{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:00:13Z","timestamp":1776844813096,"version":"3.51.2"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2023,5,12]],"date-time":"2023-05-12T00:00:00Z","timestamp":1683849600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,5,12]],"date-time":"2023-05-12T00:00:00Z","timestamp":1683849600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["DG-2018-04449"],"award-info":[{"award-number":["DG-2018-04449"]}],"id":[{"id":"10.13039\/501100000038","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":[[2024,9]]},"DOI":"10.1007\/s11634-023-00542-w","type":"journal-article","created":{"date-parts":[[2023,5,12]],"date-time":"2023-05-12T11:02:31Z","timestamp":1683889351000},"page":"563-595","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Model-based clustering of functional data via mixtures of t distributions"],"prefix":"10.1007","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-7972-4687","authenticated-orcid":false,"given":"Cristina","family":"Anton","sequence":"first","affiliation":[]},{"given":"Iain","family":"Smith","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,5,12]]},"reference":[{"key":"542_CR1","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1017\/S0370164600022070","volume":"46","author":"AC Aitken","year":"1927","unstructured":"Aitken AC (1927) On Bernoulli\u2019s numerical solution of algebraic equations. Proc R Soc Edinb 46:289\u2013305. https:\/\/doi.org\/10.1017\/S0370164600022070","journal-title":"Proc R Soc Edinb"},{"key":"542_CR2","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2022.107496","volume":"174","author":"M Amovin-Assagba","year":"2022","unstructured":"Amovin-Assagba M, Gannaz I, Jacques J (2022) Outlier detection in multivariate functional data through a contaminated mixture model. Comput Stat Data Anal 174:107496","journal-title":"Comput Stat Data Anal"},{"key":"542_CR3","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1007\/s11222-010-9175-2","volume":"21","author":"JL Andrews","year":"2011","unstructured":"Andrews JL, McNicholas PD (2011) Extending mixtures of multivariate t-distributions. Stat Comput 21:361\u2013373. https:\/\/doi.org\/10.1007\/s11222-010-9175-2","journal-title":"Stat Comput"},{"key":"542_CR4","doi-asserted-by":"publisher","first-page":"1021","DOI":"10.1007\/s11222-011-9272-x","volume":"22","author":"JL Andrews","year":"2012","unstructured":"Andrews JL, McNicholas PD (2012) Model-based clustering, classification, and discriminant analysis via mixtures of multivariate t-distributions: the teigen family. Stat Comput 22:1021\u20131029. https:\/\/doi.org\/10.1007\/s11222-011-9272-x","journal-title":"Stat Comput"},{"issue":"1","key":"542_CR5","doi-asserted-by":"publisher","first-page":"520","DOI":"10.1016\/j.csda.2010.05.019","volume":"55","author":"JL Andrews","year":"2011","unstructured":"Andrews JL, McNicholas PD, Subedi S (2011) Model-based classification via mixtures of multivariate t-distributions. Comput Stat Data Anal 55(1):520\u2013529. https:\/\/doi.org\/10.1016\/j.csda.2010.05.019","journal-title":"Comput Stat Data Anal"},{"issue":"7","key":"542_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.18637\/jss.v083.i07","volume":"83","author":"JL Andrews","year":"2018","unstructured":"Andrews JL, Wickins JR, Boers NM et al (2018) An R package for model-based clustering and classification via the multivariate t distribution. J Stat Softw 83(7):1\u201332","journal-title":"J Stat Softw"},{"key":"542_CR7","doi-asserted-by":"crossref","unstructured":"Anton C, Smith I (2023) Model based clustering of functional data with mild outliers. In: Brito P, Dias J, Lausen B, et\u00a0al (eds) Classification and Data Science in the Digital Age. Studies in Classification, Data Analysis, and Knowledge Organization, Springer International Publishing, to appear","DOI":"10.1007\/978-3-031-09034-9_2"},{"issue":"1","key":"542_CR8","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1002\/cjs.11308","volume":"45","author":"L Bagnato","year":"2017","unstructured":"Bagnato L, Punzo A, Zoia MG (2017) The multivariate leptokurtic-normal distribution and its