{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,24]],"date-time":"2024-06-24T19:58:28Z","timestamp":1719259108774},"reference-count":35,"publisher":"MIT Press - Journals","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2018,10]]},"abstract":"<jats:p> We consider the problem of classifying data manifolds where each manifold represents invariances that are parameterized by continuous degrees of freedom. Conventional data augmentation methods rely on sampling large numbers of training examples from these manifolds. Instead, we propose an iterative algorithm, [Formula: see text], based on a cutting plane approach that efficiently solves a quadratic semi-infinite programming problem to find the maximum margin solution. We provide a proof of convergence as well as a polynomial bound on the number of iterations required for a desired tolerance in the objective function. The efficiency and performance of [Formula: see text] are demonstrated in high-dimensional simulations and on image manifolds generated from the ImageNet data set. Our results indicate that [Formula: see text] is able to rapidly learn good classifiers and shows superior generalization performance compared with conventional maximum margin methods using data augmentation methods. <\/jats:p>","DOI":"10.1162\/neco_a_01119","type":"journal-article","created":{"date-parts":[[2018,8,27]],"date-time":"2018-08-27T20:04:33Z","timestamp":1535400273000},"page":"2593-2615","source":"Crossref","is-referenced-by-count":7,"title":["Learning Data Manifolds with a Cutting Plane Method"],"prefix":"10.1162","volume":"30","author":[{"given":"SueYeon","family":"Chung","sequence":"first","affiliation":[]},{"given":"Uri","family":"Cohen","sequence":"additional","affiliation":[]},{"given":"Haim","family":"Sompolinsky","sequence":"additional","affiliation":[{"name":"Center for Brain Science, Harvard University, Cambridge, MA 02138, U.S.A., and Edmond and Lily Safra Center for Brain Sciences, Hebrew University of Jerusalem, Jerusalem 9190401, Israel"}]},{"given":"Daniel D.","family":"Lee","sequence":"additional","affiliation":[]}],"member":"281","reference":[{"key":"B1","author":"Anselmi F.","year":"2013","journal-title":"Unsupervised learning of invariant representations in hierarchical architectures"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144593251710"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1162\/089976603321780317"},{"key":"B4","first-page":"2399","volume":"7","author":"Belkin M.","year":"2006","journal-title":"Journal of Machine Learning Research"},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2013.50"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2015.2496947"},{"key":"B7","first-page":"2465","volume-title":"Advances in neural information processing systems, 25","author":"Canas G.","year":"2012"},{"key":"B8","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.93.060301"},{"key":"B9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.8.031003"},{"key":"B10","first-page":"248","author":"Deng J.","year":"2009","journal-title":"Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition"},{"key":"B11","doi-asserted-by":"publisher","DOI":"10.1016\/j.tics.2007.06.010"},{"key":"B12","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(00)00544-6"},{"key":"B13","first-page":"2672","volume-title":"Advances in neural information processing systems","volume":"27","author":"Goodfellow I.","year":"2014"},{"key":"B14","doi-asserted-by":"publisher","DOI":"10.1109\/72.554192"},{"key":"B15","doi-asserted-by":"publisher","DOI":"10.1126\/science.1117593"},{"key":"B16","doi-asserted-by":"publisher","DOI":"10.1145\/1150402.1150429"},{"key":"B17","doi-asserted-by":"publisher","DOI":"10.1137\/0803047"},{"key":"B18","first-page":"1097","volume-title":"Advances in neural information processing systems","volume":"25","author":"Krizhevsky A.","year":"2012"},{"key":"B19","first-page":"1","author":"Lee Y.-J.","year":"2001","journal-title":"Proceedings of the 2001 SIAM International Conference on Data Mining"},{"key":"B20","doi-asserted-by":"publisher","DOI":"10.1023\/B:JOGO.0000047910.80739.95"},{"key":"B21","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(01)00348-1"},{"key":"B22","doi-asserted-by":"publisher","DOI":"10.1109\/5.726787"},{"key":"B23","doi-asserted-by":"publisher","DOI":"10.1038\/nn.3433"},{"key":"B24","doi-asserted-by":"publisher","DOI":"10.1038\/14819"},{"key":"B25","doi-asserted-by":"publisher","DOI":"10.1126\/science.290.5500.2323"},{"key":"B26","first-page":"47","author":"Sch\u00f6lkopf B.","year":"1996","journal-title":"Proceedings of the International Conference on Artificial Neural Networks"},{"key":"B27","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2007.56"},{"key":"B28","first-page":"994","volume":"2","author":"Serre T.","year":"2005","journal-title":"Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition"},{"key":"B29","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1109\/ICIP.1994.413572","volume":"2","author":"Simard P. 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