ASSOCIATION RULES

They are rules that describes situation where the presence of a given element $\{A\}$ or a combination of elements $\{A,B\}$ assure the presence of a third element $\{C\}$, they are based on statistics.

DEFINITIONS

• ITEMSET⇒ A collection of one or more items.
• K-ITEMSET ⇒ An itemset that contains k items.
• SUPPORT COUNT $\sigma$ ⇒ Frequency of occurrence of an itemset.
• SUPPORT ⇒ Fraction of transactions that contain an itemset.
• FREQUENT ITEMSET ⇒ An itemset whose support is greater than or equal to a minsup threshold.

Association rules can be described by the form

$$A\to CwhereA,C\in itemset$$

$A$ is called antecedent and $C$ is called consequent

METRICS

SUPPORT $sup$

the fraction of transaction that contains both $A$ and $C$

$$sup=\frac{(A,C)}{N}$$

CONFIDENCE $conf$

the number of times $C$ appears over transactions that contains $A$

$$conf=\frac{(A,C)}{A}$$

CONFIDENCE FROM SUPPORT

confidence can also be computed from supports as

$$conf=\frac{(A,C)}{A}=\frac{\frac{(A,C)}{N}}{\frac{A}{N}}=\frac{sup(A,C)}{sup(A)}$$

support measures “how much” an occurrence can be considered a rule (there must be enough transaction cases), a rule with low support can be generated by random associations

confidence measures how much a rule is represented in the transactions that contains it

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