Slope Entropy: A New Time Series Complexity Estimator Based on Both Symbolic Patterns and Amplitude Information

[EN] The development of new measures and algorithms to quantify the entropy or related concepts of a data series is a continuous effort that has brought many innovations in this regard in recent years. The ultimate goal is usually to find new methods with a higher discriminating power, more efficient, more robust to noise and artifacts, less dependent on parameters or configurations, or any other possibly desirable feature. Among all these methods, Permutation Entropy (PE) is a complexity estimator for a time series that stands out due to its many strengths, with very few weaknesses. One of these weaknesses is the PE's disregarding of time series amplitude information. Some PE algorithm modifications have been proposed in order to introduce such information into the calculations. We propose in this paper a new method, Slope Entropy (SlopEn), that also addresses this flaw but in a different way, keeping the symbolic representation of subsequences using a novel encoding method based on the slope generated by two consecutive data samples. By means of a thorough and extensive set of comparative experiments with PE and Sample Entropy (SampEn), we demonstrate that SlopEn is a very promising method with clearly a better time series classification performance than those previous methods.Cuesta Frau, D. (2019). Slope Entropy: A New Time Series Complexity Estimator Based on Both Symbolic Patterns and Amplitude Information. Entropy. 21(12):1-22. https://doi.org/10.3390/e21121167S1222112Kannathal, N., Choo, M. L., Acharya, U. R., & Sadasivan, P. K. (2005). Entropies for detection of epilepsy in EEG. Computer Methods and Programs in Biomedicine, 80(3), 187-194. doi:10.1016/j.cmpb.2005.06.012Abásolo, D., Hornero, R., Espino, P., Álvarez, D., & Poza, J. (2006). 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Permutation entropy based time series analysis: Equalities in the input signal can lead to false conclusions. Physics Letters A, 381(22), 1883-1892. doi:10.1016/j.physleta.2017.03.052Liu, T., Yao, W., Wu, M., Shi, Z., Wang, J., & Ning, X. (2017). Multiscale permutation entropy analysis of electrocardiogram. Physica A: Statistical Mechanics and its Applications, 471, 492-498. doi:10.1016/j.physa.2016.11.102Gao, 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/e19040176Azami, 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.2016.02.008Fadlallah, B., Chen, B., Keil, A., & Príncipe, 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:10.1088/1674-1056/18/7/011Cuesta–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.2019342Koski, A., Juhola, M., & Meriste, M. (1995). Syntactic recognition of ECG signals by attributed finite automata. Pattern Recognition, 28(12), 1927-1940. doi:10.1016/0031-3203(95)00052-6Koski, A. (1996). Primitive coding of structural ECG features. Pattern Recognition Letters, 17(11), 1215-1222. doi:10.1016/0167-8655(96)00079-7Lake, D. E., Richman, J. S., Griffin, M. P., & Moorman, J. R. (2002). Sample entropy analysis of neonatal heart rate variability. 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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 results¿ 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 datasets¿whereas the standard PE method only did in four¿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-García, A., Navarro-Mesa, J., Casanova-Blancas, U., Martin-Gonzalez, S., Quintana-Morales, P., Guerra-Moreno, I., … Hernández-Pérez, E. (2015). 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Description of a Portable Wireless Device for High-Frequency Body Temperature Acquisition and Analysis

We describe a device for dual channel body temperature monitoring. The device can operate as a real time monitor or as a data logger, and has Bluetooth capabilities to enable for wireless data download to the computer used for data analysis. The proposed device is capable of sampling temperature at a rate of 1 sample per minute with a resolution of 0.01 °C . The internal memory allows for stand-alone data logging of up to 10 days. The device has a battery life of 50 hours in continuous real-time mode. In addition to describing the proposed device in detail, we report the results of a statistical analysis conducted to assess its accuracy and reproducibility

