{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T02:35:51Z","timestamp":1773455751434,"version":"3.50.1"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2014,10,30]],"date-time":"2014-10-30T00:00:00Z","timestamp":1414627200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2015,5]]},"DOI":"10.1007\/s10589-014-9711-7","type":"journal-article","created":{"date-parts":[[2014,10,29]],"date-time":"2014-10-29T08:41:18Z","timestamp":1414572078000},"page":"219-241","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["An incremental clustering algorithm based on hyperbolic smoothing"],"prefix":"10.1007","volume":"61","author":[{"given":"A. M.","family":"Bagirov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"B.","family":"Ordin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G.","family":"Ozturk","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. E.","family":"Xavier","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,10,30]]},"reference":[{"issue":"9","key":"9711_CR1","doi-asserted-by":"crossref","first-page":"1443","DOI":"10.1016\/0031-3203(95)00022-R","volume":"28","author":"KS Al-Sultan","year":"1995","unstructured":"Al-Sultan, K.S.: A tabu search approach to the clustering problem. Pattern Recognit. 28(9), 1443\u20131451 (1995)","journal-title":"Pattern Recognit."},{"key":"9711_CR2","unstructured":"Bache, K., Lichman, M.: UCI Machine Learning Repository. School of Information and Computer Science, University of California, Irvine, CA (2013). http:\/\/archive.ics.uci.edu\/ml ."},{"issue":"10","key":"9711_CR3","doi-asserted-by":"crossref","first-page":"3192","DOI":"10.1016\/j.patcog.2008.04.004","volume":"41","author":"AM Bagirov","year":"2008","unstructured":"Bagirov, A.M.: Modified global $$k$$ k -means algorithm for sum-of-squares clustering problems. Pattern Recognit. 41(10), 3192\u20133199 (2008)","journal-title":"Pattern Recognit."},{"key":"9711_CR4","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/s10957-007-9335-5","volume":"137","author":"AM Bagirov","year":"2008","unstructured":"Bagirov, A.M., Karasozen, B., Sezer, M.: Discrete gradient method: A derivative free method for nonsmooth optimization. J. Optim. Theory Appl. 137, 317\u2013334 (2008)","journal-title":"J. Optim. Theory Appl."},{"issue":"2","key":"9711_CR5","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1023\/A:1020911318981","volume":"3","author":"AM Bagirov","year":"2002","unstructured":"Bagirov, A.M., Rubinov, A.M., Yearwood, J.: A global optimisation approach to classification. Optim. Eng. 3(2), 129\u2013155 (2002)","journal-title":"Optim. Eng."},{"issue":"1","key":"9711_CR6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02578945","volume":"11","author":"AM Bagirov","year":"2003","unstructured":"Bagirov, A.M., Rubinov, A.M., Soukhoroukova, N.V., Yearwood, J.: Supervised and unsupervised data classification via nonsmooth and global optimization. TOP: Span. Oper. Res. J. 11(1), 1\u201393 (2003)","journal-title":"TOP: Span. Oper. Res. J."},{"issue":"4\u20135","key":"9711_CR7","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1080\/02331930500096155","volume":"54","author":"AM Bagirov","year":"2005","unstructured":"Bagirov, A.M., Ugon, J.: An algorithm for minimizing clustering functions. Optimization 54(4\u20135), 351\u2013368 (2005)","journal-title":"Optimization"},{"key":"9711_CR8","doi-asserted-by":"crossref","first-page":"866","DOI":"10.1016\/j.patcog.2010.10.018","volume":"44","author":"AM Bagirov","year":"2011","unstructured":"Bagirov, A.M., Ugon, J., Webb, D.: Fast modified global $$k$$ k -means algorithm for sum-of-squares clustering problems. Pattern Recognit. 44, 866\u2013876 (2011)","journal-title":"Pattern Recognit."