Solve the following set of problems using Python and submit the code file

with extension $.$ipynb.

$1.$ Load the $$Obesity$$ dataset. Remove unwanted features if required.

$2.$ Select the optimum k value using Silhouette Coefficient and plot the optimum k

values.

$3.$ Create clusters using Kmeans and Kmeans$++$ algorithms with optimal k value found in

the previous problem. Report performances using appropriate evaluation metrics.

Compare the results.

$4.$ Now repeat clustering using KMeans for $50$ times and report the average

performance. Again compare the results that you have obtained in Q$3$ using

Kmeans$++$ and explain the difference.

$5.$ Apply DBSCAN on this same Obesity dataset and find the optimum "eps" and

"min$\_$samples" value. Is the number of clusters the same as the cluster found in Q$2?$

Explain the similarity or differences that you have found between two solutions.

$6.$ Load the $$gene expression$$ dataset. Apply PCA on the genes for generating $3$

principal components. Plot the first three components of the PCA.

$7.$ Continue from question $6,$ what is the variance $(\%)$ covered by the first three

components? Explain how this percentage of variance has been computed?

$8.$ Continue from question $6,$ apply KMeans on the original features of the gene dataset

and the first three components returned by PCA. Compare the results using the given labels. Kindly share the jupyter note $($contaning the code, outputs and explanation to the answers$)$