9,502 research outputs found

### Graph-Based Permutation Patterns for the Analysis of Task-Related fMRI Signals on DTI Networks in Mild Cognitive Impairment

Permutation Entropy ($PE$) is a powerful nonlinear analysis technique for
univariate time series. Very recently, Permutation Entropy for Graph signals
($PE_G$) has been proposed to extend $PE$ to data residing on irregular
domains. However, $PE_G$ is limited as it provides a single value to
characterise a whole graph signal. Here, we introduce a novel approach to
evaluate graph signals at the vertex level: graph-based permutation patterns.
Synthetic datasets show the efficacy of our method. We reveal that dynamics in
graph signals, undetectable with $PE_G$, can be discerned using our graph-based
permutation patterns. These are then validated in the analysis of DTI and fMRI
data acquired during a working memory task in mild cognitive impairment, where
we explore functional brain signals on structural white matter networks. Our
findings suggest that graph-based permutation patterns change in individual
brain regions as the disease progresses. Thus, graph-based permutation patterns
offer promise by enabling the granular scale analysis of graph signals.Comment: 5 pages, 5 figures, 1 tabl

### Permutation Entropy and Bubble Entropy: Possible interactions and synergies between order and sorting relations

[EN] Despite its widely demonstrated usefulness, there is still room for improvement in the basic Permutation Entropy (PE) algorithm, as several subsequent studies have proposed in the recent years. For example, some improved PE variants try to address possible PE weaknesses, such as its only focus on ordinal information, and not on amplitude, or the possible detrimental impact of equal values in subsequences due to motif ambiguity. Other evolved PE methods try to reduce the influence of input parameters. A good representative of this last point is the Bubble Entropy (BE) method. BE is based on sorting relations instead of ordinal patterns, and its promising capabilities have not been extensively assessed yet. The objective of the present study was to comparatively assess the classification performance of this new method, and study and exploit the possible synergies between PE and BE. The claimed superior performance of BE over PE was first evaluated by conducting a series of time series classification tests over a varied and diverse experimental set. The results of this assessment apparently suggested that there is a complementary relationship between PE and BE, instead of a superior/inferior relationship. A second set of experiments using PE and BE simultaneously as the input features of a clustering algorithm, demonstrated that with a proper algorithm configuration, classification accuracy and robustness can benefit from both measures.Cuesta Frau, D.; Vargas-Rojo, B. (2020). Permutation Entropy and Bubble Entropy: Possible interactions and synergies between order and sorting relations. Mathematical Biosciences and Engineering. 17(2):1637-1658. https://doi.org/10.3934/mbe.2020086S163716581721. C. Bandt and B. Pompe, Permutation entropy: A natural complexity measure for time series, Phys. Rev. Lett., 88 (2002), 174102.2. M. Zanin, L. Zunino, O. A. Rosso and D. Papo, Permutation entropy and its main biomedical and econophysics applications: A review, Entropy, 14 (2012), 1553-1577.14. F. Siokis, Credit market jitters in the course of the financial crisis: A permutation entropy approach in measuring informational efficiency in financial assets, Phys. A Statist. Mechan. Appl., 499 (2018).15. A. F. Bariviera, L. Zunino, M. B. Guercio, L. Martinez and O. Rosso, Efficiency and credit ratings: A permutation-information-theory analysis, J. Statist. Mechan. Theory Exper., 2013 (2013), P08007.16. A. F. Bariviera, M. B. Guercio, L. Martinez