This paper contrasts three related regularization schemes for kernel machines using a least squares criterion, namely Tikhonov and Ivanov regularization and Morozov's discrepancy principle. We derive the conditions for optimality in a least squares support vector machine context (LS-SVMs) where they differ in the role of the regularization parameter. In particular, the Ivanov and Morozov scheme express the trade-off between data-fitting and smoothness in the trust region of the parameters and the noise level respectively which both can be transformed uniquely to an appropriate regularization constant for a standard LS-SVM. This insight is employed to tune automatically the regularization constant in an LS-SVM framework based on the estimated noise level, which can be obtained by using a nonparametric technique as e.g. the differogram estimator. © Springer-Verlag Berlin Heidelberg 2004.
CITATION STYLE
Pelckmans, K., Suykens, J. A. K., & De Moor, H. (2004). Morozov, Ivanov and Tikhonov regularization based LS-SVMs. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 3316, 1216–1222. https://doi.org/10.1007/978-3-540-30499-9_189
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