# 第7章 线性可分SVM

## 定义

给定线性可分训练数据集，通过间隔最大化或等价地求解相应的凸二次规划问题学习得到的分离超平面为:

$$
w^\* \cdot x + b^\* = 0
$$

以及相应的分类决策函数：

$$
f(x) = sign(w^\* \cdot x + b^\*)
$$

## 模型

求解**正确划分**训练数据集并且**几何间隔**最大的分离超平面\
直观解释：以充分大的确信度对训练数据进行分类。

## 策略

解凸二次规划问题得w*, b*

$$
\begin{aligned}
\min\_{w,b} \quad  \frac{1}{2}||w||^2  \\
s.t. \quad y\_i(w\cdot x\_i + b) - 1 \ge 0, i=1,2,\cdots,N
\end{aligned}
$$

得到最大间隔分离平面：

$$
w\* \cdot x + b\* = 0
$$

分类决策函数：

$$
f(x) = sign(w\* \cdot x + b\*)
$$

【？】7.1.3存在性和w的唯一性没看懂


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