论文标题
通过Fock空间进入高斯RBF内核的方法
An approach to the Gaussian RBF kernels via Fock spaces
论文作者
论文摘要
我们使用Fock空间和Segal-Bargmann理论中的方法来证明高斯RBF内核的复杂分析中的几个结果。后者是现代机器学习内核方法中最常用的内核之一，也是支持向量机（SVM）分类算法中的内核之一。复杂的分析技术使我们能够使用所谓的Segal-Bargmann变换来考虑与功能空间和特征映射等RBF内核相关的几个概念。我们还展示了RBF内核如何与量子力学和时间频率分析中最常用的运算符相关，具体来说，我们证明了此类内核与创建，an灭，傅立叶，傅立叶，翻译，调制，调制和Weyl oberator的连接。对于Weyl操作员，我们还研究了这种情况下的Semigroup物业。
We use methods from the Fock space and Segal-Bargmann theories to prove several results on the Gaussian RBF kernel in complex analysis. The latter is one of the most used kernels in modern machine learning kernel methods, and in support vector machines (SVMs) classification algorithms. Complex analysis techniques allow us to consider several notions linked to the RBF kernels like the feature space and the feature map, using the so-called Segal-Bargmann transform. We show also how the RBF kernels can be related to some of the most used operators in quantum mechanics and time frequency analysis, specifically, we prove the connections of such kernels with creation, annihilation, Fourier, translation, modulation and Weyl operators. For the Weyl operators, we also study a semigroup property in this case.
