{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T04:40:06Z","timestamp":1777610406939,"version":"3.51.4"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2018,1,5]],"date-time":"2018-01-05T00:00:00Z","timestamp":1515110400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2018,2]]},"DOI":"10.1007\/s10957-017-1213-1","type":"journal-article","created":{"date-parts":[[2018,1,5]],"date-time":"2018-01-05T15:36:55Z","timestamp":1515166615000},"page":"492-508","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A Novel Mixed Integer Linear Programming Model for Clustering Relational Networks"],"prefix":"10.1007","volume":"176","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5273-5955","authenticated-orcid":false,"given":"Harun","family":"Pirim","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Burak","family":"Eksioglu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fred W.","family":"Glover","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,1,5]]},"reference":[{"issue":"2","key":"1213_CR1","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/S1016-8478(23)17582-0","volume":"25","author":"JH Do","year":"2008","unstructured":"Do, J.H., Choi, D.K.: Clustering approaches to identifying gene expression patterns from DNA microarray data. Mol. Cells 25(2), 279\u2013288 (2008)","journal-title":"Mol. Cells"},{"issue":"04","key":"1213_CR2","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1142\/S0219622006002143","volume":"05","author":"FW Glover","year":"2006","unstructured":"Glover, F.W., Kochenberger, G.: New optimization models for data mining. Int. J. Inf. Technol. Decis. Mak. 05(04), 605\u2013609 (2006)","journal-title":"Int. J. Inf. Technol. Decis. Mak."},{"key":"1213_CR3","first-page":"269","volume-title":"Current Topics in Computational Biology","author":"R Shamir","year":"2002","unstructured":"Shamir, R., Sharan, R.: Algorithmic approaches to clustering gene expression data. In: Jiang, T., Smith, T., Xu, Y., Zhang, M. (eds.) Current Topics in Computational Biology, pp. 269\u2013299. MIT Press, Cambridge (2002)"},{"issue":"12","key":"1213_CR4","doi-asserted-by":"crossref","first-page":"3046","DOI":"10.1016\/j.cor.2012.03.008","volume":"39","author":"H Pirim","year":"2012","unstructured":"Pirim, H., Eksioglu, B., Perkins, A.D., Yuceer, C.: Clustering of high throughput gene expression data. Comput. Oper. Res. 39(12), 3046\u20133061 (2012)","journal-title":"Comput. Oper. Res."},{"issue":"335","key":"1213_CR5","doi-asserted-by":"crossref","first-page":"622","DOI":"10.1080\/01621459.1971.10482319","volume":"66","author":"MR Rao","year":"1971","unstructured":"Rao, M.R.: Cluster analysis and mathematical programming. J. Am. Stat. Assoc. 66(335), 622\u2013626 (1971)","journal-title":"J. Am. Stat. Assoc."},{"issue":"1","key":"1213_CR6","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/0262-8856(84)90042-8","volume":"2","author":"A Kusiak","year":"1984","unstructured":"Kusiak, A.: Analysis of integer programming formulations of clustering problems. Image Vis. Comput. 2(1), 35\u201340 (1984)","journal-title":"Image Vis. Comput."},{"issue":"3","key":"1213_CR7","doi-asserted-by":"crossref","first-page":"866","DOI":"10.1016\/j.ejor.2005.04.048","volume":"173","author":"B Saglam","year":"2006","unstructured":"Saglam, B., Salman, F.S., Sayin, S., Turkay, M.: A mixed-integer programming approach to the clustering problem with an application in customer segmentation. Eur. J. Oper. Res. 173(3), 866\u2013879 (2006)","journal-title":"Eur. J. Oper. Res."},{"issue":"1","key":"1213_CR8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0167-6377(98)00006-6","volume":"22","author":"A Mehrotra","year":"1998","unstructured":"Mehrotra, A., Trick, M.A.: Cliques and clustering: a combinatorial approach. Oper. Res. Lett. 22(1), 1\u201312 (1998)","journal-title":"Oper. Res. Lett."},{"issue":"2","key":"1213_CR9","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1140\/epjb\/e2007-00331-0","volume":"60","author":"G Xu","year":"2007","unstructured":"Xu, G., Tsoka, S., Papageorgiou, L.G.: Finding community structures in complex networks using mixed integer optimisation. Eur. Phys. J. B 60(2), 231\u2013239 (2007)","journal-title":"Eur. Phys. J. B"},{"key":"1213_CR10","volume-title":"Models, Algorithms and Technologies for Network Analysis, Proceedings in Mathematics & Statistics","author":"S Cafieri","year":"2014","unstructured":"Cafieri, S., Hansen, P.: Using mathematical programming to refine heuristic solutions for network clustering. In: Batsyn, M., Kalyagin, V., Pardalos, P. (eds.) Models, Algorithms and Technologies for Network Analysis, Proceedings in Mathematics & Statistics, vol. 104. Springer, Switzerland (2014)"},{"issue":"3","key":"1213_CR11","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1140\/epjb\/e2008-00425-1","volume":"66","author":"G Agarwal","year":"2008","unstructured":"Agarwal, G., Kempe, D.: Modularity-maximizing graph communities via mathematical programming. Eur. Phys. J. B 66(3), 409\u2013418 (2008)","journal-title":"Eur. Phys. J. B"},{"key":"1213_CR12","unstructured":"Martins, P.: Modeling the maximum edge-weight k-plex partitioning problem. Cornell University. arxiv:1612.06243 [math.co] (2016)"},{"issue":"8","key":"1213_CR13","doi-asserted-by":"crossref","first-page":"1381","DOI":"10.1016\/j.cor.2009.02.014","volume":"37","author":"M Nascimento","year":"2010","unstructured":"Nascimento, M., Toledo, F., de Carvalho, A.: Investigation of a new GRASP-based clustering algorithm applied to biological data. Comput. Oper. Res. 37(8), 1381\u20131388 (2010)","journal-title":"Comput. Oper. Res."