{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,4]],"date-time":"2025-05-04T04:06:27Z","timestamp":1746331587285,"version":"3.40.4"},"publisher-location":"Cham","reference-count":63,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319089782"},{"type":"electronic","value":"9783319089799"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014]]},"DOI":"10.1007\/978-3-319-08979-9_10","type":"book-chapter","created":{"date-parts":[[2014,7,17]],"date-time":"2014-07-17T14:05:07Z","timestamp":1405605907000},"page":"119-133","source":"Crossref","is-referenced-by-count":6,"title":["Manifold Learning in Data Mining Tasks"],"prefix":"10.1007","author":[{"given":"Alexander","family":"Kuleshov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Bernstein","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"10_CR1","unstructured":"Bengio, Y., Courville, A., Vincent, P.: Representation Learning: A Review and New Perspectives. arXiv preprint: arXiv:1206.5538v2, 1\u201364 (2012)"},{"key":"10_CR2","first-page":"349","volume-title":"IEEE Symposium Series in Computational Intelligence (SSCI) 2011 - Computational Intelligence and Data Mining (CIDM)","author":"K. Bunte","year":"2011","unstructured":"Bunte, K., Biehl, M., Hammer, B.: Dimensionality reduction mappings. In: IEEE Symposium Series in Computational Intelligence (SSCI) 2011 - Computational Intelligence and Data Mining (CIDM), pp. 349\u2013356. IEEE, Paris (2011)"},{"key":"10_CR3","volume-title":"Multidimensional Scaling","author":"T.F. Cox","year":"2001","unstructured":"Cox, T.F., Cox, M.A.A.: Multidimensional Scaling. Chapman and Hall\/CRC, London (2001)"},{"key":"10_CR4","volume-title":"Principal Component Analysis","author":"T. Jollie","year":"2002","unstructured":"Jollie, T.: Principal Component Analysis. Springer, New-York (2002)"},{"key":"10_CR5","doi-asserted-by":"publisher","first-page":"1373","DOI":"10.1162\/089976603321780317","volume":"15","author":"M. Belkin","year":"2003","unstructured":"Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation\u00a015, 1373\u20131396 (2003)","journal-title":"Neural Computation"},{"key":"10_CR6","doi-asserted-by":"publisher","first-page":"1860","DOI":"10.1126\/science.269.5232.1860","volume":"269","author":"R. Hecht-Nielsen","year":"1995","unstructured":"Hecht-Nielsen, R.: Replicator neural networks for universal optimal source coding. Science\u00a0269, 1860\u20131863 (1995)","journal-title":"Science"},{"issue":"5786","key":"10_CR7","doi-asserted-by":"publisher","first-page":"504","DOI":"10.1126\/science.1127647","volume":"313","author":"G.E. Hinton","year":"2006","unstructured":"Hinton, G.E., Salakhutdinov, R.R.: Reducing the dimensionality of data with neural networks. Science\u00a0313(5786), 504\u2013507 (2006)","journal-title":"Science"},{"issue":"2","key":"10_CR8","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1002\/aic.690370209","volume":"37","author":"M. Kramer","year":"1991","unstructured":"Kramer, M.: Nonlinear Principal Component Analysis using autoassociative neural networks. AIChE Journal\u00a037(2), 233\u2013243 (1991)","journal-title":"AIChE Journal"},{"key":"10_CR9","first-page":"580","volume-title":"Advances in Neural Information Processing Systems","author":"D. DeMers","year":"1993","unstructured":"DeMers, D., Cottrell, G.W.: Nonlinear dimensionality reduction. In: Hanson, D., Cowan, J., Giles, L. (eds.) Advances in Neural Information Processing Systems, vol.