{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T23:08:36Z","timestamp":1782342516870,"version":"3.54.5"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,8,30]],"date-time":"2021-08-30T00:00:00Z","timestamp":1630281600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,8,30]],"date-time":"2021-08-30T00:00:00Z","timestamp":1630281600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100012818","name":"comunidad de madrid","doi-asserted-by":"publisher","award":["P2018\/TCS4499"],"award-info":[{"award-number":["P2018\/TCS4499"]}],"id":[{"id":"10.13039\/100012818","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014440","name":"ministerio de ciencia, innovaci\u00f3n y universidades","doi-asserted-by":"publisher","award":["PID2019-109805RB-I00"],"award-info":[{"award-number":["PID2019-109805RB-I00"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014440","name":"ministerio de ciencia, innovaci\u00f3n y universidades","doi-asserted-by":"publisher","award":["PID2019-104901RBI00"],"award-info":[{"award-number":["PID2019-104901RBI00"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Data Anal Classif"],"published-print":{"date-parts":[[2022,9]]},"DOI":"10.1007\/s11634-021-00460-9","type":"journal-article","created":{"date-parts":[[2021,8,30]],"date-time":"2021-08-30T17:02:55Z","timestamp":1630342975000},"page":"725-760","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Detecting and classifying outliers in big functional data"],"prefix":"10.1007","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9629-6990","authenticated-orcid":false,"given":"Oluwasegun Taiwo","family":"Ojo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6501-2377","authenticated-orcid":false,"given":"Antonio","family":"Fern\u00e1ndez Anta","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rosa E.","family":"Lillo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Carlo","family":"Sguera","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,8,30]]},"reference":[{"key":"460_CR1","doi-asserted-by":"publisher","unstructured":"Arribas-Gil A, Romo J (2014) Shape outlier detection and visualization for functional data: the outliergram. Biostatistics 15(4):603\u2013619. https:\/\/doi.org\/10.1093\/biostatistics\/kxu006","DOI":"10.1093\/biostatistics\/kxu006"},{"issue":"1","key":"460_CR2","doi-asserted-by":"publisher","first-page":"6955","DOI":"10.1038\/s41598-018-24874-2","volume":"8","author":"A Azcorra","year":"2018","unstructured":"Azcorra A, Chiroque LF, Cuevas R, Fern\u00e1ndez Anta A, Laniado H, Lillo RE, Romo J, Sguera C (2018) Unsupervised scalable statistical method for identifying influential users in online social networks. Sci Rep 8(1):6955. https:\/\/doi.org\/10.1038\/s41598-018-24874-2","journal-title":"Sci Rep"},{"issue":"5\u20137","key":"460_CR3","doi-asserted-by":"publisher","first-page":"364","DOI":"10.1002\/cem.940","volume":"19","author":"G Brys","year":"2005","unstructured":"Brys G, Hubert M, Rousseeuw PJ (2005) A robustification of independent component analysis. J Chemom 19(5\u20137):364\u2013375. https:\/\/doi.org\/10.1002\/cem.940","journal-title":"J Chemom"},{"issue":"3","key":"460_CR4","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1016\/S0167-9473(99)00057-2","volume":"33","author":"K Carling","year":"2000","unstructured":"Carling K (2000) Resistant outlier rules and the non-gaussian case. Comput Stat Data Anal 33(3):249\u2013258. https:\/\/doi.org\/10.1016\/S0167-9473(99)00057-2","journal-title":"Comput Stat Data Anal"},{"issue":"505","key":"460_CR5","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1080\/01621459.2013.856795","volume":"109","author":"G Claeskens","year":"2014","unstructured":"Claeskens G, Hubert M, Slaets L, Vakili K (2014) Multivariate functional halfspace depth. J Am Stat Assoc 109(505):411\u2013423. https:\/\/doi.org\/10.1080\/01621459.2013.856795","journal-title":"J Am Stat Assoc"},{"key":"460_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jspi.2013.04.002","volume":"147","author":"A Cuevas","year":"2014","unstructured":"Cuevas A (2014) A partial overview of the theory of statistics with functional