April 2019
Intermediate to advanced
172 pages
4h 39m
Chinese
Content preview from 精通特征工程
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145
附录A
线性建模与线性代数基础
A.1
线性分类概述
当有个标记好的数据集时，特征空间中散布着不同类别的数据点，分类器的工作就是将不
同类别的点分隔开。分类器的实现方式是对不同类别的数据点生成不同的输出。例如，当
只有两个类别时，一个好的分类器应该对一个类别生成较大的输出，而对另一个类别生成
较小的输出。那些正好位于两个类别之间的点可以形成一个
决策面
（见图
A-1
）。
特征
1
+
+
+
+
+
+
+
+
+
–
–
–
–
–
–
–
–
–
–
特征
2
图 A-1：简单二值分类找出一个界面来分隔两个类别的数据点
可以使用很多函数作为分类器。由于若干原因，应该使用能清晰划分类别的最简单的函
数。首先，相比最好的复杂分隔符，找到最好的简单分隔符更容易。其次，简单函数通常
146
｜
附录
A
在新数据上的扩展效果更好，因为要使新数据适合过于复杂的训练数据是非常困难的（这
就是
过拟合
的概念）。简单模型或许会犯错误，比如在图
A-1
中，有些点在错误的一侧。
但是，我们宁愿牺牲一些训练准确度，来换取更加简单的、能得到更高测试准确度的决策
面。这种使复杂度最小而可用性最大的原则称为“奥卡姆剃刀”，在科学界和工程界都广
泛适用。
最简单的函数是一条直线。带有一个输入变量的
线性函数
是最常见的（见图
A-2
）。
特征1
函数
输出
1
2
3
图 A-2：一个输入变量的线性函数
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