RULES GENERATION

The goal of this phase is, given an item-set $L$ to find all non empty $f$ subsets that the association rule $f\to (L-f)$ have a $conf>threshold$ where $threshold$ is a parameter defined from the designer

It’important to understand how to generate rules with an high $conf$ from a given item-set

so from this formula we can say that for rules generated from the same item-sets:

$$conf(ABC\to D)\ge conf(AB\to CD)\ge conf(A\to BCD)$$

this means that rules confidence is anti-monotone in relation of the number of elements that creates the antecedent

this characteristic can be used to prune the generation tree when there is a rule with a $conf<threshold$

INTERESTING RULE GENERATION METRICS

Confidence metrics can be insufficient in the rule generation process, other interesting metrics are also used

so given a rule in the form of $A\to C$ we can compute the contingency table as follow

	C	$\overline{C}$
A	$f_{11}$	$f_{10}$	$f_{1+}$
$\overline{A}$	$f_{01}$	$f_{00}$	$f_{0+}$
	$f_{+1}$	$f_{+0}$

from this table we can derive some interesting measures like

LIFT

lift is defined as

$$lift(A\to C)=\frac{conf(A\to C)}{sup(C)}$$

it indicates the ratio between rule true cases and independence, it tend to $1$ when the item-sets are independent

LEVERAGE

leverage is defined as

$$leve(A\to C)=sup(A\cup C)-sup(A)sup(C)$$

leverage indicates the number of additional cases, it tends to $0$ when the item-sets are independent

CONVICTION

conviction is defined as

$$conv(A\to C)=\frac{1-sup(C)}{1-conf(A\to C)}$$

it’s the ratio that $A$ occurs without $C$ if $A$ and $C$ where independent, higher value means that the rules is violated less often (in the assumption that the $A$ and $C$ are independent)

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