Kernel Adaptive Filtering: A Comprehensive IntroductionISBN: 9780470447536
240 pages
March 2010

There is increased interest in kernel learning algorithms in neural networks and a growing need for nonlinear adaptive algorithms in advanced signal processing, communications, and controls. Kernel Adaptive Filtering is the first book to present a comprehensive, unifying introduction to online learning algorithms in reproducing kernel Hilbert spaces. Based on research being conducted in the Computational NeuroEngineering Laboratory at the University of Florida and in the Cognitive Systems Laboratory at McMaster University, Ontario, Canada, this unique resource elevates the adaptive filtering theory to a new level, presenting a new design methodology of nonlinear adaptive filters.

Covers the kernel least mean squares algorithm, kernel affine projection algorithms, the kernel recursive least squares algorithm, the theory of Gaussian process regression, and the extended kernel recursive least squares algorithm

Presents a powerful modelselection method called maximum marginal likelihood

Addresses the principal bottleneck of kernel adaptive filters—their growing structure

Features twelve computeroriented experiments to reinforce the concepts, with MATLAB codes downloadable from the authors' Web site

Concludes each chapter with a summary of the state of the art and potential future directions for original research
Kernel Adaptive Filtering is ideal for engineers, computer scientists, and graduate students interested in nonlinear adaptive systems for online applications (applications where the data stream arrives one sample at a time and incremental optimal solutions are desirable). It is also a useful guide for those who look for nonlinear adaptive filtering methodologies to solve practical problems.
ACKNOWLEDGMENTS.
NOTATION.
ABBREVIATIONS AND SYMBOLS.
1 BACKGROUND AND PREVIEW.
1.1 Supervised, Sequential, and Active Learning.
1.2 Linear Adaptive Filters.
1.3 Nonlinear Adaptive Filters.
1.4 Reproducing Kernel Hilbert Spaces.
1.5 Kernel Adaptive Filters.
1.6 Summarizing Remarks.
Endnotes.
2 KERNEL LEASTMEANSQUARE ALGORITHM.
2.1 LeastMeanSquare Algorithm.
2.2 Kernel LeastMeanSquare Algorithm.
2.3 Kernel and Parameter Selection.
2.4 StepSize Parameter.
2.5 Novelty Criterion.
2.6 SelfRegularization Property of KLMS.
2.7 Leaky Kernel LeastMeanSquare Algorithm.
2.8 Normalized Kernel LeastMeanSquare Algorithm.
2.9 Kernel ADALINE.
2.10 Resource Allocating Networks.
2.11 Computer Experiments.
2.12 Conclusion.
Endnotes.
3 KERNEL AFFINE PROJECTION ALGORITHMS.
3.1 Affine Projection Algorithms.
3.2 Kernel Affine Projection Algorithms.
3.3 Error Reusing.
3.4 Sliding Window Gram Matrix Inversion.
3.5 Taxonomy for Related Algorithms.
3.6 Computer Experiments.
3.7 Conclusion.
Endnotes.
4 KERNEL RECURSIVE LEASTSQUARES ALGORITHM.
4.1 Recursive LeastSquares Algorithm.
4.2 Exponentially Weighted Recursive LeastSquares Algorithm.
4.3 Kernel Recursive LeastSquares Algorithm.
4.4 Approximate Linear Dependency.
4.5 Exponentially Weighted Kernel Recursive LeastSquares Algorithm.
4.6 Gaussian Processes for Linear Regression.
4.7 Gaussian Processes for Nonlinear Regression.
4.8 Bayesian Model Selection.
4.9 Computer Experiments.
4.10 Conclusion.
Endnotes.
5 EXTENDED KERNEL RECURSIVE LEASTSQUARES ALGORITHM.
5.1 Extended Recursive Least Squares Algorithm.
5.2 Exponentially Weighted Extended Recursive Least Squares Algorithm.
5.3 Extended Kernel Recursive Least Squares Algorithm.
5.4 EXKRLS for Tracking Models.
5.5 EXKRLS with Finite Rank Assumption.
5.6 Computer Experiments.
5.7 Conclusion.
Endnotes.
6 DESIGNING SPARSE KERNEL ADAPTIVE FILTERS.
6.1 Definition of Surprise.
6.2 A Review of Gaussian Process Regression.
6.3 Computing Surprise.
6.4 Kernel Recursive Least Squares with Surprise Criterion.
6.5 Kernel Least Mean Square with Surprise Criterion.
6.6 Kernel Affine Projection Algorithms with Surprise Criterion.
6.7 Computer Experiments.
6.8 Conclusion.
Endnotes.
EPILOGUE.
APPENDIX.
A MATHEMATICAL BACKGROUND.
A.1 Singular Value Decomposition.
A.2 PositiveDefinite Matrix.
A.3 Eigenvalue Decomposition.
A.4 Schur Complement.
A.5 Block Matrix Inverse.
A.6 Matrix Inversion Lemma.
A.7 Joint, Marginal, and Conditional Probability.
A.8 Normal Distribution.
A.9 Gradient Descent.
A.10 Newton's Method.
B. APPROXIMATE LINEAR DEPENDENCY AND SYSTEM STABILITY.
REFERENCES.
INDEX.
José C. Principe is Distinguished Professor of Electrical and Biomedical Engineering at the University of Florida, Gainesville, where he teaches advanced signal processing and artificial neural networks modeling. He is BellSouth Professor and founder and Director of the University of Florida Computational NeuroEngineering Laboratory.
Simon Haykin is Distinguished University Professor at McMaster University, Canada.He is worldrenowned for his contributions to adaptive filtering applied to radar and communications. Haykin's current research passion is focused on cognitive dynamic systems, including applications on cognitive radio and cognitive radar.
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