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E-raamat: Kernel Adaptive Filtering: A Comprehensive Introduction

(Hewlett Packard), (University of Florida, Gainesville, FL), (McMaster University, Canada)
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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. 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 Neuro-Engineering 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 model-selection method called maximum marginal likelihood



Addresses the principal bottleneck of kernel adaptive filterstheir growing structure



Features twelve computer-oriented 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.
Preface xi
Acknowledgments xv
Notation xvii
Abbreviations and Symbols xix
Background and Preview
1(26)
Supervised, Sequential, and Active Learning
1(2)
Linear Adaptive Filters
3(7)
Nonlinear Adaptive Filters
10(2)
Reproducing Kernel Hilbert Spaces
12(4)
Kernel Adaptive Filters
16(4)
Summarizing Remarks
20(7)
Endnotes
21(6)
Kernel Least-Mean-Square Algorithm
27(42)
Least-Mean-Square Algorithm
28(3)
Kernel Least-Mean-Square Algorithm
31(3)
Kernel and Parameter Selection
34(3)
Step-Size Parameter
37(1)
Novelty Criterion
38(2)
Self-Regularization Property of KLMS
40(8)
Leaky Kernel Least-Mean-Square Algorithm
48(1)
Normalized Kernel Least-Mean-Square Algorithm
48(1)
Kernel ADALINE
49(4)
Resource Allocating Networks
53(2)
Computer Experiments
55(8)
Conclusion
63(6)
Endnotes
65(4)
Kernel Affine Projection Algorithms
69(25)
Affine Projection Algorithms
70(2)
Kernel Affine Projection Algorithms
72(5)
Error Reusing
77(1)
Sliding Window Gram Matrix Inversion
78(1)
Taxonomy for Related Algorithms
78(2)
Computer Experiments
80(9)
Conclusion
89(5)
Endnotes
91(3)
Kernel Recursive Least-Squares Algorithm
94(30)
Recursive Least-Squares Algorithm
94(3)
Exponentially Weighted Recursive Least-Squares Algorithm
97(1)
Kernel Recursive Least-Squares Algorithm
98(4)
Approximate Linear Dependency
102(1)
Exponentially Weighted Kernel Recursive Least-Squares Algorithm
103(2)
Gaussian Processes for Linear Regression
105(3)
Gaussian Processes for Nonlinear Regression
108(3)
Bayesian Model Selection
111(3)
Computer Experiments
114(5)
Conclusion
119(5)
Endnotes
120(4)
Extended Kernel Recursive Least-Squares Algorithm
124(28)
Extended Recursive Least Squares Algorithm
125(3)
Exponentially Weighted Extended Recursive Least Squares Algorithm
128(1)
Extended Kernel Recursive Least Squares Algorithm
129(2)
Ex-Krls for Tracking Models
131(6)
Ex-Krls with Finite Rank Assumption
137(4)
Computer Experiments
141(9)
Conclusion
150(2)
Endnotes
151(1)
Designing Sparse Kernel Adaptive Filters
152(25)
Definition of Surprise
152(2)
A Review of Gaussian Process Regression
154(2)
Computing Surprise
156(3)
Kernel Recursive Least Squares with Surprise Criterion
159(1)
Kernel Least Mean Square with Surprise Criterion
160(1)
Kernel Affine Projection Algorithms with Surprise Criterion
161(1)
Computer Experiments
162(11)
Conclusion
173(2)
Endnotes
174(1)
Epilogue
175(2)
Appendix
177(16)
Mathematical Background
177(9)
Singular Value Decomposition
177(2)
Positive-Definite Matrix
179(1)
Eigenvalue Decomposition
179(2)
Schur Complement
181(1)
Block Matrix Inverse
181(1)
Matrix Inversion Lemma
182(1)
Joint, Marginal, and Conditional Probability
182(1)
Normal Distribution
183(1)
Gradient Descent
184(1)
Newton's Method
184(2)
Approximate Linear Dependency and System Stability
186(7)
References 193(11)
Index 204
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. 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 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.