{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T03:47:38Z","timestamp":1784864858330,"version":"3.55.0"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,9,22]],"date-time":"2022-09-22T00:00:00Z","timestamp":1663804800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,9,22]],"date-time":"2022-09-22T00:00:00Z","timestamp":1663804800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11671059"],"award-info":[{"award-number":["11671059"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput &amp; Applic"],"published-print":{"date-parts":[[2023,1]]},"DOI":"10.1007\/s00521-022-07814-0","type":"journal-article","created":{"date-parts":[[2022,9,22]],"date-time":"2022-09-22T14:04:03Z","timestamp":1663855443000},"page":"799-814","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A novel robust nonparallel support vector classifier based on one optimization problem"],"prefix":"10.1007","volume":"35","author":[{"given":"Kai","family":"Qi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6589-8534","authenticated-orcid":false,"given":"Hu","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,9,22]]},"reference":[{"issue":"25","key":"7814_CR1","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1137\/13094829X","volume":"1","author":"A Beck","year":"2015","unstructured":"Beck A (2015) On the convergence of alternating minimization for convex programming with applications to iteratively reweighted least squares and decomposition schemes. SIAM J Optim 1(25):185\u2013209","journal-title":"SIAM J Optim"},{"issue":"62","key":"7814_CR2","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(62):1687\u20131712","journal-title":"J Mach Learn Res"},{"issue":"3","key":"7814_CR3","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1007\/BF00994018","volume":"20","author":"C Cortes","year":"1995","unstructured":"Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20(3):273\u2013297","journal-title":"Mach Learn"},{"key":"7814_CR4","first-page":"1","volume":"7","author":"J Dem\u0161ar","year":"2006","unstructured":"Dem\u0161ar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1\u201330","journal-title":"J Mach Learn Res"},{"issue":"1","key":"7814_CR5","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1016\/j.neunet.2009.08.001","volume":"23","author":"P Hao","year":"2010","unstructured":"Hao P (2010) New support vector algorithms with parametric insensitive\/margin model. Neural Netw 23(1):60\u201373","journal-title":"Neural Netw"},{"issue":"5","key":"7814_CR6","doi-asserted-by":"publisher","first-page":"984","DOI":"10.1109\/TPAMI.2013.178","volume":"36","author":"X Huang","year":"2013","unstructured":"Huang X, Shi L, Suykens J (2013) Support vector machine classifier with pinball loss. IEEE Trans Pattern Anal Mach Intell 36(5):984\u2013997","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"issue":"1","key":"7814_CR7","first-page":"2185","volume":"15","author":"X Huang","year":"2014","unstructured":"Huang X, Shi L, Suykens J (2014) Ramp loss linear programming support vector machine. J Mach Learn Res 15(1):2185\u20132211","journal-title":"J Mach Learn Res"},{"issue":"5","key":"7814_CR8","doi-asserted-by":"publisher","first-page":"905","DOI":"10.1109\/TPAMI.2007.1068","volume":"29","author":"R Khemchandani","year":"2007","unstructured":"Khemchandani R, Chandra S (2007) Twin support vector machines for pattern classification. IEEE Trans Pattern Anal Mach Intell 29(5):905\u2013910","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"issue":"11","key":"7814_CR9","doi-asserted-by":"publisher","first-page":"5286","DOI":"10.1109\/TSP.2007.896065","volume":"55","author":"W Liu","year":"2007","unstructured":"Liu W, Pokharel P, Principe J (2007) Correntropy: properties and applications in non-gaussian signal processing. IEEE Trans Signal Process 55(11):5286\u20135298","journal-title":"IEEE Trans Signal Process"},{"key":"7814_CR10","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1016\/j.ins.2017.11.035","volume":"429","author":"J L\u00f3pez","year":"2018","unstructured":"L\u00f3pez J, Maldonado S, Carrasco M (2018) Double regularization methods for robust feature selection and SVM classification via DC programming. Inf Sci 429:377\u2013389","journal-title":"Inf Sci"},{"key":"7814_CR11","doi-asserted-by":"crossref","unstructured":"Ma Y, Liang X, Sheng G, Kwok J, Wang M, Li G (2020) Noniterative sparse LS-SVM based on globally representative point selection. IEEE Trans Neural Netw Learn Syst 1\u201311","DOI":"10.1109\/TNNLS.2020.2978858"},{"issue":"5","key":"7814_CR12","doi-asserted-by":"publisher","first-page":"1032","DOI":"10.1109\/72.788643","volume":"10","author":"O Mangasarian","year":"1999","unstructured":"Mangasarian O, Musicant D (1999) Successive overrelaxation for support vector machines. IEEE Trans Neural Netw 10(5):1032\u20131037","journal-title":"IEEE Trans Neural Netw"},{"issue":"3","key":"7814_CR13","first-page":"161","volume":"1","author":"O Mangasarian","year":"2001","unstructured":"Mangasarian O, Musicant D (2001) Lagrangian support vector machines. J Mach Learn Res 1(3):161\u2013177","journal-title":"J Mach Learn Res"},{"issue":"1","key":"7814_CR14","doi-asserted-by":"publisher","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 machine classification via generalized eigenvalues. IEEE Trans Pattern Anal Mach Intell 28(1):69\u201374","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"7814_CR15","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1098\/rsta.1909.0016","volume":"209","author":"J Mercer","year":"1909","unstructured":"Mercer J (1909) Functions of positive and negative type, and their connection the theory of integral equations. Philos Trans R Soc Lond 209:415\u2013446","journal-title":"Philos Trans R Soc Lond"},{"issue":"3","key":"7814_CR16","doi-asserted-by":"publisher","first-page":"937","DOI":"10.1137\/030600862","volume":"27","author":"M Nikolova","year":"2005","unstructured":"Nikolova M, Ng M (2005) Analysis of half-quadratic minimization methods for signal and image recovery. SIAM J Sci Comput 27(3):937\u2013966","journal-title":"SIAM J Sci Comput"},{"key":"7814_CR17","doi-asserted-by":"publisher","first-page":"2678","DOI":"10.1016\/j.patcog.2011.03.031","volume":"44","author":"X Peng","year":"2011","unstructured":"Peng X (2011) TPMSVM: a novel twin parametric-margin support vector machine for pattern recognition. Pattern Recogn 44:2678\u20132692","journal-title":"Pattern Recogn"},{"key":"7814_CR18","doi-asserted-by":"publisher","first-page":"266","DOI":"10.1016\/j.knosys.2014.08.005","volume":"71","author":"X Peng","year":"2014","unstructured":"Peng X, Chen D, Kong L (2014) A clipping dual coordinate descent algorithm for solving support vector machines. Knowl Based Syst 71:266\u2013278","journal-title":"Knowl Based Syst"},{"key":"7814_CR19","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2019.104933","volume":"185","author":"K Qi","year":"2019","unstructured":"Qi K, Yang H, Hu Q, Yang D (2019) A new adaptive weighted imbalanced data classifier via improved support vector machines with high-dimension nature. Knowl Based Syst 185:104933","journal-title":"Knowl Based Syst"},{"key":"7814_CR20","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2021.3084404","author":"K Qi","year":"2021","unstructured":"Qi K, Yang H (2021) Elastic net nonparallel hyperplane support vector machine and its geometrical rationality. IEEE Trans Neural Netw Learn Syst. https:\/\/doi.org\/10.1109\/TNNLS.2021.3084404","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"7814_CR21","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1016\/j.neucom.2018.05.100","volume":"313","author":"Z Ren","year":"2018","unstructured":"Ren Z, Yang L (2018) Correntropy-based robust extreme learning machine for classification. Neurocomputing 313:74\u201384","journal-title":"Neurocomputing"},{"issue":"5","key":"7814_CR22","doi-asserted-by":"publisher","first-page":"1207","DOI":"10.1162\/089976600300015565","volume":"12","author":"B Sch\u00f6lkopf","year":"2000","unstructured":"Sch\u00f6lkopf B, Smola A, Williamson R, Bartlett P (2000) New support vector algorithms. Neural Comput 12(5):1207\u20131245","journal-title":"Neural Comput"},{"key":"7814_CR23","doi-asserted-by":"publisher","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":"7814_CR24","doi-asserted-by":"publisher","first-page":"2383","DOI":"10.1007\/s00521-019-04216-7","volume":"32","author":"D Simian","year":"2020","unstructured":"Simian D, Stoica F, B\u0103rbulescu A (2020) Automatic optimized support vector regression for financial data prediction. Neural Comput Appl 32:2383\u20132396","journal-title":"Neural Comput Appl"},{"issue":"1","key":"7814_CR25","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1016\/j.patcog.2013.07.017","volume":"47","author":"A Singh","year":"2014","unstructured":"Singh A, Pokharel R, Principe J (2014) The c-loss function for pattern classification. Pattern Recogn 47(1):441\u2013453","journal-title":"Pattern Recogn"},{"issue":"113","key":"7814_CR26","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2020.106598","volume":"212","author":"W Sleeman IV","year":"2021","unstructured":"Sleeman W IV, Krawczyk B (2021) Multi-class imbalanced big data classification on spark. Knowl Based Syst 212(113):106598","journal-title":"Knowl Based Syst"},{"issue":"3","key":"7814_CR27","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1023\/A:1018628609742","volume":"9","author":"JA Suykens","year":"1999","unstructured":"Suykens JA, Vandewalle J (1999) Least squares support vector machine classifiers. Neural Process Lett 9(3):293\u2013300","journal-title":"Neural Process Lett"},{"issue":"4","key":"7814_CR28","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1007\/s40305-015-0095-x","volume":"3","author":"Y Tian","year":"2015","unstructured":"Tian Y, Ju X (2015) Nonparallel support vector machine based on one optimization problem for pattern recognition. J Oper Res Soc China 3(4):499\u2013519","journal-title":"J Oper Res Soc China"},{"key":"7814_CR29","volume-title":"The