Using the wavelet transform for T-wave alternans detection

[EN] This paper presents T-wave alternans (TWA) detection, applying the Wavelet Transform (WT) to electrocardiographic (ECG) synthetic signals. The TWA is generated with or without the sinusoidal addition of the wave with the required electrical level from 0.01 to 1 mV. The TWA is measured using the difference between the amplitudes of the augmented T-waves and the normal ones. (C) 2009 Elsevier Ltd. All rights reservedBoix García, M.; Cantó Colomina, B.; Cuesta Frau, D.; Micó Tormos, P. (2009). Using the wavelet transform for T-wave alternans detection. Mathematical and Computer Modelling. 50(5-6):738-742. https://doi.org/10.1016/j.mcm.2009.05.002S738742505-

Multihop Latency Model for Industrial Wireless Sensor Networks Based on Interfering Nodes

[EN] Emerging Industry 4.0 applications require ever-increasing amounts of data and new sources of information to more accurately characterize the different processes of a production line. Industrial Internet of Things (IIoT) technologies, and in particular Wireless Sensor Networks (WSNs), allow a large amount of data to be digitized at a low energy cost, thanks to their easy scalability and the creation of meshed networks to cover larger areas. In industry, data acquisition systems must meet certain reliability and robustness requirements, since other systems such as predictive maintenance or the digital twin, which represents a virtual mapping of the system with which to interact without the need to alter the actual installation, may depend on it. Thanks to the IEEE 802.15.4e standard and the use of Time-Slotted Channel Hopping (TSCH) as the medium access mechanism and IPv6 Routing Protocol for Low-Power and Lossy Networks (RPL) as the routing protocol, it is possible to deploy WSNs with high reliability, autonomy, and minimal need for re-configuration. One of the drawbacks of this communication architecture is the low efficiency of its deployment process, during which it may take a long time to synchronize and connect all the devices in a network. This paper proposes an analytical model to characterize the process for the creation of downstream routes in RPL, whose transmission of multi-hop messages can present complications in scenarios with a multitude of interfering nodes and resource allocation based on minimal IPv6 over the TSCH mode of IEEE 802.15.4e (6TiSCH). This type of multi-hop message exchange has a different behaviour than the multicast control messages exchanged during the synchronization phase and the formation of upstream routes, since the number of interfering nodes changes in each retransmission.The research leading to these results is part of the i4Q project that has received funding from the European Union's Horizon 2020 Research and Innovation Programme, under Grant Agreement No. 958205.Vera-Pérez, J.; Silvestre-Blanes, J.; Sempere Paya, VM.; Cuesta Frau, D. (2021). Multihop Latency Model for Industrial Wireless Sensor Networks Based on Interfering Nodes. Applied Sciences. 11(19):1-15. https://doi.org/10.3390/app11198790115111

