Lift

Measure lift to evaluate the strength of a rule over random co-occurrence, ensuring the rule's predictive value.

Both support and confidence must be used to determine if a rule is valid. However, there are times when both of these measures may be high, and yet still produce a rule that is not useful. For example:

Convenience store customers who buy orange juice also buy milk with 
a 75% confidence. 
The combination of milk and orange juice has a support of 30%.

This at first sounds like an excellent rule, and in most cases, it would be. It has high confidence and high support. However, what if convenience store customers in general buy milk 90% of the time? In that case, orange juice customers are actually less likely to buy milk than customers in general.

A third measure is needed to evaluate the quality of the rule. Lift indicates the strength of a rule over the random co-occurrence of the antecedent and the consequent, given their individual support. It provides information about the improvement, the increase in probability of the consequent given the antecedent. Lift is defined as follows.

(Rule Support) /(Support(Antecedent) * Support(Consequent))

This can also be defined as the confidence of the combination of items divided by the support of the consequent. So in our milk example, assuming that 40% of the customers buy orange juice, the improvement would be:

30% / (40% * 90%)

which is 0.83 – an improvement of less than 1.

Any rule with an improvement of less than 1 does not indicate a real cross-selling opportunity, no matter how high its support and confidence, because it actually offers less ability to predict a purchase than does random chance.

Tip:

• Decrease the maximum rule length if you want to decrease the build time for the model and generate simpler rules.

• Increase the minimum support if you want to decrease the build time for the model and generate fewer rules.