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Week 1 Quiz Answer

Lesson 1 Quiz

Question 1)

Table 1: Transactions from a database

Given the transactions in Table 1, mini-support (minsup) s = 50%,
which of the following isnot a frequent itemset?

{Coffee}
{Beer}
{Eggs}
{Beer, Diapers}

Question 2)

Table 1: Transactions from a database

Given the transactions in Table 1, what is the confidence and
relative support of the association rule {Diapers} ⇒ {Coffee,
Nuts}?

support s = 0.4, confidence c = 0.5
support s = 0.8, confidence c = 0.5
support s = 0.4, confidence c = 1
support s = 0.8, confidence c = 1
None of the above

Question 3)

Consider the database containing the transaction T1 : {a1, a2, a3},
T2 : {a2, a3, a4}, T3 : {a1,a3, a4}. Let mini-support (minsup) = 2.
Which of the following frequent patterns is closed?

{a2}
{a1}
{a1, a3}
{a4}

Question 4)

Consider the database containing the transactions T1 : {a1, …, a3},
T2 : {a2, …, a4}. Letminsup = 1. What fraction of all frequent
patterns is max frequent patterns?

1/11
2/11
1/3
There are no max frequent patterns for the given minsup.
3/11

Question 5)

Rank the following sets by their cardinality for a given database:
{all frequent patterns}, {closed frequent patterns}, and {max frequent
patterns}.

{all frequent patterns} ≥ {closed frequent patterns} ≥ {max frequent
patterns}

{all frequent patterns} ≥ {max frequent patterns} ≥ {closed frequent
patterns}

{all frequent patterns} ≥ {max frequent patterns} = {closed
frequent patterns}, i.e. the set of max frequent patterns and the
set of closed frequent patterns are identical.

{all frequent patterns} ≥ {max frequent patterns}, {all frequent
patterns} ≥ {closed frequent patterns}, but the order of {max
frequent patterns} and {closed frequent patterns} cannot be
determined without further information.

Ranking is impossible without further information.

Question 6)

Table 1: Transactions from a database

Given the transaction in Table 1 and mini-support (minsup) s = 40%,
which of the following is a length-3 frequent item set?

Beer, Nuts, Eggs
Beer, Coffee, Milk
Coffee, Diapers, Eggs
Beer, Nuts, Diapers

Question 7)

A strong association rule satisfies both the mini-support (minsup)
and minconfthresholds. Given the transactions in Table 1, mini-support
(minsup)s = 50%, andminconf c = 50%, which of the following is not a
strong association rule?

{Beer} ⇒ {Diapers}
{Beer, Nuts} ⇒ {Diapers}
{Diapers} ⇒ {Nuts}
{Nuts} ⇒ {Diapers}
{Diapers} ⇒ {Beer}

Question 8)

Consider the database containing the transaction T1 : {a1, a2, a3},
T2 : {a2, a3, a4}, T3 : {a1,a3, a4}. Let mini-support (minsup) = 2.
Which of the following frequent patterns is NOT closed?

{a2}
{a1, a3}
{a3}
{a3, a4}

Question 9)

Consider the database containing the transactions T1 : {a1, a2, a3,
a4, a5}, T2 : {a2, a3, a4, a5,a6}. Let minsup = 1. Which of the
following is both a max frequent and a closed frequent pattern? Select
all that apply.

{a2, a3, a4, a5}
{a2, a5}
{a1, a2, a3, a4, a5}
{a2, a3, a4, a5, a6}
{a1, a2, a3, a4, a5, a6}

Question 10)

Given the set of closed frequent patterns, we can ___________. Select
all that apply.

Recover all transactions in the database
Find the set of max frequent patterns
Recover the set of all frequent patterns and their support in some
situations but not all
Always recover the set of all frequent patterns and their support

Question 11)

Given the transactions in Table 1, mini-support (minsup) s= 50%, and
minconf c = 50%, which of the following is an association rule? Select
all that apply.

Nuts ⇒ Eggs
Coffee ⇒ Milk
Diapers ⇒ Eggs
Nuts ⇒ Diapers
Beer ⇒ Nuts

Question 12)

Which of the following statements is true?

The set of closed frequent patterns is always the same as the set of
max frequent patterns.

Since both closed and max frequent patterns are a subset of all
frequent patterns, we cannot recover all frequent patterns and their
supports given just the closed and max frequent patterns.

Closed frequent patterns can always be determined from the set of
max frequent patterns.

We can recover all frequent patterns and their supports from the set
of max frequent patterns.

We can recover all frequent patterns and their supports from the
set of closed frequent patterns.

Question 13)

Given the transactions in Table 1, what is the confidence and
relative support of the association rule {Diapers} ⇒ {Coffee,
Nuts}?

support s = 0.4, confidence c = 0.5
support s = 0.8, confidence c = 0.5
support s = 0.4, confidence c = 1
support s = 0.8, confidence c = 1
None of the above

Lesson 2 Quiz

Question 1)

If we know the support of itemset {a, b} is 10, which of the
following numbers are the possible supports of itemset {a, b, c}?
Select all that apply.

