{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T06:28:56Z","timestamp":1764224936535},"reference-count":53,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2009,2,13]],"date-time":"2009-02-13T00:00:00Z","timestamp":1234483200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Process Lett"],"published-print":{"date-parts":[[2009,4]]},"DOI":"10.1007\/s11063-009-9098-0","type":"journal-article","created":{"date-parts":[[2009,2,12]],"date-time":"2009-02-12T18:33:00Z","timestamp":1234463580000},"page":"109-131","source":"Crossref","is-referenced-by-count":31,"title":["Local Dimensionality Reduction for Non-Parametric Regression"],"prefix":"10.1007","volume":"29","author":[{"given":"Heiko","family":"Hoffmann","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefan","family":"Schaal","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sethu","family":"Vijayakumar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2009,2,13]]},"reference":[{"key":"9098_CR1","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/j.csda.2003.11.021","volume":"48","author":"B Abraham","year":"2005","unstructured":"Abraham B, Merola G (2005) Dimensionality reduction approach to multivariate prediction. Comput Stat Data Anal 48: 5\u201316","journal-title":"Comput Stat Data Anal"},{"key":"9098_CR2","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1023\/A:1006559212014","volume":"11","author":"CG Atkeson","year":"1997","unstructured":"Atkeson CG, Moore AW, Schaal S (1997a) Locally weighted learning. Artif Intell Rev 11: 11\u201373","journal-title":"Artif Intell Rev"},{"key":"9098_CR3","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1023\/A:1006511328852","volume":"11","author":"CG Atkeson","year":"1997","unstructured":"Atkeson CG, Moore AW, Schaal S (1997b) Locally weighted learning for control. Artif Intell Rev 11: 75\u2013113","journal-title":"Artif Intell Rev"},{"issue":"6","key":"9098_CR4","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 for dimensionality reduction and data representation. Neural Comp 15(6): 1373\u20131396","journal-title":"Neural Comp"},{"issue":"23","key":"9098_CR5","doi-asserted-by":"crossref","first-page":"3327","DOI":"10.1016\/S0042-6989(97)00121-1","volume":"37","author":"A Bell","year":"1997","unstructured":"Bell A, Sejnowski T (1997) The independent components of natural scenes are edge filters. Vis Res 37(23): 3327\u20133338","journal-title":"Vis Res"},{"key":"9098_CR6","doi-asserted-by":"crossref","DOI":"10.1515\/9781400874668","volume-title":"Adaptive control processes: a guided tour","author":"RE Bellman","year":"1961","unstructured":"Bellman RE (1961) Adaptive control processes: a guided tour. Princeton University Press, Princeton, NJ"},{"key":"9098_CR7","doi-asserted-by":"crossref","unstructured":"Beyer K, Goldstein J, Ramakrishnan R, Shaft U (1999) When is \u2018nearest neighbor\u2019 meaningful? In: Proceedings of 7th international conference on database theory, Jerusalem, Israel, pp 217\u2013235","DOI":"10.1007\/3-540-49257-7_15"},{"key":"9098_CR8","volume-title":"Pattern recognition and machine learning","author":"CM Bishop","year":"2006","unstructured":"Bishop CM (2006) Pattern recognition and machine learning. Springer, New York"},{"key":"9098_CR9","doi-asserted-by":"crossref","DOI":"10.1002\/9781119115151","volume-title":"Statistics for spatial data","author":"N Cressie","year":"1993","unstructured":"Cressie N (1993) Statistics for spatial data. Wiley, New York"},{"key":"9098_CR10","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/0169-7439(93)85002-X","volume":"18","author":"S Jong de","year":"1993","unstructured":"de Jong S (1993) SIMPLS: an alternative approach to partial least squares regression. Chemometr Intell Lab Syst 18: 251\u2013263","journal-title":"Chemometr Intell Lab Syst"},{"key":"9098_CR11","volume-title":"Principal component neural networks","author":"KI Diamantaras","year":"1996","unstructured":"Diamantaras KI, Kung SY (1996) Principal component neural networks. Wiley, New York"},{"key":"9098_CR12","unstructured":"D\u2019Souza A, Vijayakumar S, Schaal S (2001) Are internal models of the entire body learnable? Society for Neuroscience, Abstracts"},{"key":"9098_CR13","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-009-5564-6","volume-title":"An introduction to latent variable models","author":"BS Everitt","year":"1984","unstructured":"Everitt BS (1984) An introduction to latent variable models. Chapman and