Kernel Adaptive Filtering A Comprehensive Introduction

by ; ; ;
Edition: 1st
Format: Hardcover
Pub. Date: 2010-03-01
Publisher(s): Wiley
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Summary

Reproducing kernel Hilbert spaces is a topic of great current interest for applications in signal processing, communications, and controls The first book to explain real-time learning algorithms in reproducing kernel Hilbert spaces, On-Line Kernel Learning includes simulations that illustrate the ideas discussed and demonstrate their applicability as well as MATLAB codes for simulations. This book is ideal for professionals and graduate students interested in nonlinear adaptive systems for on-line applications.

Author Biography

Weifeng Liu, PhD, is a senior engineer of the Demand Forecasting Team at Amazon.com Inc. His research interests include kernel adaptive filtering, online active learning, and solving real-life large-scale data mining problems. Jos C. Prncipe 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 Neuro-Engineering Laboratory. Simon Haykin is Distinguished University Professor at McMaster University, Canada. He is world-renowned 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.

Table of Contents

Prefacep. xi
Acknowledgmentsp. xv
Notationp. xvii
Abbreviations and Symbolsp. xix
Background and Previewp. 1
Supervised, Sequential, and Active Learningp. 1
Linear Adaptive Filtersp. 3
Nonlinear Adaptive Filtersp. 10
Reproducing Kernel Hilbert Spacesp. 12
Kernel Adaptive Filtersp. 16
Summarizing Remarksp. 20
Endnotesp. 21
Kernel Least-Mean-Square Algorithmp. 27
Least-Mean-Square Algorithmp. 28
Kernel Least-Mean-Square Algorithmp. 31
Kernel and Parameter Selectionp. 34
Step-Size Parameterp. 37
Novelty Criterionp. 38
Self-Regularization Property of KLMSp. 40
Leaky Kernel Least-Mean-Square Algorithmp. 48
Normalized Kernel Least-Mean-Square Algorithmp. 48
Kernel ADALINEp. 49
Resource Allocating Networksp. 53
Computer Experimentsp. 55
Conclusionp. 63
Endnotesp. 65
Kernel Affine Projection Algorithmsp. 69
Affine Projection Algorithmsp. 70
Kernel Affine Projection Algorithmsp. 72
Error Reusingp. 77
Sliding Window Gram Matrix Inversionp. 78
Taxonomy for Related Algorithmsp. 78
Computer Experimentsp. 80
Conclusionp. 89
Endnotesp. 91
Kernel Recursive Least-Squares Algorithmp. 94
Recursive Least-Squares Algorithmp. 94
Exponentially Weighted Recursive Least-Squares Algorithmp. 97
Kernel Recursive Least-Squares Algorithmp. 98
Approximate Linear Dependencyp. 102
Exponentially Weighted Kernel Recursive Least-Squares Algorithmp. 103
Gaussian Processes for Linear Regressionp. 105
Gaussian Processes for Nonlinear Regressionp. 108
Bayesian Model Selectionp. 111
Computer Experimentsp. 114
Conclusionp. 119
Endnotesp. 120
Extended Kernel Recursive Least-Squares Algorithmp. 124
Extended Recursive Least Squares Algorithmp. 125
Exponentially Weighted Extended Recursive Least Squares Algorithmp. 128
Extended Kernel Recursive Least Squares Algorithmp. 129
EX-KRLS for Tracking Modelsp. 131
EX-KRLS with Finite Rank Assumptionp. 137
Computer Experimentsp. 141
Conclusionp. 150
Endnotesp. 151
Definition of Surprisep. 152
A Review of Gaussian Process Regressionp. 154
Computing Surprisep. 156
Kernel Recursive Least Squares with Surprise Criterionp. 159
Kernel Least Mean Square with Surprise Criterionp. 160
Kernel Affine Projection Algorithms with Surprise Criterionp. 161
Computer Experimentsp. 162
Conclusionp. 173
Endnotesp. 174
Epiloguep. 175
Appendixp. 177
Mathematical Backgroundp. 177
Singular Value Decompositionp. 177
Positive-Definite Matrixp. 179
Eigenvalue Decompositionp. 179
Schur Complementp. 181
Block Matrix Inversep. 181
Matrix Inversion Lemmap. 182
Joint, Marginal, and Conditional Probabilityp. 182
Normal Distributionp. 183
Gradient Descentp. 184
Newton's Methodp. 184
Approximate Linear Dependency and System Stabilityp. 186
Referencesp. 193
Indexp. 204
Table of Contents provided by Ingram. All Rights Reserved.

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