Gain Ratio

Extension to Information Gain which applies Normalization to it.

 Splitlnfo A(D)=−∑j=1v∣Dj∣∣D∣log⁡2(∣Dj∣∣D∣) GainRatio (A)=Gain⁡(A) Splitlnfo A(D)\begin{array}{r} \text { Splitlnfo }_{A}(D)=-\sum_{j=1}^{v} \frac{\left|D_{j}\right|}{|D|} \log _{2}\left(\frac{\left|D_{j}\right|}{|D|}\right) \\ \text { GainRatio }(A)=\frac{\operatorname{Gain}(A)}{\text { Splitlnfo }_{A}(D)} \end{array}

Select attribute with the highest gain ratio.

Disadvantages

  • becomes unstable when Splitlnfo apporaches zero → use Information Gain in that case
  • tends to prefer unbalanced splits (one is much smaller than the others)