{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T11:01:16Z","timestamp":1774263676517,"version":"3.50.1"},"reference-count":38,"publisher":"Elsevier BV","issue":"4","license":[{"start":{"date-parts":[[1998,6,1]],"date-time":"1998-06-01T00:00:00Z","timestamp":896659200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Networks"],"published-print":{"date-parts":[[1998,6]]},"DOI":"10.1016\/s0893-6080(98)00032-x","type":"journal-article","created":{"date-parts":[[2002,7,25]],"date-time":"2002-07-25T12:59:42Z","timestamp":1027601982000},"page":"637-649","source":"Crossref","is-referenced-by-count":450,"title":["The connection between regularization operators and support vector kernels"],"prefix":"10.1016","volume":"11","author":[{"given":"Alex J.","family":"Smola","sequence":"first","affiliation":[]},{"given":"Bernhard","family":"Sch\u00f6lkopf","sequence":"additional","affiliation":[]},{"given":"Klaus-Robert","family":"M\u00fcller","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0893-6080(98)00032-X_BIB1","first-page":"821","article-title":"Theoretical foundations of the potential function method in pattern recognition learning","volume":"25","author":"Aizerman","year":"1964","journal-title":"Automation and Remote Control"},{"issue":"5","key":"10.1016\/S0893-6080(98)00032-X_BIB2","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1109\/72.623200","article-title":"Asymptotic statistical theory of overtraining and cross-validation","volume":"8","author":"Amari","year":"1997","journal-title":"IEEE Trans. Neural Networks"},{"key":"10.1016\/S0893-6080(98)00032-X_BIB3","doi-asserted-by":"crossref","unstructured":"Bishop, C.M. (1995). Neural Networks for Pattern Recognition. Oxford: Clarendon Press.","DOI":"10.1093\/oso\/9780198538493.001.0001"},{"key":"10.1016\/S0893-6080(98)00032-X_BIB4","doi-asserted-by":"crossref","unstructured":"Bochner, S. (1959). Lectures on Fourier integral. Princeton, NJ: Princeton University Press.","DOI":"10.1515\/9781400881994"},{"key":"10.1016\/S0893-6080(98)00032-X_BIB5","doi-asserted-by":"crossref","unstructured":"Boser, B.E., Guyon, I.M., & Vapnik, V.N. (1992). A training algorithm for optimal margin classifiers. In: D. Haussler (ed.), Proceedings of the 5th Annual ACM Workshop on Computational Learning Theory, Pittsburgh, PA. ACM Press, pp. 144\u2013152.","DOI":"10.1145\/130385.130401"},{"key":"10.1016\/S0893-6080(98)00032-X_BIB6","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/BF00994018","article-title":"Support vector networks","volume":"20","author":"Cortes","year":"1995","journal-title":"In Mach. Learning"},{"key":"10.1016\/S0893-6080(98)00032-X_BIB7","unstructured":"Dyn, N. (1991). Interpolation and approximation by radial and related functions. In: C.K. Chui, L.L. Schumaker, D.J. Ward, (Eds.), Approximation Theory, vol. VI. New York: Academic Press, pp. 211\u2013232."},{"key":"10.1016\/S0893-6080(98)00032-X_BIB8","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1163\/156856894X00224","article-title":"Lie transformation groups, integral transforms, and invariant pattern recognition","volume":"8","author":"Ferraro","year":"1994","journal-title":"Spatial Vision"},{"key":"10.1016\/S0893-6080(98)00032-X_BIB9","unstructured":"Girosi, F. (1997). An equivalence between sparse approximation and support vector machines. A.I. Memo No. 1606, Artificial Intelligence Laboratory, Massachusetts Institute of Technology (to appear in Neural Computation)."},{"key":"10.1016\/S0893-6080(98)00032-X_BIB10","unstructured":"Girosi, F., Jones, M., & Poggio, T. (1993). Priors, stabilizers and basis functions, From regularization to radial, tensor and additive splines. A.I. Memo No. 1430, Artificial Intelligence Laboratory, Massachusetts Institute of Technology, 1993."