{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T06:28:48Z","timestamp":1762324128803,"version":"3.37.3"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"20","license":[{"start":{"date-parts":[[2017,8,9]],"date-time":"2017-08-09T00:00:00Z","timestamp":1502236800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2017,8,9]],"date-time":"2017-08-09T00:00:00Z","timestamp":1502236800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11371242"],"award-info":[{"award-number":["11371242"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000183","name":"Army Research Office","doi-asserted-by":"publisher","award":["W911NF-15-1-0223"],"award-info":[{"award-number":["W911NF-15-1-0223"]}],"id":[{"id":"10.13039\/100000183","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2018,10]]},"DOI":"10.1007\/s00500-017-2751-z","type":"journal-article","created":{"date-parts":[[2017,8,9]],"date-time":"2017-08-09T04:24:55Z","timestamp":1502252695000},"page":"6905-6919","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["A proximal quadratic surface support vector machine for semi-supervised binary classification"],"prefix":"10.1007","volume":"22","author":[{"given":"Xin","family":"Yan","sequence":"first","affiliation":[]},{"given":"Yanqin","family":"Bai","sequence":"additional","affiliation":[]},{"given":"Shu-Cherng","family":"Fang","sequence":"additional","affiliation":[]},{"given":"Jian","family":"Luo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,8,9]]},"reference":[{"key":"2751_CR1","doi-asserted-by":"publisher","first-page":"2135","DOI":"10.1109\/TPAMI.2007.1102","volume":"29","author":"A Astorino","year":"2007","unstructured":"Astorino A, Fuduli A (2007) Nonsmooth optimization techniques for semisupervised classification. IEEE Trans Pattern Anal 29:2135\u20132142","journal-title":"IEEE Trans Pattern Anal"},{"key":"2751_CR2","doi-asserted-by":"publisher","first-page":"6351","DOI":"10.1016\/j.apm.2015.01.044","volume":"39","author":"A Astorino","year":"2015","unstructured":"Astorino A, Fuduli A (2015a) Semisupervised spherical separation. Appl Math Model 39:6351\u20136358","journal-title":"Appl Math Model"},{"key":"2751_CR3","doi-asserted-by":"publisher","first-page":"1039","DOI":"10.1007\/s10957-013-0458-6","volume":"164","author":"A Astorino","year":"2015","unstructured":"Astorino A, Fuduli A (2015b) Support vector machine polyhedral separability in semisupervised learning. J Optim Theory Appl 164:1039\u20131050","journal-title":"J Optim Theory Appl"},{"key":"2751_CR4","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1007\/s10957-015-0843-4","volume":"169","author":"Y Bai","year":"2016","unstructured":"Bai Y, Yan X (2016) Conic relaxation for semi-supervised support vector machines. J Optim Theory Appl 169:299\u2013313","journal-title":"J Optim Theory Appl"},{"issue":"1","key":"2751_CR5","first-page":"3","volume":"8","author":"Y Bai","year":"2012","unstructured":"Bai Y, Chen Y, Niu B (2012) SDP relaxation for semi-supervised support vector machine. Pac J Optim 8(1):3\u201314","journal-title":"Pac J Optim"},{"issue":"4","key":"2751_CR6","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1080\/02331934.2011.611515","volume":"62","author":"Y Bai","year":"2013","unstructured":"Bai Y, Niu B, Chen Y (2013) New SDP models for protein homology detection with semi-supervised SVM. Optimization 62(4):561\u2013572","journal-title":"Optimization"},{"key":"2751_CR7","first-page":"2399","volume":"7","author":"M Belkin","year":"2006","unstructured":"Belkin M, Niyogi P, Sindhwani V (2006) Manifold regularization: a geometric framework for learning from labeled and unlabeled examples. J Mach Learn Res 7:2399\u20132434","journal-title":"J Mach Learn Res"},{"key":"2751_CR8","first-page":"368","volume-title":"Advances in neural information processing systems 11","author":"K Bennett","year":"1999","unstructured":"Bennett K, Demiriz A (1999) Semi-supervised support vector machines. In: Kearns MJ, Solla SA, Cohn DA (eds) Advances in neural information processing systems 11. MIT Press, Cambridge, pp 368\u2013374"},{"issue":"6","key":"2751_CR9","doi-asserted-by":"publisher","first-page":"1506","DOI":"10.1109\/TNN.2003.820556","volume":"14","author":"L Cao","year":"2003","unstructured":"Cao L, Tay FEH (2003) Support vector machine with adaptive parameters in financial time series forecasting. IEEE Trans Neural Netw Learn Syst 14(6):1506\u20131518","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"2751_CR10","unstructured":"Chapelle O, Zien A (2005) Semi-supervised classification by low density separation. In: Proceedings of the 10th international workshop on artificial intelligence and statistics, pp 