{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T18:12:56Z","timestamp":1773943976051,"version":"3.50.1"},"reference-count":53,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2019,1,21]],"date-time":"2019-01-21T00:00:00Z","timestamp":1548028800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100008530","name":"European Regional Development Fund","doi-asserted-by":"crossref","award":["POCI-01-0145-FEDER-006961"],"award-info":[{"award-number":["POCI-01-0145-FEDER-006961"]}],"id":[{"id":"10.13039\/501100008530","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100008530","name":"European Regional Development Fund","doi-asserted-by":"crossref","award":["POCI-01-0145-FEDER-006961"],"award-info":[{"award-number":["POCI-01-0145-FEDER-006961"]}],"id":[{"id":"10.13039\/501100008530","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2019,9]]},"DOI":"10.1007\/s11222-018-09851-z","type":"journal-article","created":{"date-parts":[[2019,1,21]],"date-time":"2019-01-21T09:14:20Z","timestamp":1548062060000},"page":"1011-1034","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Clustering of interval time series"],"prefix":"10.1007","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5513-962X","authenticated-orcid":false,"given":"Elizabeth Ann","family":"Maharaj","sequence":"first","affiliation":[]},{"given":"Paulo","family":"Teles","sequence":"additional","affiliation":[]},{"given":"Paula","family":"Brito","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,1,21]]},"reference":[{"key":"9851_CR1","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1111\/j.1467-9892.2006.00488.x","volume":"27","author":"AMC Antunes","year":"2006","unstructured":"Antunes, A.M.C., Subba Rao, T.: On hypotheses testing for the selection of spatio-temporal models. J. Time Ser. Anal. 27, 767\u2013791 (2006)","journal-title":"J. Time Ser. Anal."},{"key":"9851_CR2","unstructured":"Arroyo, J.: M\u00e9todos de Predicci\u00f3n para Series Temporales de Intervalos e Histogramas. PhD thesis, Universidad Pontificia Comillas, Madrid (2008)"},{"issue":"1","key":"9851_CR3","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/j.ijforecast.2008.07.003","volume":"25","author":"J Arroyo","year":"2009","unstructured":"Arroyo, J., Mat\u00e9, C.: Forecasting histogram time series with k-nearest neighbours methods. Int. J. Forecast. 25(1), 192\u2013207 (2009)","journal-title":"Int. J. Forecast."},{"key":"9851_CR4","doi-asserted-by":"crossref","unstructured":"Bertrand, P., Goupil, F.: Descriptive statistics for symbolic data. In: Bock, H.-H., Diday, E. (eds.) Analysis of Symbolic Data, pp. 106\u2013124. Exploratory Methods for Extracting Statistical Information from Complex Data, Springer, Heidelberg (2000)","DOI":"10.1007\/978-3-642-57155-8_6"},{"key":"9851_CR5","unstructured":"Billard, L.: Sample covariance functions for complex quantitative data. In: Proceedings of the World IASC Conference, Yokohama, Japan, pp. 157\u2013163 (2008)"},{"issue":"462","key":"9851_CR6","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1198\/016214503000242","volume":"98","author":"L Billard","year":"2003","unstructured":"Billard, L., Diday, E.: From the statistics of data to the statistics of knowledge: symbolic data analysis. J. Am. Stat. Assoc. 98(462), 470\u2013487 (2003)","journal-title":"J. Am. Stat. Assoc."},{"key":"9851_CR7","doi-asserted-by":"crossref","DOI":"10.1002\/9780470090183","volume-title":"Symbolic Data Analysis: Conceptual Statistics and Data Mining","author":"L Billard","year":"2006","unstructured":"Billard, L., Diday, E.: Symbolic Data Analysis: Conceptual Statistics and Data Mining. Wiley, Chichester (2006)"},{"issue":"4","key":"9851_CR8","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1002\/widm.1133","volume":"4","author":"P Brito","year":"2014","unstructured":"Brito, P.: Symbolic data analysis: another look at the interaction of data mining and statistics. WIREs Data Min. Knowl. Discov. 