4. Consider the 1-dimensional data points in Figure 5a. Say we are running k-means on the data with k=2 clusters with initial cluster centers 1 and 2. Each point is assigned to the cluster with the closest center, so cluster C1={x1,x2,x3} and C2={x4,x5,x6,x7,x8,x9,x10}, as given in Figure 5b. (b) Data points assigned to clusters. Points in C1 are shown in purple. Points in C2 are shown in orange. Current cluster centers 1 and 2 are drawn with an x. Figure 5 (a) We are going to update the cluster center for C1. The algorithm's goal at this step is to pick a new cluster center 1 that decreases the loss. Recall the overall loss function for k-means from lecture: L(C1,,Ck)=n1=1kiCxi22 What is C1 's contribution to the loss with the given data points and the cluster assignments? Your answer should be a function in terms of the variable 1. You do not need to include the constant n1