{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,20]],"date-time":"2026-10-20T07:01:20Z","timestamp":1792479680684,"version":"4.5.0"},"reference-count":39,"publisher":"MIT Press","issue":"8","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2014,8]]},"abstract":"<jats:p>We propose a general information-theoretic approach to semi-supervised metric learning called SERAPH (SEmi-supervised metRic leArning Paradigm with Hypersparsity) that does not rely on the manifold assumption. Given the probability parameterized by a Mahalanobis distance, we maximize its entropy on labeled data and minimize its entropy on unlabeled data following entropy regularization. For metric learning, entropy regularization improves manifold regularization by considering the dissimilarity information of unlabeled data in the unsupervised part, and hence it allows the supervised and unsupervised parts to be integrated in a natural and meaningful way. Moreover, we regularize SERAPH by trace-norm regularization to encourage low-dimensional projections associated with the distance metric. The nonconvex optimization problem of SERAPH could be solved efficiently and stably by either a gradient projection algorithm or an EM-like iterative algorithm whose M-step is convex. Experiments demonstrate that SERAPH compares favorably with many well-known metric learning methods, and the learned Mahalanobis distance possesses high discriminability even under noisy environments.<\/jats:p>","DOI":"10.1162\/neco_a_00614","type":"journal-article","created":{"date-parts":[[2014,5,30]],"date-time":"2014-05-30T17:08:44Z","timestamp":1401469724000},"page":"1717-1762","source":"Crossref","is-referenced-by-count":44,"title":["Information-Theoretic Semi-Supervised Metric Learning via Entropy Regularization"],"prefix":"10.1162","volume":"26","author":[{"given":"Gang","family":"Niu","sequence":"first","affiliation":[{"name":"Tokyo Institute of Technology, Tokyo 152-8552, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bo","family":"Dai","sequence":"additional","affiliation":[{"name":"Georgia Institute of Technology, Atlanta, GA 30332, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Makoto","family":"Yamada","sequence":"additional","affiliation":[{"name":"Yahoo Labs, Sunnyvale, CA 94089, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Masashi","family":"Sugiyama","sequence":"additional","affiliation":[{"name":"Tokyo Institute of Technology, Tokyo 152-8552, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"281","reference":[{"key":"B1","volume-title":"Advances in neural information processing systems","volume":"19","author":"Argyriou A.","year":"2007"},{"key":"B2","volume-title":"Proceedings of the 21st International Joint Conference on Artificial Intelligence","author":"Baghshah M.","year":"2009"},{"key":"B3","volume-title":"Advances in neural information processing systems","volume":"14","author":"Belkin M.","year":"2002"},{"key":"B4","volume-title":"Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence","author":"Bellare K.","year":"2009"},{"key":"B6","first-page":"39","volume":"22","author":"Berger A.","year":"1996","journal-title":"Computational Linguistics"},{"key":"B7","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804441"},{"key":"B8","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022411301790"},{"key":"B9","doi-asserted-by":"publisher","DOI":"10.1145\/1273496.1273523"},{"key":"B10","doi-asserted-by":"publisher","DOI":"10.1007\/11776420_12"},{"key":"B11","doi-asserted-by":"publisher","DOI":"10.1111\/j.1469-1809.1936.tb02137.x"},{"key":"B12","doi-asserted-by":"publisher","DOI":"10.1214\/08-AOS637"},{"key":"B13","first-page":"455","volume":"12","author":"Gillenwater J.","year":"2011","journal-title":"Journal of Machine Learning Research"},{"key":"B14","volume-title":"Advances in neural information processing systems","volume":"18","author":"Globerson A.","year":"2006"},{"key":"B15","volume-title":"Advances in neural information processing systems","volume":"17","author":"Goldberger J.","year":"2005"},{"key":"B16","volume-title":"Advances in neural information processing systems","volume":"23","author":"Gomes R.","year":"2010"},{"key":"B17","volume-title":"Advances in neural information processing systems","volume":"20","author":"Gra\u00e7a J.","year":"2008"},{"key":"B18","volume":"22","author":"Gra\u00e7a J.","year":"2009","journal-title":"Advances in neural information processing systems"},{"key":"B19","volume-title":"Advances in neural information processing systems","volume":"17","author":"Grandvalet Y.","year":"2005"},{"key":"B20","doi-asserted-by":"crossref","first-page":"151","DOI":"10.7551\/mitpress\/6173.003.0013","volume-title":"Semi-supervised learning","author":"Grandvalet Y.","year":"2006"},{"key":"B21","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2008.4587351"},{"key":"B22","volume-title":"Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence","author":"Huang K.","year":"2010"},{"key":"B23","doi-asserted-by":"publisher","DOI":"10.1109\/ICDM.2009.22"},{"key":"B24","volume-title":"Advances in neural information processing systems","volume":"23","author":"Jain P.","year":"2010"},{"key":"B25","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.106.620"},{"key":"B26","doi-asserted-by":"publisher","DOI":"10.1145\/1835804.1835947"},{"key":"B27","volume-title":"Proceedings of the 29th International Conference on Machine Learning","author":"Niu G.","year":"2012"},{"issue":"1","key":"B28","first-page":"33","volume":"174","author":"Polyak B. 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