{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:46:59Z","timestamp":1760237219975,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,3,11]],"date-time":"2020-03-11T00:00:00Z","timestamp":1583884800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/N509644\/1 2107746"],"award-info":[{"award-number":["EP\/N509644\/1 2107746"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000265","name":"Medical Research Council","doi-asserted-by":"publisher","award":["MR\/R004498\/1"],"award-info":[{"award-number":["MR\/R004498\/1"]}],"id":[{"id":"10.13039\/501100000265","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Entropy quantification algorithms are becoming a prominent tool for the physiological monitoring of individuals through the effective measurement of irregularity in biological signals. However, to ensure their effective adaptation in monitoring applications, the performance of these algorithms needs to be robust when analysing time-series containing missing and outlier samples, which are common occurrence in physiological monitoring setups such as wearable devices and intensive care units. This paper focuses on augmenting Dispersion Entropy (DisEn) by introducing novel variations of the algorithm for improved performance in such applications. The original algorithm and its variations are tested under different experimental setups that are replicated across heart rate interval, electroencephalogram, and respiratory impedance time-series. Our results indicate that the algorithmic variations of DisEn achieve considerable improvements in performance while our analysis signifies that, in consensus with previous research, outlier samples can have a major impact in the performance of entropy quantification algorithms. Consequently, the presented variations can aid the implementation of DisEn to physiological monitoring applications through the mitigation of the disruptive effect of missing and outlier samples.<\/jats:p>","DOI":"10.3390\/e22030319","type":"journal-article","created":{"date-parts":[[2020,3,12]],"date-time":"2020-03-12T04:13:57Z","timestamp":1583986437000},"page":"319","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Augmentation of Dispersion Entropy for Handling Missing and Outlier Samples in Physiological Signal Monitoring"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9599-7656","authenticated-orcid":false,"given":"Evangelos","family":"Kafantaris","sequence":"first","affiliation":[{"name":"School of Engineering, Institute for Digital Communications, University of Edinburgh, Edinburgh EH9 3FB, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1434-6347","authenticated-orcid":false,"given":"Ian","family":"Piper","sequence":"additional","affiliation":[{"name":"MRC Centre for Reproductive Health, Department of Child Life and Health, University of Edinburgh, Edinburgh EH9 1UW, UK"},{"name":"Royal Hospital for Sick Children, NHS Lothian, Edinburgh EH9 1LF, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0701-6534","authenticated-orcid":false,"given":"Tsz-Yan Milly","family":"Lo","sequence":"additional","affiliation":[{"name":"Royal Hospital for Sick Children, NHS Lothian, Edinburgh EH9 1LF, UK"},{"name":"Usher Institute, Edinburgh Medical School, University of Edinburgh, Edinburgh EH16 4UX, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2105-8725","authenticated-orcid":false,"given":"Javier","family":"Escudero","sequence":"additional","affiliation":[{"name":"School of Engineering, Institute for Digital Communications, University of Edinburgh, Edinburgh EH9 3FB, UK"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.cobme.2019.01.001","article-title":"Windows into human health through wearables data analytics","volume":"9","author":"Witt","year":"2019","journal-title":"Curr. Opin. Biomed. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1002\/jhm.2520","article-title":"Systematic Review of Physiologic Monitor Alarm Characteristics and Pragmatic Interventions to Reduce Alarm Frequency: Review of Physiologic Monitor Alarms","volume":"11","author":"Paine","year":"2016","journal-title":"J. Hosp. Med."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1016\/j.future.2019.02.015","article-title":"Missing data resilient decision-making for healthcare IoT through personalization: A case study on maternal health","volume":"96","author":"Azimi","year":"2019","journal-title":"Future Gener. Comput. