This thesis treats kernel PCA and the Nystrom method. We present a novel incre- ¨
mental algorithm for calculation of kernel PCA, which we extend to incremental
calculation of the Nystrom approximation. We suggest a new data-dependent ¨
method to select the number of data points to include in the Nystrom subset, ¨
and create a statistical hypothesis test for the same purpose. We further present
a cross-validation procedure for kernel PCA to select the number of principal
components to retain. Finally, we derive kernel PCA with the Nystrom method ¨
in line with linear PCA and study its statistical accuracy through a confidence
bound.