Digital Signal Processing with Kernel Methods
<p><b> A realistic and comprehensive review of joint approaches to machine learning and signal processing algorithms, with application to communications, multimedia, and biomedical engineering systems </b> <p><i> Digital Signal Pr...
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| Language: | English |
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Hoboken, N.J
Wiley
2018
Wiley/IEEE Press John Wiley & Sons, Incorporated Wiley-IEEE Press Wiley-Blackwell John Wiley & Sons (UK) |
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| ISBN: | 9781118611791, 1118611799 |
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| Abstract | <p><b> A realistic and comprehensive review of joint approaches to machine learning and signal processing algorithms, with application to communications, multimedia, and biomedical engineering systems </b> <p><i> Digital Signal Processing with Kernel Methods</i> reviews the milestones in the mixing of classical digital signal processing models and advanced kernel machines statistical learning tools. It explains the fundamental concepts from both fields of machine learning and signal processing so that readers can quickly get up to speed in order to begin developing the concepts and application software in their own research. <p><i> Digital Signal Processing with Kernel Methods</i> provides a comprehensive overview of kernel methods in signal processing, without restriction to any application field. It also offers example applications and detailed benchmarking experiments with real and synthetic datasets throughout. Readers can find further worked examples with Matlab source code on a website developed by the authors. <ul> <li>Presents the necessary basic ideas from both digital signal processing and machine learning concepts</li> <li>Reviews the state-of-the-art in SVM algorithms for classification and detection problems in the context of signal processing</li> <li>Surveys advances in kernel signal processing beyond SVM algorithms to present other highly relevant kernel methods for digital signal processing</li> </ul> <br> <p> An excellent book for signal processing researchers and practitioners, <i>Digital Signal Processing with Kernel Methods</i> will also appeal to those involved in machine learning and pattern recognition. |
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| AbstractList | Offering example applications and detailed benchmarking experiments with real and synthetic datasets throughout, this book provides a comprehensive overview of kernel methods in signal processing, without restriction to any application field. -- <p><b> A realistic and comprehensive review of joint approaches to machine learning and signal processing algorithms, with application to communications, multimedia, and biomedical engineering systems </b> <p><i> Digital Signal Processing with Kernel Methods</i> reviews the milestones in the mixing of classical digital signal processing models and advanced kernel machines statistical learning tools. It explains the fundamental concepts from both fields of machine learning and signal processing so that readers can quickly get up to speed in order to begin developing the concepts and application software in their own research. <p><i> Digital Signal Processing with Kernel Methods</i> provides a comprehensive overview of kernel methods in signal processing, without restriction to any application field. It also offers example applications and detailed benchmarking experiments with real and synthetic datasets throughout. Readers can find further worked examples with Matlab source code on a website developed by the