Q.1) For the following given Transaction Data-set, Generate Rules using Apriori Algorithm.
Consider the values as Support=50% and Confidence=75%
| Transaction ID | Items Purchased |
| 1 | Bread, Cheese, Egg, Juice |
| 2 | Bread, Cheese, Juice |
| 3 | Bread, Milk, Yogurt |
| 4 | Bread, Juice, Milk |
| 5 | Cheese, Juice, Milk |
Answer:
Given Support=50% and Confidence=75%
Step 1) Find Frequent Item Set and their support
| Item | Frequency | Support (in %) |
| Bread | 4 | 4/5=80% |
| Cheese | 3 | 3/5=60% |
| Egg | 1 | 1/5=20% |
| Juice | 4 | 4/5=80% |
| Milk | 3 | 3/5=60% |
| Yogurt | 1 | 1/5=20% |
Support (item) = Frequency of item/Number of transactions
Step 2) Remove all the items whose support is below given minimum support.
| Item | Frequency | Support (in %) |
| Bread | 4 | 4/5=80% |
| Cheese | 3 | 3/5=60% |
| Juice | 4 | 4/5=80% |
| Milk | 3 | 3/5=60% |
Step 3) Now form the two items candidate set and write their frequencies.
| Items Pair | Frequency | Support (in %) |
| Bread, Cheese | 2 | 2/5=40% |
| Bread, Juice | 3 | 3/5=60% |
| Bread, Milk | 2 | 2/5=40% |
| Cheese, Juice | 3 | 3/5=60% |
| Cheese, Milk | 1 | 1/5=20% |
| Juice, Milk | 2 | 2/5=40% |
Step 4) Remove all the items whose support is below given minimum support
| Item Pair | Frequency | Support ( in %) |
| Bread, Juice | 3 | 3/5=60% |
| Cheese, Juice | 3 | 3/5=60% |
Step 5) Generate rules
For Rules we consider item pairs:
a) (Bread, Juice)
Bread->Juice and Juice->Bread
b) (Cheese, Juice)
Cheese->Juice and Juice->Cheese
Confidence (A->B) = support (AUB)/support (A)
Therefore,
- Confidence (Bread->Juice) = support (Bread U Juice)/support (Bread)
= 3/5 * 5/4=3/4= 75% - Confidence (Juice->Bread) = support (Juice U Bread)/support (Juice)
= 3/5*5/4=3/4=75% - Confidence (Cheese->Juice) = support (Cheese U Juice)/support (Cheese)
=3/5*5/3=1=100% - Confidence (Juice->Cheese) = support (Juice U Cheese)/support (Juice)
= 3/5*5/4=3/4=75%
All the above rules are good because the confidence of each rule is greater than or equal to
the minimum confidence given in the problem.
