{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T14:29:14Z","timestamp":1775744954743,"version":"3.50.1"},"reference-count":84,"publisher":"Emerald","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013,7,31]]},"abstract":"<jats:p>The metric learning problem is concerned with learning a distance function tuned to a particular task, and has been shown to be useful when used in conjunction with nearest-neighbor methods and other techniques that rely on distances or similarities. This survey presents an overview of existing research in metric learning, including recent progress on scaling to high-dimensional feature spaces and to data sets with an extremely large number of data points. A goal of the survey is to present as unified as possible a framework under which existing research on metric learning can be cast. The first part of the survey focuses on linear metric learning approaches, mainly concentrating on the class of Mahalanobis distance learning methods. We then discuss nonlinear metric learning approaches, focusing on the connections between the nonlinear and linear approaches. Finally, we discuss extensions of metric learning, as well as applications to a variety of problems in computer vision, text analysis, program analysis, and multimedia.<\/jats:p>","DOI":"10.1561\/2200000019","type":"journal-article","created":{"date-parts":[[2013,7,31]],"date-time":"2013-07-31T05:09:04Z","timestamp":1375247344000},"page":"287-364","source":"Crossref","is-referenced-by-count":592,"title":["Metric Learning: A Survey"],"prefix":"10.1561","volume":"5","author":[{"given":"Brian","family":"Kulis","sequence":"first","affiliation":[{"name":"Ohio State University, CSE Department , Columbus, 43210,","place":["OH, USA"]}]}],"member":"140","published-online":{"date-parts":[[2013,7,31]]},"reference":[{"key":"2026033014015928100_ref001","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/S0167-6377(02)00231-6","article-title":"Mirror descent and nonlinear projected subgradient methods for convex optimization","volume":"31","author":"Beck","year":"2003","journal-title":"Operations Research Letters"},{"key":"2026033014015928100_ref002","volume-title":"Nonlinear Programming","author":"Bertsekas","year":"1999"},{"key":"2026033014015928100_ref003","doi-asserted-by":"crossref","DOI":"10.1145\/1015330.1015360","article-title":"Integrating constraints and metric learning in semi-supervised clustering","volume-title":"Proceedings of International Conference on Machine Learning (ICML)","author":"Bilenko","year":"2004"},{"key":"2026033014015928100_ref004","volume-title":"Pattern Recognition and Machine Learning","author":"Bishop","year":"2006"},{"key":"2026033014015928100_ref005","volume-title":"Online Learning and Neural Networks","author":"Bottou","year":"1998"},{"key":"2026033014015928100_ref006","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex Optimization","author":"Boyd","year":"2004"},{"key":"2026033014015928100_ref007","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1007\/978-1-4613-9940-7_3","article-title":"A method for finding projections onto the intersection of convex sets in Hilbert spaces","volume":"37","author":"Boyle","year":"1986","journal-title":"Lecture Notes in Statistics"},{"issue":"3","key":"2026033014015928100_ref008","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/0041-5553(67)90040-7","article-title":"The relxation method of finding the common points of convex sets and its application to the solutionof problems in convex programming","volume":"7","author":"Bregman","year":"1967","journal-title":"USSR Computational Mathematics and Mathematical Physics"},{"key":"2026033014015928100_ref009","article-title":"Generalization bounds for metric and similarity learning","volume-title":"arXiv:1207.5437","author":"Cao","year":"2012"},{"key":"2026033014015928100_ref010","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511546921","volume-title":"Prediction, Learning, and Games","author":"Cesa-Bianchi","year":"2006"},{"issue":"10-12","key":"2026033014015928100_ref011","doi-asserted-by":"crossref","first-page":"1570","DOI":"10.1016\/j.neucom.2009.11.037","article-title":"A new kernelization framework for Mahalanobis distance learning algorithms","volume":"73","author":"Chatpatanasiri","year":"2010","journal-title":"Neurocomputing"},{"key":"2026033014015928100_ref012","article-title":"An online algorithm for lrage scale image similarity learning","volume-title":"Advances in Neural Information Processing Systems (NIPS)","author":"Chechik","year":"2009"},{"key":"2026033014015928100_ref013","article-title":"Learning a similarity metric discrimina- tively, with