},{"key":"1213_CR14","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.compbiomed.2015.03.031","volume":"62","author":"H Pirim","year":"2015","unstructured":"Pirim, H., Eksioglu, B., Perkins, A.D.: Clustering high throughput biological data with B-MST, a minimum spanning tree based heuristic. Comput. Biol. Med. 62, 94\u2013102 (2015)","journal-title":"Comput. Biol. Med."},{"issue":"1","key":"1213_CR15","first-page":"87","volume":"16","author":"H Pirim","year":"2011","unstructured":"Pirim, H., Gautam, D., Bhowmik, T., Perkins, A.D., Eksioglu, B., Alkan, A.: Performance of an ensemble clustering algorithm on biological data sets. Math. Comput. Appl. 16(1), 87\u201396 (2011)","journal-title":"Math. Comput. Appl."},{"key":"1213_CR16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1471-2105-9-1","volume":"9","author":"MP Tan","year":"2008","unstructured":"Tan, M.P., Smith, E.N., Broach, J.R., Floudas, C.A.: Microarray data mining: a novel optimization-based approach to uncover biologically coherent structures. BMC Bioinform. 9, 1\u201321 (2008)","journal-title":"BMC Bioinform."},{"issue":"9","key":"1213_CR17","doi-asserted-by":"crossref","first-page":"2658","DOI":"10.1073\/pnas.0400054101","volume":"101","author":"F Radicchi","year":"2004","unstructured":"Radicchi, F., Castellano, C., Cecconi, F., Loreto, V., Parisi, D.: Defining and identifying communities in networks. Proc. Natl. Acad. Sci. USA 101(9), 2658\u20132663 (2004)","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"1213_CR18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1103\/PhysRevE.83.056105","volume":"83","author":"S Cafieri","year":"2011","unstructured":"Cafieri, S., Hansen, P., Liberti, L.: Locally optimal heuristic for modularity maximization of networks. Phys. Rev. E 83, 1\u20138 (2011)","journal-title":"Phys. Rev. E"},{"issue":"12","key":"1213_CR19","first-page":"1","volume":"3","author":"C Prieto","year":"2008","unstructured":"Prieto, C., Risueno, A., Fontanillo, C., Rivas, J.D.L.: Human gene coexpression landscape: confident network derived from tissue transcriptomic profiles. PLoS ONE 3(12), 1\u201314 (2008)","journal-title":"PLoS ONE"},{"key":"1213_CR20","unstructured":"IBM ILOG CPLEX 12.6 (2014)"},{"key":"1213_CR21","unstructured":"R Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2014). http:\/\/www.R-project.org\/"},{"key":"1213_CR22","first-page":"1","volume":"1695","author":"G Csardi","year":"2006","unstructured":"Csardi, G., Nepusz, T.: The igraph software package for complex network research. Int. Complex Syst. 1695, 1\u20139 (2006)","journal-title":"Int. Complex Syst."},{"key":"1213_CR23","unstructured":"Maechler, M., Rousseeuw, P., Struyf, A., Hubert, M., Hornik, K.: Cluster: Cluster Analysis Basics and Extensions, R package version 2.0.6 edn. (2017)"},{"key":"1213_CR24","unstructured":"Brock, G., Pihur, V., Datta, S., Datta, S.: clValid: Validation of Clustering Results, R package version 0.6-6 edn. (2014)"},{"issue":"2","key":"1213_CR25","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1098\/rsbl.2003.0057","volume":"270","author":"D Lusseau","year":"2003","unstructured":"Lusseau, D.: The emergent properties of a dolphin social network. Proc. R. Soc. Lond. B Biol. Sci. 270(2), 186\u2013188 (2003)","journal-title":"Proc. R. Soc. Lond. B Biol. Sci."},{"key":"1213_CR26","doi-asserted-by":"crossref","first-page":"026113","DOI":"10.1103\/PhysRevE.69.026113","volume":"69","author":"MEJ Newman","year":"2004","unstructured":"Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69, 026113 (2004)","journal-title":"Phys. Rev. E"},{"issue":"1","key":"1213_CR27","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.patcog.2012.07.021","volume":"46","author":"O Arbelaitz","year":"2013","unstructured":"Arbelaitz, O., Gurrutxaga, I., Muguerza, J., Perez, J.M., Perona, I.: An extensive comparative study of cluster validity indices. Pattern Recognit. 46(1), 243\u2013256 (2013)","journal-title":"Pattern Recognit."},{"key":"1213_CR28","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/0377-0427(87)90125-7","volume":"20","author":"PJ Rousseeuw","year":"1987","unstructured":"Rousseeuw, P.J.: Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math. 20, 53\u201365 (1987)","journal-title":"J. Comput. Appl. Math."},{"issue":"1","key":"1213_CR29","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1080\/01969727408546059","volume":"4","author":"JC Dunn","year":"1974","unstructured":"Dunn, J.C.: Well-separated clusters and optimal fuzzy partitions. J. Cybernet. 4(1), 95\u2013104 (1974)","journal-title":"J. Cybernet."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-017-1213-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-017-1213-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-017-1213-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,30]],"date-time":"2024-06-30T09:08:58Z","timestamp":1719738538000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-017-1213-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,5]]},"references-count":29,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,2]]}},"alternative-id":["1213"],"URL":"https:\/\/doi.org\/10.1007\/s10957-017-1213-1","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1,5]]}}}