{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T05:41:33Z","timestamp":1725860493281},"publisher-location":"Cham","reference-count":45,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319419190"},{"type":"electronic","value":"9783319419206"}],"license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"DOI":"10.1007\/978-3-319-41920-6_23","type":"book-chapter","created":{"date-parts":[[2016,6,26]],"date-time":"2016-06-26T21:11:43Z","timestamp":1466975503000},"page":"311-325","source":"Crossref","is-referenced-by-count":0,"title":["Statistical Learning on Manifold-Valued Data"],"prefix":"10.1007","author":[{"given":"Alexander","family":"Kuleshov","sequence":"first","affiliation":[]},{"given":"Alexander","family":"Bernstein","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,6,28]]},"reference":[{"key":"23_CR1","volume-title":"Statistical Learning Theory","author":"V Vapnik","year":"1998","unstructured":"Vapnik, V.: Statistical Learning Theory. John Wiley, New York (1998)"},{"key":"23_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-84858-7","volume-title":"The Elements of Statistical Learning: Data Mining, Inference, and Prediction","author":"T Hastie","year":"2009","unstructured":"Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd edn. Springer, New York (2009)","edition":"2"},{"key":"23_CR3","series-title":"Springer Texts in Statistics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4614-7138-7","volume-title":"An Introduction to Statistical Learning with Applications in R","author":"G James","year":"2013","unstructured":"James, G., Witten, D., Hastie, T., Tibshirani, R.: An Introduction to Statistical Learning with Applications in R. Springer Texts in Statistics. Springer, New York (2013)"},{"key":"23_CR4","volume-title":"Pattern Recognition and Machine Learning","author":"CM Bishop","year":"2007","unstructured":"Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, Heidelberg (2007)"},{"issue":"5","key":"23_CR5","doi-asserted-by":"crossref","first-page":"1189","DOI":"10.1214\/aos\/1013203451","volume":"29","author":"JH Friedman","year":"2001","unstructured":"Friedman, J.H.: Greedy Function Approximation: A Gradient Boosting Machine. Ann. Stat. 29(5), 1189\u20131232 (2001)","journal-title":"Ann. Stat."},{"key":"23_CR6","volume-title":"Gaussian Processes for Machine Learning","author":"CE Rasmussen","year":"2006","unstructured":"Rasmussen, C.E., Williams, C.: Gaussian Processes for Machine Learning. MIT Press, Cambridge (2006)"},{"key":"23_CR7","doi-asserted-by":"crossref","DOI":"10.1007\/b98858","volume-title":"Local Regression and Likelihood","author":"C Loader","year":"1999","unstructured":"Loader, C.: Local Regression and Likelihood. Springer, New York (1999)"},{"issue":"3","key":"23_CR8","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1115\/1.2429697","volume":"129","author":"G Wang","year":"2007","unstructured":"Wang, G.: Gary Shan S.: Review of metamodeling techniques in support of engineering design optimization. J. Mech. Des. 129(3), 370\u2013381 (2007)","journal-title":"J. Mech. Des."},{"key":"23_CR9","doi-asserted-by":"crossref","DOI":"10.1002\/9780470770801","volume-title":"Engineering Design via Surrogate Modelling: A Practical Guide","author":"AIJ Forrester","year":"2008","unstructured":"Forrester, A.I.J., Sobester, A., Keane, A.J.: Engineering Design via Surrogate Modelling: A Practical Guide. Wiley, New York (2008)"},{"issue":"1","key":"23_CR10","first-page":"1441","volume":"13","author":"AP Kuleshov","year":"2009","unstructured":"Kuleshov, A.P., Bernstein, A.V.: Cognitive technologies in adaptive models of complex plants. Inf. Control Probl. Manuf. 