application to face verification","volume-title":"Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR)","author":"Chopra","year":"2005"},{"key":"2026033014015928100_ref014","article-title":"M-Tree: An efficient access method for similarity search in metric spaces","volume-title":"Proceedings of International Conference on Very Large Data Bases (VLDB)","author":"Ciaccia","year":"1997"},{"key":"2026033014015928100_ref015","article-title":"Online passive- aggressive algorithms","volume-title":"Advances in Neural Information Processing Systems","author":"Crammer","year":"2004"},{"issue":"1","key":"2026033014015928100_ref016","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1023\/B:VISI.0000020670.05764.55","article-title":"3D texture recognition using bidirectional feature histograms","volume":"59","author":"Cula","year":"2004","journal-title":"International Journal of Computer Vision (IJCV)"},{"key":"2026033014015928100_ref017","volume-title":"Poser 5 \u2014 Reference Manual","author":"","year":"2002"},{"key":"2026033014015928100_ref018","article-title":"Frustratingly easy domain adaptation","volume-title":"Conference of the Association for Computational Linguistics (ACL)","author":"Daume","year":"2007"},{"key":"2026033014015928100_ref019","doi-asserted-by":"crossref","DOI":"10.1145\/1401890.1401918","article-title":"Structured metric learning for high-dimensional problems","volume-title":"Proceedings of ACM SIGKDD International Conference on Knowledge Discovery and Data Mining","author":"Davis","year":"2008"},{"key":"2026033014015928100_ref020","doi-asserted-by":"crossref","DOI":"10.1145\/1273496.1273523","article-title":"Information-theoretic metric learning","volume-title":"Proceedings of International Conference on Machine Learning (ICML)","author":"Davis","year":"2007"},{"issue":"1","key":"2026033014015928100_ref021","doi-asserted-by":"crossref","DOI":"10.1137\/0801002","article-title":"A new variational result for quasi-Newton formulae","volume":"1","author":"Fletcher","year":"1991","journal-title":"SIAM Journal on Optimization"},{"issue":"3","key":"2026033014015928100_ref022","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1145\/355744.355745","article-title":"An algorithm for finding best matches in logarithmic expected time","volume":"3","author":"Friedman","year":"1977","journal-title":"ACM Transactions on Mathematics Software"},{"key":"2026033014015928100_ref023","doi-asserted-by":"crossref","DOI":"10.1109\/ICCV.2007.4408839","article-title":"Learning globally consistent local distance functions for shape-based image retrieval and classification","volume-title":"Proceedings of IEEE International Conference on Computer Vision (ICCV)","author":"Frome","year":"2007"},{"issue":"1","key":"2026033014015928100_ref024","article-title":"A survey of kernels for structured data","volume":"5","author":"Gaertner","year":"2003","journal-title":"ACM SIGKDD Explorations Newsletter"},{"key":"2026033014015928100_ref025","article-title":"Metric learning by collapsing classes","volume-title":"Advances in Neural Information Processing Systems (NIPS)","author":"Globerson","year":"2005"},{"key":"2026033014015928100_ref026","article-title":"Neighbourhood components analysis","volume-title":"Advances in Neural Information Processing Systems (NIPS)","author":"Goldberger","year":"2004"},{"key":"2026033014015928100_ref027","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1090\/S0002-9904-1964-11178-2","article-title":"Convex programming in Hilbert space","volume":"70","author":"Goldstein","year":"1964","journal-title":"Bulletin of the American Mathematical Society"},{"key":"2026033014015928100_ref028","volume-title":"Matrix Computations","author":"Golub","year":"1996"},{"key":"2026033014015928100_ref029","first-page":"725","article-title":"The pyramid match kernel: Efficient learning with sets of features","volume":"8","author":"Grauman","year":"2007","journal-title":"Journal of Machine Learning Research"},{"key":"2026033014015928100_ref030","doi-asserted-by":"crossref","DOI":"10.1109\/ICCV.2009.5459197","article-title":"Is that you? Metric learning approaches for face identification","volume-title":"Proceedings of IEEE International Conference on Computer Vision (ICCV)","author":"Guillaumin","year":"2009"},{"key":"2026033014015928100_ref031","doi-asserted-by":"crossref","DOI":"10.1145\/1250734.1250747","article-title":"Improved error reporting for software that uses black box components","volume-title":"Proceedings of Programming Language Design and Implementation (PLDI)","author":"Ha","year":"2007"},{"key":"2026033014015928100_ref032","doi-asserted-by":"crossref","DOI":"10.1109\/CVPR.2006.167","article-title":"Learning