# 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
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.
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