Using R coding $2.$ The data set in nutrients.txt contains nutrients in $27$ different kinds of food. $(25$ Credits$)$

$($a$)$ Apply K$-$means clustering with $4$ clusters and show the cluster assignment of each food $($please sort by cluster label, not the food name, using the sort$()$ function$)$ and the withincluster sum of squares of each cluster. $(10$ Credits$)$

$($b$)$ Apply agglomerative hierarchical clustering based on single$-$linkage, complete linkage, and average linkage algorithms. Plot the dendrograms for all three algorithms. $(15$ Credits$)$

Appendix

More information on the Pima Indians Diabetes Data Set

Number of Instances: $768$

Number of Attributes: $8$ plus class

Description of Each Attribute: $($all numeric$-$valued$)$

$1.$ Number of times pregnant

$2.$ Plasma glucose concentration a $2$ hours in an oral glucose tolerance test

$3.$ Diastolic blood pressure $($ mm Hg $)$

$4.$ Triceps skin fold thickness $($mm$)$

$5.2-$Hour serum insulin $(\backslash (\backslash$mathrm$\{$mu$\}\backslash$mathrm$\{$U$/$ml$\}\backslash ))$

$6.$ Body mass index $($weight in $\backslash (\backslash$mathrm$\{$kg$\}/\backslash )($height in m$\backslash ()^\{\backslash$wedge$\}2\backslash ))$

$7.$ Diabetes pedigree function

$8.$ Age $($years$)$

$9.$ Class variable $(0$ or $1)$

The diagnostic, binary$-$valued variable investigated is whether the patient shows signs of diabetes according to World Health Organization criteria $($i$.$e$.,$ if the $2$ hour post$-$load plasma glucose was at least $\backslash (200\backslash$mathrm$\{$mg$\}/\backslash$mathrm$\{$dl$\}\backslash )$ at any survey examination or if found during routine medical care$).$ The population lives near Phoenix, Arizona, USA.