Use the k-means algorithm and Euclidean distance to cluster the following 8 data points into 3 clusters:
A1=(2,10) A2=(2,5) A3=(8,4) A4=(5,8) A5=(7,5) A6=(6,4) A7=(1,2) A8=(4,9)
Suppose that the initial seeds (centers of each cluster) are A1, A4, and A7. What are the final three clusters?
The distance matrix based on the Euclidean distance is given below:
A1 A2 A3 A4 A5 A6 A7 A8
A1 0 β25 β36 β13 β50 β52 β65 β5
A2 0 β37 β18 β25 β17 β10 β20
A3 0 β25 β2 β2 β53 β41
A4 0 β13 β17 β52 β2
A5 0 β2 β45 β25
A6 0 β29 β29
A7 0 β58
A8 0