Adaptive kernel principal components tracking

Abstract

Adaptive online algorithms for simultaneously extracting nonlinear eigenvectors of kernel principal component analysis (KPCA) are developed. KPCA needs all the observed samples to represent basis functions, and the same scale of eigenvalue problem as the number of samples should be solved. This paper reformulates KPCA and deduces an expression in the Euclidean space, where an algorithm for tracking generalized eigenvectors is applicable. The developed algorithm here is least mean squares (LMS)-type and recursive least squares (RLS)-type. Numerical example is then illustrated to support the analysis.