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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无监督学习
｜
257
mclust
得到的簇可能有些出乎意料，但它们确实反映了这种算法的统计学本质。基于模型
的聚类方法的目标是找出多元正态分布的最佳拟合集合。从图
7-10
中的等高线来看
，股
票数据似乎具有一个正态分布的形状，但实际上，股票收益是一个长尾分布，不是正态分
布。为了处理这个问题，
mclust
先对数据主体拟合了一个分布，随后又拟合了第二个方差
更大的分布。
7.4.3
选择簇的数量
与
K-
均值和层次聚类不同，
mclust
可以自动选择簇的数量（在这个例子中，簇的数目是
2
）
，它的方法是选择能使
贝叶斯信息准则
（
Bayesian Information Criteria
，
BIC
）有最大值
的簇数目（
BIC
与
AIC
类
似，参见
4.2.4
节 ）。
BIC
的原理是选择带有惩罚项的最佳拟合模
型，这个惩罚项是关于模型中参数数量的。在基于模型的聚类中，加入更多簇总是会改善
拟合效果，但代价是在模型中引入了更多的参数。
请注意，在多数情况下，
BIC
要最小化。
mclust
包的作者决定使用符号相反
的
BIC
，是为了使解释图形变得更加容易。
mclust
拟合
14
种模型，每种模型中簇的数量是依次递增的，然后自动选择一个最优模型。
可以使用
mclust
中的一个函数绘制出这些模型的
BIC
值：
plot(mcl, what='BIC', ask=FALSE)
簇的数目，也就是不同多元正态模型（簇）的数量，显示在
x
轴上（见图
7-12
）。
图 7-12：14 种股票收益数据模型的 BIC 值，模型中簇的数目依次递增
258
｜
第
7
章
Python ...
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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.