Suppose that we have the following data: a b c d e f g h i j (2,0) (1,2) (2,2) (3,2) (2,3) (3,3) (2,4) (3,4) (4,4) (3,5)

Identify the cluster by applying the k-means algorithm, with k = 2. Try using initial cluster centers as far apart as possible.

Show that the ratio of the between-cluster variation to the within-cluster variation decreases with each pass of the algorithm.