Given N data points r" (n = 1,..., N), K-means clustering algorithm groups them into K clusters. With respect to K-means clustering answer the following question: 1. Consider the given single dimensional data with 4 data points # = 1,22 = 3, 23 = 6,24 = 7. Let's consider k = 3 for this situation. What is the optimal clustering for this data? [4 pts] 2. For the above part (1), show that by changing the center initialization we get a suboptimal cluster assignment that cannot be further improved. [4 pts] 3. Prove that the K-means algorithm converges to a local optimum in finite steps. [8 pts] 4. Original K-means algorithm uses Euclidian distance as the metric to compute the distance between data points. What is the disadvantage of using this distance function and suggest a solution to overcome this? [4 pts]