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Chapter $3$ Classification

Table $3\mathrm{.}6.$ Data set for Exercise $4.$

$\backslash$table$[[$Instance$,a_1,a_2,a_3,$Target Class$],[1,$T$,$T$,1\mathrm{.}0,+],[2,$T$,$T$,6\mathrm{.}0,+],[3,$T$,$F$,5\mathrm{.}0,-],[4,$F$,$F$,4\mathrm{.}0,+],[5,$F$,$T$,7\mathrm{.}0,-],[6,$F$,$T$,3\mathrm{.}0,-],[7,$F$,$F$,8\mathrm{.}0,-],[8,$T$,$F$,7\mathrm{.}0,+],[9,$F$,$T$,5\mathrm{.}0,-]]$

$($d$)$ Compute the Gini index for the Car Type attribute using multiway split.

$($e$)$ Compute the Gini index for the Shirt Size attribute using multiway split.

$($f$)$ Which attribute is better, Gender, Car Type, or Shirt Size?

$($g$)$ Explain why Customer ID should not be used as the attribute test condition even though it has the lowest Gini.

$4.$ Consider the training examples shown in Table $3\mathrm{.}6$ for a binary classification problem.

$($a$)$ What is the entropy of this collection of training examples with respect to the class attribute?

$($b$)$ What are the information gains of $a_1$ and $a_2$ relative to these training examples?

$($c$)$ For $a_3,$ which is a continuous attribute, compute the information gain for every possible split.

$($d$)$ What is the best split $($among $a_1,a_2,$ and $a_3)$ according to the information gain?

$($e$)$ What is the best split $($between $a_1$ and $a_2)$ according to the misclassification error rate?

$($f$)$ What is the best split $($between $a_1$ and $a_2)$ according to the Gini index?