Kernel trick----PRML读书笔记

最新推荐文章于 2025-06-10 17:26:15 发布

weixin_30950607

最新推荐文章于 2025-06-10 17:26:15 发布

阅读量148

点赞数

CC 4.0 BY-SA版权

文章标签：开发工具

原文链接：http://www.cnblogs.com/donggongdechen/p/10632138.html

本文介绍了核技巧的基础概念，包括核函数及其在特征空间中的定义。通过使用核技巧，许多传统算法得以扩展到非线性场景中，使得模型能够处理更复杂的任务。文中还强调了核函数的选择应当基于具体应用来确定。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

　　Many linear parametric models can be re-cast into an equivalent 'dual representstion' in which the predictions are also based on linear combinations of a kernel function evaluated at the training data points. As we shall see, for models which are based on a fixed nonlinear feature space mapping Φ(x), the kernel function is given by the relation: k(x,x')=Φ(x)^TΦ(x')=ΣΦ_i(x)Φ_i(x'). From this definition, we see that the kernel is a symmetric function of its arguments so that k(x,x')=k(x',x).

　　The simplest example of a kernel function is obtained by considering the identity mapping for the feature space so that Φ(x)=x, in which case k(x, x')=x^Tx'. We shall refer to this as the linear kernel. The concept of a kernel formulated as an inner product in a feature space allows us to build interesting extensions of many well-known algorithms by making use of the kernel trick, also known as kernel substitution. The general idea is that, if we have an algorithm formulated in such a way that the input vector x enters only in the form of scalar products, then we can replace that scalar product with some other choice of kernel.

　　We require that the kernel k(x,x') be symmetric and positive semidefinite anf that it expresses the appropriate form of similarity between x and x' according to the intended application.

转载于:https://www.cnblogs.com/donggongdechen/p/10632138.html