Package elki.itemsetmining.associationrules.interest

Association rule interestingness measures.

Much of the confusion with these measures arises from the anti-monotonicity of itemsets, which are omnipresent in the literature.

In the itemset notation, the itemset \(X\) denotes the set of matching transactions \(\{T|X\subseteq T\}\) that contain the itemset \(X\). If we enlarge \(Z=X\cup Y\), the resulting set shrinks: \(\{T|Z\subseteq T\}=\{T|X\subseteq T\}\cap\{T|Y\subseteq T\}\).

Because of this: \(\text{support}(X\cup Y) = P(X \cap Y)\) and \(\text{support}(X\cap Y) = P(X \cup Y)\). With "support" and "confidence", it is common to see the reversed semantics (the union on the constraints is the intersection on the matches, and conversely); with probabilities it is common to use "events" as in frequentist inference.

To make things worse, the "support" is sometimes in absolute (integer) counts, and sometimes used in a relative share.