{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T17:37:52Z","timestamp":1780421872050,"version":"3.54.1"},"reference-count":57,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2016,4,13]],"date-time":"2016-04-13T00:00:00Z","timestamp":1460505600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100004731","name":"Zhejiang Provincial Natural Science Foundation","doi-asserted-by":"crossref","award":["LY15F030013"],"award-info":[{"award-number":["LY15F030013"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation","doi-asserted-by":"crossref","award":["11201426"],"award-info":[{"award-number":["11201426"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Mach. Learn. &amp; Cyber."],"published-print":{"date-parts":[[2017,10]]},"DOI":"10.1007\/s13042-016-0526-y","type":"journal-article","created":{"date-parts":[[2016,4,14]],"date-time":"2016-04-14T11:32:02Z","timestamp":1460633522000},"page":"1537-1554","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["k-Proximal plane clustering"],"prefix":"10.1007","volume":"8","author":[{"given":"Li-Ming","family":"Liu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yan-Ru","family":"Guo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhen","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhi-Min","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuan-Hai","family":"Shao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2016,4,13]]},"reference":[{"key":"526_CR1","volume-title":"Data mining concepts and techniques","author":"J Han","year":"2006","unstructured":"Han J, Kamber M (2006) Data mining concepts and techniques. Morgan Kaufmann, San Francisco"},{"issue":"10","key":"526_CR2","doi-asserted-by":"crossref","first-page":"2583","DOI":"10.1109\/TNNLS.2014.2379930","volume":"26","author":"Z Wang","year":"2015","unstructured":"Wang Z, Shao Y, Bai L et al (2015) Twin support vector machine for clustering. IEEE Trans Neural Netw Learn Sys 26(10):2583\u20132588","journal-title":"IEEE Trans Neural Netw Learn Sys"},{"key":"526_CR3","volume-title":"Cluster analysis for applications","author":"M Anderberg","year":"1973","unstructured":"Anderberg M (1973) Cluster analysis for applications. Academic Press, New York"},{"key":"526_CR4","volume-title":"Cluster analysis","author":"M Aldenderfer","year":"1985","unstructured":"Aldenderfer M, Blashfield R (1985) Cluster analysis. Sage Publications, Los Angeles"},{"key":"526_CR5","volume-title":"Introduction to mathematical techniques in pattern recognition","author":"H Andrews","year":"1972","unstructured":"Andrews H (1972) Introduction to mathematical techniques in pattern recognition. Wiley, New York"},{"issue":"5","key":"526_CR6","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1016\/0031-3203(94)00125-6","volume":"28","author":"G Celeux","year":"1995","unstructured":"Celeux G, Govaert G (1995) Gaussian parsimonious clustering models. Pattern Recognit 28(5):781\u2013793","journal-title":"Pattern Recognit"},{"key":"526_CR7","volume-title":"Algorithms for clustering data","author":"A Jain","year":"1988","unstructured":"Jain A, Dubes R (1988) Algorithms for clustering data. Englewood Cliffs, NJ"},{"issue":"2","key":"526_CR8","first-page":"139","volume":"2","author":"D Fisher","year":"1987","unstructured":"Fisher D (1987) Knowledge acquisition via incremental conceptual clustering. Mach Learn 2(2):139\u2013172","journal-title":"Mach Learn"},{"key":"526_CR9","volume-title":"Fundamentals of artificial neural networks","author":"M Hassoun","year":"1995","unstructured":"Hassoun M (1995) Fundamentals of artificial neural networks. MIT, Cambridge"},{"key":"526_CR10","first-page":"368","volume":"9","author":"P Bradley","year":"1997","unstructured":"Bradley P, Mangasarian O, Street W (1997) Clustering via concave minimization. Adv Neural Inf Process Syst 9:368\u2013374","journal-title":"Adv Neural