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()
```

plot of chunk demo-a

```
## 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)
```

plot of chunk demo-b

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

plot of chunk demo-c