前言

這個筆記是北大那位老師課程的學習筆記，講的概念淺顯易懂，非常有利于我們掌握基本的概念，從而掌握相關的技術。

basic concepts

a two-class problem can be assumped as a Bernoulli distribution

$$\overline{Z}M(z|\theta ,n_1+n_m)$$

reproducing kernels

1 Cover’s theorem
A complex pattern-classification problem cast in a high-dimensional space nonlincedy is more likely to be linearly seperable than in a low-dimension space.

kernel

Def 1.1 Let $$x?R^P$$ be a non empty set: A function K:x*x -> R is called a kerne; over x.
Def 1.2A kernel k is called symmetric of $$k(x_i,x_j)=k(x_j,x_i)$$ for any $$x_{i}and{x}_j?X$$
Def1.3 A symmetric kernel is positive definite if $$\sum _{j,k=1}^n{\alpha }_j{\alpha }_{k}K(X_i,X_k)\ge 0$$
for any $$n?N$$ and $${\alpha }_1,...,{\alpha }_n$$.
we call the symmetric K a conditional.P.D if +
$$\sum _{j,k=1}^n{\alpha }_j{\alpha }_{k}K(X_i,X_k)\ge 0$$
$$foralln\ge z$$,$$x_1,x_k?X$$

Def 1.4 if k is C.P.D then we call -k negative definite.
$$k(x_i,x_j)\ge 0$$
$$?(x,y)=||x?y|{|}_2^2$$

總結

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