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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244
｜
第
7
章
图 7-5：在 XOM 和 CVX 的股票每日收益数据上使用 K-均值方法得到的簇（簇中心点使用粗黑符号
进行了突出显示）
7.2.2
K-
均值算法
通常，
K-
均值可以应用于有
p
个变量
X
1
,
…
,
X
p
的数据集。要得到
K-
均值的精确解，在计
算上非常困难，但可以使用启发式算法高效地算出一个局部最优解。
在这个算法中，首先需要用户确定
K
的值以及簇均值的一个初始集合，然后按以下步骤进
行迭代。
1.
将每条记录分配给按照距离的平方来测量的最近的簇均值。
2.
基于上面的记录分配，计算出新簇的均值。
当记录与簇的分配关系不再发生变化时，算法收敛。
对于第一次迭代，需要确定一个簇均值的初始集合。一般来说，可以随机地将每条记录分
配给
K
个簇中的一个，然后再算出这些簇的均值。
因为这种算法不能保证找到最优的解决方案，所以建议多次运行该算法，每次使用不同的
随机抽样来对算法进行初始化。进行了多次迭代之后，
K-
均值的结果就可以由具有最小的
簇内平方和的那次迭代给出。
R
函数
kmeans
的
nstart
参数可以指定算法随机启动的次数。例如，以下
R
代码使用
10
个
不同的簇均值启动算法，最后得到
5
个簇：
syms <- c( 'AAPL', 'MSFT', 'CSCO', 'INTC', 'CVX', 'XOM', 'SLB', 'COP',
'JPM', 'WFC', 'USB', 'AXP', 'WMT', 'TGT', 'HD', 'COST')
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