Q.6 Cluster Analysis [15 marks] The objective of cluster analysis is the allocation of a set of observations into k different groups. (a) Explain the methods of divisive clustering. [2 marks] (b) Given the following data points: (1,2), (2,2), (4,4.5), and (2,1.5). Suppose these points are initially in the two clusters {(1,2), (2, 2)} and {(4,4.5), (2,1.5)}. Perform k-means clustering. Show your working, but no distance calcula- tions are required. [3 marks] (c) State and explain the three measures of linkage distance between clusters. [3 marks) (a) Perform agglomerative clustering with the same points (1, 2), (2, 2), (4,4.5), and (2,1.5), using single-linkage based on the Euclidean distance. Draw the dendrogram. [3 marks] (e) Calculate the Euclidean (L2) and Minkowski (L1) distance between the points A and B where: A= (1, 2, 3, 4)' and B = (7,2,9, 1)'. (f) What is the impact of overfitting in cluster analysis? How could you overcome overfitting? [2 marks] - Q.6 Cluster Analysis [15 marks] The objective of cluster analysis is the allocation of a set of observations into k different groups. (a) Explain the methods of divisive clustering. [2 marks] (b) Given the following data points: (1,2), (2,2), (4,4.5), and (2,1.5). Suppose these points are initially in the two clusters {(1,2), (2, 2)} and {(4,4.5), (2,1.5)}. Perform k-means clustering. Show your working, but no distance calcula- tions are required. [3 marks] (c) State and explain the three measures of linkage distance between clusters. [3 marks) (a) Perform agglomerative clustering with the same points (1, 2), (2, 2), (4,4.5), and (2,1.5), using single-linkage based on the Euclidean distance. Draw the dendrogram. [3 marks] (e) Calculate the Euclidean (L2) and Minkowski (L1) distance between the points A and B where: A= (1, 2, 3, 4)' and B = (7,2,9, 1)'. (f) What is the impact of overfitting in cluster analysis? How could you overcome overfitting? [2 marks]