Assume the following dataset is given: (2,2), (4,4), (5,5), (6,6), (8,8), (9,9), (0,4), (4,0). K-Means is used with k=4 to cluster the dataset. Moreover, Manhattan distance is used as the distance function (formula below) to compute distances between centroids and objects in the dataset.
D((x1, x2), (x1', x2')) = |x1-x1'| + |x2-x2'|
Further assume that K-Means's initial clusters C1, C2, C3, and C4 are as follows:
C1: {(2, 2), (4, 4), (6, 6)}
C2: {(0, 4), (4, 0)}
C3: {(5, 5), (9, 9)}
C4: {(8, 8)}
Now apply the K-means algorithm and show the centroids and the clusters for each iteration.