1. Apply the k-means clustering to the following points in R4:

(4:1, 3:6, 4:8, 5:5)

(7:4, 3:0, 3:2, 6:1)

(3:7, 4:9, 6:5, 6:1)

(5:1, 5:6, 4:3, 5:4)

(3:3, 4:0, 4:3, 5:9)

(5:4, 3:8, 4:4, 4:3)

(a0, a1, a2, a3)

(a4, a5, a6, a7)

Where a0 a1 a2 a3 a4 a5 a6 a7 is your student enrolment number. Use two cluster centres, with initial positions (3, 0, 0, 0) and (5, 0, 0, 0). For each iteration show the current positions of the cluster centres.

2. Suppose (in one dimension), the point values x are generated from two sources, one producing points normally distributed around μ1 with variance σ2, the other producing points normally distributed around μ2 with the same variance σ2. If you used the k-means algorithm to find the centres of these clusters, would you expect the centres to be closer together, the same distance, or further apart than μ1 and μ2? Explain why.