Confidence refers to how often the right-hand side of the apriori expression is valid when the left-hand side is valid. For instance, given an expression:

{Milk} à {Bread}

We would like to know how often Bread was purchased when Milk was also purchased.

In this case:

• Transaction 1: Milk and Bread are both present
• Transaction 2: Milk is present, but not Bread
• Transactions 3 and 4: Milk is not present

Hence, based on the what we saw, there were 2 transactions where Milk was present and of them, Bread was present in 1 transaction. Hence, the confidence for the rule {Milk} à {Bread} would be ½ = 50%

Taking another expression:

{Bread} à {Butter}

We would like to know, when Bread was purchased, how often was Butter also purchased?:

• Transaction 1: Bread and Butter are both present
• Transaction 2: There is no Bread (Butter is present, but our point of reference is Bread and hence this does not count)
• Transaction 3: Bread is present but no Butter
• Transaction 4: Bread and Butter are both present

Hence, we have Bread in 3 of the transactions, and Bread & Butter in 2 of the 3 transactions. Hence, in this case, the 'confidence' of the rule {Bread} à {Butter} is 2/3 = 66.7.