Discuss Association Rule Mining and Apriori Algorithm. Apply AR mining to find all frequent item sets and association rules for the the following dataset:

Minimum support count = 2

Minimum confidence = 70%

Apriori Algorithm

The given Minimum Support Count = 2

Step 1 - Calculate the Minimum Count for each Item.

Therefore,

Step 2 - Delete the items that do not have a minimum support count of 2.

But, here all items have a minimum support count of 2 therefore, no need to delete any item.

Step 3 - Combine 2-items and find out the Minimum Count of the occurrences of the 2-items.

Therefore,

Step 4 - Delete the group of 2-items that do not have a minimum support count of 2.

Therefore,

Step 5 - Combine 3-items and find out the Minimum Count of the occurrences of the 3-items.

Therefore,

Step 6 - Delete the group of 3-items that do not have a minimum support count of 2.

Therefore,

Now, got the two item-sets {1, 2, 3} and {1, 2, 5} that are frequent.

Association Rule Mining

Generate Association Rules from the frequent itemset {1, 2, 3} and {1, 2, 5}.

Association Rules for frequent itemset {1, 2, 3} -

Rule 1 - {1, 2} => {3}

$$ Confidence = \frac{Support\{1, 2, 3\}}{Support\{1, 2\}} = \frac 24 \times 100 = 50\ \% $$

Rule 2 - {1, 3} => {2}

$$ Confidence = \frac{Support\{1, 2, 3\}}{Support\{1, 3\}} = \frac 25 \times 100 = 40\ \% $$

Rule 3 - {2, 3} => {1}

$$ Confidence = \frac{Support\{1, 2, 3\}}{Support\{2, 3\}} = \frac 23 \times 100 = 66.67\ \% $$

Rule 4 - {3} => {1, 2}

$$ Confidence = \frac{Support\{1, 2, 3\}}{Support\{3\}} = \frac 26 \times 100 = 33.34\ \% $$

Rule 5 - {2} => {1, 3}

$$ Confidence = \frac{Support\{1, 2, 3\}}{Support\{2\}} = \frac 26 \times 100 = 33.34\ \% $$

Rule 6 - {1} => {2, 3}

$$ Confidence = \frac{Support\{1, 2, 3\}}{Support\{1\}} = \frac 27 \times 100 = 28.57\ \% $$

Association Rules for frequent itemset {1, 2, 5} -

Rule 1 - {1, 2} => {5}

$$ Confidence = \frac{Support\{1, 2, 3\}}{Support\{1, 2\}} = \frac 24 \times 100 = 50\ \% $$

Rule 2 - {1, 5} => {2}

$$ Confidence = \frac{Support\{1, 2, 3\}}{Support\{1, 5\}} = \frac 22 \times 100 = 100\ \% $$

Rule 3 - {2, 5} => {1}

$$ Confidence = \frac{Support\{1, 2, 3\}}{Support\{2, 5\}} = \frac 22 \times 100 = 100\ \% $$

Rule 4 - {5} => {1, 2}

$$ Confidence = \frac{Support\{1, 2, 3\}}{Support\{5\}} = \frac 22 \times 100 = 100\ \% $$

Rule 5 - {2} => {1, 5}

$$ Confidence = \frac{Support\{1, 2, 3\}}{Support\{2\}} = \frac 26 \times 100 = 33.34\ \% $$

Rule 6 - {1} => {2, 5}

$$ Confidence = \frac{Support\{1, 2, 3\}}{Support\{1\}} = \frac 27 \times 100 = 28.57\ \% $$

The given Minimum Confidence = 70 %

Therefore,

above three rules that have the confidence more than 70 % are considered Strong Association Rules.