Note, this problem solution will involve a combination of sketching and coding .

2. Consider K-Mean clustering algorithm. Eight samples are given below. Assume that there are three clusters, i.e., k = 3. Initial partitions S10 S2(0), S30) are also given below. Suppose Euclidian distance is used. First sketch the samples and the initial partitions. Then continue with the k-mean algorithm by finding the centroids. Do more iterations of finding both the partitions and the centroids until convergence. Provide your results by showing both the partitions and the centroids. Samples: | X1 X2 X3 X4 X5 X6 X7 Xg (0,1) (0, -1), (0, 3), (0,4), (1,3), (3,0), (3,1), (4,0) Si(0) = { x1, S2O= {X4, S3(0) = {x7, x2, X5, X8} X3} X6} 2. Consider K-Mean clustering algorithm. Eight samples are given below. Assume that there are three clusters, i.e., k = 3. Initial partitions S10 S2(0), S30) are also given below. Suppose Euclidian distance is used. First sketch the samples and the initial partitions. Then continue with the k-mean algorithm by finding the centroids. Do more iterations of finding both the partitions and the centroids until convergence. Provide your results by showing both the partitions and the centroids. Samples: | X1 X2 X3 X4 X5 X6 X7 Xg (0,1) (0, -1), (0, 3), (0,4), (1,3), (3,0), (3,1), (4,0) Si(0) = { x1, S2O= {X4, S3(0) = {x7, x2, X5, X8} X3} X6}