{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T05:39:45Z","timestamp":1768973985133,"version":"3.49.0"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[2019,11,15]],"date-time":"2019-11-15T00:00:00Z","timestamp":1573776000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,11,15]],"date-time":"2019-11-15T00:00:00Z","timestamp":1573776000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Math Artif Intell"],"published-print":{"date-parts":[[2020,3]]},"DOI":"10.1007\/s10472-019-09676-0","type":"journal-article","created":{"date-parts":[[2019,11,15]],"date-time":"2019-11-15T21:02:41Z","timestamp":1573851761000},"page":"269-289","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Feature uncertainty bounds for explicit feature maps and large robust nonlinear SVM classifiers"],"prefix":"10.1007","volume":"88","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3775-1468","authenticated-orcid":false,"given":"Nicolas","family":"Couellan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sophie","family":"Jan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,11,15]]},"reference":[{"issue":"1","key":"9676_CR1","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s10107-002-0339-5","volume":"95","author":"F Alizadeh","year":"2003","unstructured":"Alizadeh, F., Goldfarb, D.: Second-order cone programming. Math. Program. 95(1), 3\u201351 (2003)","journal-title":"Math. Program."},{"issue":"1","key":"9676_CR2","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1007\/s10107-010-0415-1","volume":"127","author":"A Ben-Tal","year":"2011","unstructured":"Ben-Tal, A., Bhadra, S., Bhattacharyya, C., Nath, J.S.: Chance constrained uncertain classification via robust optimization. Math. Program. 127(1), 145\u2013173 (2011)","journal-title":"Math. Program."},{"key":"9676_CR3","first-page":"2923","volume":"13","author":"A Ben-Tal","year":"2012","unstructured":"Ben-Tal, A., Bhadra, S., Bhattacharyya, C., Nemirovski, A.: Efficient methods for robust classification under uncertainty in kernel matrices. J. Mach. Learn. Res. 13, 2923\u20132954 (2012)","journal-title":"J. Mach. Learn. Res."},{"key":"9676_CR4","doi-asserted-by":"crossref","unstructured":"Ben-Tal, A., El Ghaoui, L., Nemirovski, A.: Robust Optimization. Princeton Series in Applied Mathematics. Princeton University Press (2009)","DOI":"10.1515\/9781400831050"},{"issue":"2","key":"9676_CR5","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1137\/16M1080173","volume":"60","author":"L Bottou","year":"2018","unstructured":"Bottou, L., Curtis, F., Nocedal, J.: Optimization methods for large-scale machine learning. SIAM Rev. 60(2), 223\u2013311 (2018). https:\/\/doi.org\/10.1137\/16M1080173","journal-title":"SIAM Rev."},{"key":"9676_CR6","doi-asserted-by":"crossref","unstructured":"Caramanis, C., Mannor, S., Xu, H.: Robust optimization in machine learning. In: Sra, S., Nowozin, S., Wright, S. (eds.) Optimization for Machine Learning, Neural Information Processing Series. The MIT Press, Cambridge (2012)","DOI":"10.7551\/mitpress\/8996.003.0016"},{"key":"9676_CR7","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1016\/j.jmva.2013.05.006","volume":"120","author":"LB Chang","year":"2013","unstructured":"Chang, L.B., Bai, Z., Huang, S.Y., Hwang, C.R.: Asymptotic error bounds for kernel-based Nystr\u00f6m low-rank approximation matrices. J. Multivariate Anal. 120, 102\u2013119 (2013). https:\/\/doi.org\/10.1016\/j.jmva.2013.05.006","journal-title":"J. Multivariate Anal."},{"key":"9676_CR8","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1007\/978-3-642-40935-6_26","volume-title":"Lecture Notes in Computer Science","author":"Anna Choromanska","year":"2013","unstructured":"Choromanska, A., Jebara, T., Kim, H., Mohan, M., Monteleoni, C.: Fast spectral clustering via the Nystr\u00f6m method. In: Algorithmic Learning Theory, Lecture Notes in Comput. Sci., vol. 8139, pp 367\u2013381. Springer, Heidelberg (2013), https:\/\/doi.org\/10.1007\/978-3-642-40935-6_26"},{"key":"9676_CR9","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1016\/j.csda.2016.12.008","volume":"109","author":"N Couellan","year":"2017","unstructured":"Couellan, N., Wang, W.: Uncertainty-safe large scale support vector machines. Comput. Statist. Data Anal. 109, 215\u2013230 (2017)","journal-title":"Comput. Statist. Data Anal."},{"key":"9676_CR10","unstructured":"Couellan, N., Wang, W.: On the convergence of a stochastic approximation method for structured bi-level optimization. Preprint. https:\/\/hal.archives-ouvertes.fr\/hal-01932372 (2018)"},{"key":"9676_CR11","doi-asserted-by":"crossref","unstructured":"Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines and other Kernel-Based Learning Methods. Repr. Cambridge University Press (2001)","DOI":"10.1017\/CBO9780511801389"},{"key":"9676_CR12","first-page":"1","volume":"17","author":"A Gittens","year":"2016","unstructured":"Gittens, A., Mahoney, M.W.: Revisiting the Nystr\u00f6m method for improved large-scale machine learning. J. Mach. Learn. Res. 17, 1\u201365 (2016)","journal-title":"J. Mach. Learn. Res."},{"issue":"2","key":"9676_CR13","doi-asserted-by":"publisher","first-page":"344","DOI":"10.1080\/10618600.2014.995799","volume":"25","author":"D Homrighausen","year":"2016","unstructured":"Homrighausen, D., McDonald, D.J.: On the Nystr\u00f6m and column-sampling methods for the approximate principal components analysis of large datasets. J. Comput. Graph. Statist. 