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Pattern Discovery in Data Mining

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Pattern Discovery in Data Mining
by Jiawei Han

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Feedback — Week 2 QuizHelp Center

Thank you. Your submission for this quiz was received.

You submitted this quiz on Sun 22 Feb 2015 9:04 PM PST. You got a score of 3.15 out of 11.00. You can attempt again, if you'd like.

Question 1

Suppose a school collected some data on students’ preference for hot dogs(HD) vs. hamburgers(HM). We have the following 2×2 contingency table summarizing the statistics. If lift is used to measure the correlation between HD and HM, what is the value for lift(HD, HM)? 

	HD	¬HD	Σrow
HM	40	24	64
¬HM	210	126	336
Σcol	250	150	400

Your Answer		Score	Explanation
0	Inorrect	0.00
1
-1
-∞
Total		0.00 / 1.00

Question Explanation

The correct answer is: "1". 

The lift can be calculated by 



where supp(A) and supp(B) refer to the relative support of A and B respectively. Thus, 

Question 2

Suppose a school collected some data on students’ preference for hot dogs(HD) vs. hamburgers(HM). We have the following 2×2 contingency table summarizing the statistics. If χ2 is used to measure the correlation between HD and HM, what is the χ2 score? 

	HD	¬HD	Σrow
HM	40	24	64
¬HM	210	126	336
Σcol	250	150	400

Your Answer		Score	Explanation
1	Inorrect	0.00
-1
-∞
0
Total		0.00 / 1.00

Question Explanation

The correct answer is: "0". 

The contingency table with expected values is following table 

	HD	¬HD	Σrow
HM	40 (40)	24 (24)	64
¬HM	210 (210)	126 (126)	336
Σcol	250	150	400

χ2 can be evaluated as follows 



where Oi is the observed frequency, and Ei is the expected frequency. Since the expected values equal the observed ones, we have χ2 = 0.

Question 3

What is the value range of the χ2 measure?

Your Answer		Score	Explanation
[-1, 1]
[0, 1]
[0, +∞)	Correct	1.00
(-∞, +∞)
Total		1.00 / 1.00

Question Explanation

By definition, the correct answer is: "[0, +∞)".

Question 4

Which of the following measures is null invariant?

Your Answer		Score	Explanation
Kulcyzynski	Correct	1.00
χ2
None of the other options are correct.
Lift
Total		1.00 / 1.00

Question Explanation

The correct answer is: "Kulcyzynski". 

Null transactions are not considered in Kulcyzynski.

Question 5

Suppose we are interested in analyzing the transaction history of several supermarkets with respect to purchase of apples(A) and bananas(B). We have the following table summarizing the transactions. 

Supermarket	AB	¬AB	A ¬B	¬A ¬B
S1	100,000	7,000	3,000	300
S2	100,000	7,000	3,000	90,000

Denote χ2i as the χ2 measure and ci as the cosine measure for supermarket Si (i = 1, 2). Which of the following is correct?

Your Answer		Score	Explanation
χ21 = χ22, c1 = c2
χ21 = χ22, c1 ≠ c2	Inorrect	0.00
χ21 ≠ χ22, c1 ≠ c2
χ21 ≠ χ22, c1 = c2
Total		0.00 / 1.00

Question Explanation

The correct answer is: "χ21 ≠ χ22, c1 = c2" 

χ2 is not null invariant and therefore sensitive to the number of null transactions, while cosine is null invariant.

Question 6

Consider the support-based and null-invariant definitions for negative patterns. For negative pattern threshold ε = 0.011, which of the following patterns would be considered a negative pattern by the null-invariant definition but not the support-based definition?

Your Answer		Score	Explanation
A media content provider has 1,000,000 users. Movie A and Movie B were viewed by 1000 users each in the last month, but only 10 users viewed both.
There are 5 million registered students on an online education website. 5000 students registered for Music 101, and 50,000 students registered for Data Mining, but only 500 students registered for both.	Inorrect	0.00
Both of the above are correct.
None of the above are correct.
Total		0.00 / 1.00

Question Explanation

The correct answer is: "A media content provider has 1,000,000 users. Movie A and Movie B were viewed by 1000 users each in the last month, but only 10 users viewed both." 

Null-invariant: 



Support based: 



Thus, {Movie A, Movie B} is a negative pattern by the null-invariant definition but not the support based definition. 

Null-invariant: 



Support based: 



Thus, {DM, Music} is not a negative pattern by either definition.