13(1), 1441\u20131452 (2009)","journal-title":"Inf. Control Probl. Manuf."},{"key":"23_CR11","doi-asserted-by":"crossref","first-page":"1040","DOI":"10.1214\/aos\/1176345969","volume":"10","author":"CJ Stone","year":"1982","unstructured":"Stone, C.J.: Optimal global rates of convergence for nonparametric regression. Ann. Stat. 10, 1040\u20131053 (1982)","journal-title":"Ann. Stat."},{"issue":"5500","key":"23_CR12","doi-asserted-by":"crossref","first-page":"2268","DOI":"10.1126\/science.290.5500.2268","volume":"290","author":"HS Seung","year":"2000","unstructured":"Seung, H.S., Lee, D.D.: The Manifold Ways of Perception. Science 290(5500), 2268\u20132269 (2000)","journal-title":"Science"},{"key":"23_CR13","doi-asserted-by":"crossref","unstructured":"Rajaram, D., Pant, R.S.: An improved methodology for airfoil shape optimization using surrogate based design optimization. In: Rodrigues, H., et al. (eds.) Engineering Optimization IV, pp. 147\u2013152. CRC Press, Taylor & Francis Group, London (2015)","DOI":"10.1201\/b17488-27"},{"key":"23_CR14","unstructured":"Bernstein, A., Kuleshov, A., Sviridenko, Y., Vyshinsky, V.: Fast aerodynamic model for design technology. In: Proceedings of West-East High Speed Flow Field Conference (WEHSFF-2007), Moscow, Russia (2007). http:\/\/wehsff.imamod.ru\/pages\/s7.htm"},{"key":"23_CR15","unstructured":"Zhu, F., Qin, N., Burnaev, E.V., Bernstein, A.V., Chernova, S.S.: Comparison of three geometric parameterization methods and their effect on aerodynamic optimization. In: Poloni, C. (ed.) Eurogen 2011, Optimization and Control with Applications to Industrial and Societal Problems International Conference on Proceedings - Evolutionary and Deterministic Methods for Design, pp. 758\u2013772. Sira, Capua (2011)"},{"issue":"1","key":"23_CR16","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1080\/10485250500504828","volume":"18","author":"B Pelletier","year":"2006","unstructured":"Pelletier, B.: Nonparametric regression estimation on closed Riemannian manifolds. J. Nonparametric Stat. 18(1), 57\u201367 (2006)","journal-title":"J. Nonparametric Stat."},{"issue":"1","key":"23_CR17","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1524\/stnd.2008.0911","volume":"26","author":"J-M Loubes","year":"2008","unstructured":"Loubes, J.-M., Pelletier, B.: A kernel-based classifier on a Riemannian manifold. Statistics and Decisions 26(1), 35\u201351 (2008). Verlag, Oldenbourg","journal-title":"Statistics and Decisions"},{"key":"23_CR18","doi-asserted-by":"crossref","unstructured":"Bickel, P., Li, B.: Local polynomial regression on unknown manifolds. In: Complex Datasets and Inverse Problems: Tomography, Networks and Beyond . IMS Lecture notes \u2013 Monograph Series, vol. 54, pp. 177\u2013186 (2007)","DOI":"10.1214\/074921707000000148"},{"issue":"1","key":"23_CR19","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1214\/10-AOS823","volume":"39","author":"A Aswani","year":"2011","unstructured":"Aswani, A., Bickel, P., Tomlin, C.: Regression on manifolds: Estimation of the exterior derivative. Ann. Stat. 39(1), 48\u201381 (2011)","journal-title":"Ann. Stat."},{"issue":"504","key":"23_CR20","doi-asserted-by":"crossref","first-page":"1421","DOI":"10.1080\/01621459.2013.827984","volume":"108","author":"M-Y Cheng","year":"2013","unstructured":"Cheng, M.-Y., Wu, H.-T.: Local Linear Regression on Manifolds and its Geometric Interpretation. J. Am. Stat. Assoc. 108(504), 1421\u20131434 (2013)","journal-title":"J. Am. Stat. Assoc."