25(2), 344\u2013362 (2016). https:\/\/doi.org\/10.1080\/10618600.2014.995799","journal-title":"J. Comput. Graph. Statist."},{"issue":"1","key":"9676_CR14","doi-asserted-by":"publisher","first-page":"152","DOI":"10.1109\/TNNLS.2014.2359798","volume":"26","author":"M Li","year":"2015","unstructured":"Li, M., Bi, W., Kwok, J.T., Lu, B.L.: Large-scale Nystr\u00f6m kernel matrix approximation using randomized SVD. IEEE Trans. Neural Netw. Learn. Syst. 26(1), 152\u2013164 (2015). https:\/\/doi.org\/10.1109\/TNNLS.2014.2359798","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"9676_CR15","unstructured":"MOSEK-ApS: The MOSEK optimization toolbox for MATLAB manual. Version 7.1 (Revision 28). http:\/\/docs.mosek.com\/7.1\/toolbox\/index.html (2015)"},{"key":"9676_CR16","unstructured":"Rahimi, A., Recht, B.: Random features for large-scale kernel machines. In: Neural Information Processing Systems (2007)"},{"issue":"3","key":"9676_CR17","doi-asserted-by":"publisher","first-page":"400","DOI":"10.1214\/aoms\/1177729586","volume":"22","author":"H Robbins","year":"1951","unstructured":"Robbins, H., Monro, S.: A stochastic approximation method. Ann. Math. Stat. 22(3), 400\u2013407 (1951)","journal-title":"Ann. Math. Stat."},{"key":"9676_CR18","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/4175.001.0001","volume-title":"Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond","author":"B Scholkopf","year":"2001","unstructured":"Scholkopf, B., Smola, A.J.: Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. MIT Press, Cambridge (2001)"},{"key":"9676_CR19","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511809682","volume-title":"Kernel Methods for Pattern Analysis","author":"J Shawe-Taylor","year":"2004","unstructured":"Shawe-Taylor, J., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press, New York (2004)"},{"key":"9676_CR20","first-page":"1283","volume":"7","author":"P Shiwaswamy","year":"2006","unstructured":"Shiwaswamy, P., Bhattacharyya, C., Smola, A.: Second order cone programming approaches for handling missing and uncertain data. J. Mach. Learn. Res. 7, 1283\u20131314 (2006)","journal-title":"J. Mach. Learn. Res."},{"key":"9676_CR21","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1080\/10556789908805766","volume":"11\u201312","author":"J Sturm","year":"1999","unstructured":"Sturm, J.: Using sedumi 1.02, a matlab toolbox for optimization over symmetric cones. Optim. Methods Softw. 11\u201312, 625\u2013653 (1999)","journal-title":"Optim. Methods Softw."},{"key":"9676_CR22","unstructured":"Sutherland, D.J., Schneider, J.: On the error of random F,ourier features. arXiv:https:\/\/arxiv.org\/abs\/1506.02785 (2015)"},{"issue":"1","key":"9676_CR23","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1080\/10556780600883791","volume":"22","author":"T Trafalis","year":"2007","unstructured":"Trafalis, T., Gilbert, R.: Robust support vector machines for classification and computational issues. Optim. Methods Softw. 22(1), 187\u2013198 (2007)","journal-title":"Optim. Methods Softw."},{"issue":"3","key":"9676_CR24","doi-asserted-by":"publisher","first-page":"893","DOI":"10.1016\/j.ejor.2005.07.024","volume":"173","author":"TB Trafalis","year":"2006","unstructured":"Trafalis, T.B., Gilbert, R.C.: Robust classification and regression using support vector machines. Eur. J. Oper. Res. 173(3), 893\u2013909 (2006)","journal-title":"Eur. J. Oper. Res."},{"issue":"2","key":"9676_CR25","first-page":"569","volume":"31","author":"A Trokici\u0107","year":"2016","unstructured":"Trokici\u0107, A.: Approximate spectral learning using Nystr\u00f6m method. Facta Univ. Ser. Math. Inform. 31(2), 569\u2013578 (2016)","journal-title":"Facta Univ. Ser. Math. Inform."},{"key":"9676_CR26","volume-title":"Statistical Learning Theory. Adaptive and Learning Systems for Signal Processing, Communications, and Control","author":"VN Vapnik","year":"1998","unstructured":"Vapnik, V.N.: Statistical Learning Theory. Adaptive and Learning Systems for Signal Processing, Communications, and Control. Wiley, New York (1998)"},{"key":"9676_CR27","first-page":"21","volume-title":"SpringerBriefs in Optimization","author":"Petros Xanthopoulos","year":"2012","unstructured":"Xanthopoulos, P., Pardalos, P., Trafalis, T.: Robust Data Mining. SpringerBriefs in Optimization. Springer. https:\/\/books.google.fr\/books?id=CqMlwCO5yJcC (2012)"}],"container-title":["Annals of Mathematics and Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10472-019-09676-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10472-019-09676-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10472-019-09676-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,27]],"date-time":"2024-07-27T01:33:37Z","timestamp":1722044017000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10472-019-09676-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,15]]},"references-count":27,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[2020,3]]}},"alternative-id":["9676"],"URL":"https:\/\/doi.org\/10.1007\/s10472-019-09676-0","relation":{},"ISSN":["1012-2443","1573-7470"],"issn-type":[{"value":"1012-2443","type":"print"},{"value":"1573-7470","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,11,15]]},"assertion":[{"value":"15 November 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}