Control entropy: A complexity measure for nonstationary signals

Erik M. Bollt; Joseph D. Skufca; Stephen J . McGregor; Erik M. Bollt; Joseph D. Skufca; Stephen J . McGregor

doi:10.3934/mbe.2009.6.1

Mathematical Biosciences and Engineering

2009, Volume 6, Issue 1: 1-25. doi: 10.3934/mbe.2009.6.1

Previous Article Next Article

Control entropy: A complexity measure for nonstationary signals

1.
Clarkson University, P.O. Box 5815, Potsdam, NY 13699-5815
2.
Health Prom and Human Perf, 318 Porter Bldg, Ypsilanti, MI 48197

Received: 01 March 2008 Accepted: 29 June 2018 Published: 01 December 2008
MSC : Primary: 37M25, 58F17; Secondary: 92C30

We propose an entropy statistic designed to assess the behavior of slowly varying parameters of real systems. Based on correlation entropy, the method uses symbol dynamics and analysis of increments to achieve sufficient recurrence in a short time series to enable entropy measurements on small data sets. We analyze entropy along a moving window of a time series, the entropy statistic tracking the behavior of slow variables of the data series. We employ the technique against several physiological time series to illustrate its utility in characterizing the constraints on a physiological time series. We propose that changes in the entropy of measured physiological signal (e.g. power output) during dynamic exercise will indicate changes in underlying constraint of the system of interest. This is compelling because CE may serve as a non-invasive, objective means of determining physiological stress under non-steady state conditions such as competition or acute clinical pathologies. If so, CE could serve as a valuable tool for dynamically monitoring health status in a wide range of non-stationary systems.

Keywords:

Citation: Erik M. Bollt, Joseph D. Skufca, Stephen J . McGregor. Control entropy: A complexity measure for nonstationary signals[J]. Mathematical Biosciences and Engineering, 2009, 6(1): 1-25. doi: 10.3934/mbe.2009.6.1

Related Papers:

[1]	Baohua Hu, Yong Wang, Jingsong Mu . A new fractional fuzzy dispersion entropy and its application in muscle fatigue detection. Mathematical Biosciences and Engineering, 2024, 21(1): 144-169. doi: 10.3934/mbe.2024007
[2]	Bei Liu, Hongzi Bai, Wei Chen, Huaquan Chen, Zhen Zhang . Automatic detection method of epileptic seizures based on IRCMDE and PSO-SVM. Mathematical Biosciences and Engineering, 2023, 20(5): 9349-9363. doi: 10.3934/mbe.2023410
[3]	Dae Hyeon Kim, Jin-Oh Park, Dae-Young Lee, Young-Seok Choi . Multiscale distribution entropy analysis of short epileptic EEG signals. Mathematical Biosciences and Engineering, 2024, 21(4): 5556-5576. doi: 10.3934/mbe.2024245
[4]	Ziqi Peng, Seiroh Okaneya, Hongzi Bai, Chuangxing Wu, Bei Liu, Tatsuo Shiina . Proposal of dental demineralization diagnosis with OCT echo based on multiscale entropy analysis. Mathematical Biosciences and Engineering, 2024, 21(3): 4421-4439. doi: 10.3934/mbe.2024195
[5]	Suqi Xue, Farong Gao, Xudong Wu, Qun Xu, Xuecheng Weng, Qizhong Zhang . MUNIX repeatability evaluation method based on FastICA demixing. Mathematical Biosciences and Engineering, 2023, 20(9): 16362-16382. doi: 10.3934/mbe.2023730
[6]	Bei Liu, Wenbin Tan, Xian Zhang, Ziqi Peng, Jing Cao . Recognition study of denatured biological tissues based on multi-scale rescaled range permutation entropy. Mathematical Biosciences and Engineering, 2022, 19(1): 102-114. doi: 10.3934/mbe.2022005
[7]	Rana D. Parshad, Stephen J. McGregor, Michael A. Busa, Joseph D. Skufca, Erik Bollt . A statistical approach to the use of control entropy identifies differences in constraints of gait in highly trained versus untrained runners. Mathematical Biosciences and Engineering, 2012, 9(1): 123-145. doi: 10.3934/mbe.2012.9.123
[8]	Shaojun Zhu, Jinhui Zhao, Yating Wu, Qingshan She . Intermuscular coupling network analysis of upper limbs based on R-vine copula transfer entropy. Mathematical Biosciences and Engineering, 2022, 19(9): 9437-9456. doi: 10.3934/mbe.2022439
[9]	Xuyang Xie, Zichun Yang, Lei Zhang, Guoqing Zeng, Xuefeng Wang, Peng Zhang, Guobing Chen . An improved Autogram and MOMEDA method to detect weak compound fault in rolling bearings. Mathematical Biosciences and Engineering, 2022, 19(10): 10424-10444. doi: 10.3934/mbe.2022488
[10]	Philip A. Warrick, Emily F. Hamilton . Information theoretic measures of perinatal cardiotocography synchronization. Mathematical Biosciences and Engineering, 2020, 17(3): 2179-2192. doi: 10.3934/mbe.2020116