data. J Stat Plan Inference 147:1\u201323. https:\/\/doi.org\/10.1016\/j.jspi.2013.04.002","journal-title":"J Stat Plan Inference"},{"issue":"4","key":"460_CR7","doi-asserted-by":"publisher","first-page":"923","DOI":"10.1080\/10618600.2018.1473781","volume":"27","author":"W Dai","year":"2018","unstructured":"Dai W, Genton MG (2018) Multivariate functional data visualization and outlier detection. J Comput Graph Stat 27(4):923\u2013934. https:\/\/doi.org\/10.1080\/10618600.2018.1473781","journal-title":"J Comput Graph Stat"},{"key":"460_CR8","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1016\/j.csda.2018.03.017","volume":"131","author":"W Dai","year":"2019","unstructured":"Dai W, Genton MG (2019) Directional outlyingness for multivariate functional data. Comput Stat Data Anal 131:50\u201365. https:\/\/doi.org\/10.1016\/j.csda.2018.03.017","journal-title":"Comput Stat Data Anal"},{"key":"460_CR9","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2020.106960","author":"W Dai","year":"2020","unstructured":"Dai W, Mrkvi\u010dka T, Sun Y, Genton MG (2020) Functional outlier detection and taxonomy by sequential transformations. Comput Stat Data Anal. https:\/\/doi.org\/10.1016\/j.csda.2020.106960","journal-title":"Comput Stat Data Anal"},{"issue":"8","key":"460_CR10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.18637\/jss.v040.i08","volume":"40","author":"D Eddelbuettel","year":"2011","unstructured":"Eddelbuettel D, Francois R (2011) Rcpp: seamless r and c++ integration. J Stat Softw 40(8):1\u201318. https:\/\/doi.org\/10.18637\/jss.v040.i08","journal-title":"J Stat Softw"},{"issue":"4","key":"460_CR11","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1002\/env.878","volume":"19","author":"M Febrero","year":"2008","unstructured":"Febrero M, Galeano P, Gonz\u00e1lez-Manteiga W (2008) Outlier detection in functional data by depth measures, with application to identify abnormal nox levels. Environmetrics 19(4):331\u2013345. https:\/\/doi.org\/10.1002\/env.878","journal-title":"Environmetrics"},{"issue":"4","key":"460_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.18637\/jss.v051.i04","volume":"51","author":"M Febrero-Bande","year":"2012","unstructured":"Febrero-Bande M, de la Fuente MO (2012) Statistical computing in functional data analysis: the r package fda.usc. J Stat Softw 51(4):1\u201328. https:\/\/doi.org\/10.18637\/jss.v051.i04","journal-title":"J Stat Softw"},{"key":"460_CR13","volume-title":"Nonparametric functional data analysis: theory and practice (Springer series in statistics)","author":"F Ferraty","year":"2006","unstructured":"Ferraty F, Vieu P (2006) Nonparametric functional data analysis: theory and practice (Springer series in statistics). Springer, Berlin"},{"issue":"5","key":"460_CR14","doi-asserted-by":"publisher","first-page":"579","DOI":"10.1016\/j.cageo.2004.11.013","volume":"31","author":"P Filzmoser","year":"2005","unstructured":"Filzmoser P, Garrett RG, Reimann C (2005) Multivariate outlier detection in exploration geochemistry. Comput Geosci 31(5):579\u2013587. https:\/\/doi.org\/10.1016\/j.cageo.2004.11.013","journal-title":"Comput Geosci"},{"issue":"2","key":"460_CR15","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1007\/BF02595706","volume":"10","author":"R Fraiman","year":"2001","unstructured":"Fraiman R, Muniz G (2001) Trimmed means for functional data. Test 10(2):419\u2013440. https:\/\/doi.org\/10.1007\/BF02595706","journal-title":"Test"},{"issue":"3","key":"460_CR16","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1007\/s00180-011-0262-4","volume":"27","author":"H Fritz","year":"2012","unstructured":"Fritz H, Filzmoser P, Croux C (2012) A comparison of algorithms for the multivariate l1-median. Comput Stat 27(3):393\u2013410. https:\/\/doi.org\/10.1007\/s00180-011-0262-4","journal-title":"Comput Stat"},{"issue":"4","key":"460_CR17","doi-asserted-by":"publisher","first-page":"928","DOI":"10.1198\/106186005X77685","volume":"14","author":"J Hardin","year":"2005","unstructured":"Hardin J, Rocke DM (2005) The distribution of robust distances. J Comput Graph Stat 