Gain Ratio

Extension to Information Gain which applies Normalization to it.

$$\begin{array}{r}{\text{ Splitlnfo }}_A(D)=-{\sum }_{j=1}^v\frac{|D_j|}{|D|}{\log }_2\left(\frac{|D_j|}{|D|}\right)\\ \text{ GainRatio }(A)=\frac{\mathrm{Gain}(A)}{{\text{ Splitlnfo }}_A(D)}\end{array}$$

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)