Hall, London"},{"key":"9098_CR14","volume-title":"Local polynomial modeling and its applications","author":"J Fan","year":"1996","unstructured":"Fan J, Gijbels I (1996) Local polynomial modeling and its applications. Chapman and Hall, London, UK"},{"issue":"2","key":"9098_CR15","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1080\/00401706.1993.10485033","volume":"35","author":"IE Frank","year":"1993","unstructured":"Frank IE, Friedman JH (1993) A statistical view of some chemometrics regression tools. Technometrics 35(2): 109\u2013135","journal-title":"Technometrics"},{"issue":"1","key":"9098_CR16","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/0304-4076(95)01773-9","volume":"75","author":"J Geweke","year":"1996","unstructured":"Geweke J (1996) Bayesian reduced rank regression in econometrics. J Econometr 75(1): 121\u2013146","journal-title":"J Econometr"},{"key":"9098_CR17","first-page":"449","volume-title":"Advances in neural information processing systems, vol 12","author":"Z Ghahramani","year":"2000","unstructured":"Ghahramani Z, Beal M (2000) Variational inference for bayesian mixtures of factor analysers. In: Solla S, Leen T, M\u00fcller KR (eds) Advances in neural information processing systems, vol 12. MIT Press, Cambridge, MA, pp 449\u2013455"},{"key":"9098_CR18","volume-title":"The EM algorithm for mixtures of factor analyzers. Tech. Rep. CRG-TR-96-1","author":"Z Ghahramani","year":"1997","unstructured":"Ghahramani Z, Hinton GE (1997) The EM algorithm for mixtures of factor analyzers. Tech. Rep. CRG-TR-96-1. Department of Computer Science, University of Toronto, Canada"},{"key":"9098_CR19","first-page":"857","volume-title":"Advances in neural information processing systems, vol 15","author":"G Hinton","year":"2003","unstructured":"Hinton G, Roweis ST (2003) Stochastic neighbor embedding. In: Becker S, Thrun S, Obermayer K (eds) Advances in neural information processing systems, vol 15. MIT Press, Cambridge, MA, pp 857\u2013864"},{"issue":"1","key":"9098_CR20","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1080\/00401706.1970.10488634","volume":"12","author":"AE Hoerl","year":"1970","unstructured":"Hoerl AE, Kennard RW (1970) Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12(1): 55\u201367","journal-title":"Technometrics"},{"key":"9098_CR21","unstructured":"Hoffmann H (2005) Unsupervised learning of visuomotor associations, MPI series in biological cybernetics, vol 11. Logos Verlag Berlin, PhD thesis (2004), Bielefeld University, Germany"},{"key":"9098_CR22","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1007\/3-540-44989-2_55","volume-title":"Artificial neural networks and neural information processing\u2014ICANN\/ICONIP 2003, LNCS, vol 2714","author":"H Hoffmann","year":"2003","unstructured":"Hoffmann H, M\u00f6ller R (2003) Unsupervised learning of a kinematic arm model. In: Kaynak O, Alpaydin E, Oja E, Xu L (eds) Artificial neural networks and neural information processing\u2014ICANN\/ICONIP 2003, LNCS, vol 2714. Springer, Berlin, pp 463\u2013470"},{"issue":"2","key":"9098_CR23","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/s00422-005-0575-x","volume":"93","author":"H Hoffmann","year":"2005","unstructured":"Hoffmann H, Schenck W, M\u00f6ller R (2005) Learning visuomotor transformations for gaze-control and grasping. Biol Cybernetics 93(2): 119\u2013130","journal-title":"Biol Cybernetics"},{"issue":"2","key":"9098_CR24","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1016\/0047-259X(75)90042-1","volume":"5","author":"AJ Izenman","year":"1975","unstructured":"Izenman AJ (1975) Reduced-rank regression for the multivariate linear model. J Multivar Anal 5(2): 248\u2013264","journal-title":"J Multivar Anal"},{"key":"9098_CR25","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1207\/s15516709cog1603_1","volume":"16","author":"MI Jordan","year":"1992","unstructured":"Jordan MI, Rumelhart DE (1992) Forward models: supervised learning with a distal teacher. Cogn Sci 16: 307\u2013354","journal-title":"Cogn Sci"},{"key":"9098_CR26","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1016\/S0959-4388(99)00028-8","volume":"9","author":"M Kawato","year":"1999","unstructured":"Kawato M (1999) Internal models for motor control and trajectory planning. Curr Opin Neurobiol 9: 718\u2013727","journal-title":"Curr Opin Neurobiol"},{"key":"9098_CR27","unstructured":"Kustra R (1996) Delve census-house dataset. Available at