Part $2$: Implementing k$-$Means Clustering $(25$ points$)$

Tasks:

Data Preparation: Same as above. No points for this step.

k$-$Means Clustering code as below steps:

Initialize Centroids randomly, assign points to nearest centroid, update centroid, and repeat until convergence

Run $k-$Means for $k=2,k=3,$ and $k=5.$ For each $k,$ store the final centroids and cluster assignments.

Compute and Plot the Objective Function $($SSE$)$

Compute the SSE for each value of $,$ and $5$