Exercise 3 - Clustering

1. Perform a hierarchical clustering on the one-dimensional set of points $1, 4, 11, 16, 25, 36, 49, 64, 81$, assuming the clusters are represented by their centroid (average), and at each step the clusters with the closest centroids are merged.

2. How would the clustering of 1.) change if we use for the distance between the two clusters the minimum of the distances between any two points (one from each cluster). 

You have to show the clustering after each merge step.

Reference:  Rajaraman, A.; Leskovec, J. & Ullman, J. D. (2014). Mining Massive Datasets (3rd ed.). MA: Cambridge University Press.