{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T22:56:46Z","timestamp":1762210606354},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2009,11,17]],"date-time":"2009-11-17T00:00:00Z","timestamp":1258416000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Optim Lett"],"published-print":{"date-parts":[[2010,5]]},"DOI":"10.1007\/s11590-009-0158-1","type":"journal-article","created":{"date-parts":[[2009,11,16]],"date-time":"2009-11-16T07:49:14Z","timestamp":1258357754000},"page":"197-210","source":"Crossref","is-referenced-by-count":7,"title":["Error bounds for suboptimal solutions to kernel principal component analysis"],"prefix":"10.1007","volume":"4","author":[{"given":"Giorgio","family":"Gnecco","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marcello","family":"Sanguineti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2009,11,17]]},"reference":[{"key":"158_CR1","doi-asserted-by":"crossref","unstructured":"Achlioptas, D., McSherry, F., Sch\u00f6lkopf, B.: Sampling techniques for kernel methods. In: Advances in Neural Information Processing Systems, vol. 14 (Proc. NIPS 2001), pp. 335\u2013342. MIT Press, Cambridge (2002)","DOI":"10.7551\/mitpress\/1120.003.0048"},{"key":"158_CR2","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1090\/S0002-9947-1950-0051437-7","volume":"68","author":"N. Aronszajn","year":"1950","unstructured":"Aronszajn N.: Theory of reproducing kernels. Trans. AMS 68, 337\u2013404 (1950)","journal-title":"Trans. AMS"},{"key":"158_CR3","doi-asserted-by":"crossref","first-page":"930","DOI":"10.1109\/18.256500","volume":"39","author":"A.R. Barron","year":"1993","unstructured":"Barron A.R.: Universal approximation bounds for superpositions of a sigmoidal function. IEEE Trans. Inform. Theory 39, 930\u2013945 (1993)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"158_CR4","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1007\/BF02867116","volume":"104","author":"R. Bhatia","year":"1994","unstructured":"Bhatia R., Elsner L.: The Hoffman\u2013Wielandt inequality in infinite dimensions. Proc. Indian Acad. Sci. (Math. Sci.) 104, 483\u2013494 (1994)","journal-title":"Proc. Indian Acad. Sci. (Math. Sci.)"},{"key":"158_CR5","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898717785","volume-title":"Numerical Methods in Scientific Computing","author":"G. Dahlquist","year":"2008","unstructured":"Dahlquist G., Bjorck A.: Numerical Methods in Scientific Computing. SIAM, Philadelphia (2008)"},{"key":"158_CR6","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/s10589-007-9031-2","volume":"38","author":"P. Georgiev","year":"2007","unstructured":"Georgiev P., Pardalos P., Cichocki A.: Algorithms with high order convergence speed for blind source extraction. Comput. Optim. Appl. 38, 123\u2013131 (2007)","journal-title":"Comput. Optim. Appl."},{"key":"158_CR7","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/978-0-387-69319-4_6","volume-title":"Data Mining in Biomedicine","author":"P. Georgiev","year":"2007","unstructured":"Georgiev P., Pardalos P., Theis F.J., Cichocki A., Bakardjian H.: Sparse component analysis: a new tool for data mining. In: Pardalos, P., Boginski, V., Vazacopoulos, A. (eds) Data Mining in Biomedicine, pp. 91\u2013116. Springer, Berlin (2007)"},{"key":"158_CR8","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/s10589-007-9108-y","volume":"42","author":"G. Gnecco","year":"2009","unstructured":"Gnecco G., Sanguineti M.: Accuracy of suboptimal solutions to kernel principal component analysis. Comput. Optim. Appl. 42, 265\u2013287 (2009)","journal-title":"Comput. Optim. Appl."