Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 52, Issue 8, Pages 2275-2285Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2004.830985
Keywords
Kernel methods; nonlinear regression; online algorithms; recursive estimation; recursive least squares
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We present a nonlinear version of the recursive least squares (RLS) algorithm. Our. algorithm performs linear regression in a high-dimensional feature space induced by a Mercer kernel and can therefore be used to recursively construct minimum mean-squared-error solutions to nonlinear least-squares problems that are frequently encountered in signal processing applications. In order to regularize solutions and keep the complexity of the algorithm bounded, we use a sequential sparsification process that admits into the kernel representation a new input sample only if its feature space image cannot be sufficiently well approximated by combining the images of previously admitted samples. This sparsification procedure allows the algorithm to operate online, often in real time. We analyze the behavior of the algorithm, compare its scaling properties to those of support vector machines, and demonstrate its utility in solving two signal processing problems-time-series prediction and channel equalization.
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