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Kernel Affine Projection Algorithms


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.

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Correspondence to Weifeng Liu.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Liu, W., Príncipe, J.C. Kernel Affine Projection Algorithms. EURASIP J. Adv. Signal Process. 2008, 784292 (2008).

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  • Neural Network
  • Information Technology
  • Quantum Information
  • Unify Model
  • Computation Complexity