Sample Entropy Analysis of Noisy Atrial Electrograms during Atrial Fibrillation

[EN] Most cardiac arrhythmias can be classified as atrial flutter, focal atrial tachycardia, or atrial fibrillation. They have been usually treated using drugs, but catheter ablation has proven more effective. This is an invasive method devised to destroy the heart tissue that disturbs correct heart rhythm. In order to accurately localise the focus of this disturbance, the acquisition and processing of atrial electrograms form the usual mapping technique. They can be single potentials, double potentials, or complex fractionated atrial electrogram (CFAE) potentials, and last ones are the most effective targets for ablation. The electrophysiological substrate is then localised by a suitable signal processing method. Sample Entropy is a statistic scarcely applied to electrograms but can arguably become a powerful tool to analyse these time series, supported by its results in other similar biomedical applications. However, the lack of an analysis of its dependence on the perturbations usually found in electrogram data, such as missing samples or spikes, is even more marked. This paper applied SampEn to the segmentation between non-CFAE and CFAE records and assessed its class segmentation power loss at different levels of these perturbations. The results confirmed that SampEn was able to significantly distinguish between non-CFAE and CFAE records, even under very unfavourable conditions, such as 50% of missing data or 10% of spikes.This research was supported by Research Center for Informatics (no. CZ.02.1.01/0.0/0.0/16-019/0000765).Cirugeda Roldan, EM.; Molina Picó, A.; Novák, D.; Cuesta Frau, D.; Kremen, V. (2018). Sample Entropy Analysis of Noisy Atrial Electrograms during Atrial Fibrillation. Computational and Mathematical Methods in Medicine. https://doi.org/10.1155/2018/1874651SAhmed, S., Claughton, A., & Gould, P. A. (2015). Atrial Flutter — Diagnosis, Management and Treatment. Abnormal Heart Rhythms. doi:10.5772/60700Kirchhof, P., & Calkins, H. (2016). Catheter ablation in patients with persistent atrial fibrillation. European Heart Journal, 38(1), 20-26. doi:10.1093/eurheartj/ehw260Nademanee, K., Lockwood, E., Oketani, N., & Gidney, B. (2010). Catheter ablation of atrial fibrillation guided by complex fractionated atrial electrogram mapping of atrial fibrillation substrate. Journal of Cardiology, 55(1), 1-12. doi:10.1016/j.jjcc.2009.11.002NG, J., & GOLDBERGER, J. J. (2007). Understanding and Interpreting Dominant Frequency Analysis of AF Electrograms. Journal of Cardiovascular Electrophysiology, 18(6), 680-685. doi:10.1111/j.1540-8167.2007.00832.xKottkamp, H., & Hindricks, G. (2007). Complex fractionated atrial electrograms in atrial fibrillation: A promising target for ablation, but why, when, and how? Heart Rhythm, 4(8), 1021-1023. doi:10.1016/j.hrthm.2007.05.011Křemen, V., Lhotská, L., Macaš, M., Čihák, R., Vančura, V., Kautzner, J., & Wichterle, D. (2008). A new approach to automated assessment of fractionation of endocardial electrograms during atrial fibrillation. Physiological Measurement, 29(12), 1371-1381. doi:10.1088/0967-3334/29/12/002Nademanee, K., McKenzie, J., Kosar, E., Schwab, M., Sunsaneewitayakul, B., Vasavakul, T., … Ngarmukos, T. (2004). A new approach for catheter ablation of atrial fibrillation: mapping of the electrophysiologic substrate. Journal of the American College of Cardiology, 43(11), 2044-2053. doi:10.1016/j.jacc.2003.12.054Scherr, D., Dalal, D., Cheema, A., Cheng, A., Henrikson, C. A., Spragg, D., … Dong, J. (2007). Automated detection and characterization of complex fractionated atrial electrograms in human left atrium during atrial fibrillation. Heart Rhythm, 4(8), 1013-1020. doi:10.1016/j.hrthm.2007.04.021Almeida, T. P., Chu, G. S., Salinet, J. L., Vanheusden, F. J., Li, X., Tuan, J. H., … Schlindwein, F. S. (2016). Minimizing discordances in automated classification of fractionated electrograms in human persistent atrial fibrillation. Medical & Biological Engineering & Computing, 54(11), 1695-1706. doi:10.1007/s11517-016-1456-2Molina-Picó, A., Cuesta-Frau, D., Aboy, M., Crespo, C., Miró-Martínez, P., & Oltra-Crespo, S. (2011). Comparative