Inf Process Syst"},{"issue":"335","key":"526_CR11","doi-asserted-by":"crossref","first-page":"622","DOI":"10.1080\/01621459.1971.10482319","volume":"66","author":"M Rao","year":"1987","unstructured":"Rao M (1987) Cluster analysis and mathematical programming. Am Stat Assoc 66(335):622\u2013626","journal-title":"Am Stat Assoc"},{"issue":"1","key":"526_CR12","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1109\/TPAMI.1984.4767478","volume":"6","author":"S Selim","year":"1984","unstructured":"Selim S, Ismail M (1984) K-means-type algorithms: a generalized convergence theorem and characterization of local optimality. IEEE Trans Pattern Anal Mach Intell PAMI 6(1):81\u201387","journal-title":"IEEE Trans Pattern Anal Mach Intell PAMI"},{"issue":"5","key":"526_CR13","doi-asserted-by":"crossref","first-page":"873","DOI":"10.1109\/TSMC.1987.6499296","volume":"17","author":"JC Bezdek","year":"1987","unstructured":"Bezdek JC, Hathaway RJ, Sabin MJ, Tucker WT (1987) Convergence theory for fuzzy c-means: counterexamples and repairs. Syst Man Cybern IEEE Trans 17(5):873\u2013877","journal-title":"Syst Man Cybern IEEE Trans"},{"issue":"1","key":"526_CR14","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1109\/TPAMI.2006.17","volume":"28","author":"O Mangasarian","year":"2006","unstructured":"Mangasarian O, Wild E (2006) Multisurface proximal support vector classification via generalize eigenvalues. IEEE Trans Pattern Anal Mach Intell 28(1):69\u201374","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"issue":"1","key":"526_CR15","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1023\/A:1008324625522","volume":"16","author":"P Bradley","year":"2000","unstructured":"Bradley P, Mangasarian O (2000) k-Plane clustering. J Glob Optim 16(1):23\u201332","journal-title":"J Glob Optim"},{"issue":"1","key":"526_CR16","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1023\/A:1004678431677","volume":"105","author":"P Tseng","year":"2000","unstructured":"Tseng P (2000) Nearest q-flat to m points. J Optim Theory Appl 105(1):249\u2013252","journal-title":"J Optim Theory Appl"},{"issue":"1","key":"526_CR17","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.ejor.2012.09.026","volume":"227","author":"E Amaldi","year":"2013","unstructured":"Amaldi E, Coniglio S (2013) A distance-based point-reassignment heuristic for the k-hyperplane clustering problem. Eur J Oper Res 227(1):22\u201329","journal-title":"Eur J Oper Res"},{"key":"526_CR18","doi-asserted-by":"crossref","first-page":"784","DOI":"10.1007\/978-3-319-07176-3_68","volume":"8468","author":"MA Rahman","year":"2014","unstructured":"Rahman MA, Islam MZ, Bossomaier T (2014) Denclust: a density based seed selection approach for k-means. Artif Intell Soft Comput 8468:784\u2013795","journal-title":"Artif Intell Soft Comput"},{"issue":"3","key":"526_CR19","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1109\/3477.678624","volume":"28","author":"JC Bezdek","year":"1998","unstructured":"Bezdek JC, Pal NR (1998) Some new indexes of cluster validity. Syst Man Cybernet Part B Cybern IEEE Trans 28(3):301\u2013315","journal-title":"Syst Man Cybernet Part B Cybern IEEE Trans"},{"issue":"1","key":"526_CR20","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1109\/TFUZZ.2010.2089631","volume":"19","author":"C Li","year":"2011","unstructured":"Li C, Kuo B, Chin T (2011) Lda-based clustering algorithm and its application to an unsupervised feature extraction. Fuzzy Syst IEEE Trans 19(1):152\u2013163","journal-title":"Fuzzy Syst IEEE Trans"},{"issue":"12","key":"526_CR21","doi-asserted-by":"crossref","first-page":"2191","DOI":"10.1109\/TNNLS.2014.2306844","volume":"25","author":"Y Pang","year":"2014","unstructured":"Pang Y, Wang S, Yuan Y (2014) Learning regularized lda by clustering. Neural Netw Learn Syst IEEE Trans 25(12):2191\u20132201","journal-title":"Neural