Assignment
1. There are four coins 1, 2, 3, 4 out of which three coins are of equal
weight and one coin is heavier. Use a decision tree to identify the
heavier coin.
2. Consider the three-class problem characterized by the training data
given in the following table. Obtain the axis-parallel decision tree for
the data.
Professor Number of Students Funding Research Output
Sam 3 Low Medium
Sam 5 Low Medium
Sam 1 High High
Pam 1 High Low
Pam 5 Low Low
Pam 5 High Low
Ram 1 Low Low
Ram 3 High Medium
Ram 5 Low High
3. Consider a data set of 10 patterns which is split into 3 classes at a node
in a decision tree where 4 patterns are from class 1, 5 from class 2, and
1 from class 3. Computer Entropy Impurity. What is the Variance
Impurity?
4. For the data in problem 3, compute the Gini Impurity. How about the
Misclassification Impurity?
5. Consider the data given in the following table for a three-class problem.
If the set of 100 training patterns is split using a variable X into two
parts represented by the left and right subtrees below the decision node
as shown in the table, compute the entropy impurity.
6. Compute the variance impurity for the data given in problem 5. How
about the misclassification impurity?
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