A Robust Function Estimation in Reproducing Kernel Hilbert Space Based on Finite Dimensional Reformulations

The function estimation in RKHS (Reproducing Kernel Hilbert Space) from finite noisy samples is a typical ill-conditioned inverse problem, which has been discussed mainly based on infinite dimensional operator theoretic analysis. In this paper, we present equivalent finite dimensional reformulations of the problem. Thanks to our reformulations, we can apply robust estimation techniques, e.g. the reduced-rank techniques and L-curve method for suitable Tikhonov type regularization, developed originally for finite dimensional ill-conditioned inverse problems. Numerical examples show that the proposed estimations using finite dimensional techniques achieve quite robust performances in this seemingly infinite dimensional application.APSIPA ASC 2009: Asia-Pacific Signal and Information Processing Association, 2009 Annual Summit and Conference. 4-7 October 2009. Sapporo, Japan. Poster session: Signal Processing Theory and Methods I (6 October 2009)