Search Advanced

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 6: 6842-6857. doi: 10.3934/mbe.2019342
Previous Article Next Article
Research article Special Issues

Permutation entropy: Influence of amplitude information on time series classification performance

  • Technological Institute of Informatics(ITI), Universitat Politècnica de València, Campus Alcoi, Plaza Ferrándiz y Carbonell, 2, 03801, Alcoi, Spain
  • Received: 08 April 2019 Accepted: 07 July 2019 Published: 26 July 2019

  • Permutation Entropy (PE) is a very popular complexity analysis tool for time series. De-spite its simplicity, it is very robust and yields goods results in applications related to assessing the randomness of a sequence, or as a quantitative feature for signal classification. It is based on com-puting the Shannon entropy of the relative frequency of all the ordinal patterns found in a time series. However, there is a basic consensus on the fact that only analysing sample order and not amplitude might have a detrimental effect on the performance of PE. As a consequence, a number of methods based on PE have been proposed in the last years to include the possible influence of sample ampli-tude. These methods claim to outperform PE but there is no general comparative analysis that confirms such claims independently. Furthermore, other statistics such as Sample Entropy (SampEn) are based solely on amplitude, and it could be argued that other tools like this one are better suited to exploit the amplitude differences than PE. The present study quantifies the performance of the standard PE method and other amplitude–included PE methods using a disparity of time series to find out if there are really significant performance differences. In addition, the study compares statistics based uniquely on ordinal or amplitude patterns. The objective was to ascertain whether the whole was more than the sum of its parts. The results confirmed that highest classification accuracy was achieved using both types of patterns simultaneously, instead of using standard PE (ordinal patterns), or SampEn (ampli-tude patterns) isolatedly.

    Citation: David Cuesta–Frau. Permutation entropy: Influence of amplitude information on time series classification performance[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 6842-6857. doi: 10.3934/mbe.2019342

    Related Papers:

  • Permutation Entropy (PE) is a very popular complexity analysis tool for time series. De-spite its simplicity, it is very robust and yields goods results in applications related to assessing the randomness of a sequence, or as a quantitative feature for signal classification. It is based on com-puting the Shannon entropy of the relative frequency of all the ordinal patterns found in a time series. However, there is a basic consensus on the fact that only analysing sample order and not amplitude might have a detrimental effect on the performance of PE. As a consequence, a number of methods based on PE have been proposed in the last years to include the possible influence of sample ampli-tude. These methods claim to outperform PE but there is no general comparative analysis that confirms such claims independently. Furthermore, other statistics such as Sample Entropy (SampEn) are based solely on amplitude, and it could be argued that other tools like this one are better suited to exploit the amplitude differences than PE. The present study quantifies the performance of the standard PE method and other amplitude–included PE methods using a disparity of time series to find out if there are really significant performance differences. In addition, the study compares statistics based uniquely on ordinal or amplitude patterns. The objective was to ascertain whether the whole was more than the sum of its parts. The results confirmed that highest classification accuracy was achieved using both types of patterns simultaneously, instead of using standard PE (ordinal patterns), or SampEn (ampli-tude patterns) isolatedly.


