Citation: David Cuesta-Frau, Borja Vargas. Permutation Entropy and Bubble Entropy: Possible interactions and synergies between order and sorting relations[J]. Mathematical Biosciences and Engineering, 2020, 17(2): 1637-1658. doi: 10.3934/mbe.2020086
[1] | 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. |
[3] | D. Cuesta-Frau, P. Miró-Martínez, S. Oltra-Crespo, J. Jordán-Núñez, B. Vargas, P. González, et al., Model selection for body temperature signal classification using both amplitude and ordinalitybased entropy measures, Entropy, 20, (2018). |
[4] | D. Cuesta-Frau, P. Miró-Martínez, S. Oltra-Crespo, J. Jordán-Núñez, B. Vargas and L. Vigil, Classification of glucose records from patients at diabetes risk using a combined permutation entropy algorithm, Comput. Meth. Program. Biomed., 165 (2018), 197-204. |
[5] | D. Mateos, J. Diaz and P. Lamberti, Permutation entropy applied to the characterization of the clinical evolution of epileptic patients under pharmacological treatment, Entropy, 16 (2014), 5668-5676. |
[6] | N. Nicolaou and J. Georgiou, The use of permutation entropy to characterize sleep electroencephalograms., Clin. EEG Neurosci., 421 (2011), 24-28. |
[7] | A. Martínez-Rodrigo, B. García-Martínez, L. Zunino, R. Alcaraz and A. Fernández-Caballero, Multi-lag analysis of symbolic entropies on eeg recordings for distress recognition, Front. Neuroinform., 13 (2019), 40. |
[8] | D. Li, X. Li, Z. Liang, L. J. Voss and J. W. Sleigh, Multiscale permutation entropy analysis of EEG recordings during sevoflurane anesthesia, J. Neural Eng., 7 (2010), 046010. |
[9] | C. C. Naranjo, L. M. Sanchez-Rodriguez, M. B. Martínez, M. E. Báez and A. M. García, Permutation entropy analysis of heart rate variability for the assessment of cardiovascular autonomic neuropathy in type 1 diabetes mellitus, Comput. Biol. Med., 86 (2017), 90-97. |
[10] | A. G. Ravelo-Garcia, J. L. Navarro-Mesa, U. Casanova-Blancas, S. González, P. Quintana, I. Guerra-Moreno, et al., Application of the permutation entropy over the heart rate variability for the improvement of electrocardiogram-based sleep breathing pause detection, Entropy, 17 (2015), 914-927. |
[11] | C. Bian, C. Qin, Q. D. Y. Ma and Q. Shen, Modified Permutation-entropy analysis of heartbeat dynamics, Phys. Rev. E, 85 (2012), 021906. |
[12] | M. Henry and G. Judge, Permutation entropy and information recovery in nonlinear dynamic economic time series, Econometrics, 7 (2019). |
[13] | H. Danylchuk, N. Chebanova, N. Reznik and Y. Vitkovskyi, Modeling of investment attractiveness of countries using entropy analysis of regional stock markets, Global J. Environ. Sci. Manag., 5 (2019), 227-235. |
[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). |
[17] | J. Cánovas, G. García-Clemente and M. Muñoz-Guillermo, Comparing permutation entropy functions to detect structural changes in time series, Phys. A Statist. Mechan. Appl., 507 (2018), 153-174. |
[18] | J. Zhang, Y. Zhao, M. Liu and L. Kong, Bearings fault diagnosis based on adaptive local iterative filtering-multiscale permutation entropy and multinomial logistic model with group-lasso, Advan. Mechan. Eng., 11 (2019), 1687814019836311. |
[19] | J. Huang, X. Wang, D. Wang, Z. Wang and X. Hua, Analysis of weak fault in hydraulic system based on multi-scale permutation entropy of fault-sensitive intrinsic mode function and deep belief network, Entropy, 21 (2019). |
[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. |
[21] | J. Garland, T. R. Jones, M. Neuder, V. Morris, J. W. C. White and E. Bradley, Anomaly detection in paleoclimate records using permutation entropy, Entropy, 20 (2018). |
[22] | B. Deng, L. Cai, S. Li, R. Wang, H. Yu, Y. Chen, et al., Multivariate multi-scale weighted permutation entropy analysis of eeg complexity for alzheimer's disease, Cogn. Neurodyn., 11 (2017), 217-231. doi: 10.1007/s11571-016-9418-9 |
[23] | L. Xiao-Feng and W. Yue, Fine-grained permutation entropy as a measure of natural complexity for time series, Chinese Phys. B, 18 (2009), 2690. |
[24] | 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. |
