General Cauchy Conjugate Gradient Algorithms Based on Multiple Random Fourier Features

Abstract

The general Cauchy loss (GCL) criterion has been successfully proposed to improve the performance of the Cauchy loss (CL) criterion for linear adaptive filtering in the presence of complex non-Gaussian noise. However, the commonly used adaptive filtering algorithms based on the GCL criterion utilize the stochastic gradient descent (SGD) method to update their weights with slow convergence rate and poor steady-state performance. To overcome these issues, a general Cauchy-loss conjugate gradient (GCCG) method is first developed by solving the proposed half-quadratic general Cauchy loss (HQGCL) with the conjugate gradient method. To further tackle complex nonlinear issues, novel multiple random Fourier features (MRFF) spaces are then constructed in finite-dimensional features spaces, which is proven effective for approximation of multi-kernel adaptive filter (MKAF), theoretically. The GCCG method is thus applied into the constructed MRFF spaces to generate novel multiple random Fourier features GCCG (MRFGCG) algorithms, curbing the linear growth structures of kernel adaptive filters (KAFs) and MKAFs. The proposed MRFGCG algorithms in fixed networks have lower computational complexity and higher filtering accuracy than sparsification KAFs in non-Gaussian environments. Monte Carlo simulations on the prediction of synthetic and real-world time-series and the identification of nonlinear system confirm the superiorities of the proposed MRFGCG algorithms.