{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T11:23:58Z","timestamp":1784028238594,"version":"3.55.0"},"reference-count":60,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,2,26]],"date-time":"2019-02-26T00:00:00Z","timestamp":1551139200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1434600"],"award-info":[{"award-number":["CCF-1434600"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-0939370"],"award-info":[{"award-number":["CCF-0939370"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The aim of using atypicality is to extract small, rare, unusual and interesting pieces out of big data. This complements statistics about typical data to give insight into data. In order to find such \u201cinteresting\u201d parts of data, universal approaches are required, since it is not known in advance what we are looking for. We therefore base the atypicality criterion on codelength. In a prior paper we developed the methodology for discrete-valued data, and the current paper extends this to real-valued data. This is done by using minimum description length (MDL). We develop the information-theoretic methodology for a number of \u201cuniversal\u201d signal processing models, and finally apply them to recorded hydrophone data and heart rate variability (HRV) signal.<\/jats:p>","DOI":"10.3390\/e21030219","type":"journal-article","created":{"date-parts":[[2019,2,26]],"date-time":"2019-02-26T11:00:44Z","timestamp":1551178844000},"page":"219","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Data Discovery and Anomaly Detection Using Atypicality for Real-Valued Data"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2706-1594","authenticated-orcid":false,"given":"Elyas","family":"Sabeti","sequence":"first","affiliation":[{"name":"Department of Computational Medicine and Bioinformatics, University of Michigan, NCRC 10-A108, 2800 Plymouth Rd, Ann Arbor, MI 48109-2800, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1472-4953","authenticated-orcid":false,"given":"Anders","family":"H\u00f8st-Madsen","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, University of Hawaii at Manoa, Honolulu, HI 96822, USA"},{"name":"Shenzhen Research Institute of Big Data, Shenzhen 518172, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,26]]},"reference":[{"key":"ref_1","unstructured":"H\u00f8st-Madsen, A., Sabeti, E., and Walton, C. (2016). Data Discovery and Anomaly Detection Using Atypicality: Theory. IEEE Trans. Inf. Theory, submitted."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1109\/TKDE.2010.235","article-title":"Anomaly Detection for Discrete Sequences: A Survey","volume":"24","author":"Chandola","year":"2012","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4066","DOI":"10.1109\/TIT.2014.2317691","article-title":"Universal Outlier Hypothesis Testing","volume":"60","author":"Li","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_4","unstructured":"Li, Y., Nitinawarat, S., and Veeravalli, V.V. (2013, January 10\u201315). Universal Outlier Detection. Proceedings of the Information Theory and Applications Workshop (ITA), San Diego, CA, USA."},{"key":"ref_5","unstructured":"Li, Y., Nitinawarat, S., and Veeravalli, V.V. (July, January 29). Universal Sequential Outlier Hypothesis Testing. Proceedings of the IEEE International Symposium on Information Theory (ISIT), Honolulu, HI, USA."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Grimmett, G.R., and Stirzaker, D.R. (2001). Probability and Random Processes, Oxford University Press. [3rd ed.].","DOI":"10.1093\/oso\/9780198572237.001.0001"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Sabeti, E., and Host-Madsen, A. (2016, January 27\u201330). Atypicality for the Class of Exponential Family. Proceedings of the 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), Monticello, IL, USA.","DOI":"10.1109\/ALLERTON.2016.7852292"},{"key":"ref_8","unstructured":"Kay, S.M. (1993). Fundamentals of Statistical Signal Processing, Volume II: Detection Theory, Prentice-Hall."},{"key":"ref_9","unstructured":"Bishop, C.M. (2006). Pattern Recognition and Machine Learning, Springer."},{"key":"ref_10","unstructured":"Cover, T., and Thomas, J. (2006). Information Theory, John Wiley. [2nd ed.]."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1109\/TIT.1977.1055714","article-title":"A Universal Algorithm for Sequential Data Compression","volume":"23","author":"Ziv","year":"1977","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1109\/TIT.1978.1055934","article-title":"Compression of Individual Sequences via Variable-Rate Coding","volume":"24","author":"Ziv","year":"1978","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1109\/TASL.2012.2211014","article-title":"Sparse Modeling for Lossless Audio Compression","volume":"21","author":"Ghido","year":"2013","journal-title":"IEEE Trans. Audio Speech Lang. Proc."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1214\/aos\/1176346150","article-title":"A Universal Prior for Integers and Estimation by Minimum Description Length","volume":"11","author":"Rissanen","year":"1983","journal-title":"Ann. Stat."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4268","DOI":"10.1109\/TIT.2017.2676811","article-title":"Data Compression With Low Distortion and Finite Blocklength","volume":"63","author":"Kostina","year":"2017","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1080","DOI":"10.1214\/aos\/1176350051","article-title":"Stochastic Complexity and Modeling","volume":"14","author":"Rissanen","year":"1986","journal-title":"Ann. Stat."