{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T12:59:52Z","timestamp":1769086792593,"version":"3.49.0"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2012,2,7]],"date-time":"2012-02-07T00:00:00Z","timestamp":1328572800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2013,6]]},"DOI":"10.1007\/s10898-012-9854-y","type":"journal-article","created":{"date-parts":[[2012,2,6]],"date-time":"2012-02-06T14:34:16Z","timestamp":1328538856000},"page":"219-232","source":"Crossref","is-referenced-by-count":13,"title":["Self-learning K-means clustering: a global optimization approach"],"prefix":"10.1007","volume":"56","author":[{"given":"Z.","family":"Volkovich","sequence":"first","affiliation":[]},{"given":"D.","family":"Toledano-Kitai","sequence":"additional","affiliation":[]},{"given":"G.-W.","family":"Weber","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,2,7]]},"reference":[{"key":"9854_CR1","unstructured":"Yang, L., Jin, R.: Distance metric learning: a comprehensive survey. Technical report, Department of Computer Science and Engineering, Michigan State University (2006)"},{"key":"9854_CR2","unstructured":"MacQueen, J.B.: Some methods for classification and analysis of multivariate observations. In: Proceedings of 5-th Berkeley Symposium on Mathematical Statistics and Probability. Berkeley, University of California Press, pp. 281\u2013297 (1967)"},{"issue":"315","key":"9854_CR3","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/0167-9473(92)90042-E","volume":"14","author":"G. Celeux","year":"1992","unstructured":"Celeux G., Govaert G.: A classification EM algorithm for clustering and two stochastic versions. Comput. Stat. Data Anal. 14(315), 315\u2013332 (1992)","journal-title":"Comput. Stat. Data Anal."},{"key":"9854_CR4","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1103\/PhysRevLett.65.945","volume":"65","author":"K. Rose","year":"1990","unstructured":"Rose K., Gurewitz E., Fox G.: Statistical mechanics and phase transitions in clustering. Phys. Rev. Lett. 65, 945\u2013948 (1990)","journal-title":"Phys. Rev. Lett."},{"key":"#cr-split#-9854_CR5.2","unstructured":"BC Res, NJ Piscataway"},{"key":"9854_CR6","unstructured":"Daichi, M., Genichiro, K., Kenji, K.: Learning nonstructural distance metric by minimum cluster distortions. In: International Conference on Computational Linguistic\u2014COLING, pp. 341\u2013348 (2004), available at http:\/\/academic.research.microsoft.com\/Publication\/3317495"},{"key":"9854_CR7","unstructured":"Ishikawa, Y., Subramanya, R., Faloutsos, C.: MindReader: querying databases through multiple examples. In: Proceedings of 24rd International Conference on Very Large Data Bases, pp. 24\u201327 (1998)"},{"issue":"336","key":"9854_CR8","doi-asserted-by":"crossref","first-page":"846","DOI":"10.1080\/01621459.1971.10482356","volume":"66","author":"W.M. Rand","year":"1071","unstructured":"Rand W.M.: Objective criteria for the evaluation of clustering methods. J. Am. Stat. Assoc. (Am Stat Assoc) 66(336), 846\u2013850 (1071)","journal-title":"J. Am. Stat. Assoc. (Am Stat Assoc)"},{"key":"9854_CR9","volume-title":"Algorithms for Clustering Data","author":"A. Jain","year":"1988","unstructured":"Jain A., Dubes R.: Algorithms for Clustering Data. Prentice-Hall, Englewood Cliffs (1988)"},{"key":"9854_CR10","doi-asserted-by":"crossref","DOI":"10.1201\/9780367805302","volume-title":"Classification","author":"A.D. Gordon","year":"1999","unstructured":"Gordon A.D.: Classification. Chapman and Hall, CRC, Boca Raton (1999)"},{"key":"9854_CR11","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1080\/01969727408546059","volume":"4","author":"J.C. Dunn","year":"1974","unstructured":"Dunn J.C.: Well separated clusters and optimal fuzzy partitions. J. Cybern. 4, 95\u2013104 (1974)","journal-title":"J. Cybern."},{"key":"9854_CR12","first-page":"190","volume":"76","author":"L. Hubert","year":"1974","unstructured":"Hubert L., Schultz J.: Quadratic assignment as a general data-analysis strategy. Br. J. Math. Statist. Psychol. 76, 190\u2013241 (1974)","journal-title":"Br. J. Math. Statist. Psychol."},{"key":"9854_CR13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/03610928308827180","volume":"3","author":"R. Caliski","year":"1974","unstructured":"Caliski R., Harabasz J.: A dendrite method for cluster analysis. Common Stat. 3, 1\u201327 (1974)","journal-title":"Common Stat."