Given N data points xn(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 x1=1,x2=3,x3=6,x4=7. Let's consider k=3 for this situation. What is the optimal clustering for this data? 2. For the above part (1), show that by changing the center initialization we get a suboptimal cluster assignment that cannot be further improved. 3. Prove that the K-means algorithm converges to a local optimum in finite steps. 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