A Kernel Least Mean Square Algorithm Based on Randomized Feature Networks

Abstract

Abstract:To construct an online kernel adaptive filter in a non-stationary environment, we propose a randomized feature networks-based kernel least mean square (KLMS-RFN) algorithm. In contrast to the Gaussian kernel, which implicitly maps the input to an infinite dimensional space in theory, the randomized feature mapping transform inputs samples into a relatively low-dimensional feature space, where the transformed samples are approximately equivalent to those in the feature space using a shift-invariant kernel. The mean square convergence process of the proposed algorithm is investigated under the uniform convergence analysis method of a nonlinear adaptive filter. The computational complexity is also evaluated. In Lorenz time series prediction and nonstationary channel equalization scenarios, the simulation results demonstrate the effectiveness of the proposed algorithm.

An Integrated Kernel PCA Neural Network and EGM for Number of Sources Estimation in Wireless Communication

“…The essential concept of the kernel technique is the transformation of data Si from an input space into vectors ∅(S i ) of high dimension feature space. In which, the internal product could be calculated via a positive definitely kernel function that satisfy Mercer's conditions [11,12]:…”