authors. <ul> <li>Presents the necessary basic ideas from both digital signal processing and machine learning concepts</li> <li>Reviews the state-of-the-art in SVM algorithms for classification and detection problems in the context of signal processing</li> <li>Surveys advances in kernel signal processing beyond SVM algorithms to present other highly relevant kernel methods for digital signal processing</li> </ul> <br> <p> An excellent book for signal processing researchers and practitioners, <i>Digital Signal Processing with Kernel Methods</i> will also appeal to those involved in machine learning and pattern recognition. A realistic and comprehensive review of joint approaches to machine learning and signal processing algorithms, with application to communications, multimedia, and biomedical engineering systems Digital Signal Processing with Kernel Methods reviews the milestones in the mixing of classical digital signal processing models and advanced kernel machines statistical learning tools. It explains the fundamental concepts from both fields of machine learning and signal processing so that readers can quickly get up to speed in order to begin developing the concepts and application software in their own research. Digital Signal Processing with Kernel Methods provides a comprehensive overview of kernel methods in signal processing, without restriction to any application field. It also offers example applications and detailed benchmarking experiments with real and synthetic datasets throughout. Readers can find further worked examples with Matlab source code on a website developed by the authors: http://github.com/DSPKM - Presents the necessary basic ideas from both digital signal processing and machine learning concepts - Reviews the state-of-the-art in SVM algorithms for classification and detection problems in the context of signal processing - Surveys advances in kernel signal processing beyond SVM algorithms to present other highly relevant kernel methods for digital signal processing An excellent book for signal processing researchers and practitioners, Digital Signal Processing with Kernel Methods will also appeal to those involved in machine learning and pattern recognition. A realistic and comprehensive review of joint approaches to machine learning and signal processing algorithms, with application to communications, multimedia, and biomedical engineering systemsDigital Signal Processing with Kernel Methods reviews the milestones in the mixing of classical digital signal processing models and advanced kernel machines statistical learning tools. It explains the fundamental concepts from both fields of machine learning and signal processing so that readers can quickly get up to speed in order to begin developing the concepts and application software in their own research.Digital Signal Processing with Kernel Methods provides a comprehensive overview of kernel methods in signal processing, without restriction to any application field. It also offers example applications and detailed benchmarking experiments with real and synthetic datasets throughout. Readers can find further worked examples with Matlab source code on a website developed by the authors. Presents the necessary basic ideas from both digital signal processing and machine learning conceptsReviews the state-of-the-art in SVM algorithms for classification and detection problems in the context of signal processingSurveys advances in kernel signal processing beyond SVM algorithms to present other highly relevant kernel methods for digital signal processingAn excellent book for signal processing researchers and practitioners, Digital Signal Processing with Kernel Methods will also appeal to those involved in machine learning and pattern recognition. |