Netw Learn Syst IEEE Trans"},{"issue":"1","key":"526_CR22","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/s00521-014-1707-9","volume":"26","author":"ZM Yang","year":"2015","unstructured":"Yang ZM, Guo YR, Li CN, Shao YH (2015) Local k-proximal plane clustering. Neural Comput Appl 26(1):199\u2013211","journal-title":"Neural Comput Appl"},{"issue":"3","key":"526_CR23","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1109\/LSP.2012.2216874","volume":"20","author":"Y Shao","year":"2013","unstructured":"Shao Y, Deng N, Chen W, Wang Z (2013) Improved generalized eigenvalue proximal support vector machine. IEEE Signal Process Lett 20(3):213\u2013216","journal-title":"IEEE Signal Process Lett"},{"issue":"6","key":"526_CR24","doi-asserted-by":"crossref","first-page":"962","DOI":"10.1109\/TNN.2011.2130540","volume":"22","author":"Y Shao","year":"2011","unstructured":"Shao Y, Zhang C, Wang X, Deng N (2011) Improvements on twin support vector machines. IEEE Trans Neural Netw 22(6):962\u2013968","journal-title":"IEEE Trans Neural Netw"},{"key":"526_CR25","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.ins.2013.11.003","volume":"263","author":"Y Shao","year":"2014","unstructured":"Shao Y, Chen W, Deng N (2014) Nonparallel hyperplane support vector machine for binary classification problems. Inf Sci 263:22\u201335","journal-title":"Inf Sci"},{"key":"526_CR26","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.neunet.2012.09.004","volume":"36","author":"Z Qi","year":"2012","unstructured":"Qi Z, Tian Y, Shi Y (2012) Twin support vector machine with universum data. Neural Netw 36:112\u2013119","journal-title":"Neural Netw"},{"issue":"1","key":"526_CR27","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/j.patcog.2012.06.019","volume":"46","author":"Z Qi","year":"2012","unstructured":"Qi Z, Tian Y, Shi Y (2012) Robust twin support vector machine for pattern classification. Pattern Recognit 46(1):305\u2013316","journal-title":"Pattern Recognit"},{"key":"526_CR28","volume-title":"Data mining: concepts and techniques","author":"J Han","year":"2006","unstructured":"Han J, Kamber M (2006) Data mining: concepts and techniques, 2nd edn. China Machine Press, Beijing","edition":"2"},{"key":"526_CR29","doi-asserted-by":"crossref","unstructured":"Ding C, He X (2004) K-means clustering via principal component analysis, in: Proceedings of the twenty-first international conference on machine learning, ACM, p 29","DOI":"10.1145\/1015330.1015408"},{"key":"526_CR30","volume-title":"Numerical mathematical analysis","author":"J Scarborough","year":"1958","unstructured":"Scarborough J (1958) Numerical mathematical analysis, 4th edn. Johns Hopkins Press, New York","edition":"4"},{"key":"526_CR31","volume-title":"Support vector machines: optimization based theory, algorithms, and extensions","author":"N Deng","year":"2013","unstructured":"Deng N, Tian Y, Zhang C (2013) Support vector machines: optimization based theory, algorithms, and extensions. CRC Press, Boca Raton"},{"issue":"3","key":"526_CR32","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.neucom.2013.05.046","volume":"127","author":"M Naldi","year":"2014","unstructured":"Naldi M, Campello R (2014) Evolutionary k-means for distributed datasets. Neurocomputing 127(3):30\u201342","journal-title":"Neurocomputing"},{"key":"526_CR33","unstructured":"Bradley P, Fayyad U (1998) Refining initial points for k-means clustering, in: Proceedings of the 15th international conference on machine learning (ICML98), pp. 91\u201399"},{"key":"526_CR34","unstructured":"Fayyad U, Reina C, Bradley B (1998) Initialization of iterative refinement clustering algorithms In: Proc 14th Intl Conf on machine learning (ICML), pp. 194\u2013198"},{"key":"526_CR35","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.procs.2013.05.007","volume":"17","author":"Y-H