The Kernel Recursive Least Squares Algorithm

DMCA

The Kernel Recursive Least Squares Algorithm (2003)

Cached

Download Links

Other Repositories/Bibliography

CiteULike

by Yaakov Engel , Shie Mannor , Ron Meir

Venue:	IEEE Transactions on Signal Processing
Citations:	141 - 2 self

BibTeX

@ARTICLE{Engel03thekernel,
    author = {Yaakov Engel and Shie Mannor and Ron Meir},
    title = {The Kernel Recursive Least Squares Algorithm},
    journal = {IEEE Transactions on Signal Processing},
    year = {2003},
    volume = {52},
    pages = {2275--2285}
}

OpenURL

Abstract

We present a non-linear kernel-based version of the Recursive Least Squares (RLS) algorithm. Our Kernel-RLS (KRLS) algorithm performs linear regression in the feature space induced by a Mercer kernel, and can therefore be used to recursively construct the minimum mean squared -error regressor. Sparsity of the solution is achieved by a sequential sparsification process that admits into the kernel representation a new input sample only if its feature space image cannot be suffciently well approximated by combining the images of previously admitted samples. This sparsification procedure is crucial to the operation of KRLS, as it allows it to operate on-line, and by effectively regularizing its solutions. A theoretical analysis of the sparsification method reveals its close affinity to kernel PCA, and a data-dependent loss bound is presented, quantifying the generalization performance of the KRLS algorithm. We demonstrate the performance and scaling properties of KRLS and compare it to a stateof -the-art Support Vector Regression algorithm, using both synthetic and real data. We additionally test KRLS on two signal processing problems in which the use of traditional least-squares methods is commonplace: Time series prediction and channel equalization.

Keyphrases

kernel recursive least square algorithm feature space recursive least square krls algorithm sequential sparsification process signal processing problem theoretical analysis algorithm performs traditional least-squares method feature space image cannot new input sample data-dependent loss bound channel equalization minimum mean non-linear kernel-based version generalization performance sparsification method mercer kernel real data kernel representation time series prediction error regressor sparsification procedure close affinity

DMCA