Entropy Vs. Gini Index

(1) Difference In Entropy & Gini Index.

It is the probability of misclassifying a randomly chosen element in a set.
The range of the Gini index is [0, 1], where
0 indicates perfect purity and
1 indicates maximum impurity.
The Gini index is a linear measure.
It can be interpreted as the expected error rate in a classifier.
It is sensitive to the distribution of classes in a set.
The computational complexity of the Gini index is O(c).
It is less robust than entropy.
It is sensitive.
Formula for the Gini index is Gini(P) = 1 – ∑(Px)^2 , where Pi is
the proportion of the instances of class x in a set.
It has a bias toward selecting splits that result in a more balanced distribution of classes.
The Gini index is typically used in CART (Classification and Regression Trees) algorithms

While entropy measures the amount of uncertainty or randomness in a set.
The range of entropy is [0, log(c)], where c is the number of classes.
Entropy is a logarithmic measure.
It can be interpreted as the average amount of information needed to specify the class of an instance.
It is sensitive to the number of classes.
The computational complexity of entropy is O(c * log(c)).
It is more robust than the Gini index.
It is comparatively less sensitive.
The formula for entropy is Entropy(P) = -∑(Px)log(Px),
where pi is the proportion of the instances of class x in a set.
It has a bias toward selecting splits that result in a higher reduction of uncertainty.
Entropy is typically used in ID3 and C4.5 algorithms

The Gini index tends to be slightly faster to compute than entropy since it does not involve logarithmic calculations.
The Gini index is more sensitive to major class imbalances in the dataset compared to entropy.
Entropy may be more influenced by multi-class problems, while the Gini index performs well in both binary and multi-class scenarios.
In practice, the choice between entropy and the Gini index may not significantly affect the resulting decision tree’s performance.
Often, they lead to similar splits and produce similar decision boundaries.

It ought to be emphasized that there is no one appropriate approach for evaluating unpredictability or impurities and that the decision between the Gini index and entropy varies significantly on the particular circumstance and methodology being employed.