Q$3$: In the live session, we used the Apriori algorithm for mining frequent itemsets. The output of the Apriori algorithm is shown in L$3$ set. The frequent itemsets are used to generate association rules in the form of X$->$Y $($X implies Y$).$

For example, the data contain frequent itemset X $=\{$I$1,$ I$2,$ I$5\}.$ What are the association rules that can be generated from X$?$

Solution:

Step $1$: Find the nonempty subsets of X$.$ They are $\{$I$1,$ I$2\},\{$I$1,$ I$5\},\{$I$2,$ I$5\},\{$I$1\},\{$I$2\},$ and $\{$I$5\}.$

Step $2$: Generate the resulting association rules are as shown below:

$\{$I$1,$ I$2\}->$ I$5$

$\{$I$1,$ I$5\}->$ I$2$

$\{$I$2,$ I$5\}->$ I$3$

I$5->\{$I$1,$ I$2\}$

I$2->\{$I$1,$ I$5\}$

I$3->\{$I$2,$ I$5\}$FIGURE $4\mathrm{.}2$

Generation of the candidate itemsets and frequent itemsets, where the minimum support count is $2.$