\u00a05, pp. 580\u2013587. Morgan Kaufmann, San Mateo (1993)"},{"key":"10_CR10","doi-asserted-by":"crossref","unstructured":"Kohonen, T.: Self-organizing Maps, 3rd edn. Springer (2000)","DOI":"10.1007\/978-3-642-56927-2"},{"key":"10_CR11","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1016\/0893-6080(94)90109-0","volume":"7","author":"T. Martinetz","year":"1994","unstructured":"Martinetz, T., Schulten, K.: Topology representing networks. Neural Networks\u00a07, 507\u2013523 (1994)","journal-title":"Neural Networks"},{"issue":"9","key":"10_CR12","doi-asserted-by":"publisher","first-page":"1393","DOI":"10.1109\/TPAMI.2006.184","volume":"28","author":"S. Lafon","year":"2006","unstructured":"Lafon, S., Lee, A.B.: Diffusion Maps and Coarse-Graining: A Unified Framework for Dimensionality Reduction, Graph Partitioning and Data Set Parameterization. IEEE Transaction on Pattern Analysis and Machine Intelligence\u00a028(9), 1393\u20131403 (2006)","journal-title":"IEEE Transaction on Pattern Analysis and Machine Intelligence"},{"issue":"5","key":"10_CR13","doi-asserted-by":"publisher","first-page":"1299","DOI":"10.1162\/089976698300017467","volume":"10","author":"B. Sch\u00f6lkopf","year":"1998","unstructured":"Sch\u00f6lkopf, B., Smola, A., M\u0171ller, K.: Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation\u00a010(5), 1299\u20131319 (1998)","journal-title":"Neural Computation"},{"key":"10_CR14","doi-asserted-by":"publisher","first-page":"2323","DOI":"10.1126\/science.290.5500.2323","volume":"290","author":"L.K. Saul","year":"2000","unstructured":"Saul, L.K., Roweis, S.T.: Nonlinear dimensionality reduction by locally linear embedding. Science\u00a0290, 2323\u20132326 (2000)","journal-title":"Science"},{"key":"10_CR15","doi-asserted-by":"publisher","first-page":"5591","DOI":"10.1073\/pnas.1031596100","volume":"100","author":"D.L. Donoho","year":"2003","unstructured":"Donoho, D.L., Grimes, C.: Hessian eigenmaps: New locally linear embedding techniques for high-dimensional data. Proceedings of the National Academy of Arts and Sciences\u00a0100, 5591\u20135596 (2003)","journal-title":"Proceedings of the National Academy of Arts and Sciences"},{"key":"10_CR16","doi-asserted-by":"publisher","first-page":"2319","DOI":"10.1126\/science.290.5500.2319","volume":"290","author":"J.B. Tehenbaum","year":"2000","unstructured":"Tehenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science\u00a0290, 2319\u20132323 (2000)","journal-title":"Science"},{"issue":"1","key":"10_CR17","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/s11263-005-4939-z","volume":"70","author":"K.Q. Weinberger","year":"2006","unstructured":"Weinberger, K.Q., Saul, L.K.: Maximum Variance Unfolding: Unsupervized Learning of Image Manifolds by Semidefinite Programming. International Journal of Computer Vision\u00a070(1), 77\u201390 (2006)","journal-title":"International Journal of Computer Vision"},{"key":"10_CR18","first-page":"961","volume-title":"Advances in Neural Information Processing Systems","author":"M. Brand","year":"2003","unstructured":"Brand, M.: Charting a manifold. In: Becker, S., Thrun, S., Obermayer, K. (eds.) Advances in Neural Information Processing Systems, vol.\u00a015, pp. 961\u2013968. MIT Press, Cambridge (2003)"},{"issue":"1","key":"10_CR19","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1137\/S1064827502419154","volume":"26","author":"Z. Zhang","year":"2005","unstructured":"Zhang, Z., Zha, H.: Principal Manifolds and Nonlinear Dimension Reduction via Local Tangent Space Alignment. SIAM Journal on Scientific Computing\u00a026(1), 313\u2013338 (2005)","journal-title":"SIAM Journal on Scientific Computing"},{"issue":"10","key":"10_CR20","doi-asserted-by":"publisher","first-page":"2197","DOI":"10.1162\/0899766041732396","volume":"16","author":"Y. Bengio","year":"2004","unstructured":"Bengio, Y., Delalleau, O., Le Roux, N., Paiement, J.