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Weekend (Example) Weather Parents Money Decision (Category)

1. The document describes creating a decision tree and Naive Bayes model to predict a decision category based on weather, parents, and money attributes. 2. It analyzes the data in a table to determine the entropy and information gain of each attribute to construct the decision tree, with weather being the best predictor. 3. For a student with a prime number ending, it predicts the decision would be "Cinema" given rainy weather, parents being present, and having rich money.

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Gabriel Tomagos
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2K views12 pages

Weekend (Example) Weather Parents Money Decision (Category)

1. The document describes creating a decision tree and Naive Bayes model to predict a decision category based on weather, parents, and money attributes. 2. It analyzes the data in a table to determine the entropy and information gain of each attribute to construct the decision tree, with weather being the best predictor. 3. For a student with a prime number ending, it predicts the decision would be "Cinema" given rainy weather, parents being present, and having rich money.

Uploaded by

Gabriel Tomagos
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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1. (40pts) TABLE 1.

Decision: CATEGORY

Weekend (Example) Weather Parents Money Decision (Category)


W1 Sunny Yes Rich Cinema
W2 Sunny No Rich Tennis
W3 Windy Yes Rich Cinema
W4 Rainy Yes Poor Cinema
W5 Rainy No Rich Stay in
W6 Rainy Yes Poor Cinema
W7 Windy No Poor Cinema
W8 Windy No Rich Shopping
W9 Windy Yes Rich Cinema
W10 Sunny No Rich Tennis
a. Create a Decision Tree
b. Create a Model based on Naïve Bayes
c. Student Number ending in Prime Number: Determine the Decision if
Weather: Rainy, Parents: Yes, Money: Rich
Student Number ending in Non-Prime Number: Determine the Decision if
Weather: Sunny, Parents: Yes, Money: Poor

A. Decision Tree

Step 1

Cinema = 6

Tennis = 2

Stay in = 1

Shopping = 1

H(Category) = H(3/5, 1/5, 1/10, 1/10)

H(3/5, 2/10, 1/10, 1/10)=-(3/5 log2 3/5) – (1/5 log2 1/5) – (1/10 log2 1/10) – (1/10 log2 1/10)

=0.444+ 0.464 + 0.332 + 0.332

H(Category)=1.572

Step 2

H(Category/weather), H(Category/parents), H(Category/money)


H(Category/weather)

Sunny * H + Windy * H + Rainy * H =3/10 (1/3, 2/3, 0/3, 0/3) + 4/10 (3/4, 0/4, 0/4, 1/4) + 3/10 (2/3, 0/3,
1/3, 0/3)

H(Category, Weather) = 3/10 ((-1/3 log2 1/3)-(2/3 log2 2/3) – (0/3 log2 0/3) – (0/3 log2 0/3)) + 4/10
((3/4 log2 ¾) – (0/4 log2 0/4) – (0/4 log2 0/4) – (1/4 log2 ¼)) + 3/10 ((-2/3 log2 2/3) – (0/3 log2 0/3) -
(1/3 log2 1/3) – (0/3 log2 0/3)

= 3/10 (0.92) + 4/10 (0.82) + 3/10 ( 0.92)


=0.276 + 0.328 + 0.276

H(Category/weather) = 0.88

H(Category/parents)

Yes * H + No * H = 5/10 (5/5, 0/5, 0/5, 0/5) + 5/10 (1/5, 2/5, 1/5, 1/5)

H(Category/parents) = 5/10 ((-5/5 log2 5/5) + 5/10 ((-1/5 log2 1/5) – (2/5 log2 2/5) – (1/5 log2 1/5) –
(1/5 log2 1/5))

=5/10 (0) + 5/10 (1.92)

= 0 + 0.96

H(Category/parents) = 0.96

H(Category/money)

Rich * H + Poor * H = 7/10 (3/7 , 2/7, 1/7, 1/7) + 3/10 (3/3, 0/3, 0/3)

H(Category/money) = 7/10 ((-3/7 log2 3/7) – (2/7 log2 2/7) – (1/7 log2 1/7) – (1/7 log2 1/7)) + 3/10 ((-
3/3 log2 3/3))

= 7/10 (1.85) + 3/10 (0)

