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5.2
Lift is 1 if X and Y are statistically independent of each other. In contrast, a lift of
X Y greater than 1 indicates that there is some usefulness to the rule. A larger
value of lift suggests a greater strength of the association between X and Y.
Assuming 1,000 transactions, with {milk,eggs} appearing in 300 of them,
{milk} appearing in 500, and {eggs} appearing in 400, then
. If {bread} appears in 400 transactions
and {milk,bread} appears in 400, then
. Therefore it can be concluded that milk
and bread have a stronger association than milk and eggs.
Leverage [7] is a similar notion, but instead of using a ratio, leverage uses the
difference (see Equation 5.3 ). Leverage measures the difference in the probability
of X and Y appearing together in the dataset compared to what would be expected
if X and Y were statistically independent of each other.
5.3
In theory, leverage is 0 when X and Y are statistically independent of each other.
If X and Y have some kind of relationship, the leverage would be greater than
zero. A larger leverage value indicates a stronger relationship between X and Y.
For the previous example, and
. It again confirms that milk
and bread have a stronger association than milk and eggs.
Confidence is able to identify trustworthy rules, but it cannot tell whether a rule
is coincidental. A high-confidence rule can sometimes be misleading because
confidence does not consider support of the itemset in the rule consequent.
Measures such as lift and leverage not only ensure interesting rules are identified
but also filter out the coincidental rules.
This chapter has discussed four measures of significance and interestingness for
association rules: support, confidence, lift, and leverage. These measures ensure
the discovery of interesting and strong rules from sample datasets. Besides these
four rules, there are other alternative measures, such as correlation [8], collective
strength [9], conviction [6], and coverage [10]. Refer to the Bibliography to learn
how these measures work.
 
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