Apriori Algorithm to Discover Frequent Itemsets.
The given Minimum Support Value = 0.3
The Number of Transactions = 10
Therefore,
The Minimum Support = $0.3 \times 10 = 3$
Step 1 - Calculate the Minimum Count for each Item.
Therefore,
| Items |
Minimum Count |
| Strawberry |
5 |
| Litchi |
4 |
| Orange |
4 |
| Butter fruit |
3 |
| Vanilla |
2 |
| Banana |
3 |
| Apple |
2 |
Step 2 - Delete the items that do not have a minimum support count of 3.
Therefore, Items Vanilla and Apple are deleted.
| Items |
Minimum Count |
| Strawberry |
5 |
| Litchi |
4 |
| Orange |
4 |
| Butter fruit |
3 |
| Banana |
3 |
Step 3 - Combine 2-items and find out the Minimum Count of the occurrences of the 2-items.
| Items |
Minimum Count |
| Strawberry, Litchi |
4 |
| Strawberry, Orange |
3 |
| Strawberry, Butter fruit |
1 |
| Strawberry, Banana |
0 |
| Litchi, Orange |
3 |
| Litchi, Butter fruit |
0 |
| Litchi, Banana |
0 |
| Orange, Butter fruit |
0 |
| Orange, Banana |
1 |
| Butter fruit, Banana |
1 |
Step 4 - Delete the 2-items that do not have a minimum support count of 3.
Therefore,
| Items |
Minimum Count |
| Strawberry, Litchi |
4 |
| Strawberry, Orange |
3 |
| Litchi, Orange |
3 |
Step 5 - Combine 3-items and find out the Minimum Count of the occurrences of the 3-items.
| Items |
Minimum Count |
| Strawberry, Litchi, Orange |
3 |
| Strawberry, Litchi, Butter fruit |
0 |
| Strawberry, Litchi, Banana |
0 |
| Strawberry, Orange, Butter fruit |
0 |
| Strawberry, Orange, Banana |
0 |
| Litchi, Orange, Butter fruit |
0 |
| Litchi, Orange, Banana |
0 |
Now, got the only item-set {Strawberry, Litchi, Orange} that is frequent.
Step 6 - Generate Association Rules from the frequent itemset discovered in the above step - 5.
{Strawberry, Litchi} => {Orange}
$$Confidence = \frac {support \{Strawberry, Litchi, Orange\}}{support \{Strawberry, Litchi\}} = \frac 34 \times 100 = 75\ \%$$
{Strawberry, Orange} => {Litchi}
$$Confidence = \frac {support \{Strawberry, Litchi, Orange\}}{support \{Strawberry, Orange\}} = \frac 33 \times 100 = 100\ \%$$
{Litchi, Orange} => {Strawberry}
$$Confidence = \frac {support \{Strawberry, Litchi, Orange\}}{support \{Litchi, Orange\}} = \frac 33 \times 100 = 100\ \%$$
{Strawberry} => {Litchi, Orange}
$$Confidence = \frac {support \{Strawberry, Litchi, Orange\}}{support \{Strawberry\}} = \frac 35 \times 100 = 60\ \%$$
{Litchi} => {Strawberry, Orange}
$$Confidence = \frac {support \{Strawberry, Litchi, Orange\}}{support \{Litchi\}} = \frac 34 \times 100 = 75\ \%$$
{Orange} => {Strawberry, Litchi}
$$Confidence = \frac {support \{Strawberry, Litchi, Orange\}}{support \{Orange\}} = \frac 34 \times 100 = 75\ \%$$
In the question Minimum Confidence Threshold is not mentioned.
Therefore, if consider Confidence Threshold is 60 % then this shows that all the above Association Rules are Strong.
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