Determining the optimal kernel parameter in KPCA based on sample reconstruction

Kernel principal component analysis (KPCA) is a statistical analysis procedure that has been applied successfully for nonlinear process monitoring. However, it is still a challenging problem to determine the optimal kernel parameter during the KPCA modeling, which is very significant for both modeling and monitoring processes. In this paper, a new approach based on sample reconstruction is proposed to evaluate the KPCA modeling and determine the kernel parameter. By using artificial neural network (ANN), samples are reconstructed in the input space from the scores in the KPCA space. Then, an index named relative reconstruction error (RRE) is defined in order to search for the optimal parameter. A numerical case study is given to demonstrate the effectiveness of the proposed approach.