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Part I: Fundamentals and Basic Elements
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Part I: Fundamentals and Basic Elements
by Gustau Camps-Valls, Jordi Muñoz-Marí, Manel Martínez-Ramón, José Luis Rojo-Álvar
Digital Signal Processing with Kernel Methods
Cover
Title Page
About the Authors
Preface
Why Did We Write This Book?
Structure and Contents
Acknowledgements
List of Abbreviations
Part I: Fundamentals and Basic Elements
1 From Signal Processing to Machine Learning
1.1 A New Science is Born: Signal Processing
1.2 From Analog to Digital Signal Processing
1.3 Digital Signal Processing Meets Machine Learning
1.4 Recent Machine Learning in Digital Signal Processing
2 Introduction to Digital Signal Processing
2.1 Outline of the Signal Processing Field
2.2 From Time–Frequency to Compressed Sensing
2.3 Multidimensional Signals and Systems
2.4 Spectral Analysis on Manifolds
2.5 Tutorials and Application Examples
2.6 Questions and Problems
3 Signal Processing Models
3.1 Introduction
3.2 Vector Spaces, Basis, and Signal Models
3.3 Digital Signal Processing Models
3.4 Tutorials and Application Examples
3.5 Questions and Problems
3.A MATLAB simpleInterp Toolbox Structure
4 Kernel Functions and Reproducing Kernel Hilbert Spaces
4.1 Introduction
4.2 Kernel Functions and Mappings
4.3 Kernel Properties
4.4 Constructing Kernel Functions
4.5 Complex Reproducing Kernel in Hilbert Spaces
4.6 Support Vector Machine Elements for Regression and Estimation
4.7 Tutorials and Application Examples
4.8 Concluding Remarks
4.9 Questions and Problems
Part II: Function Approximation and Adaptive Filtering
5 A Support Vector Machine Signal Estimation Framework
5.1 Introduction
5.2 A Framework for Support Vector Machine Signal Estimation
5.3 Primal Signal Models for Support Vector Machine Signal Processing
5.4 Tutorials and Application Examples
5.5 Questions and Problems
6 Reproducing Kernel Hilbert Space Models for Signal Processing
6.1 Introduction
6.2 Reproducing Kernel Hilbert Space Signal Models
6.3 Tutorials and Application Examples
6.4 Questions and Problems
7 Dual Signal Models for Signal Processing
7.1 Introduction
7.2 Dual Signal Model Elements
7.3 Dual Signal Model Instantiations
7.4 Tutorials and Application Examples
7.5 Questions and Problems
8 Advances in Kernel Regression and Function Approximation
8.1 Introduction
8.2 Kernel‐Based Regression Methods
8.3 Bayesian Nonparametric Kernel Regression Models
8.4 Tutorials and Application Examples
8.5 Concluding Remarks
8.6 Questions and Problems
9 Adaptive Kernel Learning for Signal Processing
9.1 Introduction
9.2 Linear Adaptive Filtering
9.3 Kernel Adaptive Filtering
9.4 Kernel Least Mean Squares
9.5 Kernel Recursive Least Squares
9.6 Explicit Recursivity for Adaptive Kernel Models
9.7 Online Sparsification with Kernels
9.8 Probabilistic Approaches to Kernel Adaptive Filtering
9.9 Further Reading
9.10 Tutorials and Application Examples
9.11 Questions and Problems
Part III: Classification, Detection, and Feature Extraction
10 Support Vector Machine and Kernel Classification Algorithms
10.1 Introduction
10.2 Support Vector Machine and Kernel Classifiers
10.3 Advances in Kernel‐Based Classification
10.4 Large‐Scale Support Vector Machines
10.5 Tutorials and Application Examples
10.6 Concluding Remarks
10.7 Questions and Problems
11 Clustering and Anomaly Detection with Kernels
11.1 Introduction
11.2 Kernel Clustering
11.3 Domain Description Via Support Vectors
11.4 Kernel Matched Subspace Detectors
11.5 Kernel Anomaly Change Detection
11.6 Hypothesis Testing with Kernels
11.7 Tutorials and Application Examples
11.8 Concluding Remarks
11.9 Questions and Problems
12 Kernel Feature Extraction in Signal Processing
12.1 Introduction
12.2 Multivariate Analysis in Reproducing Kernel Hilbert Spaces
12.3 Feature Extraction with Kernel Dependence Estimates
12.4 Extensions for Large‐Scale and Semi‐supervised Problems
12.5 Domain Adaptation with Kernels
12.6 Concluding Remarks
12.7 Questions and Problems
References
Index
End User License Agreement
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1 From Signal Processing to Machine Learning
Part I
Fundamentals and Basic Elements
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