57\u201364"},{"key":"2751_CR11","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/9780262033589.001.0001","volume-title":"Semi-supervised learning","author":"O Chapelle","year":"2006","unstructured":"Chapelle O, Sch\u00f6lkopf B, Zien A (2006) Semi-supervised learning. MIT Press, Cambridge"},{"key":"2751_CR12","first-page":"203","volume":"9","author":"O Chapelle","year":"2008","unstructured":"Chapelle O, Sindhwani V, Keerthi SS (2008) Optimization techniques for semi-supervised support vector machines. J Mach Learn Res 9:203\u2013233","journal-title":"J Mach Learn Res"},{"key":"2751_CR13","first-page":"1687","volume":"7","author":"R Collobert","year":"2006","unstructured":"Collobert R, Sinz F, Weston J, Bottou L (2006) Large scale transductive SVMs. J Mach Learn Res 7:1687\u20131712","journal-title":"J Mach Learn Res"},{"issue":"1","key":"2751_CR14","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1007\/s10898-007-9162-0","volume":"4","author":"I Dagher","year":"2008","unstructured":"Dagher I (2008) Quadratic kernel-free non-linear support vector machine. J Glob Optim 4(1):15\u201330","journal-title":"J Glob Optim"},{"key":"2751_CR15","first-page":"73","volume-title":"Advances in neural information processing systems 16","author":"T De Bie","year":"2004","unstructured":"De Bie T, Cristianini N (2004) Convex methods for transduction. In: Thrun S, Saul LK, Sch\u00f6lkopf B (eds) Advances in neural information processing systems 16. MIT Press, Cambridge, pp 73\u201380"},{"key":"2751_CR16","doi-asserted-by":"publisher","DOI":"10.1201\/b14297","volume-title":"Support vector machines-optimization based theory, algorithms and extensions","author":"N Deng","year":"2012","unstructured":"Deng N, Tian Y, Zhang C (2012) Support vector machines-optimization based theory, algorithms and extensions. CRC Press, Boca Raton"},{"key":"2751_CR17","doi-asserted-by":"crossref","unstructured":"Fung G, Mangasarian OL (2001) Proximal support vector machine classifiers. In: Proceedings of 7th ACM SIGKDD international conference on Knowledge discovery and data mining, pp 77\u201386","DOI":"10.1145\/502512.502527"},{"key":"2751_CR18","unstructured":"Grant M, Boyd S, Ye YY (2016) CVX: Matlab software for disciplined convex programming (version 2.1). \n                    http:\/\/cvxr.com\/cvx\/"},{"issue":"1","key":"2751_CR19","doi-asserted-by":"publisher","first-page":"136","DOI":"10.1137\/090768813","volume":"32","author":"B He","year":"2011","unstructured":"He B, Xu M, Yuan X (2011) Solving large-scale least squares semidefinite programming by alternating direction methods. SIAM J Matrix Anal Appl 32(1):136\u2013152","journal-title":"SIAM J Matrix Anal Appl"},{"issue":"7","key":"2751_CR20","doi-asserted-by":"publisher","first-page":"679","DOI":"10.1007\/s00500-006-0130-2","volume":"11","author":"RK Jayadeva","year":"2007","unstructured":"Jayadeva RK, Suresh C (2007) Fuzzy multi-category proximal support vector classification via generalized eigenvalues. Soft Comput 11(7):679\u2013685","journal-title":"Soft Comput"},{"key":"2751_CR21","unstructured":"Joachims T (1999) Transductive inference for text classification using support vector machines. In: Proceedings of 16th international conference on machine learning, pp 200\u2013209"},{"key":"2751_CR22","unstructured":"Luo J (2014) Quadratic surface support vector machines with applications. Ph.D. thesis, North Carolina State University"},{"key":"2751_CR23","first-page":"1149","volume":"12","author":"S Melacci","year":"2011","unstructured":"Melacci S, Belkin M (2011) Laplacian support vector machines trained in the primal. J Mach Learn Res 12:1149\u20131184","journal-title":"J Mach Learn Res"},{"key":"2751_CR24","doi-asserted-by":"crossref","unstructured":"Osuna E, Freund R, Girosi F (1997) Training support vector machines: an application to face detection. In: Proceedings of IEEE conference on computer vision and pattern recognition, pp 130\u2013136","DOI":"10.1109\/CVPR.1997.609310"},{"key":"2751_CR25","doi-asserted-by":"publisher","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":"2751_CR26","doi-asserted-by":"crossref","unstructured":"Sindhwani V, Keerthi SS, Chapelle O (2006) Deterministic annealing for semi-supervised kernel machines. In: Proceedings of 23rd international conference on machine learning, pp 841\u2013848","DOI":"10.1145\/1143844.1143950"},{"issue":"3","key":"2751_CR27","doi-asserted-by":"publisher","first-page":"1210","DOI":"10.1016\/j.ejor.2010.07.020","volume":"207","author":"J Sun","year":"2010","unstructured":"Sun J, Zhang S (2010) A modified alternating direction method for convex quadratically constrained quadratic semidefinite programs. Eur