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"532","DOI":"10.1093\/jamia\/ocv206","article-title":"Automated integration of continuous glucose monitor data in the electronic health record using consumer technology","volume":"23","author":"Kumar","year":"2016","journal-title":"J. Am. Med Inform. Assoc."},{"key":"ref_5","unstructured":"Moody, G.B. (2010, January 26\u201329). The PhysioNet\/Computing in Cardiology Challenge 2010: Mind the Gap. Proceedings of the Computing in Cardiology, Belfast, UK."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1177\/193229681300700324","article-title":"\u201cTurn it Off!\u201d: Diabetes Device Alarm Fatigue Considerations for the Present and the Future","volume":"7","author":"Shivers","year":"2013","journal-title":"J. Diabetes Sci. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"588","DOI":"10.1016\/j.jelectrocard.2012.08.050","article-title":"Clinical alarm hazards: A \u201ctop ten\u201d health technology safety concern","volume":"45","author":"Keller","year":"2012","journal-title":"J. Electrocardiol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1016\/j.clp.2017.05.005","article-title":"Alarm Safety and Alarm Fatigue","volume":"44","author":"Johnson","year":"2017","journal-title":"Clin. Perinatol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1002\/j.1538-7305.1948.tb00917.x","article-title":"A Mathematical Theory of Communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2297","DOI":"10.1073\/pnas.88.6.2297","article-title":"Approximate entropy as a measure of system complexity","volume":"88","author":"Pincus","year":"1991","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"H2039","DOI":"10.1152\/ajpheart.2000.278.6.H2039","article-title":"Physiological time-series analysis using approximate entropy and sample entropy","volume":"278","author":"Richman","year":"2000","journal-title":"Am. J. Physiol.-Heart Circ. Physiol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"174102","DOI":"10.1103\/PhysRevLett.88.174102","article-title":"Permutation Entropy: A Natural Complexity Measure for Time Series","volume":"88","author":"Bandt","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1109\/TNSRE.2007.897025","article-title":"Characterization of Surface EMG Signal Based on Fuzzy Entropy","volume":"15","author":"Chen","year":"2007","journal-title":"IEEE Trans. Neural Syst. Rehabil. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1109\/LSP.2016.2542881","article-title":"Dispersion Entropy: A Measure for Time-Series Analysis","volume":"23","author":"Rostaghi","year":"2016","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1176\/appi.ajp.161.1.79","article-title":"Approximate Entropy of Respiratory Patterns in Panic Disorder","volume":"161","author":"Caldirola","year":"2004","journal-title":"Am. J. Psychiatry"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"R789","DOI":"10.1152\/ajpregu.00069.2002","article-title":"Sample entropy analysis of neonatal heart rate variability","volume":"283","author":"Lake","year":"2002","journal-title":"Am. J. Physiol.-Regul. Integr. Comp. Physiol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"810","DOI":"10.1093\/bja\/aen290","article-title":"Permutation entropy of the electroencephalogram: A measure of anaesthetic drug effect","volume":"101","author":"Olofsen","year":"2008","journal-title":"Br. J. Anaesth."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"5901","DOI":"10.3390\/e16115901","article-title":"Comparative Study of Entropy Sensitivity to Missing Biosignal Data","volume":"16","year":"2014","journal-title":"Entropy"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Dong, X., Chen, C., Geng, Q., Cao, Z., Chen, X., Lin, J., Jin, Y., Zhang, Z., Shi, Y., and Zhang, X.D. (2019). An Improved Method of Handling Missing Values in the Analysis of Sample Entropy for Continuous Monitoring of Physiological Signals. Entropy, 21.","DOI":"10.3390\/e21030274"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1109\/TBME.2008.2005951","article-title":"Errors in the Estimation of Approximate Entropy and Other Recurrence-Plot-Derived Indices Due to the Finite Resolution of RR Time Series","volume":"56","year":"2009","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.artmed.2011.06.007","article-title":"Comparative study of approximate entropy and sample entropy robustness to spikes","volume":"53","author":"Aboy","year":"2011","journal-title":"Artif. Intell. Med."