{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:12:40Z","timestamp":1740147160261,"version":"3.37.3"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2017,4,25]],"date-time":"2017-04-25T00:00:00Z","timestamp":1493078400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Data Anal Classif"],"published-print":{"date-parts":[[2018,6]]},"DOI":"10.1007\/s11634-017-0286-x","type":"journal-article","created":{"date-parts":[[2017,4,25]],"date-time":"2017-04-25T15:24:08Z","timestamp":1493133848000},"page":"341-363","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Local generalized quadratic distance metrics: application to the k-nearest neighbors classifier"],"prefix":"10.1007","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4486-3804","authenticated-orcid":false,"given":"Karim","family":"Abou-Moustafa","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Frank P.","family":"Ferrie","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,4,25]]},"reference":[{"key":"286_CR1","doi-asserted-by":"crossref","unstructured":"Abou-Moustafa K, Ferrie F (2007) The minimum volume ellipsoid metric. In: LNCS 4713, 29th Symp. of the German Association of Pattern Recognition (DAGM), Springer, Heidelberg, pp 335\u2013344","DOI":"10.1007\/978-3-540-74936-3_34"},{"key":"286_CR2","first-page":"1","volume":"25","author":"K Abou-Moustafa","year":"2012","unstructured":"Abou-Moustafa K, Ferrie F (2012) A note on metric properties of some divergence measures: the Gaussian case. JMLR W&CP 25:1\u201315","journal-title":"JMLR W&CP"},{"key":"286_CR3","first-page":"341","volume":"29","author":"K Abou-Moustafa","year":"2013","unstructured":"Abou-Moustafa K, Schuurmans D, Ferrie F (2013) Learning a metric space for neighbourhood topology estimation. Appl Manifold Learn JMLR W&CP 29:341\u2013356","journal-title":"Appl Manifold Learn JMLR W&CP"},{"key":"286_CR4","doi-asserted-by":"crossref","unstructured":"Aggarwal C, Hinneburg A, Keim D (2001) On the surprising behavior of distance metrics in high dimensional space. In: Van den Bussche J, Vianu V (eds) Database Theory, vol 1973., Lecture Notes in Computer Science, Springer, pp 420\u2013434","DOI":"10.1007\/3-540-44503-X_27"},{"key":"286_CR5","doi-asserted-by":"crossref","first-page":"1570","DOI":"10.1214\/aoms\/1177697374","volume":"40","author":"C Atwood","year":"1969","unstructured":"Atwood C (1969) Optimal and efficient design of experiments. Ann Math Stat 40:1570\u20131602","journal-title":"Ann Math Stat"},{"key":"286_CR6","first-page":"937","volume":"6","author":"A Bar-Hillel","year":"2005","unstructured":"Bar-Hillel A, Hertz T, Shental N, Weinshall D (2005) Learning a Mahalanobis metric from equivalence constraints. J Mach Learn Res 6:937\u2013965","journal-title":"J Mach Learn Res"},{"key":"286_CR7","doi-asserted-by":"crossref","first-page":"1373","DOI":"10.1162\/089976603321780317","volume":"15","author":"M Belkin","year":"2003","unstructured":"Belkin M, Niyogi P (2003) Laplacian eigenmaps and spectral techniques for data representation. Neural Comput 15:1373\u20131396","journal-title":"Neural Comput"},{"issue":"6","key":"286_CR8","doi-asserted-by":"crossref","first-page":"888","DOI":"10.1162\/neco.1992.4.6.888","volume":"4","author":"L Bottou","year":"1992","unstructured":"Bottou L, Vapnik V (1992) Local learning algorithms. Neural Comput 4(6):888\u2013900","journal-title":"Neural Comput"},{"key":"286_CR9","doi-asserted-by":"crossref","unstructured":"Boyd S, Vandenberghe L (eds) (2004) Convex Optimization. Cambridge University Press","DOI":"10.1017\/CBO9780511804441"},{"key":"286_CR10","doi-asserted-by":"crossref","unstructured":"Chang