Consider the dataset shown in Table 1 for a binary classification problem. Table 1: Dataset with 20 instances 1.1 1.1 Moviel D 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1.3 Rental Days Format DVD DVD DVD DVD DVD DVD Online Online Comedy Online Comedy Online Documentary DVD Comedy DVD Entertainment Online Entertainment 1 10 3 6 9 3 1 10 9 11 8 6 2 2153 WA W N 3 4 Category Class Days-equal-depth Entertainment Comedy Documentary 3 Comedy Comedy Documentary Comedy Online Documentary Documentary DVD Online Documentary Online Documentary Online Entertainment Online Documentary Online Documentary 0 0 0 0 OOO OOOOHLLL 0 0 0 0 0 0 1 1 Discretize the attribute 'Rental Days' to transform it into a categorical attribute with 4 attribute values, a1, a2, a3, a4 (i.e., number of bins = 4) and fill out the last column. Use the equal-depth approach for discretization. 1 1 1 1 Compute the Entropy, Gini, and Misclassification Error for the overall collection of training examples. (These will be the impurity measures on the parent node.) Compute the combined Entropy, Gini, Misclassification Error of the children nodes for all the three attributes: Rental Days, Format, and Movie Category, using multi-way splits for Rental Days and Movie

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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1
Consider the dataset shown in Table 1 for a binary classification problem.
1.1
1.1
Moviel D
LEAF ELE
1.3
2
3
4
5
6
8
9
10
11
12
13
14
15
16
17
18
19
20
Rental Days Format Category Class Days-equal-depth
DVD
Entertainment
DVD
DVD
DVD
DVD
DVD
Online
Online
Online
Online
DVD
DVD
Online
Online
DVD
Online
Online
Online
Online
Documentary
Online Documentary
1
10
3
6
9
3
1
10
9
11
∞0 6 3 33
8
2
4
1
Table 1: Dataset with 20 instances
5
Comedy
Documentary
Comedy
Comedy
Documentary
Comedy
Comedy
Comedy
Documentary
Comedy
Entertainment
Entertainment
Documentary
Documentary
Documentary
Documentary
Entertainment
0
0
0
1
1
1
1
1
Discretize the attribute 'Rental Days' to transform it into a categorical attribute with 4 attribute values,
a1, a2, a3, a4 (i.e., number of bins = 4) and fill out the last column. Use the equal-depth approach for
discretization.
1
1
Compute the Entropy, Gini, and Misclassification Error for the overall collection of training examples. (These
will be the impurity measures on the parent node.)
Compute the combined Entropy, Gini, Misclassification Error of the children nodes for all the three
attributes: Rental Days, Format, and Movie Category, using multi-way splits for Rental Days and Movie
Transcribed Image Text:1 Consider the dataset shown in Table 1 for a binary classification problem. 1.1 1.1 Moviel D LEAF ELE 1.3 2 3 4 5 6 8 9 10 11 12 13 14 15 16 17 18 19 20 Rental Days Format Category Class Days-equal-depth DVD Entertainment DVD DVD DVD DVD DVD Online Online Online Online DVD DVD Online Online DVD Online Online Online Online Documentary Online Documentary 1 10 3 6 9 3 1 10 9 11 ∞0 6 3 33 8 2 4 1 Table 1: Dataset with 20 instances 5 Comedy Documentary Comedy Comedy Documentary Comedy Comedy Comedy Documentary Comedy Entertainment Entertainment Documentary Documentary Documentary Documentary Entertainment 0 0 0 1 1 1 1 1 Discretize the attribute 'Rental Days' to transform it into a categorical attribute with 4 attribute values, a1, a2, a3, a4 (i.e., number of bins = 4) and fill out the last column. Use the equal-depth approach for discretization. 1 1 Compute the Entropy, Gini, and Misclassification Error for the overall collection of training examples. (These will be the impurity measures on the parent node.) Compute the combined Entropy, Gini, Misclassification Error of the children nodes for all the three attributes: Rental Days, Format, and Movie Category, using multi-way splits for Rental Days and Movie
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