Kernel adaptive filtering a comprehensive introduction

Online learning from a signal processing perspective 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.

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Bibliographic Details
Main Authors: Príncipe, J. C, Liu, Weifeng, Haykin, Simon S
Format: eBook Book
Language:English
Published: Hoboken, N.J Wiley 2010
WILEY
John Wiley & Sons, Incorporated
Wiley-Blackwell
John Wiley & Sons
Edition:1
Series:Adaptive and learning systems for signal processing, communication, and control
Subjects:
Adaptive filters
Kernel functions
Science
Waves & Wave Mechanics
ISBN:9780470447536, 0470447532, 0470608587, 9780470608586, 9780470608593, 0470608595
Online Access:Get full text
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Table of Contents:
  • Kernel adaptive filtering : a comprehensive introduction -- CONTENTS -- PREFACE -- ACKNOWLEDGMENTS -- NOTATION -- ABBREVIATIONS AND SYMBOLS -- 1. BACKGROUND AND PREVIEW -- 2. KERNEL LEAST-MEAN-SQUARE ALGORITHM -- 3. KERNEL AFFINE PROJECTION ALGORITHMS -- 4. KERNEL RECURSIVE LEAST-SQUARES ALGORITHM -- 5. EXTENDED KERNEL RECURSIVE LEAST-SQUARES ALGORITHM -- 6. DESIGNING SPARSE KERNEL ADAPTIVE FILTERS -- EPILOGUE -- APPENDIX A: MATHEMATICAL BACKGROUND -- APPENDIX B: APPROXIMATE LINEAR DEPENDENCY AND SYSTEM STABILITY -- REFERENCES -- INDEX
  • 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 Surprise Criterion -- 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
  • Intro -- KERNEL ADAPTIVE FILTERING -- CONTENTS -- 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-Squares Algorithm -- 4.3 Kernel Recursive Least-Squares Algorithm -- 4.4 Approximate Linear Dependency -- 4.5 Exponentially Weighted Kernel Recursive Least-Squares 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 LEAST-SQUARES 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