},{"key":"23_CR21","unstructured":"Yang, Y., Dunson, D.B.: Bayesian manifold regression. In: arXiv:1305.0167v2 [math.ST], pp. 1\u201340, June 16, 2014"},{"key":"23_CR22","unstructured":"Guhaniyogi, R., Dunson, D.B.: Compressed gaussian process. In: arXiv:1406.1916v1 [stat.ML], pp. 1\u201329, June 7, 2014"},{"key":"23_CR23","unstructured":"Fletcher, P.T.: Geodesic regression on Riemannian manifolds. In: Proceedings of International Workshop on Mathematical Foundations of Computational Anatomy (MFCA), pp. 75\u201386 (2011)"},{"key":"23_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-3-642-33712-3_1","volume-title":"Computer Vision \u2013 ECCV 2012","author":"J Hinkle","year":"2012","unstructured":"Hinkle, J., Muralidharan, P., Fletcher, P., Joshi, S.: Polynomial regression on riemannian manifolds. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part III. LNCS, vol. 7574, pp. 1\u201314. Springer, Heidelberg (2012)"},{"issue":"3","key":"23_CR25","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1137\/080744189","volume":"3","author":"F Steinke","year":"2010","unstructured":"Steinke, F., Hein, M., Sch\u00f6lkopf, B.: Nonparametric regression between general Riemannian manifolds. SIAM J. Imaging Sci. 3(3), 527\u2013563 (2010)","journal-title":"SIAM J. Imaging Sci."},{"key":"23_CR26","first-page":"777","volume-title":"Advances in Neural Information Processing Systems","author":"E Levina","year":"2005","unstructured":"Levina, E., Bickel, P.J.: Maximum likelihood estimation of intrinsic dimension. In: Saul, L., Weiss, Y., Bottou, L. (eds.) Advances in Neural Information Processing Systems, vol. 17, pp. 777\u2013784. MIT Press, Cambridge (2005)"},{"key":"23_CR27","doi-asserted-by":"crossref","first-page":"780","DOI":"10.1016\/j.patcog.2008.09.016","volume":"42","author":"M Fan","year":"2009","unstructured":"Fan, M., Qiao, H., Zhang, B.: Intrinsic dimension estimation of manifolds by incising balls. Pattern Recogn. 42, 780\u2013787 (2009)","journal-title":"Pattern Recogn."},{"key":"23_CR28","unstructured":"Fan, M., Gu, N., Qiao, H., Zhang, B.: Intrinsic dimension estimation of data by principal component analysis. In: arXiv:1002.2050v1 [cs.CV], pp. 1\u20138, February 10, 2010"},{"key":"23_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1007\/978-3-642-24085-0_45","volume-title":"Image Analysis and Processing \u2013 ICIAP 2011","author":"A Rozza","year":"2011","unstructured":"Rozza, A., Lombardi, G., Rosa, M., Casiraghi, E., Campadelli, P.: IDEA: intrinsic dimension estimation algorithm. In: Maino, G., Foresti, G.L. (eds.) ICIAP 2011, Part I. LNCS, vol. 6978, pp. 433\u2013442. Springer, Heidelberg (2011)"},{"volume-title":"Manifold Learning Theory and Applications","year":"2011","key":"23_CR30","unstructured":"Ma, Y., Fu, Y. (eds.): Manifold Learning Theory and Applications. CRC Press, London (2011)"},{"key":"23_CR31","unstructured":"Bernstein, A.V., Kuleshov, A.P.: Tangent bundle manifold learning via Grassmann&Stiefel eigenmaps. In: arXiv:1212.6031v1 [cs.LG], pp. 1\u201325, December 2012"},{"issue":"3","key":"23_CR32","first-page":"359","volume":"7","author":"AV Bernstein","year":"2013","unstructured":"Bernstein, A.V., Kuleshov, A.P.: Manifold Learning: generalizing ability and tangent proximity. Int. J. Softw. Inf. 7(3), 359\u2013390 (2013)","journal-title":"Int. J. Softw. Inf."},{"key":"23_CR33","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1007\/978-3-319-17091-6_36","volume-title":"Statistical Learning and Data Sciences","author":"A Bernstein","year":"2015","unstructured":"Bernstein, A., Kuleshov, A., Yanovich, Y.: Manifold learning in regression tasks. In: Gammerman, A., Vovk, V., Papadopoulos, H. (eds.) SLDS 2015. LNCS, vol. 9047, pp. 414\u2013423. Springer, Heidelberg (2015)"},{"key":"23_CR34","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1007\/s00454-008-9053-2","volume":"39","author":"P Niyogi","year":"2008","unstructured":"Niyogi, P., Smale, S., Weinberger, S.: Finding the homology of submanifolds with high confidence from random samples. Discrete Comput. Geom. 39, 419\u2013441 (2008)","journal-title":"Discrete Comput. Geom."