On a kernel-based method for pattern recognition, regression, approximation, and operator inversion

Algorithmica (New York)

Volumn 22, Issue 1-2, 1998, Pages 211-231

  Smola, A J ^a   Scholkopf B ^b  

^a FRAUNHOFER FIRST   (Germany)

^b MAX PLANCK INSTITUTE FOR BIOLOGICAL CYBERNETICS   (Germany)

Author keywords

Inverse problems; Kernels; Pattern Recognition; Regression; Regularization; Support vector machines

Indexed keywords

EID: 24044515976     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00013831     Document Type: Article

References (44)

1. Y. S. Abu-Mostafa. Hints. Neural Computation, 7(4):639-671, 1995.
2. H. Akaike. A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6):716-723, 1974.
3. C. M. Bishop. Neural Networks for Pattern Recognition. Clarendon Press, Oxford, 1995.
4. B. E. Boser, I. M. Guyon, and V. N. Vapnik. A training algorithm for optimal margin classifiers. In D. Haussler, editor, Proceedings of the 5th Annual ACM Workshop on Computational Learning Theory, pages 144-152. ACM Press, Pittsburgh, PA, 1992.
5. J. R. Bunch and L. Kaufman. A computational method for the indefinite quadratic programming problem. Linear Algebra and Its Applications, 341-370, 1980.
6. C. J. C. Burges. Simplified support vector decision rules. In L. Saitta, editor, Proceedings of the 13th International Conference on Machine Learning, pages 71-77. Morgan Kaufmann, San Mateo, CA, 1996.
7. S. Canu. Régularisation et l'apprentissage. Work in progress, available from http://www.hds.utc.ft/̃scanu/regul.ps, 1996.
8. C. Cortes and V. Vapnik. Support vector networks. Machine Learning, 20:273-297, 1995.
9. R. Courant and D. Hilbert. Methods of Mathematical Physics, volume 1. Interscience, New York, 1953.
10. H. Drucker, C. J. C. Burges, L. Kaufman, A. Smola, and V. Vapnik. Linear support vector regression machines. In M. C. Mozer, M. L. Jordan, and T. Petsche, editors, Advances in Neural Information Processing Systems 9, pages 155-161. MIT Press, Cambridge, MA, 1997.
11. R. O. Duda and P. E. Hart. Pattern Classification and Scene Analysis. Wiley, New York, 1973.
12. N. Dunford and J. T. Schwartz. Linear Operators, Part II: Spectral Theory, Self Adjoint Operators in Hilbert Space. Number VII in Pure and Applied Mathematics. Wiley, New York, 1963.
13. R. Gateaux. Sur les fonctionelles continues et les fonctionelles analytiques. Bulletin de la Soçiété Mathématique de France, 50:1-21, 1922.
14. S. Geva, J. Sitte, and G. Willshire. A one neuron truck backer-upper. In Proceedings of the International Joint Conference on Neural Networks, pages 850-856. IEEE, Baltimore, MD, 1992.
15. F. Girosi and G. Anzellotti. Convergence rates of approximation by translates. Technical Report AIM-1288, Artificial Intelligence Laboratory, Massachusetts Institute of Technology (MIT), Cambridge, MA, 1992.
16. T. J. Hastie and R. J. Tibshirani. Generalized Additive Models. Volume 43 of Monographs on Statistics and Applied Probability. Chapman & Hall, London, 1990.
17. A. E. Hoerl and R. W. Kennard. Ridge regression: biased estimation for nonorthogonal problems. Technometrics, 12:55-67, 1970.
18. P. J. Huber. Robust statistics: a review. Annals of Statistics, 43:1041, 1972.
19. R. Klein, G. Liebich, and W. Straßer. Mesh reduction with error control. In R. Yagel, editor, Visualization 96, pages 311-318. ACM, New York, 1996.
20. T. K. Leen. From data distribution to regularization in invariant learning. Neural Computation, 7(5):974-981, 1995.
21. J. C. Lemm. Prior information and generalized questions. Technical Report AIM-1598, Artificial Intelligence Laboratory, Massachusetts Institute of Technology (MIT), Cambridge, MA, 1996.
22. D. J. C. MacKay. Bayesian Modelling and Neural Networks. Ph.D. thesis, Computation and Neural Systems, California Institute of Technology, Pasadena, CA, 1991.
23. V A. Morozov. Methods for Solving Incorrectly Posed Problems. Springer-Verlag, New York, 1984.