and O. Rosso, A permutation information theory tour through different interest rate maturities: the libor case, Philos. Transact. Royal Soc. A Math. Phys. Eng. Sci., 373 (2015).20. B. Fadlallah, B. Chen, A. Keil and J. Príncipe, Weighted-permutation entropy: A complexity measure for time series incorporating amplitude information, Phys. Rev. E, 87 (2013), 022911.Deng, B., Cai, L., Li, S., Wang, R., Yu, H., Chen, Y., & Wang, J. (2016). Multivariate multi-scale weighted permutation entropy analysis of EEG complexity for Alzheimerâ€™s disease. Cognitive Neurodynamics, 11(3), 217-231. doi:10.1007/s11571-016-9418-924. D. Cuesta-Frau, Permutation entropy: Influence of amplitude information on time series classification performance, Math. Biosci. Eng., 5 (2019), 1-16.25. F. Traversaro, M. Risk, O. Rosso and F. Redelico, An empirical evaluation of alternative methods of estimation for Permutation Entropy in time series with tied values, arXiv e-prints, arXiv:1707.01517 (2017).26. D. Cuesta-Frau, M. Varela-Entrecanales, A. Molina-Picó and B. Vargas, Patterns with equal values in permutation entropy: Do they really matter for biosignal classification?, Complexity, 2018 (2018), 1-15.29. D. Cuesta-Frau, A. Molina-Picó, B. Vargas and P. González, Permutation entropy: Enhancing discriminating power by using relative frequencies vector of ordinal patterns instead of their shannon entropy, Entropy, 21 (2019).30. H. Azami and J. Escudero, Amplitude-aware permutation entropy: Illustration in spike detection and signal segmentation, Comput. Meth. Program. Biomed., 128 (2016), 40-51.32. G. Manis, M. Aktaruzzaman and R. Sassi, Bubble entropy: An entropy almost free of parameters, IEEE Transact. Biomed. Eng., 64 (2017), 2711-2718.34. L. Zunino, F. Olivares, F. Scholkmann and O. A. Rosso, Permutation entropy based time series analysis: Equalities in the input signal can lead to false conclusions, Phys. Lett. A, 381 (2017), 1883-1892.38. D. E. Lake, J. S. Richman, M. P. Griffin and J. R. Moorman, Sample entropy analysis of neonatal heart rate variability, Am. J. Physiology-Regulatory Integrat. Comparat. Physiol., 283 (2002), R789-R797, PMID: 12185014.41. I. Unal, Defining an Optimal Cut-Point Value in ROC Analysis: An Alternative Approach, Comput. Math. Methods Med., 2017 (2017), 14.47. A. K. Jain, M. N. Murty and P. J. Flynn, Data clustering: A review, ACM Comput. Surv., 31 (1999), 264-323.51. J. Sander, M. Ester, H.-P. Kriegel and X. Xu, Density-based clustering in spatial databases: The algorithm gdbscan and its applications, Data Min. Knowl. Discov., 2 (1998), 169-194.52. J. Wu, Advances in K-means Clustering: A Data Mining Thinking, Springer Publishing Company, Incorporated, 2012.53. S. Panda, S. Sahu, P. Jena and S. Chattopadhyay, Comparing fuzzy-c means and k-means clustering techniques: A comprehensive study, in Advances in Computer Science, Engineering & Applications (eds. D. C. Wyld, J. Zizka and D. Nagamalai), Springer Berlin Heidelberg, Berlin, Heidelberg, 2012, 451-460.54. A. L. Goldberger, L. A. N. Amaral, L. Glass, J. M. Hausdorff, P. C. Ivanov, R. G. Mark, et al., PhysioBank, PhysioToolkit, and PhysioNet: Components of a new research resource for complex physiologic signals, Circulation, 101 (2000), 215-220.58. R. G. Andrzejak, K. Lehnertz, F. Mormann, C. Rieke, P. David and C. E. Elger, Indications of nonlinear deterministic and finite-dimensional structures in time series of brain electrical activity: Dependence on recording region and brain state, Phys. Rev. E, 64 (2001), 061907.60. N. Iyengar, C. K. Peng, R. Morin, A. L. Goldberger and L. A. Lipsitz, Age-related alterations in the fractal scaling of cardiac interbeat interval dynamics, Am. J. Physiology-Regulatory Integrat. Comparat. Physiol., 271 (1996), R1078-R1084, PMID: 8898003

