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# Lesson 36 - Module 12 Machine Learning Version 1 CSE IIT...

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Module 12 Machine Learning Version 1 CSE IIT, Kharagpur

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Lesson 36 Rule Induction and Decision Tree - II Version 1 CSE IIT, Kharagpur
Splitting Functions What attribute is the best to split the data? Let us remember some definitions from information theory. A measure of uncertainty or entropy that is associated to a random variable X is defined as H(X) = - Σ pi log pi where the logarithm is in base 2. This is the “average amount of information or entropy of a finite complete probability scheme”. We will use a entropy based splitting function. Consider the previous example: t1 t2 t3 S S Size divides the sample in two. S1 = { 6P, 0NP} S2 = { 3P, 5NP} H(S1) = 0 H(S2) = -(3/8)log2(3/8) -(5/8)log2(5/8) Version 1 CSE IIT, Kharagpur

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t2 t3 S1 S3 S2 humidity divides the sample in three. S1 = { 2P, 2NP} S2 = { 5P, 0NP} S3 = { 2P, 3NP} H(S1) = 1 H(S2) = 0 H(S3) = -(2/5)log2(2/5) -(3/5)log2(3/5) Let us define information gain as follows: Information gain IG over attribute A: IG (A) IG(A)
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Lesson 36 - Module 12 Machine Learning Version 1 CSE IIT...

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