= 1.295 + 0

H(Category/money) = 1.295

Step 3

H(Category/weather) = 0.88 | H(Category/parents) = 0.96 | H(Category/money) = 1.295

I(Category/weather) = 1.572 – 0.88 = 0.692

I(Category/parents) = 1.572 – 0.96 = 0.612

I(Category/money) = 1.572 – 1.295 = 0.277

Max(0.692, 0.612, 0.277) = 0.692, so Weather is best

Step 4
Sunny = H(1/3, 2/3, 0/3, 0/3) = 0.92

H (Category/parents)

1/3 (1/1, 0/1, 0/1, 0/1) + 2/3 (0/2, 2/2, 0/2, 0/2)

H (Category/parents) = 1/3 ((-1/1 log2 1/1)) + 2/3 ((-2/2 log2 2/2))

= 1/3 (0) + 2/3 (0)

H (Category/parents) = 0

I (Category/parents) = H(1/3, 2/3, 0/3, 0/3) – 0

I (Category/parents) = 0.92

H (Category/money)

3/3 ( 1/3, 2/3, 0/3, 0/3) + 0/3 (0,0,0,0)

H (Category/money) = 3/3 ((-1/3 log2 1/3) – (2/3 log2 2/3))

= 3/3 (0.92)

H (Category/money) = 0.92

I (Category/money) = 0.92 – 0.92 = 0

Max (0.92) = 0.92


Windy = H (3/4, 0/4, 0/4, ¼) = 0.815

H (Category/parents)

2/4 (2/2, 0/2, 0/2, 0/2) + 2/4 (1/2, 0/2, 0/2, ½)

H (Category/parents) = 2/4 ((-2/2 log2 2/2)) + 2/4 ((-1/2 log2 ½) - (-1/2 log2 ½))

= 2/4 (0) + 2/4 (1)

= 0 + 0.5

H (Category/parents) = 0.5

I (Category/parents) = 0.815 – 0.5 = 0.315

H (Category/money)

3/4 (2/3, 0/3, 0/3, 1/3) + ¼ (1/1, 0/1, 0/1, 0/1)

H (Category/money) = ¾ ((-2/3 log2 2/3) – (1/3 log2 1/3)) + ¼ (-1/1 log2 1/1)

= ¾ (0.92)

H (Category/money) =0.69

I (Category/money) = 0.815 – 0.69 = 0.315


B)
Stud Number: 2020100575 Prime
Given: Weather: Rainy, Parents: Yes, Money: Rich

Step 1
P(C1) = P (Decision = Cinema) = 6/10 = 0.6
P (C2) = P (Decision = Tennis) = 2/10 = 0.2
P (C3) = P (Decision = Stay In) = 1/10 = 0.1
P (C4) = P (Decision = Shopping) = 1/10 = 0.1

Step 2
P(Rainy/Cinema) = 2/6 = 0.333
P(Rainy/Tennis) = 0/2 = 0
P(Rainy/Stay In) = 1/1 = 1
P(Rainy/Shopping) = 0/1 = 0

P (Yes / Cinema) = 5/6 = 0.833


P (Yes/ Tennis) = 0/2 = 0
P (Yes/ Stay In) = 0/1 = 0
P (Yes/ Shopping) = 0/1 = 0
P (Rich/ Cinema) = 3/6 = 0.5
P (Rich/ Tennis) = 2/2 = 1
P (Rich/ Stay In) = 1/1 = 1
P (Rich/ Shopping) = 1/1 =1

P(x/Cinema) = 0.333 * 0.833 * 0.5 = 0.139


P(x/Tennis) = 0 * 0* 1 = 0
P(x/Stay In) = 1 * 0 * 1 = 0
P(x/Shopping) = 0 * 0 * 1 = 0

P(Cinema) * P(x/cinema) = 0.6 * 0.139


P(Cinema) * P(x/cinema) = 0.083
Prediction: Cinema

2. (40pts) Table 2. Decision: BUYS-RRSP

a. Create a Decision Tree


b. Create a Model based on Naïve Bayes
c. Student Number ending in Prime Number: Determine the Decision if
Sector: Farming, Income: medium, Self-Employed: Yes, Credit-Rating: Fair
Student Number ending in Non-Prime Number: Determine the Decision if
Sector: Banking, Income: medium, Self-Employed: Yes, Credit-Rating: Excellent