H, Yeung DY (2007) Locally smooth metric learning with application to image retrieval. In: IEEE Proceedings of ICCV, pp 1\u20137","DOI":"10.1109\/ICCV.2007.4408862"},{"key":"286_CR11","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/j.acha.2006.04.006","volume":"21","author":"R Coifman","year":"2006","unstructured":"Coifman R, Lafon S (2006) Diffusion maps. Appl Comput Harmonic Anal 21:5\u201330","journal-title":"Appl Comput Harmonic Anal"},{"issue":"1","key":"286_CR12","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1109\/TIT.1967.1053964","volume":"13","author":"T Cover","year":"1967","unstructured":"Cover T, Hart P (1967) Nearest neighbor pattern classification. IEEE Trans Inf Theory 13(1):21\u201327","journal-title":"IEEE Trans Inf Theory"},{"key":"286_CR13","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1080\/10556780701589669","volume":"23","author":"S Damla","year":"2008","unstructured":"Damla S, Sun P, Todd M (2008) Linear convergence of a modified Frank\u2013Wolfe algorithm for computing minimum-volume enclosing ellipsoids. J Optim Methods Softw 23:5\u201319","journal-title":"J Optim Methods Softw"},{"issue":"1\u20133","key":"286_CR14","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1023\/A:1012454411458","volume":"46","author":"D DeCoste","year":"2002","unstructured":"DeCoste D, Sch\u00f6lkopf B (2002) Training invariant support vector machines. J Mach Learn 46(1\u20133):161\u2013190","journal-title":"J Mach Learn"},{"key":"286_CR15","doi-asserted-by":"crossref","unstructured":"Ding C, Li T (2007) Adaptive dimension reduction using discriminant analysis and K\u2013means clustering. In: ACM Proceedings of the 24th ICML","DOI":"10.1145\/1273496.1273562"},{"key":"286_CR16","doi-asserted-by":"crossref","unstructured":"Dolia A, Bie TD, Harris C, Shawe-Taylor J, Titterington D (2006) The minimum\u2013volume covering ellipsoid estimation in kernel\u2013defined feature spaces. In: Proceedings of the 17th ECML, Springer","DOI":"10.1007\/11871842_61"},{"key":"286_CR17","doi-asserted-by":"crossref","unstructured":"Domeniconi C, Gunopulos D (2002) Adaptive nearest neighbor classification using support vector machines. In: NIPS 14","DOI":"10.7551\/mitpress\/1120.003.0090"},{"issue":"9","key":"286_CR18","doi-asserted-by":"crossref","first-page":"1281","DOI":"10.1109\/TPAMI.2002.1033219","volume":"24","author":"C Domeniconi","year":"2002","unstructured":"Domeniconi C, Peng J, Gunopulos D (2002) Locally adaptive metric nearest neighbor classification. IEEE Trans PAMI 24(9):1281\u20131285","journal-title":"IEEE Trans PAMI"},{"issue":"1","key":"286_CR19","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1109\/TCYB.2015.2399456","volume":"46","author":"F Dornaika","year":"2015","unstructured":"Dornaika F, El\u00a0Traboulsi Y (2015) Learning flexible graph-based semi-supervised embedding. IEEE Trans Cybern 46(1):206\u2013218","journal-title":"IEEE Trans Cybern"},{"key":"286_CR20","doi-asserted-by":"crossref","first-page":"873","DOI":"10.1109\/TKDE.2007.1037","volume":"19","author":"D Fran\u00e7ois","year":"2007","unstructured":"Fran\u00e7ois D, Wertz V, Verleysen M (2007) The concentration of fractional distances. IEEE Trans Knowl Data Eng 19:873\u2013886","journal-title":"IEEE Trans Knowl Data Eng"},{"key":"286_CR21","unstructured":"Friedman J (1994) Flexible metric nearest neighbor classification. Department of Statistics, Stanford University, Technical report"},{"volume-title":"Introduction to statistical pattern recognition","year":"1972","key":"286_CR22","unstructured":"Fukunaga K (ed) (1972) Introduction