Question

The following is a list of five transactions that include items A, B, C, and D:

•T1 : { A,B,C }
•T2 : { A,C }
•T3 : { B,C }
•T4 : { A,D }
•T5 : { A,C,D }
Which item set satisfies a minimum support of 0.5? (Hint: An Itemset may include more than one item.)

note: this is a data mining subject.

Answer 1

To find the item set that satisfies a minimum support of 0.5, we need to calculate the support for each possible itemset and compare it with the threshold. The itemsets that satisfy a minimum support of 0.5 are {A}, {B}, {C}, {A,C}, {B,C}.

Step-by-step explanation:

The student is looking for the item set that satisfies a minimum support of 0.5. In data mining, support refers to the frequency of occurrence of an itemset in a transaction dataset. To find the itemset that satisfies a minimum support of 0.5, we need to calculate the support for each possible itemset and compare it with the threshold.

Let's calculate the support for each itemset:

1. {A}: Support = 4/5 = 0.8
2. {B}: Support = 3/5 = 0.6
3. {C}: Support = 4/5 = 0.8
4. {D}: Support = 2/5 = 0.4
5. {A,B}: Support = 2/5 = 0.4
6. {A,C}: Support = 4/5 = 0.8
7. {A,D}: Support = 2/5 = 0.4
8. {B,C}: Support = 3/5 = 0.6
9. {B,D}: Support = 1/5 = 0.2
10. {C,D}: Support = 2/5 = 0.4
11. {A,B,C}: Support = 2/5 = 0.4
12. {A,B,D}: Support = 1/5 = 0.2
13. {A,C,D}: Support = 2/5 = 0.4
14. {B,C,D}: Support = 1/5 = 0.2
15. {A,B,C,D}: Support = 1/5 = 0.2

Based on the support values, the itemsets that satisfy a minimum support of 0.5 are {A}, {B}, {C}, {A,C}, {B,C}.

Answer 2

Itemsets {A}, {C}, and {A,C} satisfy a minimum support of 0.5, appearing in 80%, 80%, and 60% of the transactions respectively.

Step-by-step explanation:

The student's question pertains to the concept of minimum support in the context of data mining, particularly within the frequent itemset generation for association rule mining. Transactions include item sets and the support of an itemset is defined as the proportion of transactions in the database in which the itemset appears.

Given the list of transactions:

• T1 : { A,B,C }
• T2 : { A,C }
• T3 : { B,C }
• T4 : { A,D }
• T5 : { A,C,D }

To find the itemsets that satisfy a minimum support of 0.5, we need to calculate the support for each itemset:

• Support(A) = 4/5 = 0.8
• Support(B) = 2/5 = 0.4
• Support(C) = 4/5 = 0.8
• Support(D) = 2/5 = 0.4
• Support(A,C) = 3/5 = 0.6

The itemsets that satisfy a minimum support of 0.5 are:

• {A} (Support = 0.8)
• {C} (Support = 0.8)
• {A,C} (Support = 0.6)