基于随机傅里叶特征空间的高斯核近似模型选择算法  

Gaussian Kernel Approximation Model Selection Algorithm Based on Random Fourier Feature Space

作　　者：张凯 门昌骞[1] 王文剑[1,2] ZHANG Kai;MEN Changqian;WANG Wenjian(College of Computer and Information Technology,Shanxi University,Taiyuan 030006,China;Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学计算机与信息技术学院,太原030006 [2]山西大学计算智能与中文信息处理教育部重点实验室,太原030006

出　　处：《数据采集与处理》2023年第3期616-628,共13页Journal of Data Acquisition and Processing

基　　金：国家自然科学基金(U21A20513,62076154);中央引导地方科技发展资金(YDZX20201400001224);山西省国际科技合作计划项目(201903D421050);山西省自然科学基金(201901D111030)。

摘　　要：核方法是一种把低维空间的线性不可分问题转化为高维空间中线性可分问题的方法,其广泛应用于多种学习模型。然而现有的核模型选择方法在大规模数据中计算效率较低,时间成本很大。针对这一问题,本文引入随机傅里叶特征变换,将原始核特征空间转换为另一个相对低维的显式随机特征空间,并给出核近似误差上界理论分析以及在核近似的随机特征空间中训练学习模型的误差上界,得到核近似的收敛一致性和误差上界与核近似参数之间的关系。基于随机傅里叶特征空间选择出最优模型参数,避免了对最优原始高斯核模型参数的大规模搜索,从而大幅降低原始高斯核模型选择所需的时间成本。实验表明,本文给出的误差上界确由核近似参数控制,核近似选择的最优模型相较于原始高斯核模型有较高的准确率,并且模型选择时间相对网格搜索法大幅减小。Kernel method transforms 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.However,the existing kernel selection methods have low computational efficiency and high time cost in large-scale data.Aiming at above problems,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 are given.The convergence consistency of kernel approximation and the relationship between error upper bound and kernel approximation parameters are obtained.Moreover,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.

关 键 词：核方法 高斯核 傅里叶变换 核近似 模型选择 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]