to statistical pattern recognition. Academic Press, Cambridge"},{"issue":"6","key":"286_CR23","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1109\/34.506411","volume":"18","author":"T Hastie","year":"1996","unstructured":"Hastie T, Tibshirani R (1996) Discriminant adaptive nearest neighbor classification. IEEE Trans PAMI 18(6):607\u2013615","journal-title":"IEEE Trans PAMI"},{"issue":"6","key":"286_CR24","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1109\/TSMCC.2011.2109710","volume":"41","author":"W Hu","year":"2011","unstructured":"Hu W, Xie N, Li L, Zeng X, Maybank S (2011) A survey on visual content-based video indexing and retrieval. IEEE Trans Syst Man Cybern C Appl Rev 41(6):797\u2013819","journal-title":"IEEE Trans Syst Man Cybern C Appl Rev"},{"key":"286_CR25","unstructured":"Keysers D (1998) United States Postal Service (USPS) data set. http:\/\/www-i6.informatik.rwth-aachen.de\/keysers\/usps.html"},{"key":"286_CR26","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/BF02289694","volume":"29","author":"J Kruskal","year":"1964","unstructured":"Kruskal J (1964) Nonmetric multidimensional scaling: a numerical method. Psychometrika 29:115\u2013129","journal-title":"Psychometrika"},{"issue":"4","key":"286_CR27","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1561\/2200000019","volume":"5","author":"B Kulis","year":"2013","unstructured":"Kulis B (2013) Metric learning: a survey. Found Trends Mach Learn 5(4):287\u2013364","journal-title":"Found Trends Mach Learn"},{"issue":"1","key":"286_CR28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10957-005-2653-6","volume":"126","author":"P Kumar","year":"2005","unstructured":"Kumar P, Yildirim E (2005) Minimum-volume enclosing ellipsoids and core sets. J Optim Theory Appl 126(1):1\u201321","journal-title":"J Optim Theory Appl"},{"key":"286_CR29","unstructured":"LeCun Y (1998) The MNIST database of handwritten digits. http:\/\/yann.lecun.com\/exdb\/mnist\/"},{"issue":"4","key":"286_CR30","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1109\/TSMC.1987.289362","volume":"17","author":"J Macleod","year":"1987","unstructured":"Macleod J, Luk A, Titterington DM (1987) A re-examination of the distance-weighted k-nearest neighbor classification rule. IEEE Trans Syst Man Cybern 17(4):689\u2013696","journal-title":"IEEE Trans Syst Man Cybern"},{"key":"286_CR31","unstructured":"Newman D, Hettich S, Blake C, Merz C (1998) UCI Repository of Machine Learning Databases. http:\/\/www.ics.uci.edu\/~mlearn\/MLRepository.html"},{"issue":"5","key":"286_CR32","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1109\/TPAMI.2004.1273978","volume":"26","author":"J Peng","year":"2004","unstructured":"Peng J, Heisterkamp D, Dai H (2004) Adaptive quasi-conformal kernel for nearest neighbor classification. IEEE Trans PAMI 26(5):656\u2013661","journal-title":"IEEE Trans PAMI"},{"key":"286_CR33","doi-asserted-by":"crossref","unstructured":"Rousseeuw P, Leroy A (eds) (1987) Robust regression and outlier detection. Wiley, New York","DOI":"10.1002\/0471725382"},{"issue":"5500","key":"286_CR34","doi-asserted-by":"crossref","first-page":"2323","DOI":"10.1126\/science.290.5500.2323","volume":"290","author":"S Roweis","year":"2000","unstructured":"Roweis S, Saul L (2000) Nonlinear dimensionality reduction by locally linear embedding (LLE). Science 290(5500):2323\u20132326","journal-title":"Science"},{"key":"286_CR35","unstructured":"Schultz M, Joachims T (2004) Learning a distance metric from relative comparisons. In: Thrun S, Saul LK, Sch\u00f6lkopf PB (eds) NIPS 16, MIT