# 选择变量

## 选择$$a\_1$$

目标：选择违反KKT最严重的点

**KKT条件**:

* 位于间隔边界外的点：$$a\_i=0 \Leftrightarrow y\_ig(x\_i) \ge 1$$  
* 位于间隔边界上的点：$$0 \lt a\_i \lt C=0 \Leftrightarrow y\_ig(x\_i) = 1$$  
* 位于间隔边界内的点：$$a\_i = C \Leftrightarrow y\_ig(x\_i) \le 1$$    

其中：

$$
g(x\_i) = \sum\_{j=1}^Na\_jy\_jK(x\_i, x\_j) + b
$$

$$g(x\_i)$$代表对$$x\_i$$的预测结果。

1. 满足$$0 \lt a\_i \lt C=0$$的样本点（即位于间隔边界上的点）中寻找违反KKT最严重的点。  
2. 所有点中违反KKT最严重的点。  

## 选择$$a\_2$$

此时已找到$$a\_1$$\
目标：选择使a\_2有足够大变化的点

1. 如果$$E\_1 \gt 0$$，选择最小的Ei对应的a2，  

   如果$$E\_1 \lt 0$$，选择最大的Ei对应的a2，  
2. 遍历位于间隔边界外的点，找到使目标函数有足够下降的样本  
3. 遍历所有数据集，找到使目标函数有足够下降的样本    


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