چکیده (انگلیسی):

In kernel methods, choosing a suitable kernel is indispensable for favorable results. No well-founded
methods, however, have been established in general for unsupervised learning. We focus on kernel Principal
Component Analysis (kernel PCA), which is a nonlinear extension of principal component analysis and has
been used electively for extracting nonlinear features and reducing dimensionality. As a kernel method,
kernel PCA also suffers from the problem of kernel choice. Although cross-validation is a popular method
for choosing hyperparameters, it is not applicable straightforwardly to choose a kernel in kernel PCA
because of the incomparable norms given by different kernels. It is important, thus, to develop a wellfounded
method for choosing a kernel in kernel PCA. This study proposes a method for choosing
hyperparameters in kernel PCA (kernel and the number of components) based on cross-validation for the
comparable reconstruction errors of pre-images in the original space. The experimental results on
synthesized and real-world datasets demonstrate that the proposed method successfully selects an
appropriate kernel and the number of components in kernel PCA in terms of visualization and
classification errors on the principal components. The results imply that the proposed method enables
automatic design of hyperparameters in kernel PCA.