On the use of approximate entropy and sample entropy with centre of pressure time-series

Abstract

BackgroundApproximate entropy (ApEn) and sample entropy (SampEn) have been previously used to quantify the regularity in centre of pressure (COP) time-series in different experimental groups and/or conditions. ApEn and SampEn are very sensitive to their input parameters: m (subseries length), r (tolerance) and N (data length). Yet, the effects of changing those parameters have been scarcely investigated in the analysis of COP time-series. This study aimed to investigate the effects of changing parameters m, r and N on ApEn and SampEn values in COP time-series, as well as the ability of these entropy measures to discriminate between groups.MethodsA public dataset of COP time-series was used. ApEn and SampEn were calculated for m = {2, 3, 4, 5}, r = {0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5} and N = {600, 1200} (30 and 60 s, respectively). Subjects were stratified in young adults (age < 60, n = 85), and older adults (age ≥ 60) with (n = 18) and without (n = 56) falls in the last year. The effects of changing parameters m, r and N on ApEn and SampEn were investigated with a three-way ANOVA. The ability of ApEn and SampEn to discriminate between groups was investigated with a mixed ANOVA (within-subject factors: m, r and N; between-subject factor: group). Specific combinations of m, r and N producing significant differences between groups were identified using the Tukey’s honest significant difference procedure.ResultsA significant three-way interaction between m, r and N confirmed the sensitivity of ApEn and SampEn to the input parameters. SampEn showed a higher consistency and ability to discriminate between groups than ApEn. Significant differences between groups were mostly observed in longer (N = 1200) COP time-series in the anterior-posterior direction. Those differences were observed for specific combinations of m and r, highlighting the importance of an adequate selection of input parameters.ConclusionsFuture studies should favour SampEn over ApEn and longer time-series (≥ 60 s) over shorter ones (e.g. 30 s). The use of parameter combinations such as SampEn (m = {4, 5}, r = {0.25, 0.3, 0.35}) is recommended.Electronic supplementary materialThe online version of this article (10.1186/s12984-018-0465-9) contains supplementary material, which is available to authorized users.

Approximate Entropy and Sample Entropy: A Comprehensive Tutorial

“…While the presented algorithms were initially developed for clinical research, they later spread to diverse fields such as neuroengineering [ 35 ], visual pattern recognition [ 36 ], neuroinformatics [ 37 ], ecology [ 38 ], psychiatry [ 39 ], electronics [ 40 ], voice recognition [ 41 ] or finance [ 42 ]. As their application is increasing lately, in this paper we have presented a clear path for understanding the logic behind ApEn and SampEn to help researchers understand their foundations and correct application.…”

A New Lightweight Stream Cipher Based on Chaos

“…Approximate Entropy (ApEn) [35] is a non-linear dynamic parameter that is used to quantify the regularity and unpredictability of time series fluctuations. It uses a non-negative number to represent the complexity of a time series and it reflects the possibility of new information occurring in the time series.…”

Slope Entropy: A New Time Series Complexity Estimator Based on Both Symbolic Patterns and Amplitude Information

“…The influence of m in the performance of PE and SampEn is a well known issue [ 58 ]. Although some efforts have been devoted to minimise this influence [ 59 ], it still plays an important role, and its impact should be characterised, and compared.…”

“…The comparative results of the length analysis shown in Figure 8 a–d indicate that SlopEn is reasonably robust against short datasets. The classification performance provided by PE has already been demonstrated to be robust in these terms [ 22 ], and SampEn has also been claimed to exhibit less dependence on length than other very successful methods like ApEn [ 58 ]. In this context of already robust methods, SlopEn was capable of outperforming them, with an even more stable behaviour, in addition to higher accuracy performances, discussed in other experiments.…”