Research on Kernel Approximation Algorithm Based on Random Fourier Feature Space

EasyChair Preprint no. 7360

Abstract

 Kernel method is a method to transform the linear non separable problem in low-dimensional space into the linear separable problem in high-dimensional space. It is widely used in a variety of learning models. The existing kernel selection methods may have low computational efficiency and high time cost in large-scale data. Aiming at above problem, this paper introduces the random Fourier feature to transform the original kernel feature space into another relatively low dimensional explicit random feature space. The theoretical analysis of the upper bound of the kernel approximation error and the upper bound of the error of training the learning model in the kernel approximation random feature space is given. The convergence consistency of kernel approximation and the relationship between error upper bound and kernel approximation parameters are obtained. Then, the optimal model parameters are selected based on random Fourier feature space, which can avoid the large-scale search for the optimal original Gaussian kernel model parameters, so as to greatly reduce the time cost required for the selection of the original Gaussian kernel model. Experiments show that the error upper bound proved in this paper is controlled by the kernel approximation parameters. The optimal model selected by the kernel approximation has good performance compared with the original Gaussian kernel function model, and the model selection time is greatly reduced compared with the grid search method.

Keyphrases: 核方法；, 核近似；, 模型选择, 随机傅里叶特征；, 高斯核；

@Booklet{EasyChair:7360,
  author = {Kai Zhang and Changqian Men and Wenjian Wang},
  title = {Research on Kernel Approximation Algorithm Based on Random Fourier Feature Space},
  howpublished = {EasyChair Preprint no. 7360},

  year = {EasyChair, 2022}}