A. Decision Tree

Step 1

Yes = 8
No = 6

H(Buys-RRSP) = H(8/14, 6/14)

=-(8/14 log2 8/14) – (6/14 log2 6/14)

=0.463 + 0.527

H(Buys-RRSP) =0.99

Step 2

H(Buys-RRSP/Sector), H(Buys-RRSP/Income), H(Buys-RRSP/Self-Employed), H(Buys-RRSP/Credit-Rating)

H(Buys-RRSP/Sector)

Farming * H + Oil * H + Banking * H = 5/14 (2/5, 3/5) + 5/14 (2/5, 3/5) + 4/14 (4/4, 0/4)

H(Buys-RRSP/Sector) = 5/14 ((-2/5 log2 2/5) – (3/5 log2 3/5)) + 5/14 ((-2/5 log2 2/5) – (3/5 log2 3/5)) +
4/14 (-4/4 log2 4/4)

= 5/14(0.97) + 5/14 (0.97) + 4/14 (0)

= 0.346 + 0.346

H(Buys-RRSP/Sector) = 0.692

H(Buys-RRSP/Income)

Low * H + Medium * H + High * H = 4/14(3/4, ¼) + 6/14 (3/6, 3/6) + 4/14 (2/4, 2/4)

H(Buys-RRSP/Income) = 4/14 ((-3/4 log2 ¾) – (1/4 log2 ¼)) + 6/14 ((-3/6 log2 3/6) – (3/6 log2 3/6)) +
4/14 ((-2/4 log2 2/4) – (2/4 log2 2/4))

= 0.232 + 0.429 + 0.286

H(Buys-RRSP/Income) = 0.947

H(Buys-RRSP/Self-Employed)

Yes * H + No * H = 7/14 (5/7, 2/7) + 7/14 (4/7, 3/7)

H(Buys-RRSP/Self-Employed) = 7/14 ((-5/7 log2 5/7) – (2/7 log2 2/7)) + 7/14 ((-4/7 log2 4/7) – (3/7 log2
3/7))

= 0.432 + 0.493

H(Buys-RRSP/Self-Employed) = 0.925

H(Buys-RRSP/Credit-Rating)

Fair * H + Excellent * H = 8/14 (3/8, 5/8) + 6/14 ( 5/6, 1/6)

H(Buys-RRSP/Credit-Rating) = 8/14 ((-3/8 log2 3/8) – (5/8 log2 5/8)) + 6/14 ((-5/6 log2 5/6) – (1/6 log2
1/6))
= 0.545 + 0.279

H(Buys-RRSP/Credit-Rating) = 0.824

Step 3

H(Buys-RRSP/Sector) = 0.692 | H(Buys-RRSP/Income) = 0.947 | H((Buys-RRSP/Self-Employed) =0.925


|H (Buys-RRSP/Credit-Rating) = 0.824

I(Buys-RRSP/Sector) = 0.99 – 0.692 = 0.298

I(Buys-RRSP/Income) = 0.99 – 0.947 = 0.043

I(Buys-RRSP/Self-employed) = 0.99 – 0.925 = 0.065

I(Buys-RRSP/credit-rating) = 0.99 – 0.824 = 0.166

Max (0.298, 0.043, 0.065, 0.166) = 0.298, so Sector is Best

Step 4

H(Buys-RRSP/Income), H(Buys-RRSP/Self-Employed), H(Buys-RRSP/Credit-Rating)

H(Buys-RRSP/Income)= 3/5 (1/3 , 2/3) + 2/5 (1/2,1/2) + 0/5 (0,0)

= 0.551 + 0.4

H(Buys-RRSP/Income)= = 0.951

I (Buys-RRSP/Income)= 0.99 – 0.951 = 0.039

H (Buys-RRSP/Self-Employed) = 3/5 (1/3, 2/3) + 2/5 (1/2 , ½)

= 0.551 + 0.4

H (Buys-RRSP/Self-Employed) = 0.951

I (Buys-RRSP/Self-Employed) = 0.99 – 0.951 = 0.039

I(Buys-RRSP/Credit-Rating) = 0.99 – 0 = 0.99


Max (0.039, 0.039, 0.99) = 0.99

B)