Press"},{"key":"286_CR36","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/BF02289621","volume":"27","author":"R Shepard","year":"1962","unstructured":"Shepard R (1962) The analysis of proximities: multidimensional scaling with an unknown distance function. Psychometrika 27:219\u2013246","journal-title":"Psychometrika"},{"issue":"5","key":"286_CR37","doi-asserted-by":"crossref","first-page":"622","DOI":"10.1109\/TIT.1981.1056403","volume":"27","author":"R Short","year":"1981","unstructured":"Short R, Fukunaga K (1981) The optimal distance measure for nearest neighbor classification. IEEE Trans Inf Theory 27(5):622\u2013627","journal-title":"IEEE Trans Inf Theory"},{"key":"286_CR38","doi-asserted-by":"crossref","first-page":"690","DOI":"10.1287\/opre.1040.0115","volume":"52","author":"P Sun","year":"2004","unstructured":"Sun P, Freund R (2004) Computation of minimum-volume covering ellipsoids. Op Res 52:690\u2013706","journal-title":"Op Res"},{"issue":"5500","key":"286_CR39","doi-asserted-by":"crossref","first-page":"2319","DOI":"10.1126\/science.290.5500.2319","volume":"290","author":"J Tenenbaum","year":"2000","unstructured":"Tenenbaum J, de Silva V, Langford J (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290(5500):2319\u20132323","journal-title":"Science"},{"issue":"3","key":"286_CR40","doi-asserted-by":"crossref","first-page":"227","DOI":"10.2307\/2347157","volume":"27","author":"D Titterington","year":"1978","unstructured":"Titterington D (1978) Estimation of correlation coefficients by ellipsoidal trimming. J Appl Stat 27(3):227\u2013234","journal-title":"J Appl Stat"},{"key":"286_CR41","unstructured":"Todd M (2006) On minimum\u2013volume ellipsoids. From John and Kiefer\u2013Wolfowitz to Khachiyan and Nesterov\u2013Nemirovski. Slides presented in the ABEL Symposium, http:\/\/people.orie.cornell.edu\/~miketodd\/ublndeta.pdf"},{"key":"286_CR42","unstructured":"Vincent P, Bengio Y (2002) K\u2013Local hyperplane and convex distance nearest neighbor algorithms. In: Dietterich TG, Becker S, Ghahramani Z (eds) NIPS 14, The MIT Press, pp 985\u2013992"},{"key":"286_CR43","unstructured":"Weinberger K, Blitzer J, Saul L (2006) Distance metric learning for large margin nearest neighbor classification. In: Weiss Y, Sch\u00f6lkopf PB, Platt JC (eds) NIPS 18, MIT Press, pp 1473\u20131480"},{"key":"286_CR44","unstructured":"Xing E, Ng A, Jordan M, Russell S (2003) Distance metric learning with application to clustering with side\u2013information. In: Becker S, Thrun S, Obermayer K (eds) NIPS 15, MIT Press, pp 505\u2013512"},{"key":"286_CR45","unstructured":"Yang L (2006) Distance metric learning: A comprehensive review. Technical report, Department of Computer Science and Engineering, Michigan State University"}],"container-title":["Advances in Data Analysis and Classification"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11634-017-0286-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11634-017-0286-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11634-017-0286-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,23]],"date-time":"2024-06-23T19:25:57Z","timestamp":1719170757000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11634-017-0286-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4,25]]},"references-count":45,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,6]]}},"alternative-id":["286"],"URL":"https:\/\/doi.org\/10.1007\/s11634-017-0286-x","relation":{},"ISSN":["1862-5347","1862-5355"],"issn-type":[{"type":"print","value":"1862-5347"},{"type":"electronic","value":"1862-5355"}],"subject":[],"published":{"date-parts":[[2017,4,25]]}}}