Multiscale permutation entropy analysis of electrocardiogram

Permutation entropy has become a standard tool for time series analysis that exploits the temporal and ordinal relationships within data. Motivated by a Kullback-Leibler divergence interpretation of permutation entropy as divergence from white noise, we extend pattern-based methods to the setting of random walk data. We analyze random walk null models for correlated time series and describe a method for determining the corresponding ordinal pattern distributions. These null models more accurately reflect the observed pattern distributions in some economic data. This leads us to define a measure of complexity using the deviation of a time series from an associated random walk null model. We demonstrate the applicability of our methods using empirical data drawn from a variety of fields, including to a variety of stock market closing prices.

Section: Introductionmentioning

confidence: 99%

Random Walk Null Models for Time Series Data

DeFord

Moore

2017

“…The embedded dimension m is also related to the amount of information captured by a subsequence. A multiscale approach, with different time scales for PE [ 64 , 65 ], could also contribute to gain more insights into the dynamics of the time series. In this regard, it has been demonstrated that higher values of m frequently provide more discriminating power [ 24 , 60 ], as well as an optimal set of time delays [ 66 ].…”

Section: Discussionmentioning

confidence: 99%

Permutation Entropy: Enhancing Discriminating Power by Using Relative Frequencies Vector of Ordinal Patterns Instead of Their Shannon Entropy

Cuesta–Frau

Picó

Vargas

et al. 2019

Many measures to quantify the nonlinear dynamics of a time series are based on estimating the probability of certain features from their relative frequencies. Once a normalised histogram of events is computed, a single result is usually derived. This process can be broadly viewed as a nonlinear I R n mapping into I R , where n is the number of bins in the histogram. However, this mapping might entail a loss of information that could be critical for time series classification purposes. In this respect, the present study assessed such impact using permutation entropy (PE) and a diverse set of time series. We first devised a method of generating synthetic sequences of ordinal patterns using hidden Markov models. This way, it was possible to control the histogram distribution and quantify its influence on classification results. Next, real body temperature records are also used to illustrate the same phenomenon. The experiments results confirmed the improved classification accuracy achieved using raw histogram data instead of the PE final values. Thus, this study can provide a very valuable guidance for the improvement of the discriminating capability not only of PE, but of many similar histogram-based measures.

“…After that, this algorithm has attracted the attention of many researchers because it has superior robustness and requires less computation [ 14 , 15 , 16 ]. Many derivative algorithms, such as multiscale permutation entropy [ 17 , 18 ], weighted permutation entropy (WPE) [ 19 , 20 , 21 ], Rényi permutation entropy [ 22 , 23 ], generalized permutation entropy [ 24 ], multivariate permutation entropy [ 25 ], and amplitude-aware permutation entropy (AAPE) [ 26 ] have been proposed to extend the application of PE to a variety of fields.…”

Section: Introductionmentioning

confidence: 99%

Coded Permutation Entropy: A Measure for Dynamical Changes Based on the Secondary Partitioning of Amplitude Information

Kang

Zhang

2020

An improved permutation entropy (PE) algorithm named coded permutation entropy (CPE) is proposed in this paper to optimize the problems existing in PE based on the secondary partitioning. The principle of CPE algorithm is given, and the performance of it for dynamical change detection is analyzed using synthetic signal, logistic map and Lorenz map. The detection ability of CPE algorithm in different signal-to-noise ratios (SNR) is studied and the algorithm complexity is discussed. The results show that CPE can accurately capture minor feature information and amplify the detection results of dynamical changes compared with PE, weighted permutation entropy (WPE) and amplitude-aware permutation entropy (AAPE), but it has less robustness to noise and requires a higher computation cost than the others. Finally, we use the new algorithm to analyze the rolling bearing fault signals. The application of actual signals illustrates that CPE performs better in detecting abnormal pulse of the rolling bearing when the embedded dimension is small. From all the analyses in this paper, we find that CPE has a better performance for dynamical change detection compared with the other three algorithms when there is a larger repetition rate of permutation pattern in the position sequences.