Random Fourier Features Kernel Recursive Generalized Loss for Online Time Series Prediction

With the highlight of the dynamic characteristics of complex systems, the online prediction method of time series has become a key means to master the dynamic changes of complex systems. In this paper, we propose a novel kernel adaptive algorithm, called kernel recursive generalized loss (KRGL) algorithm, which is derived from generalized loss (GL) function in the kernel space in the form of online recursion. Different from the traditional fixed loss function, GL function is a synthesis of various loss functions, which can adaptively learn weights according to errors and effectively weaken outliers or non-Gaussian noise. It has high superiority in real-time tracking of the dynamic changes of the complex systems. At the same time, considering the infinite expansion of the kernel matrix, the sparse method is used in the general form of GL function, and random Fourier features kernel recursive generalized loss (RFF-KRGL) algorithm is proposed. By using the finite-dimensional inner product to approximate the kernel function, the weight network structure is fixed and the computational complexity is significantly reduced. Finally, simulations are performed on a benchmark dataset and a real-world dataset to verily the robustness of the proposed KRGL and RFF-KRGL in the online prediction of nonlinear, non-Gaussian and non-stationary time series.