14(4):928\u2013946. https:\/\/doi.org\/10.1198\/106186005X77685","journal-title":"J Comput Graph Stat"},{"issue":"4","key":"460_CR18","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1080\/00401706.2019.1574241","volume":"61","author":"H Huang","year":"2019","unstructured":"Huang H, Sun Y (2019) A decomposition of total variation depth for understanding functional outliers. Technometrics 61(4):445\u2013458. https:\/\/doi.org\/10.1080\/00401706.2019.1574241","journal-title":"Technometrics"},{"issue":"3\u20134","key":"460_CR19","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1002\/cem.1123","volume":"22","author":"M Hubert","year":"2008","unstructured":"Hubert M, Van der Veeken S (2008) Outlier detection for skewed data. J Chemom 22(3\u20134):235\u2013246. https:\/\/doi.org\/10.1002\/cem.1123","journal-title":"J Chemom"},{"issue":"12","key":"460_CR20","doi-asserted-by":"publisher","first-page":"5186","DOI":"10.1016\/j.csda.2007.11.008","volume":"52","author":"M Hubert","year":"2008","unstructured":"Hubert M, Vandervieren E (2008) An adjusted boxplot for skewed distributions. Comput Stat Data Anal 52(12):5186\u20135201. https:\/\/doi.org\/10.1016\/j.csda.2007.11.008","journal-title":"Comput Stat Data Anal"},{"issue":"2","key":"460_CR21","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1007\/s10260-015-0297-8","volume":"24","author":"M Hubert","year":"2015","unstructured":"Hubert M, Rousseeuw PJ, Segaert P (2015) Multivariate functional outlier detection. Stat Methods Appl 24(2):177\u2013202. https:\/\/doi.org\/10.1007\/s10260-015-0297-8","journal-title":"Stat Methods Appl"},{"issue":"1","key":"460_CR22","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1198\/jcgs.2009.08158","volume":"19","author":"RJ Hyndman","year":"2010","unstructured":"Hyndman RJ, Shang HL (2010) Rainbow plots, bagplots, and boxplots for functional data. J Comput Graph Stat 19(1):29\u201345. https:\/\/doi.org\/10.1198\/jcgs.2009.08158","journal-title":"J Comput Graph Stat"},{"key":"460_CR23","unstructured":"Izrailev S (2014) Tictoc: functions for timing R scripts, as well as implementations of Stack and List structures. R package version 1.0"},{"key":"460_CR24","unstructured":"Long JP, Huang JZ (2015) A study of functional depths. arXiv preprint arXiv:1506.01332"},{"issue":"486","key":"460_CR25","doi-asserted-by":"publisher","first-page":"718","DOI":"10.1198\/jasa.2009.0108","volume":"104","author":"S L\u00f3pez-Pintado","year":"2009","unstructured":"L\u00f3pez-Pintado S, Romo J (2009) On the concept of depth for functional data. J Am Stat Assoc 104(486):718\u2013734. https:\/\/doi.org\/10.1198\/jasa.2009.0108","journal-title":"J Am Stat Assoc"},{"issue":"4","key":"460_CR26","doi-asserted-by":"publisher","first-page":"1679","DOI":"10.1016\/j.csda.2010.10.024","volume":"55","author":"S L\u00f3pez-Pintado","year":"2011","unstructured":"L\u00f3pez-Pintado S, Romo J (2011) A half-region depth for functional data. Comput Stat Data Anal 55(4):1679\u20131695. https:\/\/doi.org\/10.1016\/j.csda.2010.10.024","journal-title":"Comput Stat Data Anal"},{"issue":"4","key":"460_CR27","doi-asserted-by":"publisher","first-page":"883","DOI":"10.1080\/10618600.2017.1336445","volume":"26","author":"S Nagy","year":"2017","unstructured":"Nagy S, Gijbels I, Hlubinka D (2017) Depth-based recognition of shape outlying functions. J Comput Graph Stat 26(4):883\u2013893. https:\/\/doi.org\/10.1080\/10618600.2017.1336445","journal-title":"J Comput Graph Stat"},{"key":"460_CR28","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1051\/ps\/2016005","volume":"20","author":"S Nagy","year":"2016","unstructured":"Nagy S, Gijbels I, Omelka M, Hlubinka D (2016) Integrated depth for functional data: statistical properties and consistency. ESAIM Probab Stat 20:95\u2013130. https:\/\/doi.org\/10.1051\/ps\/2016005","journal-title":"ESAIM Probab Stat"},{"issue":"516","key":"460_CR29","doi-asserted-by":"publisher","first-page":"1705","DOI":"10.1080\/01621459.2015.1110033","volume":"111","author":"NN Narisetty","year":"2016","unstructured":"Narisetty NN, Nair VN (2016) Extremal depth for functional data and applications. J Am Stat Assoc 