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1145\/1541880.1541882","article-title":"Anomaly Detection: A Survey","volume":"41","author":"Chandola","year":"2009","journal-title":"ACM Comput. Surv."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1002\/wics.1347","article-title":"Anomaly Detection in Dynamic Networks: A Survey","volume":"7","author":"Ranshous","year":"2015","journal-title":"WIREs Comput. Stat."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1460","DOI":"10.1109\/TKDE.2012.99","article-title":"Anomaly Detection via Online Oversampling Principal Component Analysis","volume":"25","author":"Lee","year":"2013","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/j.sigpro.2013.12.026","article-title":"A Review of Novelty Detection","volume":"99","author":"Pimentel","year":"2014","journal-title":"Signal Process."},{"key":"ref_21","first-page":"12","article-title":"Time-Series Data Mining","volume":"45","author":"Esling","year":"2012","journal-title":"ACM Comp. Surv. (CSUR)"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1109\/TPAMI.2013.111","article-title":"Anomaly Detection and Localization in Crowded Scenes","volume":"36","author":"Li","year":"2014","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Jia, Z., Shen, C., Yi, X., Chen, Y., Yu, T., and Guan, X. (2017, January 20\u201323). Big-Data Analysis of Multi-Source Logs for Anomaly Detection on Network-Based System. Proceedings of the 13th IEEE Conference on Automation Science and Engineering (CASE), Xi\u2019an, China.","DOI":"10.1109\/COASE.2017.8256257"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.jnca.2015.11.016","article-title":"A Survey of Network Anomaly Detection Techniques","volume":"60","author":"Ahmed","year":"2016","journal-title":"J. Netw. Comp. Appl."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Yoon, M.K., Mohan, S., Choi, J., Christodorescu, M., and Sha, L. (2017, January 18\u201321). Learning Execution Contexts from System Call Distribution for Anomaly Detection in Smart Embedded System. Proceedings of the Second International Conference on Internet-of-Things Design and Implementation, Pittsburgh, PA, USA.","DOI":"10.1145\/3054977.3054999"},{"key":"ref_26","first-page":"142","article-title":"A Review of Anomaly Detection Systems in Cloud Networks and Survey of Cloud Security Measures in Cloud Storage Applications","volume":"6","author":"Sari","year":"2015","journal-title":"J. Inf. Secur."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"H\u00f8st-Madsen, A., Sabeti, E., Walton, C., and Lim, S.J. (2016, January 5\u20138). Universal Data Discovery Using Atypicality. Proceedings of the 3rd International Workshop on Pattern Mining and Application of Big Data (BigPMA 2016) at the 2016 IEEE International Conference on Big Data (Big Data 2016), Washington, DC, USA.","DOI":"10.1109\/BigData.2016.7841010"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"866","DOI":"10.1109\/18.661537","article-title":"A Detection Optimal Min-Max Test for Transient Signals","volume":"44","author":"Han","year":"1998","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2682","DOI":"10.1109\/78.863080","article-title":"A Performance Study of Some Transient Detectors","volume":"48","author":"Wang","year":"2000","journal-title":"IEEE Trans. Signal Proc."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2454","DOI":"10.1109\/78.960393","article-title":"All-Purpose and Plug-In Power-Law Detectors for Transient Signals","volume":"49","author":"Wang","year":"2001","journal-title":"Trans. Signal Proc."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"4397","DOI":"10.1109\/TSP.2005.857060","article-title":"A Variable Threshold Page Procedure for Detection of Transient Signals","volume":"53","author":"Wang","year":"2005","journal-title":"IEEE Trans. Signal Proc."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1080\/07474946.2012.719443","article-title":"Sequential Detection of Transient Changes","volume":"31","author":"Fillatre","year":"2012","journal-title":"Seq. Anal."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1594","DOI":"10.1109\/TSP.2017.2788416","article-title":"Performance Bounds for Finite Moving Average Tests in Transient Change Detection","volume":"66","author":"Poor","year":"2018","journal-title":"IEEE Trans. Signal Proc."},{"key":"ref_34","first-page":"3039","article-title":"Detecting a Suddenly Arriving Dynamic Profile of Finite Duration","volume":"63","author":"Fillatre","year":"2017","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Hirai, S., and Yamanishi, K. (2012, January 12\u201316). Detecting Changes of Clustering Structures Using Normalized Maximum Likelihood Coding. Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Beijing, China.","DOI":"10.1145\/2339530.2339587"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Yamanishi, K., and Miyaguchi, K. (2016, January 5\u20138). Detecting Gradual Changes from Data Stream Using MDL-Change Statistics. Proceedings of the IEEE International Conference on Big Data (Big Data), Washington, DC, USA.","DOI":"10.1109\/BigData.2016.7840601"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1590","DOI":"10.1080\/01621459.2012.737745","article-title":"Optimal Detection of Changepoints with a Linear Computational Cost","volume":"107","author":"Killick","year":"2012","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Zou, S., Fellouris, G., and Veeravalli, V.V. (2018). Quickest Change Detection under Transient Dynamics: Theory and Asymptotic Analysis. IEEE Trans. Inf. Theory, 1.","DOI":"10.1109\/TIT.2018.2877972"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Molloy, T.L., and Ford, J.J. (2018). Minimax Robust Quickest Change Detection in Systems and Signals with Unknown Transients. IEEE Trans. Autom. Control, 1.","DOI":"10.1109\/LCSYS.2017.2714262"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/B978-0-12-411597-2.00006-0","article-title":"Quickest Change Detection","volume":"3","author":"Veeravalli","year":"2013","journal-title":"Acad. Press Library Signal Proc."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1109\/TIT.2018.2843379","article-title":"Asymptotic Bayesian Theory of Quickest Change Detection for Hidden Markov Models","volume":"65","author":"Fuh","year":"2019","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1501","DOI":"10.1016\/j.sigpro.2005.01.012","article-title":"Using Penalized Contrasts for the Change-Point Problem","volume":"85","author":"Lavielle","year":"2005","journal-title":"Signal Proc."},{"key":"ref_43","unstructured":"Larsen, R.J., and Marx, M. (1986). An Introduction to Mathematical Statistics and Its Applications, Prentice-Hall."},{"key":"ref_44","unstructured":"Roos, T., and Rissanen, J. (2008, January 18). On Sequentially Normalized Maximum Likelihood Models. Proceedings of the Workshop on Information Theoretic Methods in Science and Engineering (WITMSE-08), Tampere, Finland."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Sabeti, E., and Host-Madsen, A. (2017, January 25\u201330). Enhanced MDL with Application to Atypicality. Proceedings of the IEEE International Symposium on Information Theory (ISIT), Aachen, Germany.","DOI":"10.1109\/ISIT.2017.8007125"},{"key":"ref_46","unstructured":"Scharf, L.L. (1990). Statistical Signal Processing: Detection, Estimation, and Time Series Analysis, Addison-Wesley."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Grunwald, P.D. (2007). The Minimum Description Length Principle, MIT Press.","DOI":"10.7551\/mitpress\/4643.001.0001"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Rissanen, J. (1998). Stochastic Complexity in Statistical Inquiry, World Scientific.","DOI":"10.1142\/0822"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/S0167-7152(00)00111-5","article-title":"The Density of the Sufficient Statistics for a Gaussian AR(1) Model in Terms of Generalized Functions","volume":"50","author":"Forchini","year":"2000","journal-title":"Stat. Probab. Let."},{"key":"ref_50","unstructured":"Mallat, S. (2008). A Wavelet Tour of Signal Processing: The Sparse Way, Academic Press."},{"key":"ref_51","unstructured":"Vetterli, M., and Kovacevic, J. (1995). Wavelets and Subband Coding, Prentice Hall."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"2207","DOI":"10.1109\/78.157221","article-title":"Wavelets and Filter Banks: Theory and Design","volume":"40","author":"Vetterli","year":"1992","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_53","unstructured":"Mitra, S.K., and Kuo, Y. (2006). Digital Signal Processing: A Computer-Based Approach, McGraw-Hill New York."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1109\/18.382012","article-title":"The Context-Tree Weighting Method: Basic Properties","volume":"41","author":"Willems","year":"1995","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_55","first-page":"1","article-title":"Reflections on \u201cThe Context Tree Weighting Method: Basic properties\u201d","volume":"47","author":"Willems","year":"1997","journal-title":"Newslett. IEEE Inf. Theory Soc."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Sabeti, E., and H\u00f8st-Madsen, A. (2016, January 5\u20138). How interesting images are: An Atypicality Approach For Social Networks. Proceedings of the IEEE International Conference on Big Data (Big Data), Washington, DC, USA.","DOI":"10.1109\/BigData.2016.7840742"},{"key":"ref_57","unstructured":"Muirhead, R.J. (2009). Aspects of Multivariate Statistical Theory, John Wiley & Sons."},{"key":"ref_58","unstructured":"Silver, K. (2014). A Passive Acoustic Automated Detector for Sei and Fin Whale Calls. [Master\u2019s Thesis, University of Hawaii]."},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Host-Madsen, A., and Sabeti, E. (2015, January 14\u201319). Atypical Information Theory for Real-Valued Data. Proceedings of the IEEE International Symposium on Information Theory (ISIT), Hong Kong, China.","DOI":"10.1109\/ISIT.2015.7282538"},{"key":"ref_60","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"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/3\/219\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:34:41Z","timestamp":1760186081000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/3\/219"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,26]]},"references-count":60,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,3]]}},"alternative-id":["e21030219"],"URL":"https:\/\/doi.org\/10.3390\/e21030219","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,2,26]]}}}