Answer: To calculate entropy in a decision tree, compute the sum of probabilities of each class multiplied by the logarithm of those probabilities, then negate the result.
To calculate entropy in a decision tree, follow these steps:
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Compute Class Probabilities:
- Calculate the proportion of data points belonging to each class in the dataset.
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Calculate Entropy:
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Use the formula for entropy:
- Where pi is the proportion of data points belonging to class i and c is the number of classes.
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Use the formula for entropy:
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Interpretation:
- Higher entropy values indicate higher disorder or uncertainty in the dataset, while lower entropy values indicate more homogeneous datasets with respect to the target variable.
Conclusion:
Entropy quantifies the amount of disorder or uncertainty in a dataset. In decision tree algorithms, entropy is used as a measure of impurity to determine the best attribute for splitting the data at each node. By selecting splits that minimize entropy, decision trees can effectively partition the data into subsets that are more homogeneous with respect to the target variable.