J Oper Res 207(3):1210\u20131220","journal-title":"Eur J Oper Res"},{"key":"2751_CR28","doi-asserted-by":"publisher","first-page":"1076","DOI":"10.1007\/11759966_158","volume-title":"Advances in neural networks-ISNN 2006, Lecture notes in computer science","author":"L Sun","year":"2006","unstructured":"Sun L, Jing L, Xia XD (2006) A new proximal support vector machine for semi-supervised classification. In: Wang J, Yi Z, Zurada JM, Lu B, Yin H (eds) Advances in neural networks-ISNN 2006, Lecture notes in computer science, vol 3971. Springer, Heidelburg, pp 1076\u20131082"},{"issue":"2","key":"2751_CR29","doi-asserted-by":"publisher","first-page":"882","DOI":"10.1137\/140964357","volume":"25","author":"Defeng Sun","year":"2015","unstructured":"Sun D, Toh KC, Yang L (2015) A convergent 3-block semiproximal alternating direction method of multipliers for conic programming with 4-type constraints. SIAM J Optim 25(2):882\u2013915","journal-title":"SIAM Journal on Optimization"},{"issue":"1","key":"2751_CR30","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1007\/s00500-016-2089-y","volume":"21","author":"Ye Tian","year":"2016","unstructured":"Tian Y, Luo J (2017) A new branch-and-bound approach to semi-supervised support vector machine. Soft Comput 21(1):245\u2013254","journal-title":"Soft Computing"},{"key":"2751_CR31","first-page":"1417","volume-title":"Advances in neural information processing systems 19","author":"H Valizadegan","year":"2006","unstructured":"Valizadegan H, Jin R (2006) Generalized maximum margin clustering and unsupervised kernel learning. In: Sch\u00f6lkopf B, Platt J, Hofmann T (eds) Advances in neural information processing systems 19. MIT Press, Cambridge, pp 1417\u20131424"},{"issue":"3\u20134","key":"2751_CR32","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/s12532-010-0017-1","volume":"2","author":"Z Wen","year":"2010","unstructured":"Wen Z, Goldfarb D, Yin W (2010) Alternating direction augmented Lagrangian methods for semidefinite programming. Math Prog Comp 2(3\u20134):203\u2013230","journal-title":"Math Prog Comp"},{"key":"2751_CR33","unstructured":"Xu L, Schuurmans D (2005) Unsupervised and semi-supervised multi-class support vector machines. In: Proceedings of 20th National conference on artificial intelligence, pp 904\u2013910"},{"key":"2751_CR34","first-page":"1641","volume-title":"Advances in neural information processing systems 20","author":"Z Xu","year":"2008","unstructured":"Xu Z, Jin R, Zhu J, King I, Lyu M (2008) Efficient convex relaxation for transductive support vector machine. In: Platt JC, Koller D, Singer Y, Roweis S (eds) Advances in neural information processing systems 20. MIT Press, Cambridge, pp 1641\u20131648"},{"issue":"7","key":"2751_CR35","doi-asserted-by":"publisher","first-page":"1001","DOI":"10.1057\/jors.2015.89","volume":"67","author":"X Yan","year":"2016","unstructured":"Yan X, Bai Y, Fang SC, Luo J (2016) A kernel-free quadratic surface support vector machine for semi-supervised learning. J Oper Res Soc 67(7):1001\u20131011","journal-title":"J Oper Res Soc"},{"key":"2751_CR36","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-015-1994-9","author":"J Yang","year":"2017","unstructured":"Yang J, Deng J, Li S, Hao Y (2017) Improved traffic detection with support vector machine based on restricted boltzmann machine. Soft Comput. doi:\n                    10.1007\/s00500-015-1994-9","journal-title":"Soft Comput"},{"key":"2751_CR37","doi-asserted-by":"crossref","unstructured":"Zhao B, Wang F, Zhang C (2008) CutS3VM: a fast semi-supervised SVM algorithm. In: Proceedings of 4th ACM SIGKDD international conference on knowledge discovery and data mining, pp 830\u2013838","DOI":"10.1145\/1401890.1401989"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-017-2751-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-017-2751-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-017-2751-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,16]],"date-time":"2020-05-16T15:13:35Z","timestamp":1589642015000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-017-2751-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,9]]},"references-count":37,"journal-issue":{"issue":"20","published-print":{"date-parts":[[2018,10]]}},"alternative-id":["2751"],"URL":"https:\/\/doi.org\/10.1007\/s00500-017-2751-z","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"type":"print","value":"1432-7643"},{"type":"electronic","value":"1433-7479"}],"subject":[],"published":{"date-parts":[[2017,8,9]]},"assertion":[{"value":"9 August 2017","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"All the authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}