We want to develop a Divisive (top-down) Hierarchical Clustering method. This method starts with the whole dataset as one cluster. In each iteration, it (1) chooses one of the clusters to split and (2) splits the chosen cluster into two clusters. (1) How to choose the cluster to be split? Present your solution in plain English and include a rationale for your choice (2) To determine how to split the chosen cluster into two clusters, first consider an optimum split that s the opposite inverse the merge in agglomerative (bottom-up) hierarchical clustering. How is this optimum split defined? Present an (inefficient) algorithm to determine the optimum split. What is the runtime complexity of this algorithm in terms of the number n of elements of the cluster to be split? (3) Now suggest a more efficient algorithm to find a "good" split approximating the optimum split. What is the runtime complexity of this algorithm in terms of the number n of elements of the cluster to be split? We want to develop a Divisive (top-down) Hierarchical Clustering method. This method starts with the whole dataset as one cluster. In each iteration, it (1) chooses one of the clusters to split and (2) splits the chosen cluster into two clusters. (1) How to choose the cluster to be split? Present your solution in plain English and include a rationale for your choice (2) To determine how to split the chosen cluster into two clusters, first consider an optimum split that s the opposite inverse the merge in agglomerative (bottom-up) hierarchical clustering. How is this optimum split defined? Present an (inefficient) algorithm to determine the optimum split. What is the runtime complexity of this algorithm in terms of the number n of elements of the cluster to be split? (3) Now suggest a more efficient algorithm to find a "good" split approximating the optimum split. What is the runtime complexity of this algorithm in terms of the number n of elements of the cluster to be split