Permutation Entropy: New Ideas and Challenges

Keller, Karsten; Mangold, Teresa; Stolz, Inga; Werner, Jenna

doi:10.3390/e19030134

Cited by 63 publications

(26 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This normalization motivates a recently introduced, alternative interpretation of permutation entropy as the Kullback-Leibler divergence (KL divergence) of the deviation of the empirical distribution from that of white noise (see [16,25] for some exposition about this perspective). The KL divergence was originally defined in [26] to measure the information theoretic distance between a distribution and another expected distribution, and has become a standard measure in many fields.…”

Section: Permutation Entropy and Kl Divergencementioning

confidence: 89%

See 1 more Smart Citation

Random Walk Null Models for Time Series Data

DeFord

Moore

2017

Entropy

View full text Add to dashboard Cite

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.

show abstract

Section: Permutation Entropy and Kl Divergencementioning

confidence: 89%

“…Datasets of a similar scale are increasingly available in the current big data paradigm, and permutation methods are well positioned to contribute to comprehensive and meaningful analyses. Three recent surveys [16][17][18] provide a comprehensive overview of recent developments and applications.…”

Section: Introductionmentioning

confidence: 99%

Random Walk Null Models for Time Series Data

DeFord

Moore

2017

Entropy

View full text Add to dashboard Cite

show abstract

“…It has been applied in the fields of biomedical sciences [8,9], mechanical diagnosis [10] and underwater acoustic signal processing [11]. PE is one of the most effective ways to detect the randomness and dynamic changes of time sequence based on comparison of neighboring values [12][13][14]. However, NPE [15], a new kind of PE, was proposed to classify different sleep stages by Bandt in 2017.…”

Section: Introductionmentioning

confidence: 99%

Denoising and Feature Extraction Algorithms Using NPE Combined with VMD and Their Applications in Ship-Radiated Noise

Xiao

et al. 2017

Symmetry

View full text Add to dashboard Cite

Abstract:A new denoising algorithm and feature extraction algorithm that combine a new kind of permutation entropy (NPE) and variational mode decomposition (VMD) are put forward in this paper. VMD is a new self-adaptive signal processing algorithm, which is more robust to sampling and noise, and also can overcome the problem of mode mixing in empirical mode decomposition (EMD) and ensemble EMD (EEMD). Permutation entropy (PE), as a nonlinear dynamics parameter, is a powerful tool that can describe the complexity of a time series. NPE, a new version of PE, is interpreted as distance to white noise, which shows a reverse trend to PE and has better stability than PE. In this paper, three kinds of ship-radiated noise (SN) signal are decomposed by VMD algorithm, and a series of intrinsic mode functions (IMF) are obtained. The NPEs of all the IMFs are calculated, the noise IMFs are screened out according to the value of NPE, and the process of denoising can be realized by reconstructing the rest of IMFs. Then the reconstructed SN signal is decomposed by VMD algorithm again, and one IMF containing the most dominant information is chosen to represent the original SN signal. Finally, NPE of the chosen IMF is calculated as a new complexity feature, which constitutes the input of the support vector machine (SVM) for pattern recognition of SN. Compared with the existing denoising algorithms and feature extraction algorithms, the effectiveness of proposed algorithms is validated using the numerical simulation signal and the different kinds of SN signal.

show abstract

“…Here we suggest a statistic on the basis of the conditional entropy of ordinal patterns introduced in [18]. The latter is a complexity measure similar to the celebrated permutation entropy [9] with particularly better performance (see [17,18]). Let us provide an "obvious" example only to motivate our approach and to illustrate its idea.…”

Section: Introductionmentioning

confidence: 99%

“…A result of this transformation is demonstrated in Figure 1 for order d = 1. Note that the distribution of ordinal patterns contain much information on the original time series making them interesting for data analysis, especially for data from nonlinear systems (see [16,17]). …”

Section: Introductionmentioning

confidence: 99%

Change-Point Detection using the Conditional Entropy of Ordinal Patterns

Keller¹,

Unakafov²

2018

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Permutation Entropy: New Ideas and Challenges

Cited by 63 publications

References 30 publications

Random Walk Null Models for Time Series Data

Random Walk Null Models for Time Series Data

Denoising and Feature Extraction Algorithms Using NPE Combined with VMD and Their Applications in Ship-Radiated Noise

Change-Point Detection using the Conditional Entropy of Ordinal Patterns

Contact Info

Product

Resources

About

Permutation Entropy: New Ideas and Challenges

Cited by 63 publications

References 30 publications

Random Walk Null Models for Time Series Data

Random Walk Null Models for Time Series Data

Denoising and Feature Extraction Algorithms Using NPE Combined with VMD and Their Applications in Ship-Radiated Noise

Change-Point Detection using the Conditional&nbsp;Entropy of Ordinal Patterns

Contact Info

Product

Resources

About

Change-Point Detection using the Conditional Entropy of Ordinal Patterns