| Author | Mu&ntilde;oz-Mar&iacute, Jordi Rojo-Álvarez, José Luis Camps-Valls, Gustau Martínez-Ramón, Manel |
| Author_xml | – sequence: 1 givenname: José Luis surname: Rojo-Álvarez fullname: Rojo-Álvarez, José Luis – sequence: 2 givenname: Manel surname: Martínez-Ramón fullname: Martínez-Ramón, Manel – sequence: 3 givenname: Jordi surname: Mu&ntilde;oz-Mar&iacute fullname: Mu&ntilde;oz-Mar&iacute, Jordi – sequence: 4 givenname: Gustau surname: Camps-Valls fullname: Camps-Valls, Gustau organization: University of Valencia, Spain |
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| Copyright | 2018 Wiley |
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| DOI | 10.1002/9781118705810 |
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| Keywords | signal processing for multimedia lvarez advanced kernel machines Gustau Camps-Valls microprocessor electronic systems digital communications circuits and linear systems signal processing for communications digital signal processing Digital Signal Processing with Kernel Methods oz-Mar&iacute image processing brain imaging statistical learning statistical learning tools statistical learning theory signal processing algorithms signal processing in communications Jordi Mu&ntilde signal processing for biomedical engineering systems machine learning kernel signal processing SVM algorithms Luis Rojo-&Aacute Manel Mart&iacute n introduction to programmable logical devices digital signal processing models cardiac signal processing digital electronic systems complex system modelling nez-Ram&oacute Jos&eacute |
| LCCN | 2017033418 |
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| Notes | Includes bibliographical references (p. 589-630) and index "With website"--P. [1] of cover |
| OCLC | 1017489244 |
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| Publisher | Wiley Wiley/IEEE Press John Wiley & Sons, Incorporated Wiley-IEEE Press Wiley-Blackwell John Wiley & Sons (UK) |
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| Snippet | <p><b> A realistic and comprehensive review of joint approaches to machine learning and signal processing algorithms, with application to... A realistic and comprehensive review of joint approaches to machine learning and signal processing algorithms, with application to communications, multimedia,... Offering example applications and detailed benchmarking experiments with real and synthetic datasets throughout, this book provides a comprehensive overview of... |
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| SubjectTerms | Bioengineering Communication, Networking and Broadcast Technologies Components, Circuits, Devices and Systems Computing and Processing Digital techniques Fields, Waves and Electromagnetics Machine learning Signal processing Signal processing -- Digital techniques Signal Processing and Analysis |
| SubjectTermsDisplay | Electronic books. Signal processing -- Digital techniques. |
| TableOfContents | About the Authors xiii Preface xvii Acknowledgements xxi List of Abbreviations xxiii Part I Fundamentals and Basic Elements 1 1 From Signal Processing to Machine Learning 3 1.1 A New Science is Born: Signal Processing 3 1.1.1 Signal Processing Before Being Coined 3 1.1.2 1948: Birth of the Information Age 4 1.1.3 1950s: Audio Engineering Catalyzes Signal Processing 4 1.2 From Analog to Digital Signal Processing 5 1.2.1 1960s: Digital Signal Processing Begins 5 1.2.2 1970s: Digital Signal Processing Becomes Popular 6 1.2.3 1980s: Silicon Meets Digital Signal Processing 6 1.3 Digital Signal Processing Meets Machine Learning 7 1.3.1 