Gini index for binary variables in data mining

By: Prof. Dr. Fazal Rehman | Last updated: March 3, 2022

What is Gini index?

Gini index is the most commonly used measure of inequality. Also referred as Gini ratio or Gini coefficient. Gini index for binary variables is calculated in the example below.
Student inHostel Target Class
Yes True Yes
Yes True Yes
Yes False No
False False Yes
False True No
False True No
False False No
True False Yes
False True No
Now we will calculate Gini index of student and inHostel. Step 1: Gini(X) = 1 – [(4/9)2 + (5/9)2] = 40/81 Step 2: Gini(Student = False) = 1 – [(1/5)2 + (4/5)2] = 8/25 Gini(Student = True) = 1 – [(3/4)2 + (1/4)2] = 3/8 GiniGain(Student) = Gini(X) – [4/9· Gini(Student = True) + 5/9· Gini(Student = False)] = 0.149 Step 3: Gini(inHostel = False) = 1 – [(2/4)2 + (2/4)2] = 1/2  Gini(inHostel = True) = 1 – [(2/5)2 + (3/5)2] = 12/25 GiniGain(inHostel) = Gini(X) – [5/9· Gini(inHostel = True) + 4/9· Gini(inHostel = False)] = 0.005 Results Best split point is Student because it has high gini gain.

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