Question 2)

If we know the support of itemset {a} is 50 and the support of
itemset {a, b, c} is 30, which of the following numbers are the
possible supports of itemset {a, b}? Select all that apply.

Question 3)

Considering the Apriori algorithm, assume we have obtained all size-2
(i.e., containing 2 items, e.g. {A, B}) frequent itemsets. They are
{A, B}, {A, C}, {A, D}, {B, C}, {B, E}, and {C, E}. In the following
size-3 itemsets, which of them should be considered, i.e., have
potential to be size-3 frequent itemsets? Select all that apply.

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

Question 4)

Given the FP-tree as shown in Figure 1, how many transactions do we
have in total?

Question 5)

If we know the support of itemset {a} is 50 and the support of
itemset {a, b, c} is 10, which of the following numbers are the
possible supports of itemset {a, b}? Select all that apply.

Question 6)

Considering the Apriori algorithm, assume we have 5 items (A to E) in
total. In the 1st scan, we find out all frequent items A, B, C, and E.
How many size-2 (i.e., containing 2 items, e.g. A, B) itemsets should
be considered in the 2nd scan, i.e., have potential to be size-2
frequent itemsets? Select all that apply.

Question 7)

Given the FP-tree as shown Figure 1, which of the following choices
is in the f-conditional database? Select all that apply.

{c, a, b, m} : 1
{c, b, p} : 1
{b} : 1
{c, a, m, p} : 2

Extra Question

Question 1)

Which of the following tasks does not fall under the scope of data
mining? Select all that apply.

Data entry.
Data Cleaning.

Question 2)

Given the transaction in Table 1 and minsup s = 50%, how many
frequent 3-itemsets are there?

Answer:

Question 3)

A strong association rule satisfies both the minsup and minconf
thresholds. Given the transactions in Table 1, minsup s = 50%, and
minconf c = 50%, how many strong association rules are there? Note
that the association rule A => B and B => A are distinct.

Answer:

Question 4)

Given the transactions in Table 1, minsup s = 50%, and minconf c =
50%, which of the following is an association rule? Select all that
apply.

Answer:

Beer => Nuts
Nuts => Diaper

Question 5)

Consider the database containing the transaction T1 : {a1, …, a5},
T2 : {a1, …, a1}, T3 : {a3, …, a7}, T4 : {a4, …, a8}. For what
value of minsup do we have the most number of closed frequent
patterns?

Answer:

minsup = 1

Question 6)

Consider the database containing the transactions T1 : {a1, …, a3},
T2 : {a2, …, a4}. Let minsup = 1. What fraction of all frequent
patterns is max frequent patterns?

Answer:

2/11

Question 7)

Consider the database containing the transaction T1 : {a1, a2, a3},
T2 : {a2, a3, a4}. Let minsup = 1. What fraction of all frequent
patterns is closed?

Answer:

3/11

Question 8)

Rank the following sets by their cardinality for a given database:
{all frequent patterns}, {closed frequent patterns}, {max frequent
patterns}

Answer:

{all frequent patterns} >= {closed frequent patterns} >= {max
frequent patterns}

Question 9)

Which of the following statements is true?

Answer:

We can recover all frequent patterns from the set of closed
frequent patterns.

Question 10)

If we know the support of itemset {a, b, c} is 10, which of the
following numbers are the possible supports of the itemset {a, b}?

Answer:

Question 11)

If we know the support of itemset {a, b} is 10, which of the
following numbers are the possible supports of itemset {a, b, c}?

Answer:

Question 12)

If we know the support of itemset {a} is 50, and the support of
itemset {a, b, c} is 10, which of the following numbers are the
possible supports of itemset {a, d}?

Answer:

Question 13)

Considering Apriori Algorithm, assume we have 5 items (A to E) in
total. In the 1-st scan, we find out all frequent items A, B, C, and
E. How many size-2 (i.e. containing 2 items, e.g. A, B) itemsets
should be considered in 2-nd scan, i.e. are potential to be size-2
frequent itemsets?

Answer:

Question 14)

Considering Apriori Algorithm, assume we have obtained all size-2
(i.e. containing 2 items, e.g. {A, B}) frequent itemsets. They are {A,
B}, {A, C}, {A, D}, {B, C}, {B, E}, {C, E}. In the following size-3
itemsets, which of them should be considered, i.e. are potential to be
size-3 frequent itemsets?

Answer:

{A, B, C}
{B, C, E}

Question 15)

Given the FP-tree as shown in Figure 1, what is the support of {c,
p}?

Answer:

Pattern Discovery in Data Mining

Week 2 Quiz Answer

Lesson 3 Quiz

Question 1)

What is the value range of the Kulczynski measure?