1990s: New Application Areas 7 1.3.2 1990s: Neural Networks, Fuzzy Logic, and Genetic Optimization 7 1.4 Recent Machine Learning in Digital Signal Processing 8 1.4.1 Traditional Signal Assumptions Are No Longer Valid 8 1.4.2 Encoding Prior Knowledge 8 1.4.3 Learning and Knowledge from Data 9 1.4.4 From Machine Learning to Digital Signal Processing 9 1.4.5 From Digital Signal Processing to Machine Learning 10 2 Introduction to Digital Signal Processing 13 2.1 Outline of the Signal Processing Field 13 2.1.1 Fundamentals on Signals and Systems 14 2.1.2 Digital Filtering 21 2.1.3 Spectral Analysis 24 2.1.4 Deconvolution 28 2.1.5 Interpolation 30 2.1.6 System Identi&#64257;cation 31 2.1.7 Blind Source Separation 36 2.2.3 Sparsity, Compressed Sensing, and Dictionary Learning 44 2.3 Multidimensional Signals and Systems 48 2.3.1 Multidimensional Signals 49 2.3.2 Multidimensional Systems 51 2.4 Spectral Analysis on Manifolds 52 2.4.1 Theoretical Fundamentals 52 2.4.2 Laplacian Matrices 54 2.5 Tutorials and Application Examples 57 2.5.1 Real and Complex Signal Processing and Representations 57 2.5.2 Convolution, Fourier Transform, and Spectrum 63 2.5.3 Continuous-Time Signals and Systems 67 2.5.4 Filtering Cardiac Signals 70 2.5.5 Nonparametric Spectrum Estimation 74 2.5.6 Parametric Spectrum Estimation 77 2.5.7 Source Separation 81 2.5.8 Time&ndash;Frequency Representations and Wavelets 84 2.5.9 Examples for Spectral Analysis on Manifolds 87 2.6 Questions and Problems 94 3 Signal Processing Models 97 3.1 Introduction 97 3.2 Vector Spaces, Basis, and Signal Models 98 3.2.1 Basic Operations for Vectors 98 3.2.2 Vector Spaces 100 3.2.3 Hilbert Spaces 101 3.2.4 Signal Models 102 3.2.5 Complex Signal Models 104 3.2.6 Standard Noise Models in Digital Signal Processing 105 3.2.7 The Role of the Cost Function 107 3.2.8 The Role of the Regularizer 109 3.3 Digital Signal Processing Models 111 3.3.1 Sinusoidal Signal Models 112 3.3.2 System Identi&#64257;cation Signal Models 113 3.3.3 Sinc Interpolation Models 116 3.3.4 Sparse Deconvolution 120 3.3.5 Array Processing 121 3.4 Tutorials and Application Examples 122 3.4.1 Examples of Noise Models 123 3.4.2 Autoregressive Exogenous System Identi&#64257;cation Models 132 3.4.3 Nonlinear System Identi&#64257;cation Using Volterra Models 138 3.4.4 Sinusoidal Signal Models 140 3.4.5 Sinc-based Interpolation 144 3.4.6 Sparse Deconvolution 152 3.4.7 Array Processing 157 3.5 Questions and Problems 160 3.A MATLABsimpleInterp Toolbox Structure 161 4 Kernel Functions and Reproducing Kernel Hilbert Spaces 165 4.1 Introduction 165 4.2 Kernel Functions and Mappings 169 4.2.1 Measuring Similarity with Kernels 169 4.2.2 Positive-De&#64257;nite Kernels 169 4.2.3 Reproducing Kernel in Hilbert Space and Reproducing Property 170 4.2.4 Mercer&rsquo;s Theorem 173 4.3 Kernel Properties 174 4.3.1 Tikhonov&rsquo;s Regularization 175 4.3.2 Representer Theorem and Regularization Properties 176 4.3.3 Basic Operations with Kernels 178 4.4 Constructing Kernel Functions 179 4.4.1 Standard Kernels 179 4.4.2 Properties of Kernels 180 4.4.3 Engineering Signal Processing Kernels 181 4.5 Complex Reproducing Kernel in Hilbert Spaces 184 4.6 Support Vector Machine Elements for Regression and Estimation 186 4.6.1 Support Vector Regression Signal Model and Cost Function 186 4.6.2 Minimizing Functional 187 4.7 Tutorials and Application Examples 191 4.7.1 Kernel Calculations and Kernel Matrices 191 4.7.2 Basic Operations with Kernels 194 4.7.3 Constructing Kernels 197 4.7.4 Complex Kernels 199 4.7.5 Application Example for Support Vector Regression Elements 202 4.8 Concluding Remarks 205 4.9 Questions and Problems 205 Part II Function Approximation