1 Consider the dataset shown in Table 1 for a binary classification problem. Table 1: Dataset with 20 instances 1.1 MovielD Rental Days Format 1 DVD 2 DVD 3 DVD 4 DVD 5 DVD 6 DVD 7 Online 8 Online Online 1 10 3 6 9 3 1 10911 91012 13 14 15 16 17 18 19 20 10 11 8 6 2253WAW79 2 3 4 3 2 1 5 3 Category Entertainment Online DVD Class Days-equal-depth 0 0 0 0 Comedy Documentary Comedy Comedy Documentary Comedy 0 Comedy 0 Comedy 0 Documentary 0 Comedy 0 Entertainment 1 DVD Online Entertainment 1 Online Documentary 1 Documentary 1 DVD Online Documentary Online Documentary 1 Online Entertainment Online Documentary Online Documentary 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.) 1.3 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
Section: Chapter Questions
Problem 1PE
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Question
1
Consider the dataset shown in Table 1 for a binary classification problem.
Table 1: Dataset with 20 instances
1.1
MovielD Rental Days Format Category
DVD
Entertainment
DVD
Comedy
DVD
Documentary
DVD
Comedy
DVD
Comedy
DVD
Online
Online
Online
Online
10
1121314 15 16 17 18 19 20
1
10
3
6
Attribute
child node
class=0
class=1
9
3
1
10
9
11
8
nt
po
P₁
log₂ (po)
log₂ (P1)
Entropy
Gini
Cl Error
6
2
3
4
Entropy(children)
Gini(children)
CI Error(children)
1
5
3
DVD
DVD
Online
Online
DVD
Online
Online
Online
Online
Online
Documentary
Comedy
Comedy
Comedy
Documentary
Comedy
Format=
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.)
1.3
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
1
Gain(Entropy) (IG)
Gain(Gini)
Gain(Error)
Splitinfo
Gain Ratio (GR)
Class Days-equal-depth
0
0
0
Entertainment
1
Entertainment
1
Documentary
1
Documentary 1
Documentary 1
Documentary
Entertainment
1
1
Documentary
Documentary 1
Category, and binary split for Format. Fill out the Table 2 that will guide you through the process. Every
column correspond to a child node, t.
Category=
DVD Online Entert. Comedy
0
0
• Rows 3-4: the count matrices for every child node.
• Row 5: the total number of instances associated with each child node, t.
Table 2
0
• Rows 6-7: the probability of observing class label 0 or 1 in each child node.
• Rows 8-9: the log of the probability of observing class label 0 or 1 in each child node.
• Rows 10-12: the three impurity measures calculated for each child node.
• Rows 13-15: the three impurity measures calculated for each splitting attribute.
0
0
Table 3
Format
0
0
0
2
Docum.
a1
1.4
Compute the Gain for all three impurity measures and the Gain Ratio (GR) for all three attributes. You may
use Table 3 to easily show your results. Which attribute would you choose as your splitting criterion, and
why?
Category Days
Days=
a2
a3
a4
Transcribed Image Text:1 Consider the dataset shown in Table 1 for a binary classification problem. Table 1: Dataset with 20 instances 1.1 MovielD Rental Days Format Category DVD Entertainment DVD Comedy DVD Documentary DVD Comedy DVD Comedy DVD Online Online Online Online 10 1121314 15 16 17 18 19 20 1 10 3 6 Attribute child node class=0 class=1 9 3 1 10 9 11 8 nt po P₁ log₂ (po) log₂ (P1) Entropy Gini Cl Error 6 2 3 4 Entropy(children) Gini(children) CI Error(children) 1 5 3 DVD DVD Online Online DVD Online Online Online Online Online Documentary Comedy Comedy Comedy Documentary Comedy Format= 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.) 1.3 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 1 Gain(Entropy) (IG) Gain(Gini) Gain(Error) Splitinfo Gain Ratio (GR) Class Days-equal-depth 0 0 0 Entertainment 1 Entertainment 1 Documentary 1 Documentary 1 Documentary 1 Documentary Entertainment 1 1 Documentary Documentary 1 Category, and binary split for Format. Fill out the Table 2 that will guide you through the process. Every column correspond to a child node, t. Category= DVD Online Entert. Comedy 0 0 • Rows 3-4: the count matrices for every child node. • Row 5: the total number of instances associated with each child node, t. Table 2 0 • Rows 6-7: the probability of observing class label 0 or 1 in each child node. • Rows 8-9: the log of the probability of observing class label 0 or 1 in each child node. • Rows 10-12: the three impurity measures calculated for each child node. • Rows 13-15: the three impurity measures calculated for each splitting attribute. 0 0 Table 3 Format 0 0 0 2 Docum. a1 1.4 Compute the Gain for all three impurity measures and the Gain Ratio (GR) for all three attributes. You may use Table 3 to easily show your results. Which attribute would you choose as your splitting criterion, and why? Category Days Days= a2 a3 a4
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