},{"key":"158_CR9","volume-title":"Advances in Neural Information Processing Systems 21 (Proc. NIPS 2008)","author":"Z. Hussain","year":"2009","unstructured":"Hussain Z., Shawe-Taylor J.: Theory of matching pursuit. In: Koller, D., Schuurmans, D., Bengio, Y., Bottou, L. (eds) Advances in Neural Information Processing Systems 21 (Proc. NIPS 2008), MIT Press, Cambridge (2009)"},{"key":"158_CR10","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-1904-8","volume-title":"Principal Component Analysis","author":"I.T. Jolliffe","year":"1986","unstructured":"Jolliffe I.T.: Principal Component Analysis. Springer, New York (1986)"},{"key":"158_CR11","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1007\/978-1-4612-1996-5_16","volume-title":"Computer-Intensive Methods in Control and Signal Processing. The Curse of Dimensionality","author":"V. K\u016frkov\u00e1","year":"1997","unstructured":"K\u016frkov\u00e1 V.: Dimension-independent rates of approximation by neural networks. In: Warwick, K., K\u00e1rn\u00fd, M. (eds) Computer-Intensive Methods in Control and Signal Processing. The Curse of Dimensionality, pp. 261\u2013270. Birkh\u00e4user, Boston (1997)"},{"key":"158_CR12","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1109\/18.971754","volume":"48","author":"V. K\u016frkov\u00e1","year":"2002","unstructured":"K\u016frkov\u00e1 V., Sanguineti M.: Comparison of worst-case errors in linear and neural network approximation. IEEE Trans. Inform. Theory 48, 264\u2013275 (2002)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"158_CR13","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1137\/S1052623403426507","volume":"15","author":"V. K\u016frkov\u00e1","year":"2005","unstructured":"K\u016frkov\u00e1 V., Sanguineti M.: Error estimates for approximate optimization by the extended Ritz method. SIAM J. Optim. 15, 261\u2013287 (2005)","journal-title":"SIAM J. Optim."},{"key":"158_CR14","doi-asserted-by":"crossref","first-page":"113","DOI":"10.2307\/3318636","volume":"6","author":"V. Koltchinskii","year":"1994","unstructured":"Koltchinskii V., Gin\u00e9 E.: Random matrix approximation of spectra of integral operators. Bernoulli 6, 113\u2013167 (1994)","journal-title":"Bernoulli"},{"key":"158_CR15","volume-title":"Functional Analysis","author":"B.V. Limaye","year":"1996","unstructured":"Limaye B.V.: Functional Analysis. New Age Publishers, New Delhi (1996)"},{"key":"158_CR16","volume-title":"Data Mining and Mathematical Programming","year":"2008","unstructured":"Pardalos, P., Hansen, P. (eds): Data Mining and Mathematical Programming. American Mathematical Society, Providence (2008)"},{"key":"158_CR17","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611971163","volume-title":"The Symmetric Eigenvalue Problem","author":"B.N. Parlett","year":"1998","unstructured":"Parlett B.N.: The Symmetric Eigenvalue Problem. SIAM, Philadelphia (1998)"},{"key":"158_CR18","doi-asserted-by":"crossref","first-page":"1299","DOI":"10.1162\/089976698300017467","volume":"10","author":"B. Sch\u00f6lkopf","year":"1998","unstructured":"Sch\u00f6lkopf B., Smola A., M\u00fcller K.R.: Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput. 10, 1299\u20131319 (1998)","journal-title":"Neural Comput."},{"key":"158_CR19","volume-title":"Learning with Kernels\u2014Support Vector Machines Regularization Optimization and Beyond","author":"B. Sch\u00f6lkopf","year":"2002","unstructured":"Sch\u00f6lkopf B., Smola A.J.: Learning with Kernels\u2014Support Vector Machines Regularization Optimization and Beyond. MIT Press, Cambridge (2002)"},{"key":"158_CR20","unstructured":"Shawe-Taylor, J., Cristianini, N.: Estimating the moments of a random vector with applications. In: Proceedings of GRETSI 2003 Conference, pp. 47\u201352 (2003)"},{"key":"158_CR21","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970531","volume-title":"Variational Methods for Eigenvalue Approximation","author":"H.F. Weinberger","year":"1974","unstructured":"Weinberger H.F.: Variational Methods for Eigenvalue Approximation. SIAM, Philadelphia (1974)"}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-009-0158-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11590-009-0158-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-009-0158-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,17]],"date-time":"2024-03-17T17:00:34Z","timestamp":1710694834000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11590-009-0158-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,11,17]]},"references-count":21,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,5]]}},"alternative-id":["158"],"URL":"https:\/\/doi.org\/10.1007\/s11590-009-0158-1","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"value":"1862-4472","type":"print"},{"value":"1862-4480","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,11,17]]}}}