(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
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