Simultaneous estimation of the number of principal components and kernel parameter in KPCA

This article proposed a novel method to determine the number of principal components and the optimal values of tuning factors for kernel principal component models. Existing work predominantly relies on ad-hoc rules or cross-validatory approaches to estimate. To guarantee statistical independence, the proposed technique incorporates a two-fold cross-validatory approach by omitting one variable in turn, which is predicted by the remaining ones. For these regressions, the number of principal components varies. This finally yields an optimum selection for the parameters, which application and the analysis of recorded industrial data from a glass melter process confirm.