application in model-based clustering. Can J Stat 45(1):95\u2013119","journal-title":"Can J Stat"},{"issue":"4","key":"542_CR9","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1007\/s11634-011-0095-6","volume":"5","author":"C Bouveyron","year":"2011","unstructured":"Bouveyron C, Jacques J (2011) Model-based clustering of time series in group-specific functional subspaces. Adv Data Anal Classif 5(4):281\u2013300","journal-title":"Adv Data Anal Classif"},{"issue":"1","key":"542_CR10","doi-asserted-by":"publisher","first-page":"502","DOI":"10.1016\/j.csda.2007.02.009","volume":"52","author":"C Bouveyron","year":"2007","unstructured":"Bouveyron C, Girard S, Schmid C (2007) High-dimensional data clustering. Comput Stat Data Anal 52(1):502\u2013519","journal-title":"Comput Stat Data Anal"},{"issue":"5","key":"542_CR11","doi-asserted-by":"publisher","first-page":"781","DOI":"10.1016\/0031-3203(94)00125-6","volume":"28","author":"G Celeux","year":"1995","unstructured":"Celeux G, Govaert G (1995) Gaussian parsimonious clustering models. Pattern Recogn 28(5):781\u2013793. https:\/\/doi.org\/10.1016\/0031-3203(94)00125-6","journal-title":"Pattern Recogn"},{"issue":"2","key":"542_CR12","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1214\/aos\/1031833664","volume":"25","author":"JA Cuesta-Albertos","year":"1997","unstructured":"Cuesta-Albertos JA, Gordaliza A, Matr\u00e1n C (1997) Trimmed $$k$$-means: an attempt to robustify quantizers. Ann Stat 25(2):553\u2013576. https:\/\/doi.org\/10.1214\/aos\/1031833664","journal-title":"Ann Stat"},{"issue":"3","key":"542_CR13","doi-asserted-by":"publisher","first-page":"481","DOI":"10.1007\/s00180-007-0053-0","volume":"22","author":"A Cuevas","year":"2007","unstructured":"Cuevas A, Febrero M, Fraiman R (2007) Robust estimation and classification for functional data via projection-based depth notions. Comput Stat 22(3):481\u2013496. https:\/\/doi.org\/10.1007\/s00180-007-0053-0","journal-title":"Comput Stat"},{"issue":"4","key":"542_CR14","doi-asserted-by":"publisher","first-page":"1081","DOI":"10.1111\/biom.12351","volume":"71","author":"UJ Dang","year":"2015","unstructured":"Dang UJ, Browne RP, McNicholas PD (2015) Mixtures of multivariate power exponential distributions. Biometrics 71(4):1081\u20131089","journal-title":"Biometrics"},{"issue":"2","key":"542_CR15","doi-asserted-by":"publisher","first-page":"1171","DOI":"10.1214\/09-AOS741","volume":"38","author":"A Delaigle","year":"2010","unstructured":"Delaigle A, Hall P (2010) Defining probability density for a distribution of random functions. Ann Stat 38(2):1171\u20131193","journal-title":"Ann Stat"},{"issue":"1","key":"542_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","volume":"39","author":"AP Dempster","year":"1977","unstructured":"Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc Series B Stat Methodol 39(1):1\u201338","journal-title":"J R Stat Soc Series B Stat Methodol"},{"issue":"4","key":"542_CR17","doi-asserted-by":"publisher","first-page":"989","DOI":"10.1007\/s11749-019-00693-","volume":"29","author":"A Farcomeni","year":"2020","unstructured":"Farcomeni A, Punzo A (2020) Robust model-based clustering with mild and gross outliers. TEST Off J Span Soc Stat Oper Res 29(4):989\u20131007. https:\/\/doi.org\/10.1007\/s11749-019-00693-","journal-title":"TEST Off J Span Soc Stat Oper Res"},{"issue":"4","key":"542_CR18","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":"542_CR19","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1002\/env.878","volume":"19","author":"M Febrero-Bande","year":"2008","unstructured":"Febrero-Bande M, Galeano P, Gonz\u00e3lez-Manteiga W (2008) Outlier detection in functional data by depth measures, with application to identify abnormal nox levels. Environmetrics 19:331\u2013345. https:\/\/doi.org\/10.1002\/env.878","journal-title":"Environmetrics"},{"key":"542_CR20","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 Offi J Span Soc Stat Oper Res 10:419\u2013440. https:\/\/doi.org\/10.1007\/BF02595706","journal-title":"TEST Offi J Span Soc Stat Oper Res"},{"key":"542_CR21","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1007\/s00357-005-0013-8","volume":"22","author":"L