{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T12:19:12Z","timestamp":1783426752746,"version":"3.54.6"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T00:00:00Z","timestamp":1778630400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T00:00:00Z","timestamp":1778630400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100002555","name":"Seoul Women\u2019s University","doi-asserted-by":"crossref","award":["2025-0246"],"award-info":[{"award-number":["2025-0246"]}],"id":[{"id":"10.13039\/501100002555","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Stat"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1007\/s00180-026-01757-z","type":"journal-article","created":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T05:04:28Z","timestamp":1778648668000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Functional k-means clustering with elastic distances accounting for phase and amplitude variation"],"prefix":"10.1007","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-2572-0630","authenticated-orcid":false,"given":"Kyungmin","family":"Ahn","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jeong Hoon","family":"Jang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,13]]},"reference":[{"key":"1757_CR1","doi-asserted-by":"crossref","unstructured":"Ahn K, Tucker JD, Wu W, Srivastava A (2018) Elastic handling of predictor phase in functional regression models. In: Proceedings of the IEEE conference on computer vision and pattern recognition workshops. IEEE, Salt Lake City, UT, USA. pp 324\u2013331","DOI":"10.1109\/CVPRW.2018.00072"},{"key":"1757_CR2","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2020.107017","author":"K Ahn","year":"2020","unstructured":"Ahn K, Tucker JD, Wu W, Srivastava A (2020) Regression models using shapes of functions as predictors. Comput Stat Data Anal. https:\/\/doi.org\/10.1016\/j.csda.2020.107017","journal-title":"Comput Stat Data Anal"},{"issue":"4","key":"1757_CR3","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. https:\/\/doi.org\/10.1007\/s11634-011-0095-6","journal-title":"Adv Data Anal Classif"},{"issue":"4","key":"1757_CR4","doi-asserted-by":"publisher","first-page":"1726","DOI":"10.1214\/15-AOAS861","volume":"9","author":"C Bouveyron","year":"2015","unstructured":"Bouveyron C, C\u00f4me E, Jacques J (2015) The discriminative functional mixture model for a comparative analysis of bike sharing systems. Ann Appl Stat 9(4):1726\u20131760. https:\/\/doi.org\/10.1214\/15-AOAS861","journal-title":"Ann Appl Stat"},{"key":"1757_CR5","unstructured":"Chen Y, Keogh E, Hu B, Begum N, Bagnall A, Mueen A, Batista G (2015) The UCR time series classification archive . University of California, Riverside. Available at: http:\/\/www.cs.ucr.edu\/~eamonn\/time_series_data\/"},{"key":"1757_CR6","doi-asserted-by":"publisher","unstructured":"Febrero-Bande M, Oviedo 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","DOI":"10.18637\/jss.v051.i04"},{"issue":"7","key":"1757_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.18637\/jss.v031.i07","volume":"31","author":"T Giorgino","year":"2009","unstructured":"Giorgino T (2009) Computing and visualizing dynamic time warping alignments in R: the dtw package. J Stat Softw 31(7):1\u201324. https:\/\/doi.org\/10.18637\/jss.v031.i07","journal-title":"J Stat Softw"},{"issue":"1","key":"1757_CR8","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. https:\/\/doi.org\/10.1007\/BF01908075","journal-title":"J Classif"},{"key":"1757_CR9","unstructured":"Kaplan D (2025) Knee point. MATLAB Central File Exchange. https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/35094-knee-point. Retrieved 21 Oct 2025"},{"issue":"2","key":"1757_CR10","doi-asserted-by":"publisher","first-page":"1697","DOI":"10.1214\/14-ejs901","volume":"8","author":"JS Marron","year":"2014","unstructured":"Marron JS, Ramsay JO, Sangalli LM, Srivastava A (2014) Statistics of time warpings and phase variations. Electron J Stat 8(2):1697\u20131702. https:\/\/doi.org\/10.1214\/14-ejs901","journal-title":"Electron J Stat"},{"key":"1757_CR11","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, 2nd edn. Springer, Berlin","edition":"2"},{"issue":"5","key":"1757_CR12","doi-asserted-by":"publisher","first-page":"1219","DOI":"10.1016\/j.csda.2009.12.008","volume":"54","author":"LM Sangalli","year":"2010","unstructured":"Sangalli LM, Secchi P, Vantini S, Vitelli V (2010) K-mean alignment for curve clustering. Comput Stat Data Anal 54(5):1219\u20131233. https:\/\/doi.org\/10.1016\/j.csda.2009.12.008","journal-title":"Comput Stat Data Anal"},{"key":"1757_CR13","doi-asserted-by":"publisher","unstructured":"Sarda-Espinosa A (2019) Time-series clustering in R using the dtwclust package. The R Journal 11(1): 22\u201343. https:\/\/doi.org\/10.32614\/RJ-2019-023","DOI":"10.32614\/RJ-2019-023"},{"key":"1757_CR14","doi-asserted-by":"crossref","unstructured":"Satopaa