Evaluation of scale invariance in physiological signals by means of balanced estimation of diffusion entropy

Abstract

By means of the concept of the balanced estimation of diffusion entropy, we evaluate the reliable scale invariance embedded in different sleep stages and stride records. Segments corresponding to waking, light sleep, rapid eye movement (REM) sleep, and deep sleep stages are extracted from long-term electroencephalogram signals. For each stage the scaling exponent value is distributed over a considerably wide range, which tell us that the scaling behavior is subject and sleep cycle dependent. The average of the scaling exponent values for waking segments is almost the same as that for REM segments (∼0.8). The waking and REM stages have a significantly higher value of the average scaling exponent than that for light sleep stages (∼0.7). For the stride series, the original diffusion entropy (DE) and the balanced estimation of diffusion entropy (BEDE) give almost the same results for detrended series. The evolutions of local scaling invariance show that the physiological states change abruptly, although in the experiments great efforts have been made to keep conditions unchanged. The global behavior of a single physiological signal may lose rich information on physiological states. Methodologically, the BEDE can evaluate with considerable precision the scale invariance in very short time series (∼10^{2}), while the original DE method sometimes may underestimate scale-invariance exponents or even fail in detecting scale-invariant behavior. The BEDE method is sensitive to trends in time series. The existence of trends may lead to an unreasonably high value of the scaling exponent and consequent mistaken conclusions.

Evaluation of Scaling Invariance Embedded in Short Time Series

“…Recently, by minimizing the summation of statistical error and bias, Bonachela et al [33] , [34] proposed a balanced estimation of Shannon entropy for a small set of data, which performs well even when a data set contains few tens of records. Replacing the original Shannon entropy with the balanced entropy estimation, we convert the DE method to a new version, called balanced estimation of diffusion entropy (BEDE) [35] , [36] . Detailed calculations on constructed fractional Brownian series, stock market records, and physiological signals show that the BEDE is a possible way to evaluate scaling behaviors embedded in a single and short time series with several hundreds length.…”

Brain Network Constancy and Participant Recognition: an Integrated Approach to Big Data and Complex Network Analysis

“…This study was limited in catching the flexible and dynamic characteristics of EEG signals when calculating the STE (McAuliffe, 2014). Further studies with the STE of short EEG sequences (about 10 2 points) (Zhang et al, 2012;Pan et al, 2014) would be required to avoid excessive reduction of brainwave features. 3.…”

In search of coding and non-coding regions of DNA sequences based on balanced estimation of diffusion entropy

“…To overcome this, the original form of the entropy can be replaced by a balanced estimator of DE (BEDE), which can evaluate the scale invariance in very short time series with considerable precision. In recent papers, BEDE was applied to detect scaling properties and structural breaks in stock price series on the Shanghai stock market [14], to evaluate scaling behaviors in heartbeat series for different sleep stages, and to assess stride time series for normal, fast, and slow walkers [15]. Here, we use BEDE (see Section 2.3) to find the coding and non-coding regions of DNA sequences; the results indicate that it reliably recognizes both borders.…”