Garc\u00eda-Escudero","year":"2005","unstructured":"Garc\u00eda-Escudero L, Gordaliza A (2005) A proposal for robust curve clustering. J Classif 22:185\u2013201. https:\/\/doi.org\/10.1007\/s00357-005-0013-8","journal-title":"J Classif"},{"issue":"4","key":"542_CR22","doi-asserted-by":"publisher","first-page":"753","DOI":"10.1111\/j.1467-9469.2006.00505.x","volume":"33","author":"H Holzmann","year":"2006","unstructured":"Holzmann H, Munk A, Gneitting T (2006) Identifiability of finite mixtures of elliptical distributions. Scand J Stat 33(4):753\u2013763. https:\/\/doi.org\/10.1111\/j.1467-9469.2006.00505.x","journal-title":"Scand J Stat"},{"issue":"1","key":"542_CR23","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1007\/BF01908075","volume":"2","author":"L Hubert","year":"1985","unstructured":"Hubert L, Arabie P (1985) Comparing partitions. J Classif 2(1):193\u2013218","journal-title":"J Classif"},{"key":"542_CR24","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1016\/j.neucom.2012.11.042","volume":"112","author":"J Jacques","year":"2013","unstructured":"Jacques J, Preda C (2013) Funclust: a curves clustering method using functional random variables density approximation. Neurocomputing 112:164\u2013171. https:\/\/doi.org\/10.1016\/j.neucom.2012.11.042","journal-title":"Neurocomputing"},{"issue":"3","key":"542_CR25","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1007\/s11634-013-0158-y","volume":"8","author":"J Jacques","year":"2014","unstructured":"Jacques J, Preda C (2014) Functional data clustering: a survey. Adv Data Anal Classif 8(3):231\u2013255. https:\/\/doi.org\/10.1007\/s11634-013-0158-y","journal-title":"Adv Data Anal Classif"},{"issue":"C","key":"542_CR26","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1016\/j.csda.2012.12.004","volume":"71","author":"J Jacques","year":"2014","unstructured":"Jacques J, Preda C (2014b) Model-based clustering for multivariate functional data. Comput Stat Data Anal 71(C):92\u2013106","journal-title":"Comput Stat Data Anal"},{"key":"542_CR27","unstructured":"McLachlan G, Peel D (2004) Finite Mixture Models. Wiley Series in Probability and Statistics, Wiley"},{"issue":"3","key":"542_CR28","doi-asserted-by":"publisher","first-page":"711","DOI":"10.1016\/j.csda.2009.02.011","volume":"54","author":"PD McNicholas","year":"2010","unstructured":"McNicholas PD, Murphy TB, McDaid AF et al (2010) Serial and parallel implementations of model-based clustering via parsimonious Gaussian mixture models. Comput Stat Data Anal 54(3):711\u2013723","journal-title":"Comput Stat Data Anal"},{"issue":"2","key":"542_CR29","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1093\/biomet\/80.2.267","volume":"80","author":"XL Meng","year":"1993","unstructured":"Meng XL, Rubin DB (1993) Maximum likelihood estimation via the ECM algorithm: a general framework. Biometrika 80(2):267\u2013278. https:\/\/doi.org\/10.1093\/biomet\/80.2.267","journal-title":"Biometrika"},{"issue":"4","key":"542_CR30","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1023\/A:1008981510081","volume":"10","author":"D Peel","year":"2000","unstructured":"Peel D, McLachlan GJ (2000) Robust mixture modelling using the t distribution. Stat Comput 10(4):339\u2013348","journal-title":"Stat Comput"},{"issue":"6","key":"542_CR31","doi-asserted-by":"publisher","first-page":"1506","DOI":"10.1002\/bimj.201500144","volume":"58","author":"A Punzo","year":"2016","unstructured":"Punzo A, McNicholas PD (2016) Parsimonious mixtures of multivariate contaminated normal distributions. Biom J 58(6):1506\u20131537. https:\/\/doi.org\/10.1002\/bimj.201500144","journal-title":"Biom J"},{"issue":"10","key":"542_CR32","doi-asserted-by":"publisher","first-page":"1","DOI":"10.18637\/jss.v085.i10","volume":"85","author":"A Punzo","year":"2018","unstructured":"Punzo A, Mazza A, McNicholas PD (2018) Contaminatedmixt: an R package for fitting parsimonious mixtures of multivariate contaminated normal distributions. J Stat Softw 85(10):1\u201325","journal-title":"J Stat Softw"},{"key":"542_CR33","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2019.107031","volume":"98","author":"A