a$.$ Following the example in this chapter$($page $543$ q$20\mathrm{.}4,$ data mining for business analytics using Python, preprocess the documents, except do not create a label vector.

b$.$ Use the LSA to create $10$ concepts.

c$.$ Before doing the clustering, state how many natural clusters you expect to find.

d$.$ Perform hierarchical clustering and inspect the dendrogram.

i$.$ From the dendrogram, how many natural clusters appear?

ii$.$ Examining the dendrogram as it branches beyond the number of main clusters, select a sub$-$cluster and assess its characteristics.

e$.$ Perform k$-$means clustering for two clusters and report how distant and separated they are $($using between$-$cluster distance and within cluster$$dispersion$).$