},{"key":"23_CR35","unstructured":"Bernstein, A.V., Kuleshov, A.P.: Data-based manifold reconstruction via tangent bundle manifold learning. In: ICML-2014, Topological Methods for Machine Learning Workshop, Beijing, June 25, 2014. http:\/\/topology.cs.wisc.edu\/KuleshovBernstein.pdf"},{"key":"23_CR36","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/978-3-319-08979-9_10","volume-title":"Machine Learning and Data Mining in Pattern Recognition","author":"A Kuleshov","year":"2014","unstructured":"Kuleshov, A., Bernstein, A.: Manifold learning in data mining tasks. In: Perner, P. (ed.) MLDM 2014. LNCS, vol. 8556, pp. 119\u2013133. Springer, Heidelberg (2014)"},{"key":"23_CR37","unstructured":"Kuleshov, A., Bernstein, A., Yanovich, Yu.: Asymptotically optimal method in manifold estimation. In: M\u00e1rkus, L., Prokaj, V. (eds.) Abstracts of the XXIX-th European Meeting of Statisticians, July 20\u201325, 2013, Budapest, p. 325 (2013)"},{"key":"23_CR38","first-page":"1263","volume":"13","author":"CR Genovese","year":"2012","unstructured":"Genovese, C.R., Perone-Pacifico, M., Verdinelli, I., Wasserman, L.: Minimax Manifold Estimation. J. Mach. Learn. Res. 13, 1263\u20131291 (2012)","journal-title":"J. Mach. Learn. Res."},{"key":"23_CR39","volume-title":"Matrix Computation","author":"GH Golub","year":"1996","unstructured":"Golub, G.H., Van Loan, C.F.: Matrix Computation, 3rd edn. Johns Hopkins University Press, Baltimore (1996)","edition":"3"},{"key":"23_CR40","unstructured":"Wasserman, L.: All of Nonparametric Statistics. Springer Texts in Statistics, Berlin (2007)"},{"key":"23_CR41","volume-title":"Principal Component Analysis","author":"T Jollie","year":"2002","unstructured":"Jollie, T.: Principal Component Analysis. Springer, New York (2002)"},{"issue":"8","key":"23_CR42","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1002\/cpa.21395","volume":"65","author":"A Singer","year":"2012","unstructured":"Singer, A., Wu, H.-T.: Vector Diffusion Maps and the Connection Laplacian. Commun. Pure Appl. Math. 65(8), 1067\u20131144 (2012)","journal-title":"Commun. Pure Appl. Math."},{"key":"23_CR43","unstructured":"Tyagi, H., Vural, E., Frossard, P.: Tangent space estimation for smooth embeddings of Riemannian manifold. In: arXiv:1208.1065v2 [stat.CO], pp. 1\u201335, May 17, 2013"},{"key":"23_CR44","doi-asserted-by":"crossref","unstructured":"Hamm, J., Lee, D.D.: Grassmann discriminant analysis: a unifying view on subspace-based learning. In: Proceedings of the 25th International Conference on Machine Learning (ICML 2008), pp. 376\u2013383 (2008)","DOI":"10.1145\/1390156.1390204"},{"key":"23_CR45","first-page":"913","volume":"4","author":"L Wolf","year":"2003","unstructured":"Wolf, L., Shashua, A.: Learning over sets using kernel principal angles. J. Mach. Learn. Res. 4, 913\u2013931 (2003)","journal-title":"J. Mach. Learn. Res."}],"container-title":["Lecture Notes in Computer Science","Machine Learning and Data Mining in Pattern Recognition"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-41920-6_23","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,2]],"date-time":"2022-07-02T02:00:33Z","timestamp":1656727233000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-41920-6_23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9783319419190","9783319419206"],"references-count":45,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-41920-6_23","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2016]]}}}