http:\/\/www.cs.toronto.edu\/~delve\/data\/datasets.html"},{"issue":"8","key":"9098_CR28","doi-asserted-by":"crossref","first-page":"1246","DOI":"10.2113\/gsecongeo.58.8.1246","volume":"58","author":"G Matheron","year":"1963","unstructured":"Matheron G (1963) Principles of geostatistics. Econ Geol 58(8): 1246\u20131266","journal-title":"Econ Geol"},{"key":"9098_CR29","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1016\/S0925-2312(02)00671-9","volume":"49","author":"R M\u00f6ller","year":"2002","unstructured":"M\u00f6ller R (2002) Interlocking of learning and orthonormalization in RRLSA. Neurocomputing 49: 429\u2013433","journal-title":"Neurocomputing"},{"key":"9098_CR30","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1207\/s15516709cog1704_1","volume":"17","author":"JR Movellan","year":"1993","unstructured":"Movellan JR, McClelland JL (1993) Learning continuous probability distributions with symmetric diffusion networks. Cogn Sci 17: 463\u2013496","journal-title":"Cogn Sci"},{"issue":"3","key":"9098_CR31","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1007\/BF00275687","volume":"15","author":"E Oja","year":"1982","unstructured":"Oja E (1982) A simplified neuron model as a principal component analyzer. J Math Biol 15(3): 267\u2013273","journal-title":"J Math Biol"},{"issue":"1","key":"9098_CR32","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1142\/S0129065789000475","volume":"1","author":"E Oja","year":"1989","unstructured":"Oja E (1989) Neural networks, principle components, and subspaces. Int J Neural Syst 1(1): 61\u201368","journal-title":"Int J Neural Syst"},{"key":"9098_CR33","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1038\/381607a0","volume":"381","author":"BA Olshausen","year":"1996","unstructured":"Olshausen BA, Field DJ (1996) Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature 381: 607\u2013609","journal-title":"Nature"},{"issue":"1","key":"9098_CR34","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1109\/72.822524","volume":"11","author":"S Ouyang","year":"2000","unstructured":"Ouyang S, Bao Z, Liao GS (2000) Robust recursive least squares learning algorithm for principal component analysis. IEEE Trans Neural Netw 11(1): 215\u2013221","journal-title":"IEEE Trans Neural Netw"},{"key":"9098_CR35","volume-title":"Gaussian processes for machine learning","author":"CE Rasmussen","year":"2006","unstructured":"Rasmussen CE, Williams CKI (2006) Gaussian processes for machine learning. MIT Press, Cambridge, MA"},{"key":"9098_CR36","doi-asserted-by":"crossref","first-page":"2323","DOI":"10.1126\/science.290.5500.2323","volume":"290","author":"ST Roweis","year":"2000","unstructured":"Roweis ST, Saul LK (2000) Nonlinear dimensionality reduction by locally linear embedding. Science 290: 2323\u20132326","journal-title":"Science"},{"key":"9098_CR37","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1016\/0893-6080(89)90044-0","volume":"2","author":"TD Sanger","year":"1989","unstructured":"Sanger TD (1989) Optimal unsupervised learning in a single-layer linear feedforward neural network. Neural Netw 2: 459\u2013473","journal-title":"Neural Netw"},{"key":"9098_CR38","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1007\/s002210000505","volume":"136","author":"S Schaal","year":"2001","unstructured":"Schaal S, Sternad D (2001) Origins and violations of the 2\/3 power law in rhythmic 3d movements. Exp Brain Res 136: 60\u201372","journal-title":"Exp Brain Res"},{"key":"9098_CR39","first-page":"633","volume-title":"Advances in neural information processing systems, vol 10","author":"S Schaal","year":"1998","unstructured":"Schaal S, Vijayakumar S, Atkeson CG (1998) Local dimensionality reduction. In: Jordan M, Kearns M, Solla S (eds) Advances in neural information processing systems, vol 10. MIT Press, Cambridge, MA, pp 633\u2013639"},{"key":"9098_CR40","volume-title":"Learning with kernels","author":"B Sch\u00f6lkopf","year":"2002","unstructured":"Sch\u00f6lkopf B, Smola AJ (2002) Learning with kernels. MIT Press, Cambridge, MA"},{"key":"9098_CR41","doi-asserted-by":"crossref","first-page":"2319","DOI":"10.1126\/science.290.5500.2319","volume":"290","author":"JB Tenenbaum","year":"2000","unstructured":"Tenenbaum JB, de Silva V, Langford JC (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290: 2319\u20132323","journal-title":"Science"},{"key":"9098_CR42","first-page":"211","volume":"1","author":"ME Tipping","year":"2001","unstructured":"Tipping ME (2001) Sparse bayesian learning and the relevance vector machine. J