[8 marks] Assume K-Means is used with k=3 to cluster a 2-dimensional dataset: {(1,1), (4,4),(5,5),(7,7),(9,9),(0,6),(6,0)}. The Manhattan distance is used as the distance function d((x1,y1),(x2,y2))=x1x2+y1y2 to compute the distances between cluster means and objects in the dataset. The initial K-Means clusters (C1, C2 and C3) are shown below. C1:{(1,1),(4,4),(7,7)} C2:{(0,6),(6,0)} C3:{(5,5),(9,9)} (a) [4 marks] Assume that K-Means is run for a single iteration. Which are the new clusters and what are their means? (b) [4 marks] "K-Means would always produce the same clusters when re-executed on the same dataset". Is the above statement true or false? Justify your answer in no more than 3 sentences