Kernel Adaptive Filtering: A Comprehensive Introduction

Kernel Adaptive Filtering: A Comprehensive Introduction

Language: English

Pages: 240

ISBN: 0470447532

Format: PDF / Kindle (mobi) / ePub

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 filters—their 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.

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Network. This method of network growing is computationally intensive. Platt [1991] proposed a more feasible design called resource allocating networks, where the structure of a neural network was dynamically altered to optimize resource allocation. Since then, many researchers have proposed methods of both growing and pruning radial-basis function networks reported in Cheng and Lin [1994], Karayiannis and Mi [1997], and Huang et al. [2005]. Martinetz and Schulten [1991] started a new strand of.

However, this method does not apply in situations where the environment is nonstationary. 2.2 KERNEL LEAST-MEAN-SQUARE ALGORITHM A linear finite impulse response filter is assumed in the LMS algorithm. If the mapping between d and u is highly nonlinear, then poor performance can be expected from LMS. To overcome the limitation of linearity, we are well motivated to formulate a “similar” algorithm that is capable of learning arbitrary nonlinear mappings. For that purpose, the kernel-induced.

Excellent tutorial book on this topic is Rasmussen and Williams [2006]. 5 EXTENDED KERNEL RECURSIVE LEAST-SQUARES ALGORITHM In this chapter, the kernel recursive least-squares algorithm (KRLS) will be used to implement state space models in reproducing kernel Hilbert spaces (RKHS). Nonlinear state space models are useful in their own right and will open a new research direction in the area of nonlinear Kalman filtering on par with the extended Kalman filter, the cubature Kalman filter, and the.

EX-KRLS. Note that r(i) in the EX-KRLS equation (5.35) plays a similar role to r(i) in KRLS. Although its meaning is not as clear as in KRLS, it is at least a good approximation of the distance especially when α, β are close to 1 and q is small, which is usually valid in slow-fading applications. Therefore, ALD is readily applicable for EX-KRLS, EW-KRLS, and RW-KRLS without extra computation. Of course, because of the long-term effect of state transition model, EX-KRLS can deviate significantly.

RECURSIVE LEAST SQUARES WITH SURPRISE CRITERION (KRLS-SC) It is easy to verify that ¯ d(i + 1) in equation (6.8) and σ 2(i + 1) in equation (6.9) equal fi(u(i + 1)) and r(i + 1), respectively, in KRLS with σ n2 = λ . Therefore, the surprise criterion can be integrated into KRLS seamlessly, and we call the algorithm KRLS-SC. The system starts with f1 = a(1)κ(u(1),·) with a(1) = Q(1)d(1), Q(1) = [λ + κ(u(1), u(1))]−1 and C(1) = {c1 = u(1)}. Then, it iterates the following procedure for i ≥ 1: For a.

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