Stud Number: 2020100575 Prime

Given: Sector: Farming, Income: medium, Self-Employed: Yes, Credit-Rating: Fair

Step 1

P (C1) = P (Buys – RRSP = Yes) = 8/14 = 0.571

P (C2) = P (Buys – RRSP = No) = 6/14 = 0.429

Step 2

P(Farming/Yes) = 2/8 = 0.25

P(farming/No) = 3/6 = 0.5

P(Medium / Yes) = 3/8 = 0.375

P(Medium / No) = 3/6 = 0.5

P(Yes/ Yes) = 5/8 = 0.625

P(Yes/ No) = 2/6 = 0.333

P(Fair/Yes) = 3/8 = 0.375

P(Fair/No) = 5/6 = 0.833

P(x/yes) = 0.25 * 0.375 * 0.625 * 0.375 = 0.021

P(x/no) = 0.5 * 0.5 * 0.333 * 0.833 = 0.069


P(x/yes) * P(yes) = 0.021 * 0.571 = 0.012

P(x/no) * P(no) = 0.069 * 0.429 = 0.030

Prediction: No with 0.030 probability

3. (20PTS) TABLE 3. APPLY APRIORI ALGORITHM FOR BASKET ANALYSIS

Min support: 2
Min Confidence: 50%

Step 1

Items Bought Support Count


A 5
B 7
C 5
D 9
E 6
Min support: 2
Min Confidence: 50%

Step 2

Items Bought Support Count


{A,B} 3
{A,C} 2
{A,D} 4
{A,E} 4
{B,C} 3
{B,D} 6
{B,E} 4
{C,D} 4
{C,E} 2
{D,E} 6
A, B, C ,D ,E

Min support: 2
Min Confidence: 50%

Step 3

ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE

Min support: 2
Min Confidence: 50%

Items Bought Support Count


{A, B, C} 1 x
{A, B, D} 2
{A, B, E} 2
{A, C, D} 1x
{A, C, E} 1x
{A, D, E} 4
{B, C, D} 2
{B, C, E} 1x
{B, D, E} 4
{C, D, E} 2

New table with matching min support

Items Bought Support Count


{A, B, D} 2
{A, B, E} 2
{A, D, E} 4
{B, C, D} 2
{B, D, E} 4
{C, D, E} 2

{A, B, D}, {A, B, E}, {A, D, E}, {B, C, D}, {B, D, E}, and {C, D, E}
Step 4

{A, B, D}, {A, B, E}, {A, D, E}, {B, C, D}, {B, D, E}, and {C, D, E}

RULES SUPPORT CONFIDENCE


A -> D^E 3 Sup{ ( A ^(D^E)}/Sup (A) =3/5 =.6 =60%
B -> D^E 4 Sup { (B ^(D^E)}/ Sup (B) = 4/7 = .57 =57%
A - > B^D 2 Sup { A - > B^D}/Sup (A) = 2/5 = 0.4 = 40%
B -> C^D 2 Sup{ B -> C^D }/ Sup(B) = 2/7 = 0.26 = 26%
B^D -> E 4 Sup { (B^D)^E}/ Sup (B^D) = 4/5 = .8 =80%
B^E -> D 4 Sup { (B^E)^D}/ Sup (B^E) = 4/4 = 1 =100%
C^D -> E 2 Sup { C^D -> E }/ Sup (C^D) = 2/4 = .5 = 50%
D^A -> E 3 Sup { (D^A)^E}/ Sup (D^A) = 3/4 = .75 =75%
D -> E^A 3 Sup { (D^(E^A)}/ Sup (D) = 3/9 = .33 = 33%
C -> B^D 2 Sup { C -> B^D} / Sup (C) = 2/5 = .4 = 40%
D^E -> A 3 Sup { (D^E)^A}/ Sup (D^E) = 3/6 = .5 =50%
D^E -> B 4 Sup { (D^E)^B}/ Sup (D^E) = 4/6 = .67 =67%
D -> B^E 4 Sup { (D^(B^E)}/ Sup (D) = 4/9 = .44 =44%
E^A -> D 3 Sup { (E^A)^D}/ Sup (E^A) = 3/4 = .75 =75%
E -> B^D 4 Sup { (E^(B^D)}/ Sup (E) = 4/6 = .67 =67%
E -> D^A 3 Sup { (E(D^A)}/ Sup (E) = 3/6 = .5 =50

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