First split is at Feature Legs
In my working of the entire set, I obtain the first split will happen at Feature "Legs" where the information gain is the highest = 0.88, which is equal to the overall entropy. Hence, the decision stops at Legs because if we split it further, we obtain no information gain. Please let me know if my understanding is correct
Hello Dhaivat!
Thanks for reaching out!
Firstly, it's great to see you engaging deeply with the concept of information gain and its role in decision tree splits. You've identified that the "Legs" feature provides a significant amount of information gain, which is correct and indicates a strong discriminator for our dataset. However, there are a few things to consider in your interpretation.
You mentioned that the first split on "Legs" gives the highest information gain of 0.88, which equals the overall entropy, and suggests no further splits are necessary. This interpretation needs a bit of adjustment. In practice, the overall entropy of the dataset before any split represents the total amount of disorder based on the target variable (Species). The first split aims to reduce this disorder as much as possible. However, achieving an information gain equal to the initial entropy doesn't necessarily mean the tree should stop growing. Instead, it indicates a very effective split.
Even after a split with high information gain, like "Legs," there could still be room for further information gain from other features. The process doesn't stop at the first split because subsequent splits might still offer additional insights, especially when dealing with complex data and multiple classes. Each feature contributes its part to refining the classification, depending on the diversity and distribution of the data.
In essence, while your understanding that the "Legs" feature significantly impacts the model is correct, the decision-making process in a decision tree doesn't halt solely because of a highly effective first split. Instead, it's part of a larger strategy to incrementally reduce uncertainty (entropy) in predicting the target variable, considering all available features until the stopping criteria are met.
Hope this helps!
Best,
The 365 Team