Question 4 - Programming and evaluation of clustering [25 marks] a. Write code to apply k-means to cluster 6 data points (1,1),(1,2),(1,3),(2,1), (2,2), and (4,3) to 2 clusters. Use the initial centroids (1,0) and (2,2). Display the resulting cluster labels of the data points, cluster centroids, number of iterations performed, and inertia. [10] b. Repeat part (a) by varying the initial centroids to obtain a different clustering scheme. That is, you need to find a set of initial centroids to produce cluster labels and cluster centroids that are different from the scheme of part (a). Show the resulting cluster labels and cluster centroids. [3] c. Write code to apply the silhouette method to determine the optimal number of clusters for the dataset in part (a). Use agglomerative hierarchical clustering, and plot the resulting silhouette coefficients for 2 to 5 clusters. [10] d. Using the resulting graph of part (c), determine the optimal number of clusters for the dataset. [2]