1. We have a cluster containing points [7,5], [2,2], [3,8]. What would be its best partitioning according to the minimization of the sum of squared distance criterion?

2. What would be our choice for the initial k=4 cluster centroids for the data set X = [0,0; 10,10; 1,6; 3,7; 4,3; 7,7; 8,2; 9,5] when applying the cluster initialization heuristic mentioned at the lecture. Suppose that the first cluster centroid we choose is point [0,0].

3. BFR clustering
What would be the representation of the cluster that contain points [1,4,5], [2,3,7], [-3,5,8]?
Supposing we have two further clusters that are described by [4,13,6,28,81,12,202], [5,20,9,17,94,61,87]. Which cluster would we assign the data point [0,-2,3] to?
How would the cluster representations look like after assigning this point to the appropriate cluster?

4. Given two centroids, is it possible that for some point x different centroids fall closed to x depending on whether its distance is measured according to different norms (e.g. L1 and L2 norms)?