-F., Vincent, P., Ouimet, M.: Learning Eigenfunctions Link Spectral Embedding and Kernel PCA. Neural Computation\u00a016(10), 2197\u20132219 (2004)","journal-title":"Neural Computation"},{"key":"10_CR21","first-page":"177","volume-title":"Advances in Neural Information Processing Systems","author":"Y. Bengio","year":"2004","unstructured":"Bengio, Y., Delalleau, O., Le Roux, N., Paiement, J.-F., Vincent, P., Ouimet, M.: Out-of-sample extension for LLE, Isomap, MDS, Eigenmaps, and spectral clustering. In: Thrun, S., Saul, L., Sch\u00f6lkopf, B. (eds.) Advances in Neural Information Processing Systems, vol.\u00a016, pp. 177\u2013184. MIT Press, Cambridge (2004)"},{"key":"10_CR22","first-page":"119","volume":"4","author":"L.K. Saul","year":"2003","unstructured":"Saul, L.K., Roweis, S.T.: Think globally, fit locally: unsupervised learning of low dimensional manifolds. Journal of Machine Learning Research\u00a04, 119\u2013155 (2003)","journal-title":"Journal of Machine Learning Research"},{"key":"10_CR23","doi-asserted-by":"crossref","first-page":"293","DOI":"10.7551\/mitpress\/6173.003.0022","volume-title":"Semisupervised Learning","author":"L.K. Saul","year":"2006","unstructured":"Saul, L.K., Weinberger, K.Q., Ham, J.H., Sha, F., Lee, D.D.: Spectral methods for dimensionality reduction. In: Chapelle, O., Sch\u00f6lkopf, B., Zien, A. (eds.) Semisupervised Learning, pp. 293\u2013308. MIT Press, Cambridge (2006)"},{"issue":"4","key":"10_CR24","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1561\/2200000002","volume":"2","author":"C.J.C. Burges","year":"2010","unstructured":"Burges, C.J.C.: Dimension Reduction: A Guided Tour. Foundations and Trends in Machine Learning\u00a02(4), 275\u2013365 (2010)","journal-title":"Foundations and Trends in Machine Learning"},{"key":"10_CR25","series-title":"Computational Intelligence and Machine Learning","first-page":"531","volume-title":"Proceedings of European Symposium on Artificial Neural Networks, ESANN 2012","author":"A. Gisbrecht","year":"2012","unstructured":"Gisbrecht, A., Lueks, W., Mokbel, B., Hammer, B.: Out-of-Sample Kernel Extensions for Nonparametric Dimensionality Reduction. In: Proceedings of European Symposium on Artificial Neural Networks, ESANN 2012. Computational Intelligence and Machine Learning, pp. 531\u2013536. Bruges, Belgium (2012)"},{"key":"10_CR26","first-page":"471","volume-title":"Proceedings of the Twenty-Fifth AAAI Conference on Artificial Intelligence","author":"H. Strange","year":"2011","unstructured":"Strange, H., Zwiggelaar, R.: A Generalised Solution to the Out-of-Sample Extension Problem in Manifold Learning. In: Proceedings of the Twenty-Fifth AAAI Conference on Artificial Intelligence, San Francisco, California, USA, pp. 471\u2013478. AAAI Press, Menlo Park (2011)"},{"key":"10_CR27","unstructured":"Cayton, L.: Algorithms for manifold learning. Univ of California at San Diego (UCSD), Technical Report CS2008-0923, pp. 541\u2013555. Citeseer (2005)"},{"key":"10_CR28","first-page":"691","volume-title":"Recent Advances in Data Mining of Enterprise Data","author":"X. Huo","year":"2007","unstructured":"Huo, X., Ni, X., Smith, A.K.: Survey of Manifold-based Learning Methods. In: Liao, T.W., Triantaphyllou, E. (eds.) Recent Advances in Data Mining of Enterprise Data, pp. 691\u2013745. World Scientific, Singapore (2007)"},{"issue":"5","key":"10_CR29","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1002\/wics.1222","volume":"4","author":"A.J. Izenman","year":"2012","unstructured":"Izenman, A.J.: Introduction to manifold learning. Computational Statistics\u00a04(5), 439\u2013446 (2012)","journal-title":"Computational Statistics"},{"volume-title":"Manifold Learning Theory and Applications","year":"2011","key":"10_CR30","unstructured":"Ma, Y., Fu, Y. (eds.): Manifold Learning Theory and Applications. CRC Press, London (2011)"},{"key":"10_CR31","first-page":"1786","volume-title":"Advances in Neural Information Processing Systems","author":"H. Narayanan","year":"2010","unstructured":"Narayanan, H., Mitter, S.: Sample complexity of testing the manifold hypothesis. In: Lafferty, J., Williams, C.K.I., Shawe-Taylor, J., Zemel, R., Culotta, A. (eds.) Advances in Neural Information Processing Systems, vol.