Morozov, Ivanov and Tikhonov Regularization Based LS-SVMs

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.

• Type: Conference
• Year: 2004
• Where: ICONIP
• Authors: Kristiaan Pelckmans, Johan A. K. Suykens, Bart De Moor
• Keywords: ICONIP 2004, ICONIP 2007, Ivanov Regularization, Regularization Constant, Related Regularization Schemes