$4.[$Total $20$ marks$]$ With the following data $($pt$\mathrm{.}1-$pt$\mathrm{.}12)$ for spatial clustering, you are asked to apply the DBSCAN algorithm as follows.

$($a$)$ For parameter eps $\backslash (=1\mathrm{.}9\backslash ),$ what MinPts parameter value$($s$)$ will DBSCAN form only one cluster? List ALL possible integer MinPts values.

$(3$ marks$)$

$($b$)$ For parameter MinPts$=4,$ what eps parameter value$($s$)$ will DBSCAN form only one cluster? State the range of all possible eps values.

$(3$ marks$)$

$($c$)$ For parameter $\backslash ($ e p s$=1\mathrm{.}9\backslash ),$ write down one MinPts parameter value that DBSCAN will form no cluster $($i$.$e$.,$ all the data points $1-12$ are considered as noise$).$

$(3$ marks$)$

$($d$)$ For parameter MinPts$=4,$ write down one eps parameter value that DBSCAN will form no cluster $($i$.$e$.,$ all the data points $1-12$ are considered as noise$).$

$(3$ marks$)$

$($e$)$ DBSCAN clustering is sensitive to parameters $($MinPt and eps$)$ used. Suggest an approach to determine appropriate parameter values.

$(4$ marks$)$

$($f$)$ DBSCAN clustering does not work well when the data densities are varying. Give a brief idea to alleviate this problem.

$(4$ marks$)$