\u00a023, pp. 1786\u20131794. MIT Press, Cambridge (2010)"},{"key":"10_CR32","first-page":"2294","volume-title":"Advances in Neural Information Processing Systems","author":"S. Rifai","year":"2011","unstructured":"Rifai, S., Dauphin, Y.N., Vincent, P., Bengio, Y., Muller, X.: The manifold Tangent Classifier. In: Shawe-Taylor, J., Zemel, R.S., Bartlett, P., Pereira, F., Weinberger, K.Q. (eds.) Advances in Neural Information Processing Systems, vol.\u00a024, pp. 2294\u20132302. MIT Press, Cambridge (2011)"},{"issue":"3","key":"10_CR33","doi-asserted-by":"publisher","first-page":"877","DOI":"10.1109\/TPWRS.2008.926091","volume":"23","author":"J. Chen","year":"2008","unstructured":"Chen, J., Deng, S.-J., Huo, X.: Electricity price curve modeling and forecasting by manifold learning. IEEE Transaction on Power Systems\u00a023(3), 877\u2013888 (2008)","journal-title":"IEEE Transaction on Power Systems"},{"key":"10_CR34","doi-asserted-by":"crossref","unstructured":"Song, W., Keane, A.J.: A Study of Shape Parameterisation Methods for Airfoil Optimisation. In: Proceedings of the 10th AIAA \/ ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA 2004-4482. American Institute of Aeronautics and Astronautics, Albany (2004)","DOI":"10.2514\/6.2004-4482"},{"key":"10_CR35","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. IMM RAS, Moscow (2007), http:\/\/wehsff.imamod.ru\/pages\/s7.htm"},{"key":"10_CR36","first-page":"6","volume":"2","author":"A. Bernstein","year":"2008","unstructured":"Bernstein, A., Kuleshov, A.: Cognitive technologies in the problem of dimension reduction of geometrical object descriptions. Information Technologies and Computer Systems\u00a02, 6\u201319 (2008)","journal-title":"Information Technologies and Computer Systems"},{"key":"10_CR37","unstructured":"Bernstein, A.V., Burnaev, E.V., Chernova, S.S., Zhu, F., Qin, N.: Comparison of Three Geometric Parameterization methods and Their Effect on Aerodynamic Optimization. In: Control with Applications to Industrial and Societal Problems (Eurogen 2011), Capua, Italy, September 14 - 16 (2011)"},{"key":"10_CR38","series-title":"New Challenges for Feature Selection in Data Mining and Knowledge Discovery","first-page":"21","volume-title":"JMLR Workshop and Conference Proceedings","author":"J.A. Lee","year":"2008","unstructured":"Lee, J.A., Verleysen, M.: Quality assessment of dimensionality reduction based on k-ary neighborhoods. In: Saeys, Y., Liu, H., Inza, I., Wehenkel, L., Van de Peer, Y. (eds.) JMLR Workshop and Conference Proceedings. New Challenges for Feature Selection in Data Mining and Knowledge Discovery, vol.\u00a04, pp. 21\u201335. Antwerpen, Belgium (2008)"},{"issue":"7-9","key":"10_CR39","doi-asserted-by":"publisher","first-page":"1431","DOI":"10.1016\/j.neucom.2008.12.017","volume":"72","author":"J.A. Lee","year":"2009","unstructured":"Lee, J.A., Verleysen, M.: Quality assessment of dimensionality reduction: Rank-based criteria. Neurocomputing\u00a072(7-9), 1431\u20131443 (2009)","journal-title":"Neurocomputing"},{"issue":"10","key":"10_CR40","doi-asserted-by":"publisher","first-page":"1349","DOI":"10.1109\/TPAMI.2002.1039206","volume":"24","author":"D. Freedman","year":"2002","unstructured":"Freedman, D.: Efficient simplicial reconstructions of manifold from their samples. IEEE Transaction on Pattern Analysis and Machine Intelligence\u00a024(10), 1349\u20131357 (2002)","journal-title":"IEEE Transaction on Pattern Analysis and Machine Intelligence"},{"key":"10_CR41","unstructured":"Karygianni, S., Frossard, P.: Tangent-based manifold approximation with locally linear models. In: arXiv preprint:\u00a0arXiv:1211.1893v1\u00a0[cs.LG] (November 6, 2012)"},{"key":"10_CR42","volume-title":"Matrix Computation","author":"G.H. Golub","year":"1996","unstructured":"Golub, G.H., Van Loan, C.F.: Matrix Computation, 3rd edn. Johns Hopkins University Press, MD (1996)","edition":"3"},{"key":"10_CR43","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1093\/biomet\/28.3-4.321","volume":"28","author":"H. Hotelling","year":"1936","unstructured":"Hotelling, H.: Relations between two sets of variables. Biometrika\u00a028, 321\u2013377 (1936)","journal-title":"Biometrika"},{"key":"10_CR44","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1214\/aoms\/1177728846","volume":"25","author":"A.T. James","year":"1954","unstructured":"James, A.T.: Normal multivariate analysis and the orthogonal group. Ann. Math. Statistics\u00a025, 40\u201375 (1954)","journal-title":"Ann. Math. Statistics"},{"issue":"3","key":"10_CR45","doi-asserted-by":"publisher","first-page":"456","DOI":"10.1016\/j.patcog.2005.08.015","volume":"39","author":"L. Wang","year":"2006","unstructured":"Wang, L., Wang, X., Feng, J.: Subspace Distance Analysis with Application to Adaptive Bayesian Algorithm for Face Recognition. Pattern Recognition\u00a039(3), 456\u2013464 (2006)","journal-title":"Pattern Recognition"},{"issue":"2","key":"10_CR46","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1137\/S0895479895290954","volume":"20","author":"A. Edelman","year":"1999","unstructured":"Edelman, A., Arias, T.A., Smith, T.: The Geometry of Algorithms with Orthogonality Constraints. SIAM Journal on Matrix Analysis and Applications\u00a020(2), 303\u2013353 (1999)","journal-title":"SIAM Journal on Matrix Analysis and Applications"},{"key":"10_CR47","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"},{"issue":"3","key":"10_CR48","first-page":"359","volume":"7","author":"A.V. Bernstein","year":"2013","unstructured":"Bernstein, A.V., Kuleshov, A.P.: Manifold Learning: generalizing ability and tangent proximity. International Journal of Software and Informatics\u00a07(3), 359\u2013390 (2013)","journal-title":"International Journal of Software and Informatics"},{"issue":"1","key":"10_CR49","first-page":"1441","volume":"13","author":"A.P. Kuleshov","year":"2009","unstructured":"Kuleshov, A.P., Bernstein, A.V.: Cognitive Technologies in Adaptive Models of Complex Plants. Information Control Problems in Manufacturing\u00a013(1), 1441\u20131452 (2009)","journal-title":"Information Control Problems in Manufacturing"},{"key":"10_CR50","series-title":"Graduate Studies in Mathematics","doi-asserted-by":"crossref","DOI":"10.1090\/gsm\/107","volume-title":"Manifolds and Differential Geometry","author":"J.M. Lee","year":"2009","unstructured":"Lee, J.M.: Manifolds and Differential Geometry. Graduate Studies in Mathematics, vol.