associationrule

An association rule is a data mining technique used to discover interesting relationships between items in large transactional databases. An association rule X -> Y expresses that transactions containing all items in X tend to also contain items in Y. Here X and Y are disjoint itemsets, and the rule is evaluated by how frequently the items appear together and how reliably X predicts Y.

Key metrics used to assess rules include support, confidence, and lift. Support of a rule (X -> Y) is the proportion of transactions that contain X ∪ Y. Confidence is the conditional probability that a transaction containing X also contains Y, calculated as confidence(X -> Y) = support(X ∪ Y) / support(X). Lift measures the strength of the association relative to random co-occurrence, computed as lift(X -> Y) = confidence(X -> Y) / support(Y) (equivalently support(X ∪ Y) / [support(X) × support(Y)]). Higher support, confidence, and lift indicate more meaningful rules, with lift greater than 1 suggesting a positive association.

Mining process typically first identifies frequent itemsets—those with support above a user-defined minimum. From these itemsets, rules are generated and filtered by a minimum confidence threshold. Common algorithms include Apriori, Eclat, and FP-Growth, which use different pruning strategies to manage combinatorial growth.

Applications of association rules include market basket analysis, cross-selling, catalog design, and inventory optimization. Limitations include the tendency to reveal correlations rather than causation, potential generation of many rules with low practical relevance, sensitivity to data discretization and support thresholds, and computational complexity for large item sets.

Extensions cover additional interestingness measures, mining closed or maximal itemsets, quantitative association rules, and methods for streaming data or privacy-preserving mining.