ML Wiki

Lift (Data Mining)

Lift is an interestness measure used in Rule Mining

Lift:

• for a rule $X \to Y$ with $\text{supp}(X) \ne 0$ and $\text{supp}(Y) \ne 0$
• $\text{lift}(X \to Y) = \cfrac{\text{supp}(X \to Y)}{\text{supp}(X) \cdot \text{supp}(Y)}$
• since $\text{conf}(X \to Y) = \cfrac{\text{supp}(X \to Y)}{\text{supp}(X)}$, can rewrite the formula as
• $\text{lift}(X \to Y) = \cfrac{\text{conf}(X \to Y)}{\text{supp}(Y)}$

Properties

• $\text{lift}(X \to Y) \ne 0$
• $\text{conf}(X \to Y) \in [0, 1]$, and $\text{supp}(Y) \in [0, 1]$
• so $\text{lift}(X \to Y) \in (0, +\infty)$

Example

Consider this dataset $D$:

• $T_1 = ABCD, T_2 = ADE, T_3 = BDE, T_4 = E$

Lift:

• $\text{lift}(A \to \varnothing) = 1 / 1 = 1$ (everything gives 0, so it's not interesting)
• $\text{lift}(A \to B) = 0.5 / 0.5 = 1$ ($A$ and $B$ are independent, so nothing interesting)
• $\text{lift}(A \to BC) = 0.5 / 0.24 = 2$
• so lift is 1 when two items are independent, and higher when there's some correlation between them