Problem $3$: DBSCAN $(30$ points$)$

Consider the following $2$D dataset:

$(10$ points$)$ Apply the DBSCAN algorithm to the given dataset using Euclidean distance with

the following parameters: epsi$=2$ and MinPts $=3.$ Identify the core points, border points, and

noise points in the final clustering result.

$(10$ points$)$ Discuss the effect of changing the epsi value in DBSCAN. What happens when you

increase or decrease its value? How does it affect the resulting clusters and noise points?

$(10$ points$)$ Discuss the advantages and limitations of DBSCAN compared to KMeans and

hierarchical clustering.

Please solve this problem step by step. Thank you