},{"key":"9711_CR9","doi-asserted-by":"crossref","first-page":"578","DOI":"10.1016\/j.ejor.2004.06.014","volume":"170","author":"AM Bagirov","year":"2006","unstructured":"Bagirov, A.M., Yearwood, J.: A new nonsmooth optimization algorithm for minimum sum-of-squares clustering problems. Eur. J. Oper. Res. 170, 578\u2013596 (2006)","journal-title":"Eur. J. Oper. Res."},{"issue":"6","key":"9711_CR10","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1080\/02331934.2012.675335","volume":"62","author":"AM Bagirov","year":"2013","unstructured":"Bagirov, A.M., Al Nuaimat, A., Sultanova, N.: Hyperbolic smoothing method for minimax problems. Optimization 62(6), 759\u2013782 (2013)","journal-title":"Optimization"},{"key":"9711_CR11","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/978-3-642-72253-0_37","volume-title":"Advances in Data Science and Classification","author":"HH Bock","year":"1998","unstructured":"Bock, H.H.: Clustering and neural networks. In: Rizzi, A., Vichi, M., Bock, H.H. (eds.) Advances in Data Science and Classification, pp. 265\u2013277. Springer, Berlin (1998)"},{"key":"9711_CR12","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1016\/0031-3203(92)90088-Z","volume":"25","author":"DE Brown","year":"1992","unstructured":"Brown, D.E., Entail, C.L.: A practical application of simulated annealing to the clustering problem. Pattern Recognit. 25, 401\u2013412 (1992)","journal-title":"Pattern Recognit."},{"key":"9711_CR13","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1137\/0906020","volume":"6","author":"G Diehr","year":"1985","unstructured":"Diehr, G.: Evaluation of a branch and bound algorithm for clustering. SIAM J. Sci. Stat. Comput. 6, 268\u2013284 (1985)","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"9711_CR14","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/0031-3203(76)90045-5","volume":"8","author":"R Dubes","year":"1976","unstructured":"Dubes, R., Jain, A.K.: Clustering techniques: the user\u2019s dilemma. Pattern Recognit. 8, 247\u2013260 (1976)","journal-title":"Pattern Recognit."},{"key":"9711_CR15","volume-title":"The Solver Manuals","author":"GAMS","year":"2012","unstructured":"GAMS: The Solver Manuals. GAMS Development Corporation, Washington, D.C. (2012)"},{"issue":"1\u20133","key":"9711_CR16","first-page":"191","volume":"79","author":"P Hansen","year":"1997","unstructured":"Hansen, P., Jaumard, B.: Cluster analysis and mathematical programming. Math. Programm. 79(1\u20133), 191\u2013215 (1997)","journal-title":"Math. Programm."},{"key":"9711_CR17","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1016\/S0031-3203(99)00216-2","volume":"4","author":"P Hansen","year":"2001","unstructured":"Hansen, P., Mladenovic, N.: $$J$$ J -means: a new heuristic for minimum sum-of-squares clustering. Pattern Recognit. 4, 405\u2013413 (2001)","journal-title":"Pattern Recognit."},{"key":"9711_CR18","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1023\/A:1011336210885","volume":"7","author":"P Hansen","year":"2001","unstructured":"Hansen, P., Mladenovic, N.: Variable neighborhood decomposition search. J. Heuristic. 7, 335\u2013350 (2001)","journal-title":"J. Heuristic."},{"key":"9711_CR19","doi-asserted-by":"crossref","first-page":"908","DOI":"10.1109\/T-C.1975.224336","volume":"24","author":"WLG Koontz","year":"1975","unstructured":"Koontz, W.L.G., Narendra, P.M., Fukunaga, K.: A branch and bound clustering algorithm. IEEE Trans. Comput. 24, 908\u2013915 (1975)","journal-title":"IEEE Trans. Comput."},{"key":"9711_CR20","first-page":"1034","volume":"28","author":"RE Jensen","year":"1969","unstructured":"Jensen, R.E.: A dynamic programming algorithm for cluster analysis. Appl. Stat. 28, 1034\u20131057 (1969)","journal-title":"Appl. Stat."