Kernel Affine Projection Algorithms

The combination of the famed kernel trick and affine projection algorithms (APA) yields powerful nonlinear extensions, named collectively here KAPA. This paper is a follow-up study of the recently introduced kernel leastmean-square algorithm (KLMS). KAPA inherits the simplicity and online nature of KLMS while reducing its gradient noise, boosting performance. More interestingly, it provides a unifying model for several neural network techniques, including kernel least-mean-square algorithms, kernel adaline, sliding-window kernel recursive-least-squares (KRLS) and regularization networks. Therefore, many insights can be gained into the basic relations among them and the trade-off between computation complexity and performance. Several simulations illustrate its wide applicability. Index Terms Affine projection algorithms, kernel methods.