Dictionary Learning for Gaussian Kernel Adaptive Filtering with Variablekernel Center and Width

Abstract

This paper establishes an adaptive update method for the Gaussian kernel parameters in the application to the kernel adaptive filtering (KAF). In this method, the kernel parameters are all adaptive and data-driven, although they should be given or estimated by cross-validation. In terms of the Gaussian KAF, every input sample or signal has its own width and center, which are updated at each iteration based on the proposed least-square-type rules to minimize the estimation error. In particular, the proposed update rule keeps the width in the manifold of the positive numbers. Together with the $\ell_{1}-$ regularized least squares, the overall KAF algorithm can avoid the overfitting and the increase of dimensionality. Experimental results support the validity of the method.