Question

(1) set the minimum support criterion at 0.6, identify the frequent 2-itemsets;

Transaction	Item Purchased
1	A	B	C
2	A	C	D
3	B	C	D
4	A	D	E
5	B	C	E

1 item set	Support

2 itemset	Support

Frequent 2 Itemsets

calculate lift ratio for below rules and interpret the results

Rule	Support of Antecedent {a}	Support of Consequent {c}	Support of {a & c}	The confidence of the Rule	Lift Ratio of the Rule	Interpretation on Lift Ratio
A-->D
C-->A
A-->C
B&C-->D

Answer 1

According to Association , the minimum support = number of transaction * support criterion = 5 * 60 /100 = 3

Item set = A B C D E

Support count ($\sigma$) = frequency of an item set

• $\sigma$(B,C) = 3 (* B and C occur thrice in the 5 transactions )
• $\sigma$(A,C)= 2
• $\sigma$(C,D)= 2

Hence, the three minimum support and frequent data sets are B,C ; A,C ; C,D

Calculating the lift ratio

Rule	Support of Antecedent {a}	Support of Consequent {c}	Support of {a & c}	The confidence of the Rule	Lift Ratio of the Rule
A-->D	3/5 = 0.6	3/5 = 0.6	2/5 = 0.4	$\sigma$(A,D)/ $\sigma$(A) = 0.67	Confidence(A,D)/ Expected confidence(D) = 40% /60%= 0.67
C-->A	4/5= 0.8	3/5 = 0.6	2/5 = 0.4	0.5	0.4/0.6 = 0.67
A-->C	3/5 = 0.6	4/5=0.8	2/5= 0.4	0.67	0.4/ 0.8 = 0.5
B&C-->D	1/5=0.2	3/5 = 0.6	1/5= 0.2	$\sigma$(B,C,D)/$\sigma$(B,C)= 1	0.2/0.6= 0.33

( *The below value means that the number of transaction occurance of A->D and the total transactions  of A.

Rule	Support of Antecedent {a}
A-->D	2/4 = 0.5

)

Based on the Lift ratio,

• The probability of person taking A will take D & the person taking C will take A is 67 %
• The probability of person taking A will take C is 50%
• The probability of person taking B&C will take D is 33%

The life ratio implies the relationship between the antecedent and consequent. The probability will increase with the increase in the lift ratio.