{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T12:27:50Z","timestamp":1762432070493,"version":"3.37.3"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2021,8,28]],"date-time":"2021-08-28T00:00:00Z","timestamp":1630108800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,8,28]],"date-time":"2021-08-28T00:00:00Z","timestamp":1630108800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100006753","name":"CMUP","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100006753","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["SN COMPUT. SCI."],"published-print":{"date-parts":[[2021,11]]},"DOI":"10.1007\/s42979-021-00822-2","type":"journal-article","created":{"date-parts":[[2021,8,28]],"date-time":"2021-08-28T15:02:43Z","timestamp":1630162963000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Clustering of Longitudinal Trajectories Using Correlation-Based Distances"],"prefix":"10.1007","volume":"2","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3991-2715","authenticated-orcid":false,"given":"Joaquim F.","family":"Pinto da Costa","sequence":"first","affiliation":[]},{"given":"F\u00e1bio","family":"Ferreira","sequence":"additional","affiliation":[]},{"given":"Martina","family":"Mascarello","sequence":"additional","affiliation":[]},{"given":"Rita","family":"Gaio","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,8,28]]},"reference":[{"key":"822_CR1","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1111\/1467-9469.00350","volume":"30","author":"C Abraham","year":"2003","unstructured":"Abraham C, Cornillon P, Matzner-Lober E, Molinari N. Unsupervised curve clustering using B-splines. Scand J Stat. 2003;30:581\u201395.","journal-title":"Scand J Stat"},{"key":"822_CR2","unstructured":"Bagirov MA, Karmitsa N, Taheri S. Metaheuristic clustering algorithms. In: Partitional clustering via nonsmooth optimization. Unsupervised and semi-supervised learning. Springer, 2020."},{"issue":"2","key":"822_CR3","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1037\/1082-989X.7.2.245","volume":"7","author":"TP Beauchaine","year":"2002","unstructured":"Beauchaine TP, Beauchaine RJ. A comparison of maximum covariance and K-means cluster analysis in classifying cases into known taxon groups. Psychol Methods. 2002;7(2):245\u201361.","journal-title":"Psychol Methods"},{"issue":"1","key":"822_CR4","first-page":"1","volume":"3","author":"T Calinski","year":"1974","unstructured":"Calinski T, Harabasz J. A dendrite method for cluster analysis. Commun Stat. 1974;3(1):1\u201327.","journal-title":"Commun Stat."},{"issue":"6","key":"822_CR5","first-page":"1","volume":"63","author":"M Charrad","year":"2014","unstructured":"Charrad M, Ghazzali N, Boiteau V, Niknafs A. NbClust: an R package for determining the relevant number of clusters in a data set. J Stat Softw. 2014;63(6):1\u201336.","journal-title":"J Stat Softw"},{"issue":"7","key":"822_CR6","doi-asserted-by":"publisher","first-page":"992","DOI":"10.1080\/03610918.2012.625767","volume":"41","author":"A Ciampi","year":"2012","unstructured":"Ciampi A, et al. Model-based clustering of longitudinal data: application to modeling disease course and gene expression trajectories. Commun Stat. 2012;41(7):992\u20131005.","journal-title":"Commun Stat."},{"issue":"1","key":"822_CR7","first-page":"36","volume":"106","author":"EC Delmelle","year":"2016","unstructured":"Delmelle EC. Mapping the DNA of urban neighborhoods: clustering longitudinal sequences of neighborhood socioeconomic change. Ann Am Assoc Geogr. 2016;106(1):36\u201356.","journal-title":"Ann Am Assoc Geogr."},{"key":"822_CR8","doi-asserted-by":"crossref","unstructured":"Den Teuling NGP, Pauws SC, van den Heuvel ER. A comparison of methods for clustering longitudinal data with slowly changing trends. Commun Stat. (Published online: 19 Jan 2021).","DOI":"10.1080\/03610918.2020.1861464"},{"key":"822_CR9","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198524847.001.0001","volume-title":"Analysis of longitudinal data","author":"P Diggle","year":"2002","unstructured":"Diggle P, Heagerty P, Liang K-Y, Zeger S. Analysis of longitudinal data. New York: Oxford University Press Inc.; 2002."},{"key":"822_CR10","volume-title":"Applied longitudinal analysis","author":"G Fitzmaurice","year":"2004","unstructured":"Fitzmaurice G, Laird N, Ware J. Applied longitudinal analysis. New Jersey: Wiley; 2004."