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An Efficient Nonlinear Dichotomous Coordinate Descent Adaptive Algorithm Based on Random Fourier Features

The auxiliary normal equation is proposed to construct an incremental update (IU) system in which the increment of weight vector rather than the weight itself is optimized at each iteration, which however, can only deal with problems under linearity assumption. In this letter, we establish the IU system in a fixed-dimension feature space induced by the random Fourier features mapping, enabling it to address nonlinear issues efficiently. Then, to obtain the solution vector to the IU system and overcome high complexity and instability incurred by matrix inversion, a dichotomous coordinate descent (DCD) method is employed to propose an efficient random Fourier features kernel dichotomous coordinate descent (RFFKDCD) algorithm. The proposed RFFKDCD algorithm can tackle nonlinear issues efficiently while avoiding high computational complexity existing widely in kernel-based algorithms. Simulations on both synthetic and real-world examples show that the proposed RFFKDCD algorithm outperforms the recursive least squares-based algorithms in terms of computational load.