study of approximate entropy and sample entropy robustness to spikes. Artificial Intelligence in Medicine, 53(2), 97-106. doi:10.1016/j.artmed.2011.06.007Cuesta–Frau, D., Miró–Martínez, P., Jordán Núñez, J., Oltra–Crespo, S., & Molina Picó, A. (2017). Noisy EEG signals classification based on entropy metrics. Performance assessment using first and second generation statistics. Computers in Biology and Medicine, 87, 141-151. doi:10.1016/j.compbiomed.2017.05.028Demont-Guignard, S., Benquet, P., Gerber, U., & Wendling, F. (2009). Analysis of Intracerebral EEG Recordings of Epileptic Spikes: Insights From a Neural Network Model. IEEE Transactions on Biomedical Engineering, 56(12), 2782-2795. doi:10.1109/tbme.2009.2028015Molina–Picó, A., Cuesta–Frau, D., Miró–Martínez, P., Oltra–Crespo, S., & Aboy, M. (2013). Influence of QRS complex detection errors on entropy algorithms. Application to heart rate variability discrimination. Computer Methods and Programs in Biomedicine, 110(1), 2-11. doi:10.1016/j.cmpb.2012.10.014Ganesan, P., Cherry, E. M., Pertsov, A. M., & Ghoraani, B. (2015). Characterization of Electrograms from Multipolar Diagnostic Catheters during Atrial Fibrillation. BioMed Research International, 2015, 1-9. doi:10.1155/2015/272954Lake, D. E., Richman, J. S., Griffin, M. P., & Moorman, J. R. (2002). Sample entropy analysis of neonatal heart rate variability. American Journal of Physiology-Regulatory, Integrative and Comparative Physiology, 283(3), R789-R797. doi:10.1152/ajpregu.00069.2002Kim, K. K., Baek, H. J., Lim, Y. G., & Park, K. S. (2012). Effect of missing RR-interval data on nonlinear heart rate variability analysis. Computer Methods and Programs in Biomedicine, 106(3), 210-218. doi:10.1016/j.cmpb.2010.11.011Richman, J. S., & Moorman, J. R. (2000). Physiological time-series analysis using approximate entropy and sample entropy. American Journal of Physiology-Heart and Circulatory Physiology, 278(6), H2039-H2049. doi:10.1152/ajpheart.2000.278.6.h2039Cirugeda–Roldán, E., Novak, D., Kremen, V., Cuesta–Frau, D., Keller, M., Luik, A., & Srutova, M. (2015). Characterization of Complex Fractionated Atrial Electrograms by Sample Entropy: An International Multi-Center Study. Entropy, 17(12), 7493-7509. doi:10.3390/e17117493PORTER, M., SPEAR, W., AKAR, J. G., HELMS, R., BRYSIEWICZ, N., SANTUCCI, P., & WILBER, D. J. (2008). Prospective Study of Atrial Fibrillation Termination During Ablation Guided by Automated Detection of Fractionated Electrograms. Journal of Cardiovascular Electrophysiology, 19(6), 613-620. doi:10.1111/j.1540-8167.2008.01189.xKonings, K. T., Kirchhof, C. J., Smeets, J. R., Wellens, H. J., Penn, O. C., & Allessie, M. A. (1994). High-density mapping of electrically induced atrial fibrillation in humans. Circulation, 89(4), 1665-1680. doi:10.1161/01.cir.89.4.1665Fay, M. P., & Proschan, M. A. (2010). Wilcoxon-Mann-Whitney or t-test? On assumptions for hypothesis tests and multiple interpretations of decision rules. Statistics Surveys, 4(0), 1-39. doi:10.1214/09-ss051Richman, J. S. (2007). Sample Entropy Statistics and Testing for Order in Complex Physiological Signals. Communications in Statistics - Theory and Methods, 36(5), 1005-1019. doi:10.1080/03610920601036481Pincus, S. M., Gladstone, I. M., & Ehrenkranz, R. A. (1991). A regularity statistic for medical data analysis. Journal of Clinical Monitoring, 7(4), 335-345. doi:10.1007/bf01619355Alcaraz, R., & Rieta, J. J. (2009). Non-invasive organization variation assessment in the onset and termination of paroxysmal atrial fibrillation. Computer Methods and Programs in Biomedicine, 93(2), 148-154. doi:10.1016/j.cmpb.2008.09.001Alcaraz, R., Abásolo, D., Hornero, R., & Rieta, J. J. (2010). Optimal parameters study for sample entropy-based atrial fibrillation organization analysis. Computer Methods and Programs in Biomedicine, 99(1), 124-132. doi:10.1016/j.cmpb.2010.02.009Costa, M., Goldberger, A. L., & Peng, C.-K. (2002). Multiscale Entropy Analysis of Complex Physiologic Time Series. Physical Review Letters, 89(6). doi:10.1103/physrevlett.89.06810

