Clustering Practice

\(K\)-means

通过一个简单的例子来说明用 kmeans() 进行 \(K\)-means 聚类。

set.seed(123)
x = matrix(rnorm(50*2), ncol=2)
x[1:25, 1] = x[1:25, 1] + 3
x[1:25, 2] = x[1:25, 2] - 4

然后进行 \(K\)-means 聚类，

km.out = kmeans(x, 2, nstart = 20)
plot(x, col = (km.out$cluster+1), main = "K-means (K=2)", xlab = "", ylab = "", pch = 20, cex = 2)

其中 nstart 表示随机初始划分的个数。可以比较下 \(K=3\) 时 nstart = 1 和 nstart = 20 的差异

set.seed(1234)
km.out = kmeans(x, 3, nstart = 1)
km.out$tot.withinss

## [1] 64.24859

km.out = kmeans(x, 3, nstart = 20)
km.out$tot.withinss

## [1] 62.43309

Hierarchical Clustering

可以采用不同的 linkage 进行 系统聚类 (Hierarchical Clustering)

hc.complete = hclust(dist(x), method = "complete")
hc.average = hclust(dist(x), method = "average")
hc.single = hclust(dist(x), method = "single")

并且作出 dendrograms.

par(mfrow=c(1,3))
plot(hc.complete, main = "Complete Linkage", xlab = "", sub = "", cex=.9)
plot(hc.average, main = "Average Linkage", xlab = "", sub = "", cex=.9)
plot(hc.single, main = "Single Linkage", xlab = "", sub = "", cex=.9)

为了确定分类结果，可以用 cutree() 返回类别标签，

cutree(hc.complete, 2)

##  [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2
## [36] 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2

当使用基于相关系数的距离度量时，可以采用 as.dist() 函数，比如

x = matrix(rnorm(30*3), ncol = 3)
dd = as.dist(1-cor(t(x)))
plot(hclust(dd, method="complete"), main = "Complete Linkage with Correlation-Based Distance", xlab = "", sub = "")

References

James, G., Witten, D., Hastie, T., & Tibshirani, R. (Eds.). (2013). An introduction to statistical learning: with applications in R. New York: Springer.