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.

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:
JMeasure	J-Measure interestingness measure.
Klosgen	Klösgen interestingness measure.
LaplaceCorrectedConfidence	Laplace Corrected Confidence interestingness measure.
Leverage	Leverage interestingness measure.
Lift	Lift interestingness measure.
OddsRatio	Odds ratio interestingness measure.
PhiCorrelationCoefficient	Phi Correlation Coefficient interestingness measure.
SebagSchonauer	Sebag Schonauer interestingness measure.
YulesQ	Yule's Q interestingness measure.
YulesY	Yule's Y interestingness measure.