V, Albrecht J, Irwin D, Raghavan B (2011) Finding a \u201cKneedle\u201d in a haystack: detecting knee points in system behavior. In: 2011 31st International conference on distributed computing systems workshops. IEEE, Minneapolis, MN, USA. pp 166\u2013171","DOI":"10.1109\/ICDCSW.2011.20"},{"key":"1757_CR15","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4939-4020-2","volume-title":"Functional and shape data analysis","author":"A Srivastava","year":"2016","unstructured":"Srivastava A, Klassen E (2016) Functional and shape data analysis. Springer, Berlin"},{"key":"1757_CR16","doi-asserted-by":"publisher","unstructured":"Srivastava A, Wu W, Kurtek S, Klassen E, Marron JS (2011) Registration of functional data using Fisher\u2013Rao metric. arXiv preprint. https:\/\/doi.org\/10.48550\/arXiv.1103.3817","DOI":"10.48550\/arXiv.1103.3817"},{"issue":"4","key":"1757_CR17","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1007\/BF02289263","volume":"18","author":"RL Thorndike","year":"1953","unstructured":"Thorndike RL (1953) Who belongs in the family? Psychometrika 18(4):267\u2013276. https:\/\/doi.org\/10.1007\/BF02289263","journal-title":"Psychometrika"},{"issue":"2","key":"1757_CR18","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1111\/1467-9868.00293","volume":"63","author":"R Tibshirani","year":"2001","unstructured":"Tibshirani R, Walther G, Hastie T (2001) Estimating the number of clusters in a data set via the gap statistic. J R Stat Soc B 63(2):411\u2013423. https:\/\/doi.org\/10.1111\/1467-9868.00293","journal-title":"J R Stat Soc B"},{"key":"1757_CR19","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1016\/j.csda.2012.12.001","volume":"61","author":"JD Tucker","year":"2013","unstructured":"Tucker JD, Wu W, Srivastava A (2013) Generative models for functional data using phase and amplitude separation. Comput Stat Data Anal 61:50\u201366. https:\/\/doi.org\/10.1016\/j.csda.2012.12.001","journal-title":"Comput Stat Data Anal"},{"issue":"2","key":"1757_CR20","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1002\/sam.11399","volume":"12","author":"JD Tucker","year":"2019","unstructured":"Tucker JD, Lewis JR, Srivastava A (2019) Elastic functional principal component regression. Stat Anal Data Min ASA Data Sci J 12(2):101\u2013115. https:\/\/doi.org\/10.1002\/sam.11399","journal-title":"Stat Anal Data Min ASA Data Sci J"},{"issue":"1","key":"1757_CR21","doi-asserted-by":"publisher","DOI":"10.1002\/sta4.551","volume":"12","author":"JD Tucker","year":"2023","unstructured":"Tucker JD, Martinez MT, Laborde JM (2023) Dimensionality reduction using elastic measures. Stat 12(1):e551. https:\/\/doi.org\/10.1002\/sta4.551","journal-title":"Stat"},{"key":"1757_CR22","doi-asserted-by":"crossref","unstructured":"Vinh NX, Epps J, Bailey J (2009) Information theoretic measures for clusterings comparison: is a correction for chance necessary? In: Proceedings of the 26th annual international conference on machine learning. ACM, Montreal, QC, Canada. pp 1073\u20131080","DOI":"10.1145\/1553374.1553511"},{"issue":"2","key":"1757_CR23","doi-asserted-by":"publisher","first-page":"1776","DOI":"10.1214\/14-EJS865B","volume":"8","author":"W Wu","year":"2014","unstructured":"Wu W, Srivastava A (2014) Analysis of spike train data: alignment and comparisons using the extended Fisher\u2013Rao metric. Electron J Stat 8(2):1776\u20131785. https:\/\/doi.org\/10.1214\/14-EJS865B","journal-title":"Electron J Stat"},{"key":"1757_CR24","doi-asserted-by":"publisher","unstructured":"Zang X, Kurtek S, Chkrebtii O, Tucker JD (2020) Elastic $$ k $$-means clustering of functional data for posterior exploration, with an application to inference on acute respiratory infection dynamics. arXiv preprint. https:\/\/doi.org\/10.48550\/arXiv.2011.12397","DOI":"10.48550\/arXiv.2011.12397"}],"container-title":["Computational Statistics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-026-01757-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00180-026-01757-z","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-026-01757-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T11:49:41Z","timestamp":1783424981000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00180-026-01757-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,13]]},"references-count":24,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2026,6]]}},"alternative-id":["1757"],"URL":"https:\/\/doi.org\/10.1007\/s00180-026-01757-z","relation":{},"ISSN":["0943-4062","1613-9658"],"issn-type":[{"value":"0943-4062","type":"print"},{"value":"1613-9658","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,13]]},"assertion":[{"value":"14 November 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 April 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 May 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"80"}}