How to find the Entropy – Decision Tree Learning

How to find the Entropy – Decision Tree Learning – Machine Learning

In this tutorial we will understand, how to find the entropy given the four probabilities p1=0.1, p2=0.2, p3=0.3 and p4=0.4 in the decision tree.

Solution:

We know that the equation to find Entropy is,

Entropy = -∑pi * log2⁡(pi)  

We were give four probabilities, hence after expanding the equation will become,

Entropy =-p1∗log2(p1 )-p2∗log2(p2)-p3∗log2(p3 )-p4∗log2(p4 )

Now we will put the values of p1, p2, p3, and p4 in eqaution.

Entropy =-0.1∗log2(0.1 )-0.2∗log2(0.2)-0.3∗log2(0.3 )-0.4∗log2(0.4 )

Entropy =-0.1∗(-3.322)-0.2∗(-2.322)-0.3∗(-1.736)-0.4∗(-1.322)

Entropy =0.3322+0.4644+0.5208+0.5288

Entropy =1.8462

The Entropy is 1.8462 for the given four Probabilities p1=0.1, p2=0.2, p3=0.3 and p4=0.4.

Summary:

In this tutorial we understood, how to find the entropy given the probabilities in decision tree learning.

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