R：除了 nstart 和 iter.max 的不同设置外，k-means 中的相同集群

Question

尽管我对 kmeans() 的 iter.max 和 nstart 使用（非常）不同的设置，但为什么我得到相同的聚类？

set.seed(1)
ff_1 <- kmeans(faithful, 2, iter.max = 1, nstart = 1)

set.seed(1)
ff_2 <- kmeans(faithful, 2, iter.max = 2, nstart = 1)

set.seed(1)
ff_300 <- kmeans(faithful, 2, iter.max = 300, nstart = 300)

identical(ff_1, ff_2) # TRUE
identical(ff_1, ff_300) # TRUE

我的真正目标是通过比较一次迭代的聚类与 2、3 或 10 次迭代的聚类来可视化 k-means 聚类的收敛（用于教育目的）。这就是我加入 set.seed 行的原因。

Answer 1

kmeans 的初始质心是随机选择的，因为

(1) 您在所有情况下都选择了相同的随机种子 = 1（这将强制为所有情况选择完全相同的质心）并且

(2) 簇是完全可分离的，您在这些情况下得到相同的结果（在第一次迭代后收敛发生得非常快）。

如下图所示

library(grid)
library(gridExtra)
library(ggplot2)

set.seed(1)
ff_1 <- kmeans(faithful, 2, iter.max = 1, nstart = 1)

set.seed(1)
ff_2 <- kmeans(faithful, 2, iter.max = 2, nstart = 1)

set.seed(1)
ff_300 <- kmeans(faithful, 2, iter.max = 300, nstart = 300)

grid.arrange(
  ggplot(faithful, aes(eruptions, waiting, col=as.factor(ff_1$cluster))) + geom_point() +
    geom_point(data=as.data.frame(ff_1$centers), aes(eruptions, waiting), col='black', pch='*', cex=15) +
    labs(title = "kmeans seed 1\n", color = "ff1 cluster\n"), 
  ggplot(faithful, aes(eruptions, waiting, col=as.factor(ff_2$cluster))) + geom_point() +
    geom_point(data=as.data.frame(ff_2$centers), aes(eruptions, waiting), col='black', pch='*', cex=15) +
    labs(title = "kmeans seed 1\n", color = "ff2 cluster\n"),
  ggplot(faithful, aes(eruptions, waiting, col=as.factor(ff_300$cluster))) + geom_point() +
    geom_point(data=as.data.frame(ff_300$centers), aes(eruptions, waiting), col='black', pch='*', cex=15) +
    labs(title = "kmeans seed 1\n", color = "ff300 cluster\n"))

identical(ff_1, ff_2) # TRUE
identical(ff_1, ff_300) # TRUE

现在，让我们改变种子，迫使kmeans选择不同的初始质心，结果会有所不同，如下图所示。

set.seed(1)
ff_1 <- kmeans(faithful, 2, iter.max = 1, nstart = 1)

set.seed(12)
ff_2 <- kmeans(faithful, 2, iter.max = 2, nstart = 1)

set.seed(123)
ff_300 <- kmeans(faithful, 2, iter.max = 300, nstart = 300)

grid.arrange(
  ggplot(faithful, aes(eruptions, waiting, col=as.factor(ff_1$cluster))) + geom_point() +
    geom_point(data=as.data.frame(ff_1$centers), aes(eruptions, waiting), col='black', pch='*', cex=15) +
    labs(title = "kmeans seed 1\n", color = "ff1 cluster\n"), 
  ggplot(faithful, aes(eruptions, waiting, col=as.factor(ff_2$cluster))) + geom_point() +
    geom_point(data=as.data.frame(ff_2$centers), aes(eruptions, waiting), col='black', pch='*', cex=15) +
    labs(title = "kmeans seed 12\n", color = "ff2 cluster\n"),
  ggplot(faithful, aes(eruptions, waiting, col=as.factor(ff_300$cluster))) + geom_point() +
    geom_point(data=as.data.frame(ff_300$centers), aes(eruptions, waiting), col='black', pch='*', cex=15) +
    labs(title = "kmeans seed 123\n", color = "ff300 cluster\n"))

identical(ff_1, ff_2) # FALSE
identical(ff_1, ff_300) # FALSE

R：除了 nstart 和 iter.max 的不同设置外，k-means 中的相同集群

R: Same clusters in k-means besides different settings for nstart and iter.max

r

cluster-analysis

k-means