Consider the hypothesis space defined over instances shown below, we characterize eac hypothesis (apple taste) by 4-tuples. Please hand trace the ID3 classifier to build a decisio tree, then predict the target value Taste=Sweet/Tart for the following instances: a) b) c) d) e) Now suppose the actual taste of the five apples above are actually "Sweet, Sweet, Sweet, Tart, Tart", what is the accuracy of the decision tree? Please show all the steps and include the corresponding confusion matrix for accuracy calculation. (10pts) Melon Color 1 Red 2 Red 3 Yellow 4 Yellow 5 Yellow 6 Yellow 7 Green 8 Red 9 Red 10 Yellow Crispiness Spot Fragrant None Yes None No None Yes Some No None No Some Yes Some No None Yes None No None Yes High High High Mid Low Mid Low Low Low Mid Taste Sweet Sweet Sweet Tart Sweet Tart Sweet Tart Sweet Sweet
Consider the hypothesis space defined over instances shown below, we characterize eac hypothesis (apple taste) by 4-tuples. Please hand trace the ID3 classifier to build a decisio tree, then predict the target value Taste=Sweet/Tart for the following instances: a) b) c) d) e) Now suppose the actual taste of the five apples above are actually "Sweet, Sweet, Sweet, Tart, Tart", what is the accuracy of the decision tree? Please show all the steps and include the corresponding confusion matrix for accuracy calculation. (10pts) Melon Color 1 Red 2 Red 3 Yellow 4 Yellow 5 Yellow 6 Yellow 7 Green 8 Red 9 Red 10 Yellow Crispiness Spot Fragrant None Yes None No None Yes Some No None No Some Yes Some No None Yes None No None Yes High High High Mid Low Mid Low Low Low Mid Taste Sweet Sweet Sweet Tart Sweet Tart Sweet Tart Sweet Sweet
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
can you please give correct and proper solution.
Transcribed Image Text:Consider the hypothesis space defined over instances shown below, we characterize each
hypothesis (apple taste) by 4-tuples. Please hand trace the ID3 classifier to build a decision
tree, then predict the target value Taste=Sweet/Tart for the following instances:
a) <Red, High, Some, No>
b) <Red, Low, Some, Yes>
c) <Yellow, Low, Some, No>
d) <Green, High, None, No>
e) <Green, Mid, Some, Yes>
Now suppose the actual taste of the five apples above are actually "Sweet, Sweet,
Sweet, Tart, Tart", what is the accuracy of the decision tree? Please show all the steps
and include the corresponding confusion matrix for accuracy calculation. (10pts)
Melon
Color
1 Red
2
Red
3
Yellow
4
Yellow
5 Yellow
6 Yellow
7 Green
8
Red
9
Red
10 Yellow
(Please give me a correct solution)
Crispiness Spot
High
High
High
Mid
Low
Mid
Low
Low
Low
Mid
Fragrant
None Yes
None No
None Yes
Some No
None No
Some Yes
Some No
None Yes
None
No
None Yes
Taste
Sweet
Sweet
Sweet
Tart
Sweet
Tart
Sweet
Tart
Sweet
Sweet
Expert Solution
Step 1
Answers:-
1st step:-
the formulas -
Entropy (class)
= -P/P+Nlog2(P/P+N)-N/P+N log2(N/P+N)
for each attribute
I(Pi,Ni)=-P/P+N log2(P/P+N)-N/P+N log2(N/P+N)
Entrophy (attribute)
= ΣPi+Ni/P+N(I(Pi,Ni))
Gain
=Entrophy - Entrophy(attribute) calss)
The Entropy of class - P(Yes) = 7, P(No) = 5
The Entropy = -7/12log2 (7/12) -5/12 log2(5/12) = 0.453 +0.526 = 0.979
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Outlook
P
N
I(P,N)
Rain 3 4 0.984
Sunny
2
0
0
Overcast
2
1 0.918
Wind
Weak
Strong
PN
I(P,N)
4
3
0.984
3 2 0.970
Day
PNI(P,N)
Weekend 2
4 0.918
Weekday 5 1 0.650
The Entropy(Outlook) = (7x0.984 + 2x0 + 3x0.918) /
12 = 0.8035
Entropy(Wind) = (7x0.984 +5x0.97) / 12 = 0.978
Entropy(Day) = (6x0.918+ 6x0.65) / 12 = 0.784 Gain(Outlook) = 0.979-0.803 = 0.176
Gain (Wind) = 0.979-0.978 0.001 Gain (Day) = 0.979-0.784 0.195
Since the gain of the from Day is maximum hence Day will be
root node
Now for Day = weekend - Entropy of class -
P(Yes) = 2, P(No) = 4 Entropy = = 0.918
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