},{"issue":"5","key":"10.1016\/S0893-6080(98)00032-X_BIB11","doi-asserted-by":"crossref","first-page":"1143","DOI":"10.1162\/neco.1997.9.5.1143","article-title":"A bound on the error of cross validation using the approximation and estimation rates, with consequences for the training-test split","volume":"9","author":"Kearns","year":"1997","journal-title":"Neural Comput."},{"key":"10.1016\/S0893-6080(98)00032-X_BIB12","first-page":"495","article-title":"A correspondence between Bayesan estimation on stochastic processes and smoothing by splines","volume":"2","author":"Kimeldorf","year":"1971","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/S0893-6080(98)00032-X_BIB13","unstructured":"MacKay, D.J.C. (1991). Bayesian modelling and neural networks. Ph.D. thesis, Computation and Neural Systems, California Institute of Technology, Pasadena, CA."},{"issue":"189","key":"10.1016\/S0893-6080(98)00032-X_BIB14","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1090\/S0025-5718-1990-0993931-7","article-title":"Multivariate interpolation and conditionally positive definite functions. II.","volume":"54","author":"Madych","year":"1990","journal-title":"Math. Comput."},{"key":"10.1016\/S0893-6080(98)00032-X_BIB15","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/BF01893414","article-title":"Interpolation of scattered data, distance matrices and conditionally positive definite functions","volume":"2","author":"Micchelli","year":"1986","journal-title":"Constr. Approx."},{"issue":"1","key":"10.1016\/S0893-6080(98)00032-X_BIB16","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1137\/0801008","article-title":"On the solution of large quadratic programming problems with bound counstraints","volume":"1","author":"More","year":"1991","journal-title":"SIAM J. Optimization"},{"key":"10.1016\/S0893-6080(98)00032-X_BIB17","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/BF02281970","article-title":"On optimal nonlinear associative recall","volume":"19","author":"Poggio","year":"1975","journal-title":"Biolog. Cybernetics"},{"key":"10.1016\/S0893-6080(98)00032-X_BIB18","unstructured":"Riesz, F., & Nagy, B.Sz. (1955). Functional Analysis. Frederick Ungar, New York, 1955."},{"key":"10.1016\/S0893-6080(98)00032-X_BIB19","first-page":"461","article-title":"Minimum-description-length principle","volume":"6","author":"Rissanen","year":"1985","journal-title":"Ann. Statist."},{"key":"10.1016\/S0893-6080(98)00032-X_BIB20","doi-asserted-by":"crossref","unstructured":"Schoenberg I.J. (1938a). Metric spaces and completely monotone functions. Ann. Math., 39, 811\u2013841.","DOI":"10.2307\/1968466"},{"key":"10.1016\/S0893-6080(98)00032-X_BIB21","doi-asserted-by":"crossref","unstructured":"Schoenberg I.J. (1938b). Metric spaces and positive definite functions. Trans. Amer. Math. Soc., 44, 522\u2013536.","DOI":"10.1090\/S0002-9947-1938-1501980-0"},{"key":"10.1016\/S0893-6080(98)00032-X_BIB22","unstructured":"Sch\u00f6lkopf, B. (1997). Support vector learning, Ph.D. thesis, Technische Universit\u00e4t Berlin. Also, GMD-Bericht Nr. 287, Oldenbourg Verlag, Munich."},{"key":"10.1016\/S0893-6080(98)00032-X_BIB23","unstructured":"Sch\u00f6lkopf, B., Burges, C., & Vapnik, V. (1995). Extracting support data for a given task. In: U.M. Fayyad, R. Uthurusamy (Eds.), Proceedings, First International Conference on Knowledge Discovery and Data Mining, Menlo Park. AAAI Press."},{"key":"10.1016\/S0893-6080(98)00032-X_BIB24","unstructured":"Sch\u00f6lkopf, B., Simard, P.Y., Smola, A.J., & Vapnik, V.N. (1998). Prior knowledge in support vector kernels. In: M.I. Jordan, M.J. Kearns, & S.A. Solla (Eds.), Advances in Neural information Processings Systems, vol. 10. Cambridge, MA: MIT Press (in press)."},{"key":"10.1016\/S0893-6080(98)00032-X_BIB25","unstructured":"Sch\u00f6lkopf, B., Smola, A.J. and M\u00fcller, K.R. (1996). Nonlinear component analysis as a kernel eigenvalue problem. Technical Report 44, MPI f\u00fcr biologische Kybernetik (to appear in Neural Computation)."