and Adaptive Filtering 209 5 A Support Vector Machine Signal Estimation Framework 211 5.1 Introduction 211 5.2 A Framework for Support Vector Machine Signal Estimation 213 5.3 Primal Signal Models for Support Vector Machine Signal Processing 216 5.3.1 Nonparametric Spectrum and System Identi&#64257;cation 218 5.3.2 Orthogonal Frequency Division Multiplexing Digital Communications 220 5.3.3 Convolutional Signal Models 222 5.3.4 Array Processing 225 5.4 Tutorials and Application Examples 227 5.4.1 Nonparametric Spectral Analysis with Primal Signal Models 227 5.4.2 System Identi&#64257;cation with Primal Signal Model &#55349;&#57086;-&#64257;lter 228 5.4.3 Parametric Spectral Density Estimation with Primal Signal Models 230 5.4.4 Temporal Reference Array Processing with Primal Signal Models 231 5.4.5 Sinc Interpolation with Primal Signal Models 233 6 Reproducing Kernel Hilbert Space Models for Signal Processing 241 6.1 Introduction 241 6.2 Reproducing Kernel Hilbert Space Signal Models 242 6.2.1 Kernel Autoregressive Exogenous Identi&#64257;cation 244 6.2.2&nbsp; Kernel Finite Impulse Response and the &#55349;&#57086;-Filter 247 6.2.3 Kernel Array Processing with Spatial Reference 248 6.2.4 Kernel Semiparametric Regression 249 6.3 Tutorials and Application Examples 258 6.3.1 Nonlinear System Identi&#64257;cation with Support Vector Machine&ndash;Autoregressive and Moving Average 258 6.3.2 Nonlinear System Identi&#64257;cation with the &#55349;&#57086;-&#64257;lter 260 6.3.3 Electric Network Modeling with Semiparametric Regression 264 6.3.4 Promotional Data 272 6.3.5 Spatial and Temporal Antenna Array Kernel Processing 275 6.4 Questions and Problems 279 7 Dual Signal Models for Signal Processing 281 7.1 Introduction 281 7.2 Dual Signal Model Elements 281 7.3 Dual Signal Model Instantiations 283 7.3.1 Dual Signal Model for Nonuniform Signal Interpolation 283 7.3.2 Dual Signal Model for Sparse Signal Deconvolution 284 7.3.3 Spectrally Adapted Mercer Kernels 285 7.4 Tutorials and Application Examples 289 7.4.1 Nonuniform Interpolation with the Dual Signal Model 290 7.4.2 Sparse Deconvolution with the Dual Signal Model 292 7.4.3 Doppler Ultrasound Processing for Fault Detection 294 7.4.4 Spectrally Adapted Mercer Kernels 296 7.4.5 Interpolation of Heart Rate Variability Signals 304 7.4.6 Denoising in Cardiac Motion-Mode Doppler Ultrasound Images 309?m 7.4.7 Indoor Location from Mobile Devices Measurements 316 7.4.8 Electroanatomical Maps in Cardiac Navigation Systems 322 7.5 Questions and Problems 331 8 Advances in Kernel Regression and Function Approximation 333 8.1 Introduction 333 8.2 Kernel-Based Regression Methods 333 8.2.1 Advances in Support Vector Regression 334 8.2.2 Multi-output Support Vector Regression 338 8.2.3 Kernel Ridge Regression 339 8.2.4 Kernel Signal-To-Noise Regression 341 8.2.5 Semisupervised Support Vector Regression 343 8.2.6 Model Selection in Kernel Regression Methods 345 8.4.1 Comparing Support Vector Regression, Relevance Vector Machines, and Gaussian Process Regression 360 8.4.2 Pro&#64257;le-Dependent Support Vector Regression 362 8.4.3 Multi-output Support Vector Regression 364 8.4.4 Kernel Signal-to-Noise Ratio Regression 366 8.4.5 Semisupervised Support Vector Regression 368 8.4.6 Bayesian Nonparametric Model 369 8.4.7 Gaussian Process Regression 370 8.4.8 Relevance Vector Machines 379 8.5 Concluding Remarks 382 8.6 Questions and Problems 383 9 Adaptive Kernel Learning for Signal Processing 387 9.1 Introduction 387 9.2 Linear Adaptive Filtering 387 9.2.1 Least Mean Squares Algorithm 388 9.2.2 Recursive Least-Squares Algorithm 389 9.3 Kernel Adaptive Filtering 392 9.4 Kernel Least Mean Squares 392 