Department of Mathematics
Leming Qu
Boise State University
Regularization is a common technique to obtain reasonable solutions to ill-posed problems. In Tikhonov regularization, both the data-fitting and the penalty terms are in L2 norm. The L-curve is a plot of the size of the regularized solution versus the size of the corresponding residual for all valid regularization parameters. It is a useful tool for determining a suitable value of the regularization parameter in Tikhonov regularization. LASSO replaces the L2 norm by L1 norm for the penalty term. The LARS algorithm computes the whole path of the LASSO with a computational complexity in the same magnitude as the ordinary least squares. Thus, the L-curve for LASSO can be very efficiently obtained by the LARS-LASSO algorithm. The tuning point of the L-curve is chosen as the value of the regularization parameter. We compare L-curve method with the existing cross-validation method. The simulation suggests a better performance for the L-curve method.
All interested persons are welcome.