},{"key":"9854_CR14","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/BF01908064","volume":"2","author":"J.A. Hartigan","year":"1985","unstructured":"Hartigan J.A.: Statistical theory in clustering. J. Classif. 2, 63\u201376 (1985)","journal-title":"J. Classif."},{"key":"9854_CR15","doi-asserted-by":"crossref","first-page":"23","DOI":"10.2307\/2531893","volume":"44","author":"W. Krzanowski","year":"1985","unstructured":"Krzanowski W., Lai Y.: A criterion for determining the number of groups in a dataset using sum of squares clustering. Biometrics 44, 23\u201334 (1985)","journal-title":"Biometrics"},{"key":"9854_CR16","doi-asserted-by":"crossref","first-page":"750","DOI":"10.1198\/016214503000000666","volume":"98","author":"C. Sugar","year":"2003","unstructured":"Sugar C., James G.: Finding the number of clusters in a data set: an information theoretic approach. J. Am. Stat. Assoc. 98, 750\u2013763 (2003)","journal-title":"J. Am. Stat. Assoc."},{"key":"9854_CR17","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1016\/0167-9473(94)90085-X","volume":"18","author":"A.D. Gordon","year":"1994","unstructured":"Gordon A.D.: Identifying genuine clusters in a classification. Computat. Stat. Data Anal. 18, 561\u2013581 (1994)","journal-title":"Computat. Stat. Data Anal."},{"key":"9854_CR18","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/BF02294245","volume":"50","author":"G. Milligan","year":"1985","unstructured":"Milligan G., Cooper M.: An examination of procedures for determining the number of clusters in a data set. Psychometrika 50, 159\u2013179 (1985)","journal-title":"Psychometrika"},{"issue":"2","key":"9854_CR19","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1111\/1467-9868.00293","volume":"63","author":"R. Tibshirani","year":"2001","unstructured":"Tibshirani R., Walther G., Hastie T.: Estimating the number of clusters via the gap statistic. J. R. Statist. Soc. B 63(2), 411\u2013423 (2001)","journal-title":"J. R. Statist. Soc. B"},{"key":"9854_CR20","doi-asserted-by":"crossref","first-page":"2573","DOI":"10.1162\/089976601753196030","volume":"13","author":"E. Levine","year":"2001","unstructured":"Levine E., Domany E.: Resampling method for unsupervised estimation of cluster validity. Neural Comput. 13, 2573\u20132593 (2001)","journal-title":"Neural Comput."},{"key":"9854_CR21","first-page":"6","volume":"2","author":"A. Ben-Hur","year":"2002","unstructured":"Ben-Hur A., Elisseeff A., Guyon I.: A stability based method for discovering structure in clustered data. Pac. Symp. Biocomput. 2, 6\u201317 (2002)","journal-title":"Pac. Symp. Biocomput."},{"key":"9854_CR22","first-page":"159","volume-title":"Methods in Molecular Biology","author":"A. Ben-Hur","year":"2003","unstructured":"Ben-Hur A., Guyon I.: Detecting stable clusters using principal component analysis. In: Brownstein, M.J., Khodursky, A. (eds) Methods in Molecular Biology, pp. 159\u2013182. Humana Press, Clifton (2003)"},{"key":"9854_CR23","unstructured":"Mufti, G.B., Bertrand, P., El Moubarki, L.: Determining the number of groups from measures of cluster validity. In: Proceedings of ASMDA 2005, pp. 404\u2013414 (2005)"},{"issue":"7","key":"9854_CR24","doi-asserted-by":"crossref","first-page":"2174","DOI":"10.1016\/j.patcog.2008.01.008","volume":"41","author":"Z. Volkovich","year":"2008","unstructured":"Volkovich Z., Barzily Z., Morozensky L.: A statistical model of cluster stability. Pattern Recognit. 41(7), 2174\u20132188 (2008)","journal-title":"Pattern Recognit."},{"issue":"2","key":"9854_CR25","doi-asserted-by":"crossref","first-page":"187","DOI":"10.15388\/Informatica.2009.245","volume":"20","author":"Z. Barzily","year":"2009","unstructured":"Barzily Z., Volkovich Z., Akteko-Ozturk B., Weber G.-W.: On a minimal spanning tree approach in the cluster validation problem. Informatica 20(2), 187\u2013202 (2009)","journal-title":"Informatica"},{"key":"9854_CR26","unstructured":"Volkovich, Z., Barzily, Z.: On application probability metrics in the cluster problem. In: 1st European Conference on Data Mining (ECDM07). Lisbon, Portugal, pp. 57\u201359 (2007)"},{"issue":"2","key":"9854_CR27","first-page":"233","volume":"68","author":"D. Toledano-Kitai","year":"2011","unstructured":"Toledano-Kitai D., Avros R., Volkovich Z.: A fractal dimension standpoint to the cluster validation problem. Int. J. Pure Appl. Math. 68(2), 233\u2013252 (2011)","journal-title":"Int. J. Pure Appl. Math."