24. K.-R. Müller, A. J. Smola, G. Ratsch, B. Schölkopf, J. Kohlmorgen, and V Vapnik. Predicting time series with support vector machines. In Proceedings of the International Conference on Artificial Neural Networks (ICANN 97), pages 999-1004, 1997.
25. N. Murata, S. Yoshizawa, and S. Amari. Network information criterion - determining the number of hidden units for artificial neural network models. IEEE Transactions on Neural Networks, 5:865-872, 1994.
26. M. Z. Nashed and G. Wahba. Generalized inverses in reproducing kernel spaces: an approach to regularization of linear operator equations. SIAM Journal on Mathematical Analysis, 5(6):974-987, 1974.
27. E. Osuna, R. Freund, and F. Girosi. Improved training algorithm for support vector machines. In Neural Networks for Signal Processing VII - Proceedings of the 1997 IEEE Workshop, 1997.
28. T. Poggio and F. Girosi. A theory of networks for approximation and learning. Technical Report AIM-1140, Artificial Intelligence Laboratory, Massachusetts Institute of Technology (MIT), Cambridge, MA, 1989.
29. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical Recipes in C: The Art of Scientific Computing (2nd edn.). Cambridge University Press, Cambridge, 1992.
30. J. Rissanen. Minimum-description-length principle. Annals of Statistics, 6:461-464, 1985.
31. B. Schölkopf, C. Burges, and V. Vapnik. Extracting support data for a given task. In U. M. Fayyad and R. Uthurusamy, editors, Proceedings, First International Conference on Knowledge Discovery & Data Mining, pages 252-257. AAAI Press, Menlo Park, CA, 1995.
32. B. Schölkopf, C. Burges, and V. Vapnik. Incorporating invariances in support vector learning machines. In C. von der Malsburg, W. von Seelen, J. C. Vorbrüggen, and B. Sendhoff, editors, Artificial Neural Networks - ICANN '96, pages 47-52. Lecture Notes in Computer Science, Vol. 1112. Springer-Verlag, Berlin, 1996.
33. B. Schölkopf, K. Sung, C. Burges, F. Girosi, P. Niyogi, T. Poggio, and V. Vapnik. Comparing support vector machines with gaussian kernels to radial basis function classifiers. IEEE Transactions on Signal Processing, 45(11):2758-2765, 1997.
34. P. Simard, Y. Le Cun, and J. Denker. Efficient pattern recognition using a new transformation distance. In S. J. Hanson, J. D. Cowan, and C. L. Giles, editors, Advances in Neural Information Processing Systems 5. Proceedings of the 1992 Conference, pages 50-58. Morgan Kaufmann, San Mateo, CA, 1993.
35. P. Simard, B. Victorri, Y. Le Cun, and J. Denker. Tangent prop - a formalism for specifying selected invariances in an adaptive network. In J. E. Moody, S. J. Hanson, and R. P. Lippmann, editors, Advances in Neural Information Processing Systems 4, pages 895-903. Morgan Kaufmann, San Mateo, CA, 1992.
36. A. J. Smola. Regression estimation with support vector learning machines. Master's thesis, Fakultät für Physik, Technische Universität München, Munich, 1996.
37. E. M. Stein. Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton, NJ, 1970.
38. A. N. Tikhonov and V Y Arsenin. Solution of Ill-Posed Problems. Winston, Washington, DC, 1977.
39. R. J. Vanderbei. LOQO: an interior point code for quadratic programming. Technical report SOR-94-15, Program in Statistics & Operations Research, Princeton University, Princeton, NJ, 1994.
40. V. Vapnik. Estimation of Dependences Based on Empirical Data (in Russian). Nauka, Moscow, 1979. (English translation: Springer-Verlag, New York, 1982.)
41. V. Vapnik. The Nature of Statistical Learning Theory. Springer-Verlag, New York, 1995.
42. V. Vapnik, S. Golowich, and A. Smola. Support vector method for function approximation, regression estimation, and signal processing. In M. C. Mozer, M. L. Jordan, and T. Petsche, editors, Advances in Neural Information Processing Systems 9, pages 281-287. MIT Press, Cambridge, MA, 1997.
43. V. N. Vapnik. Estimation of Dependences Based on Empirical Data. Springer-Verlag, Berlin, 1982.
44. J. Wood and J. Shawe-Taylor. A unifying framework for invariant pattern recognition. Pattern Recognition Letters, 17:1415-1422, 1996.