# Demonstration of the K-means Cluster Algorithm

### Yihui Xie & Lijia Yu / 2017-04-04

This function provides a demo of the k-Means cluster algorithm for data containing only two variables (columns).

The k-Means cluster algorithm may be regarded as a series of iterations of: finding cluster centers, computing distances between sample points, and redefining cluster membership.

The data given by x is clustered by the $$k$$-means method, which aims to partition the points into $$k$$ groups such that the sum of squares from points to the assigned cluster centers is minimized. At the minimum, all cluster centres are at the mean of their Voronoi sets (the set of data points which are nearest to the cluster centre).

library(animation)
## set larger 'interval' if the speed is too fast
ani.options(interval = 1)
par(mar = c(3, 3, 1, 1.5), mgp = c(1.5, 0.5, 0))
kmeans.ani()

## the kmeans() example; very fast to converge!
x = rbind(matrix(rnorm(100, sd = 0.3), ncol = 2), matrix(rnorm(100,
mean = 1, sd = 0.3), ncol = 2))
colnames(x) = c("x", "y")
kmeans.ani(x, centers = 2)

## what if we cluster them into 3 groups?
kmeans.ani(x, centers = 3)