4(4), 281\u2013295 (2014)","journal-title":"WIREs Data Min. Knowl. Discov."},{"key":"9851_CR9","doi-asserted-by":"publisher","unstructured":"Caldwell, P.C., Merrifield, M.A., Thompson, P.R.: Sea level measured by tide gauges from global oceans\u2013the joint archive for sea level holdings (NCEI Accession 0019568), Version 5.5. In: NOAA National Centers for Environmental Information, Dataset (2015). https:\/\/doi.org\/10.7289\/V5V40S7W","DOI":"10.7289\/V5V40S7W"},{"key":"9851_CR10","volume-title":"Handbook of Cluster Analysis","author":"J Caiado","year":"2015","unstructured":"Caiado, J., Maharaj, E.A., D\u2019Urso, P.: Time series clustering. In: Hennig, C., Meila, M., Murtagh, F., Rocci, R. (eds.) Handbook of Cluster Analysis. Chapman and Hall, New York (2015)"},{"key":"9851_CR11","doi-asserted-by":"crossref","unstructured":"Chavent, M., Lechevallier, Y.: Dynamical clustering of interval data: optimization of an adequacy criterion based on Hausdorff distance. In: Classification, Clustering, and Data Analysis, pp. 53\u201360. Springer, Berlin (2002)","DOI":"10.1007\/978-3-642-56181-8_5"},{"key":"9851_CR12","first-page":"297","volume":"37","author":"AD Cliff","year":"1975","unstructured":"Cliff, A.D., Ord, J.K.: Model building and the analysis of spatial pattern in human geography. J. R. Stat. Soc. B 37, 297\u2013328 (1975)","journal-title":"J. R. Stat. Soc. B"},{"key":"9851_CR13","doi-asserted-by":"crossref","unstructured":"Crespo, F., Peters, G., Weber, R.: Rough clustering approaches for dynamic environments. In: Peters, G., Lingras, P., \u015al\u0229zak, D., Yao, Y. (eds.) Rough Sets: Selected Methods and Applications in Management and Engineering. Advanced Information and Knowledge Processing. Springer, London (2012)","DOI":"10.1007\/978-1-4471-2760-4_3"},{"key":"9851_CR14","doi-asserted-by":"crossref","DOI":"10.1002\/9781119115151","volume-title":"Statistics for Spatial Data","author":"NAC Cressie","year":"1993","unstructured":"Cressie, N.A.C.: Statistics for Spatial Data. Wiley, New York (1993)"},{"key":"9851_CR15","volume-title":"Statistics for Spatio-temporal Data","author":"NAC Cressie","year":"2011","unstructured":"Cressie, N.A.C., Wikle, C.K.: Statistics for Spatio-temporal Data. Wiley, Hoboken (2011)"},{"issue":"7","key":"9851_CR16","doi-asserted-by":"crossref","first-page":"1223","DOI":"10.1016\/j.patcog.2008.11.016","volume":"42","author":"FAT Carvalho De","year":"2009","unstructured":"De Carvalho, F.A.T., Lechevallier, Y.: Partitional clustering algorithms for symbolic interval data based on single adaptive distances. Pattern Recognit. 42(7), 1223\u20131236 (2009)","journal-title":"Pattern Recognit."},{"issue":"2","key":"9851_CR17","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/s00180-006-0261-z","volume":"21","author":"FAT Carvalho De","year":"2006","unstructured":"De Carvalho, F.A.T., Brito, P., Bock, H.-H.: Dynamic clustering for interval data based on $$L_2$$ L 2 distance. Comput. Stat. 21(2), 231\u2013250 (2006a)","journal-title":"Comput. Stat."},{"issue":"3","key":"9851_CR18","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.patrec.2005.08.014","volume":"27","author":"FAT Carvalho De","year":"2006","unstructured":"De Carvalho, F.A.T., De Souza, R.M.C.R., Chavent, M., Lechevallier, Y.: Adaptive Hausdorff distances and dynamic clustering of symbolic interval data. Pattern Recognit. Lett. 27(3), 167\u2013179 (2006b)","journal-title":"Pattern Recognit. Lett."},{"key":"9851_CR19","doi-asserted-by":"crossref","unstructured":"De Carvalho, F.A.T., Lechevallier, Y., Verde R.: Clustering methods in symbolic data analysis. In: Diday, E., Noirhomme-Fraiture, M. (eds) Symbolic Data Analysis and the SODAS Software, Chichester, pp. 182\u2013203 (2008)","DOI":"10.1002\/9780470723562.ch11"},{"issue":"3","key":"9851_CR20","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1016\/j.patrec.2003.10.016","volume":"25","author":"RMCR Souza De","year":"2004","unstructured":"De Souza, R.M.C.R., De Carvalho, F.A.T.: Clustering of interval data based on city-block distances. Pattern Recognit. Lett. 25(3), 353\u2013365 (2004)","journal-title":"Pattern Recognit. Lett."