},{"key":"822_CR11","doi-asserted-by":"publisher","first-page":"611","DOI":"10.1198\/016214502760047131","volume":"97","author":"C Fraley","year":"2002","unstructured":"Fraley C, Raftery AE. Model-based clustering, discriminant analysis, and density estimation. J Am Stat Assoc. 2002;97:611\u201331.","journal-title":"J Am Stat Assoc"},{"key":"822_CR12","volume-title":"KmL: k-means for longitudinal data","author":"C Genolini","year":"2009","unstructured":"Genolini C, et al. KmL: k-means for longitudinal data. Berlin: Springer; 2009."},{"issue":"4","key":"822_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.18637\/jss.v065.i04","volume":"65","author":"C Genolini","year":"2015","unstructured":"Genolini C, et al. kml and kml3d: packages to cluster longitudinal data. J Stat Softw. 2015;65(4):1\u201334.","journal-title":"J Stat Softw"},{"issue":"04","key":"822_CR14","doi-asserted-by":"publisher","first-page":"26","DOI":"10.4236\/ojs.2013.34A004","volume":"3","author":"C Genolini","year":"2013","unstructured":"Genolini C, \u00c9cochard R, Jacqmin-Gadda H. Copy mean: a new method to impute intermittent missing values in longitudinal studies. Open J Stat. 2013;3(04):26.","journal-title":"Open J Stat."},{"key":"822_CR15","volume-title":"The elements of statistical learning. Data mining inference and predictions","author":"T Hastie","year":"2009","unstructured":"Hastie T, et al. The elements of statistical learning. Data mining inference and predictions. Berlin: Springer; 2009."},{"key":"822_CR16","unstructured":"Hedeker D, Gibbons RD. Longitudinal data analysis. Wiley Series in Probability and Statistics; 2006."},{"key":"822_CR17","volume-title":"Longitudinal cluster analysis with applications to growth trajectories","author":"BC Heggeseth","year":"2013","unstructured":"Heggeseth BC. Longitudinal cluster analysis with applications to growth trajectories. Berkeley: University of California; 2013."},{"key":"822_CR18","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1198\/016214503000189","volume":"98","author":"G James","year":"2003","unstructured":"James G, Sugar C. Clustering for sparsely sampled functional data. J Am Stat Assoc. 2003;98:397\u2013408.","journal-title":"J Am Stat Assoc"},{"key":"822_CR19","first-page":"979","volume":"26","author":"E Kurum","year":"2016","unstructured":"Kurum E, Li R, Shiffman S, Yao W. Time-varying coefficient models for joint modeling binary and continuous outcomes in longitudinal data. Stat Sin. 2016;26:979\u20131000.","journal-title":"Stat Sin"},{"issue":"1","key":"822_CR20","first-page":"1","volume":"31","author":"LP C\u00e9line","year":"2015","unstructured":"C\u00e9line LP, et al. Using a continuous riverscape survey to examine the effects of the spatial structure of functional habitats on fish distribution. J Freshwater Ecol. 2015;31(1):1\u201319.","journal-title":"J Freshwater Ecol."},{"key":"822_CR21","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1186\/1471-2105-5-172","volume":"5","author":"Y Lu","year":"2004","unstructured":"Lu Y, Lu S, Fotouhi F, Deng Y, Brown SJ. Incremental genetic K-means algorithm and its application in gene expression data analysis. BMC Bioinform. 2004;5:172.","journal-title":"BMC Bioinform"},{"issue":"2","key":"822_CR22","doi-asserted-by":"publisher","first-page":"430","DOI":"10.1080\/03610926.2013.821488","volume":"45","author":"A Maruotti","year":"2016","unstructured":"Maruotti A, et al. Time-varying clustering of multivariate longitudinal observations. Commun Stat. 2016;45(2):430\u201343.","journal-title":"Commun Stat."},{"key":"822_CR23","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1214\/09-SS053","volume":"4","author":"V Melnykov","year":"2010","unstructured":"Melnykov V, Maitra R. Finite mixture models and model-based clustering. Stat Surv. 2010;4:80\u2013116.","journal-title":"Stat Surv"},{"issue":"2","key":"822_CR24","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1007\/BF02294245","volume":"50","author":"GW Milligan","year":"1985","unstructured":"Milligan GW, Cooper MC. An examination of procedures for determining the number of clusters in a data set. Psychometrika. 1985;50(2):159\u201379.","journal-title":"Psychometrika"},{"issue":"4","key":"822_CR25","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1080\/01688638608401328","volume":"8","author":"R Morris","year":"1986","unstructured":"Morris R, et al. Developmental classification of reading-disabled children. J Clin Exp Neuropsychol. 1986;8(4):371\u201392.","journal-title":"J Clin Exp Neuropsychol."