Development of a novel scheme for long-term body temperature monitoring: a review of benefits and applications

Body temperature is a health or disease marker that has been in clinical use for centuries. The threshold currently applied to define fever, with small variations, is 38 °C. However, current approaches do not provide a full picture of the thermoregulation process and its correlation with disease. This paper describes a new non-invasive body temperature device that improves the understanding of the pathophysiology of diseases by integrating a variety of temperature data from different body locations. This device enables to gain a deeper insight into fever, endogenous rhythms, subject activity and ambient temperature to provide anticipatory and more efficient treatments. Its clinical use would be a big step in the overcoming of the anachronistic febrile/afebrile dichotomy and walking towards a system medicine approach to certain diseases. This device has already been used in some clinical applications successfully. Other possible applications based on the device features and clinical requirements are also described in this paper.Cuesta Frau, D.; Varela Entrecanales, M.; Valor Pérez, R.; Vargas, B. (2015). Development of a novel scheme for long-term body temperature monitoring: a review of benefits and applications. Journal of Medical Systems. 39(4):1-7. doi:10.1007/s10916-015-0209-3S17394Gai, M., Merlo, I., Dellepiane, S., Cantaluppi, V., Leonardi, G., Fop, F., Guarena, C., Grassi, G., and Biancore, L., Glycemic pattern in diabetic patients on hemodialysis: Continuous Glucose Monitoring (CGM) analysis. Blood Purif. 38(1):68–73 , 2014.Kondziella, D., Friberg, C.K., Wellwood, I., Reiffurth, C., Fabricius, M., and Dreier, J.P.: Continuous EEG monitoring in aneurysmal subarachnoid hemorrhage: A systematic review. Neurocrit. Care (2014)Ciccone, A., Celani, M.G., Chiaramonte, R., Rossi, C., and Righetti, E., Continuous versus intermittent physiological monitoring for acute stroke. Cochrane Database Syst. Rev. 31, 2013.Kushimoto, S., Yamanouchi, S., Endo, T., Sato, T., Nomura, R., Fujita, M., Kudo, D., Omura, T., Miyagawa, N., and Sato, T., Body temperature abnormalities in non-neurological critically ill patients: A review of the literature. J. Intensive Care 2, 2014.Mc Callum, L., and Higgings, D., Measuring body temperature. Nursing Times 108:20–22, 2012.Varela, M., Ruiz-Esteban, R., Martinez-Nicolas, A., Cuervo-Arango, A., Barros, C., and Delgado, E.G., Catching the spike and tracking the flow: Holter-temperature monitoring in patients admitted in a general internal medicine ward. Int. J. Clin. Pract. 65(12):1283–1288, 2011.Lopes, F., Peres, D., Bross, A., Melot, C., and Vincent, J.L., Serial evaluation of the SOFA score to predict outcome in critically ill patients. J. Am. Med. Assoc. 286:1754–1758, 2001.Vincent, J.L., and Moreno, R., Clinical review: Scoring systems in the critically ill. Crit. Care, 14, 2010.Sund-Levander, M., and Grodzinsky, E., Time for a change to assess and evaluate body temperature in clinical practice. Int. J. Nurs. Pract. 15:241–249, 2009.Cuesta-Frau, D., Varela, M., Aboy, M., and Miro, P., Description of a portable wireless device for body temperature acquisition and analysis. Sensors 9(10):7648–7663, 2009.Varela, M., Cuesta-Frau, D., Madrid, J.A., Churruca, J., Miro-Matinez, P., Ruiz, R., and Marinez, C., Holter monitoring of central peripheral temperature: Possible uses and feasibility study in outpatient settings. J. Clin. Monit. Comput. 4(23):209–216, 2009.Jordan, J., Miro, P., Cuesta-Frau, D., Varela, M., and Vargas B.: Aplicacion de analisis multivariante para la deteccion de estados prefebriles en pacientes ingresados (in Spanish), XXXIV Congreso Nacional de Estadistica e Investigacion Operativa, Castellon (Spain) (2013)Richman, J., and Moorman, J.R., Physiological time-series analysis using approximate entropy and sample entropy. Am. J. Physiol. Heart Circ. Physiol. 278(6):H2039–2049, 2000.Young, P., Saxena, M., Eastwood, G.M., Bellomo, R., and Beasley, R., Fever and fever management among intensive care patients with known or suspected infection: A multicentre prospective cohort study. Crit. Care Resusc. 13:97–102 , 2011.Drewry, A.M., Fuller, B.M., Bailey, T.C., and Hotchkiss, R.S., Body temperature patterns as a predictor of hospital-acquired sepsis in afebrile adult intensive care unit patients: A case-control study. Crit. Care,17, 2013.Musher, D., Fainstein, V., Young, E., and Pruett, T., Fever patterns. Their lack of significance. Arch. Intern. Med. 139(11):1225–8, 1979.Varela, M., Calvo, M., Chana, M., Gomez-Mestre, I., Asensio, R., and Galdos, P., Clinical implications of temperature curve complexity in critically ill patients. Crit. Care Med. 33(12):2764–2771, 2005.Varela, M., Churruca, J., Gonzalez, A., Martin, A., Ode, J., and Galdos, P., Temperature curve complexity predicts survival in critically ill patients. Am. J. Respir. Crit. Care Med. 174(3):290–298, 2006.Cuesta-Frau, D., Varela, M., Miro, P., Galdos, P., Abasolo, D., Hornero, R., and Aboy, M., Predicting survival in critical patients by use of body temperature regularity measurement based on Approximate Entropy. Med. Biol. Eng. Computing 45:671–678, 2007.Mackiowak, P. Temperature regulation and the pathogenesis of fever, Principles and Practice of Infectious Diseases, pp. 765–778. New York: Churchill Livingston Elsevier, 2010.Cherbuin N., and Brinkman C., Cognition is cool: Can hemispheric activation be assessed by tympanic membrane thermometry? Brain Cogn. 54:228–231, 2004