Shao","year":"2013","unstructured":"Shao Y-H, Bai L, Wang Z, Hua X-Y, Deng N-Y (2013) Proximal plane clustering via eigenvalues. Proc Comput Sci 17:41\u201347","journal-title":"Proc Comput Sci"},{"issue":"4","key":"526_CR36","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/s11222-007-9033-z","volume":"17","author":"U Luxburg","year":"2007","unstructured":"Luxburg U (2007) A tutorial on spectral clustering. Stat Comput 17(4):395\u2013416","journal-title":"Stat Comput"},{"issue":"3","key":"526_CR37","first-page":"305","volume":"13","author":"RJ Hathaway","year":"2005","unstructured":"Hathaway RJ, Bezdek JC, Huband JM (2005) Kernelized non-euclidean relational c-means algorithms. Neural Parallel Sci Comput 13(3):305\u2013326","journal-title":"Neural Parallel Sci Comput"},{"key":"526_CR38","volume-title":"Learning with kernels","author":"B Scholk\u00f6pf","year":"2002","unstructured":"Scholk\u00f6pf B, Smola A (2002) Learning with kernels. MIT Press, Cambridge, MA"},{"key":"526_CR39","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.neunet.2011.08.003","volume":"25","author":"Y Shao","year":"2012","unstructured":"Shao Y, Deng N (2012) A coordinate descent margin based-twin support vector machine for classification. Neural Netw 25:114\u2013121","journal-title":"Neural Netw"},{"key":"526_CR40","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.neunet.2012.07.011","volume":"35","author":"Z Qi","year":"2012","unstructured":"Qi Z, Tian Y, Shi Y (2012) Laplacian twin support vector machine for semi-supervised classification. Neural Netw 35:46\u201353","journal-title":"Neural Netw"},{"key":"526_CR41","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/j.knosys.2012.08.001","volume":"37","author":"Y-H Shao","year":"2013","unstructured":"Shao Y-H, Wang Z, Chen W-J, Deng N-Y (2013) A regularization for the projection twin support vector machine. Knowl Based Syst 37:203\u2013210","journal-title":"Knowl Based Syst"},{"key":"526_CR42","unstructured":"Blake CL, Merz CJ (199 8) UCI repository for machine learning databases. http:\/\/www.ics.uci.edu\/mlearn\/MLRepository.html . Accessed Jan 2015"},{"issue":"1","key":"526_CR43","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/j.datak.2006.01.013","volume":"60","author":"B Derya","year":"2007","unstructured":"Derya B, Alp K (2007) ST-DBSCAN: an algorithm for clustering spatial\u2013temporal data. Data Knowl Eng 60(1):208\u2013221","journal-title":"Data Knowl Eng"},{"issue":"6","key":"526_CR44","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1007\/BF02948834","volume":"15","author":"A Zhou","year":"2000","unstructured":"Zhou A, Zhou S, Cao J, Fan Y, Hu Y (2000) Approaches for scaling DBSCAN algorithm to large spatial databases. J Comput Sci Technol 15(6):509\u2013526","journal-title":"J Comput Sci Technol"},{"key":"526_CR45","unstructured":"The MathWorks Inc (1994\u20132001) Matlab, User\u2019s guide. http:\/\/www.mathworks.com"},{"key":"526_CR46","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1023\/A:1012801612483","volume":"17","author":"M Halkidi","year":"2001","unstructured":"Halkidi M, Batistakis Y, Vazirgiannis M (2001) On clustering validation techniques. Intell Inf Syst J 17:107\u2013145","journal-title":"Intell Inf Syst J"},{"issue":"1","key":"526_CR47","first-page":"1","volume":"7","author":"J Demsar","year":"2006","unstructured":"Demsar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mac Learn Res 7(1):1\u201330","journal-title":"J Mac Learn Res"},{"issue":"2","key":"526_CR48","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1214\/aoms\/1177728261","volume":"27","author":"J Hodges Jr","year":"1956","unstructured":"Hodges J Jr, Lehmann EL (1956) The efficiency of some nonparametric competitors of the t-test. Ann Math Stat 27(2):324\u2013335","journal-title":"Ann Math Stat"},{"key":"526_CR49","volume-title":"Nonparametric