Package de.lmu.ifi.dbs.elki.algorithm.itemsetmining.associationrules.interest

Association rule interestingness measures.

See: Description

Interface Summary

Interface	Description
InterestingnessMeasure	Interface for interestingness measures.

Class Summary

Class	Description
AddedValue	Added value (AV) interestingness measure: \( \text{confidence}(X \rightarrow Y) - \text{support}(Y) = P(Y|X)-P(Y) \).
CertaintyFactor	Certainty factor (CF; Loevinger) interestingness measure. \( \tfrac{\text{confidence}(X \rightarrow Y) - \text{support}(Y)}{\text{support}(\neg Y)} \).
Confidence	Confidence interestingness measure, \( \tfrac{\text{support}(X \cup Y)}{\text{support}(X)} = \tfrac{P(X \cap Y)}{P(X)}=P(Y|X) \).
Conviction	Conviction interestingness measure: \(\frac{P(X) P(\neg Y)}{P(X\cap\neg Y)}\).
Cosine	Cosine interestingness measure, \(\tfrac{\text{support}(A\cup B)}{\sqrt{\text{support}(A)\text{support}(B)}} =\tfrac{P(A\cap B)}{\sqrt{P(A)P(B)}}\).
GiniIndex	Gini-index based interestingness measure, using the weighted squared conditional probabilities compared to the non-conditional priors.
Jaccard	Jaccard interestingness measure: \[\tfrac{\text{support}(A \cup B)}{\text{support}(A \cap B)} =\tfrac{P(A \cap B)}{P(A)+P(B)-P(A \cap B)} =\tfrac{P(A \cap B)}{P(A \cup B)}\] Reference: P.
JMeasure	J-Measure interestingness measure.
Klosgen	Klösgen interestingness measure.
Leverage	Leverage interestingness measure.
Lift	Lift interestingness measure.

Package de.lmu.ifi.dbs.elki.algorithm.itemsetmining.associationrules.interest Description

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.