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 NeuroEngineering 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 modelselection method called maximum marginal likelihood

Addresses the principal bottleneck of kernel adaptive filters—their growing structure

Features twelve computeroriented 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 radialbasis 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 LEASTMEANSQUARE 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 kernelinduced.
Excellent tutorial book on this topic is Rasmussen and Williams [2006]. 5 EXTENDED KERNEL RECURSIVE LEASTSQUARES ALGORITHM In this chapter, the kernel recursive leastsquares 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.
EXKRLS. Note that r(i) in the EXKRLS 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 slowfading applications. Therefore, ALD is readily applicable for EXKRLS, EWKRLS, and RWKRLS without extra computation. Of course, because of the longterm effect of state transition model, EXKRLS can deviate signiﬁcantly.
RECURSIVE LEAST SQUARES WITH SURPRISE CRITERION (KRLSSC) 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 KRLSSC. 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.