$1.$ Consider the following clustering method called Leader Clustering. It receives two parameters: an integer k and a real number t$.$ Similar to k$-$means, it starts by selecting k instances

$($which will be called leaders$)$ and assigns each training instances to the cluster of the closest leader. During the assignment step, however, if the distance of a training instance to its closest leader is greater than the input threshold t$,$ then this training instance becomes a

new leader. During the same assignment step, remaining points can be assigned to these new leaders. After all the training instances have been assigned to a leader$$s cluster, new leaders are calculated by averaging each cluster. The process is then repeated until the cluster assignments do not change. $[$Use diagram to illustrate following answers$]$