Noisy EEG signals classification based on entropy metrics. Performance assessment using first and second generation statistics

[EN] This paper evaluates the performance of first generation entropy metrics, featured by the well known and widely used Approximate Entropy (ApEn) and Sample Entropy (SampEn) metrics, and what can be considered an evolution from these, Fuzzy Entropy (FuzzyEn), in the Electroencephalogram (EEG) signal classification context. The study uses the commonest artifacts found in real EEGs, such as white noise, and muscular, cardiac, and ocular artifacts. Using two different sets of publicly available EEG records, and a realistic range of amplitudes for interfering artifacts, this work optimises and assesses the robustness of these metrics against artifacts in class segmentation terms probability. The results show that the qualitative behaviour of the two datasets is similar, with SampEn and FuzzyEn performing the best, and the noise and muscular artifacts are the most confounding factors. On the contrary, there is a wide variability as regards initialization parameters. The poor performance achieved by ApEn suggests that this metric should not be used in these contexts.Cuesta Frau, D.; Miró Martínez, P.; Jordán Núñez, J.; Oltra Crespo, S.; Molina Picó, A. (2017). Noisy EEG signals classification based on entropy metrics. Performance assessment using first and second generation statistics. Computers in Biology and Medicine. 87:141-151. doi:10.1016/j.compbiomed.2017.05.028S1411518

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. 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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. 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Classification of glucose records from patients at diabetes risk using a combined permutation entropy algorithm

[EN] Background and objectives : The adoption in clinical practice of electronic portable blood or interstitial glucose monitors has enabled the collection, storage, and sharing of massive amounts of glucose level readings. This availability of data opened the door to the application of a multitude of mathematical methods to extract clinical information not discernible with conventional visual inspection. The objective of this study is to assess the capability of Permutation Entropy (PE) to find differences between glucose records of healthy and potentially diabetic subjects. Methods : PE is a mathematical method based on the relative frequency analysis of ordinal patterns in time series that has gained a lot of attention in the last years due to its simplicity, robustness, and per- formance. We study in this paper the applicability of this method to glucose records of subjects at risk of diabetes in order to assess the predictability value of this metric in this context. Results : PE, along with some of its derivatives, was able to find significant differences between diabetic and non¿diabetic patients from records acquired up to 3 years before the diagnosis. The quantitative results for PE were 3.5878 ±0.3916 for the nondiabetic class, and 3.1564 ±0.4166 for the diabetic class. With a classification accuracy higher than 70%, and by means of a Cox regression model, PE demonstrated that it is a very promising candidate as a risk stratification tool for continuous glucose monitoring. Conclusion : PE can be considered as a prospective tool for the early diagnosis of the glucoregulatory system.Cuesta Frau, D.; Miró Martínez, P.; Oltra Crespo, S.; Jordán Núñez, J.; Vargas-Rojo, B.; Vigil-Medina, 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. https://doi.org/10.1016/j.cmpb.2018.08.018S19720416