Question $3$ Decision Tree Classifier ${?}^{[45\%]}$

Consider the Data $Se{t}^2$ in Table $2$ for a classification problem, where all attributes are nominal.

a$)[24\%]$ Use data records $1-12$ as the training set to build a decision tree for predicting the class attribute. Use entropy as the impurity measure and the information gain $<mn>0</mn><mn>.</mn><mn>4</mn>$ as the pre$-$pruning criteria. Show your steps.

b$)[9\%]$ Use data records $1-12$ as the training set to complete the decision tree in Figure $1$ by assigning a class label to each of the leaf nodes.

c$)[12\%]$ Use the data records $13-18$ as the test set.

i$.$ Construct the confusion matrix for the completed decision tree in part b$).$

ii$.$ Calculate the corresponding accuracy.

iii. Calculate the precision and recall with respect to class $"B".$

$\backslash$table$[[,$Record,LW$,$LD$,$RW$,$RD$,$Class$],[$Training$,1,$Low,Low,Low,Low,R$],[$set$,2,$Low,Low,Low,High,B$],[,3,$Low,Low,High,Low,R$],[,4,$Low,Low,High,Low,B$],[,5,$Low,High,Low,Low,B$],[,6,$Low,High,Low,High,L$],[,7,$Low,High,High,Low,R$],[,8,$High,Low,Low,High,L$],[,9,$High,Low,Low,High,B$],[,10,$High,Low,High,Low,R$],[,11,$High,High,Low,High,L$],[,12,$High,High,High,High,L$],[$Test set,$13,$Low,Low,Low,High,B$],[,14,$Low,High,Low,Low,L$],[,15,$Low,High,High,High,R$],[,16,$High,Low,Low,Low,B$],[,17,$High,Low,High,High,R$],[,18,$High,High,High,Low,L$]]$

Table $2$ Dataset for classification