April 2019
Intermediate to advanced
172 pages
4h 39m
Chinese
Content preview from 精通特征工程
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线性建模与线性代数基础
｜
147
更高维度的线性函数很难可视化。高维线性函数被称为
超平面
。但超平面很容易用代数公
式表示。一个输入集合为
x
1
,
x
2
,
…
,
x
n
，权重参数集合为
w
0
,
w
1
,
…
,
w
n
的多维线性函数可以
表示如下：
f
w
(
x
1
,
x
2
,
…
,
x
n
) =
w
0
+
w
1
*
x
1
+
w
2
*x
2
+
…
+
w
n
*
x
n
使用向量表示时，公式可以更简洁：
f
w
(
x
) =
x
T
w
我们遵循数学表示的常用惯例，用粗体字母表示向量，非粗体字母表示标量。向量
x
在最
前面加上了一个
1
，作为截距项
w
0
的占位符。如果所有输入特征都是
0
，那么函数的输出
就是
w
0
。所以，
w
0
也称为
偏差
或
截距项
。
训练一个线性分类器等价于找出类别之间的最佳分隔超平面，这个问题可以转化为找出空
间中方向完全正确的最佳向量
w
。因为每个数据点都有一个目标标签
y
，所以我们就是要
找到一个
w
来直接预测这个目标标签：
1
x
T
w
=
y
因为通常有多个数据点，所以要找到一个
w
，能同时使得所有预测都接近目标标签：
Aw
=
y
其中，
A
被称为
数据矩阵
（在统计学中也称为设计矩阵）。它包含特定形式的数据：每行是一
个数据点，每列是一个特征。（有时人们使用它的转置形式，其中行是特征，列是数据点。）
A.2
矩阵的解析
为了求解前面的方程，需要一些基本的线性代数知识。如果想系统地学习线性代数，我们
强烈推荐
Strang (2006)
。
这个方程阐述了这一事实：一个特定的矩阵乘以一个特定的向量，可以得到一个具体的结
果。矩阵也称为线性算子，这个名称更加清楚地说明了矩阵就是一台小型机器 ...
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O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.Julian F.
I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.