},{"issue":"6","key":"822_CR26","first-page":"730","volume":"43","author":"CC Ng","year":"2014","unstructured":"Ng CC. Examining the self-congruent engagement hypothesis: the link between academic self-schemas, motivational goals, learning approaches and achievement within an academic year. Educ Psychol. 2014;43(6):730\u201362.","journal-title":"Educ Psychol."},{"key":"822_CR27","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1198\/106186007X236127","volume":"16","author":"M-S Oh","year":"2007","unstructured":"Oh M-S, Raftery AE. Model-based clustering with dissimilarities: a Bayesian approach. J Comput Graph Stat. 2007;16:559\u201385.","journal-title":"J Comput Graph Stat"},{"issue":"3","key":"822_CR28","doi-asserted-by":"publisher","first-page":"677","DOI":"10.1093\/biomet\/86.3.677","volume":"86","author":"M Pourahmadi","year":"1999","unstructured":"Pourahmadi M. Joint mean-covariance models with applications to longitudinal data: unconstrained parameterisation. Biometrika. 1999;86(3):677\u201390.","journal-title":"Biometrika"},{"issue":"2","key":"822_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.18637\/jss.v078.i02","volume":"78","author":"C Proust-Lima","year":"2017","unstructured":"Proust-Lima C, Philipps V, Liquet B. Estimation of extended mixed models using latent classes and latent processes: the R package lcmm. J Stat Softw. 2017;78(2):1\u201356.","journal-title":"J Stat Softw."},{"issue":"3","key":"822_CR30","first-page":"229","volume":"66","author":"S Qin","year":"2016","unstructured":"Qin S, et al. Forage crops alter soil bacterial and fungal communities in an apple orchard. Acta Agriculturae Scandinavica. 2016;66(3):229\u201336.","journal-title":"Acta Agriculturae Scandinavica."},{"key":"822_CR31","unstructured":"Rossi F, Conan-Guez B, Golli AE. Clustering functional data with the SOM algorithm. In: Proceedings of ESANN, 2004;305\u2013312."},{"key":"822_CR32","unstructured":"Shim Y, Chung J, Choi I-C. A comparison study of cluster validity indices using a nonhierarchical clustering algorithm. IEEE Comput Soc. 2005."},{"issue":"8","key":"822_CR33","doi-asserted-by":"publisher","first-page":"1027","DOI":"10.5588\/ijtld.15.0522","volume":"20","author":"P Sousa","year":"2016","unstructured":"Sousa P, Oliveira A, Gomes M, Gaio AR, Duarte R. Longitudinal clustering of tuberculosis incidence and predictors for the time profiles: the impact of HIV. Int J Tuberc Lung Dis. 2016;20(8):1027\u201332.","journal-title":"Int J Tuberc Lung Dis."},{"key":"822_CR34","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/s00357-003-0007-3","volume":"20","author":"T Tarpey","year":"2003","unstructured":"Tarpey T, Kinateder K. Clustering functional data. J Classif. 2003;20:93\u2013114.","journal-title":"J Classif"},{"issue":"2","key":"822_CR35","doi-asserted-by":"publisher","first-page":"1010","DOI":"10.1214\/12-AOAS617","volume":"7","author":"DQ Vu","year":"2013","unstructured":"Vu DQ, Hunter DR, Schweinberger M. Model-based clustering of large networks. Ann Appl Stat. 2013;7(2):1010.","journal-title":"Ann Appl Stat"},{"key":"822_CR36","doi-asserted-by":"publisher","first-page":"619","DOI":"10.1093\/biomet\/asz011","volume":"106","author":"P-S Zhong","year":"2019","unstructured":"Zhong P-S, Li R, Santo S. Homogeneity test of covariance matrices and change-points identification with high-Dimensional longitudinal data. Biometrika. 2019;106:619\u201334.","journal-title":"Biometrika"}],"container-title":["SN Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42979-021-00822-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s42979-021-00822-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42979-021-00822-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,7]],"date-time":"2023-11-07T23:30:11Z","timestamp":1699399811000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s42979-021-00822-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,28]]},"references-count":36,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2021,11]]}},"alternative-id":["822"],"URL":"https:\/\/doi.org\/10.1007\/s42979-021-00822-2","relation":{},"ISSN":["2662-995X","2661-8907"],"issn-type":[{"type":"print","value":"2662-995X"},{"type":"electronic","value":"2661-8907"}],"subject":[],"published":{"date-parts":[[2021,8,28]]},"assertion":[{"value":"1 March 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 August 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 August 2021","order":3,"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"}}],"article-number":"432"}}