Consider the following 1-D points (i.e., numbers): 0, 2, 4, 7, 10. Your task is to apply the standard k-means algorithm to partition these numbers into two clusters (i.e., k = 2). Use the following pseudo-code for this problem: . Initialize the prototypes . Repeat until "convergence" . Assign each sample to the cluster of the closest prototype. . Recalculate each prototype as the mean of all the samples belonging to that cluster.

A common approach to initialize the prototypes (cluster representatives) is to use points that are most distant from one another. For the numbers here, this means that the initial prototypes p1 and p2 are at 0 and 10, respectively. Now follow the pseudo-code until convergence, and give the final clusters and their prototypes.