Kernel relative principal component analysis for pattern recognition

Principal component analysis (PCA) is widely used in signal processing, pattern recognition, etc. PCA was extended to the relative PCA (RPCA). RPCA provides principal components of a signal while suppressing effects of other signals. PCA was also extended to the kernel PCA (KPCA). By using a mapping from the original space to a higher dimensional space and its kernel, we can perform PCA in the higher dimensional space. In this paper, we propose the kernel RPCA (KRPCA) and give its solution. Similarly to KPCA, the order of matrices that we should calculate for the solution is the number of samples, that is 'kernel trick'. We provide experimental results of an application to pattern recognition in order to show the advantages of KRPCA over KPCA.