{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T21:09:21Z","timestamp":1761340161309,"version":"3.37.3"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2021,4,20]],"date-time":"2021-04-20T00:00:00Z","timestamp":1618876800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,4,20]],"date-time":"2021-04-20T00:00:00Z","timestamp":1618876800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11871081","11201333"],"award-info":[{"award-number":["11871081","11201333"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002790","name":"Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["06446"],"award-info":[{"award-number":["06446"]}],"id":[{"id":"10.13039\/501100002790","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11771386","11728104"],"award-info":[{"award-number":["11771386","11728104"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Comb Optim"],"published-print":{"date-parts":[[2022,11]]},"DOI":"10.1007\/s10878-021-00737-x","type":"journal-article","created":{"date-parts":[[2021,4,20]],"date-time":"2021-04-20T09:03:36Z","timestamp":1618909416000},"page":"2375-2394","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The spherical k-means++ algorithm via local search scheme"],"prefix":"10.1007","volume":"44","author":[{"given":"Xiaoyun","family":"Tian","sequence":"first","affiliation":[]},{"given":"Dachuan","family":"Xu","sequence":"additional","affiliation":[]},{"given":"Donglei","family":"Du","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0710-8498","authenticated-orcid":false,"given":"Ling","family":"Gai","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,4,20]]},"reference":[{"key":"737_CR1","doi-asserted-by":"crossref","unstructured":"Ahmadian S, Norouzi-Fard A, Svensson O, Ward J (2017) Better guarantees for $$k$$-means and euclidean $$k$$-median by primal-dual algorithms. In: Proceedings of the 58th annual symposium on foundations of computer science (FOCS), pp 61\u201372","DOI":"10.1109\/FOCS.2017.15"},{"key":"737_CR2","unstructured":"Arthur D, Vassilvitskii S (2007) $$k$$-means++: the advantages of careful seeding. In: Proceedings of the 18th annual ACM-SIAM symposium on discrete algorithms (SODA), pp 1027\u20131035"},{"key":"737_CR3","unstructured":"Choo D, Grunau C, Portmann J, Rozhon V (2020) $$k$$-means++: few more steps yield constant approximation. In: Proceedings of the 37th international conference on machine learning (ICML)"},{"issue":"1","key":"737_CR4","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1023\/A:1007612920971","volume":"42","author":"I Dhillon","year":"2001","unstructured":"Dhillon I, Modha D (2001) Concept decompositions for large sparse text data using clustering. Mach Learn 42(1):143\u2013175","journal-title":"Mach Learn"},{"key":"737_CR5","doi-asserted-by":"crossref","unstructured":"Endo Y, Miyamoto S (2015) Spherical $$k$$-means++ clustering. In: Proceedings of the 14th modeling decisions for artificial intelligence (MDAI), pp 103\u2013114","DOI":"10.1007\/978-3-319-23240-9_9"},{"issue":"3","key":"737_CR6","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1137\/18M1209854","volume":"49","author":"D Feldman","year":"2020","unstructured":"Feldman D, Schmidt M, Sohler C (2020) Turning big data into tiny data: constant-size coresets for $$k$$-means. SIAM J Comput 49(3):601\u2013657","journal-title":"SIAM J Comput"},{"issue":"10","key":"737_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.18637\/jss.v050.i10","volume":"50","author":"K Hornik","year":"2012","unstructured":"Hornik K, Feinerer I, Kober M, Buchta C (2012) Spherical $$k$$-means clustering. J Stat Softw 50(10):1\u201322","journal-title":"J Stat Softw"},{"issue":"2","key":"737_CR8","first-page":"227","volume":"32","author":"A Jain","year":"1988","unstructured":"Jain A, Dubes R (1988) Algorithms for clustering data. Technometrics 32(2):227\u2013229","journal-title":"Technometrics"},{"issue":"3","key":"737_CR9","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1145\/331499.331504","volume":"31","author":"A