9.4.1 Derivation of Kernel Least Mean Squares 393 9.4.2 Implementation Challenges and Dual Formulation 394 9.5.3 Prediction of the Mackey&ndash;Glass Time Series with Kernel Recursive Least Squares 401 9.5.4 Beyond the Stationary Model 402 9.5.5 Example on Nonlinear Channel Identi&#64257;cation and Reconvergence 405 9.6 Explicit Recursivity for Adaptive Kernel Models 406 9.6.1 Recursivity in Hilbert Spaces 406 9.6.2 Recursive Filters in Reproducing Kernel Hilbert Spaces 408 9.7 Online Sparsi&#64257;cation with Kernels 411 9.7.1 Sparsity by Construction 411 9.7.2 Sparsity by Pruning 413 9.8 Probabilistic Approaches to Kernel Adaptive Filtering 414 9.8.1 Gaussian Processes and Kernel Ridge Regression 415 9.8.2 Online Recursive Solution for Gaussian Processes Regression 416 9.8.3 Kernel Recursive Least Squares Tracker 417 9.8.4 Probabilistic Kernel Least Mean Squares 418 9.9 Further Reading 418 9.9.1 Selection of Kernel Parameters 418 9.9.2 Multi-Kernel Adaptive Filtering 419 9.9.3 Recursive Filtering in Kernel Hilbert Spaces 419 9.10 Tutorials and Application Examples 419 9.10.1 Kernel Adaptive Filtering Toolbox 420 9.10.2 Prediction of a Respiratory Motion Time Series 421 9.10.3 Online Regression on the KIN?h?eK Dataset 423 9.10.4 The Mackey&ndash;Glass Time Series 425 9.10.5 Explicit Recursivity on Reproducing Kernel in Hilbert Space and Electroencephalogram Prediction 427 9.10.6 Adaptive Antenna Array Processing 428 9.11 Questions and Problems 430 Part III Classification, Detection, and Feature Extraction 433 10 Support Vector Machine and Kernel Classification Algorithms 435 10.1 Introduction 435 10.2 Support Vector Machine and Kernel Classi&#64257;ers 435 10.2.1 Support Vector Machines 435 10.2.2 Multiclass and Multilabel Support Vector Machines 441 10.2.3 Least-Squares Support Vector Machine 447 10.2.4 Kernel Fisher&am 9.8.3 Kernel Recursive Least Squares Tracker 6.2.2 Kernel Finite Impulse Response and the γ-filter -- 6.2.3 Kernel Array Processing with Spatial Reference -- 6.2.4 Kernel Semiparametric Regression -- 6.3 Tutorials and Application Examples -- 6.3.1 Nonlinear System Identification with Support VectorMachine-Autoregressive and Moving Average -- 6.3.2 Nonlinear System Identification with the γ-filter -- 6.3.3 Electric Network Modeling with Semiparametric Regression -- 6.3.4 Promotional Data -- 6.3.5 Spatial and Temporal Antenna Array Kernel Processing -- 6.4 Questions and Problems -- Chapter 7 Dual Signal Models for Signal Processing -- 7.1 Introduction -- 7.2 Dual Signal Model Elements -- 7.3 Dual Signal Model Instantiations -- 7.3.1 Dual Signal Model for Nonuniform Signal Interpolation -- 7.3.2 Dual Signal Model for Sparse Signal Deconvolution -- 7.3.3 Spectrally Adapted Mercer Kernels -- 7.4 Tutorials and Application Examples -- 7.4.1 Nonuniform Interpolation with the Dual Signal Model -- 7.4.2 Sparse Deconvolution with the Dual Signal Model -- 7.4.3 Doppler Ultrasound Processing for Fault Detection -- 7.4.4 Spectrally Adapted Mercer Kernels -- 7.4.5 Interpolation of Heart Rate Variability Signals -- 7.4.6 Denoising in Cardiac Motion-Mode Doppler Ultrasound Images -- 7.4.7 Indoor Location from Mobile Devices Measurements -- 7.4.8 Electroanatomical Maps in Cardiac Navigation Systems -- 7.5 Questions and Problems -- Chapter 8 Advances in Kernel Regression and Function Approximation -- 8.1 Introduction -- 8.2 Kernel-Based Regression Methods -- 8.2.1 Advances in Support Vector Regression -- 8.2.2 Multi-output Support Vector Regression -- 8.2.3 Kernel Ridge Regression -- 8.2.4 Kernel Signal-to-Noise Regression -- 8.2.5 Semi-supervised Support Vector Regression -- 8.2.6 Model Selection in Kernel Regression Methods -- 8.3 