Question# 03: Use the k-means algorithm and Euclidean distance to cluster the following 8 examples into 3 clusters: A1=(2,10), A2=(2,5), A3=(8,4), A4=(5,8), A5=(7,5), A6=(6,4), A7=(1,2), A8=(4,9). The distance matrix based on the Euclidean distance is given. Suppose that the initial seeds (centers of each cluster) are A1, A4 and A7. 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.