Kernel Adaptive Filtering: A Comprehensive Introduction
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.
Why Read This Book
You will get a practical, signal-processing–oriented treatment of kernel methods that brings RKHS theory down to online adaptive algorithms you can implement and test. The book balances theory, algorithm derivation, and simulation/MATLAB examples so you can move quickly from understanding to prototyping nonlinear adaptive filters.
Who Will Benefit
Graduate students, researchers, and DSP engineers who already know linear adaptive filtering and want to extend their toolset to nonlinear, kernel-based online learning for system identification, prediction, and equalization.
Level: Advanced — Prerequisites: Familiarity with linear adaptive filtering (e.g., LMS/RLS), basic DSP and linear algebra, probability and estimation. MATLAB experience is helpful to run the book's examples.
Key Takeaways
- Understand the reproducing kernel Hilbert space (RKHS) framework and how kernels map signals into feature spaces for nonlinear processing.
- Implement kernel-based online learning algorithms such as KLMS, KRLS and kernel versions of affine-projection methods.
- Apply and tune sparsification/complexity-control techniques (novelty criterion, ALD, budget methods) to keep kernel models tractable in real time.
- Analyze convergence, stability, and regularization trade-offs for kernel adaptive filters in practical signal-processing settings.
- Design and evaluate nonlinear adaptive solutions for tasks like system identification, time-series prediction, noise cancellation, and channel equalization using provided MATLAB code.
Topics Covered
- Introduction and motivation: nonlinear adaptive filtering
- Mathematical background: RKHS and kernel functions
- Kernel-based learning: representer theorem and regularization
- Kernel LMS (KLMS) and basic online kernel algorithms
- Kernel Recursive Least Squares (KRLS) and projection methods
- Kernel affine-projection and extensions
- Sparsification and complexity-control: novelty criterion, ALD, budgets
- Convergence analysis and regularization trade-offs
- Implementation issues and computational considerations
- Applications: nonlinear system identification, prediction, equalization
- Simulations, case studies and MATLAB examples
- Advanced topics and future directions
Languages, Platforms & Tools
How It Compares
More applied and DSP-focused than Schölkopf & Smola's Learning with Kernels (which is theory-heavy); extends classical adaptive-filter texts (e.g., Haykin) into nonlinear RKHS-based online algorithms rather than linear theory.