Mach Learn Res 1: 211\u2013244","journal-title":"J Mach Learn Res"},{"issue":"3","key":"9098_CR43","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1111\/1467-9868.00196","volume":"61","author":"ME Tipping","year":"1999","unstructured":"Tipping ME, Bishop CM (1999) Probabilistic principal component analysis. J Roy Stat Soc Ser B 61(3): 611\u2013622","journal-title":"J Roy Stat Soc Ser B"},{"key":"9098_CR44","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2440-0","volume-title":"The nature of statistical learning theory","author":"VN Vapnik","year":"1995","unstructured":"Vapnik VN (1995) The nature of statistical learning theory. Springer-Verlag, New York"},{"key":"9098_CR45","doi-asserted-by":"crossref","unstructured":"Vijayakumar S, Schaal S (2000a) Fast and efficient incremental learning for high-dimensional movement systems. In: Proceedings of the international conference on robotics and automation, San Francisco, CA","DOI":"10.1109\/ROBOT.2000.844871"},{"key":"9098_CR46","unstructured":"Vijayakumar S, Schaal S (2000b) Locally weighted projection regression: an O(n) algorithm for incremental real time learning in high dimensional space. In: Proceedings of the 17th international conference on machine learning, Montreal, Canada, pp 1079\u20131086"},{"issue":"1","key":"9098_CR47","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1023\/A:1013258808932","volume":"12","author":"S Vijayakumar","year":"2002","unstructured":"Vijayakumar S, D\u2019Souza A, Shibata T, Conradt J, Schaal S (2002) Statistical learning for humanoid robots. Auton Robots 12(1): 55\u201369","journal-title":"Auton Robots"},{"key":"9098_CR48","doi-asserted-by":"crossref","first-page":"2602","DOI":"10.1162\/089976605774320557","volume":"17","author":"S Vijayakumar","year":"2005","unstructured":"Vijayakumar S, D\u2019Souza A, Schaal S (2005) Incremental online learning in high dimensions. Neural Comput 17: 2602\u20132634","journal-title":"Neural Comput"},{"key":"9098_CR49","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1162\/089976602753284491","volume":"14","author":"N Vlassis","year":"2002","unstructured":"Vlassis N, Motomura Y, Kr\u00f6se B (2002) Supervised dimension reduction of intrinsically low-dimensional data. Neural Comput 14: 191\u2013215","journal-title":"Neural Comput"},{"issue":"4","key":"9098_CR50","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1080\/00401706.1974.10489232","volume":"16","author":"JT Webster","year":"1974","unstructured":"Webster JT, Gunst RF, Mason RL (1974) Latent root regression analysis. Technometrics 16(4): 513\u2013522","journal-title":"Technometrics"},{"key":"9098_CR51","doi-asserted-by":"crossref","unstructured":"Weinberger KQ, Sha F, Saul LK (2004) Learning a kernel matrix for nonlinear dimensionality reduction. In: Proceedings of the 21st international conference on machine learning, Washington, DC","DOI":"10.1145\/1015330.1015345"},{"issue":"3","key":"9098_CR52","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1137\/0905052","volume":"5","author":"S Wold","year":"1984","unstructured":"Wold S, Ruhe A, Wold H, Dunn WJ III (1984) The collinearity problem in linear regression. The partial least squares (PLS) approach to generalized inverses. SIAM J Sci Stat Comput 5(3): 735\u2013743","journal-title":"SIAM J Sci Stat Comput"},{"issue":"2","key":"9098_CR53","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/BF02294050","volume":"42","author":"AL Wollenberg van den","year":"1977","unstructured":"van den Wollenberg AL (1977) Redundancy analysis an alternative for canonical correlation analysis. Psychometrika 42(2): 207\u2013219","journal-title":"Psychometrika"}],"container-title":["Neural Processing Letters"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11063-009-9098-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11063-009-9098-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11063-009-9098-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T04:22:57Z","timestamp":1559362977000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11063-009-9098-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,2,13]]},"references-count":53,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2009,4]]}},"alternative-id":["9098"],"URL":"https:\/\/doi.org\/10.1007\/s11063-009-9098-0","relation":{},"ISSN":["1370-4621","1573-773X"],"issn-type":[{"value":"1370-4621","type":"print"},{"value":"1573-773X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,2,13]]}}}