Refined Composite Multiscale Permutation Entropy to Overcome Multiscale Permutation Entropy Length Dependence

Humeau-Heurtier, Anne; Wu, Chiu-Wen; Wu, Shuen-De

doi:10.1109/lsp.2015.2482603

Cited by 85 publications

(50 citation statements)

References 14 publications

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“…Since the CRLB is equal to the first term on the Taylor series approximation for the variance, this implies that the efficiency limit also changes with the MPE measurement itself. Since this effect also comes purely from the pattern distribution, we cannot correct it with the established improvements of the MPE algorithm, like Composite MPE or Refined Composite MPE [13].…”

Section: Discussionmentioning

confidence: 99%

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On the Statistical Properties of Multiscale Permutation Entropy: Characterization of the Estimator’s Variance

Dávalos

Jabloun

Ravier

et al. 2019

Entropy

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Permutation Entropy (PE) and Multiscale Permutation Entropy (MPE) have been extensively used in the analysis of time series searching for regularities. Although PE has been explored and characterized, there is still a lack of theoretical background regarding MPE. Therefore, we expand the available MPE theory by developing an explicit expression for the estimator’s variance as a function of time scale and ordinal pattern distribution. We derived the MPE Cramér–Rao Lower Bound (CRLB) to test the efficiency of our theoretical result. We also tested our formulation against MPE variance measurements from simulated surrogate signals. We found the MPE variance symmetric around the point of equally probable patterns, showing clear maxima and minima. This implies that the MPE variance is directly linked to the MPE measurement itself, and there is a region where the variance is maximum. This effect arises directly from the pattern distribution, and it is unrelated to the time scale or the signal length. The MPE variance also increases linearly with time scale, except when the MPE measurement is close to its maximum, where the variance presents quadratic growth. The expression approaches the CRLB asymptotically, with fast convergence. The theoretical variance is close to the results from simulations, and appears consistently below the actual measurements. By knowing the MPE variance, it is possible to have a clear precision criterion for statistical comparison in real-life applications.

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Section: Discussionmentioning

confidence: 99%

“…This is especially important in MPE, where the signal length is reduced geometrically at each time scale. Signal-length limitations have been addressed and improved with Composite MPE and Refined Composite MPE [13].…”

Section: Introductionmentioning

confidence: 99%

On the Statistical Properties of Multiscale Permutation Entropy: Characterization of the Estimator’s Variance

Dávalos

Jabloun

Ravier

et al. 2019

Entropy

View full text Add to dashboard Cite

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“…This can be observed by listing the new entropybased algorithms that have recently been proposed to improve and extend one of the most well-known irregularity measures, sample entropy (SampEn 1D ) [1]: see, e.g., [2]- [6]. This growing interest is probably due to the ability of the entropy-based algorithms to analyze large sets of signals [3] and also to their ability -when associated with a multiscale approach -to give information on the system's complexity [3], [7]. Among these recent methods, distribution entropy (DistrEn 1D ) showed good performances when applied to both synthetic and experimental data [5].…”

Section: Introductionmentioning

confidence: 99%

Bidimensional Distribution Entropy to Analyze the Irregularity of Small-Sized Textures

Azami

Escudero

Humeau-Heurtier

2017

IEEE Signal Process. Lett.

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Abstract-Two-dimensional sample entropy (SampEn 2D ) has been recently proposed to quantify the irregularity of textures. However, when dealing with small-sized textures, SampEn 2D may lead to either undefined or unreliable values. Moreover, SampEn 2D is too slow for most real-time applications. To alleviate these deficiencies, we introduce bidimensional distribution entropy (DistrEn 2D ). We evaluate DistrEn 2D on both synthetic and real texture datasets. The results indicate that DistrEn 2D can detect different amounts of white Gaussian and salt and pepper noise, and discriminate periodic from synthesized textures. The results also show that DistrEn 2D distinguishes different kinds of textured surfaces. In addition, DistrEn 2D , unlike SampEn 2D , does not lead to undefined values. Moreover, DistrEn 2D is noticeably faster than SampEn 2D . Overall, DistrEn 2D -as an insensitive feature extraction method to rotation -is expected to be very useful for the analysis of real image textures.

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“…Examples include composite MSEn [72], generalized MSEn [73], and refined composite MSEn [74]. Moreover, the use of different single-scale entropy algorithms can improve the performance in analyzing coarsegrained time series further, such as Multiscale Permutation Entropy (MPEn) [36], refined composite MPEn [75], Multiscale Fuzzy Entropy (MFEn) [76], and modified multiscale symbolic dynamic entropy [77]. • Filter-inspired scale-extraction based entropy approaches: improved scale-extraction procedures are applied for entropy analysis where both low-and high-frequency information is refined and maintained in extracted multiple-scale time series via filter-inspired operations.…”

Section: E Multiple-scale Entropy Measuresmentioning

confidence: 99%

Entropy Measures in Machine Fault Diagnosis: Insights and Applications

Huo

Martínez-García

Zhang

et al. 2020

IEEE Trans. Instrum. Meas.

137

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Entropy, as a complexity measure, has been widely applied for time series analysis. One preeminent example is the design of machine condition monitoring and industrial fault diagnostic systems. The occurrence of failures in a machine will typically lead to non-linear characteristics in the measurements, caused by instantaneous variations, which can increase the complexity in the system response. Entropy measures are suitable to quantify such dynamic changes in the underlying process, distinguishing between different system conditions. However, notions of entropy are defined differently in various contexts (e.g., information theory and dynamical systems theory), which may confound researchers in the applied sciences. In this paper, we have systematically reviewed the theoretical development of some fundamental entropy measures and clarified the relations among them. Then, typical entropy-based applications of machine fault diagnostic systems are summarized. Further, insights into possible applications of the entropy measures are explained, as to where and how these measures can be useful towards future datadriven fault diagnosis methodologies. Finally, potential research trends in this area are discussed, with the intent of improving online entropy estimation and expanding its applicability to a wider range of intelligent fault diagnostic systems.

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Refined Composite Multiscale Permutation Entropy to Overcome Multiscale Permutation Entropy Length Dependence

Cited by 85 publications

References 14 publications

On the Statistical Properties of Multiscale Permutation Entropy: Characterization of the Estimator’s Variance

On the Statistical Properties of Multiscale Permutation Entropy: Characterization of the Estimator’s Variance

Bidimensional Distribution Entropy to Analyze the Irregularity of Small-Sized Textures

Entropy Measures in Machine Fault Diagnosis: Insights and Applications

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