},{"key":"10.1016\/S0893-6080(98)00032-X_BIB26","doi-asserted-by":"crossref","first-page":"2758","DOI":"10.1109\/78.650102","article-title":"Comparing support vector machines with gaussian kernels to radial basis function classifiers","volume":"45","author":"Sch\u00f6lkopf","year":"1997","journal-title":"IEEE Trans. Sign. Process."},{"key":"10.1016\/S0893-6080(98)00032-X_BIB27","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1109\/34.177382","article-title":"The canonical coordinates method for pattern deformation, Theoretical and computational considerations","volume":"14","author":"Segman","year":"1992","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"10.1016\/S0893-6080(98)00032-X_BIB28","unstructured":"Smola, A.J., & Sch\u00f6lkopf, B. (1997). On a kernel-based method for pattern recognition, regression, approximation and operator inversion. Technical Report 1064, GMD FIRST. Algorithmica, 1998, in press."},{"key":"10.1016\/S0893-6080(98)00032-X_BIB29","unstructured":"Smola, A.J., & Sch\u00f6lkopf, B. (1998). From regularization operators to support vector kernels. In: M.I. Jordan, M.J. Kearns, S.A. Solla (Eds.), Advances in Neural Information Processings Systems, vol. 10. Cambridge, MA: MIT Press (in press)."},{"key":"10.1016\/S0893-6080(98)00032-X_BIB30","unstructured":"Smola, A.J., Sch\u00f6lkopf, B., & M\u00fcller, K.-R. (1998). General cost functions for support vector regression. In: Proceedings of the ACNN`98, Australian Congress on Neural Networks (in press)."},{"key":"10.1016\/S0893-6080(98)00032-X_BIB31","unstructured":"Tikhonov, A.N., & Arsenin, V.Y. (1977). Solution of Ill-Posed Problems. Washington, DC: Winston."},{"issue":"3","key":"10.1016\/S0893-6080(98)00032-X_BIB32","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1109\/34.75515","article-title":"Fast B-spline transforms for continuous image representation and interpolation","volume":"13","author":"Unser","year":"1991","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"10.1016\/S0893-6080(98)00032-X_BIB33","unstructured":"Vanderbei, R.J. (1994). LOQO, An interior point code for quadratic programming. Technical Report SOR 94-15, Princeton University."},{"key":"10.1016\/S0893-6080(98)00032-X_BIB34","unstructured":"Vapnik, V.N. (1982). Estimation of Dependences Based on Empirical Data. Berlin: Springer."},{"key":"10.1016\/S0893-6080(98)00032-X_BIB35","doi-asserted-by":"crossref","unstructured":"Vapnik, V.N. (1995). The Nature of Statistical Learning Theory. New York: Springer.","DOI":"10.1007\/978-1-4757-2440-0"},{"key":"10.1016\/S0893-6080(98)00032-X_BIB36","unstructured":"Vapnik, V.N., Golowich, S., & Smola, A.J. (1997) Support vector method for function approximation, regression estimation, and signal processing, in: NIPS 9, San Mateo, CA."},{"key":"10.1016\/S0893-6080(98)00032-X_BIB37","doi-asserted-by":"crossref","unstructured":"Wahba, G. (1990). Splines Models for Observational Data, Series in Applied Mathematics, vol. 59. Philadelphia: SIAM.","DOI":"10.1137\/1.9781611970128"},{"key":"10.1016\/S0893-6080(98)00032-X_BIB38","unstructured":"Yuille, A., & Grzywacz, N. (1998). The motion coherence theory, in: Proceedings of the International Conference on Computer Vision, pp. 344\u2013354. Washington, D.C., December 1988. IEEE Computer Society Press."}],"container-title":["Neural Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S089360809800032X?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S089360809800032X?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2023,12,31]],"date-time":"2023-12-31T05:35:56Z","timestamp":1704000956000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S089360809800032X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,6]]},"references-count":38,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1998,6]]}},"alternative-id":["S089360809800032X"],"URL":"https:\/\/doi.org\/10.1016\/s0893-6080(98)00032-x","relation":{},"ISSN":["0893-6080"],"issn-type":[{"value":"0893-6080","type":"print"}],"subject":[],"published":{"date-parts":[[1998,6]]}}}