K-Means Clustering

Suppose that the data mining task is to cluster the following points (with (x, y) representing location):

P1(20, 100), P2(20, 50), P3(80, 40), P4(50, 80), P5(70, 50), P6(60, 40), P7(10, 20), P8(40, 90)

The distance function is Euclidean distance.

Suppose initially centroids are P1, P4, and P7. Use the k-means algorithm to compute:

a.) The three clusters (K = 3) and their centers after the first iteration. Compute the total Sum of Squared Error for this iteration.

b.) The three clusters (K = 3) and their centers after the second iteration. Compute the total Sum of Squared Error for this iteration.

c.) Between the first iteration and the second iteration, which one produces optimal clusters? Justify your answer.