    加载中


    [1] R. Alcaraz, D. Abásolo, R. Hornero, et al., Study of Sample Entropy ideal computational pa-rameters in the estimation of atrial fibrillation organization from the ECG, in 2010 Computing in Cardiology, 2010, 1027–1030.
    [2] R. G. Andrzejak, K. Lehnertz, F. Mormann, et al., 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.
    [3] K. N. Aronis, R. D. Berger, H. Calkins, et al., Is human atrial fibrillation stochastic or determinis-tic? Insights from missing ordinal patterns and causal entropy–complexity plane analysis, Chaos, 28 (2018), 063130.
    [4] H. Azami and J. Escudero, Amplitude-aware permutation entropy: Illustration in spike detection and signal segmentation, Comput. Meth. Prog. Bio., 128 (2016), 40–51.
    [5] A. Bagnall, J. Lines, A. Bostrom, et al., The great time series classification bake off: A review and experimental evaluation of recent algorithmic advances, Data Min. Knowl. Disc., 31 (2017), 606–660.
    [6] C. Bandt and B. Pompe, Permutation entropy: A natural complexity measure for time series, Phys. Rev. Lett., 88 (2002), 174102.
    [7] C. Bian, C. Qin, Q. D. Y. Ma, et al., Modified Permutation-entropy analysis of heartbeat dynamics, Phys. Rev. E, 85 (2012), 021906.
    [8] A. E. X. Brown, E. I. Yemini, L. J. Grundy, et al., A dictionary of behavioral motifs reveals clusters of genes affecting caenorhabditis elegans locomotion, Proceed. Nat. Aca. Sci., 110 (2013), 791–796.
    [9] C. Carricarte-Naranjo, D. J. Cornforth, L. M. Sánchez-Rodríguez, et al., Rényi and permutation entropy analysis for assessment of cardiac autonomic neuropathy, in EMBEC & NBC 2017 (eds. H. Eskola, O. Väisänen, J. Viik and J. Hyttinen), Springer Singapore, Singapore, 2018, 755–758.
    [10] E. Cirugeda-Roldán, D. Cuesta-Frau, P. Miró-Martínez, et al., A new algorithm for quadratic sample entropy optimization for very short biomedical signals: Application to blood pressure records, Comput. Meth. Prog. Bio., 114 (2014), 231–239.
    [11] E. Cirugeda-Roldán, D. Novák, V. Kremen, et al., Characterization of complex fractionated atrial electrograms by Sample Entropy: An international multi–center study, Entropy, 17 (2015), 7493–7509.
    [12] D. Cuesta-Frau, P. Miró-Martínez, S. Oltra-Crespo, et al., Classification of glucose records from patients at diabetes risk using a combined permutation entropy algorithm, Comput. Meth. Prog. Bio., 165 (2018), 197–204.
    [13] D. Cuesta-Frau, P. Miró-Martínez, S. Oltra-Crespo, et al., Model selection for body temperature signal classification using both amplitude and ordinality-based entropy measures, Entropy, 20.
    [14] D. Cuesta-Frau, D. Novák, V. Burda, et al., Characterization of artifact influence on the classifi-cation of glucose time series using sample entropy statistics, Entropy, 20.
    [15] D. Cuesta-Frau, M. Varela-Entrecanales, A. Molina-Picó, et al., Patterns with equal values in permutation entropy: Do they really matter for biosignal classification?, Complexity, 2018 (2018), 1–15.
    [16] B. Deng, L. Cai, S. Li, et al., Multivariate multi-scale weighted Permutation Entropy analysis of EEG complexity for Alzheimer's disease, Cogn. Neurodynamics, 11 (2017), 217–231.
    [17] B. Fadlallah, B. Chen, A. Keil, et al., Weighted-permutation entropy: A complexity measure for time series incorporating amplitude information, Phys. Rev. E, 87 (2013), 022911.
    [18] Y. Gao, F. Villecco, M. Li, et al., Multi-scale permutation entropy based on improved LMD and HMM for rolling bearing diagnosis, Entropy, 19.
    [19] J. Garland, T. R. Jones, M. Neuder, et al., Anomaly detection in paleoclimate records using permutation entropy, Entropy, 20.
    [20] A. L. Goldberger, L. A. N. Amaral, L. Glass, et al., PhysioBank, PhysioToolkit, and PhysioNet: Components of a new research resource for complex physiologic signals, Circulation, 101 (2000), 215–220.
    [21] M. Henry and G. Judge, Permutation entropy and information recovery in nonlinear dynamic economic time series, Econometrics, 7.