111(516):1705\u20131714. https:\/\/doi.org\/10.1080\/01621459.2015.1110033","journal-title":"J Am Stat Assoc"},{"issue":"1","key":"460_CR30","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1214\/15-STS532","volume":"31","author":"A Nieto-Reyes","year":"2016","unstructured":"Nieto-Reyes A, Battey H (2016) A topologically valid definition of depth for functional data. Stat Sci 31(1):61\u201379. https:\/\/doi.org\/10.1214\/15-STS532","journal-title":"Stat Sci"},{"key":"460_CR31","unstructured":"Ojo OT, Lillo RE, Fernandez Anta A (2021) Fdaoutlier: outlier detection tools for functional data analysis. https:\/\/cran.r-project.org\/package=fdaoutlier. R package version 0.2.9000"},{"key":"460_CR32","unstructured":"R Core Team (2020) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna"},{"key":"460_CR33","doi-asserted-by":"publisher","DOI":"10.1007\/b98888","volume-title":"Functional data analysis","author":"JO Ramsay","year":"2005","unstructured":"Ramsay JO, Silverman BW (2005) Functional data analysis. Springer, Berlin"},{"issue":"3","key":"460_CR34","doi-asserted-by":"publisher","first-page":"212","DOI":"10.1080\/00401706.1999.10485670","volume":"41","author":"PJ Rousseeuw","year":"1999","unstructured":"Rousseeuw PJ, Driessen KV (1999) A fast algorithm for the minimum covariance determinant estimator. Technometrics 41(3):212\u2013223. https:\/\/doi.org\/10.1080\/00401706.1999.10485670","journal-title":"Technometrics"},{"issue":"2","key":"460_CR35","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1080\/10618600.2017.1366912","volume":"27","author":"PJ Rousseeuw","year":"2018","unstructured":"Rousseeuw PJ, Raymaekers J, Hubert M (2018) A measure of directional outlyingness with applications to image data and video. J Comput Graph Stat 27(2):345\u2013359. https:\/\/doi.org\/10.1080\/10618600.2017.1366912","journal-title":"J Comput Graph Stat"},{"issue":"4","key":"460_CR36","doi-asserted-by":"publisher","first-page":"1115","DOI":"10.1007\/s00477-015-1096-3","volume":"30","author":"C Sguera","year":"2016","unstructured":"Sguera C, Galeano P, Lillo RE (2016) Functional outlier detection by a local depth with application to no x levels. Stoch Environ Res Risk Assess 30(4):1115\u20131130. https:\/\/doi.org\/10.1007\/s00477-015-1096-3","journal-title":"Stoch Environ Res Risk Assess"},{"issue":"2","key":"460_CR37","doi-asserted-by":"publisher","first-page":"316","DOI":"10.1198\/jcgs.2011.09224","volume":"20","author":"Y Sun","year":"2011","unstructured":"Sun Y, Genton MG (2011) Functional boxplots. J Comput Graph Stat 20(2):316\u2013334. https:\/\/doi.org\/10.1198\/jcgs.2011.09224","journal-title":"J Comput Graph Stat"},{"key":"460_CR38","doi-asserted-by":"publisher","DOI":"10.1007\/s11634-020-00412-9","author":"G Vinue","year":"2020","unstructured":"Vinue G, Epifanio I (2020) Robust archetypoids for anomaly detection in big functional data. Adv Data Anal Classif. https:\/\/doi.org\/10.1007\/s11634-020-00412-9","journal-title":"Adv Data Anal Classif"}],"container-title":["Advances in Data Analysis and Classification"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11634-021-00460-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11634-021-00460-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11634-021-00460-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,26]],"date-time":"2022-08-26T10:28:21Z","timestamp":1661509701000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11634-021-00460-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,30]]},"references-count":38,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,9]]}},"alternative-id":["460"],"URL":"https:\/\/doi.org\/10.1007\/s11634-021-00460-9","relation":{},"ISSN":["1862-5347","1862-5355"],"issn-type":[{"value":"1862-5347","type":"print"},{"value":"1862-5355","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,30]]},"assertion":[{"value":"19 January 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 August 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 August 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 August 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}