Statistical learning

Suppose we have a 1-dimensional data set with 7 data points, {0,1,3,25,31,44,56}. Answer the following question. You can use a calculator. There is a web-based one made by Google. Just Google “calculator”.

Consider using a bottom-up agglomerative hierarchical clustering method on this data set. What will be the top two clusters (K=2) if we use the single linkage function? How about the top three clusters (K=3)? Hint: you may merge the clusters manually from bottom up. The last 2 or last 3 clusters that remain will be the answer. Hint #2: you may define a 7×7 distance matrix on your answer sheet as a starting point. Then you would need a 6×6 distance matrix as you merge clusters. Then a 5×5 matrix, a 4×4 matrix, …
Consider using a K-means clustering algorithm on this data set with K=2. What will be the resulting 2 clusters after one iteration if the initial values for the cluster centroids are 0 and 50? What will be the updated cluster centroids after one iteration? What will be resulting clusters and the cluster centroids after two iterations?

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