distance metrics with contextual constraints for image retrieval","volume-title":"Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR)","author":"Hoi","year":"2006"},{"key":"2026033014015928100_ref033","doi-asserted-by":"crossref","DOI":"10.1109\/ICCV.2007.4408857","article-title":"Discriminant embedding for local image descriptors","volume-title":"Proceedings of IEEE International Conference on Computer Vision (ICCV)","author":"Hua","year":"2007"},{"key":"2026033014015928100_ref034","doi-asserted-by":"crossref","DOI":"10.1145\/276698.276876","article-title":"Approximate nearest neighbors: Towards removing the curse of dimensionality","volume-title":"Proceedings of Symposium on Theory of Computing (STOC)","author":"Indyk","year":"1998"},{"key":"2026033014015928100_ref035","first-page":"519","article-title":"Metric and kernel learning using a linear transformation","volume":"13","author":"Jain","year":"2012","journal-title":"Journal of Machine Learning Research"},{"key":"2026033014015928100_ref036","article-title":"Inductive regularized learning of kernel functions","volume-title":"Advances in Neural Information Processing Systems (NIPS)","author":"Jain","year":"2010"},{"key":"2026033014015928100_ref037","article-title":"Online metric learning and fast similarity search","volume-title":"Advances in Neural Information Processing Systems (NIPS)","author":"Jain","year":"2008"},{"key":"2026033014015928100_ref038","doi-asserted-by":"crossref","DOI":"10.1109\/CVPR.2008.4587841","article-title":"Fast image search for learned metrics","volume-title":"Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR)","author":"Jain","year":"2008"},{"key":"2026033014015928100_ref039","first-page":"361","article-title":"Estimation with quadratic loss","volume-title":"Proceedings of Berkeley Symposium on Mathematical Statistics and Probability","author":"James","year":"1961"},{"key":"2026033014015928100_ref040","article-title":"Regularized distance metric learning: Theory and algorithm","volume-title":"Advances in Neural Information Processing Systems (NIPS)","author":"Jin","year":"2009"},{"key":"2026033014015928100_ref041","article-title":"Informative discriminant analysis","volume-title":"Proceedings of International Conference on Machine Learning (ICML)","author":"Kaski","year":"2003"},{"key":"2026033014015928100_ref042","article-title":"Nonlinear metric learning","volume-title":"Advances in Neural Information Processing Systems (NIPS)","author":"Kedern","year":"2012"},{"issue":"12","key":"2026033014015928100_ref043","doi-asserted-by":"crossref","first-page":"2143","DOI":"10.1109\/TPAMI.2009.151","article-title":"Fast similarity search for learned metrics","volume":"31","author":"Kulis","year":"2009","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"2026033014015928100_ref044","doi-asserted-by":"crossref","DOI":"10.1109\/CVPR.2011.5995702","article-title":"What you saw is not what you get: Domain adaptation using asymmetric kernel transforms","volume-title":"Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR)","author":"Kulis","year":"2011"},{"key":"2026033014015928100_ref045","doi-asserted-by":"crossref","DOI":"10.1145\/1143844.1143908","article-title":"Learning low-rank kernel matrices","volume-title":"Proceedings of International Conference on Machine Learning (ICML)","author":"Kulis","year":"2006"},{"key":"2026033014015928100_ref046","first-page":"341","article-title":"Low-rank kernel learning with Breg- man matrix divergences","volume":"10","author":"Kulis","year":"2009","journal-title":"Journal of Machine Learning Research"},{"key":"2026033014015928100_ref047","article-title":"Learning with idealized kernels","volume-title":"Proceedings of International Conference on Machine Learning (ICML)","author":"Kwok","year":"2003"},{"issue":"4","key":"2026033014015928100_ref048","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1109\/TPAMI.2006.77","article-title":"Metric learning for text documents","volume":"28","author":"Lebanon","year":"2006","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"2026033014015928100_ref049","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0041-5553(66)90114-5","article-title":"Constrained minimization problems","volume":"6","author":"Levitin","year":"1966","journal-title":"USSR Computational Mathematics and Mathematical Physics"},{"key":"2026033014015928100_ref050","first-page":"419","article-title":"Text classification using string kernels","volume":"2","author":"Lodhi","year":"2002","journal-title":"Journal of Machine Learning Research"},{"issue":"1","key":"2026033014015928100_ref051","first-page":"49","article-title":"On