly-versus-young differences at nearly all scale factors, whereas RCMSE lacked significant differences at scales 1 and 2.The second scale showed only a significant difference for MDE and RCMDE; RCMSE differences became significant at scales 3–10 and very significant at 11–20.
- Surface EEG in Alzheimer’s Disease: AD patients had lower MDE and RCMDE entropy than controls at scale factors 1–7 but higher entropy after scale factor 8, a pattern also observed with RCMSE.The comparison was based on resting-state EEG activity.
- Surface EEG in Alzheimer’s Disease: MDE and RCMDE achieved very significant AD-versus-control differences at scale factors 2–7, 11, and 12, while RCMSE did so only at scales 11 and 12.MDE and RCMDE also produced significant differences at scales 1 and 10.
V. CONCLUSIONS
The study introduced MDE and RCMDE to address undefined, unstable, and slow multiscale entropy results. Across synthetic and physiological signals, the proposed methods showed similar complexity behavior while improving speed, short-signal applicability, stability, and discrimination in selected datasets.
- Contribution: MDE and RCMDE were introduced as complexity estimators to improve diagnostic or therapeutic analyses of physiological signals.The methods were evaluated on synthetic datasets and clinically relevant real-world signals.
- Performance: MDE and RCMDE produced complexity profiles similar to MSE or RCMSE but were significantly faster, especially for long signals.The conclusion compares the proposed methods with existing multiscale entropy methods.
- Stability: RCMDE was more stable than MDE for noisy signals, while their performance was quite similar for filtered biomedical signals.This stability distinction was reported specifically for noisy signals.
- Short Signals: Unlike MSE and RCMSE, MDE and RCMDE did not produce undefined values for short signals.The conclusion identifies short-signal behavior as a limitation addressed by the proposed methods.
- Biomedical Applications: MDE and RCMDE discriminated elderly from young subjects and controls from AD patients better than RCMSE in the Fantasia and AD datasets, respectively.These comparisons concern the physiological datasets evaluated in the study.