nature of statistical learning theory","author":"V Vapnik","year":"2013","unstructured":"Vapnik V (2013) The nature of statistical learning theory. Springer, Berlin"},{"key":"7814_CR30","first-page":"69","volume":"6","author":"G Wahba","year":"1999","unstructured":"Wahba G (1999) Support vector machines, reproducing kernel Hilbert spaces and the randomized GACV. Adv Kernel Methods Support Vector Learn 6:69\u201387","journal-title":"Adv Kernel Methods Support Vector Learn"},{"key":"7814_CR31","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/j.neunet.2019.01.016","volume":"114","author":"C Wang","year":"2019","unstructured":"Wang C, Ye Q, Luo P, Ye N, Fu L (2019) Robust capped l1-norm twin support vector machine. Neural Netw 114:47\u201359","journal-title":"Neural Netw"},{"key":"7814_CR32","doi-asserted-by":"crossref","unstructured":"Wang D, Zhang X, Chen H, Zhou Y, Cheng F (2020) A sintering state recognition framework to integrate prior knowledge and hidden information considering class imbalance. IEEE Trans Ind Electron 1\u20131","DOI":"10.1109\/TIE.2020.2973886"},{"key":"7814_CR33","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2019.105946","volume":"88","author":"M Wang","year":"2020","unstructured":"Wang M, Chen H (2020) Chaotic multi-swarm whale optimizer boosted support vector machine for medical diagnosis. Appl Soft Comput 88:105946","journal-title":"Appl Soft Comput"},{"key":"7814_CR34","first-page":"1","volume":"20","author":"X Wang","year":"2019","unstructured":"Wang X, Yang Z, Chen X, Liu W (2019) Distributed inference for linear support vector machine. J Mach Learn Res 20:1\u201341","journal-title":"J Mach Learn Res"},{"issue":"2","key":"7814_CR35","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1080\/10618600.2012.680866","volume":"22","author":"Y Wu","year":"2013","unstructured":"Wu Y, Liu Y (2013) Adaptively weighted large margin classifiers. J Comput Graph Stat 22(2):416\u2013432","journal-title":"J Comput Graph Stat"},{"key":"7814_CR36","doi-asserted-by":"publisher","first-page":"274","DOI":"10.1016\/j.neunet.2019.05.023","volume":"117","author":"B Xu","year":"2019","unstructured":"Xu B, Shen S, Shen F, Zhao J (2019) Locally linear SVMs based on boundary anchor points encoding. Neural Netw 117:274\u2013284","journal-title":"Neural Netw"},{"key":"7814_CR37","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1016\/j.patcog.2016.09.045","volume":"63","author":"G Xu","year":"2017","unstructured":"Xu G, Cao Z, Hu B, Principe J (2017) Robust support vector machines based on the rescaled hinge loss function. Pattern Recogn 63:139\u2013148","journal-title":"Pattern Recogn"},{"issue":"3","key":"7814_CR38","doi-asserted-by":"publisher","first-page":"510","DOI":"10.1109\/TNNLS.2016.2637351","volume":"29","author":"G Xu","year":"2018","unstructured":"Xu G, Hu B, Principe J (2018) Robust c-loss kernel classifiers. IEEE Trans Neural Netw Learn Syst 29(3):510\u2013522","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"7814_CR39","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2019.105483","volume":"81","author":"L Yang","year":"2019","unstructured":"Yang L, Dong H (2019) Robust support vector machine with generalized quantile loss for classification and regression. Appl Soft Comput 81:105483","journal-title":"Appl Soft Comput"},{"key":"7814_CR40","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/j.knosys.2019.01.031","volume":"170","author":"J Zhao","year":"2019","unstructured":"Zhao J, Xu Y, Fujita H (2019) An improved non-parallel Universum support vector machine and its safe sample screening rule. Knowl Based Syst 170:79\u201388","journal-title":"Knowl Based Syst"},{"key":"7814_CR41","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1016\/j.ins.2021.01.006","volume":"599","author":"X Zheng","year":"2021","unstructured":"Zheng X, Zhang L, Yan L (2021) CTSVM: a robust twin support vector machine with correntropy-induced loss function for binary classification problems. Inf Sci 599:22\u201345","journal-title":"Inf Sci"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-022-07814-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00521-022-07814-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-022-07814-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,7]],"date-time":"2023-01-07T06:16:54Z","timestamp":1673072214000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00521-022-07814-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,22]]},"references-count":41,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,1]]}},"alternative-id":["7814"],"URL":"https:\/\/doi.org\/10.1007\/s00521-022-07814-0","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,22]]},"assertion":[{"value":"18 May 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 September 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 September 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare that they have no conflict of interest.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}