(-∞, +∞)
[-1, 1]
[0, 1]
[0, +∞)

Question 2)

What is the value range of the χ2 measure?

(-∞, +∞)
[-1, 1]
[0, 1]
[0, +∞)

Question 6)

Which of the following measures is NOT null invariant?

Cosine
Lift
All confidence
Kulcyzynski

Question 7)

Suppose we are interested in analyzing the purchase of comics
(CM) and fiction (FC) in the transaction history of a bookstore. We have
the following 2 × 2 contingency table summarizing the transactions. If
χ2 is used to measure the correlation between CM and FC, what is the χ2
score?

-240
-80
80
240

Question 7)

What is the value range of the Kulczynski measure?

[0, 1]
(-∞, +∞)
[-1, 1]
[0, +∞)

Question 10)

Suppose we are interested in analyzing the purchase of comics (CM) and
fiction (FC) in the transaction history of a bookstore. We have the
following 2 × 2 contingency table summarizing the transactions. If lift
is used to measure the correlation between CM and FC, what is the value
for lift(CM, FC)?

-0.6
0.6
-2e-4
2e-4

Questine 11)

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.

Which of the following measures would you use to determine the
correlation of purchases between apples and bananas across all these
supermarkets?

χ2
Kulcyzynski
Lift
Cosine

Question 12)

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 χ2score?

0
-1
-∞
1

Lesson 4 Quiz

Question 1)

Suppose one needs to frequent patterns at two different levels, with
mini-support (minsup) of 5% (higher level) and 3% (lower level),
respectively. If using shared multi-level mining, which mini-support
(minsup) threshold should be used to generate candidate patterns for
the higher level?

Question 2)

A store had 100,000 total transactions in Q4 2014. 10,000
transactions contained eggs, while 5,000 contained bacon. 2000
transactions contained both eggs and bacon. Which of the following
choices for the value of ε is the smallest such that {eggs, bacon} is
considered a negative pattern under the null-invariant definition?

0.1
0.81
0.5
01
A value for ε such that {eggs, bacon} is a negative pattern under
the null-invariant definition does not exist.

Question 3)

Below is a table of transactions. According to the introduced pattern
distance measure, what is the distance between pattern “abc” and
pattern “abd”?

0
0.5
0.2
0.333

Question 4)

Given the itemsets in Table 1 and a cluster quality measure δ =
0.001, what could be a set of representative patterns that covers all
itemsets in Table 1?

Hint: The pattern with the least support is {F, A, C, E, T, S}. Consider
which pattern in the table may δ-cover the pattern {F, A, C, E, T, S}.

{{F, A, C, E, T, S}}

{{F, A, C, E, S}, {A, C, E, S}}

{{F, A, C, E, S}, {F, A, C, T, S}}

{{F, A, C, E, S}, {F, A, C, E, T, S}, {F, A, C, T, S}}

{{A, C, E, S}, {A, C, T, S}}

Question 5)

A store had 100,000 total transactions in Q4 2014. 10,000
transactions contained beer, while 5,000 contained frying pans. 600
transactions contained both beer and frying pans. Which of the
following is true?

More information is needed to determine if {beer, frying pans} is a
negative pattern.

{beer, frying pans} is a negative pattern under the support-based
definition of negatively correlated patterns.

For ε = 0.1, {beer, frying pans} is a negative pattern under the
null-invariant definition of negatively correlated patterns.

There does not exist a value for ε such that {beer, frying pans} is
a negative pattern by the null-invariant definition of negative
patterns.

Question 6)

Given the itemsets in Table 1, which of the following patterns are in
the δ-cluster containing the pattern {A, C, E, S} for δ = 0.0001?

Hint: 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:

{A, C, T, S}

{F, A, C, E, S}

{F, A, C, T, S}

{F, A, C, E, T, S}

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.

{A, C, E, S}

{F, A, C, T, S}

{A, C, T, S}

{F, A, C, E, S}

Extra Questions

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)?

Answer:

1
-∞
0
-1

Question 2)

Suppose Coursera collected statistics on the number of students
who take courses on data mining (DM) and machine learning (ML). We
have the following 2×2 contingency table summarizing the
statistics. If χ2 is used to measure the correlation between DM
and ML, what is the χ2 score?

Answer:

562.5
-562.5
-225
225

Question 3)

What is the value range of the Lift measure?

Answer:

ric: normal; vertical-align: baseline; white-space: pre-wrap;”>[0, +∞)
[0, 1]
(-∞, +∞)
[-1, 1]

Question 4)

Which of the following measures is NOT null invariant?

Answer:

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.

Denote li as the lift measure and ki as the Kulcyzynski measure
for supermarket Si(i = 1, 2). Which of the following is
correct?

Answer:

l1 ≠ l2, k1 = k2

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