Kernel Methods for De-noising with Neuroimaging Application

www.imm.dtu.dk This thesis examines the use of kernel methods for non-linear data analysis. In particular kernel principal component analysis (kPCA) is used for de-noising. In this context, solution of the pre-image problem is a key element to efficient de-noising. Pre-image estimation is inherently ill-posed for many common choices of kernel function. In this thesis it is shown, how many of the often used estima-tion schemes lack stability. A new pre-image estimation method for de-noising is proposed, by including input space distance regularization. By extensive ex-periments on handwritten digits from the USPS data set, the new method is compared to three of the widely used schemes. Thereby it is shown how the pre-vious methods deteriorate when the feature space mapping is very non-linear. However, by the new input space distance regularization approach the variability is reduced with very limited sacrifice in terms of de-noising efficiency. The pre-image methodology has furthermore been successfully applied to rea