Abstract

We propose an entropy statistic designed to assess the behavior of slowly varying parameters of real systems. Based on correlation entropy, the method uses symbol dynamics and analysis of increments to achieve sufficient recurrence in a short time series to enable entropy measurements on small data sets. We analyze entropy along a moving window of a time series, the entropy statistic tracking the behavior of slow variables of the data series. We employ the technique against several physiological time series to illustrate its utility in characterizing the constraints on a physiological time series. We propose that changes in the entropy of measured physiological signal (e.g. power output) during dynamic exercise will indicate changes in underlying constraint of the system of interest. This is compelling because CE may serve as a non-invasive, objective means of determining physiological stress under non-steady state conditions such as competition or acute clinical pathologies. If so, CE could serve as a valuable tool for dynamically monitoring health status in a wide range of non-stationary systems.

This article has been cited by:

1.	Mohit Kumar, Norbert Stoll, Kerstin Thurow, Regina Stoll, 2012, Physiological signals to individual assessment for application in wireless health systems, 978-1-4673-1591-3, 1, 10.1109/SSD.2012.6198121
2.	Michael A. Busa, Richard E.A. van Emmerik, Multiscale entropy: A tool for understanding the complexity of postural control, 2016, 5, 20952546, 44, 10.1016/j.jshs.2016.01.018
3.	W. Jeffrey Armstrong, Wavelet-based intensity analysis of mechanomyographic signals during single-legged stance following fatigue, 2011, 21, 10506411, 803, 10.1016/j.jelekin.2011.05.011
4.	Kevin Schultz, 2011, Towards agile control of ship auxiliary systems, 978-1-4244-9294-7, 154, 10.1109/ISRCS.2011.6016108
5.	Meir Russ, The probable foundations of sustainabilism: Information, energy and entropy based definition of capital, Homo Sustainabiliticus and the need for a “new gold”, 2016, 130, 09218009, 328, 10.1016/j.ecolecon.2016.07.013
6.	Mohit Kumar, Matthias Weippert, Norbert Stoll, Regina Stoll, A mixture of fuzzy filters applied to the analysis of heartbeat intervals, 2010, 9, 1568-4539, 383, 10.1007/s10700-010-9089-7
7.	Véronique Louise Billat, Florent Palacin, Matthieu Correa, Jean-Renaud Pycke, Pacing Strategy Affects the Sub-Elite Marathoner’s Cardiac Drift and Performance, 2020, 10, 1664-1078, 10.3389/fpsyg.2019.03026
8.	Jiaxiang Zhang, James B. Rowe, The neural signature of information regularity in temporally extended event sequences, 2015, 107, 10538119, 266, 10.1016/j.neuroimage.2014.12.021
9.	Mohit Kumar, Norbert Stoll, Kerstin Thurow, Regina Stoll, 2015, 978-1-4822-3658-3, 411, 10.1201/b19210-23
10.	Brian L. Cone, Daniel J. Goble, Christopher K. Rhea, Relationship between changes in vestibular sensory reweighting and postural control complexity, 2017, 235, 0014-4819, 547, 10.1007/s00221-016-4814-2
11.	David Arroyo, Roberto Latorre, Pablo Varona, Francisco B. Rodríguez, Application of symbolic dynamics to characterize coordinated activity in the context of biological neural networks, 2013, 350, 00160032, 2967, 10.1016/j.jfranklin.2013.03.018
12.	Stephen J. McGregor, Michael A. Busa, Joseph Skufca, James A. Yaggie, Erik M. Bollt, Control entropy identifies differential changes in complexity of walking and running gait patterns with increasing speed in highly trained runners, 2009, 19, 1054-1500, 026109, 10.1063/1.3147423
