October 2021
Intermediate to advanced
289 pages
8h 31m
Chinese
Content preview from 数据科学中的实用统计学(第2版)
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198
｜
第
6
章
6.1.2
距离的度量
相似度（或邻近度）是通过
距离度量
来确定的，这种度量是一个函数，它测量的是两条记
录
(
x
1
,
x
2
,
…
,
x
p
)
和
(
u
1
,
u
2
,
…
,
u
p
)
之间的距离有多远。两个向量之间最常用的距离度量是
欧
氏距离
。要计算两个向量之间的
欧氏距离
，先将它们的分量依次相减，再对得到的差进行
平方，加总之后再取平方根即可：
22 2
11 2 2
( )( ) ( )
pp
xu x u x u− + − ++ −
针对数值型数据的另一种常用距离度量是
曼哈顿距离
：
11 2 2
| || | | |
pp
xu x u x u− + − ++ −
欧氏距离相当于两点之间的直线距离（就像乌鸦飞行一样），而曼哈顿距离是两点之间依
次按照单一方向经过的距离（例如，沿着矩形的城市街区行走）。因此，如果相似度定义
为点对点的行程时间，那么曼哈顿距离就是一种非常有用的近似。
在测量两个向量之间的距离时，使用较大的数量级进行测量的变量（特征）会主导测量结
果。举例来说，在贷款数据中，距离几乎就是收入变量和贷款数额变量的函数，它们的值
都是几万或者几十万的，与之相比，比率变量所起的作用微乎其微。通过对数据进行标准
化可以解决这一问题，参见
6.1.4
节。
其他距离度量
向量之间还有多种其他类型的度量方式。对于数值型数据，
马氏距离
非常引
人关注，因为它考虑了两个变量之间的相关性。马氏距离非常有用，因为如
果两个变量高度相关，它就会将它们作为一个变量来处理。欧氏距离和曼哈
顿距离都没有考虑相关性，在构成相关性的属性上赋予了过多权重。马氏距 ...
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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.