Problem 2. Given the following unlabelled dataset: x= {x}=1= {23, 52, 29, 37, 46, 47, 32, 25, 49}. (a) 20% Execute the K-centers algorithm with K = 3. The initial centroid is chosen as x(7); show all your iterations. Then, compute the SSE and BSS of the resultant clustering. (b) 20% Execute the K-means algorithm with K = 3, where the initial centroid set is Z = {x, 20, 50} Use no more than 8 iterations; show all your steps. Then, compute the SSE and BSS of the resultant clustering. (c) 20% Calculate the dissimilarity matrix D over X. Thereby, execute the single linkage algorithm. In each iteration, capture (i) the updated dissimilarity matrix and (ii) intermediate clustering results. Then, sketch its corresponding dendrogram.

Problem 2. Given the following unlabelled dataset: x= {x}=1= {23, 52, 29, 37, 46, 47, 32, 25, 49}. (a) 20% Execute the K-centers algorithm with K = 3. The initial centroid is chosen as x(7); show all your iterations. Then, compute the SSE and BSS of the resultant clustering. (b) 20% Execute the K-means algorithm with K = 3, where the initial centroid set is Z = {x, 20, 50} Use no more than 8 iterations; show all your steps. Then, compute the SSE and BSS of the resultant clustering. (c) 20% Calculate the dissimilarity matrix D over X. Thereby, execute the single linkage algorithm. In each iteration, capture (i) the updated dissimilarity matrix and (ii) intermediate clustering results. Then, sketch its corresponding dendrogram.