Consider the following dataset consisting of $10$ instances in $($x$,$ y$)$ coordinates,

classified as either Class P or Class N:

P$1$ : $(2\mathrm{.}3,3\mathrm{.}1)-$ Class P

P$2$ : $(5\mathrm{.}0,6\mathrm{.}0)-$ Class P

P$3$ : $(6\mathrm{.}0,3\mathrm{.}0)-$ Class P

P$4$ : $(4\mathrm{.}0,4\mathrm{.}0)-$ Class P

P$5$ : $(6\mathrm{.}0,5\mathrm{.}0)-$ Class P

N$1$ : $(7\mathrm{.}0,7\mathrm{.}0)-$ Class N

N$2$ : $(8\mathrm{.}8,3\mathrm{.}2)-$ Class N

N$3$ : $(9\mathrm{.}6,6\mathrm{.}1)-$ Class N

N$4$ : $(6\mathrm{.}2,8\mathrm{.}2)-$ Class N

N$5$ : $(4\mathrm{.}5,7\mathrm{.}9)-$ Class N

A new instance U of unknown class is at $(6,6).$

$($a$)$ Use the KNN$-$algorithm to determine the class of U$.$

i$.$ First use the Euclidian distance measure $($see Appendix on p$.8)$ and k $=5.$

Show all your distance calculations, the ordering of instances, and the

process of selecting the class for the unknown instance U$.$

Appendix$-$log$2$

for some fractions

x log$2$

$($x$)$

$1/2=0\mathrm{.}5001\mathrm{.}000$

$1/3=0\mathrm{.}3331\mathrm{.}585$

$2/3=0\mathrm{.}6670\mathrm{.}585$

$1/4=0\mathrm{.}2502\mathrm{.}000$

$3/4=0\mathrm{.}7500\mathrm{.}415$

$1/5=0\mathrm{.}2002\mathrm{.}322$

$2/5=0\mathrm{.}4001\mathrm{.}322$

$3/5=0\mathrm{.}6000\mathrm{.}734$

$4/5=0\mathrm{.}8000\mathrm{.}322$

$1/6=0\mathrm{.}1672\mathrm{.}585$

$5/6=0\mathrm{.}8330\mathrm{.}263$

$1/7=0\mathrm{.}1432\mathrm{.}807$

$2/7=0\mathrm{.}2861\mathrm{.}807$

$3/7=0\mathrm{.}4291\mathrm{.}222$

$4/7=0\mathrm{.}5710\mathrm{.}807$

$5/7=0\mathrm{.}7140\mathrm{.}485$

$6/7=0\mathrm{.}8570\mathrm{.}222$

$2/9=0\mathrm{.}2222\mathrm{.}170$

$4/9=0\mathrm{.}4441\mathrm{.}170$

$5/9=0\mathrm{.}5560\mathrm{.}848$

$7/9=0\mathrm{.}7780\mathrm{.}363$

$8/9=0\mathrm{.}8890\mathrm{.}170$

$1/36=0\mathrm{.}0285\mathrm{.}170$

$5/36=0\mathrm{.}1392\mathrm{.}848$

$7/36=0\mathrm{.}1942\mathrm{.}363$

$11/36=0\mathrm{.}3061\mathrm{.}710$

$13/36=0\mathrm{.}3611\mathrm{.}469$

$17/36=0\mathrm{.}4721\mathrm{.}082$

$19/36=0\mathrm{.}5280\mathrm{.}922$

$23/36=0\mathrm{.}6390\mathrm{.}646$

$25/36=0\mathrm{.}6940\mathrm{.}526$

$29/36=0\mathrm{.}8060\mathrm{.}312$

$31/36=0\mathrm{.}8610\mathrm{.}216$

$35/36=0\mathrm{.}9720\mathrm{.}041$

$1=1\mathrm{.}0000\mathrm{.}000$