| Abstract | 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 denoising. 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 estimation schemes lack stability. A new pre-image estimation method for de-noising is proposed, by including input space distance regularization. By extensive experiments 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 previous 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 real world biomedical data analysis. Using data from the Center for Integrated Molecular Brain Imaging (Cimbi), it is investigated how kernel PCA de-noising enhances personality trait and brain function correlations. The data set include regional binding potentials (BPs) of the serotonin receptor subtype 5-HT2A and the scores from a NEO-PI-R personality assessment. Finally, it is demonstrated how a notable improvement of the correlations between frontolimbic 5-HT2A receptor BP and the traits neuroticism, anxiety, and vulnerability can be achieved by kernel PCA de-noising. |