Please provide python code and explanations:

Clustering $[16]$

Use the file umap.csv to answer the following questions. The file umap.csv

contains the UMAP embeddings of the documents.

Question $5\mathrm{.}1[1]$

How many features do the UMAP embeddings have? What parameter was

specified when performing UMAP to obtain the required number of features?

Question $5\mathrm{.}2[3]$

Create a scatterplot matrix $($SPLOM$)$ of the UMAP embeddings. Comment on

the clustering tendency of the data.

Question $5\mathrm{.}3[3]$

Create a k$-$dist graph using the UMAP embeddings, where the k$-$distance

is defined as the Euclidean distance from each instance to its $99$th nearest

neighbour. Based on the graph, suggest an appropriate range for the k$-$distance.

Question $5\mathrm{.}4[2]$

Apply density$-$based spatial clustering of applications with noise $($DBSCAN$)$ to

the UMAP embeddings. Select an eps value that will result in approximately

thirteen clusters $($excluding noise$).$ Display the number of instances assigned to

each cluster using an appropriate visualization.

Question $5\mathrm{.}5[3]$

Create a scatterplot matrix $($SPLOM$)$ of the UMAP embeddings where the

colour of an instance should be based on the cluster label of the instance. From

the SPLOM suggest a rule that can be used to assign instances to one cluster.

Question $5\mathrm{.}6[3]$

Select the largest clusters $($excluding the noise cluster$).$ For all the instances

assigned to this cluster:

$$ sum the values of the tf$-$idf embeddings per column,

$$ sort the values from large to small,

$$ select the largest ten values and

$$ display the ten associated tokens.

Does the cluster correspond to a specific infrastructure category? Motivate your

answer.