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Azami, H., and Escudero, J. (2018). Amplitude- and Fluctuation-Based Dispersion Entropy. Entropy, 20.","DOI":"10.3390\/e20030210"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/j.jsv.2018.08.025","article-title":"Application of dispersion entropy to status characterization of rotary machines","volume":"438","author":"Rostaghi","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.cmpb.2010.11.011","article-title":"Effect of missing RR-interval data on nonlinear heart rate variability analysis","volume":"106","author":"Kim","year":"2012","journal-title":"Comput. Methods Programs Biomed."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1273","DOI":"10.1080\/01621459.1993.10476408","article-title":"Alternatives to the Median Absolute Deviation","volume":"88","author":"Rousseeuw","year":"1993","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"764","DOI":"10.1016\/j.jesp.2013.03.013","article-title":"Detecting outliers: Do not use standard deviation around the mean, use absolute deviation around the median","volume":"49","author":"Leys","year":"2013","journal-title":"J. Exp. Soc. Psychol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.jcrc.2003.08.005","article-title":"Heart rate variability as early marker of multiple organ dysfunction syndrome in septic patients","volume":"18","author":"Pontet","year":"2003","journal-title":"J. Crit. Care"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/j.jelectrocard.2010.11.014","article-title":"Wearable wireless heart rate monitor for continuous long-term variability studies","volume":"44","author":"Augustyniak","year":"2011","journal-title":"J. Electrocardiol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"R1078","DOI":"10.1152\/ajpregu.1996.271.4.R1078","article-title":"Age-related alterations in the fractal scaling of cardiac interbeat interval dynamics","volume":"271","author":"Iyengar","year":"1996","journal-title":"Am. J. Physiol.-Regul. Integr. Comp. Physiol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"e215","DOI":"10.1161\/01.CIR.101.23.e215","article-title":"PhysioBank, PhysioToolkit, and PhysioNet: Components of a New Research Resource for Complex Physiologic Signals","volume":"101","author":"Goldberger","year":"2000","journal-title":"Circulation"},{"key":"ref_31","unstructured":"Shoeb, A.H. (2009). Application of Machine Learning to Epileptic Seizure Onset Detection and Treatment. [Ph.D. Thesis, Harvard University\u2013MIT Division of Health Sciences and Technology]."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1914","DOI":"10.1109\/TBME.2016.2613124","article-title":"Toward a Robust Estimation of Respiratory Rate From Pulse Oximeters","volume":"64","author":"Pimentel","year":"2017","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Kafantaris, E., Piper, I., Lo, T.Y.M., and Escudero, J. (2019, January 23\u201327). Application of Dispersion Entropy to Healthy and Pathological Heartbeat ECG Segments. Proceedings of the 2019 41st Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Berlin, Germany.","DOI":"10.1109\/EMBC.2019.8856554"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1007\/s11517-006-0119-0","article-title":"Heart rate variability: A review","volume":"44","author":"Kannathal","year":"2006","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/BF02368321","article-title":"Assessment of time-domain analyses for estimation of low-frequency respiratory mechanical properties and impedance spectra","volume":"23","author":"Kaczka","year":"1995","journal-title":"Ann. Biomed. Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1109\/memb.2007.289121","article-title":"Modeling Human Respiratory Impedance","volume":"26","author":"Diong","year":"2007","journal-title":"IEEE Eng. Med. Biol. Mag."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"806","DOI":"10.1093\/bja\/aeh270","article-title":"Awareness and the EEG power spectrum: Analysis of frequencies","volume":"93","author":"Dressler","year":"2004","journal-title":"Br. J. Anaesth."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/3\/319\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:06:10Z","timestamp":1760173570000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/3\/319"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,11]]},"references-count":37,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,3]]}},"alternative-id":["e22030319"],"URL":"https:\/\/doi.org\/10.3390\/e22030319","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2020,3,11]]}}}