Commenced in January 2007
Paper Count: 31830
Online Prediction of Nonlinear Signal Processing Problems Based Kernel Adaptive Filtering
Abstract:This paper presents two of the most knowing kernel adaptive filtering (KAF) approaches, the kernel least mean squares and the kernel recursive least squares, in order to predict a new output of nonlinear signal processing. Both of these methods implement a nonlinear transfer function using kernel methods in a particular space named reproducing kernel Hilbert space (RKHS) where the model is a linear combination of kernel functions applied to transform the observed data from the input space to a high dimensional feature space of vectors, this idea known as the kernel trick. Then KAF is the developing filters in RKHS. We use two nonlinear signal processing problems, Mackey Glass chaotic time series prediction and nonlinear channel equalization to figure the performance of the approaches presented and finally to result which of them is the adapted one.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1131725Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 720
 T. Hofmann, B. Scholkopf, and A. J. Smola, “A Tutorial Review of RKHS Methods in Machine Learning,” 2005.
 B. Scholkopf and A. J. Smola, Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. Cambridge, MA, USA: MIT Press, 2001.
 B. Sch¨olkopf, A. Smola, and K.-R. M¨uller, “Nonlinear component analysis as a kernel eigenvalue problem,” Neural Comput., vol. 10, no. 5, pp. 1299–1319, Jul 1998.
 W. Liu, J. C. Principe, and S. Haykin, Kernel Adaptive Filtering: A Comprehensive Introduction, 1st ed. Wiley Publishing, 2010.
 W. Liu, P. P. Pokharel, and J. C. Principe, “The kernel least-mean-square algorithm,” IEEE Transactions on Signal Processing, vol. 56, no. 2, pp. 543–554, 2008.
 Y. Engel, S. Mannor, and R. Meir, “The kernel recursive least-squares algorithm,” IEEE Transactions on Signal Processing, vol. 52, no. 8, pp. 2275–2285, 2004.
 K. Fukumizu, Elements of Positive Definite Kernel and Reproducing Kernel Hilbert Space, 1st ed., Institute of Statistical Mathematics, ROIS, Department of Statistical Science, Graduate University for Advanced Studies, 4 2008.