[27] | Y. Zou, R. V. Donner, N. Marwan, J. F. Donges and J. Kurths, Complex network approaches to nonlinear time series analysis, Phys. Rep., 787 (2019), 1-97, Complex network approaches to nonlinear time series analysis. |
[28] | M. McCullough, M. Small, T. Stemler and H. Iu, Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems, Chaos Interdisciplin. J. Nonlinear Sci., 25 (2015). |
[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. |
[31] | Z. Chen, L. Yaan, H. Liang and J. Yu, Improved permutation entropy for measuring complexity of time series under noisy condition, Complexity, 2019 (2019), 1-12. |
[32] | G. Manis, M. Aktaruzzaman and R. Sassi, Bubble entropy: An entropy almost free of parameters, IEEE Transact. Biomed. Eng., 64 (2017), 2711-2718. |
[33] | M. Riedl, A. Müller and N. Wessel, Practical considerations of permutation entropy, European Phys. J. Special Topics, 222 (2013), 249-262. |
[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. |
[35] | L. Citi, G. Guffanti and L. Mainardi, Rank-based multi-scale entropy analysis of heart rate variability, in Computing in Cardiology 2014, 2014, 597-600. |
[36] | A. M. Unakafov and K. Keller, Conditional entropy of ordinal patterns, Phys. D Nonlinear Phenom., 269 (2014), 94-102. |
[37] | Z. Liang, Y. Wang, X. Sun, D. Li, L. Voss, J. Sleigh, et al., Eeg entropy measures in anesthesia, Front. Comput. Neurosci., 9 (2015), 16. |
[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. |
[39] | S. M. Pincus, Approximate entropy as a measure of system complexity., Proceed. Nat. Acad. Sci., 88 (1991), 2297-2301. |
[40] | T. Fawcett, An introduction to ROC analysis, Patt. Recogn. Lett., 27 (2006), 861-874, ROC Analysis in Pattern Recognition. |
[41] | I. Unal, Defining an Optimal Cut-Point Value in ROC Analysis: An Alternative Approach, Comput. Math. Methods Med., 2017 (2017), 14. |
[42] | A. Tharwat, Classification assessment methods, Appl. Comput. Inform., (2018). |
[43] | A. M. Zoubir and D. R. Iskander, Bootstrap Techniques for Signal Processing, Cambridge University Press, 2004. |
[44] | D. Kalpić, N. Hlupić and M. Lovrić, Student's t-Tests, 1559-1563, Springer Berlin Heidelberg, Berlin, Heidelberg, 2011. |
[45] | C.-Y. J. Peng, K. L. Lee and G. M. Ingersoll, An introduction to logistic regression analysis and reporting, J. Educat. Res., 96 (2002), 3-14. |
[46] | C. M. Bishop, Neural Networks Patt. Recogn., Oxford University Press, Inc., New York, NY, USA, 1995. |
[47] | A. K. Jain, M. N. Murty and P. J. Flynn, Data clustering: A review, ACM Comput. Surv., 31 (1999), 264-323. |
[48] | J. Rodríguez-Sotelo, D. Peluffo-Ordoñez, D. Cuesta-Frau and G. Castellanos-Domínguez, Unsupervised feature relevance analysis applied to improve ecg heartbeat clustering, Comput. Meth. Program. Biomed., 108 (2012), 250-261. |
[49] | D. Cuesta-Frau, J. C. Pérez-Cortés and G. Andreu-García, Clustering of electrocardiograph signals in computer-aided Holter analysis, Comput. Meth. Program. Biomed., 72 (2003), 179-196. |
[50] | C. Murthy and N. Chowdhury, In search of optimal clusters using genetic algorithms, Patt. Recogn. Lett., 17 (1996), 825-832. |
[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. |
[55] | J. Jordán-Núnez, P. Miró-Martínez, B. Vargas, M. Varela-Entrecanales and D. Cuesta-Frau, Statistical models for fever forecasting based on advanced body temperature monitoring, J. Crit. Care, 37 (2017), 136-140. |
[56] | D. Cuesta-Frau, M. Varela, P. Miró-Martínez, P. Galdos, D. Abásolo, R. Hornero, et al,, Predicting survival in critical patients by use of body temperature regularity measurement based on approximate entropy, Med. Biol. Eng. Comput., 45 (2007), 671-678. |
[57] | C. Rodriguez de Castro, L. Vigil, B. Vargas, E. Garcia Delgado, R. Garcia-Carretero, J. RuizGaliana, et al., Glucose time series complexity as a predictor of type 2 diabetes, Diabetes Metab. Res. Rev., 30 (2016). |
[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. |
[59] | D. Cuesta-Frau, J. P. Murillo-Escobar, D. A. Orrego and E. Delgado-Trejos, Embedded dimension and time series length. practical influence on permutation entropy and its applications, Entropy, 21 (2019). |
[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. |