},{"issue":"3","key":"9851_CR21","doi-asserted-by":"crossref","first-page":"1118","DOI":"10.1016\/j.ejor.2016.09.006","volume":"258","author":"S Dias","year":"2017","unstructured":"Dias, S., Brito, P.: Off the beaten track: a new linear model for interval data. Eur. J. Oper. Res. 258(3), 1118\u20131130 (2017)","journal-title":"Eur. J. Oper. Res."},{"key":"9851_CR22","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/978-3-642-96303-2_3","volume-title":"Clustering Analysis. Digital Pattern Recognition","author":"E Diday","year":"1976","unstructured":"Diday, E., Simon, J.C.: Clustering Analysis. Digital Pattern Recognition, pp. 47\u201394. Springer, Berlin (1976)"},{"key":"9851_CR23","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-48536-2","volume-title":"Model-Based Geostatistics","author":"PJ Diggle","year":"2007","unstructured":"Diggle, P.J., Ribeiro Jr., P.J.: Model-Based Geostatistics. Springer, New York (2007)"},{"issue":"2","key":"9851_CR24","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1002\/sam.10118","volume":"4","author":"A Douzal-Chouakria","year":"2011","unstructured":"Douzal-Chouakria, A., Billard, L., Diday, E.: Principal component analysis for interval-valued observations. Stat. Anal. Data Min. 4(2), 229\u2013246 (2011)","journal-title":"Stat. Anal. Data Min."},{"issue":"2","key":"9851_CR25","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1007\/s00180-006-0264-9","volume":"21","author":"AP Duarte Silva","year":"2006","unstructured":"Duarte Silva, A.P., Brito, P.: Linear discriminant analysis for interval data. Comput. Stat. 21(2), 289\u2013308 (2006)","journal-title":"Comput. Stat."},{"issue":"3","key":"9851_CR26","doi-asserted-by":"crossref","first-page":"516","DOI":"10.1007\/s00357-015-9189-8","volume":"32","author":"AP Duarte Silva","year":"2015","unstructured":"Duarte Silva, A.P., Brito, P.: Discriminant analysis of interval data: an assessment of parametric and distance-based approaches. J. Classif. 32(3), 516\u2013541 (2015)","journal-title":"J. Classif."},{"key":"9851_CR27","doi-asserted-by":"crossref","first-page":"3565","DOI":"10.1016\/j.fss.2009.04.013","volume":"160","author":"P D\u2019Urso","year":"2009","unstructured":"D\u2019Urso, P., Maharaj, E.A.: Autocorrelation-based fuzzy clustering of time series. Fuzzy Sets Syst. 160, 3565\u20133589 (2009)","journal-title":"Fuzzy Sets Syst."},{"key":"9851_CR28","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.fss.2011.10.002","volume":"193","author":"P D\u2019Urso","year":"2012","unstructured":"D\u2019Urso, P., Maharaj, E.A.: Wavelets-based clustering of multivariate time series. Fuzzy Sets Syst. 193, 33\u201361 (2012)","journal-title":"Fuzzy Sets Syst."},{"key":"9851_CR29","doi-asserted-by":"crossref","unstructured":"Finkenstadt, B., Held, L., Isham, V. (eds).: Statistical Methods for Spatio-Temporal Systems. Chapman and Hall, London (2007)","DOI":"10.1201\/9781420011050"},{"issue":"2","key":"9851_CR30","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1016\/j.enpol.2009.10.007","volume":"38","author":"C Garc\u00eda-Ascanio","year":"2010","unstructured":"Garc\u00eda-Ascanio, C., Mat\u00e9, C.: Electric power demand forecasting using interval time series: a comparison between var and imlp. Energy Policy 38(2), 715\u2013725 (2010)","journal-title":"Energy Policy"},{"key":"9851_CR31","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/s00180-009-0178-4","volume":"25","author":"C Genolini","year":"2010","unstructured":"Genolini, C., Falissard, B.: Kml: k-means for longitudinal data. Comput. Stat. 25, 317\u2013328 (2010)","journal-title":"Comput. Stat."