Unsupervised Learning is a great way of dealing with datasets that are not structured, clustering thus helps in segregating the dataset based on common features. This dataset can further be used as a labeled dataset for Supervised Learning.

Considering "housing.csv$"$ dataset, find and plot the clusters with different colors by applying DBSCAN algorithm.

Again, considering the same dataset, "housing.csv$",$ find optimal k$-$value $($optimal number of clusters$)$ for k$-$means clustering algorithm and plot the clusters with different colors. You should use following methods for finding K$.$

Elbow Method

Silhoutte Mehod

Gap Statistic

Compare and discuss of your findings.