$8.$ Visualizing K$-$means Clustering

$3$ points possible $($graded$)$

As above, we continue to use the log$-$transformed data projected onto the top PC$\text{'}$s $.$

Run K$-$Means on the projected data with the number of clusters by selected by looking at the T$-$SNE plot.

Redo the PCA, MDS$,$ and T$-$SNE plots from previous part, but now with colors representing the different cluster identities $($e$.$g$.$ use $10$ colors if there were $10$ K$-$means clusters, one color for each K$-$means cluster$).$

Hint: For question $8\mathrm{.}1,$ first, you do k$-$means on the log$-$transformed data projected on $50$ PC$\text{'}$s$.$ Next, you save the cluster assignment for each of the point. Now, you copy and paste whatever you have in the previous part, and don't change anything, except you assign the cluster you just obtained in the first step. In the last step, you count the max number of clusters there are in any big cluster.

Consider the clusters that you can distinguish visually in the PCA plot. What is the maximum number of K$-$means clusters $($i$.$e maximum number of colors$)$ in one visual cluster? Ignore outliers.