### A method based on multiscale base-scale entropy and random forests for roller bearings faults diagnosis

A method based on multiscale base-scale entropy (MBSE) and random forests (RF) for roller bearings faults diagnosis is presented in this study. Firstly, the roller bearings vibration signals were decomposed into base-scale entropy (BSE), sample entropy (SE) and permutation entropy (PE) values by using MBSE, multiscale sample entropy (MSE) and multiscale permutation entropy (MPE) under different scales. Then the computation time of the MBSE/MSE/MPE methods were compared. Secondly, the entropy values of BSE, SE, and PE under different scales were regarded as the input of RF and SVM optimized by particle swarm ion (PSO) and genetic algorithm (GA) algorithms for fulfilling the fault identification, and the classification accuracy was utilized to verify the effect of the MBSE/MSE/MPE methods by using RF/PSO/GA-SVM models. Finally, the experiment result shows that the computational efficiency and classification accuracy of MBSE method are superior to MSE and MPE with RF and SVM

### Application of Permutation Entropy and Permutation Min-Entropy in Multiple Emotional States Analysis of RRI Time Series

This studyâ€™s aim was to apply permutation entropy (PE) and permutation min-entropy (PME) over an RR interval time series to quantify the changes in cardiac activity among multiple emotional states. Electrocardiogram (ECG) signals were recorded under six emotional states (neutral, happiness, sadness, anger, fear, and disgust) in 60 healthy subjects at a rate of 1000 Hz. For each emotional state, ECGs were recorded for 5 min and the RR interval time series was extracted from these ECGs. The obtained results confirm that PE and PME increase significantly during the emotional states of happiness, sadness, anger, and disgust. Both symbolic quantifiers also increase but not in a significant way for the emotional state of fear. Moreover, it is found that PME is more sensitive than PE for discriminating non-neutral from neutral emotional states.Facultad de IngenierÃ

### Using the Information Provided by Forbidden Ordinal Patterns in Permutation Entropy to Reinforce Time Series Discrimination Capabilities

