V2EX kernel function

Kernel Function

Definition / 定义

核函数:一种把两个输入(向量、样本点等)映射为“相似度”的函数,常用于机器学习与统计(如支持向量机、核岭回归、核密度估计)。它通常等价于在某个(可能是高维)特征空间里计算内积,从而在不显式做高维映射的情况下进行非线性建模(“核技巧”)。(在不同领域也可能指其他类型的“核”,但此处以最常见的机器学习含义为主。)

Pronunciation / 发音

/knl fkn/

Examples / 例句

A Gaussian kernel function is common in machine learning.
高斯核函数在机器学习中很常见。

By choosing an appropriate kernel function, the model can capture nonlinear patterns without explicitly mapping data into a higher-dimensional space.
通过选择合适的核函数,模型可以在不显式把数据映射到更高维空间的情况下捕捉非线性模式。

Etymology / 词源

kernel 原义是“谷粒的仁、核心”,引申为“最核心的部分”;在数学与工程里也常指“核/核状结构(如积分核)”。function 来自拉丁语 functio,意为“执行、作用”。合在一起,kernel function 字面意思是“起核心作用的函数”,在现代统计学习中逐渐固定为“用于度量相似性、实现核技巧的函数”。

Related Words 相关词

Literary Works / 作品例证

  • The Elements of Statistical Learning(Hastie, Tibshirani, Friedman)
  • Pattern Recognition and Machine Learning(Christopher M. Bishop)
  • Learning with Kernels(Schlkopf & Smola)
  • Support Vector Machines(Cristianini & Shawe-Taylor)
  • Gaussian Processes for Machine Learning(Rasmussen & Williams)
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