(Hint: only the leaves of the old decision tree need to be changed.) Does the decision tree capture the “+” concept?

Following is a data set that contains two attributes, X and Y , and two class


labels, “+” and “?”. Each attribute can take three different values: 0, 1, or 2.





The concept for the “+” class is Y = 1 and the concept for the “?” class is


X = 0 ? X = 2.


Build a new decision tree with the following cost function:

The cost matrix can be summarized as follows:





The decision tree in part (a) has 7 leaf nodes, X = 1, X = 0 ? Y = 0,


X = 0 ? Y = 1, X = 0 ? Y = 2, X = 2 ? Y = 0, X = 2 ? Y = 1, and


X = 2 ? Y = 2. Only X = 0 ? Y = 1 and X = 2 ? Y = 1 are impure


nodes. The cost of misclassifying these impure nodes as positive class


is:





10 ? 0+1 ? 100 = 100


while the cost of misclassifying them as negative class is:


10 ? 20 + 0 ? 100 = 200.


These nodes are therefore labeled as +.


The resulting concept is