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Digital Signal Processing with Kernel Methods

Book Description

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. 

  • 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. 

Table of Contents

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