Formal Definition
Let denote a set of training examples, each of the form where is the value of the th attribute of example and is the corresponding class label. The information gain for an attribute is defined in terms of entropy as follows:
The information gain is equal to the total entropy for an attribute if for each of the attribute values a unique classification can be made for the result attribute. In this case the relative entropies subtracted from the total entropy are 0.
Read more about this topic: Information Gain In Decision Trees
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