$($a$)$ The figure below shows a dataset consisting of $32$ points in a two dimensional feature space, that has been clustered using methods from the course, with $K=2.$ Cluster assignments are denoted by black circles for cluster $1,$ and red triangles for cluster $2.$

For each of these methods: K$-$means, GMM$,$ Single$-$link Agglomerative:

Say whether or not the method could result in the clusters shown.

If the method could produce the clusters shown then describe how.

If the method could not produce the clusters shown, then briefly explain why not.

$($b$)$ The figure below shows, for a different dataset, an intermediate clustering

marks