Punzo","year":"2020","unstructured":"Punzo A, Blostein M, McNicholas PD (2020) High-dimensional unsupervised classification via parsimonious contaminated mixtures. Pattern Recogn 98:107031. https:\/\/doi.org\/10.1016\/j.patcog.2019.107031","journal-title":"Pattern Recogn"},{"key":"542_CR34","volume-title":"Functional data analysis","author":"J Ramsay","year":"2006","unstructured":"Ramsay J, Silverman B (2006) Functional data analysis. Springer Series in Statistics, Springer, New York"},{"key":"542_CR35","doi-asserted-by":"crossref","unstructured":"Ritter G (2014) Robust cluster analysis and variable selection, monographs on statistics and applied probability, vol 37. Chapman and Hall\/CRC","DOI":"10.1201\/b17353"},{"issue":"1","key":"542_CR36","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/s11634-018-0312-7","volume":"13","author":"D Rivera-Garc\u00eda","year":"2019","unstructured":"Rivera-Garc\u00eda D, Garc\u00eda-Escudero LA, Mayo-Iscar A et al (2019) Robust clustering for functional data based on trimming and constraints. Adv Data Anal Classif 13(1):201\u2013225. https:\/\/doi.org\/10.1007\/s11634-018-0312-7","journal-title":"Adv Data Anal Classif"},{"issue":"1","key":"542_CR37","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1007\/s00180-011-0239-3","volume":"27","author":"P Sawant","year":"2012","unstructured":"Sawant P, Billor N, Shin H (2012) Functional outlier detection with robust functional principal component analysis. Comput Stat 27(1):83\u2013102. https:\/\/doi.org\/10.1007\/s00180-011-0239-3","journal-title":"Comput Stat"},{"key":"542_CR38","doi-asserted-by":"publisher","first-page":"1101","DOI":"10.1007\/s00180-020-00958-4","volume":"35","author":"A Schmutz","year":"2020","unstructured":"Schmutz A, Jacques J, Bouveyron C et al (2020) Clustering multivariate functional data in group-specific functional subspaces. Comput Stat 35:1101\u20131131","journal-title":"Comput Stat"},{"key":"542_CR39","doi-asserted-by":"crossref","unstructured":"Schwarz G (1978) Estimating the dimension of a model. Ann Stat pp 461\u2013464","DOI":"10.1214\/aos\/1176344136"},{"key":"542_CR40","doi-asserted-by":"publisher","first-page":"1115","DOI":"10.1007\/s00477-015-1096-3","volume":"30","author":"C Sguera","year":"2015","unstructured":"Sguera C, Galeano P, Lillo RE (2015) Functional outlier detection by a local depth with application to nox levels. Stoch Environ Res Risk Assess 30:1115\u20131130","journal-title":"Stoch Environ Res Risk Assess"},{"issue":"2","key":"542_CR41","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1007\/s10182-021-00430-8","volume":"106","author":"SD Tomarchio","year":"2022","unstructured":"Tomarchio SD, Bagnato L, Punzo A (2022) Model-based clustering via new parsimonious mixtures of heavy tailed distributions. AStA Adv Stat Anal 106(2):315\u2013347","journal-title":"AStA Adv Stat Anal"}],"container-title":["Advances in Data Analysis and Classification"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11634-023-00542-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11634-023-00542-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11634-023-00542-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,19]],"date-time":"2024-09-19T03:40:41Z","timestamp":1726717241000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11634-023-00542-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,12]]},"references-count":41,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,9]]}},"alternative-id":["542"],"URL":"https:\/\/doi.org\/10.1007\/s11634-023-00542-w","relation":{},"ISSN":["1862-5347","1862-5355"],"issn-type":[{"value":"1862-5347","type":"print"},{"value":"1862-5355","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,12]]},"assertion":[{"value":"11 November 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 March 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 April 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 May 2023","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 they have no financial interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}