From fc51779d992417c4adb3d6e11772dd42ff7cf203 Mon Sep 17 00:00:00 2001
From: benjas <909336740@qq.com>
Date: Wed, 28 Apr 2021 16:10:00 +0800
Subject: [PATCH] optimize. Adjust the topic of the folder

---
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index 21b8183..c956715 100644
--- a/机器学习算法理论及应用/李航——统计学习方法/7.支持向量机——升维打击.md
+++ b/机器学习算法原理及推导/李航——统计学习方法/7.支持向量机——升维打击.md
@@ -138,7 +138,14 @@ Support vector machines
 
 > 图中心，虚线到实线的距离我们称之为γ，我们要做的是最大化γ，使得这个超平面调整为γ的一个最大值，等价于找到了最优的超平面
 
-![1619585628157](assets/1619585628157.png)
+**式子如下：**
+$$
+\max_{w,b} \quad γ
+$$
+
+$$
+s.t.\quad y_i(\frac{w}{||w||}*x_i+\frac{b}{||w||})≥γ \quad i=1,2,...,N
+$$
 
 > γ：表示几何间隔
 >
@@ -161,10 +168,43 @@ $$
 y_i(wx_i+b)≥\hat{γ}，其中\hat{γ}是函数间隔
 $$
 
+max的时候是几何间隔，也就是最终s.t. 还是会约束着它朝着几何间隔去走，但是这样的好处就是下方的||w||就没有了
+
+**简化后如下：**
+$$
+\max_{w,b} \quad \frac{\hat{γ}}{||w||}
+$$
+
+$$
+s.t.\quad y_i(w*x_i+b)≥γ \quad i=1,2,...,N
+$$
+
+之前我们说过，对于函数间隔，我们等比例放大缩小w、b可以让最终结果变成1，也就是γ=1
+
+**再简化后：**
+$$
+\max_{w,b} \quad \frac{1}{||w||}
+$$
+
+$$
+s.t.\quad y_i(w*x_i+b)≥1 \quad i=1,2,...,N
+$$
 
 
+$$
+我们想要最大化\frac{1}{||w||}，那么相当于最小化||w||
+$$
 
+$$
+后面要用到拉格朗日乘子法，我们把\frac{1}{||w||}变成\frac{1}{2}||w||^2，这两者是等价的
+$$
 
+**再简化后：**
+$$
+\min_{w,b} \quad \frac{1}{2}||w||^2
+$$
 
+$$
+s.t.\quad y_i(w*x_i+b)-1≥0 \quad i=1,2,...,N
+$$
 
-![1619585642761](assets/1619585642761.png)
\ No newline at end of file
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