},{"issue":"6","key":"9854_CR28","doi-asserted-by":"crossref","first-page":"1299","DOI":"10.1162\/089976604773717621","volume":"16","author":"T. Lange","year":"2004","unstructured":"Lange T., Braun M., Roth V., Buhmann J.M.: Stability-based model validation of clustering solutions. Neural Comput. 16(6), 1299\u20131323 (2004)","journal-title":"Neural Comput."},{"key":"9854_CR29","doi-asserted-by":"crossref","unstructured":"Roth, V., Lange, T., Braun, M., Buhmann, J.: A resampling approach to cluster validation. In: Proceedings of the International Conference on Computational Statistics (COMPSTAT), pp. 123\u2013128 (2002), available at http:\/\/www.cs.uni-bonn.De\/braunm","DOI":"10.1007\/978-3-642-57489-4_13"},{"key":"9854_CR30","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1214\/009053607000000758","volume":"36","author":"P. Bickel","year":"2008","unstructured":"Bickel P., Levina E.: Regularized estimation of large covariance matrices. Ann. Stat. 36, 199\u2013227 (2008)","journal-title":"Ann. Stat."},{"key":"9854_CR31","first-page":"2261","volume":"11","author":"M. Yuan","year":"2010","unstructured":"Yuan M.: High dimensional inverse covariance matrix estimation via linear programming. J. Mach. Learn. Res. 11, 2261\u20132286 (2010)","journal-title":"J. Mach. Learn. Res."},{"key":"9854_CR32","doi-asserted-by":"crossref","unstructured":"Dhillon, I.S., Modha, D.S.: Concept decompositions for large sparse text data using clustering. Mach. Learn., 42(1), 143\u2013175 (2001), Also appears as IBM Research Report RJ 10147, July 1999","DOI":"10.1023\/A:1007612920971"},{"issue":"6","key":"9854_CR33","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1109\/MCISE.2003.1238704","volume":"5","author":"J. Kogan","year":"2003","unstructured":"Kogan J., Nicholas C., Volkovich V.: Text mining with information\u2013theoretical clustering. Comput. Sci. Eng. 5(6), 52\u201359 (2003)","journal-title":"Comput. Sci. Eng."},{"key":"9854_CR34","doi-asserted-by":"crossref","unstructured":"Kogan, J., Nicholas, C., Volkovich, V.: Text mining with hybrid clustering schemes. In Proceedings of the Workshop on Text Mining held in conjunction with the Third SIAM International Conference on Data Mining. M.W. Berry and W.M. Pottenger, pp. 5\u201316 (2003)","DOI":"10.1109\/MCISE.2003.1238704"},{"key":"9854_CR35","unstructured":"Kogan, J., Teboulle, M., Nicholas, C.: Optimization approach to generating families of k-means like algorithms. In: Proceedings of the Workshop on Clustering High Dimensional Data and its Applications (held in Conjunction with the Third SIAM International Conference on Data Mining), 2003"},{"key":"9854_CR36","unstructured":"Volkovich, V., Kogan, J., Nicholas, C.: k-means initialization by sampling large datasets. In: Proceedings of the Workshop on Clustering High Dimensional Data and its Applications (held in Conjunction with SDM 2004). I. Dhillon and J. Kogan, pp. 17\u201322 (2004)"},{"key":"9854_CR37","first-page":"73","volume-title":"Feature Selection and Document Clustering. A Comprehensive Survey of Text Mining","author":"I. Dhillon","year":"2003","unstructured":"Dhillon I., Kogan J., Nicholas C.: Feature Selection and Document Clustering. A Comprehensive Survey of Text Mining, pp. 73\u2013100. Springer, Berlin (2003)"},{"issue":"7","key":"9854_CR38","doi-asserted-by":"crossref","first-page":"0036.1","DOI":"10.1186\/gb-2002-3-7-research0036","volume":"3","author":"S. Dudoit","year":"2002","unstructured":"Dudoit S., Fridlyand J.: A prediction-based resampling method for estimating the number of clusters in a dataset. Genome Biol. 3(7), 0036.1\u20130036.21 (2002)","journal-title":"Genome Biol."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-012-9854-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-012-9854-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-012-9854-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,27]],"date-time":"2021-12-27T23:49:39Z","timestamp":1640648979000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-012-9854-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2,7]]},"references-count":38,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2013,6]]}},"alternative-id":["9854"],"URL":"https:\/\/doi.org\/10.1007\/s10898-012-9854-y","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,2,7]]}}}