Consider the following initialization of a K-Means Clustering problem (K=3 with labels [A, B, C]).
We have 8 points indexed from 1 to 8 with the following (X, Y) coordinates:
p_1 (1,2), p_2 (2,1), p_3 (3,2), p_4 (3,3), p_5 (4,1), p_6 (5,2), p_7 (5,5), p_8 (6,4).
In our initialization of K-means, we choose p_1 (1,2) as centroid A, p_4 (3,3) as centroid B, and p_7 (5,5) as centroid C.
After the first round of K-Means clustering, which cluster would each point be assigned to? What is the position of the new centroids? Show key steps of your computation.
