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Problem 3: In the following figure, 2-class (circle or triangle) classification is being considered based on two input features \( f_{1} \) and \( f_{2} \). Our goal is to construct a decision tree using the algorithm described in the class/notes for the data above. For that purpose, pick the decision boundary which falls halfway between each pair of adjacent points in each dimension, and which produces the minimum average entropy of each split. a. How many total splits - horizontal as well as vertical - are there if we pick the decision boundaries which fall halfway between each pair of adjacent points in each dimension? b. Compute the average entropy of each split. c. Construct the resultant tree that you obtain. d. Mark the regions in the final diagram by labeling them correctly at the end of leaf nodes as well. e. Write down the label (circle or triangle) in front of the following \( \mathrm{x}_{\text {new }} \) if wee apply your constructed decision tree classification algorithm (a) \( \mathbf{x}_{\text {new }}=\left[\begin{array}{ll}0 & 0\end{array}\right]^{T} \) (b) \( \mathbf{x}_{\text {new }}=\left[\begin{array}{ll}-1 & 2\end{array}\right]^{T} \) (c) \( \mathrm{x}_{\text {new }}=[-1.5-1.5]^{T} \)

          Problem 3: In the following figure, 2-class (circle or triangle) classification is being considered based on two input features \( f_{1} \) and \( f_{2} \). Our goal is to construct a decision tree using the algorithm described in the class/notes for the data above. For that purpose, pick the decision boundary which falls halfway between each pair of adjacent points in each dimension, and which produces the minimum average entropy of each split.
a. How many total splits - horizontal as well as vertical - are there if we pick the decision boundaries which fall halfway between each pair of adjacent points in each dimension?
b. Compute the average entropy of each split.
c. Construct the resultant tree that you obtain.
d. Mark the regions in the final diagram by labeling them correctly at the end of leaf nodes as well.
e. Write down the label (circle or triangle) in front of the following \( \mathrm{x}_{\text {new }} \) if wee apply your constructed decision tree classification algorithm
(a) \( \mathbf{x}_{\text {new }}=\left[\begin{array}{ll}0 & 0\end{array}\right]^{T} \)
(b) \( \mathbf{x}_{\text {new }}=\left[\begin{array}{ll}-1 & 2\end{array}\right]^{T} \)
(c) \( \mathrm{x}_{\text {new }}=[-1.5-1.5]^{T} \)

Problem 3: In the following figure, 2-class (circle or triangle) classification is being considered based on two input features f1 and f2. Our goal is to construct a decision tree using the algorithm described in the class/notes for the data above. For that purpose, pick the decision boundary which falls halfway between each pair of adjacent points in each dimension, and which produces the minimum average entropy of each split.
a. How many total splits - horizontal as well as vertical - are there if we pick the decision boundaries which fall halfway between each pair of adjacent points in each dimension?
b. Compute the average entropy of each split.
c. Construct the resultant tree that you obtain.
d. Mark the regions in the final diagram by labeling them correctly at the end of leaf nodes as well.
e. Write down the label (circle or triangle) in front of the following xnew if wee apply your constructed decision tree classification algorithm
(a) 𝐱new =[
0 0
]^T
(b) 𝐱new =[
-1 2
]^T
(c) xnew =[-1.5-1.5]^T

Added by Darnell C.

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