$[30$ points$]$ DBSCAN.

Please manually apply DBSCAN to the following small dataset to identify three types of

points in the dataset, core, border and outliers$/$noises$.$ eps $=0\mathrm{.}6$ and MinPts $=4.$ You need to

provide the detailed steps to get the full points.

$x=\left[\begin{array}{cc}1\mathrm{.}0& 2\mathrm{.}0\\ 3\mathrm{.}0& 4\mathrm{.}0\\ 2\mathrm{.}5& 4\mathrm{.}0\\ 1\mathrm{.}5& 2\mathrm{.}5\\ 3\mathrm{.}0& 5\mathrm{.}0\\ 2\mathrm{.}8& 4\mathrm{.}5\\ 2\mathrm{.}5& 4\mathrm{.}5\\ 1\mathrm{.}2& 2\mathrm{.}5\\ 1\mathrm{.}0& 3\mathrm{.}0\\ 1\mathrm{.}0& 5\mathrm{.}0\\ 1\mathrm{.}0& 2\mathrm{.}5\\ 5\mathrm{.}0& 6\mathrm{.}0\end{array}\right]$