Bayesian Nonparametric Kernel Regression Models Intro -- Title Page -- Copyright Page -- Contents -- About the Authors -- Preface -- Acknowledgements -- List of Abbreviations -- Part I Fundamentals and Basic Elements -- Chapter 1 From Signal Processing to Machine Learning -- 1.1 A New Science is Born: Signal Processing -- 1.1.1 Signal Processing Before Being Coined -- 1.1.2 1948: Birth of the Information Age -- 1.1.3 1950s: Audio Engineering Catalyzes Signal Processing -- 1.2 From Analog to Digital Signal Processing -- 1.2.1 1960s: Digital Signal Processing Begins -- 1.2.2 1970s: Digital Signal Processing Becomes Popular -- 1.2.3 1980s: Silicon Meets Digital Signal Processing -- 1.3 Digital Signal Processing Meets Machine Learning -- 1.3.1 1990s: New Application Areas -- 1.3.2 1990s: Neural Networks, Fuzzy Logic, and Genetic Optimization -- 1.4 Recent Machine Learning in Digital Signal Processing -- 1.4.1 Traditional Signal Assumptions Are No Longer Valid -- 1.4.2 Encoding Prior Knowledge -- 1.4.3 Learning and Knowledge from Data -- 1.4.4 From Machine Learning to Digital Signal Processing -- 1.4.5 From Digital Signal Processing to Machine Learning -- Chapter 2 Introduction to Digital Signal Processing -- 2.1 Outline of the Signal Processing Field -- 2.1.1 Fundamentals on Signals and Systems -- 2.1.2 Digital Filtering -- 2.1.3 Spectral Analysis -- 2.1.4 Deconvolution -- 2.1.5 Interpolation -- 2.1.6 System Identification -- 2.1.7 Blind Source Separation -- 2.2 From Time-Frequency to Compressed Sensing -- 2.2.1 Time-Frequency Distributions -- 2.2.2 Wavelet Transforms -- 2.2.3 Sparsity, Compressed Sensing, and Dictionary Learning -- 2.3 Multidimensional Signals and Systems -- 2.3.1 Multidimensional Signals -- 2.3.2 Multidimensional Systems -- 2.4 Spectral Analysis on Manifolds -- 2.4.1 Theoretical Fundamentals -- 2.4.2 Laplacian Matrices -- 2.5 Tutorials and Application Examples 4.4 Constructing Kernel Functions -- 4.4.1 Standard Kernels -- 4.4.2 Properties of Kernels -- 4.4.3 Engineering Signal Processing Kernels -- 4.5 Complex Reproducing Kernel in Hilbert Spaces -- 4.6 Support Vector Machine Elements for Regression and Estimation -- 4.6.1 Support Vector Regression Signal Model and Cost Function -- 4.6.2 Minimizing Functional -- 4.7 Tutorials and Application Examples -- 4.7.1 Kernel Calculations and Kernel Matrices -- 4.7.2 Basic Operations with Kernels -- 4.7.3 Constructing Kernels -- 4.7.4 Complex Kernels -- 4.7.5 Application Example for Support Vector Regression Elements -- 4.8 Concluding Remarks -- 4.9 Questions and Problems -- Part II Function Approximation and Adaptive Filtering -- Chapter 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 -- 5.3.1 Nonparametric Spectrum and System Identification -- 5.3.2 Orthogonal Frequency Division Multiplexing Digital Communications -- 5.3.3 Convolutional Signal Models -- 5.3.4 Array Processing -- 5.4 Tutorials and Application Examples -- 5.4.1 Nonparametric Spectral Analysis with Primal Signal Models -- 5.4.2 System Identification with Primal Signal Model γ-filter -- 5.4.3 Parametric Spectral Density Estimation with Primal Signal Models -- 5.4.4 Temporal Reference Array Processing with Primal Signal Models -- 5.4.5 Sinc Interpolation with Primal Signal Models -- 5.4.6 Orthogonal Frequency Division Multiplexing with Primal Signal Models -- 5.5 Questions and Problems -- Chapter 6 Reproducing Kernel Hilbert Space Models for Signal Processing -- 6.1 Introduction -- 6.2 Reproducing Kernel Hilbert Space Signal Models -- 6.2.1 Kernel Autoregressive Exogenous Identification 2.5.1 Real and Complex Signal Processing and Representations -- 2.5.2 Convolution, Fourier Transform, and Spectrum -- 