1.1. 核函数

X{\Bbb X}是输入空间(欧氏空间RnR^n的子集或离散集合),又设H{\Bbb H}为特征空间(希尔伯特空间),如果存在从x到H{\Bbb H}的映射
ϕ(x):XH \phi(x): {\Bbb X} \rightarrow {\Bbb H} 使得对所有x,zXx,z \in {\Bbb X},函数K(x,z)K(x,z)满足条件:
K(x,z)=ϕ(x)ϕ(z) K(x, z) = \phi(x) \cdot \phi(z) 则称K(x,z)K(x,z)为核函数,ϕ(x)\phi(x)为映射函数,式中ϕ(x)ϕ(z)\phi(x) \cdot \phi(z)ϕ(x)\phi(x)ϕ(z)\phi(z)的内积。

1.2. 核技巧

在学习与预测中只定义核函数K(x,z)K(x,z),而不显式地定义映射函数ϕ\phi

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