The connection between regularization operators and support vector kernels

 SMOLA Alex J.
 GMD First

 SCHOLKOPF Bernhard
 GMD First

 MULLER KlausRobert
 GMD First
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Author(s)

 SMOLA Alex J.
 GMD First

 SCHOLKOPF Bernhard
 GMD First

 MULLER KlausRobert
 GMD First
Journal

 Neural networks : the official journal of the International Neural Network Society

Neural networks : the official journal of the International Neural Network Society 11(4), 637649, 19980601
References: 38

1
 Theoretical foundations of the potential function method in pattern recognition learning

AIZERMAN M. A.
Automation and Remote Control 25, 821837, 1964
Cited by (3)

2
 <no title>

BISHOP C. M.
Neural Networks for Pattern Recognition, 1995
Cited by (116)

3
 <no title>

BOCHNER S.
Lectures on Fourier integral. Princeton, 1959
Cited by (1)

4
 A training algorithm for optimal margin classifiers.

BOSER B. E.
Proceedings of the 5th Annual ACM Workshop on Computational Learning Theory, 144152, 1992
Cited by (1)

5
 Support vector networks.

CORTES C.
Mach. Learning 20, 273297, 1995
Cited by (1)

6
 Interpolation and approximation by radial and related functions.

DYN N.
Approximation Theory, 211232, 1991
Cited by (1)

7
 An equivalence between sparse approximation and support vector machines.

GIROSI F.
A. I. Memo No. 1606, 1997
Cited by (1)

8
 Priors, stabilizers and basis functions, From regularization to radial, tensor and additive splines.

GIROSI F.
A. I. Memo No. 1430, 1993
Cited by (1)

9
 Bayesian modelling and neural networks.

MACKAY D. J. C.
Ph. D. thesis, Computation and Neural Systems, California Institute of Technology, 1991
Cited by (1)

10
 <no title>

RIESZ F.
Functional Analysis., 1995
Cited by (1)

11
 Minimumdescriptionlength principle.

RISSANEN J.
Ann. Statist. 6, 461464, 1985
Cited by (1)

12
 Support vector learning

SCHOLKOPF B.
Ph. D. thesis, Technische Universitat Berlin., 1997
Cited by (1)

13
 Extracting support data for a given task.

SCHOLKOPF B.
Proceedings, First International Conference on Knowledge Discovery and Data Mining, 1995
Cited by (1)

14
 Prior knowledge in support vector kernels.

SCHOLKOPF B.
Advances in Neural information Processings Systems 10, 1998
Cited by (1)

15
 On a kernelbased method for pattern recognition, regression, approximation and operator inversion.

SMOLA A. J.
Technical Report 1064, 1997
Cited by (1)

16
 From regularization operators to support vector kernels.

SMOLA A. J.
Advances in Neural Information Processings Systems 10, 1998
Cited by (1)

17
 General cost functions for support vector regression.

SMOLA A. J.
Proceedings of the ACNN'98, 1998
Cited by (1)

18
 <no title>

TIKHONOV A. N.
Solution of illposed problems, 1977
Cited by (12)

19
 LOQO, An interior point code for quadratic programming.

VANDERBEI R. J.
Technical Report SOR 9415, 1994
Cited by (1)

20
 <no title>

VAPNIK V. N.
Estimation of Dependences Based on Empirical Data, 1982
Cited by (5)

21
 <no title>

VAPNIK V. N.
The Nature of Statistical Learning Theory, 1995
Cited by (57)

22
 Support vector method for function approximation, regression estimation, and signal processing

VAPNIK V. N.
NIPS 9, 1997
Cited by (1)

23
 <no title>

WAHBA G.
Splines Models for Observational Data, Series in Applied Mathematics 59, 1990
Cited by (1)

24
 The motion coherence theory

YUILLE A.
Proceedings of the International Conference on Computer Vision, 344354, 1998
Cited by (1)

25
 Asymptotic statistical theory of overtraining and crossvalidation

AMARI S.
IEEE Trans. Neural Networks 8(5), 985986, 1997
Cited by (7)

26
 Lie transformation groups, integral transforms, and invariant pattern recognition.

FERRARO M.
Spatial Vision 8, 3344, 1994
Cited by (1)

27
 A bound on the error of cross validation using the approximation and estimation rates, with consequences for the trainingtest split.

KEARNS M.
Neural Comput. 9(5), 11431161, 1997
Cited by (1)

28
 A correspondence between Bayesan estimation on stochastic processes and smoothing by splines.

Kimeldorf G.
Ann. Math. Statist. 2, 495502, 1971
DOI Cited by (2)

29
 Multivariable interpolation and conditionally positive definite functionsII

MADYCH W. R.
Mathematical Computations 54, 211230, 1990
DOI Cited by (2)

30
 Interpolation of scattered data : distance matrices and conditionally positive definite functions

MICCHELLI C. A.
Constr.Approx. 2, 1122, 1986
DOI Cited by (10)

31
 On the solution of large quadratic programming problems with bound constraints

MORE J. J.
SIAM Journal of Optimization 1(1), 93113, 1991
DOI Cited by (2)

32
 On optimal nonlinear associative recall.

POGGIO T.
Biolog. Cybernetics 19, 201209, 1975
Cited by (1)

33
 Metric spaces and completely monotone functions

SCHOENBERG I. J.
Ann. Math. 39, 811841, 1938
DOI Cited by (2)

34
 Metric spaces and positive definite functions

SCHOENBERG I. J.
Transactions of the American Mathematical Society 44, 522536, 1938
DOI Cited by (2)

35
 Nonlinear component analysis as a Kernel eigenvalue problem

SCHOLKOPF B.
Neural Computation 10, 12991319, 1998
DOI Cited by (139)

36
 Comparing support vector machines with Gaussiankernels to radialbasis function classifiers

SCHOLKOPF B.
IEEE Trans. Signal Process. 45(11), 27582765, 1997
Cited by (21)

37
 The canonical coordinates method for pattern deformation, Theoretical and computational considerations.

SEGMAN J.
IEEE Trans. Pattern Anal. Mach. Intell. 14, 11711183, 1992
Cited by (1)

38
 Fast BSpline transformas for continuous image representation and interpolation

UNSER M.
IEEE Trans. on Pattern & Machine Intelligence 13(3), 277285, 1991
Cited by (16)