How to calculate support / confidence and uplift for combined item sets such as {A} & # 8594; {B, C}

Question

I have a list of element sets {A_i}->{X} .

how

 {A}->{X} {A}->{Z} {A,B}->{X} {A,B}->{W} 

Now I want to combine the elements, for example:

 {A}->{X,Z} {A,B}->{X,W} 

But I do not know how to calculate the support, confidence and rise of any rule.
Is this a sum / counter or is it the minimum of all the same sets of items?

For support, minimal support for all such sets makes sense. But confidence and recovery?

Answer 1

I think you are referring to association rules.

For an X → Y association rule, rule support is denoted by sup (X-> Y) and represents the number of transactions in which XUY is displayed divided by the total number of transactions.

trust is the number of transactions in which XUY is displayed divided by the number of transactions in which X appears.

elevator is defined as: rise (X → Y) = ((sup (XUY) / N) / (sup (X) / N * sup (Y) / N), where N is the number of transactions in the transaction database, sup (X ∪Y) is the number of transactions containing X and Y, sup (X) is the number of transactions containing X sup (Y) is the number of transactions containing Y.

An example of elevator calculation can be checked in example 23 of the SPMF software:

http://www.philippe-fournier-viger.com/spmf/index.php?link=documentation.php#lift