[EN] Despite its widely tested and proven usefulness, there is still room for improvement in the basic permutation entropy (PE) algorithm, as several subsequent studies have demonstrated in recent years. Some of these new methods try to address the well-known PE weaknesses, such as its focus only on ordinal and not on amplitude information, and the possible detrimental impact of equal values found in subsequences. Other new methods address less specific weaknesses, such as the PE resultsÂ¿ dependence on input parameter values, a common problem found in many entropy calculation methods. The lack of discriminating power among classes in some cases is also a generic problem when entropy measures are used for data series classification. This last problem is the one specifically addressed in the present study. Toward that purpose, the classification performance of the standard PE method was first assessed by conducting several time series classification tests over a varied and diverse set of data. Then, this performance was reassessed using a new Shannon Entropy normalisation scheme proposed in this paper: divide the relative frequencies in PE by the number of different ordinal patterns actually found in the time series, instead of by the theoretically expected number. According to the classification accuracy obtained, this last approach exhibited a higher class discriminating power. It was capable of finding significant differences in six out of seven experimental datasetsÂ¿whereas the standard PE method only did in fourÂ¿and it also had better classification accuracy. It can be concluded that using the additional information provided by the number of forbidden/found patterns, it is possible to achieve a higher discriminating power than using the classical PE normalisation method. The resulting algorithm is also very similar to that of PE and very easy to implement.Cuesta Frau, D. (2020). Using the Information Provided by Forbidden Ordinal Patterns in Permutation Entropy to Reinforce Time Series Discrimination Capabilities. Entropy. 22(5):1-17. https://doi.org/10.3390/e22050494S117225Bandt, C., & Pompe, B. (2002). Permutation Entropy: A Natural Complexity Measure for Time Series. Physical Review Letters, 88(17). doi:10.1103/physrevlett.88.174102Zanin, M., Zunino, L., Rosso, O. A., & Papo, D. (2012). Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review. Entropy, 14(8), 1553-1577. doi:10.3390/e14081553Li, J., Yan, J., Liu, X., & Ouyang, G. (2014). Using Permutation Entropy to Measure the Changes in EEG Signals During Absence Seizures. Entropy, 16(6), 3049-3061. doi:10.3390/e16063049Ravelo-GarcÃa, A., Navarro-Mesa, J., Casanova-Blancas, U., Martin-Gonzalez, S., Quintana-Morales, P., Guerra-Moreno, I., â€¦ HernÃ¡ndez-PÃ©rez, E. (2015). Application of the Permutation Entropy over the Heart Rate Variability for the Improvement of Electrocardiogram-based Sleep Breathing Pause Detection. Entropy, 17(3), 914-927. doi:10.3390/e17030914Cuesta-Frau, D., MirÃ³-MartÃnez, P., Oltra-Crespo, S., JordÃ¡n-NÃºÃ±ez, J., Vargas, B., GonzÃ¡lez, P., & Varela-Entrecanales, M. (2018). Model Selection for Body Temperature Signal Classification Using Both Amplitude and Ordinality-Based Entropy Measures. Entropy, 20(11), 853. doi:10.3390/e20110853Cuestaâ€“Frau, D., MirÃ³â€“MartÃnez, P., Oltraâ€“Crespo, S., JordÃ¡nâ€“NÃºÃ±ez, J., Vargas, B., & Vigil, L. (2018). Classification of glucose records from patients at diabetes risk using a combined permutation entropy algorithm. Computer Methods and Programs in Biomedicine, 165, 197-204. doi:10.1016/j.cmpb.2018.08.018Gao, Y., Villecco, F., Li, M., & Song, W. (2017). Multi-Scale Permutation Entropy Based on Improved LMD and HMM for Rolling Bearing Diagnosis. Entropy, 19(4), 176. doi:10.3390/e19040176Wang, X., Si, S., Wei, Y., & Li, Y. (2019). The Optimized Multi-Scale Permutation Entropy and Its Application in Compound Fault Diagnosis of Rotating Machinery. Entropy, 21(2), 170. doi:10.3390/e21020170Wang, Q. C., Song, W. Q., & Liang, J. K. (2014). Road Flatness Detection Using Permutation Entropy (PE). Applied Mechanics and Materials, 721, 420-423. doi:10.4028/www.scientific.net/amm.721.420Glynn, C. C., & Konstantinou, K. I. (2016). Reduction of randomness in seismic noise as a short-term precursor to a volcanic eruption. Scientific Reports, 6(1). doi:10.1038/srep37733Zhang, Y., & Shang, P. (2017). Permutation entropy analysis of financial time series based on Hillâ€™s diversity number. Communications in Nonlinear Science and Numerical Simulation, 53, 288-298. doi:10.1016/j.cnsns.2017.05.003Fadlallah, B., Chen, B., Keil, A., & PrÃncipe, J. (2013). Weighted-permutation entropy: A complexity measure for time series incorporating amplitude information. Physical Review E, 87(2). doi:10.1103/physreve.87.022911Xiao-Feng, L., & Yue, W. (2009). Fine-grained permutation entropy as a measure of natural complexity for time series. Chinese Physics B, 18(7), 2690-2695. doi:10.1088/1674-1056/18/7/011Azami, H., & Escudero, J. (2016). Amplitude-aware permutation entropy: Illustration in spike detection and signal segmentation. Computer Methods and Programs in Biomedicine, 128, 40-51. doi:10.1016/j.cmpb.2016.02.008Cuestaâ€“Frau, D. (2019). Permutation entropy: Influence of amplitude information on time series classification performance. Mathematical Biosciences and Engineering, 16(6), 6842-6857. doi:10.3934/mbe.2019342Bian, C., Qin, C., Ma, Q. D. Y., & Shen, Q. (2012). Modified permutation-entropy analysis of heartbeat dynamics. 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### Delay Parameter Selection in Permutation Entropy Using Topological Data Analysis

Permutation Entropy (PE) is a powerful tool for quantifying the
predictability of a sequence which includes measuring the regularity of a time
series. Despite its successful application in a variety of scientific domains,
PE requires a judicious choice of the delay parameter $\tau$. While another
parameter of interest in PE is the motif dimension $n$, Typically $n$ is
selected between $4$ and $8$ with $5$ or $6$ giving optimal results for the
majority of systems. Therefore, in this work we focus solely on choosing the
delay parameter. Selecting $\tau$ is often accomplished using trial and error
guided by the expertise of domain scientists. However, in this paper, we show
that persistent homology, the flag ship tool from Topological Data Analysis
(TDA) toolset, provides an approach for the automatic selection of $\tau$. We
evaluate the successful identification of a suitable $\tau$ from our TDA-based
approach by comparing our results to a variety of examples in published
literature

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