    [22] N. Iyengar, C. K. Peng, R. Morin, et al., Age-related alterations in the fractal scaling of cardiac interbeat interval dynamics, Am. J. Physiol. Integrat. Comparat. Physiol., 271 (1996), R1078–R1084, PMID: 8898003.
    [23] D. E. Lake, J. S. Richman, M. P. Griffin, et al., Sample entropy analysis of neonatal heart rate variability, Am. J. Physiol. Integrat. Comparat. Physiol., 283 (2002), R789–R797.
    [24] H. Li, C. Peng and D. Ye, A study of sleep staging based on a sample entropy analysis of electroencephalogram, Bio-Med. Mater. Eng., 26 (2015), S1149–S1156.
    [25] G. B. Moody, A. L. Goldberger, S. McClennenm, et al., Predicting the onset of Paroxysmal Atrial Fibrillation: The Computers in Cardiology Challenge 2001, Comput. Cardiol., 28 (2011), 113–116.
    [26] D. Murray, J. Liao, L. Stankovic, et al., A data management platform for personalised real-time energy feedback, in Procededings of the 8th International Conference on Energy Efficiency in Domestic Appliances and Lighting, 2015.
    [27] N. Nicolaou and J. Georgiou, The use of permutation entropy to characterize sleep electroen-cephalograms, Clin. EEG Neurosci., 42 (2011), 24–28, PMID: 21309439.
    [28] E. Olofsen, J. Sleigh and A. Dahan, Permutation entropy of the electroencephalogram: A measure of anaesthetic drug effect, Br. J. Anaesth., 101 (2008), 810–821.
    [29] A. G. Ravelo-García, J. L. Navarro-Mesa, Casanova-Blancas, et al., Application of the permuta-tion entropy over the heart rate variability for the improvement of electrocardiogram-based sleep breathing pause detection, Entropy, 17 (2015), 914–927.
    [30] J. S. Richman, Sample entropy statistics and testing for order in complex physiological signals, Commun. Stat. Theor. M., 36 (2007), 1005–1019.
    [31] M. O. Sokunbi, Sample entropy reveals high discriminative power between young and elderly adults in short fMRI data sets, Front. Neuroinform., 8 (2014), 69.
    [32] X. Wang, S. Si, Y. Wei, et al., The optimized multi-scale permutation entropy and its application in compound fault diagnosis of rotating machinery, Entropy, 21.
    [33] Y. Xia, L. Yang, L. Zunino, et al., Application of permutation entropy and permutation min-entropy in multiple emotional states analysis of RRI time series, Entropy, 20 (2018), 148.
    [34] X. F. Liu and Y. Wang, Fine-grained permutation entropy as a measure of natural complexity for time series, Chinese Phys. B, 18 (2009), 2690.
    [35] Y. Yang, M. Zhou, Y. Niu, et al., Epileptic seizure prediction based on permutation entropy, in Front. Comput. Neurosci., 2018.
    [36] E. Yemini, T. Jucikas, L. J. Grundy, et al., A database of caenorhabditis elegans behavioral phenotypes, Nat. Meth., 10 (2013), 877–879.
    [37] M. Zanin, D. Gómez-Andrés, I. Pulido-Valdeolivas, et al., Characterizing normal and pathological gait through permutation entropy, Entropy, 20.
    [38] M. Zanin, L. Zunino, O. A. Rosso, et al., Permutation entropy and its main biomedical and econophysics applications: A review, Entropy, 14 (2012), 1553–1577.
    [39] Y. Zhang and P. Shang, Permutation entropy analysis of financial time series based on hills diversity number, Commun. Nonlinear Sci. Numer. Simul., 53 (2017), 288–298.
    [40] L. Zunino and C. W. Kulp, Detecting nonlinearity in short and noisy time series using the permu-tation entropy, Phys. Lett. A, 381 (2017), 3627–3635.
    [41] L. Zunino, F. Olivares, F. Scholkmann, et al., Permutation entropy based time series analysis: Equalities in the input signal can lead to false conclusions, Phys. Lett. A, 381 (2017), 1883–1892.
    [42] L. Zunino, M. Zanin, B. M. Tabak, et al., Forbidden patterns, permutation entropy and stock market inefficiency, Physica A, 388 (2009), 2854–2864.
  • Reader Comments
  • © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
3.9

Metrics

Article views(5036) PDF downloads(676) Cited by(20)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Figures(1)  /  Tables(8)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog