Tikhonov Regularization - Determination of The Tikhonov Factor

Determination of The Tikhonov Factor

The optimal regularization parameter is usually unknown and often in practical problems is determined by an ad hoc method. A possible approach relies on the Bayesian interpretation described above. Other approaches include the discrepancy principle, cross-validation, L-curve method, restricted maximum likelihood and unbiased predictive risk estimator. Grace Wahba proved that the optimal parameter, in the sense of leave-one-out cross-validation minimizes:

where is the residual sum of squares and is the effective number of degrees of freedom.

Using the previous SVD decomposition, we can simplify the above expression:

and