},{"issue":"1","key":"9851_CR32","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.ijforecast.2011.02.007","volume":"28","author":"G Gonz\u00e1lez-Rivera","year":"2012","unstructured":"Gonz\u00e1lez-Rivera, G., Arroyo, J.: Time series modeling of histogram-valued data: the daily histogram time series of s&p500 intradaily returns. Int. J. Forecast. 28(1), 20\u201333 (2012)","journal-title":"Int. J. Forecast."},{"issue":"4","key":"9851_CR33","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1007\/s11424-008-9135-5","volume":"21","author":"A Han","year":"2008","unstructured":"Han, A., Yongmiao, H., La, K.K., Shouyang, W.: Interval time series analysis with an application to the sterling-dollar exchange rate. J. Syst. Sci. Complex. 21(4), 558\u2013573 (2008)","journal-title":"J. Syst. Sci. Complex."},{"key":"9851_CR34","unstructured":"Han, A., Hong, Y., Wang, S.: Autoregressive conditional models for interval-valued time series data. In: The 3rd International Conference on Singular Spectrum Analysis and Its Applications (2012)"},{"key":"9851_CR35","doi-asserted-by":"crossref","unstructured":"Hennig, C., Meila, M., Murtagh, F., Rocci, R. (eds): Handbook of Cluster Analysis. Chapman and Hall\/CRC, London (2015)","DOI":"10.1201\/b19706"},{"issue":"1","key":"9851_CR36","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/BF01908075","volume":"2","author":"L Hubert","year":"1985","unstructured":"Hubert, L., Arabie, P.: Comparing partitions. J. Classif. 2(1), 193\u2013218 (1985)","journal-title":"J. Classif."},{"key":"9851_CR37","doi-asserted-by":"crossref","unstructured":"Irpino, A., Verde, R. (2006) A new Wasserstein based distance for the hierarchical clustering of histogram symbolic data. In: Batagelj V, Bock HH, Ferligoj A (eds.) Proceedings of the Conference of the International Federation of Classification Societies (IFCS06), pp. 185\u2013192. Springer, Heidelberg","DOI":"10.1007\/3-540-34416-0_20"},{"key":"9851_CR38","volume-title":"Econometric Methods","author":"J Johnston","year":"1997","unstructured":"Johnston, J., Dinardo, J.: Econometric Methods, 2nd edn. McGraw-Hill, New York (1997)","edition":"2"},{"key":"9851_CR39","volume-title":"Statistical Analysis of Environmental Space-Time Processes","author":"ND Le","year":"2006","unstructured":"Le, N.D., Zidek, J.V.: Statistical Analysis of Environmental Space-Time Processes. Springer, New York (2006)"},{"issue":"2","key":"9851_CR40","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1080\/10618600.2012.679895","volume":"21","author":"J Le-Rademacher","year":"2012","unstructured":"Le-Rademacher, J., Billard, L.: Symbolic covariance principal component analysis and visualization for interval-valued data. J. Comput. Gr. Stat. 21(2), 413\u2013432 (2012)","journal-title":"J. Comput. Gr. Stat."},{"issue":"3","key":"9851_CR41","doi-asserted-by":"crossref","first-page":"1500","DOI":"10.1016\/j.csda.2007.04.014","volume":"52","author":"E LimaNeto","year":"2008","unstructured":"LimaNeto, E., De Carvalho, F.A.T.: Centre and range method for fitting a linear regression model to symbolic interval data. Comput. Stat. Data Anal. 52(3), 1500\u20131515 (2008)","journal-title":"Comput. Stat. Data Anal."},{"issue":"2","key":"9851_CR42","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/j.csda.2009.08.010","volume":"54","author":"E LimaNeto","year":"2010","unstructured":"LimaNeto, E., De Carvalho, F.A.T.: Constrained linear regression models for symbolic interval-valued variables. Comput. Stat. Data Anal. 54(2), 333\u2013347 (2010)","journal-title":"Comput. Stat. Data Anal."},{"issue":"11","key":"9851_CR43","doi-asserted-by":"crossref","first-page":"1727","DOI":"10.1080\/00949655.2010.500470","volume":"81","author":"E LimaNeto","year":"2011","unstructured":"LimaNeto, E., De Carvalho, F.A.T.: Bivariate symbolic regression models for interval-valued variables. J. Stat. Comput. Simul. 81(11), 1727\u20131744 (2011)","journal-title":"J. Stat. Comput. Simul."