Use the k-means algorithm and Euclidean distance to cluster the following 8 examples into 3 clusters:

P1= (2,10), P2= (2,5), P3= (8,4), P4= (5,8), P5= (7,5), P6= (6,4), P7= (1,2), P8= (4,9).

The distance matrix based to be used on the basis of Euclidean distance is given below:

	P1	P2	P3	P4	P5	P6	P7	P8
P1
P2
P3
P4
P5
P6
P7
P8

Suppose that the initial seeds (centers of each cluster) are P1, P3 and P8. Run the k-means algorithm for 1 epoch only. At the end of this epoch show:

1. The new clusters (i.e. the examples belonging to each cluster)
2. The centers of the new clusters
3. Draw a 10 by 10 space with all the 8 points and show the clusters after the first epoch and the new centroids.
4. How many more iterations are needed to converge? Draw the result for each epoch.

1. MSE(Cluster 1) =

   MSE(Cluster 2) =

   MSE(Cluster 3) =

   For the clustering you obtained at the end of the iteration above, give the mean square error of each cluster

MSE = Error =1 Ni=1k(xi-)2