Generalized Gaussian Kernel Adaptive Filtering
This work addresses a specific bottleneck in kernel adaptive filtering for signal processing or machine learning applications, representing an incremental improvement over conventional methods.
The paper tackles the problem of inflexibility in kernel adaptive filtering by proposing a method where Gaussian kernel parameters are adaptively updated using a least-square-type rule, resulting in a more flexible regressor that avoids overfitting and dictionary growth.
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.