},{"issue":"16","key":"9851_CR44","doi-asserted-by":"crossref","first-page":"3344","DOI":"10.1016\/j.neucom.2008.02.022","volume":"71","author":"ALS Maia","year":"2008","unstructured":"Maia, A.L.S., De Carvalho, F.A.T., Ludermir, T.B.: Forecasting models for interval-valued time series. Neurocomputing 71(16), 3344\u20133352 (2008)","journal-title":"Neurocomputing"},{"key":"9851_CR45","volume-title":"Wavelets Analysis for Time Series Analysis","author":"D Percival","year":"2000","unstructured":"Percival, D., Walden, A.: Wavelets Analysis for Time Series Analysis. Cambridge University Press, Cambridge (2000)"},{"key":"9851_CR46","doi-asserted-by":"crossref","first-page":"35","DOI":"10.2307\/1268381","volume":"22","author":"P Pfeifer","year":"1980","unstructured":"Pfeifer, P., Deutsch, S.: A three stage interactive procedure for space-time modeling. Technometrics 22, 35\u201347 (1980)","journal-title":"Technometrics"},{"key":"9851_CR47","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1016\/j.ins.2016.08.068","volume":"372","author":"AB Ramos-Guajardo","year":"2016","unstructured":"Ramos-Guajardo, A.B., Grzegorzewski, P.: Distance-based linear discriminant analysis for interval-valued data. Inf. Sci. 372, 591\u2013607 (2016)","journal-title":"Inf. Sci."},{"issue":"1","key":"9851_CR48","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/s11634-014-0170-x","volume":"9","author":"PM Rodrigues","year":"2015","unstructured":"Rodrigues, P.M., Salish, N.: Modeling and forecasting interval time series with threshold models. Adv. Data Anal. Classif. 9(1), 41\u201357 (2015)","journal-title":"Adv. Data Anal. Classif."},{"key":"9851_CR49","unstructured":"Teles, P., Brito, P.: Modelling interval time series data. In: Proceedings of the 3rd IASC World Conference on Computational Statistics and Data Analysis, Limassol, Cyprus (2005)"},{"issue":"17","key":"9851_CR50","doi-asserted-by":"crossref","first-page":"3599","DOI":"10.1080\/03610926.2013.782200","volume":"44","author":"P Teles","year":"2015","unstructured":"Teles, P., Brito, P.: Modeling interval time series with space-time processes. Commun. Stat.Theory Methods 44(17), 3599\u20133627 (2015)","journal-title":"Commun. Stat.Theory Methods"},{"key":"9851_CR51","doi-asserted-by":"crossref","unstructured":"Verde, R., Irpino, A.: Dynamic clustering of histogram data: Using the right metric. In: Brito, P., Bertrand, P., Cucumel, G., De Carvalho, F.A.T. (eds.) Selected Contributions in Data Analysis and Classification, pp. 123\u2013134. Springer, Heidelberg (2007)","DOI":"10.1007\/978-3-540-73560-1_12"},{"key":"9851_CR52","doi-asserted-by":"crossref","unstructured":"Verde, R., Irpino, A.: Comparing histogram data using a Mahalanobis-Wasserstein distance. In: Brito, P. (ed) Proceedings of the COMPSTAT\u20192008, pp. 77\u201389. Springer, Heidelberg (2008)","DOI":"10.1007\/978-3-7908-2084-3_7"},{"key":"9851_CR53","volume-title":"Time Series Analysis\u2013Univariate and Multivariate Methods","author":"WWS Wei","year":"2006","unstructured":"Wei, W.W.S.: Time Series Analysis\u2013Univariate and Multivariate Methods, 2nd edn. Pearson, New York (2006)","edition":"2"}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11222-018-09851-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-018-09851-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-018-09851-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T02:19:43Z","timestamp":1694571583000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11222-018-09851-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,21]]},"references-count":53,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2019,9]]}},"alternative-id":["9851"],"URL":"https:\/\/doi.org\/10.1007\/s11222-018-09851-z","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"value":"0960-3174","type":"print"},{"value":"1573-1375","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,21]]},"assertion":[{"value":"12 April 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 December 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 January 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}