再生核Banach空间核的乘积性质
Product properties of kernels in reproducing kernel Banach spaces
孙靖 1许安见1
作者信息
- 1. 重庆理工大学理学院,重庆 400054
- 折叠
摘要
为了解决机器学习中最小范数插值、正则化网络、支持向量机、核主成分分析等问题,再生核Hilbert空间已经不能满足需要,于是Zhang等引入了再生核Banach空间.本文利用张量积及半内积的方法,证明了两个半内积再生核Banach空间的张量积也为对应再生核乘积所诱导的半内积再生核Banach空间.
Abstract
In order to solve the problems of minimum norm interpolation,regularized networks,support vector ma-chines,and kernel principal component analysis in machine learning,reproducing kernel Hilbert space is no longer sufficient.Zhang et al.introduced the reproducing kernel Banach space.Using the method of tensor product and semi-inner product,it is proved that the tensor product of two semi-inner-product reproducing kernel Banach space is also the semi-inner-product repro-ducing kernel Banach space induced by the product of the corresponding reproducing kernels.
关键词
再生核Hilbert空间/再生核Banach空间/半内积Key words
reproducing kernel Hilbert space/reproducing kernel Banach space/semi-inner product引用本文复制引用
基金项目
国家自然科学基金面上项目(11871127)
重庆市自然科学基金(cstc2019jcyjmsxmX0295)
重庆市教委科学技术研究计划(KJZD-K202301109)
出版年
2024
NETL
NSTL
万方数据