Calculate the gain in the Gini index when splitting on A and B. Which attribute would the decision tree induction algorithm choose?
Consider the following data set for a binary class problem.
The overall gini before splitting is:
Gorig = 1 ? 0.42 ? 0.62 = 0.48
The gain in gini after splitting on A is:
The gain in gini after splitting on B is:
GB=T = 1?
1
4
2
?
3
4
2
= 0.3750
GB=F = 1=
1
6
2
?
5
6
2
= 0.2778
? = Gorig ? 4/10GB=T ? 6/10GB=F = 0.1633
Therefore, attribute B will be chosen to split the node.
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