Link to the previous post : https://statinfer.com/204-3-4-how-to-calculate-entropy-for-decision-tree-split/
In the previous post of this series we calculated the entropy for each split. In this post we will calculate the information gain or decrease in entropy after split.
Information Gain
- Information Gain= entropyBeforeSplit – entropyAfterSplit.
- Easy way to understand Information gain= (overall entropy at parent node) – (sum of weighted entropy at each child node).
- Attribute with maximum information is best split attribute.
Information Gain- Calculation
- Entropy Ovearll = 100% (Impurity)
- Entropy Young Segment = 99%
- Entropy Old Sgment = 99%
- Information Gain for Age =100-(0.699+0.499)=1
- Entropy Ovearll = 100% (Impurity)
- Entropy Male Segment = 72%
- Entropy Female Sgment = 29%
- Information Gain for Age =100-(0.672+0.429)=45.2
Practice : Information Gain
Calculate the information gain this example base on the variable split
Output-Information Gain
Split With Respect to ‘Owning a car’
- Entropy([28+,39-]) Ovearll = -28/67 log2 28/67 – 39/67 log2 39/67 = 98% (Impurity)
- Entropy([25+,4-]) Owing a car = 57%
- Entropy([3+,35-]) No car = 40%
- Information Gain for Owing a car =98-((29/67)57+(38/67)40)=50.6
Split With Respect to ‘Gender’
- Entropy([19+,21-]) Male= 99%
- Entropy([9+,18-]) Female = 91%
- Information Gain for Gender=98-((40/67)99+(27/67)91) =2.2
Other Purity (Diversity) Measures
- Chi-square measure of association
- Gini Index : Gini(T) = 1−∑p2j
- Information Gain Ratio
- Misclassification error
The next post is about the decision tree algorithm.
Link to the next post : https://statinfer.com/204-3-6-the-decision-tree-algorithm/
