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

$$ A \rightarrow C \space where \space A,C \in itemset $$

$A$ 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