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# Decision Trees

The goal of this part is to write a script to compute the decision tree for an input dataset. You can assume that all attributes are numeric, except for the last attribute which is the class.

You should use the Information Gain based on Entropy for computing the best split value for each attribute. For the stopping criteria at a node, stop if the purity is at least 95% or stop if the node size is five or lower.

Note that the best way to implement the splits for numeric attributes is to sort the values of that attribute from smallest to largest. Then you can use the mid-point between two distinct (consecutive) values as the split test of the form $$A \le v$$. You can then update the class frequencies on both sides of the split and compute the split entropy for each decision. After comparing with the entropy for the node, you can find the best split for the current attribute. Now repeat the whole process for each numeric attribute at that node, and choose the best split over all attributes. Finally, split the data according to the best split, and repeat the whole method recursively, until the stopping conditions are met.

Your script should output the final decision tree using the format described below. For example, for toy data below:

AgeCarTypeRisk
251L
203H
251L
452H
201H
252H

The decision tree should be printed in the following format:

Decision: Car <= 1.5 , Gain= 0.4591479
Decision: Age <= 22.5 , Gain= 0.9182958
Leaf: label= H purity= 1 size= 1
Leaf: label= L purity= 1 size= 2
Leaf: label= H purity= 1 size= 3


Note that each internal node, print the decision followed by the Information Gain, and for each leaf, print the majority label, purity of the leaf, and the size. The indentation indicates the tree level. All nodes at the same level of indentation (tabs) are at the same level in the tree. For the tree above, $$Car <= 1.5$$ is the root decision. Its left child is $$Age <= 22.5$$, and its right child is a leaf. Also, for $$Age \le 22.5$$ its left and right children appear immediately below it.

You may test your program on the iris.txt dataset.