Question 7

Consider two patterns P1 and P2 such that O(P1) ⊆ O(P2), where O(Pi) is the corresponding itemset of pattern Pi. Take a second to convince yourself that the following is true: 



Which of the following patterns in Table 1 is δ-covered by {F, A, C, E, T, S} for δ=0.4? Select all that apply.

Your Answer		Score	Explanation
{A, C, E, S}	Correct	0.25
{A, C, T, S}	Correct	0.25
{F, A, C, T, S}	Inorrect	0.00
{F, A, C, E, S}	Correct	0.25
Total		0.75 / 1.00

Question Explanation

The correct answers are: "{F, A, C, T, S}" and "{A, C, T, S}". 

Dist({F, A, C, E, T, S}, {A, C, E, S}) = 1- 101758/205227 = 0.504 
Dist({F, A, C, E, T, S}, {F, A, C, E, S}) = 1- 101758/205211 = 0.504 
Dist({F, A, C, E, T, S}, {F, A, C, T, S}) = 1- 101758/161563 = 0.370 
Dist({F, A, C, E, T, S}, {A, C, T, S}) = 1- 101758/161576 = 0.370 

Thus, {F, A, C, T, S}, {A, C, T, S} are 0.4-covered by {F, A, C, E, T, S}

Question 8

Given the transactions in Table 2, which of the following is true? Select all that apply.

Your Answer		Score	Explanation
(abcef) is a (3, 0.5)-robust pattern	Correct	0.20
(a) is a 0.5-core pattern of (abe)	Correct	0.20
(ac) is a 0.5-core pattern of (abcef)	Inorrect	0.00
(f) is a 0.5-core pattern of (bcf)	Inorrect	0.00
(abe) is a (2, 0.5)-robust pattern	Inorrect	0.00
Total		0.40 / 1.00

Question Explanation

The correct answers are: "(abe) is a (2, 0.5)-robust pattern", "(ac) is a 0.5-core pattern of (abcef)", "(a) is a 0.5-core pattern of (abe)", and "(f) is a 0.5-core pattern of (bcf)". 

Since (e) is still a 0.5-core pattern of (abe), (abe) is a (2, 0.5)-robust pattern. By the same token, (abcef) is a (4, 0.5)-robust pattern, not a (3, 0.5)-robust pattern. (ac) is a 0.5-core pattern of (abcef) since only one other pattern contains (ac). (a) is a 0.5-core pattern of (abe) since it has a core ratio of 2/3. By the same token, (f) is a 0.5-core pattern of (bcf).

Question 9

A constraint is anti-monotone if an itemset S violates the constraint, so do all of its supersets. Which of following constraints is anti-monotone?

Your Answer		Score	Explanation
var(S.price) > 20
range(S.price) < 10
sum(S.price) > 25	Inorrect	0.00
avg(S.price) > 15
Total		0.00 / 1.00

Question Explanation

The correct answer is: "range(S.price) < 10"

Suppose X is the superset of S; if so, the following inequalities always hold for all X:

• avg(X.price) <> avg(S.price)
• sum(X.price) ≥ sum(S.price)
• var(X.price) <> var(S.price)
• range(X.price) ≥ range(S.price)

From these inequalities, we can easily verify that range(S.price) < 10 is anti-monotone.

Question 10

A constraint is monotone if an itemset S satisfies the constraint, so do all of its supersets. Which of following constraints is monotone?

Your Answer		Score	Explanation
Support of S > 100
sum(S.price) > 20
min(S.price) > 10
avg(S.price) < 10	Inorrect	0.00
Total		0.00 / 1.00

Question Explanation

The correct answer is: "sum(S.price) > 20"

Suppose X is the superset of S; if so, the following inequalities always hold for all X:

• support of X ≤ support of S
• min(X.price) ≤ min(S.price)
• avg(X.price) <> avg(S.price)
• sum(X.price) ≥ sum(S.price)

From these inequalities, we can easily verify that sum(S.price) > 20 is monotone.

Question 11

A constraint is succinct if the constraint c can be enforced by directly manipulating the data. Which of following constraints is succinct?

Your Answer		Score	Explanation
avg(S.price) > 40
sum(S.price) < 40
max(S.price) < 20
var(S.price) > 10	Inorrect	0.00	It cannot be determined beforehand since average/sum/variance of the price of itemset S keeps changing.
Total		0.00 / 1.00

Question Explanation

The correct answer is: "max(S.price) < 20"