{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,2]],"date-time":"2025-12-02T22:14:07Z","timestamp":1764713647643,"version":"3.41.0"},"reference-count":37,"publisher":"MIT Press","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2017,11]]},"abstract":"<jats:p>Support vector machines, which maximize the margin from patterns to the separation hyperplane subject to correct classification, have received remarkable success in machine learning. Margin error bounds based on Hilbert spaces have been introduced in the literature to justify the strategy of maximizing the margin in SVM. Recently, there has been much interest in developing Banach space methods for machine learning. Large margin classification in Banach spaces is a focus of such attempts. In this letter we establish a margin error bound for the SVM on reproducing kernel Banach spaces, thus supplying statistical justification for large-margin classification in Banach spaces.<\/jats:p>","DOI":"10.1162\/neco_a_01013","type":"journal-article","created":{"date-parts":[[2017,9,28]],"date-time":"2017-09-28T20:31:40Z","timestamp":1506630700000},"page":"3078-3093","source":"Crossref","is-referenced-by-count":3,"title":["Margin Error Bounds for Support Vector Machines on Reproducing Kernel Banach Spaces"],"prefix":"10.1162","volume":"29","author":[{"given":"Liangzhi","family":"Chen","sequence":"first","affiliation":[{"name":"School of Data and Computer Science, Sun Yat-sen University, Guangzhou 510006, China"}]},{"given":"Haizhang","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Data and Computer Science and Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510006, China"}]}],"member":"281","reference":[{"key":"B1","first-page":"935","volume":"11","author":"Argyriou A.","year":"2010","journal-title":"J. Mach. Learn. Res."},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1950-0051437-7"},{"key":"B3","first-page":"43","volume-title":"Advances in kernel methods\u2014Support vector learning","author":"Bartlett P. L.","year":"1999"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1145\/130385.130401"},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.1023\/A:1009715923555"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2005.862083"},{"key":"B7","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827596304010"},{"key":"B8","volume-title":"A course in functional analysis","author":"Conway J. B.","year":"1990","edition":"2"},{"key":"B9","first-page":"91","volume":"2","author":"Der R.","year":"2007","journal-title":"JMLR Workshop and Conference Proceedings"},{"key":"B10","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0082079"},{"key":"B11","doi-asserted-by":"publisher","DOI":"10.1023\/A:1018946025316"},{"key":"B12","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2014.03.007"},{"key":"B13","first-page":"213","volume":"2","author":"Gentile C.","year":"2001","journal-title":"J. Mach. Learn. Res."},{"key":"B14","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1967-0217574-1"},{"key":"B15","doi-asserted-by":"publisher","DOI":"10.1007\/BF02589410"},{"key":"B16","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-0000(05)80062-5"},{"key":"B17","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(91)90055-5"},{"key":"B18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-35347-9"},{"key":"B19","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1961-0133024-2"},{"key":"B20","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-27819-1_18"},{"volume-title":"Support vector learning","year":"1997","author":"Sch\u00f6lkopf B.","key":"B21"},{"volume-title":"Proceedings of the First International Conference on Knowledge Discovery and Data Mining","year":"1995","author":"Sch\u00f6lkopf B.","key":"B22"},{"key":"B23","first-page":"640","volume-title":"Advances in neural information processing systems","volume":"10","author":"Sch\u00f6lkopf B.","year":"1998"},{"key":"B24","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/4175.001.0001","volume-title":"Learning with kernels: Support vector machines, regularization, optimization, and beyond","author":"Sch\u00f6lkopf B.","year":"2001"},{"key":"B25","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511809682"},{"key":"B26","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/1113.001.0001"},{"key":"B27","doi-asserted-by":"publisher","DOI":"10.1162\/NECO_a_00178"},{"key":"B28","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2012.03.009"},{"key":"B29","first-page":"67","volume":"2","author":"Steinwart I.","year":"2001","journal-title":"J. Mach. Learn. Res."},{"key":"B30","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2440-0"},{"key":"B31","first-page":"281","volume-title":"Advances in neural information processing systems","volume":"9","author":"Vapnik V. N.","year":"1997"},{"key":"B32","doi-asserted-by":"publisher","DOI":"10.1016\/0362-546X(91)90200-K"},{"key":"B33","first-page":"345","volume":"112","author":"Xu H.","year":"1989","journal-title":"Proc. Roy. Soc. Edinburgh"},{"journal-title":"Mem. Amer. Math. Soc","author":"Xu Y.","key":"B34"},{"key":"B35","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(91)90144-O"},{"key":"B36","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-06404-8_23"},{"key":"B37","first-page":"2741","volume":"10","author":"Zhang H.","year":"2009","journal-title":"J. Mach. Learn. Res."}],"container-title":["Neural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mitpressjournals.org\/doi\/pdf\/10.1162\/neco_a_01013","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T22:52:05Z","timestamp":1750891925000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/neco\/article\/29\/11\/3078-3093\/8321"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,11]]},"references-count":37,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2017,11]]}},"alternative-id":["10.1162\/neco_a_01013"],"URL":"https:\/\/doi.org\/10.1162\/neco_a_01013","relation":{},"ISSN":["0899-7667","1530-888X"],"issn-type":[{"type":"print","value":"0899-7667"},{"type":"electronic","value":"1530-888X"}],"subject":[],"published":{"date-parts":[[2017,11]]}}}