the generalized distance in statistics","volume":"2","author":"Mahalanobis","year":"1936","journal-title":"Proceedings of the National Institute of Sciences of India"},{"key":"2026033014015928100_ref052","article-title":"Metric learning to rank","volume-title":"Proceedings of International Conference on Machine Learning ICML","author":"McFee","year":"2010"},{"key":"2026033014015928100_ref053","volume-title":"Discriminant Analysis and Statistical Pattern Recognition","author":"McLachlan","year":"2004"},{"key":"2026033014015928100_ref054","article-title":"Large margin multi-task metric learning","volume-title":"Advances in Neural Information Processing Systems (NIPS)","author":"Parameswaran","year":"2010"},{"key":"2026033014015928100_ref055","doi-asserted-by":"crossref","DOI":"10.1145\/1150402.1150444","article-title":"Learning sparse metric via linear programming","volume-title":"Proceedings of SIGKDD Conference","author":"Rosales","year":"2006"},{"key":"2026033014015928100_ref056","article-title":"EM algorithms for PCA and SPCA","volume-title":"Advances in Neural Information Processing Systems","author":"Roweis","year":"1998"},{"key":"2026033014015928100_ref057","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-15561-1_16","article-title":"Adapting visual category models to new domains","volume-title":"Proceedings of European Conference on Computer Vision (ECCV)","author":"Saenko","year":"2010"},{"key":"2026033014015928100_ref058","article-title":"Learning a nonlinear embedding by preserving class neighbourhood structure","volume-title":"Proceedings of International Conference on Artificial Intelligence and Statistics (AISTATS)","author":"Salakhutdinov","year":"2007"},{"key":"2026033014015928100_ref059","volume-title":"Learning with Kernels","author":"Schoelkopf","year":"2002"},{"issue":"5","key":"2026033014015928100_ref060","doi-asserted-by":"crossref","first-page":"1299","DOI":"10.1162\/089976698300017467","article-title":"Nonlinear component analysis as a kernel eigenvalue problem","volume":"10","author":"Schoelkopf","year":"1998","journal-title":"Neural Computation"},{"key":"2026033014015928100_ref061","article-title":"Learning a distance metric from relative comparisons","volume-title":"Advances in Neural Information Processing Systems (NIPS)","author":"Schultz","year":"2003"},{"key":"2026033014015928100_ref062","doi-asserted-by":"crossref","DOI":"10.1109\/ICCV.2003.1238424","article-title":"Fast pose estimation with parameter-sensitive hashing","volume-title":"Proceedings of IEEE International Conference on Computer Vision (ICCV)","author":"Shakhnarovich","year":"2003"},{"key":"2026033014015928100_ref063","article-title":"Online learning of pseudometrics","volume-title":"Proceedings of International Conference on Machine Learninq (ICML)","author":"Shalev-Shwartz","year":"2004"},{"key":"2026033014015928100_ref064","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511809682","volume-title":"Kernel Methods for Pattern Analysis","author":"Shawe-Taylor","year":"2004"},{"key":"2026033014015928100_ref065","article-title":"Learning a metric for music similarity","volume-title":"International Symposium on Music Information Retrieval (ISMIR)","author":"Slaney","year":"2008"},{"key":"2026033014015928100_ref066","doi-asserted-by":"crossref","DOI":"10.1145\/1179352.1141964","article-title":"Photo tourism: Exploring photo collections in 3D","volume-title":"Proceedings of ACM SIGGRAPH","author":"Snavely","year":"2006"},{"key":"2026033014015928100_ref067","doi-asserted-by":"crossref","DOI":"10.1088\/1742-6596\/197\/1\/012008","article-title":"Metric learning for DNA microarray data analysis","volume-title":"Proceedingso of International Workshop on Statistical- Mechanical Informatics (IW-SMI)","author":"Takeuchi","year":"2009"},{"key":"2026033014015928100_ref068","doi-asserted-by":"crossref","DOI":"10.65109\/WBHQ9057","article-title":"Metric learning for reinforcement learning agents","volume-title":"Proceedings of International Conference on Autonomous Agents and Multiagent Systems (AAMAS)","author":"Taylor","year":"2011"},{"issue":"1","key":"2026033014015928100_ref069","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","article-title":"Regression shrinkage and selection via the lasso","volume":"58","author":"Tibshirani","year":"1996","journal-title":"Journal of the Royal Statistical Society, Series B"},{"issue":"3","key":"2026033014015928100_ref070","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1111\/1467-9868.00196","article-title":"Probabilistic principal component analysis","volume":"21","author":"Tipping","year":"1999","journal-title":"Journal