Question

Consider the dataset in the table below:

10	Beer, Nuts, Milk
20	Beer, Coffee, Diapers
30	Beer, Diapers, Eggs, Milk
40	Nuts, Eggs, Milk
50	Beer, Coffee, Milk
60	Diapers, Eggs, Milk
70	Beer, Coffee, Diapers, Eggs
80	Beer, Nuts, Coffee, Diapers, Eggs, Milk

and the itemsets with minimum support of 3: {Beer, Diapers, Eggs}.
Considering a minimum confidence threshold of 75%, which of the following association rules qualify as strong?

Group of answer choices (Select all that apply)

1. Eggs -> {Diapers, Beer}

2. Diapers -> {Eggs, Beer}

3. Beer -> { Diapers, Eggs}

4. {Diapers, Beer} -> Eggs

5. {Eggs, Beer} -> Diapers

6. Diapers, Eggs} -> Beer

Answer 1

SOLUTION :- Strong association rules must satisfy both minimum support and minimum confidence threshold.

CORRECT ANSWER :

Therefore, the only Association Rules that satisfy both the restriction of having minimum support >= 3 and confidence >= 0.75 are :

(4) {Diapers, Beer} -> Eggs

(5) {Eggs, Beer} -> Diapers

(6) {Diapers, Eggs} -> Beer

EXPLANATION :- The Options (4), (5), and (6) are qualified strong association rules. On the other hand, Options (1), (2) and (3) are not qualified. The anslysis is given below :-

(1) Eggs -> {Diapers, Beer}
where {Eggs} is X and {Diapers, Beer} is Y.
Support = {itemset (X and Y)}/transactions
= 3 / 8 = 0.375 [ Satisfy ]
Confidence = {itemset (X and Y)}/{itemset (X)}
= 3 / 5 = 0.6 [ Not Satisfy ]

But as a whole, it will Not Satisfy.

(2) Diapers -> {Eggs, Beer}
where {Diapers} is X and {Eggs, Beer} is Y.
Support = {itemset (X and Y)}/transactions
= 3 / 8 = 0.375 [ Satisfy ]
Confidence = {itemset (X and Y)}/{itemset (X)}
= 3 / 5 = 0.6 [ Not Satisfy ]

But as a whole, it will Not Satisfy.

(3) Beer -> { Diapers, Eggs}
where {Beer} is X and {Diapers, Eggs} is Y.
Support = {itemset (X and Y)}/transactions
= 3 / 8 = 0.375 [ Satisfy ]
Confidence = {itemset (X and Y)}/{itemset (X)}
= 3 / 6 = 0.5 [ Not Satisfy ]

But as a whole, it will Not Satisfy.

(4) {Diapers, Beer} -> Eggs
where {Diapers, Beer} is X and {Eggs} is Y.
Support = {itemset (X and Y)}/transactions
= 3 / 8 = 0.375 [ Satisfy ]
Confidence = {itemset (X and Y)}/{itemset (X)}
= 3 / 4 = 0.75 [ Satisfy ]
Now, as a whole, it will Satisfy and will be considered as strong association rule.

(5) {Eggs, Beer} -> Diapers
where {Eggs, Beer} is X and {Diapers} is Y.
Support = {itemset (X and Y)}/transactions
= 3 / 8 = 0.375 [ Satisfy ]
Confidence = {itemset (X and Y)}/{itemset (X)}
= 3 / 3 = 1 [ Satisfy ]

Now, as a whole, it will Satisfy and will be considered as strong association rule.

(6) {Diapers, Eggs} -> Beer
where {Diapers, Eggs} is X and {Beer} is Y.
Support = {itemset (X and Y)}/transactions
= 3 / 8 = 0.375 [ Satisfy ]
Confidence = {itemset (X and Y)}/{itemset (X)}
= 3 / 4 = 0.75 [ Satisfy ]

Now, as a whole, it will Satisfy and will be considered as strong association rule.

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