2.5.3 Continuous-Time Signals and Systems -- 2.5.4 Filtering Cardiac Signals -- 2.5.5 Nonparametric Spectrum Estimation -- 2.5.6 Parametric Spectrum Estimation -- 2.5.7 Source Separation -- 2.5.8 Time-Frequency Representations and Wavelets -- 2.5.9 Examples for Spectral Analysis on Manifolds -- 2.6 Questions and Problems -- Chapter 3 Signal Processing Models -- 3.1 Introduction -- 3.2 Vector Spaces, Basis, and Signal Models -- 3.2.1 Basic Operations for Vectors -- 3.2.2 Vector Spaces -- 3.2.3 Hilbert Spaces -- 3.2.4 Signal Models -- 3.2.5 Complex Signal Models -- 3.2.6 Standard Noise Models in DSP -- 3.2.7 The Role of the Cost Function -- 3.2.8 The Role of the Regularizer -- 3.3 Digital Signal Processing Models -- 3.3.1 Sinusoidal Signal Models -- 3.3.2 System Identification Signal Models -- 3.3.3 Sinc Interpolation Models -- 3.3.4 Sparse Deconvolution -- 3.3.5 Array Processing -- 3.4 Tutorials and Application Examples -- 3.4.1 Examples of Noise Models -- 3.4.2 Autoregressive Exogenous System Identification Models -- 3.4.3 Nonlinear System Identification Using Volterra Models -- 3.4.4 Sinusoidal Signal Models -- 3.4.5 Sinc-based Interpolation -- 3.4.6 Sparse Deconvolution -- 3.4.7 Array Processing -- 3.5 Questions and Problems -- 3.A MATLAB simpleInterp Toolbox Structure -- Chapter 4 Kernel Functions and Reproducing Kernel Hilbert Spaces -- 4.1 Introduction -- 4.2 Kernel Functions and Mappings -- 4.2.1 Measuring Similarity with Kernels -- 4.2.2 Positive-Definite Kernels -- 4.2.3 Reproducing Kernel in Hilbert Space and Reproducing Property -- 4.2.4 Mercer's Theorem -- 4.3 Kernel Properties -- 4.3.1 Tikhonov's Regularization -- 4.3.2 Representer Theorem and Regularization Properties -- 4.3.3 Basic Operations with Kernels 8.3.1 Gaussian Process Regression -- 8.3.2 Relevance Vector Machines -- 8.4 Tutorials and Application Examples -- 8.4.1 Comparing Support Vector Regression, Relevance Vector Machines, and Gaussian Process Regression -- 8.4.2 Profile-Dependent Support Vector Regression -- 8.4.3 Multi-output Support Vector Regression -- 8.4.4 Kernel Signal-to-Noise Ratio Regression -- 8.4.5 Semi-supervised Support Vector Regression -- 8.4.6 Bayesian Nonparametric Model -- 8.4.7 Gaussian Process Regression -- 8.4.8 Relevance Vector Machines -- 8.5 Concluding Remarks -- 8.6 Questions and Problems -- Chapter 9 Adaptive Kernel Learning for Signal Processing -- 9.1 Introduction -- 9.2 Linear Adaptive Filtering -- 9.2.1 Least Mean Squares Algorithm -- 9.2.2 Recursive Least-Squares Algorithm -- 9.3 Kernel Adaptive Filtering -- 9.4 Kernel Least Mean Squares -- 9.4.1 Derivation of Kernel Least Mean Squares -- 9.4.2 Implementation Challenges and Dual Formulation -- 9.4.3 Example on Prediction of the Mackey-Glass Time Series -- 9.4.4 Practical Kernel Least Mean Squares Algorithms -- 9.5 Kernel Recursive Least Squares -- 9.5.1 Kernel Ridge Regression -- 9.5.2 Derivation of Kernel Recursive Least Squares -- 9.5.3 Prediction of the Mackey-Glass Time Series with Kernel Recursive Least Squares -- 9.5.4 Beyond the Stationary Model -- 9.5.5 Example on Nonlinear Channel Identification and Reconvergence -- 9.6 Explicit Recursivity for Adaptive Kernel Models -- 9.6.1 Recursivity in Hilbert Spaces -- 9.6.2 Recursive Filters in Reproducing Kernel Hilbert Spaces -- 9.7 Online Sparsification with Kernels -- 9.7.1 Sparsity by Construction -- 9.7.2 Sparsity by Pruning -- 9.8 Probabilistic Approaches to Kernel Adaptive Filtering -- 9.8.1 Gaussian Processes and Kernel Ridge Regression -- 9.8.2 Online Recursive Solution for Gaussian Processes Regression |
| Title | Digital Signal Processing with Kernel Methods |
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