Jain","year":"1999","unstructured":"Jain A, Murty M, Flynn P (1999) Data clustering: a review. ACM Comput Surv 31(3):264\u2013323","journal-title":"ACM Comput Surv"},{"issue":"2\u20133","key":"737_CR10","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1016\/j.comgeo.2004.03.003","volume":"28","author":"T Kanungo","year":"2004","unstructured":"Kanungo T, Mount D, Netanyahu N, Piatko C, Silverman R, Wu A (2004) A local search approximation algorithm for $$k$$-means clustering. Comput Geom 28(2\u20133):89\u2013112","journal-title":"Comput Geom"},{"issue":"7","key":"737_CR11","doi-asserted-by":"publisher","first-page":"881","DOI":"10.1109\/TPAMI.2002.1017616","volume":"24","author":"T Kanungo","year":"2002","unstructured":"Kanungo T, Mount D, Netanyahu N, Piatko C, Silverman R, Wu A (2002) An efficient $$k$$-means clustering algorithm: analysis and implementation. IEEE Trans Pattern Anal Mach Intell 24(7):881\u2013892","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"737_CR12","unstructured":"Kumar A, Sabharwal Y, Sen S (2004) A simple linear time $$(1+\\varepsilon )$$-approximation algorithm for $$k$$-means clustering in any dimensions. In: Proceedings of the 32nd foundations of computer science (FOCS), pp 454\u2013462"},{"key":"737_CR13","unstructured":"Lattanzi S, Sohler C (2019) A better $$k$$-means++ algorithm via local search. In: Proceedings of the 36th international conference on machine learning (ICML), pp 3662\u20133671"},{"issue":"4","key":"737_CR14","doi-asserted-by":"publisher","first-page":"695","DOI":"10.1007\/s10898-019-00779-w","volume":"76","author":"M Li","year":"2020","unstructured":"Li M, Xu D, Zhang D, Zou J (2020) The seeding algorithms for spherical $$k$$-means clustering. J Global Optim 76(4):695\u2013708","journal-title":"J Global Optim"},{"issue":"2","key":"737_CR15","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1109\/TIT.1982.1056489","volume":"28","author":"S Lloyd","year":"1982","unstructured":"Lloyd S (1982) Least squares quantization in PCM. IEEE Trans Inf Theory 28(2):129\u2013137","journal-title":"IEEE Trans Inf Theory"},{"key":"737_CR16","unstructured":"MacQueen J (1967) Some methods for classification and analysis of multivariate observations. In: Proceedings of the 5th berkeley symposium on mathematical statistics and probability and statistics, pp 281\u2013297"},{"issue":"1","key":"737_CR17","first-page":"12","volume":"13","author":"V Tunali","year":"2016","unstructured":"Tunali V, Bilgin T, Camurcu A (2016) An improved clustering algorithm for text mining: multi-cluster spherical $$k$$-means. Int Arab J Inf Technol 13(1):12\u201319","journal-title":"Int Arab J Inf Technol"},{"key":"737_CR18","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2020.06.029","author":"D Zhang","year":"2020","unstructured":"Zhang D, Cheng Y, Li M, Wang Y, Xu D (2020) Local search approximation algorithms for the spherical $$k$$-means problem. Theor Comput Sci. https:\/\/doi.org\/10.1016\/j.tcs.2020.06.029","journal-title":"Theor Comput Sci"}],"container-title":["Journal of Combinatorial Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-021-00737-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10878-021-00737-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-021-00737-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,14]],"date-time":"2022-10-14T20:18:47Z","timestamp":1665778727000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10878-021-00737-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,20]]},"references-count":18,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,11]]}},"alternative-id":["737"],"URL":"https:\/\/doi.org\/10.1007\/s10878-021-00737-x","relation":{},"ISSN":["1382-6905","1573-2886"],"issn-type":[{"type":"print","value":"1382-6905"},{"type":"electronic","value":"1573-2886"}],"subject":[],"published":{"date-parts":[[2021,4,20]]},"assertion":[{"value":"7 April 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 April 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}