Question 3: Hierarchical Clustering [25 points] Consider the following six major cities. In the US: Madison, Seattle, Boston; and in Canada: Vancouver, Winnipeg, Montreal. For the purpose of this question ignore the curvature of the Earth, and compute the Euclidean distance. Suppose the cities are located at the following coordinates: coordinate Madison(-89, 43) Seattle (-122, 48) Boston(71, 42) Vancouver(-123, 49) Winnipeg97, 50) (-74, 46 city Montreal 1. Use hierarchical clustering with complete linkage to produce TWO clusters by hand. Specifically, show the following in each iteration: (1) the closest pair of clusters; (2) the distance bet ween them as defined by complete linkage; (3) all clusters at the end of that iteration. 2. Now repeat the above question, but with the following constraint: at no point should a US city and a Canadian city be put in the same cluster. Equivalently, whenever the complete linlage bet ween tw clusters is due to two cities in different countries, treat the two clusters as infinity apart, regardless of what other cities are in those two clusters. Show the same (1) (2) (3) as above in each iteration