Generalized Gaussian Kernel Adaptive Filtering

TL;DR

This paper introduces a flexible generalized Gaussian kernel adaptive filtering method with data-driven parameter updates, including precision matrices on the SPD manifold, enhancing adaptability and avoiding overfitting.

Contribution

It develops a novel adaptive filtering approach with SPD matrix updates and a superposition of kernels, improving flexibility over traditional methods.

Findings

Effective in minimizing estimation error

Maintains SPD constraints during updates

Reduces overfitting with l1 regularization

Abstract

The present paper proposes generalized Gaussian kernel adaptive filtering, where the kernel parameters are adaptive and data-driven. The Gaussian kernel is parametrized by a center vector and a symmetric positive definite (SPD) precision matrix, which is regarded as a generalization of the scalar width parameter. These parameters are adaptively updated on the basis of a proposed least-square-type rule to minimize the estimation error. The main contribution of this paper is to establish update rules for precision matrices on the SPD manifold in order to keep their symmetric positive-definiteness. Different from conventional kernel adaptive filters, the proposed regressor is a superposition of Gaussian kernels with all different parameters, which makes such regressor more flexible. The kernel adaptive filtering algorithm is established together with a l1-regularized least squares to avoid overfitting and the increase of dimensionality of the dictionary. Experimental results confirm the validity of the proposed method.