EURASIP Journal on Advances in Signal Processing
Volume 2008 (2008), Article ID 784292, 12 pages
doi:10.1155/2008/784292
Research Article

Kernel Affine Projection Algorithms

Weifeng Liu and José C. Príncipe

Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611, USA

Received 27 September 2007; Revised 23 January 2008; Accepted 21 February 2008

Academic Editor: Aníbal Figueiras-Vidal

Copyright © 2008 Weifeng Liu and José C. Príncipe. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The combination of the famed kernel trick and affine projection algorithms (APAs) yields powerful nonlinear extensions, named collectively here, KAPA. This paper is a follow-up study of the recently introduced kernel least-mean-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 tradeoff between computation complexity and performance. Several simulations illustrate its wide applicability.