\u00a0107. American Mathematical Society, Providence (2009)"},{"key":"10_CR51","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-21752-9","volume-title":"Introduction to Smooth Manifolds","author":"J.M. Lee","year":"2003","unstructured":"Lee, J.M.: Introduction to Smooth Manifolds. Springer, New York (2003)"},{"key":"10_CR52","first-page":"833","volume-title":"Proceedings of the 28th International Conference on Machine Learning (ICML 2011)","author":"S. Rifai","year":"2011","unstructured":"Rifai, S., Vincent, P., Muller, X., Glorot, X., Bengio, Y.: Contractive Auto-Encoders: Explicit Invariance during Feature Extraction. In: Getoor, L., Scheffer, T. (eds.) Proceedings of the 28th International Conference on Machine Learning (ICML 2011), pp. 833\u2013840. Omnipress, Bellevue (2011)"},{"key":"10_CR53","unstructured":"Silva, J.G., Marques, J.S., Lemos, J.M.: A Geometric approach to motion tracking in manifolds. In: Paul, M.J., Van Den Hof, B.W., Weiland, S. (eds.) A Proceedings Volume from the 13th IFAC Symposium on System Identification, Rotterdam (2003)"},{"key":"10_CR54","doi-asserted-by":"crossref","unstructured":"Silva, J.G., Marques, J.S., Lemos, J.M.: Non-linear dimension reduction with tangent bundle approximation. In: Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2005), vol.\u00a04, pp. 85\u201388. Conference Publications (2005)","DOI":"10.1109\/ICASSP.2005.1415951"},{"key":"10_CR55","unstructured":"Silva, J.G., Marques, J.S., Lemos, J.M.: Selecting Landmark Points for Sparse Manifold Learning. In: Weiss, Y., Sch\u00f6lkopf, B., Platt, J. (eds.) Advances in Neural Information Processing Systems, vol.\u00a018. MIT Press, Cambridge (2006)"},{"key":"10_CR56","unstructured":"Bernstein, A.V., Kuleshov, A.P.: Tangent Bundle Manifold Learning via Grassmann & Stiefel Eigenmaps. arXiv preprint: arXiv:1212.6031v1 [cs.LG], pp. 1\u201325 (December 2012)"},{"key":"10_CR57","series-title":"Lecture Notes in Artificial Intelligence","first-page":"1","volume-title":"Machine Learning: ECML 2004","author":"D. Achlioptas","year":"2004","unstructured":"Achlioptas, D.: Random matrices in data analysis. In: Boulicaut, J.-F., Esposito, F., Giannotti, F., Pedreschi, D. (eds.) ECML 2004. LNCS (LNAI), vol.\u00a03201, pp. 1\u20137. Springer, Heidelberg (2004)"},{"key":"10_CR58","unstructured":"Tyagi, H., Vural, E., Frossard, P.: Tangent space estimation for smooth embeddings of riemannian manifold. arXiv preprint: arXiv:1208.1065v2 [stat.CO], pp. 1\u201335 (May 17, 2013)"},{"key":"10_CR59","doi-asserted-by":"crossref","unstructured":"Singer, A., Wu, H.: Vector Diffusion Maps and the Connection Laplacian. Comm. on Pure and App. Math. (2012)","DOI":"10.1002\/cpa.21395"},{"key":"10_CR60","doi-asserted-by":"crossref","unstructured":"Coifman, R.R., Lafon, S., Lee, A.B., Maggioni, M., Warner, F., Zucker, S.: Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps. Proceedings of the National Academy of Sciences, 7426\u20137431 (2005)","DOI":"10.1073\/pnas.0500334102"},{"key":"10_CR61","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.\u00a04, 913\u2013931 (2003)","journal-title":"J. Mach. Learn. Res."},{"key":"10_CR62","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, Budapest, Hungary, July 20-25, p. 325 (2013), http:\/\/ems2013.eu\/conf\/upload\/BEK086_006.pdf"},{"key":"10_CR63","first-page":"1263","volume":"13","author":"C.R. Genovese","year":"2012","unstructured":"Genovese, C.R., Perone-Pacifico, M., Verdinelli, I., Wasserman, L.: Minimax Manifold Estimation. Journal Machine Learning Research\u00a013, 1263\u20131291 (2012)","journal-title":"Journal Machine Learning Research"}],"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\/978-3-319-08979-9_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,3]],"date-time":"2025-05-03T21:10:26Z","timestamp":1746306626000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-08979-9_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"ISBN":["9783319089782","9783319089799"],"references-count":63,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-08979-9_10","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2014]]}}}