7. Clustering k Means (10 pts.)

Assume the following dataset is given: (2,3), (4,3), (5,6), (6,6),(9,8) (0,4), (2,0) . K-Means is run with k=3 to cluster the dataset. Moreover, Manhattan distance is used as the distance function to compute distances between centroids and objects in the dataset.

K-Means initial centroids C1, C2, and C3 are as follows:

C1: (1,1)

C2: (6,6)

C3: (8,7)

Now K-means is run for a single iteration.

a.Assign each data point to one of the three centroid based on k-means algorithm. (5 pts)

Cluster 1 - Centroid (1,1) :

Cluster 2 Centroid (6,6):

Cluster 3 - Centroid (8,7):

b.Based on the above result, re-calculate the new centroid for each cluster (5 pts)

New Centroid for cluster 1 :

New Centroid for cluster 2 :

New Centroid for cluster 3 :