Kernel PLS Smoothing for Nonparametric Regression Curve Fitting: an Application to Event Related Potentials

We present a novel smoothing approach to nonparametric regression curve fitting. This is based on kernel partial least squares (PLS) regression in reproducing kernel Hilbert space. It is our interest to apply the methodology for smoothing experimental data, such as brain event related potentials, where some level of knowledge about areas of different degrees of smoothness, local inhomogeneities or points where the desired function changes its curvature is known or can be derived based on the observed noisy data. With this aim we propose locallybased kernel PLS regression and locally-based smoothing splines methodologies incorporating this knowledge. We illustrate the usefulness of kernel PLS and locally-based kernel PLS smoothing by comparing the methods with smoothing splines, locally-based smoothing splines and wavelet shrinkage techniques on two generated data sets. In terms of higher accuracy of the recovered signal of interest from its noisy observation we demonstrate comparable or better performance of the locally-based kernel PLS method in comparison to other methods on both data sets.