},{"key":"9711_CR21","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1016\/S0031-3203(02)00060-2","volume":"36","author":"A Likas","year":"2003","unstructured":"Likas, A., Vlassis, M., Verbeek, J.: The global $$k$$ k -means clustering algorithm. Pattern Recognit. 36, 451\u2013461 (2003)","journal-title":"Pattern Recognit."},{"key":"9711_CR22","doi-asserted-by":"crossref","first-page":"1485","DOI":"10.1137\/S1064827597328327","volume":"21","author":"O Merle du","year":"2001","unstructured":"du Merle, O., Hansen, P., Jaumard, B., Mladenovic, N.: An interior point method for minimum sum-of-squares clustering. SIAM J. Sci. Comput. 21, 1485\u20131505 (2001)","journal-title":"SIAM J. Sci. Comput."},{"key":"9711_CR23","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1287\/ijoc.3.4.376","volume":"3","author":"G Reinelt","year":"1991","unstructured":"Reinelt, G.: TSP-LIB-A traveling salesman library. ORSA J. Comput. 3, 319\u2013350 (1991)","journal-title":"ORSA J. Comput."},{"issue":"10","key":"9711_CR24","doi-asserted-by":"crossref","first-page":"1003","DOI":"10.1016\/0031-3203(91)90097-O","volume":"24","author":"SZ Selim","year":"1991","unstructured":"Selim, S.Z., Al-Sultan, K.S.: A simulated annealing algorithm for the clustering. Pattern Recognit. 24(10), 1003\u20131008 (1991)","journal-title":"Pattern Recognit."},{"key":"9711_CR25","volume-title":"Cluster Analysis Algorithms","author":"H Spath","year":"1980","unstructured":"Spath, H.: Cluster Analysis Algorithms. Ellis Horwood Limited, Chichester (1980)"},{"key":"9711_CR26","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/0097-8485(94)85003-8","volume":"18","author":"LX Sun","year":"1994","unstructured":"Sun, L.X., Xie, Y.L., Song, X.H., Wang, J.H., Yu, R.Q.: Cluster analysis by simulated annealing. Comput. Chem. 18, 103\u2013108 (1994)","journal-title":"Comput. Chem."},{"key":"9711_CR27","first-page":"65","volume":"8","author":"M Teboulle","year":"2007","unstructured":"Teboulle, M.: A unified continuous optimization framework for center-based clustering methods. J. Mach. Learn. Res. 8, 65\u2013102 (2007)","journal-title":"J. Mach. Learn. Res."},{"issue":"3","key":"9711_CR28","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1016\/j.patcog.2009.06.018","volume":"43","author":"AE Xavier","year":"2010","unstructured":"Xavier, A.E.: The hyperbolic smoothing clustering method. Pattern Recognit. 43(3), 731\u2013737 (2010)","journal-title":"Pattern Recognit."},{"issue":"3","key":"9711_CR29","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1007\/s10898-004-0737-8","volume":"31","author":"AE Xavier","year":"2005","unstructured":"Xavier, A.E., Oliveira, A.A.F.D.: Optimal covering of plane domains by circles via hyperbolic smoothing. J. Glob. Optim. 31(3), 493\u2013504 (2005)","journal-title":"J. Glob. Optim."},{"issue":"1","key":"9711_CR30","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.patcog.2010.07.004","volume":"44","author":"AE Xavier","year":"2011","unstructured":"Xavier, A.E., Xavier, V.L.: Solving the minimum sum-of-squares clustering problem by hyperbolic smoothing and partition into boundary and gravitational regions. Pattern Recognit. 44(1), 70\u201377 (2011)","journal-title":"Pattern Recognit."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-014-9711-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-014-9711-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-014-9711-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,30]],"date-time":"2019-05-30T14:37:38Z","timestamp":1559227058000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-014-9711-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,10,30]]},"references-count":30,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2015,5]]}},"alternative-id":["9711"],"URL":"https:\/\/doi.org\/10.1007\/s10589-014-9711-7","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,10,30]]}}}