13.	Yifan Xing, Jun Wu, Controlling the Shannon Entropy of Quantum Systems, 2013, 2013, 1537-744X, 1, 10.1155/2013/381219
14.	A. Cammi, M. Misale, F. Devia, M.T. Cauzzi, A. Pini, L. Luzzi, Stability analysis by means of information entropy: Assessment of a novel method against natural circulation experimental data, 2017, 166, 00092509, 220, 10.1016/j.ces.2017.03.036
15.	A statistical approach to the use of control entropy identifies differences in constraints of gait in highly trained versus untrained runners, 2012, 9, 1551-0018, 123, 10.3934/mbe.2012.9.123
16.	José Valencia, Montserrat Vallverdú, Alberto Porta, reas Voss, Rafael Vázquez, Pere Caminal, 2012, 978-1-4398-4980-4, 325, 10.1201/b12756-22
17.	Mario Abundo, Enrica Pirozzi, On the Entropy of Fractionally Integrated Gauss–Markov Processes, 2020, 8, 2227-7390, 2031, 10.3390/math8112031
18.	M. Kumar, M. Weippert, D. Arndt, S. Kreuzfeld, K. Thurow, N. Stoll, R. Stoll, Fuzzy Filtering for Physiological Signal Analysis, 2010, 18, 1063-6706, 208, 10.1109/TFUZZ.2009.2038709
19.	L. A. Aguirre, C. Letellier, Nonstationarity signatures in the dynamics of global nonlinear models, 2012, 22, 1054-1500, 033136, 10.1063/1.4748852
20.	Meir Russ, 2014, Chapter 1, 978-1-349-47216-1, 1, 10.1057/9781137355720_1
21.	Nishi Shahnaj Haider, A.K. Behera, Computerized lung sound based classification of asthma and chronic obstructive pulmonary disease (COPD), 2022, 42, 02085216, 42, 10.1016/j.bbe.2021.12.004
22.	Massimiliano Zanin, Felipe Olivares, Irene Pulido-Valdeolivas, Estrella Rausell, David Gomez-Andres, Gait analysis under the lens of statistical physics, 2022, 20, 20010370, 3257, 10.1016/j.csbj.2022.06.022
23.	Karen J. Klingman, Joseph D. Skufca, Pamela W. Duncan, Dongliang Wang, George D. Fulk, Study Protocol, 2022, 71, 1538-9847, 483, 10.1097/NNR.0000000000000611
24.	Allison H. Gruber, James McDonnell, John J. Davis, Jacob E. Vollmar, Jaroslaw Harezlak, Max R. Paquette, Monitoring Gait Complexity as an Indicator for Running-Related Injury Risk in Collegiate Cross-Country Runners: A Proof-of-Concept Study, 2021, 3, 2624-9367, 10.3389/fspor.2021.630975
25.	Joshua Liddy, Michael Busa, Considerations for Applying Entropy Methods to Temporally Correlated Stochastic Datasets, 2023, 25, 1099-4300, 306, 10.3390/e25020306
26.	Sam Tilsen, Seung-Eun Kim, Claire Wang, Leonardo Lancia, Localizing category-related information in speech with multi-scale analyses, 2021, 16, 1932-6203, e0258178, 10.1371/journal.pone.0258178
27.	Adam Świtoński, Henryk Josiński, Andrzej Polański, Konrad Wojciechowski, Correlation dimension and entropy in the assessment of sex differences based on human gait data, 2024, 17, 1662-5161, 10.3389/fnhum.2023.1233859
28.	Małgorzata Andrzejewska, Tomasz Wróblewski, Szymon Cygan, Mateusz Ozimek, Monika Petelczyc, From physiological complexity to data interactions—A case study of recordings from exercise monitoring, 2024, 34, 1054-1500, 10.1063/5.0178750
29.	Rupchand Sutradhar, D. C. Dalal, Cytoplasmic recycling of rcDNA-containing capsids enhances HBV infection, 2024, 0924-090X, 10.1007/s11071-024-09681-x
30.	Kieran S. Owens, Ben D. Fulcher, Parameter inference from a non-stationary unknown process, 2024, 34, 1054-1500, 10.1063/5.0228236

Reader Comments

Your name:*

Email:*
© 2009 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)