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Calculation of Gini Index of Open Interest for Positive Past Trend
P(Open Interest=High): 2/6
P(Open Interest=Low): 4/6
If (Open Interest = High & Return = Up), probability = 2/2
If (Open Interest = High & Return = Down), probability = 0
Gini index = 1 – (sq(2/2) + sq(0)) = 0
If (Open Interest = Low & Return = Up), probability = 2/4
If (Open Interest = Low & Return = Down), probability = 2/4
Gini index = 1 – (sq(0) + sq(2/4)) = 0.50
Weighted sum of the Gini Indices can be calculated as follows:
Gini Index for Open Interest = (2/6)*0 + (4/6)*0.50 = 0.33
Calculation of Gini Index for Trading Volume
P(Trading Volume=High): 4/6
P(Trading Volume=Low): 2/6
If (Trading Volume = High & Return = Up), probability = 4/4
If (Trading Volume = High & Return = Down), probability = 0
Gini index = 1 – (sq(4/4) + sq(0)) = 0
If (Trading Volume = Low & Return = Up), probability = 0
If (Trading Volume = Low & Return = Down), probability = 2/2
Gini index = 1 – (sq(0) + sq(2/2)) = 0
Weighted sum of the Gini Indices can be calculated as follows:
Gini Index for Trading Volume = (4/6)*0 + (2/6)*0 = 0
We will split the node further using the ‘Trading Volume’ feature, as it has the minimum Gini index.
Conclusion
Gini Index, unlike information gain, isn’t computationally intensive as it doesn’t involve the logarithm function used to calculate entropy in information gain, which is why Gini Index is preferred over Information gain.
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