statistical methods","author":"M Hollander","year":"1973","unstructured":"Hollander M, Wolfe D, Chicken E (1973) Nonparametric statistical methods, 2nd edn. Wiley, New York","edition":"2"},{"key":"526_CR50","doi-asserted-by":"crossref","unstructured":"Wang Y, Jiang Y, Wu Y, Zhou Z (2011) Localized k-flats. In: Proceedings of the twenty-fifth AAAI conference on artificial intelligence, pp. 525\u2013530","DOI":"10.1609\/aaai.v25i1.7912"},{"key":"526_CR51","doi-asserted-by":"crossref","first-page":"2935","DOI":"10.1016\/j.neucom.2010.07.015","volume":"73","author":"P Huang","year":"2010","unstructured":"Huang P, Zhang D (2010) Locality sensitive c-means clustering algorithms. Neurocomputing 73:2935\u20132943","journal-title":"Neurocomputing"},{"key":"526_CR52","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/j.neucom.2010.03.019","volume":"74","author":"B Yang","year":"2010","unstructured":"Yang B, Chen S (2010) Sample-dependent graph construction with application to dimensionality reduction. Neurocomputing 74:301\u2013314","journal-title":"Neurocomputing"},{"issue":"1","key":"526_CR53","doi-asserted-by":"crossref","first-page":"5","DOI":"10.3846\/20294913.2012.661205","volume":"18","author":"Y Tian","year":"2012","unstructured":"Tian Y, Shi Y, Liu X (2012) Recent advances on support vector machines research. Technol Econ Dev Econ 18(1):5\u201333","journal-title":"Technol Econ Dev Econ"},{"key":"526_CR54","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/j.knosys.2013.05.015","volume":"49","author":"Y-H Shao","year":"2013","unstructured":"Shao Y-H, Deng N-Y, Chen W-J (2013) A proximal classifier with consistency. Knowl Based Syst 49:171\u2013178","journal-title":"Knowl Based Syst"},{"issue":"1","key":"526_CR55","first-page":"1438","volume":"17","author":"JC Bezdek","year":"1978","unstructured":"Bezdek JC, Gunderson R, Ehrlich R, Meloy T (1978) On the extension of fuzzy k-means algorithms for detection of linear clusters. Decision and control including the 17th symposium on adaptive processes 17(1):1438\u20131443","journal-title":"Decision and control including the 17th symposium on adaptive processes"},{"issue":"2","key":"526_CR56","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1137\/0140029","volume":"40","author":"JC Bezdek","year":"1981","unstructured":"Bezdek JC, Coray C, Gunderson R, Watson J (1981) Detection and characterization of cluster substructure i. linear structure: fuzzy c-lines. SIAM J Appl Math 40(2):339\u2013357","journal-title":"SIAM J Appl Math"},{"issue":"2","key":"526_CR57","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1137\/0140030","volume":"40","author":"JC Bezdek","year":"1981","unstructured":"Bezdek JC, Coray C, Gunderson R, Watson J (1981) Detection and characterization of cluster substructure ii. fuzzy c-varieties and complex combinations thereof. SIAM J Appl Math 40(2):358\u2013372","journal-title":"SIAM J Appl Math"}],"container-title":["International Journal of Machine Learning and Cybernetics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s13042-016-0526-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-016-0526-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-016-0526-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-016-0526-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,17]],"date-time":"2023-08-17T16:55:52Z","timestamp":1692291352000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s13042-016-0526-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,4,13]]},"references-count":57,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2017,10]]}},"alternative-id":["526"],"URL":"https:\/\/doi.org\/10.1007\/s13042-016-0526-y","relation":{},"ISSN":["1868-8071","1868-808X"],"issn-type":[{"value":"1868-8071","type":"print"},{"value":"1868-808X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,4,13]]}}}