# 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.