Abstract
Dispersion entropy (DispEn) is a recently introduced entropy metric to quantify the uncertainty of time series. It is fast and, so far, it has demonstrated very good performance in the characterisation of time series. It includes a mapping step, but the effect of different mappings has not been studied yet. Here, we investigate the effect of linear and nonlinear mapping approaches in DispEn. We also inspect the sensitivity of different parameters of DispEn to noise. Moreover, we develop fluctuation-based DispEn (FDispEn) as a measure to deal with only the fluctuations of time series. Furthermore, the original and fluctuation-based forbidden dispersion patterns are introduced to discriminate deterministic from stochastic time series. Finally, we compare the performance of DispEn, FDispEn, permutation entropy, sample entropy, and Lempel–Ziv complexity on two physiological datasets. The results show that DispEn is the most consistent technique to distinguish various dynamics of the biomedical signals. Due to their advantages over existing entropy methods, DispEn and FDispEn are expected to be broadly used for the characterization of a wide variety of real-world time series. The MATLAB codes used in this paper are freely available at http://dx.doi.org/10.7488/ds/2326.
Highlights
Searching for patterns in signals and images is a fundamental problem and has a long history [1]
The standard deviation (SD) values suggest that when all signals have equal SNR values, the Dispersion entropy (DispEn) and permutation entropy (PerEn) values are stable for all the methods
We carried out an investigation aimed at gaining a better understanding of our recently developed DispEn, especially regarding the parameters and mapping techniques used in DispEn
Summary
Searching for patterns in signals and images is a fundamental problem and has a long history [1]. A pattern denotes an ordered set of numbers, shapes, or other mathematical objects, arranged based on a rule. Elements of a given set are usually arranged by the concepts of permutation and combination [2]. Combination means a way of selecting elements or objects of a given set in which the order of selection does not matter. The order of objects is usually a crucial characteristic of a pattern [1,2]. The concept of permutation pattern indicates an arrangement of the distinct elements or objects of a given set into some sequences or orders [2,3,4,5]. Permutation patterns have been studied occasionally, often implicitly, for over a century, this area has grown significantly in the last three decades [6]
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