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.

中文翻译：

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一种基于随机傅立叶特征的高效非线性二分坐标下降自适应算法

提出了辅助正规方程来构建增量更新（IU）系统，其中在每次迭代时优化权向量的增量而不是权重本身，但只能处理线性假设下的问题。在这封信中，我们在由随机傅立叶特征映射引起的固定维特征空间中建立了 IU 系统，使其能够有效地解决非线性问题。然后，为了获得IU系统的解向量并克服矩阵求逆带来的高复杂度和不稳定性，采用二分坐标下降（DCD）方法提出了一种高效的随机傅立叶特征核二分坐标下降（RFFKDCD）算法。所提出的 RFFKDCD 算法可以有效地解决非线性问题，同时避免基于内核的算法中广泛存在的高计算复杂度。对合成示例和真实示例的模拟表明，所提出的 RFFKDCD 算法在计算负载方面优于基于递归最小二乘法的算法。