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Table 2 Quality measurements of association rules

From: Mining and prioritization of association rules for big data: multi-criteria decision analysis approach

Measure Formula
Support The support defined as the proportion of transaction in the database, which contains the items A [2] \(Support(A \to B) = \frac{|t(A \cup B)|}{t(A)}\) (1)
Confidence The confidence determines how frequently items in B appear in transaction that contains A [2], ranges from 0 to 1 \(Confidence(A \to B) = \frac{Support(A \cup B)}{Support(A)}\) (2)
Lift The lift measures how far from independence are A and B [16]. It ranges within [0, +∞] \(Lift(A \to B) = \frac{Support(A \cup B)}{Support(A)*Support(B)}\) (9)
Laplace It is a confidence estimator that takes support into account [17]. It ranges within [0, 1] \(lapl(A \to B) = \frac{Support(A \cup B) + 1}{Support(A) + 2}\) (10)
Conviction Measure the degree of implication of a rule [18]. It ranges along the values [0.25, +∞] \(conv(A \to B) = \frac{1 - Support(B)}{1 - conf(A \to B)}\) (11)
Leverage Measure how much more counting is obtained from the co-occurrence of the antecedent and consequent from the independence [19] \(leve\left( {A \to B} \right) = Support\left( {A \to B} \right) - Support\left( A \right) \, \times \, Support\left( B \right)\) (12)
Jaccard Measure the degree of overlap between the cases covered by each of them [20] the Jaccard coefficient takes values in [0, 1] \(Jacc(A \to B) = \frac{Support(A \cup B)}{Support(A)\, + \,Support(B) - Support(A \cup B)}\) (13)
ϕ-Coefficient This measure can be used to measure the association between A and B [21] \(\phi (A \to B) = \frac{leve(A \cup B)}{{\sqrt {(Support(A)\, \times \,Support(B))\, \times \,(1 - Support(A))\, \times \,(1 - Support(B)} )}}\) (14)