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4. Consider a node, t, in a decision tree. The set of training records in node t is Dt, which contains records from three different classes C₁, C2, and C3. The class distribution is as follow: Class Number of records C₁ X x 2x C2 C3 What are the impurity measures of this node using Gini index and misclassification error?

4. Consider a node, t, in a decision tree. The set of training records in node t is Dt, which contains records from three different classes C₁, C2, and C3. The class distribution is as follow: Class Number of records C₁ X x 2x C2 C3 What are the impurity measures of this node using Gini index and misclassification error?

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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4. Consider a node, t, in a decision tree. The set of training records in node t is D, which contains records from three different classes C₁, C2, and C3. The class distribution is as follow: Class Number of records C₁ C2 C3 What are the impurity measures of this node using Gini index and misclassification error? Gini index = Misclassification error = X x 2x
Transcribed Image Text:4. Consider a node, t, in a decision tree. The set of training records in node t is D, which contains records from three different classes C₁, C2, and C3. The class distribution is as follow: Class Number of records C₁ C2 C3 What are the impurity measures of this node using Gini index and misclassification error? Gini index = Misclassification error = X x 2x
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Step 1 Explanation

Dear Student,

Formulae for finding Misclassification error = 1-max(p,1-p)    //for two classes where probability of one class is p

Formulae for finding Gini Index =  1-∑jp2(j/t)

Here, The estimated probability that the item is actually in class j is p(j/t).

Here if total records are 4x then class 1 and class2 will have x records and class 3 will have 2x records.

Thus, there probability = class1 = class2 = x/4x

class3=2x/4x

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