Kernel Adaptive Filtering
A Comprehensive Introduction
Published on 20. September 2011
240 pages
978-1-118-21121-2 (ISBN)
Description
Online learning from a signal processing perspective
There is increased interest in kernel learning algorithms inneural networks and a growing need for nonlinear adaptivealgorithms in advanced signal processing, communications, andcontrols. Kernel Adaptive Filtering is the first book topresent a comprehensive, unifying introduction to online learningalgorithms in reproducing kernel Hilbert spaces. Based on researchbeing conducted in the Computational Neuro-Engineering Laboratoryat the University of Florida and in the Cognitive SystemsLaboratory at McMaster University, Ontario, Canada, this uniqueresource elevates the adaptive filtering theory to a new level,presenting a new design methodology of nonlinear adaptivefilters.
* Covers the kernel least mean squares algorithm, kernel affineprojection algorithms, the kernel recursive least squaresalgorithm, the theory of Gaussian process regression, and theextended kernel recursive least squares algorithm
* Presents a powerful model-selection method called maximummarginal likelihood
* Addresses the principal bottleneck of kernel adaptivefilters--their growing structure
* Features twelve computer-oriented experiments to reinforce theconcepts, with MATLAB codes downloadable from the authors' Website
* Concludes each chapter with a summary of the state of the artand potential future directions for original research
Kernel Adaptive Filtering is ideal for engineers,computer scientists, and graduate students interested in nonlinearadaptive systems for online applications (applications where thedata stream arrives one sample at a time and incremental optimalsolutions are desirable). It is also a useful guide for those wholook for nonlinear adaptive filtering methodologies to solvepractical problems.
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03/2010
Wiley
€126.50
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Weifeng Liu | Jose C. Principe | Simon Haykin
Kernel Adaptive Filtering - A Comprehensive Introduction
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03/2010
Wiley
€121.44
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Persons
Weifeng Liu, PhD, is a senior engineer of the DemandForecasting Team at Amazon.com Inc. His research interests includekernel adaptive filtering, online active learning, and solvingreal-life large-scale data mining problems.
José C. Principe is Distinguished Professor ofElectrical and Biomedical Engineering at the University of Florida,Gainesville, where he teaches advanced signal processing andartificial neural networks modeling. He is BellSouth Professor andfounder and Director of the University of Florida ComputationalNeuro-Engineering Laboratory.
Simon Haykin is Distinguished University Professor atMcMaster University, Canada.He is world-renowned for hiscontributions to adaptive filtering applied to radar andcommunications. Haykin's current research passion is focused oncognitive dynamic systems, including applications on cognitiveradio and cognitive radar.
Content
PREFACE.
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 LEAST-MEAN-SQUARE ALGORITHM.
2.1 Least-Mean-Square Algorithm.
2.2 Kernel Least-Mean-Square Algorithm.
2.3 Kernel and Parameter Selection.
2.4 Step-Size Parameter.
2.5 Novelty Criterion.
2.6 Self-Regularization Property of KLMS.
2.7 Leaky Kernel Least-Mean-Square Algorithm.
2.8 Normalized Kernel Least-Mean-Square 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 LEAST-SQUARES ALGORITHM.
4.1 Recursive Least-Squares Algorithm.
4.2 Exponentially Weighted Recursive Least-SquaresAlgorithm.
4.3 Kernel Recursive Least-Squares Algorithm.
4.4 Approximate Linear Dependency.
4.5 Exponentially Weighted Kernel Recursive Least-SquaresAlgorithm.
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 LEAST-SQUARES ALGORITHM.
5.1 Extended Recursive Least Squares Algorithm.
5.2 Exponentially Weighted Extended Recursive Least SquaresAlgorithm.
5.3 Extended Kernel Recursive Least Squares Algorithm.
5.4 EX-KRLS for Tracking Models.
5.5 EX-KRLS 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 SurpriseCriterion.
6.7 Computer Experiments.
6.8 Conclusion.
Endnotes.
EPILOGUE.
APPENDIX.
A MATHEMATICAL BACKGROUND.
A.1 Singular Value Decomposition.
A.2 Positive-Definite 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.
