부산대학교 도서관

This thesis treats kernel PCA and the Nystrom method. We present a novel incremental 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.