of Royal Statistical Society, Series B"},{"key":"2026033014015928100_ref071","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/7503.003.0178","article-title":"Large margin component analysis","volume-title":"Advances in Neural Information Processing Systems (NIPS)","author":"Torresani","year":"2007"},{"key":"2026033014015928100_ref072","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-88682-2_42","article-title":"Human activity recognition with metric learning","volume-title":"Proceedings of European Conference on Computer Vision (ECCV)","author":"Tran","year":"2008"},{"issue":"3","key":"2026033014015928100_ref073","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1561\/0600000017","article-title":"Local invariant feature detectors: A survey","volume":"3","author":"Tuytelaars","year":"2008","journal-title":"Foundations and Trends in Computer Graphics and Vision"},{"key":"2026033014015928100_ref074","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/0020-0190(91)90074-R","article-title":"Satisfying general proximity\/similarity queries with metric trees","volume":"40","author":"Uhlmann","year":"1991","journal-title":"Information Processing Letters"},{"issue":"11","key":"2026033014015928100_ref075","doi-asserted-by":"crossref","first-page":"2032","DOI":"10.1109\/TPAMI.2008.182","article-title":"A statistical approach to material classification using image patch exemplars","volume":"31","author":"Varma","year":"2009","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"2026033014015928100_ref076","article-title":"Distance metric learning for large margin nearest neighbor classification","volume-title":"Advances in Neural Information Processing Systems (NIPS)","author":"Weinberger","year":"2005"},{"key":"2026033014015928100_ref077","doi-asserted-by":"crossref","DOI":"10.1145\/1390156.1390302","article-title":"Fast solvers and efficient implementations for distance metric learning","volume-title":"Proceedings of International Conference on Machine Learning (ICML)","author":"Weinberger","year":"2008"},{"key":"2026033014015928100_ref078","first-page":"207","article-title":"Distance metric learning for large margin nearest neighbor classification","volume":"10","author":"Weinberger","year":"2009","journal-title":"Journal of Machine Learninq Research"},{"key":"2026033014015928100_ref079","article-title":"Metric learning for kernel regression","volume-title":"Proceedings of International Conference on Artificial Intelligence and Statistics (AISTATS)","author":"Weinberger","year":"2007"},{"key":"2026033014015928100_ref080","article-title":"Distance metric learning, with application to clustering with side-information","volume-title":"Advances in Neural Information Processing Systems (NIPS)","author":"Xing","year":"2002"},{"key":"2026033014015928100_ref081","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1186\/1471-2105-7-299","article-title":"Kernel-based distance metric learning for microarray data classification","volume":"7","author":"Xiong","year":"2006","journal-title":"BMC Bioinformatics"},{"key":"2026033014015928100_ref082","article-title":"Sparse metric learning via smooth optimization","volume-title":"Advances in Neural Information Processing Systems (NIPS)","author":"Ying","year":"2009"},{"key":"2026033014015928100_ref083","first-page":"1","article-title":"Distance metric learning with eigenvalue optimization","volume":"13","author":"Ying","year":"2012","journal-title":"Journal of Machine Learning Research"},{"key":"2026033014015928100_ref084","article-title":"Online convex programming and generalized infinitesimal gradient ascent","volume-title":"Proceedings of International Conference on Machine Learninq (ICML)","author":"Zinkevich","year":"2003"}],"container-title":["Foundations and Trends\u00ae in Machine Learning"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/ftmal\/article-pdf\/5\/4\/287\/11134685\/2200000019en.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/www.emerald.com\/ftmal\/article-pdf\/5\/4\/287\/11134685\/2200000019en.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T18:02:25Z","timestamp":1774893745000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.emerald.com\/ftmal\/article\/5\/4\/287\/1331280\/Metric-Learning-A-Survey"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,7,31]]},"references-count":84,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2013,7,31]]}},"URL":"https:\/\/doi.org\/10.1561\/2200000019","relation":{},"ISSN":["1935-8237","1935-8245"],"issn-type":[{"value":"1935-8237","type":"print"},{"value":"1935-8245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,7,31]]}}}