Association Rule

Definition

Association rules (Agrawal et al. 1993) can be extracted from data sets where each example consists of a set of items. An association rule has the form $X \rightarrow Y$, where $X$ and $Y$ are itemsets, and the interpretation is that if set $X$ occurs in an example, then set $Y$ is also likely to occur in the example.

Each association rule is usually associated with two statistics measured from the given data set. The frequency or support of a rule $X \rightarrow Y$, denoted fr($X \rightarrow Y$), is the number (or alternatively the relative frequency) of examples in which $X \cup Y$ occurs. Its confidence, in turn, is the observed conditional probability $P(Y \vert X) = \text{fr}(X \cup Y )/\text{fr}(X)$.

The Apriori algorithm (Agrawal et al. 1996) finds all association rules, between any sets $X$ and $Y$, which exceed user-specified support and confidence thresholds. In association rule mining, unlike in most other learning tasks, the result thus is...