$2.$ K$-$means $(50$ points$)$: Suppose you have a dataset in which the instances are $1-$dimensional. The

instances are $1,2,4,5,10,11,12,25.$ Run k$-$means clustering on this dataset for k $=3$ with initial centroids

on the first $3$ instances in the dataset $($i$.$e$.,1,2,4).$

Draw the points on a number line and show which points belong to which clusters for each

iteration of k$-$means. Either point out the clusters or use the Ci $=$ j notation Run the algorithm until two consecutive iterations yield the same assignment of points to clusters. Draw the elbow curve with inertia as the evaluation criteria. Mention the optimal number of clusters for the above problem.